EP3597920A2 - Rotor pair for a compressor block of a screw machine - Google Patents

Abstract

The invention relates to a pair of rotors for a compressor block of a screw machine, the pair of rotors consisting of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2), the number of teeth ( z ₂) for the main rotor (HR) 4 and the number of teeth (z ₁) for the secondary rotor (NR) 5, whereby the relative profile depth of the secondary rotorPTrel = rk1 − rf1rk1at least 0.515, and at most 0.58, where rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is one at the base of the profile of the secondary rotor starting root radius, the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk ₁ ark1 being at least 1.683, and at most 1.836, preferably at most 1.782, where the main rotor is designed with a wrap angle Φ _HR for which the gi lt 320 ° ≤ Φ _HR ≤ 360 °, and preferably for a rotor length ratio L _HR / a: 1.4≤LHR / a≤3.3, where that Rotor length ratio is formed from the ratio of the rotor length LHR of the main rotor and the center distance a and the rotor length LHR of the main rotor is formed by the distance between a suction-side main rotor-rotor end face and an opposite pressure-side main rotor-rotor end face.

Description

The invention relates to a pair of rotors for a compressor block of a screw machine, the pair of rotors consisting of a main rotor rotating about a first axis and a secondary rotor rotating about a second axis. Furthermore, the invention relates to a compressor block with a corresponding rotor pair.

Screw machines, whether as screw compressors or as screw expanders, have been in practical use for several decades. Designed as screw compressors, they have displaced reciprocating compressors as compressors in many areas. With the principle of the interlocking screw pair, not only gases can be compressed using a certain amount of work. The use as a vacuum pump also opens up the use of screw machines to achieve a vacuum. Finally, the passage of pressurized gases the other way around can also generate work, so that mechanical pressure can also be obtained from pressurized gases by means of the principle of the screw machine.

Screw machines generally have two shafts arranged parallel to each other, on which on the one hand a main rotor and on the other hand a secondary rotor are seated. The main rotor and secondary rotor interlock with corresponding helical teeth. Between the teeth and one A compressor chamber, in which the main and secondary rotors are accommodated, forms a compression chamber (working chambers) through the tooth space volumes. Starting from a suction area, as the main and secondary rotors continue to rotate, the working chamber is initially closed and then continuously reduced in volume, so that the medium is compressed. Finally, as the rotation progresses, the working chamber is opened to a print window and the medium is pushed out into the print window. This internal compression process differentiates screw machines designed as screw compressors from Roots blowers that work without internal compression.

Depending on the required pressure ratio (ratio of outlet pressure to inlet pressure), different tooth number ratios are useful for efficient compression.

Depending on the number of teeth ratio, typical pressure ratios can be between 1.1 and 20, the pressure ratio being the ratio of the compression pressure to the suction pressure. The compression can take place in one or more stages. Achievable final pressures can be, for example, in the range from 1.1 bar to 20 bar. Insofar as reference is made at this point or subsequently in the present application to pressure information in “bar”, such pressure information relates in each case to absolute pressures.

Screw machines can be used in addition to the function already mentioned as a vacuum pump or as a screw expander in various fields of technology as a compressor. A particularly preferred field of application is the compression of gases, such as air or inert gases (helium, nitrogen, ...). However, it is also possible, although this places special structural requirements, on a screw machine for compressing refrigerants, for example for air conditioning systems or refrigeration applications. When compressing gases, especially at higher pressure ratios, a fluid-injected compression, in particular an oil-injected compression, is usually used; however, it is also possible to operate a screw machine on the principle of dry compression. In the low pressure range, screw compressors are sometimes referred to as screw blowers.

In the past decades, considerable success has been achieved with regard to the manufacturability, reliability, smooth running and the efficiency of screw machines. Improvements or optimizations often relate to optimizations of the efficiency depending on the number of teeth, wrap angle and length / diameter ratio of the rotors. The addition of the face cuts to the optimization process has only recently been found.

Tests have shown that the face cut of the rotors, especially the face cut of the secondary rotor, has a significant influence on energy efficiency. To comply with the gearing laws, the face cut of the secondary rotor must find its counterpart in the face cut of the main rotor. Here, the profile of the rotor in a plane perpendicular to the axis of the rotor is referred to as an end cut. Different types of forehead incision generation, for example rotor- or rack-based forehead incision generation methods, are now known from the prior art. Once you have decided on a certain procedure, a first design front section is created in a first step. Traditionally, this is further optimized in several subsequent (revision) steps according to various criteria.

Both the optimization goals themselves (energy efficiency, smooth running, low costs) as well as the fact that the improvements of a parameter are partly inevitably lead to the deterioration of another parameter, known. However, there is a lack of a concrete solution on how a good overall optimization result (i.e. a compromise between the various individual parameter optimizations) can be achieved.

Some optimization approaches which are known in the prior art with regard to an improvement in energy efficiency, smooth running and costs are to be explained by way of example below. Furthermore, problems that may arise here should be named.

1 energy efficiency

• Über den Profilspalt haben die druckseitigen Arbeitskammern direkte Verbindung zur Ansaugseite und damit eine größtmögliche Druckdifferenz für Rückströmungen.
• Aufeinanderfolgende Arbeitskammern sind über einen theoretisch nicht notwendigen Durchlass miteinander verbunden, der als Blasloch bezeichnet wird. Zum Teil wird dieser auch als Kopfrundungsöffnung bezeichnet. Dieses Blasloch ergibt sich durch die Kopfrundung der Profile, insbesondere des Profils des Nebenrotors.
  Druckseitige Arbeitskammern sind über druckseitige Blaslöcher mit den jeweils benachbarten Arbeitskammern verbunden, saugseitige Arbeitskammern sind über saugseitige Blaslöcher mit den jeweils benachbarten Arbeitskammern verbunden. Soweit nicht anders angegeben ist im Folgenden der Begriff "Blasloch" als "druckseitiges Blasloch" zu verstehen.

The energy efficiency of compressor blocks can advantageously be influenced in a known manner by minimizing the internal leaks in the compressor block and in particular by reducing the gaps between the main rotor and the secondary rotor. The profile gap and the blow hole can be differentiated here:

• The pressure-side working chambers have a direct connection to the suction side via the profile gap and thus the greatest possible pressure difference for backflows.
• Successive working chambers are connected to one another via a passage that is not theoretically necessary and is called a blowhole. In some cases, this is also known as the tip rounding opening. This blow hole results from the tip rounding of the profiles, in particular the profile of the secondary rotor.
  Pressure-side working chambers are connected to the adjacent working chambers via pressure-side blowholes, suction-side working chambers are connected to the respectively adjacent working chambers via suction-side blowing holes. Unless otherwise stated, the term “blow hole” is to be understood below as a “pressure-side blow hole”.

Ideally, to minimize internal leakage, a short profile gap length should be combined with a small (pressure-side) blow hole. However, the two sizes basically behave in opposite directions. This means that the smaller the blow hole is modeled, the greater the profile gap length becomes. Conversely, the shorter the profile gap length, the larger the blow hole. Helpertz explains this in his Dissertation "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003 on page 162 ,

The requirement for a short profile gap length can be realized in a known manner with a flat profile with a correspondingly smaller relative profile depth of the secondary rotor. Whether a profile is rather shallow (shallow profile depth) or deep (large profile depth) can be clearly quantified using the so-called "relative profile depth of the secondary rotor", which relates the difference between the tip and root radius to the tip radius of the auxiliary rotor. ever the larger the value, the more compact the compressor block and has, for example, more delivery quantity than a comparable compressor block with the same external dimensions.

Correspondingly, very flat profiles have a poor use of space, i.e. they lead to large compressor blocks with a comparatively high cost of materials or comparatively high manufacturing costs.

Blow holes on the pressure side must not be made too large, as described above, in order to minimize the backflow of already compressed medium into previous working chambers (i.e. in working chambers of lower pressure). Such backflows increase the energy expenditure for the total delivery volume achieved and lead to an undesirable increase in the temperature and pressure level during compression, which overall reduces the efficiency. The area of the blow hole (blow hole area) can be kept small by making the head curves of the profiles small in the face cut. Specifically, this can be caused by a strong curvature in the head region of the leading tooth flank of the secondary rotor and in the head region of the trailing tooth flank of the main rotor. However, the greater this curvature, the more likely it is to reach manufacturing limits, as this leads to high wear on profile cutters and profile grinding wheels in the manufacture of the main rotor and secondary rotor.

Large blowholes on the suction side, on the other hand, do not have a negative impact on energy efficiency, since these only connect working chambers in the suction area at the same pressure.

Another cause for efficiency-reducing internal leaks is the so-called chamber gusset volume, which can arise when the last working chamber (ie the working chamber with the highest pressure) is pushed out into the pressure window. The working chamber then no longer has a connection to the pressure window from a certain rotational angle position of the rotors. A so-called chamber gusset volume remains between the two rotors and the pressure-side housing end wall.

This chamber gusset volume is disadvantageous because the enclosed compressed medium can no longer be pushed out into the pressure window, the further rotation of the rotors further compresses, which leads to unnecessarily high power consumption (for over-compression), an unnecessarily high additional heat input, noise and a reduction the service life of the roller bearings of the rotors in particular. In addition, the specific performance is deteriorated by the fact that the portion enclosed in the chamber gusset volume returns to the suction side after over-compression and is therefore not available to the compressed air user. In the case of oil-injected compressors, there is also incompressible oil in the chamber gusset and is squeezed.

2 smooth running

However, other properties such as smooth running have a decisive influence on a good profile for the main rotor or secondary rotor.

In addition to good flank-hugging and low relative speeds between the tooth flanks of the main and secondary rotors, the distribution of the drive torque between the two rotors has a major impact on smooth running. As is well known, an unfavorable division often leads to the so-called rotor rattling of the secondary rotor, in which the secondary rotor has undefined flank contact with the main rotor, and the secondary rotor consequently has alternating contact with the leading and the trailing main rotor flank. If the two rotors are kept at a distance via a synchronous gear, the above-mentioned is shifted. Rotor rattling inevitably into the synchronized gear. Smooth running not only ensures low noise emissions from the compressor block, but also ensures, for example, a compressor block that is less susceptible to vibration, a long service life of the rolling bearings and low wear in the toothing of the rotors.

3 costs

The manufacturability and the degree of utilization of the construction volume have a particular impact on the material and manufacturing costs of screw compressor blocks.

Compact compressor blocks with a high construction volume utilization are achieved by a large tooth gap volume, which in turn depends on the profile depth and the tooth thickness.

• Mit zunehmender Profiltiefe werden insbesondere die Zahnprofile des Nebenrotors zwangsläufig immer dünner und demzufolge immer biegeweicher. Dies macht die Rotoren zunehmend temperaturempfindlicher und wirkt sich insgesamt betrachtet ungünstig auf die Spalte im Verdichterblock aus. Die Spalte haben erheblichen Einfluss auf die inneren Leckagen, d.h. Rückströmungen von Verdichtungskammern höheren Drucks in Richtung Saugseite, und können damit die Energieeffizienz des Verdichterblocks verschlechtern.
• Des Weiteren steigen bei biegeweichen Zähnen die Schwierigkeiten bei der Rotorfertigung.
  • ∘ So steigt beispielsweise das Risiko, dass beim Profilschleifen die ohnehin schon hohen Anforderungen insbesondere an die Formtoleranzen nicht eingehalten werden können.
  • ∘ Weiterhin erfordern biegeweiche Zähne geringere Vorschub- und Schnittgeschwindigkeiten sowohl beim Profilfräsen als auch beim anschließenden Profilschleifen und erhöhen dadurch die Bearbeitungszeit und in der Folge die Herstellkosten.
• Eine zunehmende Profiltiefe führt auch dazu, dass der Rotor an sich biegeweicher wird. Je biegeweicher die Rotoren ausgeführt sind, desto mehr nimmt die Gefahr zu, dass die Rotoren untereinander bzw. im Verdichtergehäuse anlaufen. Zur Gewährleistung der Betriebssicherheit auch bei hohen Temperaturen bzw. bei hohen Drücken müssen folglich die Spalte größer dimensioniert werden. Dies wirkt sich wiederrum negativ auf die Energieeffizienz des Verdichterblocks aus.

The further you increase the relative depth of profit, the higher the utilization of the construction volume, the higher the risk of problems with the running properties and the manufacturability:

• With increasing profile depth, the tooth profiles of the secondary rotor in particular are inevitably becoming thinner and consequently increasingly flexible. This makes the rotors increasingly temperature-sensitive and, viewed overall, has an unfavorable effect on the gaps in the compressor block. The gaps have a considerable influence on the internal leakages, ie backflows from compression chambers of higher pressure towards the suction side, and can therefore impair the energy efficiency of the compressor block.
• Furthermore, the difficulty with rotor production increases with flexible teeth.
  • ∘ For example, the risk increases that profile grinding, which is already very demanding, especially when it comes to shape tolerances, cannot be met.
  • ∘ Furthermore, flexible teeth require lower feed and cutting speeds both for profile milling and subsequent profile grinding, thereby increasing the machining time and consequently the manufacturing costs.
• An increasing profile depth also leads to the rotor itself becoming more flexible. The more flexible the rotors are, the more the risk increases that the rotors start up against each other or in the compressor housing. To ensure operational safety even at high temperatures or at high pressures, the gaps must therefore be dimensioned larger. This in turn has a negative impact on the energy efficiency of the compressor block.

4 conclusion

The above explanations are intended to show that optimization of the individual parameters is not very effective in itself, but for one good overall result a compromise between the different (and sometimes contradictory) requirements must be found.

The theoretical basis for the calculation of screw rotor profiles has already been dealt with in the literature and general criteria for good face cut profiles are also described. With the computer program developed by Grafinger, for example, rotor profiles can be created and modified ( Habilitation "The computer-aided development of the flank profiles for special toothing of screw compressors", Vienna, 2010 ).

Helpertz deals with his Dissertation "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003 with automated optimization based on a design profile with regard to differently weighted parameters.

Accordingly, the object of the present invention is to provide a pair of rotors for a compressor block of a screw machine, which is characterized by a high level of operational reliability and reasonable manufacturing costs due to its quiet running and special energy efficiency.

This object is achieved with a pair of rotors according to the features of claims 1, 9 or 14. Advantageous refinements are specified in the subclaims. Furthermore, the object is also achieved with a compressor block, which comprises an appropriately designed pair of rotors.

The rotor geometry is essentially characterized by the shape of the face cut as well as by the rotor length and the wrap angle, cf. " Method for the stochastic optimization of screw rotor profiles ", dissertation by Markus Helpertz, Dortmund, 2003, p. 11/12 ,

In a frontal sectional view, the secondary rotor or main rotor have a predetermined, often different number of teeth of the same design per rotor. The outermost circle around the vertices of the teeth around the C1 and C2 axes is referred to as the tip circle. A base circle is defined in the face cut by the points on the outer surface of the rotors closest to the axis. The ribs are called the teeth of the rotor. The grooves (or recesses) are referred to as tooth gaps. The area of the tooth on and above the root circle defines the tooth profile. The contour of the ribs defines the course of the tooth profile. Base points F1 and F2 and a vertex F5 are defined for the tooth profile. The apex F5 or H5 is defined by the radially outermost point of the tooth profile. If the tooth profile has several points with the same maximum radial distance from the center point defined by the axis C1 or C2, i.e. if the tooth profile follows a circular arc on the tip circle at its radially outer end, the vertex F5 lies exactly in the middle of this circular arc. A tooth gap is defined between two adjacent vertices F5.

The points radially closest to the axis C1 or C2 between a viewed tooth and the adjacent tooth define base points F1 and F2. In this case, too, if several points come close to the axis C1 or C2, i.e. the tooth profile at its lowest point follows the base circle in sections, the corresponding base point F1 or F2 then lies on half of this circular arc lying on the base circle ,

Finally, the meshing of the main rotor and the secondary rotor defines a rolling circle for both the secondary rotor and the main rotor. With screw machines as well as with gears or friction wheels, there are always two circles in the face section of the toothing, which roll against each other during the movement. These circles, on which the main rotor and secondary rotor roll against each other in the present case, are referred to as respective pitch circles. The pitch circle diameters of the main rotor and secondary rotor can be determined using the center distance and the number of teeth ratio.

The circumferential speeds of the main rotor and the secondary rotor are identical on the pitch circles.

Finally, tooth space areas between the teeth and the respective tip circle KK are defined, namely tooth space area A6 between the profile profile of the secondary rotor NR between two adjacent vertices F5 and the tip circle KK _1, or an area A7 as tooth space area between the profile profile of the main rotor (HR) between two neighboring vertices H5 and the tip circle KK ₂ .

The tooth profile of the secondary rotor (but also of the main rotor) has a tooth flank leading in the direction of rotation as well as a tooth flank trailing in the direction of rotation. For the secondary rotor (NR), the leading tooth flank is referred to below as F _V and the trailing tooth flank as F _N.

The trailing tooth flank F _N forms a point in its section between the tip circle and the base circle, in which the curvature of the course of the tooth profile changes. This point is referred to below as F8 and divides the trailing tooth flank F _N into a convexly curved part between F8 and the tip circle and a concave curved part between the root circle and F8. Small-scale profile changes, for example due to sealing strips or other local profile changes, are not taken into account when considering the change in curvature described above.

In addition to the pure frontal cut, the following terms and parameters for a rotor, in particular the secondary rotor, are also decisive for the three-dimensional configuration: First, a wrap angle Φ is defined. This wrap angle is the angle by which the face cut is rotated from the suction-side to the pressure-side rotor face, cf. also the more detailed explanations in connection with Figure 8 ,

The main rotor has a rotor length L _HR , which is defined as the distance between a suction-side main rotor rotor end face and a pressure-side main rotor rotor end face. The distance between the first axis C1 of the secondary rotor running parallel to one another and the second axis C2 of the main rotor is referred to below as the center distance a. It is pointed out that in most cases the length of the main rotor L _HR corresponds to the length of the secondary rotor L _NR , the length of the secondary rotor also being understood as the distance from a suction-side secondary rotor rotor end face to a pressure-side secondary rotor rotor end face. Finally, a rotor length ratio L _HR / a is defined, that is, a ratio of the rotor length of the main rotor to the center distance. The ratio L _HR / a is therefore a measure of the axial dimensioning of the rotor profile.

The line of engagement or the profile gap arise from the interaction of the main rotor and the secondary rotor. The line of engagement results as follows: The tooth flanks of the main rotor and secondary rotor touch each other with play-free toothing depending on the angular position of the rotors in certain points. These points are called engagement points. The geometrical location of all engagement points is called the engagement line and can already be calculated in two dimensions based on the end cut of the rotors, cf. Figure 7j ,

The line of engagement is divided into two sections in the forehead section view by the connecting line between the two center points C1 and C2, namely into a (comparatively short) suction-side and a (comparatively long) pressure-side section.

If the wrap angle and the rotor length (= distance between the suction-side face and the pressure-side face) are also specified, the line of engagement can also be expanded three-dimensionally and corresponds to the line of contact between the main rotor and the secondary rotor. The axial projection of the three-dimensional line of engagement onto the face incision plane in turn yields that based on Figure 7j illustrated two-dimensional line of intervention. The term "line of intervention" is used in the literature for both two-dimensional and three-dimensional viewing. In the following, unless otherwise stated, "line of engagement" should be understood to mean the two-dimensional line of engagement, ie the projection onto the forehead incision.

The profile engagement gap is defined as follows: In the real compressor block of a screw machine, there is play between the two rotors when there is a clearance between the main rotor and the secondary rotor. The gap between the main rotor and the secondary rotor is called the profile engagement gap and is the geometrical location of all points at which the two paired rotors touch each other or are at the smallest distance from each other. Due to the profile engagement gap, the compressing and extending working chambers are connected to chambers that are still in contact with the suction side. The entire maximum pressure ratio is thus present at the profile engagement gap. Working fluid that has already been compressed is transported back to the suction side through the profile engagement gap and thus reduces the efficiency of the compression. Since the profile engagement gap would be the line of engagement with play-free toothing, the profile engagement gap is also referred to as a "quasi-line of engagement".

Blowholes between working chambers are caused by rounded corners of the teeth of the profile. The working chambers with leading and connected downstream working chambers, so that (in contrast to the profile engagement gap) at a blow hole only the pressure difference from one working chamber to the next working chamber is present.

Furthermore, it is known that certain tooth pairings are common in screw machines, for example a rotor pair in which the main rotor 3 and the secondary rotor 4 teeth or a rotor pairing in which the main rotor 4 teeth and the secondary rotor 5 teeth or furthermore a rotor pair geometry in which the main rotor 5 teeth and the secondary rotor has 6 teeth. For different areas of application or purposes, rotor pairs or screw machines with different number of teeth ratio may be used. For example, rotor pair arrangements with a tooth / number ratio of 4/5 (main rotor with 4 teeth, secondary rotor with 5 teeth) are considered to be a suitable pairing for oil-injected compression applications in moderate pressure ranges.

In this respect, the number of teeth or the number of teeth ratio specifies different types of rotor pairings and, as a result, also different types of screw machines, in particular screw compressors.

wobei PT_rel mindestens 0,5, bevorzugt mindestens 0,515, und höchstens 0,65, bevorzugt höchstens 0,595, beträgt, wobei es sich bei PT_rel um die relative Profiltiefe, bei rk₁ um einen um den Außenumfang des Nebenrotors gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund ansetzenden Fußkreisradius handelt. Weiterhin ist das Verhältnis vom Achsabstand α der ersten Achse C1 zur zweiten Achse C2 und dem Kopfkreisradius rk₁ $$\frac{a}{{\mathit{rk}}_1}$$

so festgelegt, dass $\frac{a}{{\mathit{rk}}_1}$

mindestens 1,636 und höchstens 1,8, bevorzugt höchstens 1,733, beträgt, wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$\mathrm{1},\mathrm{4}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{3},\mathrm{4},$$

wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.For a screw machine or a rotor pair with 3 teeth on the main rotor and 4 teeth on the secondary rotor, a geometry with the following specifications is claimed, which is to be regarded as particularly energy-efficient:
A relative profile depth of the secondary rotor is formed with $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}.$$

where PT _{rel is} at least 0.5, preferably at least 0.515, and at most 0.65, preferably at most 0.595, where PT _rel is the relative profile depth, rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor, and rf ₁ is a root circle radius starting from the base of the profile. Furthermore, the ratio of the center distance α of the first axis C1 to the second axis C2 and the tip radius rk is ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

set so that $\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$

is at least 1.636 and at most 1.8, preferably at most 1.733, the main rotor preferably being designed with a wrap angle Φ _HR , for which applies 240 ° Φ Φ _HR 360 360 °, and preferably for a rotor length ratio L _HR / a: $$\mathrm{1}.\mathrm{4}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{3}.\mathrm{4}.$$

wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.

wobei PT_rel mindestens 0,5, bevorzugt mindestens 0,515 und höchstens 0,58 beträgt, wobei es sich bei PT_rel um die relative Profiltiefe, bei rk₁ um einen um den Außenumfang des Nebenrotors gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund ansetzenden Fußkreisradius handelt. Weiterhin ist das Verhältnis vom Achsabstand a der ersten Achse C1 zur zweiten Achse C2 und dem Kopfkreisradius rk₁ $$\frac{a}{{\mathit{rk}}_1}$$

so festgelegt, dass $\frac{a}{{\mathit{rk}}_1}$

mindestens 1,683 und höchstens 1,836, bevorzugt höchstens 1,782 beträgt, wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$\mathrm{1},\mathrm{4}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{3},\mathrm{3},$$

wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.For a screw machine or a pair of rotors with four teeth on the main rotor and five teeth on the secondary rotor, a geometry with the following requirements is claimed, which is to be regarded as particularly energy-efficient: A relative profile depth of the secondary rotor is formed with $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}.$$

where PT _{rel is} at least 0.5, preferably at least 0.515 and at most 0.58, with PT _{rel being} the relative profile depth, rk _{1 being} a tip circle radius drawn around the outer circumference of the secondary rotor, and rf _{1 being} a start on the profile base Foot circle radius. Furthermore, the ratio of the center distance a of the first axis C1 to the second axis C2 and the tip radius rk is ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

set so that $\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$

is at least 1.683 and at most 1.836, preferably at most 1.782, the main rotor preferably being designed with a wrap angle Φ _HR , for which 240 ° Φ Φ _HR 360 360 °, and preferably for a rotor length ratio L _HR / a: $$\mathrm{1}.\mathrm{4}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{3}.\mathrm{3}.$$

wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the Main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.

wobei PT_rel mindestens 0,44 und höchstens 0,495, bevorzugt höchstens 0,48 beträgt, wobei es sich bei PT_rel um die relative Profiltiefe, bei rk₁ um einen um den Außenumfang des Nebenrotors gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund ansetzenden Fußkreisradius handelt. Weiterhin ist das Verhältnis von Achsabstand a der ersten Achse C1 zur zweiten Achse C2 und den Kopfkreisradius rk₁ $$\frac{a}{{\mathit{rk}}_1}$$

so festgelegt, dass $\frac{a}{{\mathit{rk}}_1}$

mindestens 1,74, bevorzugt mindestens 1,75 und höchstens 1,8, bevorzugt höchstens 1,79 beträgt, wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$\mathrm{1},\mathrm{4}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{3},\mathrm{2},$$

wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.For a screw machine or a pair of rotors with five teeth on the main rotor and six teeth on the secondary rotor, a geometry with the following specifications is claimed, which is to be regarded as particularly energy-efficient:
A relative profile depth of the secondary rotor is formed with $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}.$$

where PT _{rel is} at least 0.44 and at most 0.495, preferably at most 0.48, where PT _rel is the relative profile depth, rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor, and rf ₁ is one that starts at the base of the profile Foot circle radius. Furthermore, the ratio of the center distance a of the first axis C1 to the second axis C2 and the tip radius rk is ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

set so that $\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$

is at least 1.74, preferably at least 1.75 and at most 1.8, preferably at most 1.79, the main rotor preferably being designed with a wrap angle Φ _HR , for which applies 240 ° Φ Φ _HR 360 360 °, and preferably for a rotor length ratio L _HR / a: $$\mathrm{1}.\mathrm{4}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{3}.\mathrm{2}.$$

wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.

mit PT₁ = rk₁ - rf₁ und rf₁ = a - rk₂ If the values for the relative profile depth on the one hand and the ratio of the center distance to the tip radius of the secondary rotor on the other hand for the specified number of teeth ratios are in the specified advantageous ranges, then the basic requirements for a good secondary rotor profile or a good interaction of secondary rotor profile and Main rotor profile created, in particular this enables a particularly favorable ratio of blow hole area to profile gap length. With regard to the decisive parameters, all of the tooth number ratios mentioned are supplemented by the illustration in Figure 7a directed. The relative profile depth of the secondary rotor is a measure of how deep the profiles are cut. With increasing profile depth, for example, the construction volume utilization increases, but at the expense of the bending stiffness of the secondary rotor. The following applies to the relative profile depth of the secondary rotor: $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="1"\; label="PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">PT</figure-callout>}}_1}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=\frac{{\mathit{rk}}_1-\left(a-{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2\right)}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=1-\frac{a-{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

with PT ₁ = rk ₁ - rf ₁ and rf ₁ = a - rk ₂

Achsabstand a zum Nebenrotor-Kopfkreisradius rk₁.In this respect there is a connection with the ratio of $\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}}.$

Center distance a to secondary rotor tip radius rk ₁ .

The specified values for the rotor length ratio L _HR / a and the wrap angle Φ _HR represent advantageous or expedient values for the respectively specified number of teeth ratio in order to determine an advantageous rotor pairing in the axial dimension.

1. Preferred configurations for a rotor pair with a number of teeth ratio of 3/4

Preferred configurations for a pair of rotors with a number-of-teeth ratio of 3/4 are set out below, that is to say for a pair of rotors in which the main rotor has 3 teeth and the secondary rotor 4 teeth.
A first preferred embodiment provides that circular arcs B ₂₅ , B ₅₀ , B ₇₅ , the common center of which is given by the axis C1, are defined in a frontal section view within a secondary rotor tooth, the radius r ₂₅ of B _{25 being} the value r ₂₅ = rf ₁ + 0.25 ^∗ (rk ₁ - rf ₁ ), the radius r ₅₀ of B _{50 has} the value r ₅₀ = rf ₁ + 0.5 ^∗ (rk ₁ - rf ₁ ) and the radius r ₇₅ of B _{75 has} the value r ₇₅ = rf ₁ + 0.75 ^∗ (rk ₁ - rf ₁ ), and the arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and the trailing tooth flank F _N , where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b _{75 of} the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed :
0.65 ≤ ε ₁ <1.0 and / or 0.50 ≤ ε ₂ ≤ 0.85, preferably 0.80 ≤ ε ₁ <1.0 and / or 0.50 ≤ ε ₂ ≤ 0.79.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the greater the length of the profile engagement gap is inevitable. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole. A particularly favorable combination of the two parameters is achieved in the areas claimed. At the same time, a sufficiently high bending stiffness of the secondary rotor is guaranteed. There are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, the Figure 7c directed.

A further preferred embodiment provides that in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 at the base circle and at the radially outermost point of the tooth define an apex F5, F1, F2 and F5 a triangle D _{Z is} defined and wherein in a radially outer area the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 over the triangle D _Z survives and 8 ≤ A2 / A1 ≤ 60 is observed.

The partial tooth surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The partial tooth surface A2 on the trailing tooth flank F _{N of} the secondary rotor, on the other hand, has a significant influence on the length of the profile engagement gap, the chamber extension and the secondary rotor torque. There is an advantageous range for the tooth part area ratio A2 / A1, which enables a good compromise between the length of the profile engagement gap on the one hand and the blow hole on the other. With regard to the illustration of the parameters is also supplementary Figure 7d directed.

In a further preferred embodiment, the pair of rotors has a secondary rotor, in which, in an end sectional view, the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the In addition to rotor base points F1 and F2 and at the radially outermost point of the tooth, a vertex F5 is defined, a triangle D _{Z being} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 in a radially outer region of the tooth with a surface A1 protrudes beyond the triangle D _Z and in a radially inner region it _retracts with respect to the triangle D _Z with a surface A3 and 7.0 ≤ A3 / A1 ≤ 35 is observed. With regard to the illustration of the parameters, the Figure 7d directed.

Furthermore, with regard to the design of the secondary rotor, it is considered to be advantageous if, in a frontal section view, a base point F5 is defined between the tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) in each case and at the radially outermost point of the tooth a triangle D _{Z is} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1, the tooth itself being a has the cross-sectional area A0 bounded by the circular arc B running between F1 and F2 around the center point defined by the axis C1 and 0.5% ≤ A1 / A0 4,5 4.5% being maintained. With regard to the illustration of the parameters, the Figures 7d and 7e referenced.

A further preferred embodiment provides that in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth, an apex F5 is defined, the between F1 and F2 circular arc B around the center defined by axis C1 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor (NR), with a point F11 being defined on the half circular arc B between F1 and F2, one of which The radial axis R drawn through the vertex F5 and the center point of the secondary rotor (NR) defined by the axis C1 intersects the circular arc B at a point F12, an offset angle β being defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and wherein 14% ≤ δ ≤ 25% is observed with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$

First, it is clarified again that the offset angle is preferably always positive, that is, the offset in the direction of the direction of rotation is given and not contrary. To this extent, the tooth of the secondary rotor is curved toward the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blow hole area, the shape of the line of engagement, the length and shape of the profile engagement gap, the secondary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, is supplementary to Figure 7f directed.

It is considered advantageous if the trailing tooth flank F _{N of} a tooth of the secondary rotor (NR), formed between F1 and F5, has a convex length fraction of at least 45% to at most 95% in a frontal section examination.

The relatively long convex length component of the trailing tooth flank F _{N of} a tooth of the secondary rotor, which is defined with the area, allows a good compromise between the length of the profile engagement gap, chamber extension, secondary rotor torque on the one hand, and bending stiffness of the secondary rotor on the other hand. With regard to the illustration of the parameters is also supplementary Figure 7g directed.

eingehalten ist. Es sei an dieser Stelle nochmals darauf hingewiesen, dass das Zahnprofil nach radial innen zur Achse C1 hin durch den Fußkreis FK₁ begrenzt ist. Hierbei kann es auftreten, dass der Radialstrahl R das Zahnprofil derart teilt, dass zwei disjunkte Flächenanteile mit einem Gesamtflächenanteil A5, die der vorlaufenden Zahnflanke F_V zugeordnet sind, entstehen, vgl. Figur 7g. Würde der Scheitelpunkt F5 derart zur vorlaufenden Zahnflanke hin versetzt sein, dass der Radialstrahl R die vorlaufende Zahnflanke F_V nicht nur berührt, sondern in zwei Punkten schneidet, so sind wiederum zwei der vorlaufenden Zahnflanke zugeordnete disjunkte Flächenanteile mit einem Gesamtflächenanteil A5 definiert. Der der nachlaufenden Zahnflanke F_N zugeordnete Flächenanteil A4 wird dann zum einen durch den Radialstrahl R und abschnittsweise, nämlich zwischen den zwei Schnittpunkten der vorlaufenden Zahnflanke F_V mit dem Radialstrahl R, zum anderen auch durch die vorlaufende Zahnflanke F_V begrenzt.The secondary rotor is preferably designed in such a way that, in an end section view, the radial beam R drawn from the axis C1 of the secondary rotor (NR) through F5 divides the tooth profile into a surface portion A5 assigned to the leading tooth flank F _V and a surface portion A4 assigned to the trailing tooth flank F _N and in which $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{14}$$

is adhered to. At this point it should be pointed out again that the tooth profile is delimited radially inwards towards the axis C1 by the root circle FK ₁ . In this case, it can occur that the radial beam R divides the tooth profile in such a way that two disjunct surface portions with a total surface portion A5, which are assigned to the leading tooth flank F _V , arise. Figure 7g , If the apex F5 were displaced towards the leading tooth flank in such a way that the radial beam R not only touches the leading tooth flank F _V but intersects at two points, then again two of the leading tooth flank are assigned disjoint areas with a total area A5 defined. The area portion A4 assigned to the trailing tooth flank F _N is then limited on the one hand by the radial beam R and in sections, namely between the two intersections of the leading tooth flank F _V with the radial beam R, and on the other hand also by the leading tooth flank F _V.

Another preferred embodiment has a pair of rotors, which is characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 290 ° ≤ Φ _HR 360 360 °, preferably 320 ° Φ Φ _HR ≤ 360 °.

With increasing wrap angle, the print window area can be made larger with the same built-in volume ratio. This also shortens the axial extension of the working chamber to be pushed out, the so-called profile pocket depth. This reduces the throttling throttle losses, especially at higher speeds, and thus enables better specific performance. If the wrap angle is too large, however, this in turn adversely affects the construction volume and leads to larger rotors.

und
wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und den Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In addition, it is provided in an advantageous embodiment of a rotor pair, which is constructed and cooperates with each other, that a Blaslochfaktor μ _Bl at least 0.02% and at most 0.4%, more preferably masses, is at most 0.25%,
in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

While the absolute size of the blow hole on the pressure side alone does not provide any meaningful information about the effect on the leakage mass flows, a ratio of the absolute pressure side blow hole area A _Bl to the sum of the Tooth gap area A6 of the secondary rotor and the tooth gap area A7 of the main rotor are much more meaningful. With regard to the further illustration of the parameters, this is also supplemented by Figure 7b directed. The smaller the numerical value µ _Bl , the smaller the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole area can thus be displayed regardless of the size of the screw machine.

eingehalten ist mit $${\mathit{\mu }}_l=\frac{l_{\mathit{sp}}}{{\mathit{PT}}_1},$$

wobei I_sp die Länge des räumlichen, also dreidimensionalen Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnen
und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}*100\left[\%\right]$

wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und den Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In a further preferred embodiment, a pair of rotors is designed and matched to one another in such a way that for a blow hole / profile gap length factor μ _l ∗ μ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{72}\%$$

is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$

where I _sp denotes the length of the spatial, that is to say three-dimensional, profile engagement gap of a tooth gap of the secondary rotor and PT ₁ denotes the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

µ _l denotes a profile gap length factor, the length of the profile engagement gap of a tooth gap being set in relation to the profile depth PT ₁ . This allows a measure to be made of the length of the profile engagement gap regardless of the size of the screw machine. The smaller the numerical value of the key figure µ _l , the shorter the profile gap of a tooth pitch with the same profile depth and thus the lower the leakage volume flow back to the suction side. The factor µ _l ∗ µ _Bl results in the goal of combining a small pressure-side blow hole with a short profile gap. As already mentioned, the two key figures behave in opposite directions.

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio Druck of up to 3, in particular with a pressure ratio Π of greater than 1 and up to 3 , can be achieved, the pressure ratio denoting the ratio of the discharge pressure to the intake pressure.

A further preferred embodiment provides a pair of rotors such that the main rotor (HR) is designed to be operable with a circumferential speed in a range from 20 to 100 m / s in relation to a tip circle KK ₂ .

$$1,145\le D_v\le 1,30$$

eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und Dk₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnen.A further embodiment has a pair of rotors, which is characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

$$1.145\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.30$$

is observed, Dk ₁ denoting the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denoting the diameter of the tip circle KK _{2 of} the main rotor (HR).

2. Preferred configurations for a rotor pair with a number of teeth ratio of 4/5

Preferred configurations for a pair of rotors with a number of teeth ratio of 4/5, that is to say for a pair of rotors in which the main rotor has four teeth and the secondary rotor five teeth, are set out below:
A further preferred embodiment provides that in an end section observation circular arcs B ₂₅ , B ₅₀ , running within a secondary rotor tooth, B ₇₅ , whose common center is given by axis C1, are defined, the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 ^∗ (rk ₁ - rf ₁ ), the radius r ₅₀ of B _{50 has} the value r ₅₀ = rf ₁ + 0.5 ^∗ (rk ₁ - rf ₁ ) and the radius r ₇₅ of B _{75 has} the value r ₇₅ = rf ₁ + 0.75 ^∗ (rk ₁ - rf ₁ ) , and wherein the circular arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and the trailing tooth flank F _N , and wherein tooth thickness ratios as ratios of the arc lengths b ₂₅ , b ₅₀ , b _{75 of} the circular arches B ₂₅ , B ₅₀ , B _{75 can be defined} with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed:
0.75 ≤ ε ₁ ≤ 0.85 and / or 0.65 ≤ ε ₂ ≤ 0.74.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the greater the length of the profile engagement gap is inevitable. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole. A particularly favorable combination of the two parameters is achieved in the areas claimed. At the same time, a sufficiently high bending stiffness of the secondary rotor is guaranteed. There are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, the Figure 7c directed.

A further preferred embodiment provides that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 are defined at the base circle and at the radially outermost point of the tooth, wherein a triangle D _{Z is} defined by F1, F2 and F5 and in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a Surface A2 protrudes beyond the triangle D _Z and 6 ≤ A2 / A1 ≤ 15 is observed.

The partial tooth surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The partial tooth surface A2 on the trailing tooth flank F _{N of} the secondary rotor, on the other hand, has a significant influence on the length of the profile engagement gap, the chamber extension and the secondary rotor torque. There is an advantageous range for the tooth part area ratio A2 / A1, which is a good compromise between the length of the Profile engagement gap on the one hand and blow hole on the other. With regard to the illustration of the parameters is also supplementary Figure 7d directed.

In a further embodiment, the pair of rotors has a secondary rotor, in which, in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth define an apex F5 where a triangle D _{Z is} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 projects beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and in a radially inner region withdraws with respect to the triangle D _Z with an area A3 and 9.0 ≤ A3 / A1 ≤ 18 is observed. With regard to the illustration of the parameters, the Figure 7d directed.

Furthermore, with regard to the design of the secondary rotor, it is considered to be advantageous if, in a frontal section view, a base point F5 is defined between the tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) in each case and at the radially outermost point of the tooth a triangle D _{Z is} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1, the tooth itself being a has the cross-sectional area A0 bounded by the circular arc B running between F1 and F2 around the center point defined by the axis C1 and 1.5% ≤ A1 / A0 3,5 3.5% being maintained.

With regard to the definition of the parameters, reference is made to the Figures 7d and 7e referenced.

eingehalten ist, mit $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{.}$

A further preferred embodiment provides that in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth, an apex F5 is defined, the between F1 and F2 running circular arc B around the center defined by the axis C1 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR, with half of the circular arc B A point F11 is defined between F1 and F2, a radial beam R drawn through the apex F5 from the center point of the secondary rotor (NR) defined by the axis C1 intersecting the circular arc B at a point F12, an offset angle β being that in the direction of rotation of the secondary rotor (NR) considered offset from F11 to F12 is defined and where $$14\%\le \mathrm{\delta }\le 18\%$$

is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$

First of all, it is clarified again that the offset angle is preferably always positive, that is, the offset in the direction of the direction of rotation is always given and not in the opposite direction. To this extent, the tooth of the secondary rotor is curved toward the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blow hole area, the shape of the line of engagement, the length and shape of the profile engagement gap, the secondary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, is supplementary to Figure 7f directed.

It is furthermore considered to be advantageous if the trailing tooth flank F _{N of} a tooth of the secondary rotor (NR) formed between F1 and F5 has a convex length fraction of at least 55% to at most 95% in a frontal section examination.

The relatively long convex length component of the trailing tooth flank F _{N of} a tooth of the secondary rotor, which is defined with the area, allows a good compromise between the length of the profile engagement gap, chamber extension, secondary rotor torque on the one hand, and bending stiffness of the secondary rotor on the other hand. With regard to the illustration of the parameters is also supplementary Figure 7g directed.

eingehalten ist. Es sei an dieser Stelle nochmals darauf hingewiesen, dass das Zahnprofil nach radial innen zur Achse C1 hin durch den Fußkreis FK₁ begrenzt ist. Hierbei kann es auftreten, dass der Radialstrahl R das Zahnprofil derart teilt, dass zwei disjunkte Flächenanteile mit einem Gesamtflächenanteil A5, die der vorlaufenden Zahnflanke F_V zugeordnet sind, entstehen, vgl. Figur 7g. Würde der Scheitelpunkt F5 derart zur vorlaufenden Zahnflanke hin versetzt sein, dass der Radialstrahl R die vorlaufende Zahnflanke F_V nicht nur berührt, sondern in zwei Punkten schneidet, so sind wiederum zwei der vorlaufenden Zahnflanke zugeordnete disjunkte Flächenanteile mit einem Gesamtflächenanteil A5 definiert. Der der nachlaufenden Zahnflanke F_N zugeordnete Flächenanteil A4 wird dann zum einen durch den Radialstrahl R abschnittsweise, nämlich zwischen den zwei Schnittpunkten der vorlaufenden Zahnflanke F_V mit dem Radialstrahl R, zum anderen auch durch die vorlaufende Zahnflanke F_V begrenzt.The secondary rotor is preferably designed in such a way that, in an end section view, the radial beam R drawn from the axis C1 of the secondary rotor (NR) through F5 divides the tooth profile into a surface portion A5 assigned to the leading tooth flank F _V and a surface portion A4 assigned to the trailing tooth flank F _N and in which $$\mathrm{4}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{9}$$

is adhered to. At this point it should be pointed out again that the tooth profile is delimited radially inwards towards the axis C1 by the root circle FK ₁ . In this case, it can occur that the radial beam R divides the tooth profile in such a way that two disjunct surface portions with a total surface portion A5, which are assigned to the leading tooth flank F _V , arise. Figure 7g , If the apex F5 were displaced towards the leading tooth flank in such a way that the radial beam R not only touches the leading tooth flank F _V , but intersects in two points, then two disjoint area parts associated with the leading tooth flank are defined with a total area proportion A5. The area portion A4 assigned to the trailing tooth flank F _N is then delimited on the one hand by the radial beam R in sections, namely between the two intersections of the leading tooth flank F _V with the radial beam R, and on the other hand also by the leading tooth flank F _V.

A further preferred embodiment has a pair of rotors, which is characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 320 ° Φ Φ _HR 360 360 °, preferably 330 ° Φ Φ _HR 360 360 °.

With increasing wrap angle, the print window area can be made larger with the same built-in volume ratio. This also shortens the axial extension of the working chamber to be pushed out, the so-called profile pocket depth. This reduces the throttling throttle losses, especially at higher speeds, and thus enables better specific performance. If the wrap angle is too large, however, this in turn adversely affects the construction volume and leads to larger rotors.

und
wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In addition, it is provided in an advantageous embodiment of a rotor pair, which is constructed and cooperates with each other, that a Blaslochfaktor μ _Bl at least 0.02% and at most 0.4%, more preferably masses, is at most 0.25%,
is complied with ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor NR or of the main rotor (HR), the area A6 in a frontal section view that between the Profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ and the area A7 in an end sectional view indicate the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

While the absolute size of the blowhole on the pressure side alone does not provide any meaningful information about the effect on the leakage mass flows, a ratio of the absolute pressure-side blowhole area A _Bl to the sum of the tooth space area A6 of the secondary rotor and the tooth space area A7 of the main rotor is significantly more meaningful. With regard to the illustration of the parameters, this is also supplemented by Figure 7b directed. The smaller the numerical value µ _Bl , the smaller the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole area can thus be displayed regardless of the size of the screw machine.

eingehalten ist mit $${\mathit{\mu }}_l=\frac{l_{\mathit{sp}}}{{\mathit{PT}}_1},$$

wobei I_sp die Länge des räumlichen, also dreidimensionalen Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnen
und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}*100\left[\%\right]$

wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In a further preferred embodiment, a pair of rotors is designed and matched to one another in such a way that for a blow hole / profile gap length factor μ _l ∗ μ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{72}\%$$

is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$

where I _sp denotes the length of the spatial, that is to say three-dimensional, profile engagement gap of a tooth gap of the secondary rotor and PT ₁ denotes the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the head circle KK ₁ and the area A7 in an end sectional view indicate the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the head circle KK ₂ .

µ _l denotes a profile gap length factor, the length of the profile engagement gap of a tooth gap being set in relation to the profile depth PT ₁ . This means that a measure of the length of the profile engagement gap can be defined regardless of the size of the screw machine. The smaller the numerical value of the key figure µ _l , the shorter the profile gap with the same profile depth and thus the lower the leakage volume flow back to the suction side. The factor µ _l ^∗ µ _Bl results in the goal of combining a small pressure-side blow hole with a short profile gap. As already mentioned, the two key figures behave in opposite directions.

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio of up to 5, in particular with a pressure ratio größer greater than 1 and up to 5, or alternatively, a fluid-injected compression with a pressure ratio of up to 16, in particular with a pressure ratio greater than 1 and up to 16, can be achieved, the pressure ratio denoting the ratio of the compression pressure to the intake pressure.

A further preferred embodiment provides a pair of rotors such that in the case of dry compression the main rotor with respect to a tip circle KK ₂ with a peripheral speed in a range from 20 to 100 m / s and in the case of fluid-injected compression the main rotor with a peripheral speed in is operable in a range of 5 to 50 m / s.

$$1,195\le D_v\le 1,33$$

eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und Dk₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnet.A further embodiment has a pair of rotors, which is characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

$$1.195\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.33$$

is observed, where Dk ₁ denotes the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and Dk ₂ the diameter of the tip circle KK _{2 of} the main rotor (HR).

3. Preferred configurations for a rotor pair with a number of teeth ratio of 5/6

Preferred configurations for a pair of rotors with a number of teeth ratio of 5/6, that is to say for a pair of rotors in which the main rotor has five teeth and the secondary rotor six teeth, are set out below:
A further preferred embodiment provides that circular arcs B ₂₅ , B ₅₀ , B ₇₅ , the common center of which is given by the axis C1, are defined in a frontal section view within a secondary rotor tooth, the radius r ₂₅ of B _{25 being} the value r ₂₅ = rf ₁ + 0.25 ^∗ (rk ₁ - rf ₁ ), the radius r ₅₀ of B _{50 has} the value r ₅₀ = rf ₁ + 0.5 ^∗ (rk ₁ - rf ₁ ) and the radius r ₇₅ of B _{75 has} the value r ₇₅ = rf ₁ + 0.75 ^∗ (rk ₁ - rf ₁ ), and the arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and the trailing tooth flank F _N , where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b _{75 of} the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed : 0.76 ≤ ε ₁ ≤ 0.86 and / or 0.62 ≤ ε ₂ ≤ 0.72.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the greater the length of the profile engagement gap is inevitable. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole. A particularly favorable combination of the two parameters is achieved in the areas claimed. At the same time, a sufficiently high bending stiffness of the secondary rotor is guaranteed. There are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, the Figure 7c directed.

A further preferred embodiment provides that in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 at the base circle and at the radially outermost point of the tooth have an apex F5 are defined, wherein a triangle D _{Z is} defined by F1, F2 and F5 and in a radially outer area the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank formed between F1 and F5 F _N with a surface A2 protrudes beyond the triangle D _Z and 4 ≤ A2 / A1 ≤ 7 is observed.

The partial tooth surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The partial tooth surface A2 on the trailing tooth flank F _{N of} the secondary rotor, on the other hand, has a significant influence on the length of the profile engagement gap, the chamber extension and the secondary rotor torque. There is an advantageous range for the tooth part area ratio A2 / A1, which enables a good compromise between the length of the profile engagement gap on the one hand and the blow hole on the other. With regard to the illustration of the parameters is supplementary Figure 7d directed.

In a further preferred embodiment, the pair of rotors has a secondary rotor, in which, in an end-sectional view, between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth an apex F5 are defined, wherein a triangle D _{Z is} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and in a radially inner one Area opposite the triangle D _Z with a surface A3 and 8 ≤ A3 / A1 ≤ 14 is observed. With regard to the illustration of the parameters, the Figure 7d directed.

Furthermore, with regard to the design of the secondary rotor, it is considered to be advantageous if, in a frontal section view, a base point F5 is defined between the tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) in each case and at the radially outermost point of the tooth a triangle D _{Z is} defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1, the tooth itself being a has the cross-sectional area A0 bounded by the circular arc B running between F1 and F2 around the center defined by the axis C1 and 1.9% ≤ A1 / A0 ≤ 3.2% is adhered to. With regard to the illustration of the parameters, the Figures 7d and 7e referenced.

eingehalten ist, mit $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{.}$

A further preferred embodiment provides that in an end-sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth, an apex F5 is defined, the between F1 and F2 circular arc B around the center defined by axis C1 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR, with a point F11 being defined on the half circular arc B between F1 and F2, one of which is defined by the Axis C1 defined center point of the secondary rotor (NR) through radial apex R5 drawn through the apex F5 intersects the circular arc B at a point F12, an offset angle β being defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and wherein $$13.5\%\le \mathrm{\delta }\le 18\%$$

is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$

First of all, it is clarified again that the offset angle is preferably always positive, that is, the offset in the direction of the direction of rotation is always given and not in the opposite direction. To this extent, the tooth of the secondary rotor is curved toward the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blow hole area, the shape of the line of engagement, the profile gap length and shape, the secondary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, is supplementary to Figure 7f directed.

Another preferred embodiment has a pair of rotors, which is characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 320 ° ≤ Φ _HR 360 360 °, preferably 330 ° Φ Φ _HR ≤ 360 ° increasing wrap angle, the print window area can be made larger with the same built-in volume ratio. In addition, this shortens the axial extension of the ones to be pushed out Working chamber, the so-called profile pocket depth. This reduces the throttling throttle losses, especially at higher speeds, and thus enables better specific performance. If the wrap angle is too large, however, this in turn adversely affects the construction volume and leads to larger rotors.

und
wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In addition, it is provided in an advantageous embodiment of a rotor pair, which is constructed and cooperates with each other, that a Blaslochfaktor μ _Bl at least 0.03% and at most 0.25%, more preferably at most 0.2% or less by weight,
in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor NR or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view denote the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

While the absolute size of the blowhole on the pressure side alone does not provide any meaningful information about the effect on the leakage mass flows, a ratio of the absolute pressure-side blowhole area A _Bl to the sum of the tooth space area A6 of the secondary rotor and the tooth space area A7 of the main rotor is significantly more meaningful. With regard to the illustration of the parameters, this is also supplemented by Figure 7b directed. The smaller the numerical value µ _Bl , the smaller the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole area can thus be displayed regardless of the size of the screw compressor.

eingehalten ist mit $${\mathit{\mu }}_l=\frac{l_{\mathit{sp}}}{{\mathit{PT}}_1},$$

wobei I_sp die Länge des räumlichen, also dreidimensionalen Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnen
und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}*100\left[\%\right]$

wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In a further preferred embodiment, a pair of rotors is designed and matched to one another in such a way that for a blow hole / profile gap length factor μ _l ∗ μ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{26}\%$$

is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$

where I _sp denotes the length of the spatial, that is to say three-dimensional, profile engagement gap of a tooth gap of the secondary rotor and PT ₁ denotes the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

where A _{Bl is} an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

µ _l denotes a profile gap length factor, the length of the profile engagement gap of a tooth gap being set in relation to the profile depth PT ₁ . This means that a measure of the length of the profile engagement gap can be defined regardless of the size of the screw machine. The smaller the numerical value of the key figure µ _l , the shorter the profile gap with the same profile depth and thus the lower the leakage volume flow back to the suction side. The factor µ _l ^∗ µ _Bl results in the goal of combining a small pressure-side blow hole with a short profile gap. As already mentioned, the two key figures behave in opposite directions.

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio of up to 5, in particular with a pressure ratio größer greater than 1 and up to 5, or alternatively, a fluid-injected compression with a pressure ratio of up to 20, in particular with a pressure ratio Π greater than 1 and up to 20, can be achieved are, the pressure ratio denotes the ratio of the discharge pressure to the suction pressure.

A further preferred embodiment provides a pair of rotors such that the main rotor (HR) with respect to a tip circle KK ₂ in the case of a dry compression with a peripheral speed in a range from 20 to 100 m / s and in the case of a fluid-injected compression with a peripheral speed is designed to be operable in a range from 5 to 50 m / s.

$$1,19\le D_v\le 1,26$$

eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und Dk₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnet.A further embodiment has a pair of rotors, which is characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

$$1.19\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.26$$

is observed, where Dk ₁ denotes the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and Dk ₂ the diameter of the tip circle KK _{2 of} the main rotor (HR).

4. Preferred embodiment for a pair of rotors with a number of teeth ratio of 3/4, 4/5 or 5/6

In general, it is regarded as preferred that the teeth of the secondary rotor taper towards the outside in a frontal section observation, that is to say all of the circular arcs running perpendicularly from the trailing tooth flank F _N to a radial beam starting from the center point defined by axis C1 and drawn through point F5 Remove the leading tooth flank F _V from F1 to F2 in the sequence radially outwards (or at least remain the same in sections). In other words, in a forehead section observation, all arc lengths b (r) of the associated concentric circular arcs with the radius rf ₁ <r <rk ₁ and the common center defined by the axis C1, which are each defined by the axis C1, run within a tooth of the secondary rotor leading tooth flank F _V and the trailing tooth flank F _{N are} limited so that the arc lengths b (r) decrease monotonically with increasing radius r.

In this preferred embodiment, the teeth of the secondary rotor are thus designed in such a way that there are no constrictions, that is to say the width of a tooth of the secondary rotor does not increase at any point, but rather decreases radially outwards or remains at most the same. This is considered useful in order to achieve a small blow hole on the pressure side with a short profile engagement gap length.

The end section design of the secondary rotor (NR) is advantageously carried out in such a way that the effective direction of the torque, which results from a reference pressure on the partial surface of the secondary rotor delimiting a working chamber, is directed against the direction of rotation of the secondary rotor.

Such a face cut design causes the total torque from the gas forces on the secondary rotor to be directed in the opposite direction to the direction of rotation of the secondary rotor. As a result, a defined flank contact between the trailing secondary rotor flank F _N and the leading main rotor flank is achieved. This helps to avoid the problem of so-called rotor rattling, which can occur in unfavorable, especially unsteady operating situations. Rotor rattling is understood to mean the leading and lagging of the secondary rotor about its axis of rotation, superimposed on the uniform rotary movement, which is associated with a rapidly changing impact of the trailing secondary rotor flanks on the leading main rotor flanks and then the leading secondary rotor flanks on the trailing main rotor flanks, etc. This problem occurs in particular when the moment from the gas forces together with other moments (eg from bearing friction) on the secondary rotor is undefined (eg near zero), which is effectively avoided by the advantageous face cut design.

In a concretely possible, optional embodiment, the main rotor (HR) and secondary rotor (NR) for conveying air or inert gases, such as helium or nitrogen, are designed and matched to one another.

The profile of a tooth of the secondary rotor is preferably asymmetrical in relation to the radial beam R drawn from the center point, which is defined by the axis C1, through the apex F5. In the secondary rotor, leading tooth flank and trailing tooth flank of each tooth are thus asymmetrical to each other.

This asymmetrical design is already known per se for screw compressors. However, it contributes significantly to efficient compaction.

mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR).A further preferred embodiment provides that a point C on the connecting section is viewed in a face section C 1 C 2 is defined between the first axis C1 and the second axis C2, where the rolling circles WK _{1 of} the secondary rotor (NR) and WK _{2 of} the main rotor (HR) touch that K5 the intersection of the root circle FK _{1 of} the secondary rotor (NR) with the connecting path C 1 C 2 defined, where r ₁ measures the distance between K5 and C, and that K4 denotes the point of the suction-side part of the line of engagement, which is farthest from the connecting path C 1 C 2 is spaced between C1 and C2, where r ₂ measures the distance between K4 and C and where: $$0.9\le \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\le 0.875\times \frac{z_1}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2}+0.22$$

with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR).

About the course of the suction-side part of the line of engagement between the straight section C 1 C 2 and the cutting edge on the suction side can be influenced, among other things, the secondary rotor torque (= torque on the secondary rotor) and the chamber extension into the pressure window.
Characteristic features of the above-mentioned course of the suction-side part of the line of engagement can be described on the basis of the radius ratio r ₁ / r _{2 of} two concentric circles around the point C (= contact point of pitch circle WK _{1 of} the secondary rotor and pitch circle WK _{2 of} the main rotor). If the radius ratio r ₁ / r _{2 is} in the specified range, the working chamber is essentially completely pushed out into the pressure window.

bevorzugt $$\mathrm{0},\mathrm{89}*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{0},\mathrm{94}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{1},\mathrm{05}*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{1},\mathrm{22},$$

mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR), wobei das Rotorlängenverhältnis L_HR/a das Verhältnis der Rotorlänge L_HR zum Achsabstand a angibt und Rotorlänge L_HR der Abstand der saugseitigen Hauptrotor-Rotorstirnfläche zur druckseitigen Hauptrotor-Rotorstirnfläche ist.In a preferred embodiment, the pair of rotors is designed and configured in such a way that the following applies to a rotor length ratio LHR / a: $$\mathrm{0}.\mathrm{85}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{67}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{26}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{18}.$$

prefers $$\mathrm{0}.\mathrm{89}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{94}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{05}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{22}.$$

with z ₁ : number of teeth in the secondary rotor (NR) and z ₂ : number of teeth in the main rotor (HR), the rotor length ratio L _HR / a being the ratio of the Specifies rotor length L _HR to center distance a and rotor length L _{HR is} the distance between the suction-side main rotor-rotor end face and the pressure-side main rotor-rotor end face.

The smaller the value of L _HR / a, the higher (with the same absorption volume) the bending stiffness of the rotors. In the stressed area, the bending stiffness of the rotors is sufficiently high that the rotors do not bend significantly during operation and therefore the gaps (between the rotors or between the rotors and the compressor housing) can be made relatively narrow without the risk of that the rotors start up against each other or start up in the compressor housing under unfavorable operating conditions (high temperatures and / or high pressures). Narrow gaps offer the advantage of low backflow and thus contribute to energy efficiency. At the same time, operational safety is guaranteed despite the small gap dimensions. A high bending stiffness of the rotors is also advantageous in rotor manufacture in order to meet the high demands on the shape tolerances.

On the other hand, the ratio of L _HR / a is so large that the center distance a is not excessively large in relation to the rotor length L _HR . This is advantageous because, as a consequence, the rotor diameters and, more specifically, the end faces of the rotors are not excessively large. On the one hand, this allows the gap lengths to be kept small; thereby reducing the backflow into previous working chambers and thereby again improving energy efficiency. On the other hand, the axial forces resulting from the pressurized pressure-side end faces of the rotors can advantageously be kept small by means of small-sized end faces, these axial forces act on the rotors and in particular on the rotor bearing during operation. By minimizing these axial forces, the load on the (rolling) bearings can be minimized or the bearings can be dimensioned smaller.

It can advantageously also be provided that, in a frontal section view, the tooth profile of the secondary rotor (NR) follows a circular arc with radius rk ₁ at its radially outer section, i.e. several points of the leading tooth flank F _V and the trailing tooth flank F _N on the circular arc Radius rk ₁ lie around the center point defined by axis C1, the circular arc ARC ₁ preferably includes an angle with respect to the axis C1 between 0.5 ° and 5 °, more preferably between 0.5 ° and 2.5 °,
where F10 is the most distant point from F5 on the leading tooth flank on this arc and
the radial beam R ₁₀ drawn between F10 and the center point of the secondary rotor (NR) defined by the axis C1 touches the front tooth flank F _V in at least one point or intersects in two points, cf. especially the illustration in Fig. 7h ,

The above-described design of the tooth profile of the secondary rotor is particularly relevant for a tooth / number ratio of 3/4 or 4/5. With such a tooth number ratio, the blow hole area can be reduced by complying with the condition reproduced above. With the number of teeth ratio 5/6, on the other hand, the aforementioned contact point or intersection point with the leading tooth flank F _V does not appear to be desirable, since the teeth of the secondary rotor may then become too thin and consequently too flexible.

Furthermore, a compressor block comprising a compressor housing and a pair of rotors as described above is claimed as claimed in the invention, the pair of rotors comprising a main rotor HR and a secondary rotor NR, each of which is rotatably mounted in the compressor housing.

In a preferred embodiment, the compressor block is designed in such a way that the face cut design is carried out in such a way that the working chamber formed between the tooth profiles of the main rotor (HR) and secondary rotor (NR) can essentially be pushed out completely into the pressure window.

In general, it is also considered advantageous that the choice of the secondary rotor and main rotor profiles propagated here makes it possible to dispense entirely with a relief groove / noise groove or to make it smaller.

The design of the front section of the two rotors advantageously ensures that no chamber gusset volume is formed between the two rotors when the working chamber is pushed out into the pressure window. The compression can be carried out particularly efficiently, since there is no backflow of already compressed medium to the suction side, and therefore none additional heat input occurs. In addition, the entire compressed volume can be used by downstream compressed air consumers. By avoiding over-compression, there are advantages for energy efficiency, for the smooth running of the compressor block and for the service life of the rotor bearings. With oil-injected compressors, the oil is prevented from being crushed, thus improving the smooth running of the compressor, reducing the load on the rotor bearing and reducing the stress on the oil.

In a further preferred embodiment, one shaft end of the main rotor is led out of the compressor housing and designed for connection to a drive, preferably both shaft ends of the secondary rotor being completely accommodated within the compressor housing.

Figur 1

einen Stirnschnitt einer ersten Ausführungsform mit einem Zähne-Zahlverhältnis 3/4.

Figur 2

einen Stirnschnitt einer zweiten Ausführungsform mit einem Zähne-Zahlverhältnis 3/4.

Figur 3

einen Stirnschnitt einer dritten Ausführungsform mit einem Zähne-Zahlverhältnis 4/5.

Figur 4

ein viertes Ausführungsbeispiel in einer Stirnschnittbetrachtung mit einem Zähne-Zahlverhältnis 5/6.

Figur 5

eine Veranschaulichung des isentropen Blockwirkungsgrads für das zweite Ausführungsbeispiel zum 3/4 Zähne-Zahlverhältnis im Vergleich zum Stand der Technik.

Figur 6

eine Veranschaulichung des isentropen Blockwirkungsgrads für das vierte Ausführungsbeispiel zum 5/6 Zähne-Zahlverhältnis im Vergleich zum Stand der Technik.

Figur 7a - 7k

Veranschaulichungsdiagramme für die verschiedenen Parameter der Geometrie des Nebenrotors bzw. des Rotorpaars bestehend aus Hauptrotor und Nebenrotor.

Figur 8

eine Veranschaulichung des Umschlingungswinkels beim Hauptrotor.

Figur 9

eine schematische Schnittzeichnung einer Ausführungsform eines Verdichterblocks.

Figur 10

eine Ausführungsform für ein miteinander verzahntes Rotorpaar bestehend aus einem Hauptrotor und einem Nebenrotor in dreidimensionaler Darstellung.

Figur 11

eine perspektivische Darstellung einer Ausführungsform eines Nebenrotors zur Veranschaulichung der räumlichen Eingriffslinie.

Figuren 12a, 12b

eine Veranschaulichung der für die Drehmomentwirkungen relevanter Flächen bzw. Teilflächen einer Arbeitskammer einer Ausführungsform des Nebenrotors.

Figur 13

den Stirnschnitt der Ausführungsform nach Figur 1 zur Erläuterung des Profilverlaufs von Haupt- und Nebenrotor bei dieser Ausführungsform.

Figur 14

den Stirnschnitt der Ausführungsform nach Figur 2 zur Erläuterung des Profilverlaufs von Haupt- und Nebenrotor bei dieser Ausführungsform.

Figur 15

den Stirnschnitt der Ausführungsform nach Figur 3 zur Erläuterung des Profilverlaufs von Haupt- und Nebenrotor bei dieser Ausführungsform.

Figur 16

den Stirnschnitt der Ausführungsform nach Figur 4 zur Erläuterung des Profilverlaufs von Haupt- und Nebenrotor bei dieser Ausführungsform.

The invention is also explained in more detail below with regard to further features and advantages on the basis of the description of exemplary embodiments. Here show:

Figure 1

an end section of a first embodiment with a number of teeth ratio 3/4.

Figure 2

an end section of a second embodiment with a number of teeth ratio 3/4.

Figure 3

an end section of a third embodiment with a number of teeth ratio 4/5.

Figure 4

a fourth embodiment in a forehead section view with a number of teeth ratio 5/6.

Figure 5

an illustration of the isentropic block efficiency for the second embodiment to the 3/4 teeth ratio in comparison to the prior art.

Figure 6

an illustration of the isentropic block efficiency for the fourth embodiment to the 5/6 teeth ratio in comparison to the prior art.

Figure 7a - 7k

Illustration diagrams for the various parameters of the geometry of the secondary rotor or the rotor pair consisting of the main rotor and the secondary rotor.

Figure 8

an illustration of the wrap angle in the main rotor.

Figure 9

is a schematic sectional drawing of an embodiment of a compressor block.

Figure 10

an embodiment for a toothed pair of rotors consisting of a main rotor and a secondary rotor in a three-dimensional representation.

Figure 11

a perspective view of an embodiment of a secondary rotor to illustrate the spatial line of engagement.

Figures 12a, 12b

an illustration of the surfaces or partial surfaces of a working chamber relevant to the torque effects of an embodiment of the secondary rotor.

Figure 13

the forehead section of the embodiment Figure 1 to explain the profile profile of the main and secondary rotor in this embodiment.

Figure 14

the forehead section of the embodiment Figure 2 to explain the profile profile of the main and secondary rotor in this embodiment.

Figure 15

the forehead section of the embodiment Figure 3 to explain the profile profile of the main and secondary rotor in this embodiment.

Figure 16

the forehead section of the embodiment Figure 4 to explain the profile profile of the main and secondary rotor in this embodiment.

The exemplary embodiments according to FIGS Figures 1 to 4 are explained. All four exemplary embodiments are suitable profiles in the sense of the present invention.

The corresponding geometric default values for the main rotor HR and the secondary rotor NR are given in Tables 1 to 4 shown below. <u> Table 1 </u> Embodiment 1 Embodiment 2 Embodiment 3 Embodiment 4 Number of teeth HR z ₂ 3 3 4 5 Number of teeth NR z ₁ 4 4 5 6 PT _rel [-] 0.588 0.54 0.528 0,455 a / rk ₁ [-] 1.66 1.72 1.764 1.78 The profiles were created with the following center distances a: Embodiment 1 Embodiment 2 Embodiment 3 Embodiment 4 Center distance a [mm] 127 111 This results in the following main face cut dimensions: Embodiment 1 Embodiment 2 Embodiment 3 Embodiment 4 Dk ₂ [mm] 191 186.1 186 154 Dk ₁ [mm] 153 147.7 144 124.7 rw ₂ [mm] 54.4 56.4 50.5 rw ₁ [mm] 72.6 70.6 60.5 Other main dimensions of the rotors: Embodiment 1 Embodiment 2 Embodiment 3 Embodiment 4 Rotor length L _HR [mm] 307 293 235.5

The following features and characteristics according to the invention, which are summarized in Table 5, result in the exemplary embodiments shown: <u> Table 5 </u> Compilation of further characteristics and parameters: characteristic Embodiment 1 Embodiment 2 Embodiment 3 Embodiment 4 Tooth thickness ratio ε ₁ [-] 0.85 0.82 0.80 0.79 Tooth thickness ratio ε ₂ [-] 0.74 0.64 0.69 0.65 Area ratio A2 / A1 [-] 15.7 37.8 10.0 6.2 Area ratio A1 / A0 [%] 2.3 1.1 2.2 2.3 Area ratio A3 / A1 [-] 9.9 19.6 12.6 11.6 Tooth curvature ratio δ [%] 18.5 21.1 15.7% 15.2 Convex length fraction [%] 66.9% 71.2% 62.7% - Radial tooth thickness curve The tooth thickness of the secondary rotor teeth decreases monotonically from the root radius rf ₁ to the tip radius rk ₁ . Radial beam R ₁₀ Radial beam R ₁₀ has 2 intersections with the leading tooth flank F _V - Area ratio A4 / A5 [-] 7.5 10.1 5.5 - Wrap angle Φ _HR 334.7 ° 330.3 330.3 µBl [%] 0,159 0.086 0.106 0.18 µBl ^∗ µl [%] 0.94 0.53 0.631 1,058 Profile face section design with regard to chamber extension The working chamber can essentially be pushed out completely into the printing window. Profile face section design with regard to secondary rotor torque The direction of action of the NR torque resulting from the gas forces is directed against the direction of rotation of the secondary rotor. Shape of the line of engagement r ₁ / r ₂ 1,037 1,044 0.984 1.0 Diameter ratio D _v 1,248 1.26 1,292 1,235 Rotor length ratio L _HR / a 2.42 2.42 2.31 2.12

The isentropic block efficiency in comparison to the prior art is for the second embodiment to the 3/4 teeth ratio in Figure 5 illustrated. Two curves of the same pressure ratio are shown there.

The specific pressure ratio shown is 2.0 (ratio of outlet pressure to inlet pressure). The isentropic block efficiency could be significantly improved compared to the values achievable with the prior art.

In Figure 6 the isentropic block efficiency is illustrated in comparison with the prior art in the fourth exemplary embodiment (5/6 tooth number ratio). Here too, two curves with the same pressure ratio are shown. The pressure ratio shown here is 9.0 (ratio of outlet pressure to inlet pressure). Here too, the isentropic block efficiency could be significantly improved compared to the values achievable with the prior art.

The in the Figures 5 and 6 The specified delivery quantity corresponds to the delivery volume flow of the compressor block in relation to the suction condition.

• Kopfkreis KK₁ des Nebenrotors mit zugehörigem Kopfkreisradius rk₁ bzw. Kopfkreisdurchmesser Dk₁
• Kopfkreis KK₂ des Hauptrotors mit zugehörigem Kopfkreisradius rk₂ bzw. Kopfkreisdurchmesser Dk₂
• Fußkreis FK₁ des Nebenrotors mit zugehörigem Fußkreisradius rf₁ bzw. Fußkreisdurchmesser Df₁
• Fußkreis FK₂ des Hauptrotors mit zugehörigem Fußkreisradius rf₂ bzw. Fußkreisdurchmesser Df₂
• Achsabstand a zwischen der ersten Achse C1 und der zweiten Achse C2
• Wälzkreis WK₁ des Nebenrotors mit zugehörigem Wälzkreisradius rw₁ bzw. Wälzkreisdurchmesser Dw₁
• Wälzkreis WK₂ des Hauptrotors mit zugehörigem Wälzkreisradius rw₂ bzw. Wälzkreisdurchmesser Dw₂

Figure 7a shows in an end sectional view an embodiment for secondary rotor NR and main rotor HR with the center points given by the corresponding axes C1 and C2. The main geometrical dimensions and main parameters of the forehead section examination are also shown:

• Tip circle KK _{1 of} the secondary rotor with associated tip circle radius rk ₁ or tip circle diameter Dk ₁
• Tip circle KK _{2 of} the main rotor with associated tip circle radius rk ₂ or tip circle diameter Dk ₂
• Foot circle FK _{1 of} the secondary rotor with associated foot circle radius rf ₁ or foot circle diameter Df ₁
• Foot circle FK _{2 of} the main rotor with associated foot circle radius rf ₂ or foot circle diameter Df ₂
• Center distance a between the first axis C1 and the second axis C2
• Rolling circle WK _{1 of} the secondary rotor with the associated rolling circle radius rw ₁ or rolling circle diameter Dw ₁
• Rolling circle WK _{2 of} the main rotor with the associated rolling circle radius rw ₂ or rolling circle diameter Dw ₂

Also shown are the direction of rotation 24 of the secondary rotor and the direction of rotation of the main rotor that necessarily results when operating as a compressor.

Representing all teeth of the secondary rotor, the leading tooth flank F _V and the trailing tooth flank F _{N are} marked on a secondary rotor tooth. A tooth gap 23 is identified as representative of all tooth gaps of the secondary rotor. The based on Figure 7a shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to that based on the Figure 4 for a tooth number ratio of 5/6 exemplary embodiment explained.

Figure 7b shows the tooth gap surfaces A6 and A7 as well as a side view of a blow hole in an end sectional view. In the Figure 7b to explain the tooth space areas A6 and A7 shown profile profiles correspond to that for a number of teeth ratio of 3/4 using Figure 1 illustrated embodiment.

Furthermore shows Fig. 7b the location of the coordinate system of in Fig. 7k shown blow hole area A _Bl in relation to the rotor pair.

The coordinate system is spanned by the u-axis parallel to the rotor end faces along the intersection edge 11 on the pressure side.

The pressure-side blow hole lies in the coordinate system described and very specifically in a plane perpendicular to the rotor end faces between the pressure-side intersection edge 11 and an engagement line point K2 of the pressure-side part of the engagement line.

In an end sectional view, the line of engagement 10 is divided into two sections by the connecting line between the two center points C1 and C2: the suction-side part of the engagement line is shown below, the pressure-side part above the connecting line.

K2 denotes the point of the pressure-side part of the engagement line 10 which is the most distant from the straight line through C1 and C2. The intersection of the tip circles of the two rotors creates an intersection edge 11 on the pressure side and an intersection edge 12 on the suction side. In Fig. 7b is the cutting edge 11 on the pressure side in one Forehead section examination shown as a point. The same applies to the representation of the intersection edge 12 on the suction side.

The u-axis is a parallel to the rotor end faces and corresponds to the vector from the line of engagement point K2 to the intersection edge 11 on the pressure side in an end sectional view.
Further details on the blow hole area A _Bl on the pressure side result from Figure 7k ,

Figure 7c shows a front sectional view of a tooth of the secondary rotor with the concentric circular arcs B ₂₅ , B ₅₀ , B ₇₅ running within the rotor tooth around the center C1 with the associated radii r ₂₅ , r ₅₀ , r ₇₅ and the associated arc lengths b ₂₅ , b ₅₀ , b ₇₅ .

The circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each limited by the leading tooth flank F _V and the trailing tooth flank F _N. The based on Figure 7c shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to that based on the Figure 4 for a tooth number ratio of 5/6 exemplary embodiment explained.

Figure 7d shows in a frontal section view between the tooth of the secondary rotor under consideration and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 at the base circle and at the radially outermost point of the tooth, a vertex F5. The triangle D _Z defined by the points F1, F2 and F5 is also shown.

Figure 7d shows the following (tooth part) surfaces:
Tooth partial area A1 corresponds to the area with which the tooth under consideration, with its leading tooth flank F _V formed between F5 and F2, projects beyond the triangle D _Z in a radially outer region.

Tooth partial area A2 corresponds to the area with which the tooth under consideration, with its trailing tooth flank F _N formed between F5 and F1, projects beyond the triangle D _Z in a radially outer region.

Surface A3 corresponds to the surface with which the tooth under consideration with its leading tooth flank formed between F5 and F2 withdraws from the triangle D _Z.

The tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor is also shown. The based on Figure 7d shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to that based on the Figure 4 for a tooth number ratio of 5/6 exemplary embodiment explained.

Figure 7e shows a cross-sectional view of the cross-sectional area A0 of a tooth of the secondary rotor, which is delimited by the circular arc B running between F1 and F2 around the center C1. The based on Figure 7e shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to that based on the Figure 4 for a tooth number ratio of 5/6 exemplary embodiment explained.

Figure 7f shows the offset angle β in a frontal section view. This is defined by the offset from point F11 to point F12 viewed in the direction of rotation of the secondary rotor. F11 is a point on the half arc B between F1 and F2 around the center C1 and therefore corresponds to the intersection of the bisector of the tooth pitch angle γ with the arc B.
F12 results from the point of intersection of the radial beam R drawn from the center C1 to the vertex F5 with the circular arc B. The on the basis of Figure 7f shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to that based on the Figure 4 for a tooth number ratio of 5/6 exemplary embodiment explained.

Figure 7g shows, in an end sectional view, the turning point F8 on the trailing tooth flank F _{N of} the secondary rotor, in which the curvature of the course of the tooth profile changes between the tip and root circles.

The trailing tooth flank F _{N of} the secondary rotor is divided by the point F8 into an essentially convexly curved portion between F8 and the apex F5 and an essentially concavely curved portion between F8 and the base point F1.

Figure 7h shows in an end sectional view two intersection points of the radial beam R ₁₀ from C1 to F10 with the leading tooth flank F _{V of} the secondary rotor, the point F10 designating that point of the leading tooth flank F _V which lies on the tip circle KK ₁ with rk ₁ and furthest from F5 is spaced. The tooth flank follows a circular arc ARC ₁ with radius rk ₁ around the center point of the secondary rotor defined by axis C1. The based on Figure 7h explained profile profiles of the leading tooth flank F _V and the trailing tooth flank F _N correspond to the exemplary embodiment described for a tooth number ratio of 3/4 Figure 1 ,

Figure 7i shows the tooth profile divided by the radial beam R drawn from C1 to F5 in an end section view.

Specifically, in the illustrated embodiment, the tooth profile is divided into an area A4 assigned to the trailing tooth flank F _N and an area A5 assigned to the leading tooth flank F _V. The based on Figure 7i explained profile profiles of the leading tooth flank F _V and the trailing tooth flank F _N correspond to the embodiment described for a tooth number ratio of 5/6 Figure 4 ,

Figure 7j shows in an end sectional view the line of engagement 10 between the main and secondary rotors and the two concentric circles around the point C with the radii r ₁ and r ₂ to describe the characteristic features of the course of the suction-side part of the line of engagement.

The line of engagement 10 is divided into two sections by the connecting line between the first axis C1 and the second axis C2: the suction-side part of the line of engagement is below, the pressure-side part above the connecting line C 1 C 2 shown.

Point C is the point of contact of the pitch circle WK _{1 of} the secondary rotor with the pitch circle WK _{2 of} the main rotor.

K4 denotes the point of the suction-side part of the line of engagement which is the most distant from the connecting path between C1 and C2.

Radius r ₁ is the distance between K5 and C, radius r ₂ denotes the distance between K4 and C.

Figure 7k:

Figure 7k shows a pressure-side blow hole area A _{Bl of} a working chamber in a sectional view perpendicular to the rotor end faces. The limitation of the blow hole area A _Bl arises from the intersection line 27 of the imaginary flat surface described above with the leading secondary rotor flank F _v , the intersection line 26 of the plane with the trailing HR flank and a straight line section [K1 K3] of the intersection edge 11 on the pressure side.

• die zu den Rotorstirnflächen parallele u-Achse (Vektor vom Eingriffslinienpunkt K2 zu der druckseitigen Verschneidungskante 11 )
  und
• die druckseitige Verschneidungskante 11.

The coordinate system of the blow hole on the pressure side lies in the Fig. 7b described flat surface and is spanned by

• the u-axis parallel to the rotor end faces (vector from the line of engagement point K2 to the intersection edge 11 on the pressure side)
  and
• the intersection edge 11 on the pressure side.

In Figure 8 the wrap angle Φ, which has already been mentioned several times, is illustrated once again. Specifically, it is the angle Φ by which the face cut is rotated from the suction-side to the pressure-side rotor face. This is illustrated here by the rotation of the profile between a pressure-side end face 13 and a suction-side end face 14 by the angle Φ _HR in the main rotor HR.

Figure 9 shows a schematic sectional view of a compressor block 19 comprising a housing 15 and mounted therein two rotors toothed together in pairs, namely a main rotor HR and a secondary rotor NR. Main rotor HR and secondary rotor NR are each rotatably supported in the housing 15 via suitable bearings 16. Drive power can be applied to a shaft 17 of the main rotor HR, for example with a motor (not shown) via a clutch 18.

The compressor block shown is an oil-injected screw compressor, in which the torque transmission between the main rotor HR and the secondary rotor NR takes place directly via the rotor flanks. In contrast to In the case of a dry screw compressor, touching the rotor flanks by means of a synchronization gear (not shown) can be avoided.

Also not shown are a suction nozzle for sucking in the medium to be compressed and an outlet for the compressed medium.

In Figure 10 A toothed main rotor HR and secondary rotor NR are also shown in a perspective view.

Figure 11 shows the spatial line of engagement 10 of exactly one tooth gap 23. The profile gap length I _sp is the length of the spatial line of engagement of exactly one tooth gap 23. This consequently corresponds to the profile gap length of exactly one tooth pitch.

The total torque from the gas forces on the secondary rotor is made up of the sum of the torque effects of the gas pressures in all working chambers on the partial surfaces of the secondary rotor delimiting the respective working chambers. In Fig. 12a Such a partial surface (22) of the secondary rotor that delimits a working chamber is shown by hatching as an example.

Figure 12b shows the distribution of the in Figure 12a shown part surface (22) delimiting a working chamber into a dotted area (28) and a cross-hatched area (29). Only the cross-hatched area (29) contributes to the torque.

The partial surface (22) results from the specific face cut design and the pitch of the secondary rotor. The pitch of the secondary rotor refers to the pitch of the helical toothing of the secondary rotor. In the Fig. 12a Also shown, the three-dimensional line of engagement (10) delimiting the partial surface is also determined by the end cut design of the secondary rotor and the slope.

Partial surface (22) is also limited by cutting line (27). Details of section line (27) have already been given in the context of the Figures 7b and 7k shown and described. The same applies to the line of engagement point K2.

The specific length of a working chamber in the direction of the rotor axis between the secondary rotor end face (20) on the one hand and the limitation by the three-dimensional line of engagement (10) and cutting line (27) on the other hand, which is dependent on the angular position of the secondary rotor relative to the main rotor, does not play an important role here, because - as in the relevant literature is described - the gas pressures on areas of the rotor surface which correspond to complete tooth gaps in a sectional plane perpendicular to the axis of the rotor (in Fig. 12b dotted), make no contribution to the torque. The slope of the secondary rotor affects only the amount, but not the direction of the torque.

In the Fig. 12b dotted area (28) and the in Fig. 12b Cross-hatched area (29) together form the partial surface (22).

Only the in Fig. 12b cross-hatched area (29) contributes to the torque.

Thus, in each working chamber, the direction of action of the torque which the gas pressure in the working chamber (or any reference pressure) brings about on the partial surface of the secondary rotor delimiting the working chamber is determined by the face cut design of the secondary rotor.

The above-described advantageous end section design of the secondary rotor (NR) therefore leads to a direction of action (25) of the torque from the gas forces for each partial surface (22) of the secondary rotor delimiting a working chamber, and thus against the direction of rotation (24) of the secondary rotor is directed, whereby the rotor rattling is effectively avoided.

The exemplary embodiments shown prove that the present invention was able to achieve a considerable increase in efficiency for a pair of rotors used in screw machines consisting of a main rotor and a secondary rotor with the corresponding profile geometry.

With the present invention, it has been possible to further improve the efficiency and smoothness of rotor profiles compared to the prior art, regardless of a specifically claimed profile definition.

Although it will be readily possible for the person skilled in the art on the basis of the specified parameter values to generate suitable profile profiles using the methods customary in the prior art, the profile profiles in the above-discussed exemplary embodiments according to FIGS Figures 1 to 4 explained in more detail. To generate profile profiles - as is well known to those skilled in the art - profile profiles can also be generated by means of publicly accessible computer programs.

In this context, purely by way of example, SV_Win, a project of the Vienna University of Technology, is mentioned, whereby this software is described in great detail in the aforementioned habilitation thesis by Grafinger. An alternative, publicly accessible computer program is also the DISCO software and in particular the module SCORPATH of the City University London (Center for Positive Displacement Compressor Technology). General information can be found at http://www.city-compressors.co. uk /. Information on installing the software can be found at http://www.staff.city.ac.uk/∼ra600/DISCO/DISCO/Instalation%20instructions.pdf. A preview of the DISCO software can be found at http://www.staff.city.ac.uk/∼ra600/DISCO/DISCO%20Preview.htm.

Another alternative software is the ScrewView software, which is also available in the Dissertation "Directed Evolutionary Algorithms" by Stefan Berlik, Dortmund 2006 (p. 173 f .) mentioned. On the website http://pi.informatik.unisiegen.de/Mitarbeiter/berlik/projekte/ the ScrewView software is described in connection with the project "Method for the design of dry-running rotary displacement machines".

In the Figures 13 to 16 a tooth with a trailing rotor flank F _N and a leading rotor flank F _V is generated as follows: Section S1 to S2 results from an arc on the secondary rotor NR around the center C1, generated by the arc section T1 to T2 around the center C2 on the Main rotor HR. The section S2 to S3 results from an envelope to a trochoid, generated from the arc section T2 to T3 around the center M4 on the main rotor HR. The section S3 to S4 is surrounded by an arc defines the center point M1. The section S4 to S5 is predetermined by an arc around the center M2.

The section S5 to S6 is defined by an arc around the center C1. The subsequent section S6 to S7 is specified by an arc around the center M3. The section S7 to S1 is finally predetermined by an envelope to form a trochoid, generated by the arc section T7 to T1 around the center M5 on the main rotor HR. The above-mentioned sections are seamlessly connected in the order given. The tangents at the end of a section and at the beginning of the adjacent section are the same. In this respect, the sections merge directly, continuously and without kinks.

The profile profile of the teeth of the main rotor HR is for the embodiment according to the Figures 1 to 4 also based on the Figures 13 to 16 explained briefly below. The section T1-T2 results from an arc on the main rotor HR around the center C2 on the main rotor HR. The section T2-T3 is defined by the circular arc on the main rotor HR around the center M4. The section T3-T4 results from an envelope to a trochoid, generated by the section S3-S4 on the secondary rotor NR. The section T4-T5 is defined by an envelope to a trochoid, generated by the section S4-S5 on the secondary rotor. The section T5-T6 is defined by an arc around the center C2, generated by the arc section S5-S6 around the center C1 on the secondary rotor NR. The section T6-T7 results from an envelope to a trochoid, generated by the section S6-S7 on the secondary rotor NR. The section T7-T1 is finally defined by an arc around the center M5. The following also applies here: The sections described above are each seamlessly connected in the order given. The tangents at the end of a section and at the beginning of the adjacent section are the same. In this respect, the sections merge directly, continuously and without kinks.

In general, it should be noted that the profile profiles of the secondary rotor NR and main rotor HR are of course coordinated with one another and, in this respect, the envelopes for a trochoid each correspond to circular arc sections on the counter rotor. In addition, as already mentioned, a tangential transition from one section to the next is guaranteed. A general The procedure for calculating the profile profile of the counter rotor is, for example, in the Dissertation by Helpertz, "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003, p. 60 ff , described.

1. 1. Rotorpaar für einen Verdichterblock einer Schraubenmaschine, wobei das Rotorpaar aus einem um eine erste Achse (C1) rotierenden Nebenrotor (NR) und einen um eine zweite Achse (C2) rotierenden Hauptrotor (HR) besteht,
   wobei die Anzahl der Zähne (z₂) beim Hauptrotor (HR) 3 und die Anzahl der Zähne (z₁) beim Nebenrotor (NR) 4 beträgt,
   wobei die relative Profiltiefe des Nebenrotors $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_{\mathrm{1}}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}}$$
   
   mindestens 0,5, bevorzugt mindestens 0,515, und höchstens 0,65, bevorzugt höchstens 0,595, beträgt, wobei es sich bei rk₁ um einen um den Außenumfang des Nebenrotors (NR) gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund des Nebenrotors ansetzenden Fußkreisradius handelt,
   wobei das Verhältnis vom Achsabstand α der ersten Achse (C1) zur zweiten Achse (C2) und dem Kopfkreisradius rk₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}}$$
   
   mindestens 1,636, und höchstens 1,8, bevorzugt höchstens 1,733, beträgt, wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$1,4\le L_{\mathit{HR}}/a\le 3,4,$$
   
   wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.
2. 2. Rotorpaar nach Aspekt 1, dadurch gekennzeichnet,
   dass in einer Stirnschnittbetrachtung innerhalb eines Nebenrotorzahns verlaufende Kreisbögen B₂₅, B₅₀, B₇₅, deren gemeinsamer Mittelpunkt durch die Achse C1 gegeben ist, definiert sind, wobei der Radius r₂₅ von B₂₅ den Wert r₂₅ = rf₁+0.25*(rk₁-rf₁) hat, der Radius r₅₀ von B₅₀ den Wert r₅₀ = rf₁+0.5*(rk₁-rf₁) hat und der Radius r₇₅ von B₇₅ den Wert rf₁+0.75*(rk₁-rf₁) hat, und wobei die Kreisbögen B₂₅, B₅₀, B₇₅ jeweils durch die vorlaufende Zahnflanke F_V und nachlaufenden Zahnflanke F_N begrenzt werden,
   wobei Zahndickenverhältnisse als Verhältnisse der Bogenlängen b₂₅, b₅₀, b75 der Kreisbögen B₂₅, B₅₀, B₇₅ mit ε₁ = b₅₀/b₂₅ und ε₂ = b₇₅/b₂₅ definiert sind und folgende Bemessung eingehalten ist:
   0,65 ≤ ε₁ < 1,0 und/oder 0,50 ≤ ε₂ ≤ 0,85, bevorzugt 0,80 ≤ ε₁ < 1,0 und/oder 0,50 ≤ ε₂ ≤ 0,79.
3. 3. Rotorpaar nach Aspekt 1 oder 2, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
   wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
   wobei in einem radial äußeren Bereich der Zahn mit seiner zwischen F5 und F2 ausgebildeten vorlaufenden Zahnflanke F_V mit einer Fläche A1 und mit seiner nachlaufenden zwischen F1 und F5 ausgebildeten Zahnflanke F_N mit einer Fläche A2 über das Dreieck D_Z übersteht und
   wobei 8 ≤ A2/A1 ≤ 60 eingehalten ist.
4. 4. Rotorpaar nach einem der Aspekte 1 bis 3, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors Fußpunkte F1und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
   wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
   wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht und in einem radial inneren Bereich gegenüber dem Dreieck D_Z mit einer Fläche A3 zurücktritt und wobei 7,0 ≤ A3/A1 ≤ 35 eingehalten sind.
5. 5. Rotorpaar nach einem der Aspekte 1 bis 4, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
   wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
   wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht,
   wobei der Zahn selbst eine durch den zwischen F1 und F2 verlaufenden Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt begrenzte Querschnittsfläche A0 aufweist und
   wobei 0,5 % ≤ A1/A0 ≤ 4,5 % eingehalten ist.
6. 6. Rotorpaar nach einem der Aspekte 1 bis 5, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
   wobei der zwischen F1 und F2 verlaufende Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt einen Zahnteilungswinkel γ entsprechend 360°/Zahl der Zähne des Nebenrotors (NR) definiert,
   wobei auf dem halben Kreisbogen B zwischen F1 und F2 ein Punkt F11 definiert ist,
   wobei ein vom durch die Achse C1 definierten Mittelpunkt des Nebenrotors (NR) durch den Scheitelpunkt F5 gezogener Radialstrahl R den Kreisbogen B in einem Punkt F12 schneidet,
   wobei ein Versatzwinkel β durch den in Rotationsrichtung des Nebenrotors (NR) betrachteten Versatz von F11 zu F12 definiert wird und
   wobei $$14\%\le \mathrm{\delta }\le 25\%$$
   
   eingehalten ist, mit $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{.}$
   
7. 7. Rotorpaar nach einem der Aspekte 1 bis 6, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung die zwischen F1 und F5 ausgebildete nachlaufende Zahnflanke F_N eines Zahns des Nebenrotors (NR) einen konvexen Längenanteil von mindestens 45 % bis höchstens 95 % aufweist.
8. 8. Rotorpaar nach einem der Aspekte 1 bis 7, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung der von der Achse C1 des Nebenrotors (NR) durch F5 gezogene Radialstrahl das Zahnprofil in einen der vorlaufenden Zahnflanke F_V zugeordneten Flächenanteil A5 und einen der nachlaufenden Zahnflanke F_N zugeordneten Flächenanteil A4 teilt und
   wobei $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{4}$$
   
   eingehalten ist.
9. 9. Rotorpaar nach einem der Aspekte 1 bis 8, dadurch gekennzeichnet, dass der Hauptrotor HR mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt: 290° ≤ Φ_HR ≤ 360°, vorzugsweise 320° ≤ Φ_HR ≤ 360°.
10. 10. Rotorpaar nach einem der Aspekte 1 bis 9, dadurch gekennzeichnet, dass ein Blaslochfaktor µ_Bl mindestens 0,02 % und höchstens 0,4 %, bevorzugtermaßen höchstens 0,25 % beträgt,
    wobei ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    und
    wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
11. 11. Rotorpaar nach einem der Aspekte 1 bis 10, dadurch gekennzeichnet, dass für einen Blasloch-/Profilspaltlängenfaktor µ_l * µ_Bl $$\mathrm{0},\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1},\mathrm{72}\%$$
    
    eingehalten ist mit $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
    
    wobei I_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    wobei A_Bl eine absolute Blaslochfläche und A6 und A7 Profilflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
12. 12. Rotorpaar nach einem der Aspekte 1 bis 11, dadurch gekennzeichnet, dass Hauptrotor (HR) und Nebenrotor (NR) derart ausgebildet und aufeinander abgestimmt sind, dass eine trockene Verdichtung mit einem Druckverhältnis Π von bis zu 3, insbesondere mit einem Druckverhältnis Π größer als 1 und bis zu 3, erzielbar ist, wobei das Druckverhältnis das Verhältnis von Verdichtungsenddruck zu Ansaugdruck ist, erzielbar ist.
13. 13. Rotorpaar nach einem der Aspekte 1 bis 12, dadurch gekennzeichnet, dass der Hauptrotor (HR) bezogen auf einen Kopfkreis KK₂ mit einer Umfangsgeschwindigkeit in einem Bereich von 20 bis 100 m/s betreibbar ausgebildet ist.
14. 14. Rotorpaar nach einem der Aspekte 1 bis 13, dadurch gekennzeichnet, dass für ein durch das Verhältnis der Kopfkreisradien von Hauptrotor (HR) und Nebenrotor (NR) definierte Durchmesserverhältnis $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="Dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="Dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1,145\le D_v\le 1,30$$
    
    eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und Dk₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnen.
15. 15. Rotorpaar für einen Verdichterblock einer Schraubenmaschine, wobei das Rotorpaar aus einem um eine erste Achse (C1) rotierenden Nebenrotor (NR) und einen um eine zweite Achse (C2) rotierenden Hauptrotor (HR) besteht,
    wobei die Anzahl der Zähne (z₂) beim Hauptrotor (HR) 4 und die Anzahl der Zähne (z₁) beim Nebenrotor (NR) 5 beträgt,
    wobei die relative Profiltiefe des Nebenrotors $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    mindestens 0,5, bevorzugt mindestens 0,515, und höchstens 0,58, beträgt, wobei es sich bei rk₁ um einen um den Außenumfang des Nebenrotors (NR) gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund des Nebenrotors ansetzenden Fußkreisradius handelt,
    wobei das Verhältnis vom Achsabstand α der ersten Achse (C1) zur zweiten Achse (C2) und dem Kopfradius rk₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    mindestens 1,683, und höchstens 1,836, bevorzugt höchstens 1,782, beträgt,
    wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$1,4\le L_{\mathit{HR}}/a\le 3,3,$$
    
    wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.
16. 16. Rotorpaar nach Aspekt 15, dadurch gekennzeichnet,
    dass in einer Stirnschnittbetrachtung innerhalb eines Nebenrotorzahns verlaufende Kreisbögen B₂₅, B₅₀, B₇₅, deren gemeinsamer Mittelpunkt C1 ist, definiert sind, wobei der Radius r₂₅ von B₂₅ den Wert rf₁+0.25*(rk₁-rf₁) hat, der Radius r₅₀ von B₅₀ den Wert rf₁+0.5*(rk₁-rf₁) hat und der Radius r₇₅ von B₇₅ den Wert rf₁+0.75*(rk₁-rf₁) hat, und wobei die Kreisbögen B₂₅, B₅₀, B₇₅ jeweils durch die vorlaufende Zahnflanke F_V und nachlaufenden Zahnflanke F_N begrenzt werden,
    wobei Zahndickenverhältnisse als Verhältnisse der Bogenlängen b₂₅, b₅₀, b₇₅ der Kreisbögen B₂₅, B₅₀, B₇₅ mit ε₁ = b₅₀/b₂₅ und ε₂ = b₇₅/b₂₅ definiert sind und folgende Bemessung eingehalten ist:
    0,75 ≤ ε₁ ≤ 0,85 und/oder 0,65 ≤ ε₂ ≤ 0,74.
17. 17. Rotorpaar nach Aspekt 15 oder 16, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei in einem radial äußeren Bereich der Zahn mit seiner zwischen F5 und F2 ausgebildeten vorlaufenden Zahnflanke F_V mit einer Fläche A1 und mit seiner nachlaufenden zwischen F1 und F5 ausgebildeten Zahnflanke F_N mit einer Fläche A2 über das Dreieck D_Z übersteht und
    wobei 6 ≤ A2/A1 ≤ 15 eingehalten ist.
18. 18. Rotorpaar nach einem der Aspekte 15 bis 17, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht und in einem radial inneren Bereich gegenüber dem Dreieck D_Z mit einer Fläche A3 zurücktritt und wobei 9,0 ≤ A3/A1 ≤ 18 eingehalten ist.
19. 19. Rotorpaar nach einem der Aspekte 15 bis 18, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht,
    wobei der Zahn selbst eine durch den zwischen F1 und F2 verlaufenden Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt begrenzte Querschnittsfläche A0 aufweist und
    wobei 1,5 % ≤ A1/A0 ≤ 3,5 % eingehalten ist.
20. 20. Rotorpaar nach einem der Aspekte 15 bis 19, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei der zwischen F1 und F2 verlaufende Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt einen Zahnteilungswinkel γ entsprechend 360°/Zahl der Zähne des Nebenrotors NR definiert,
    wobei auf dem halben Kreisbogen B zwischen F1 und F2 ein Punkt F11 definiert ist,
    wobei ein vom durch die Achse C1 definierten Mittelpunkt des Nebenrotors (NR) durch den Scheitelpunkt F5 gezogener Radialstrahl R den Kreisbogen B in einem Punkt F12 schneidet,
    wobei ein Versatzwinkel β durch den in Rotationsrichtung des Nebenrotors (NR) betrachteten Versatz von F11 zu F12 definiert wird und
    wobei $$14\%\le \mathrm{\delta }\le 18\%$$
    
    eingehalten ist, mit ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
21. 21. Rotorpaar nach einem der Aspekte 15 bis 20, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung die zwischen F1 und F5 ausgebildete nachlaufende Zahnflanke F_N eines Zahns des Nebenrotors (NR) einen konvexen Längenanteil von mindestens 55 % bis höchstens 95 % aufweist.
22. 22. Rotorpaar nach einem der Aspekte 15 bis 21, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung der von der Achse C1 des Nebenrotors (NR) durch F5 gezogene Radialstrahl das Zahnprofil in einen der vorlaufenden Zahnflanke F_V zugeordneten Flächenanteil A5 und einen der nachlaufenden Zahnflanke F_N zugeordneten Flächenanteil A4 teilt und wobei $$\mathrm{4}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{9}$$
    
    eingehalten ist.
23. 23. Rotorpaar nach einem der Aspekte 15 bis 22, dadurch gekennzeichnet, dass der Hauptrotor HR mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt: 320° ≤ Φ_HR ≤ 360°, vorzugsweise 330° ≤ Φ_HR ≤ 360°.
24. 24. Rotorpaar nach einem der Aspekte 15 bis 23, dadurch gekennzeichnet, dass ein Blaslochfaktor µ_Bl mindestens 0,02 % und höchstens 0,4 %, bevorzugtermaßen höchstens 0,25 % beträgt,
    wobei ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    und
    wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
25. 25. Rotorpaar nach einem der Aspekte 15 bis 24, dadurch gekennzeichnet, dass für einen Blasloch-/Profilspaltlängenfaktor µ_l * µ_Bl $$\mathrm{0},\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1},\mathrm{72}\%$$
    
    eingehalten ist mit $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
    
    wobei I_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    wobei A_Bl eine absolute Blaslochfläche und A6 und A7 Profilflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
26. 26. Rotorpaar nach einem der Aspekte 15 bis 25, dadurch gekennzeichnet, dass Hauptrotor (HR) und Nebenrotor (NR) derart ausgebildet und aufeinander abgestimmt sind, dass eine trockene Verdichtung mit einem Druckverhältnis Π von bis zu 5, insbesondere mit einem Druckverhältnis Π von größer als 1 und bis zu 5, oder alternativ eine fluideingespritzte Verdichtung mit einem Druckverhältnis Π von bis zu 16, insbesondere mit einem Druckverhältnis Π von größer als 1 und bis zu 16, erzielbar ist, wobei das Druckverhältnis das Verhältnis von Verdichtungsenddruck zu Ansaugdruck ist.
27. 27. Rotorpaar nach einem der Aspekte 15 bis 26, dadurch gekennzeichnet, dass im Fall einer trockenen Verdichtung der Hauptrotor bezogen auf einen Kopfkreis KK₂ mit einer Umfangsgeschwindigkeit in einem Bereich von 20 bis 100 m/s und im Fall einer fluideingespritzten Verdichtung der Hauptrotor bezogen auf einen Kopfkreis KK₂ mit einer Umfangsgeschwindigkeit in einem Bereich von 5 bis 50 m/s betreibbar ausgebildet ist.
28. 28. Rotorpaar nach einem der Aspekte 15 bis 27, dadurch gekennzeichnet, dass für ein durch das Verhältnis der Kopfkreisradien von Hauptrotor (HR) und Nebenrotor (NR) definierte Durchmesserverhältnis $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="Dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="Dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1,195\le D_v\le 1,33$$
    
    eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und DK₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnen.
29. 29. Rotorpaar für einen Verdichterblock einer Schraubenmaschine, wobei das Rotorpaar aus einem um eine erste Achse (C1) rotierenden Nebenrotor (NR) und einen um eine zweite Achse (C2) rotierenden Hauptrotor (HR) besteht,
    wobei die Anzahl der Zähne (z₂) beim Hauptrotor (HR) 5 und die Anzahl der Zähne (z₁) beim Nebenrotor (NR) 6 beträgt,
    wobei die relative Profiltiefe des Nebenrotors $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    mindestens 0,44 und höchstens 0,495, bevorzugt höchstens 0,48, beträgt, wobei es sich bei rk₁ um einen um den Außenumfang des Nebenrotors (NR) gezogenen Kopfkreisradius und bei rf₁ um einen am Profilgrund des Nebenrotors ansetzenden Fußkreisradius handelt,
    wobei das Verhältnis vom Achsabstand α der ersten Achse (C1) zur zweiten Achse (C2) und dem Kopfradius rk₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    mindestens 1,74, bevorzugt mindestens 1,75, und höchstens 1,8, bevorzugt höchstens 1,79, beträgt,
    wobei vorzugsweise der Hauptrotor mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt 240° ≤ Φ_HR ≤ 360°, und wobei vorzugsweise für ein Rotorlängenverhältnis L_HR/a gilt: $$1,4\le L_{\mathit{HR}}/a\le 3,2,$$
    
    wobei das Rotorlängenverhältnis aus dem Verhältnis der Rotorlänge L_HR des Hauptrotors und dem Achsabstand a gebildet ist und die Rotorlänge L_HR des Hauptrotors durch den Abstand einer saugseitigen Hauptrotor-Rotorstirnfläche zu einer gegenüberliegenden druckseitigen Hauptrotor-Rotorstirnfläche gebildet ist.
30. 30. Rotorpaar nach Aspekt 29, dadurch gekennzeichnet,
    dass in einer Stirnschnittbetrachtung innerhalb eines Nebenrotorzahns verlaufenden Kreisbögen B₂₅, B₅₀, B₇₅, deren gemeinsamer Mittelpunkt C1 ist, definiert sind, wobei der Radius r₂₅ von B₂₅ den Wert rf₁+0.25*(rk₁-rf₁) hat, der Radius r₅₀ von B₅₀ den Wert rf₁+0.5*(rk₁-rf₁) hat und der Radius r₇₅ von B₇₅ den Wert rf₁+0.75*(rk₁-rf₁) hat, und wobei die Kreisbögen B₂₅, B₅₀, B₇₅ jeweils durch die vorlaufende Zahnflanke F_V und nachlaufenden Zahnflanke F_N begrenzt werden,
    wobei Zahndickenverhältnisse als Verhältnisse der Bogenlängen b₂₅, b₅₀, b75 der Kreisbögen B₂₅, B₅₀, B₇₅ mit ε₁ = b₅₀/b₂₅ und ε₂ = b₇₅/b₂₅ definiert sind und folgende Bemessung eingehalten ist:
    0,76 ≤ ε₁ ≤ 0,86 und/oder 0,62 ≤ ε₂ ≤ 0,72.
31. 31. Rotorpaar nach Aspekt 29 oder 30, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei in einem radial äußeren Bereich der Zahn mit seiner zwischen F5 und F2 ausgebildeten vorlaufenden Zahnflanke F_V mit einer Fläche A1 und mit seiner nachlaufenden zwischen F1 und F5 ausgebildeten Zahnflanke F_N mit einer Fläche A2 über das Dreieck D_Z übersteht und
    wobei 4 ≤ A2/A1 ≤ 7 eingehalten ist.
32. 32. Rotorpaar nach einem der Aspekte 29 bis 31, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht und in einem radial inneren Bereich gegenüber dem Dreieck D_Z mit einer Fläche A3 zurücktritt und wobei 8 ≤ A3/A1 ≤ 14 eingehalten ist.
33. 33. Rotorpaar nach einem der Aspekte 29 bis 32, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei durch F1, F2 und F5 ein Dreieck D_Z definiert ist und
    wobei die zwischen F5 und F2 ausgebildete vorlaufende Zahnflanke F_V in einem radial äußeren Bereich des Zahns mit einer Fläche A1 über das Dreieck D_Z übersteht,
    wobei der Zahn selbst eine durch den zwischen F1und F2 verlaufenden Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt begrenzte Querschnittsfläche A0 aufweist und
    wobei 1,9 % ≤ A1/A0 ≤ 3,2 % eingehalten ist.
34. 34. Rotorpaar nach einem der Aspekte 29 bis 33, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung zwischen dem betrachteten Zahn des Nebenrotors (NR) und dem jeweils benachbarten Zahn des Nebenrotors (NR) Fußpunkte F1 und F2 und am radial äußersten Punkt des Zahns ein Scheitelpunkt F5 definiert sind,
    wobei der zwischen F1 und F2 verlaufende Kreisbogen B um den durch die Achse C1 definierten Mittelpunkt einen Zahnteilungswinkel γ entsprechend 360°/Zahl der Zähne des Nebenrotors NR definiert,
    wobei auf dem halben Kreisbogen B zwischen F1 und F2 ein Punkt F11 definiert ist,
    wobei ein vom durch die Achse C1 definierten Mittelpunkt des Nebenrotors (NR) durch den Scheitelpunkt F5 gezogener Radialstrahl R den Kreisbogen B in einem Punkt F12 schneidet,
    wobei ein Versatzwinkel β durch den in Rotationsrichtung des Nebenrotors (NR) betrachteten Versatz von F11 zu F12 definiert wird und
    wobei $$13,5\%\le \mathrm{\delta }\le 18\%$$
    
    eingehalten ist, mit $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{.}$
    
35. 35. Rotorpaar nach einem der Aspekte 29 bis 34, dadurch gekennzeichnet, dass der Hauptrotor HR mit einem Umschlingungswinkel Φ_HR ausgebildet ist, für den gilt: 320° ≤ Φ_HR ≤ 360°, vorzugsweise 330° ≤ Φ_HR ≤ 360°.
36. 36. Rotorpaar nach einem der Aspekte 29 bis 35, dadurch gekennzeichnet, dass ein Blaslochfaktor µ_Bl mindestens 0,03 % und höchstens 0,25 %, bevorzugtermaßen höchstens 0,2 % beträgt,
    wobei ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    und
    wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
37. 37. Rotorpaar nach einem der Aspekte 29 bis 36, dadurch gekennzeichnet, dass für einen Blasloch-/Profilspaltlängenfaktor µ_l * µ_Bl $$\mathrm{0},\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1},\mathrm{26}\%$$
    
    eingehalten ist mit $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
    
    wobei I_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und ${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}*100\left[\%\right]$
    
    wobei A_Bl eine absolute Blaslochfläche und A6 und A7 Profilflächen des Nebenrotors (NR) bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.
38. 38. Rotorpaar nach einem der Aspekte 29 bis 37, dadurch gekennzeichnet, dass Hauptrotor (HR) und Nebenrotor (NR) derart ausgebildet und aufeinander abgestimmt sind, dass eine trockene Verdichtung mit einem Druckverhältnis Π von bis zu 5, insbesondere mit einem Druckverhältnis Π von größer 1 und bis zu 5, erzielbar ist oder alternativ eine fluideingespritzte Verdichtung mit einem Druckverhältnis Π von bis zu 20, insbesondere mit einem Druckverhältnis Π von größer 1 und bis zu 20, erzielbar ist, wobei das Druckverhältnis das Verhältnis von Verdichtungsenddruck zu Ansaugdruck ist.
39. 39. Rotorpaar nach einem der Aspekte 29 bis 38, dadurch gekennzeichnet, dass der Hauptrotor (HR) bezogen auf einen Kopfkreis KK₂ im Falle einer trockenen Verdichtung mit einer Umfangsgeschwindigkeit in einem Bereich von 20 bis 100 m/s und im Falle einer fluideingespritzten Verdichtung mit einer Umfangsgeschwindigkeit in einem Bereich von 5 bis 50 m/s betreibbar ausgebildet ist.
40. 40. Rotorpaar nach einem der Aspekte 29 bis 39, dadurch gekennzeichnet, dass für ein durch das Verhältnis der Kopfkreisradien von Hauptrotor (HR) und Nebenrotor (NR) definierte Durchmesserverhältnis $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="Dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="Dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1,19\le D_v\le 1,26$$
    
    eingehalten ist, wobei Dk₁ den Durchmesser des Kopfkreises KK₁ des Nebenrotors (NR) und Dk₂ den Durchmesser des Kopfkreises KK₂ des Hauptrotors (HR) bezeichnen.
41. 41. Rotorpaar nach einem der Aspekte 1 bis 40, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung die innerhalb eines Zahns des Nebenrotors verlaufenden Bogenlängen b(r) der jeweils zugehörigen konzentrischen Kreisbögen mit dem Radius rf₁ < r < rk₁ und dem gemeinsamen, durch die Achse C1 definierten Mittelpunkt jeweils durch die vorlaufende Zahnflanke F_V und die nachlaufende Zahnflanke F_N begrenzt werden und die Bogenlängen b(r) mit zunehmendem Radius r monoton abnehmen.
42. 42. Rotorpaar nach einem der Aspekte 1 bis 41, dadurch gekennzeichnet, dass die Stirnschnittgestaltung des Nebenrotors (NR) derart vorgenommen ist, dass die Wirkrichtung des Drehmoments, das aus einem Referenzdruck auf die eine Arbeitskammer begrenzende Teiloberfläche des Nebenrotors resultiert, entgegen der Drehrichtung des Nebenrotors gerichtet ist.
43. 43. Rotorpaar nach einem der Aspekte 1 bis 42, dadurch gekennzeichnet, dass Hauptrotor (HR) und Nebenrotor (NR) zum Fördern von Luft oder inerten Gasen, wie Helium oder Stickstoff, ausgebildet und aufeinander abgestimmt sind.
44. 44. Rotorpaar nach einem der Aspekte 1 bis 43, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung das Profil eines Zahns des Nebenrotors bezogen auf den vom Mittelpunkt, der durch die Achse C1 definiert ist, durch den Scheitelpunkt F5 gezogenen Radialstrahl R asymmetrisch ausgebildet ist.
45. 45. Rotorpaar nach einem der Aspekte 1 bis 44, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung ein Punkt C auf der Verbindungsstrecke ( C1C2) zwischen der ersten Achse (C1) und der zweiten Achse (C2) definiert ist, wo sich die Wälzkreise WK₁ des Nebenrotors (NR) und WK₂ des Hauptrotors (HR) berühren, dass K5 den Schnittpunkt des Fußkreises FK₁ des Nebenrotors (NR) mit der Verbindungsstrecke ( C1C2) definiert, wobei r₁ den Abstand zwischen K5 und C bemisst,
    und dass K4 den Punkt des saugseitigen Teils der Eingriffslinie bezeichnet, der am weitesten von der Verbindungsstrecke C1C2 zwischen C1 und C2 beabstandet liegt, wobei r₂ den Abstand zwischen K4 und C bemisst und wobei gilt: $$0,9\le \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\le 0,875-\frac{z_1}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2}+0,22$$
    
    mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR).
46. 46. Rotorpaar nach einem der Aspekte 1 bis 45, dadurch gekennzeichnet, dass für ein Rotorlängenverhältnis L_HR/a gilt: $$\mathrm{0},\mathrm{85}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0},\mathrm{67}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{1},\mathrm{26}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1},\mathrm{18},$$
    
    bevorzugt $$\mathrm{0},\mathrm{89}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0},\mathrm{94}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{1},\mathrm{05}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1},\mathrm{22},$$
    
    mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR), wobei das Rotorlängenverhältnis L_HR/a das Verhältnis der Rotorlänge L_HR zum Achsabstand a angibt und Rotorlänge L_HR der Abstand der saugseitigen Hauptrotor-Rotorstirnfläche zur druckseitigen Hauptrotor-Rotorstirnfläche ist.
47. 47. Rotorpaar nach einem der Aspekte 1 bis 28, dadurch gekennzeichnet, dass in einer Stirnschnittbetrachtung das Zahnprofil des Nebenrotors (NR) an seinem radial äußeren Abschnitt abschnittsweise einem Kreisbogen ARC₁ mit Radius rk₁ folgt, also mehrere Punkte der vorlaufenden Zahnflanke F_V und der nachlaufenden Zahnflanke F_N auf dem Kreisbogen mit Radius rk₁ um den durch die Achse C1 definierten Mittelpunkt liegen, wobei bevorzugtermaßen der Kreisbogen ARC₁ ein Winkel bezogen auf die Achse C1 zwischen 0,5° und 5°, weiter vorzugsweise zwischen 0,5° und 2,5° einschließt,
    wobei F10 der von F5 am weitest beabstandete Punkt auf der vorlaufenden Zahnflanke auf diesem Kreisbogen ist und
    wobei der zwischen F10 und den durch die Achse C1 definierten Mittelpunkt des Nebenrotors (NR) gezogene Radialstrahl R₁₀ die vorlaufende Zahnflanke F_V in mindestens einem Punkt berührt oder in zwei Punkten schneidet.
48. 48. Verdichterblock umfassend ein Verdichtergehäuse (15) sowie ein Rotorpaar nach einem der Aspekte 1 bis 47, wobei das Rotorpaar einen Hauptrotor (HR) und einen Nebenrotor (NR) umfasst, die jeweils rotierbar im Verdichtergehäuse (15) gelagert sind.
49. 49. Verdichterblock nach Aspekt 48, dadurch gekennzeichnet, dass die Stirnschnittgestaltung derart vorgenommen ist, dass die zwischen den Zahnprofilen von Hauptrotor (HR) und Nebenrotor (NR) gebildete Arbeitskammer im Wesentlichen komplett ins Druckfenster ausgeschoben werden kann.
50. 50. Verdichterblock nach Aspekt 48 oder 49,
    dadurch gekennzeichnet, dass
    ein Wellenende des Hauptrotors aus dem Verdichtergehäuse herausgeführt ist und zur Anbindung an einen Antrieb ausgebildet ist, wobei
    vorzugsweise beide Wellenenden des Nebenrotors vollständig innerhalb des Verdichtergehäuses aufgenommen sind.

The invention is further characterized by the following preferred aspects:

1. 1. pair of rotors for a compressor block of a screw machine, the pair of rotors consisting of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
   the number of teeth (z ₂ ) for the main rotor (HR) is 3 and the number of teeth (z ₁ ) for the secondary rotor (NR) is 4,
   where the relative profile depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_{\mathrm{1}}-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_{\mathrm{1}}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}}$$
   
   is at least 0.5, preferably at least 0.515, and at most 0.65, preferably at most 0.595, where rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is one that starts at the profile base of the secondary rotor Root circle radius
   the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_{\mathrm{1}}}$$
   
   is at least 1.636, and at most 1.8, preferably at most 1.733, the main rotor preferably being designed with a wrap angle Φ _HR , for which 240 ° Φ Φ _HR 360 360 °, and preferably for a rotor length ratio L _HR / a : $$1.4\le L_{\mathit{MR}}/a\le 3.4.$$
   
   wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.
2. 2. pair of rotors according to aspect 1, characterized in
   that circular arcs B ₂₅ , B ₅₀ , B ₇₅ , whose common center point is given by the axis C1, are defined in a frontal section view, the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 * ( rk ₁ -rf ₁ ), the radius r ₅₀ of B _{50 has} the value r ₅₀ = rf ₁ + 0.5 * (rk ₁ -rf ₁ ) and the radius r ₇₅ of B _{75 has} the value rf ₁ + 0.75 * (rk ₁ -rf ₁ ), and the circular arcs B ₂₅ , B ₅₀ , B _{75 are} each delimited by the leading tooth flank F _V and trailing tooth flank F _N ,
   where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b75 of the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed:
   0.65 ≤ ε ₁ <1.0 and / or 0.50 ≤ ε ₂ ≤ 0.85, preferably 0.80 ≤ ε ₁ <1.0 and / or 0.50 ≤ ε ₂ ≤ 0.79.
3. 3. A pair of rotors according to aspect 1 or 2, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 and an apex F5 are defined at the radially outermost point of the tooth,
   where a triangle D _{Z is} defined by F1, F2 and F5 and
   in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 protrudes beyond the triangle D _Z and
   where 8 ≤ A2 / A1 ≤ 60 is observed.
4. 4. A pair of rotors according to one of the aspects 1 to 3, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 and an apex F5 are defined at the radially outermost point of the tooth,
   where a triangle D _{Z is} defined by F1, F2 and F5 and
   wherein the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and withdraws with a surface A3 in a radially inner region opposite the triangle D _Z and wherein 7.0 ≤ A3 / A1 ≤ 35 are complied with.
5. 5. rotor pair according to one of the aspects 1 to 4, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
   where a triangle D _{Z is} defined by F1, F2 and F5 and
   the leading tooth flank F _V formed between F5 and F2 protruding in a radially outer region of the tooth with a surface A1 over the triangle D _Z ,
   wherein the tooth itself has a cross-sectional area A0 delimited by the circular arc B running between F1 and F2 around the center point defined by the axis C1 and
   where 0.5% ≤ A1 / A0 ≤ 4.5% is observed.
6. 6. Pair of rotors according to one of the aspects 1 to 5, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
   the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor (NR) around the center point defined by the axis C1,
   where a point F11 is defined on the half arc B between F1 and F2,
   a radial beam R drawn through the apex F5 from the center point of the secondary rotor (NR) defined by the axis C1 intersects the circular arc B at a point F12,
   wherein an offset angle β is defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and
   in which $$14\%\le \mathrm{\delta }\le 25\%$$
   
   is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$
   
7. 7. A rotor pair according to one of the aspects 1 to 6, characterized in that the trailing tooth flank F _{N of} a tooth of the secondary rotor (NR), formed between F1 and F5, has a convex length fraction of at least 45% to at most 95% in an end sectional view.
8. 8. A pair of rotors according to one of the aspects 1 to 7, characterized in that in a front sectional view of the radial jet drawn by the axis C1 of the secondary rotor (NR) through F5, the tooth profile into a surface portion A5 assigned to the leading tooth flank F _V and one of the trailing tooth flank F _N assigned area share A4 divides and
   in which $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{4}$$
   
   is adhered to.
9. 9. A pair of rotors according to one of the aspects 1 to 8, characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 290 ° ≤ Φ _HR ≤ 360 °, preferably 320 ° ≤ Φ _HR ≤ 360 °.
10. 10. pair of rotors according to one of the aspects 1 to 9, characterized in that a blow hole factor µ _{Bl is} at least 0.02% and at most 0.4%, preferably at most 0.25%,
    in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    where A _{Bl is} an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .
11. 11. rotor pair according to one of the aspects 1 to 10, characterized in that for a blow hole / profile gap length factor µ _l * µ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{72}\%$$
    
    is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$
    
    where I _sp the length of the profile engagement gap of a tooth gap of the secondary rotor and PT ₁ the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
    and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    where A _Bl denotes an absolute blow hole area and A6 and A7 profile areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .
12. 12. A pair of rotors according to one of the aspects 1 to 11, characterized in that the main rotor (HR) and the secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio Π of up to 3, in particular with a pressure ratio Π larger than 1 and up to 3, can be achieved, the pressure ratio being the ratio of the discharge pressure to the intake pressure.
13. 13. A pair of rotors according to one of the aspects 1 to 12, characterized in that the main rotor (HR) is designed to be operable with respect to a tip circle KK ₂ with a peripheral speed in a range from 20 to 100 m / s.
14. 14. A pair of rotors according to one of the aspects 1 to 13, characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.145\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.30$$
    
    is observed, Dk ₁ denoting the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denoting the diameter of the tip circle KK _{2 of} the main rotor (HR).
15. 15. pair of rotors for a compressor block of a screw machine, the pair of rotors consisting of a secondary rotor (NR) rotating around a first axis (C1) and a main rotor (HR) rotating around a second axis (C2),
    the number of teeth (z ₂ ) for the main rotor (HR) is 4 and the number of teeth (z ₁ ) for the secondary rotor (NR) is 5,
    where the relative profile depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    is at least 0.5, preferably at least 0.515, and at most 0.58, where rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is a root circle radius applied to the profile base of the subsidiary rotor,
    the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    is at least 1.683, and at most 1.836, preferably at most 1.782,
    wherein the main rotor is preferably designed with a wrap angle Φ _HR , for which 240 ° ≤ Φ _HR ≤ 360 °, and preferably for a rotor length ratio L _HR / a: $$1.4\le L_{\mathit{MR}}/a\le 3.3.$$
    
    wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.
16. 16. A pair of rotors according to aspect 15, characterized in
    that in a forehead section view within a secondary rotor tooth running circular arcs B ₂₅ , B ₅₀ , B ₇₅ , whose common center is C1, are defined, the radius r ₂₅ of B ₂₅ having the value rf ₁ + 0.25 * (rk ₁ -rf ₁ ), the radius r ₅₀ of B _{50 has} the value rf ₁ + 0.5 * (rk ₁ -rf ₁ ) and the radius r ₇₅ of B _{75 has} the value rf ₁ + 0.75 * (rk ₁ -rf ₁ ), and where the arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and trailing tooth flank F _N ,
    where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b _{75 of} the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed:
    0.75 ≤ ε ₁ ≤ 0.85 and / or 0.65 ≤ ε ₂ ≤ 0.74.
17. 17. A pair of rotors according to aspect 15 or 16, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth define an apex F5 are,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 protrudes beyond the triangle D _Z and
    where 6 ≤ A2 / A1 ≤ 15 is observed.
18. 18. A pair of rotors according to one of the aspects 15 to 17, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and a vertex at the radially outermost point of the tooth F5 are defined,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    wherein the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and withdraws with a surface A3 in a radially inner region opposite the triangle D _Z and wherein 9.0 ≤ A3 / A1 ≤ 18 is complied with.
19. 19. A pair of rotors according to one of the aspects 15 to 18, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR) base points F1 and F2 and an apex F5 are defined at the radially outermost point of the tooth,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    the leading tooth flank F _V formed between F5 and F2 protruding in a radially outer region of the tooth with a surface A1 over the triangle D _Z ,
    wherein the tooth itself has a cross-sectional area A0 delimited by the circular arc B running between F1 and F2 around the center point defined by the axis C1 and
    whereby 1.5% ≤ A1 / A0 ≤ 3.5% is observed.
20. 20. A pair of rotors according to one of the aspects 15 to 19, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and a vertex at the radially outermost point of the tooth F5 are defined,
    wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR around the center point defined by the axis C1,
    where a point F11 is defined on the half arc B between F1 and F2,
    a radial beam R drawn through the apex F5 from the center point of the secondary rotor (NR) defined by the axis C1 intersects the circular arc B at a point F12,
    wherein an offset angle β is defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and
    in which $$14\%\le \mathrm{\delta }\le 18\%$$
    
    is complied with ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
21. 21. A pair of rotors according to one of the aspects 15 to 20, characterized in that the trailing tooth flank F _{N of} a tooth of the secondary rotor (NR), formed between F1 and F5, has a convex length fraction of at least 55% to at most 95% in an end section view.
22. 22. A pair of rotors according to one of the aspects 15 to 21, characterized in that in a front sectional view the radial jet drawn by the axis C1 of the secondary rotor (NR) through F5 converts the tooth profile into a surface portion A5 assigned to the leading tooth flank F _V and one of the trailing tooth flank F _N assigned area share A4 divides and where $$\mathrm{4}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{9}$$
    
    is adhered to.
23. 23. A pair of rotors according to one of the aspects 15 to 22, characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 320 ° ≤ Φ _HR ≤ 360 °, preferably 330 ° ≤ Φ _HR ≤ 360 °.
24. 24. A rotor pair according to one of the aspects 15 to 23, characterized in that a blow hole factor µ _{Bl is} at least 0.02% and at most 0.4%, preferably at most 0.25%,
    in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor NR or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view denote the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .
25. 25. rotor pair according to one of the aspects 15 to 24, characterized in that for a blow hole / profile gap length factor µ _l * µ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{72}\%$$
    
    is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$
    
    where I _sp the length of the profile engagement gap of a tooth gap of the secondary rotor and PT ₁ the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
    and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    where A _Bl denotes an absolute blow hole area and A6 and A7 profile areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .
26. 26. A pair of rotors according to one of the aspects 15 to 25, characterized in that the main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio Π of up to 5, in particular with a pressure ratio Π of greater than 1 and up to 5, or alternatively a fluid-injected compression with a pressure ratio Π of up to 16, in particular with a pressure ratio Π of greater than 1 and up to 16, can be achieved, the pressure ratio being the ratio of the compression pressure to the intake pressure.
27. 27. A pair of rotors according to one of the aspects 15 to 26, characterized in that in the case of a dry compression the main rotor is related to a tip circle KK ₂ with a peripheral speed in a range from 20 to 100 m / s and in the case of a fluid-injected compression the main rotor is designed to be operable on a tip circle KK ₂ with a peripheral speed in a range from 5 to 50 m / s.
28. 28. A rotor pair according to one of the aspects 15 to 27, characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.195\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.33$$
    
    is observed, Dk ₁ denoting the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and DK ₂ denoting the diameter of the tip circle KK _{2 of} the main rotor (HR).
29. 29. A pair of rotors for a compressor block of a screw machine, the pair of rotors consisting of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
    the number of teeth (z ₂ ) for the main rotor (HR) is 5 and the number of teeth (z ₁ ) for the secondary rotor (NR) is 6,
    where the relative profile depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    is at least 0.44 and at most 0.495, preferably at most 0.48, where rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is a root circle radius applied to the profile base of the subsidiary rotor,
    the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    is at least 1.74, preferably at least 1.75, and at most 1.8, preferably at most 1.79,
    wherein the main rotor is preferably designed with a wrap angle Φ _HR , for which 240 ° ≤ Φ _HR ≤ 360 °, and preferably for a rotor length ratio L _HR / a: $$1.4\le L_{\mathit{MR}}/a\le 3.2.$$
    
    wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face.
30. 30. rotor pair according to aspect 29, characterized in
    that arcs B ₂₅ , B ₅₀ , B ₇₅ , whose common center point is C1, are defined in a frontal section view within a secondary rotor tooth, the radius r ₂₅ of B ₂₅ having the value rf ₁ + 0.25 * (rk ₁ -rf ₁ ) , the radius r ₅₀ of B _{50 has} the value rf ₁ + 0.5 * (rk ₁ -rf ₁ ) and the radius r ₇₅ of B _{75 has} the value rf ₁ + 0.75 * (rk ₁ -rf ₁ ), and where the Circular arcs B ₂₅ , B ₅₀ , B _{75 are} each delimited by the leading tooth flank F _V and trailing tooth flank F _N ,
    where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b75 of the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed:
    0.76 ≤ ε ₁ ≤ 0.86 and / or 0.62 ≤ ε ₂ ≤ 0.72.
31. 31. A pair of rotors according to aspect 29 or 30, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth define an apex F5 are,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 protrudes beyond the triangle D _Z and
    where 4 ≤ A2 / A1 ≤ 7 is observed.
32. 32. pair of rotors according to one of the aspects 29 to 31, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and a vertex at the radially outermost point of the tooth F5 are defined,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and withdraws with a surface A3 in a radially inner region opposite the triangle D _Z and where 8 ≤ A3 / A1 ≤ 14 is complied with.
33. 33. pair of rotors according to one of the aspects 29 to 32, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    where a triangle D _{Z is} defined by F1, F2 and F5 and
    the leading tooth flank F _V formed between F5 and F2 protruding in a radially outer region of the tooth with a surface A1 over the triangle D _Z ,
    wherein the tooth itself has a cross-sectional area A0 delimited by the circular arc B running between F1 and F2 around the center defined by the axis C1 and
    whereby 1.9% ≤ A1 / A0 ≤ 3.2% is observed.
34. 34. A pair of rotors according to one of the aspects 29 to 33, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and a vertex at the radially outermost point of the tooth F5 are defined,
    wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR around the center point defined by the axis C1,
    where a point F11 is defined on the half arc B between F1 and F2,
    a radial beam R drawn through the apex F5 from the center point of the secondary rotor (NR) defined by the axis C1 intersects the circular arc B at a point F12,
    wherein an offset angle β is defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and
    in which $$13.5\%\le \mathrm{\delta }\le 18\%$$
    
    is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$
    
35. 35. Pair of rotors according to one of the aspects 29 to 34, characterized in that the main rotor HR is designed with a wrap angle Φ _HR , for which the following applies: 320 ° ≤ Φ _HR ≤ 360 °, preferably 330 ° ≤ Φ _HR ≤ 360 °.
36. 36. pair of rotors according to one of the aspects 29 to 35, characterized in that a blow hole factor µ _{Bl is} at least 0.03% and at most 0.25%, preferably at most 0.2%,
    in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor NR or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view denote the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .
37. 37. rotor pair according to one of the aspects 29 to 36, characterized in that for a blow hole / profile gap length factor µ _l * µ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{26}\%$$
    
    is complied with $${\mathit{\mu }}_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">l\; </figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}}.$$
    
    where I _sp the length of the profile engagement gap of a tooth gap of the secondary rotor and PT ₁ the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
    and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    where A _Bl denotes an absolute blow hole area and A6 and A7 profile areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view between the profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ denote the area enclosed.
38. 38. pair of rotors according to one of the aspects 29 to 37, characterized in that the main rotor (HR) and the secondary rotor (NR) are designed and matched to one another such that dry compression with a pressure ratio Druck of up to 5, in particular with a pressure ratio Π of greater than 1 and up to 5, can be achieved or, alternatively, a fluid-injected compression with a pressure ratio Π of up to 20, in particular with a pressure ratio Π of greater than 1 and up to 20, can be achieved, the pressure ratio being the ratio of the discharge pressure to the intake pressure.
39. 39. pair of rotors according to one of the aspects 29 to 38, characterized in that the main rotor (HR) based on a tip circle KK ₂ in the case of a dry compression with a peripheral speed in a range of 20 to 100 m / s and in the case of a fluid-injected compression is designed to be operable with a peripheral speed in a range from 5 to 50 m / s.
40. 40. pair of rotors according to one of the aspects 29 to 39, characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.19\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.26$$
    
    is observed, Dk ₁ denoting the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denoting the diameter of the tip circle KK _{2 of} the main rotor (HR).
41. 41. A pair of rotors according to one of the aspects 1 to 40, characterized in that in an end sectional view the arc lengths b (r) of the respectively associated concentric circular arcs running within a tooth of the secondary rotor with the radius rf ₁ <r <rk ₁ and the common one the axis C1 defined center point are limited by the leading tooth flank F _V and the trailing tooth flank F _N and the arc lengths b (r) decrease monotonically with increasing radius r.
42. 42. pair of rotors according to one of the aspects 1 to 41, characterized in that the end section design of the secondary rotor (NR) is made in such a way that the effective direction of the torque, which results from a reference pressure on the partial surface of the secondary rotor delimiting a working chamber, against the direction of rotation of the Secondary rotor is directed.
43. 43. Pair of rotors according to one of the aspects 1 to 42, characterized in that the main rotor (HR) and the secondary rotor (NR) for conveying air or inert gases, such as helium or nitrogen, are designed and matched to one another.
44. 44. A pair of rotors according to one of the aspects 1 to 43, characterized in that the profile of a tooth of the secondary rotor is asymmetrical with respect to the radial beam R drawn from the center point, which is defined by the axis C1, through the vertex F5.
45. 45. Pair of rotors according to one of the aspects 1 to 44, characterized in that a point C on the connecting section ( C 1 C 2 ) is defined between the first axis (C1) and the second axis (C2), where the pitch circles WK _{1 of} the secondary rotor (NR) and WK _{2 of} the main rotor (HR) touch, that K5 the intersection of the root circle FK _{1 of} the secondary rotor ( NR) with the link ( C 1 C 2 ) defined, where r ₁ measures the distance between K5 and C,
    and that K4 designates the point of the suction-side part of the line of engagement that is farthest from the connecting path C 1 C 2 is spaced between C1 and C2, where r ₂ measures the distance between K4 and C and where: $$0.9\le \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\le 0.875-\frac{z_1}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2}+0.22$$
    
    with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR).
46. 46. Rotor pair according to one of the aspects 1 to 45, characterized in that for a rotor length ratio L _HR / a applies: $$\mathrm{0}.\mathrm{85}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{67}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{26}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{18}.$$
    
    prefers $$\mathrm{0}.\mathrm{89}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{94}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{05}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{22}.$$
    
    with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR), where the rotor length ratio L _HR / a indicates the ratio of the rotor length L _HR to the center distance a and the rotor length L _HR the distance between the suction sides Main rotor-rotor end face to the pressure-side main rotor-rotor end face.
47. 47. pair of rotors according to one of the aspects 1 to 28, characterized in that, in an end sectional view, the tooth profile of the secondary rotor (NR) sectionally follows an arc ARC ₁ with radius rk ₁ at its radially outer section, that is to say several points of the leading tooth flank F _V and of the trailing tooth flank F _N lie on the circular arc with radius rk ₁ around the center point defined by the axis C1, the circular arc ARC ₁ preferably making an angle with respect to the axis C1 between 0.5 ° and 5 °, more preferably between 0.5 ° and 2.5 °,
    where F10 is the most distant point from F5 on the leading tooth flank on this arc and
    wherein the radial jet R ₁₀ drawn between F10 and the center point of the secondary rotor (NR) defined by the axis C1 touches the leading tooth flank F _V in at least one point or intersects in two points.
48. 48. Compressor block comprising a compressor housing (15) and a pair of rotors according to one of the aspects 1 to 47, the pair of rotors comprising a main rotor (HR) and a secondary rotor (NR), each of which is rotatably mounted in the compressor housing (15).
49. 49. Compressor block according to aspect 48, characterized in that the face cut design is carried out in such a way that the working chamber formed between the tooth profiles of the main rotor (HR) and secondary rotor (NR) can essentially be pushed out completely into the pressure window.
50. 50. compressor block according to aspect 48 or 49,
    characterized in that
    a shaft end of the main rotor is led out of the compressor housing and is designed for connection to a drive, wherein
    preferably both shaft ends of the secondary rotor are completely accommodated within the compressor housing.

Claims (24)

Rotor pair for a compressor block of a screw machine, the rotor pair consisting of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
the number of teeth (z ₂ ) for the main rotor (HR) is 4 and the number of teeth (z ₁ ) for the secondary rotor (NR) is 5,
where the relative profile depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_{\mathrm{1}}-{\mathrm{rf}}_{\mathrm{1}}}{{\mathrm{rk}}_{\mathrm{1}}}$$

is at least 0.515, and at most 0.58, where rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is a root circle radius applied to the profile base of the subsidiary rotor,
the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{rk}}_1}$$

is at least 1.683, and at most 1.836, preferably at most 1.782,
the main rotor being designed with a wrap angle Φ _HR , for which 320 ° ≤ Φ _HR ≤ 360 ° applies, and preferably for a rotor length ratio L _HR / a: $$1.4\le L_{\mathit{MR}}/a\le 3.3.$$

wherein the rotor length ratio is formed from the ratio of the rotor length L _{HR of} the main rotor and the center distance a and the rotor length L _{HR of} the main rotor is formed by the distance from a suction-side main rotor-rotor end face to an opposite pressure-side main rotor-rotor end face. Rotor pair according to claim 1, characterized in
that in an end sectional view within a secondary rotor tooth circular arcs B ₂₅ , B ₅₀ , B ₇₅ , whose common center C1 is defined, the radius r ₂₅ of B ₂₅ having the value rf ₁ + 0.25 * (rk ₁ -rf ₁ ), the radius r ₅₀ of B ₅₀ having the value rf ₁ + 0.5 * (rk ₁ -rf ₁ ) and the radius r ₇₅ of B _{75 has} the value rf ₁ + 0.75 * (rk ₁ -rf ₁ ), and the circular arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and trailing tooth flank F _N become,
where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b _{75 of} the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b ₂₅ and the following dimensioning is observed:
0.75 ≤ ε ₁ ≤ 0.85 and / or 0.65 ≤ ε ₂ ≤ 0.74. A pair of rotors according to claim 1 or 2, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and an apex F5 are defined at the radially outermost point of the tooth,
where a triangle D _{Z is} defined by F1, F2 and F5 and
in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 with a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 protrudes beyond the triangle D _Z and
where 6 ≤ A2 / A1 ≤ 15 is observed. A pair of rotors according to one of claims 1 to 3, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR) defines base points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are,
where a triangle D _{Z is} defined by F1, F2 and F5 and
wherein the leading tooth flank F _V formed between F5 and F2 protrudes beyond the triangle D _Z in a radially outer region of the tooth with a surface A1 and withdraws with a surface A3 in a radially inner region opposite the triangle D _Z and wherein 9.0 ≤ A3 / A1 ≤ 18 is complied with. Rotor pair according to one of claims 1 to 4, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth Vertices F5 are defined,
where a triangle D _{Z is} defined by F1, F2 and F5 and
the leading tooth flank F _V formed between F5 and F2 protruding in a radially outer region of the tooth with a surface A1 over the triangle D _Z ,
wherein the tooth itself has a cross-sectional area A0 delimited by the circular arc B running between F1 and F2 around the center point defined by the axis C1 and
whereby 1.5% ≤ A1 / A0 ≤ 3.5% is observed. A pair of rotors according to one of claims 1 to 5, characterized in that in an end sectional view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 and at the radially outermost point of the tooth define an apex F5 are,
wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR around the center point defined by the axis C1,
where a point F11 is defined on the half arc B between F1 and F2,
a radial beam R drawn through the apex F5 from the center point of the secondary rotor (NR) defined by the axis C1 intersects the circular arc B at a point F12,
wherein an offset angle β is defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR) and
in which $$\mathrm{14}\%\le \mathrm{\delta }\le \mathrm{18}\%$$

is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$

A pair of rotors according to one of claims 1 to 6, characterized in that the trailing tooth flank F _{N of} a tooth of the secondary rotor (NR), formed between F1 and F5, has a convex length fraction of at least 55% to at most 95% in a front section view. A pair of rotors according to one of claims 1 to 7, characterized in that the radial profile drawn from the axis C1 of the secondary rotor (NR) by F5 in an end sectional view shows the tooth profile in one of the leading tooth flank F _V assigned area portion A5 and an area share A4 assigned to the trailing tooth flank F _N and where $$\mathrm{4}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{9}$$

is adhered to. Rotor pair according to one of claims 1 to 8, characterized in that the main rotor HR is formed with a wrap angle Φ _HR , for which the following applies: 330 ° ≤ Φ _HR ≤ 360 °. Rotor pair according to one of claims 1 to 9, characterized in that a blow hole factor µ _{Bl is} at least 0.02% and at most 0.4%, preferably at most 0.25%,
in which ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{bl}}}{A6+A7}*100\left[\%\right]$

and
where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth space areas of the secondary rotor NR or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view denote the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ . Rotor pair according to one of claims 1 to 10, characterized in that for a blow hole / profile gap length factor µ _l * µ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.72\%$$

is complied with $${\mathit{\mu }}_l=\frac{l_{\mathrm{sp}}}{{\mathit{PT}}_1}.$$

where I _sp the length of the profile engagement gap of a tooth gap of the secondary rotor and PT ₁ the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
and ${\mu }_{\mathit{bl}}=\frac{A_{\mathit{bl}}}{A6+A7}*100\left[\%\right]$

where A _Bl denotes an absolute blow hole area and A6 and A7 profile areas of the secondary rotor (NR) or the main rotor (HR), the area A6 in a frontal section view that between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in an end sectional view indicate the area enclosed between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ . Rotor pair according to one of claims 1 to 11, characterized in that the main rotor (HR) and secondary rotor (NR) are designed and matched to one another in such a way that dry compression with a pressure ratio Π of up to 5, in particular with a pressure ratio Π of greater than 1 and up to 5, or alternatively a fluid-injected compression with a pressure ratio Π of up to 16, in particular with a pressure ratio Π of greater than 1 and up to 16, can be achieved, the pressure ratio being the ratio of the compression pressure to the intake pressure. Rotor pair according to one of claims 1 to 12, characterized in that in the case of a dry compression the main rotor based on a tip circle KK ₂ with a peripheral speed in a range of 20 to 100 m / s and in the case of a fluid-injected compression the main rotor based on a Head circle KK _{2 is designed} to be operable with a peripheral speed in a range from 5 to 50 m / s. Rotor pair according to one of claims 1 to 13, characterized in that for a diameter ratio defined by the ratio of the tip circle radii of the main rotor (HR) and the secondary rotor (NR) $$D_v=\frac{{\mathit{dk}}_2}{{\mathit{dk}}_1}=\frac{{\mathit{rk}}_2}{{\mathit{rk}}_1}$$

$$1.195\le D_v\le 1.33$$

is observed, Dk ₁ denoting the diameter of the tip circle KK _{1 of} the secondary rotor (NR) and DK ₂ denoting the diameter of the tip circle KK _{2 of} the main rotor (HR). A pair of rotors according to one of claims 1 to 14, characterized in that in an end sectional view the arc lengths b (r) of the respectively associated concentric circular arcs running within a tooth of the secondary rotor with the radius rf ₁ <r <rk ₁ and the common one, through the axis C1 defined center are limited by the leading tooth flank F _V and the trailing tooth flank F _N and the arc lengths b (r) decrease monotonically with increasing radius r. Rotor pair according to one of claims 1 to 15, characterized in that the end cut design of the secondary rotor (NR) is made such that the effective direction of the torque, which results from a reference pressure on the partial surface of the secondary rotor delimiting a working chamber, is directed against the direction of rotation of the secondary rotor is. Rotor pair according to one of claims 1 to 16, characterized in that the main rotor (HR) and secondary rotor (NR) for conveying air or inert gases, such as helium or nitrogen, are designed and matched to one another. A pair of rotors according to one of claims 1 to 17, characterized in that in an end sectional view the profile of a tooth of the secondary rotor is asymmetrical with respect to the radial beam R drawn from the center point, which is defined by the axis C1, through the apex F5. A pair of rotors according to one of claims 1 to 18, characterized in that a point C on the connecting section ( C 1 C 2 ) is defined between the first axis (C1) and the second axis (C2), where the pitch circles WK _{1 of} the secondary rotor (NR) and WK _{2 of} the main rotor (HR) touch, that K5 the intersection of the root circle FK _{1 of} the secondary rotor ( NR) with the link ( C 1 C 2 ) defined, where r ₁ measures the distance between K5 and C,
and that K4 denotes the point of the suction-side part of the line of engagement, the farthest from the link C 1 C 2 is spaced between C1 and C2, where r ₂ measures the distance between K4 and C and where: $$0.9\le \frac{r_1}{r_2}\le 0.875\times \frac{z_1}{z_2}+0.22$$

with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR). Rotor pair according to one of claims 1 to 19, characterized in that for a rotor length ratio L _HR / a applies: $$\mathrm{0}.\mathrm{85}*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{67}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{26}*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{18}.$$

prefers $$\mathrm{0}.\mathrm{89}*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{0}.94\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.05*\left({\mathrm{z}}_{\mathrm{1}}/{\mathrm{z}}_{\mathrm{2}}\right)+\mathrm{1}.22.$$

with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR), where the rotor length ratio L _HR / a indicates the ratio of the rotor length L _HR to the center distance a and the rotor length L _HR the distance between the suction sides Main rotor-rotor end face to the pressure-side main rotor-rotor end face. A pair of rotors according to one of claims 1 to 14, characterized in that, in an end sectional view, the tooth profile of the secondary rotor (NR) sectionally follows an arc ARC ₁ with radius rk ₁ at its radially outer section, i.e. several points of the leading tooth flank F _V and the trailing one Tooth flank F _N lie on the circular arc with radius rk ₁ around the center point defined by the axis C1, the circular arc ARC ₁ preferably making an angle with respect to the axis C1 between 0.5 ° and 5 °, more preferably between 0.5 ° and 2.5 ° includes
where F10 is the most distant point from F5 on the leading tooth flank on this arc and
wherein the radial jet R ₁₀ drawn between F10 and the center point of the secondary rotor (NR) defined by the axis C1 touches the leading tooth flank F _V in at least one point or intersects in two points. Compressor block comprising a compressor housing (15) and a pair of rotors according to one of claims 1 to 21, the pair of rotors being a main rotor (HR) and a secondary rotor (NR), each rotatably mounted in the compressor housing (15). Compressor block according to claim 22, characterized in that the face cut configuration is made such that the working chamber formed between the tooth profiles of the main rotor (HR) and secondary rotor (NR) can essentially be pushed out completely into the pressure window. Compressor block according to claim 22 or 23,
characterized in that
a shaft end of the main rotor is led out of the compressor housing and is designed for connection to a drive, preferably both shaft ends of the secondary rotor being completely accommodated within the compressor housing.

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