EP3358189A1 - Rotor pair for a compressor block of a screw machine - Google Patents

Abstract

A pair of rotors for a compressor block of a screw machine is proposed: The pair of rotors consists of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2), with the number of teeth (z 2 ) in the main rotor (HR) is 3 and the number of teeth (z 1 ) in the secondary rotor (NR) is 4, with the relative profile depth of the secondary rotor PT rel = rk 1 ˆ’ rf 1 rk 1 being 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 a root circle radius starting at the profile base of the secondary rotor, where the ratio of the center distance ± the first axis (C1) to the second axis (C2) and the tip circle radius rk 1 a rk 1 is at least 1.636, and at most 1.8, preferably at most 1.733, with the main rotor preferably having a wrap angle ¦ HR is formed, for which applies 240 ° ¤ ¦ HR ¤ 360 °, and preferably for a rotor length ratio LHR / a applies: 1, 4 ¤ L HR / a ¤ 3, 4, the rotor length ratio from the ratio of Rotor length LHR of the main rotor and the center distance a is formed and the rotor length LHR of the main rotor is formed by the distance between a suction-side main rotor rotor face and an opposite pressure-side main rotor rotor face.

Description

The invention relates to a rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a main rotor rotating about a first axis and a secondary rotor rotating about a second axis according to the features of claim 1, 9 or 14. 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 forced reciprocating compressors as compressors in many areas. With the principle of the intermeshing screw pair not only gases can be compressed by applying a certain amount of work. The use as a vacuum pump also opens up the use of screw machines to achieve a vacuum. Finally, by passing pressurized gases the other way around, a workload can be generated, so that from pressurized gases by means of the principle of the screw machine and mechanical energy can be obtained.

Screw machines generally have two shafts arranged parallel to one another, on which, on the one hand, a main rotor and, on the other hand, a secondary rotor are seated. Main rotor and secondary rotor interlock with corresponding helical teeth. Between the gears and one Compressor housing, are included in the main and secondary rotor, a compression space (working chambers) is formed by the tooth space volumes. Starting from a suction area, the working chamber is first closed and then continuously reduced in volume as the main and secondary rotor rotate, so that a compression of the medium occurs. Finally, as the rotation progresses, the working chamber is opened to a pressure window and the medium is ejected into the pressure window. By this process of internal compression, screw machines designed as screw compressors differ from Roots blowers which operate without internal compression.

Depending on the required pressure ratio (ratio of outlet pressure to inlet pressure), different tooth number ratios make sense for efficient compaction.

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

Screw machines can be used in addition to the already mentioned function as a vacuum pump or as a screw expander in various fields of technology as a compressor. A particularly preferred field of application is in the compression of gases, such as air or inert gases, (helium, nitrogen, ...). But it is also possible, although this in particular structurally different requirements, a screw machine for the compression of refrigerants, for example, for air conditioning or refrigeration applications to use. In the compression of gases, especially at higher pressure conditions is usually worked with a fluid-injected compression, in particular an oil-injected compression; but 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 a screw blower.

Considerable success has been achieved in recent decades in terms of manufacturability, reliability, smoothness and efficiency of screw machines. Improvements or optimizations often refer to optimizations of the efficiency as a function of the number of teeth, wrap angle and length / diameter ratio of the rotors. The addition of the incisions in the optimization process can only be found in recent times.

Experiments have shown that the front section of the rotors, in particular the front section of the secondary rotor, has a significant influence on the energy efficiency. To comply with the gearing laws, the endcut of the secondary rotor must find its equivalent in the end section of the main rotor. As an incision here the profile of the rotor is referred to in a plane perpendicular to the axis of the rotor. In the meantime, different types of face cutting production, such as rotor or rack-based face cutting production methods, are known from the prior art. Once you have decided on a particular procedure, a first design frontal incision is created in a first step. This is conventionally further optimized in several subsequent (revision) steps according to various criteria.

Here are both the optimization goals per se (energy efficiency, smoothness, low cost) and the fact that the improvements of a parameter z.T. inevitably lead to the deterioration of another parameter known. However, there is a lack of a concrete solution on how to achieve a good overall optimization result (i.e., a trade-off between the various single-parameter optimizations).

By way of example, some optimization approaches known from the standpoint of improving energy efficiency, smoothness and cost in the prior art will be explained below. Furthermore, problems should be named, which can occur here.

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 be advantageously influenced in a known manner by minimizing the internal leakage in the compressor block and in particular by reducing the gap between the main rotor and secondary rotor. Specifically, here are the profile gap and the blow hole to distinguish:

• Via the profile gap, the pressure-side working chambers have a direct connection to the suction side and thus the greatest possible pressure difference for backflow.
• Successive working chambers are interconnected via a theoretically unnecessary passage, called a blow hole. In part, this is also referred to as head opening. This blow hole results from the head rounding of the profiles, in particular the profile of the secondary rotor.
  Pressure-side working chambers are connected via pressure-side blow holes with the respective adjacent working chambers, suction-side working chambers are connected via suction blow holes with the respective adjacent working chambers. Unless stated otherwise, the term "blow hole" is to be understood in the following text as "pressure-side blowing hole".

Ideally, a short profile gap length should be combined with a small (pressure side) blow hole to minimize internal leakage. The two sizes, however, behave in opposite directions. This means that the smaller the blow hole is modeled, the larger the profile gap length inevitably becomes. Conversely, the shorter the profile gap length, the larger the blow hole becomes. This explains Helpertz in his example Dissertation "Method for 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 running profile with correspondingly smaller relative tread depth of the secondary rotor. Whether a profile is rather flat (low tread depth) or deep (large tread depth) is executed, can be graphically quantified with the so-called "relative tread depth of the secondary rotor", which refers to the difference between the head and root radius on the tip circle radius of the secondary rotor. The larger the value, the more compact the compressor block is and, for example more delivery volume than a comparable compressor block with the same external dimensions.

Accordingly, very flat profiles have a poor build volume utilization, i. They lead to large compressor blocks with comparatively high material costs and comparatively high production costs.

Pressure side blow holes must not be made too large as described above to minimize the backflow of already compressed media into previous working chambers (i.e., lower pressure working chambers). Such backflows increase the energy consumption for the total achieved flow rate and lead to an undesirable increase in the temperature and pressure levels during compression, which reduces the overall efficiency. The area of the blowing hole (blow hole area) can be kept small by making the head roundings of the profiles small in the face cut. Specifically, this can be effected 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 stronger this curvature is, the sooner one gets into production-related boundary areas, since this leads, for example, to high wear on profile cutters and profile grinding wheels in the production of main rotor and secondary rotor.

On the other hand, large blowing holes on the intake side do not have a negative effect on the energy efficiency since they only connect working chambers in the intake region at the same pressure.

Another cause of efficiency-reducing internal leakage is the so-called chamber gusset volume, which can arise in the pressure window when the last working chamber (that is, the working chamber in which the highest pressure prevails) is ejected. The working chamber then has no connection to the pressure window from a certain angular position of the rotors. There remains a so-called. Chamber gusset volume between the two rotors and the pressure-side housing end wall.

This Kammerzwickelvolumen is disadvantageous because the enclosed compressed medium can not be pushed out into the printing window, at the further rotation of the rotors is further compressed, resulting in unnecessarily high power consumption (for over-compression), an unnecessarily high additional heat input, noise and a reduction in the life of the particular bearings of the rotors. In addition, the specific performance is worsened by the fact that the portion enclosed in the chamber gusset volume returns to the suction side after over-compression and is thus not available to the compressed-air user. In the case of oil-injected compressors, incompressible oil is additionally present in the chamber gusset and is squeezed.

2 smoothness

On a good profile for main rotor or side rotor, however, have other properties such as smoothness decisive influence.

In addition to good flank smoothness and low relative velocities between the tooth flanks of the main and secondary rotor, the distribution of the drive torque between the two rotors has a significant effect on smoothness. As is known, an unfavorable division often leads to the so-called rotor clattering 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 edge and the trailing main rotor flank. If the two rotors are kept at a distance by a synchromesh, the o.g. Rotorklappern inevitably synchromesh. 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

On the material and manufacturing costs of screw compressor blocks affect in particular the manufacturability and the degree of construction volume utilization.

Compact compressor blocks with a high construction volume utilization are achieved by a large tooth space 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 one increases the relative profit depth, the higher volume utilization is achieved, but the higher the risk of problems in terms of runnability and manufacturability:

• As the tread depth increases, the tooth profiles of the secondary rotor inevitably become increasingly thinner and therefore always more flexible. This makes the rotors increasingly sensitive to temperature and, overall, has an unfavorable effect on the gaps in the compressor block. The gaps have a significant impact on the internal leakages, ie, backflow of higher pressure compression chambers towards the suction side, and thus may degrade the energy efficiency of the compressor block.
• Furthermore, with flexible teeth the difficulties in rotor production increase.
  • ∘ For example, there is an increased risk that profile grinding can not meet the already high requirements, especially with regard to the form tolerances.
  • B Furthermore, flexible teeth require lower feed and cutting speeds both during profile milling and during subsequent profile grinding, thereby increasing the processing time and, as a result, the manufacturing costs.
• An increasing tread depth also causes the rotor itself to be more flexible. The more flexible the rotors are designed, the more the risk increases that the rotors start up with each other or in the compressor housing. To ensure operational safety even at high temperatures or at high pressures, therefore, the gaps must be sized larger. This in turn has a negative effect on the energy efficiency of the compressor block.

4 conclusion

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

In the literature, the theoretical calculation bases for the generation of screw rotor profiles are already often treated and also general criteria for good frontal cutting profiles are described. With the computer program developed by Grafinger, for example, it is possible to create and modify rotor profiles (habilitation "The Computer-aided Development of Flank Profiles for Special Gearings of Screw Compressors", Vienna, 2010).

Helpertz deals in his Dissertation "Method for stochastic optimization of screw rotor profiles", Dortmund, 2003 with automated optimization based on a design profile with different weighted characteristics.

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 high operational reliability and reasonable manufacturing costs by high smoothness and a special energy efficiency.

This object is achieved with a rotor pair according to the features of claim 1, 9 or 14. Advantageous embodiments are specified in the subclaims. Furthermore, the object is also achieved with a compressor block comprising a correspondingly designed pair of rotors.

The rotor geometry is essentially characterized by the shape of the front section and by the rotor length and the wrap angle, cf. " Method for Stochastic Optimization of Screw Rotor Profiles ", Dissertation by Markus Helpertz, Dortmund, 2003, p. 11/12 ,

In a front-sectional view, secondary rotor or main rotor have a predetermined, often different number per rotor of identically designed teeth. The extreme circle drawn through the axis C1 or C2 via the vertices of the teeth is referred to as the tip circle. By the axis closest points of the outer surface of the rotors a foot circle is defined in the end section. The ribs are referred to as teeth of the rotor. The grooves (or recesses) are referred to as tooth gaps. The area of the tooth at and above the root defines the tooth profile. The contour of the ribs defines the course of the tooth profile. For the tooth profile, foot points F1 and F2 and a vertex F5 are defined. The vertex 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 defined by the axis C1 or C2, ie if the tooth profile follows a circular arc on the top circle at its radially outer end, then the vertex F5 lies exactly in the center of this circular arc. Between two adjacent vertices F5, a tooth space is defined.

The points closest to the axis C1 or C2 between a considered and the adjacent tooth define foot points F1 and F2. Again, in the case that several points of the axis C1 or C2 come close, so that the tooth profile follows the root circle in sections at its lowest point, the corresponding foot point F1 or F2 then lies on half of this circular arc lying on the root circle ,

Finally, a pitch circle is defined by the meshing of the main rotor and the secondary rotor both for the secondary rotor and for the main rotor. In screw machines as well as in gears or friction wheels, there are always two circles in the front section of the toothing, which roll when moving together. These circles, on which in the present case main rotor and secondary rotor roll against each other, are referred to as respective pitch circles. The pitch circle diameters of the main rotor and secondary rotor can be determined with the help of the center distance and the number of teeth ratios.

On the rolling circles, the circumferential speeds of the main rotor and the secondary rotor are identical.

Finally, tooth space areas between the teeth and the respective top 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 the tooth gap area between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

The tooth profile of the secondary rotor (but also of the main rotor) has a respective tooth flank leading in the direction of rotation and a tooth flank trailing in the direction of rotation. In the case of the secondary rotor (NR), the leading tooth flank is designated below by F _V , the trailing tooth flank by F _N.

The trailing tooth flank F _N forms a point in its section between tip circle and root circle in which the curvature of the profile 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 portion between F8 and the tip circle and a concavely curved portion between the root circle and F8. Small-scale profile changes, such as by sealing strips or by other local profile transformations are not taken into account in the consideration of the above-described curvature change.

Beyond the pure endcut, the following terms or parameters for a rotor, in particular the secondary rotor, are still relevant for the three-dimensional design: First, a wrap angle φ is defined. This wrap angle is the angle by which the end cut is twisted from the suction side to the pressure side rotor end face, cf. also the further explanations in connection with FIG. 8 ,

The main rotor has a rotor length LHR, which is defined as the distance of a suction-side main rotor rotor end face to a pressure-side main rotor rotor end face. The distance between the mutually parallel first axis C1 of the secondary rotor to the second axis C2 of the main rotor is referred to below as the axial distance a. It should be noted that in most cases the length of the main rotor L _HR corresponds to the length of the secondary rotor L _NR , whereby the length is also understood as the distance of a suction-side secondary rotor rotor face to a pressure-side slave rotor rotor face in the secondary rotor. Finally, a rotor length ratio L _HR / a is defined, ie a ratio of the rotor length of the main rotor to the axial distance. The ratio L _HR / a is a measure of the axial dimensioning of the rotor profile.

The engagement line or the profile gap created by the interaction of main rotor and secondary rotor with each other. The engagement line is as follows: The tooth flanks of the main rotor and secondary rotor touch each other with backlash-free teeth depending on the angular position of the rotors in certain points. These points are called engagement points. The geometric location of all engagement points is called the engagement line and can already be calculated in two-dimensional terms from the front section of the rotors, cf. FIG. 7j ,

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

With additional indication of the wrap angle and the rotor length (= distance between the suction-side end face and the pressure-side end face), the engagement line can also be extended three-dimensionally and corresponds to the contact line of main rotor and secondary rotor. The axial projection of the three-dimensional line of action on the end section plane in turn results in the basis of FIG. 7j illustrated two-dimensional engagement line. The term "line of action" is used in the literature for both two-dimensional and three-dimensional viewing. In the following, unless otherwise stated, the term "engagement line" is understood to mean, however, the two-dimensional engagement line, that is to say the projection onto the endcut.

The profile engagement gap is defined as follows: In the real compressor block of a screw machine clearance between the two rotors is present at installation axis distance of main rotor and side rotor. The gap between the main rotor and the secondary rotor is referred to as the profile engaging gap and is the locus of any point where the two paired rotors are in contact with each other or the least spaced apart. Through the profile engagement gap, the compressing and ejecting working chambers are connected to chambers which are still in contact with the suction side. At the profile engagement gap is thus the entire maximum pressure ratio. By the profile engagement gap already compressed working fluid is transported back to the suction side and thus reduces the efficiency of compaction. Since the profile engagement gap would be the engagement line with backlash-free teeth, the profile engagement gap is also referred to as a "quasi-engagement line".

Blowholes between working chambers are created by head rounding of the teeth of the profile. About blowholes are the working chambers with leading and connected subsequent working chambers, so that (in contrast to the profile engagement gap) at a blow hole rests only the pressure difference from one working chamber to the next working chamber.

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 sub rotor 4 teeth or a rotor pairing, in which the main rotor 4 teeth and the secondary rotor 5 teeth or further a rotor pair geometry, in which the main rotor 5 teeth and the secondary rotor has 6 teeth. Rotor pairs or screw machines with different tooth number ratio may be used for different fields of application or purposes. For example, rotor pair arrangements having a 4/5 teeth ratio (4 tooth main rotor, 5 teeth secondary rotor) are considered to be a suitable mating for oil injected compression applications in moderate pressure ranges.

In this respect, the number of teeth or the number of teeth gives 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: $$1,4\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 3,4,$$

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.For a screw machine or a rotor pair with 3 teeth in the main rotor and 4 teeth in the secondary rotor, a geometry is claimed with the following specifications, which should be regarded as particularly energy efficient:
It is a relative tread depth of the secondary rotor 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 tread depth, at rk ₁ a tip radius drawn around the outer circumference of the secondary rotor and at rf ₁ is a Fußkreisradius beginning at the profile base. Furthermore, the ratio of the axial distance α of the first axis C1 to the second axis C2 and the tip circle radius rk ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

so set 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, wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which 240 ° ≤ φ _HR ≤ 360 °, and wherein preferably for a rotor length ratio L _HR / a: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.4.$$

wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor 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: $$1,4\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 3,3,$$

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.For a screw machine or a rotor pair with four teeth in the main rotor and five teeth in the secondary rotor, a geometry is claimed with the following specifications, which is considered to be particularly energy efficient: It is a relative tread depth of the secondary rotor 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, where PT _rel is the relative tread depth, at rk ₁ a tip radius drawn around the outer periphery of the secondary rotor and at rf ₁ a profile ground Root radius is. Furthermore, the ratio of the axial distance a of the first axis C1 to the second axis C2 and the tip circle radius rk ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

so set 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, wherein preferably the main rotor is formed with a wrap angle φ _HR , for which applies 240 ° ≤ φ _HR ≤ 360 °, and wherein preferably applies to a rotor length ratio L _HR / a: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.3.$$

wherein the rotor length ratio of the ratio of the rotor length L _{HR of} the main rotor and the axial distance a is formed and the rotor length L _HR of Main rotor is formed by the distance of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor 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: $$1,4\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 3,2,$$

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.For a screw machine or a rotor pair with five teeth in the main rotor and six teeth in the secondary rotor, a geometry is claimed with the following specifications, which should be regarded as particularly energy efficient:
It is a relative tread depth of the secondary rotor 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 tread depth, at rk ₁ a tip radius drawn around the outer circumference of the secondary rotor and at rf ₁ a profile ground Root radius is. Furthermore, the ratio of the center distance a of the first axis C1 to the second axis C2 and the tip circle radius rk ₁ $$\frac{a}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

so set 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, wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which applies 240 ° ≤ φ _HR ≤ 360 °, and preferably for a rotor length ratio L _HR / a, the following applies: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.2.$$

wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face.

mit PT₁ = rk₁ - rf₁ und rf₁ = a - rk₂ If the values for the relative tread depth on the one hand and the ratio of center distance to pitch radius of the secondary rotor on the other hand for the specified teeth-number ratios in the specified advantageous ranges, so are the basic requirements for a good side rotor profile or a good interaction of secondary rotor profile and Created main rotor profile, in particular, this is a particularly favorable ratio of Blaslochfläche allows profile gap length. With regard to the decisive parameters, for all of the mentioned number of teeth ratios, supplementary to the illustration in Figure 7a directed. The relative tread depth of the secondary rotor is a measure of how deep the profiles are cut. As the tread depth increases, for example, the volume of construction volume increases, but at the expense of the flexural rigidity of the secondary rotor. For the relative tread 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.Insofar, 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 head circle radius rk ₁ .

The values given for the rotor length ratio L _HR / a and the wrap angle φ _HR represent advantageous or expedient values for the respectively indicated tooth-number ratio in order to determine an advantageous rotor pairing in the axial dimension.

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

Hereinafter, preferred embodiments for a rotor pair with teeth-number ratio 3/4, that is, for a pair of rotors, in which the main rotor 3 teeth and the secondary rotor has 4 teeth, set out:
A first preferred embodiment provides that, in an end-face view within a secondary rotor tooth, circular arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is given by the axis C 1 are defined, wherein the radius r ₂₅ of B _{25 is} 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 limited by the leading tooth flank F _V and the trailing tooth flank F _N , wherein 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 design 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 goal 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 inevitable length of the profile engagement gap. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole becomes. In the claimed areas, a particularly favorable combination of the two parameters is achieved. At the same time a sufficiently high bending stiffness of the secondary rotor is ensured. In addition, there are also advantages in terms of the chamber ejection, and the side rotor torque. With regard to the illustration of the parameters, reference is also made to the FIG. 7c directed.

A further preferred embodiment provides that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor, foot points F1 and F2 are defined at the root circle and at the radially outermost point of the tooth a vertex F5, where F1, F2 and F5 a triangle D _{Z is} defined and wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank F _N with a surface A2 via the triangle D _Z survives and wherein 8 ≤ A2 / A1 ≤ 60 is maintained.

The tooth part surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The tooth part 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. For the tooth area ratio A2 / A1, there is an advantageous range that allows 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 on FIG. 7d directed.

In a further preferred embodiment, the pair of rotors has a secondary rotor, in which, in a cross-sectional view, between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the Nebenrotors Fußpunkte F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined, wherein by F1, F2 and F5, a triangle D _{Z is} defined and wherein the formed between F5 and F2 leading tooth flank F _V in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z and in a radially inner region with respect to the triangle D _{Z recedes} with an area A3 and wherein 7.0 ≤ A3 / A1 ≤ 35 is maintained. With regard to the illustration of the parameters, reference is also made to the FIG. 7d directed.

Furthermore, it is considered advantageous with respect to the design of the sub-rotor, when in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) defines foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined by F1, F2 and F5 a triangle D _Z and wherein the leading tooth flank formed between F5 and F2 F _V in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z , the tooth itself a by the circular arc B extending between F1 and F2 around the center defined by the axis C1 has limited cross-sectional area A0 and wherein 0.5% ≤ A1 / A0 ≤ 4.5% is maintained. With regard to the illustration of the parameters, reference is also made to the FIGS. 7d and 7e referenced.

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

First of all, it is again clarified that the offset angle is always always positive, ie always the offset in the direction of the direction of rotation is given and not contrary. The tooth of the secondary rotor is curved in this respect to the direction of rotation of the secondary rotor. However, the offset should be in the range indicated to be favorable to allow 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 minor rotor torque, the flexural stiffness of the rotors, and the chamber thrust into the pressure window. With regard to an illustration of the parameters is in addition to Figure 7f directed.

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

The fixed relative to the area, relatively long convex length portion of the trailing tooth surface F _{N of} a tooth of the secondary rotor allows a good compromise between length of the profile engagement gap, Kammerausschub, secondary rotor torque on the one hand and flexural rigidity of the secondary rotor on the other. With regard to the illustration of the parameters is also on FIG. 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.Preferred dimensions of the female rotor is designed such that in an end section view of the axis C1 of the slave rotor (NR) the tooth profile associated by F5 solid radial line R in one of the leading tooth flank F _V surface portion A5, and a trailing tooth flank F _N associated surface portion divides A4 and in which $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{14}$$

is complied with. It should be pointed out again at this point that the tooth profile is limited radially inward toward the axis C1 through the root circle FK ₁ . In this case, it may occur that the radial ray R divides the tooth profile in such a way that two disjoint surface portions with a total surface area A5, which are assigned to the leading tooth flank F _V , arise, cf. FIG. 7g , If the vertex F5 were to be offset from the leading tooth flank in such a way that the radial ray R not only touched the leading tooth flank F _V , but intersected it at two points, then again two of the leading tooth flank are assigned disjoint area shares defined with a total area proportion A5. The trailing tooth flank F _N associated surface portion A4 is then limited on the one hand by the radial beam R and sections, namely between the two intersections of the leading tooth flank F _V with the radial beam R, on the other hand by the leading tooth flank F _V.

A further preferred embodiment has a rotor pair, which is characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 290 ° ≤ φ _HR ≤ 360 °, preferably 320 ° ≤ φ _HR ≤ 360 °.

With increasing wrap angle, the pressure window area can be made larger with the same volume ratio built-in. In addition, thereby shortening the axial extent of auszuschiebenden working chamber, the so-called. Profile pocket depth. This reduces the Ausschiebedrosselverluste especially at higher speeds and thus allows a better specific performance. However, too great a wrap angle has a disadvantageous effect on the overall 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, in an advantageous embodiment, a rotor pair is provided, which is designed and cooperates with each other such that a blow hole factor μ _{Bl is} at least 0.02% and at most 0.4%, preferably at most 0.25%,
in which ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
where A _{Bl is} an absolute pressure-side blow hole area and A6 and A7 tooth space surfaces of the secondary rotor (NR) and the main rotor (HR), wherein the surface A6 in an end-sectional view between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the top circle KK ₁ enclosed area and the area A7 in an end-sectional view denote between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.

While the absolute size of the discharge-side blow hole alone does not make any meaningful statement 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 significantly more meaningful. With regard to the further illustration of the parameters, this is supplemented by FIG. 7b directed. The smaller the numerical value μ _Bl , the lower the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole surface can thus be displayed independently of the size of the screw machine.

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

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

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 rotor pair is designed and matched to one another such that for a blow hole / profile gap length factor μ ₁ * 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 l _{sp is} the length of the spatial, ie three-dimensional profile engagement gap of a tooth space of the secondary rotor and PT _{1 is} the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁ and $${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$$

where A _{Bl is} an absolute pressure-side blow hole area and A6 and A7 tooth space surfaces of the secondary rotor (NR) and the main rotor (HR), wherein the surface A6 in an end-sectional view between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the top circle KK ₁ enclosed area and the area A7 in an end-sectional view denote between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.

μ _l denotes a profile gap length factor, wherein the length of the profile engagement gap of a tooth gap is set in relation to the profile depth PT ₁ . This can be a measure of the length of the profile engagement gap set regardless of the size of the screw machine. The smaller the numerical value of the characteristic μ _l is, the shorter is the profile gap of a tooth pitch and thus the lower the leakage volume flow back to the suction side at the same profile depth. From the factor μ _l * μ _Bl , the goal is to combine a small pressure-side blow hole with a short profile gap. However, the two ratios behave, as already mentioned, but in opposite directions.

It is also considered advantageous if main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that a dry compression with a pressure ratio Π of up to 3, in particular with a pressure ratio Π of greater than 1 and up to 3 , is obtainable, wherein the pressure ratio refers to the ratio of compression end pressure to suction pressure.

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

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

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 rotor pair, which is characterized in that a diameter ratio defined by the ratio of the head circle radii of the main rotor (HR) and 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 complied with, wherein Dk ₁ the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denote the diameter of the top circle KK _{2 of} the main rotor (HR).

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

Hereinafter, preferred embodiments for a rotor pair with teeth number ratio 4/5, ie for a pair of rotors, in which the main rotor has four teeth and the secondary rotor has five teeth, set out:
A further preferred embodiment provides that circular arcs B ₂₅ , B ₅₀ extending within a secondary rotor tooth in a cross-sectional view B ₇₅ whose common center is given by the axis C1, are defined, wherein the radius r ₂₅ of B _{25 has} 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 arcs B ₂₅ , B ₅₀ , B _{75 are} each bounded 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 arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ / b ₂₅ and ε ₂ = b ₇₅ / b _{25 are} defined and the following dimensioning is maintained: $$\mathrm{0}.\mathrm{75}\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{1}}\le \mathrm{0}.\mathrm{85}\mathrm{and}/\mathrm{or}\mathrm{0}.\mathrm{65}\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{2}}\le \mathrm{0}.\mathrm{74th}$$

The goal 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 inevitable length of the profile engagement gap. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole becomes. In the claimed areas, a particularly favorable combination of the two parameters is achieved. At the same time a sufficiently high bending stiffness of the secondary rotor is ensured. In addition, there are also advantages in terms of the chamber ejection, and the side rotor torque. With regard to the illustration of the parameters, reference is also made to the FIG. 7c directed.

A further preferred embodiment provides that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR), foot points F1 and F2 at the root circle and at the radially outermost point of the tooth a vertex F5 are defined is defined by F1, F2 and F5, a triangle D _Z and wherein in a radially outer region of the tooth with its formed between F5 and F2 leading edge tooth F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank F _N with a Area A2 over the triangle D _Z survives and wherein 6 ≤ A2 / A1 ≤ 15 is met.

The tooth part surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The tooth part 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. For the tooth area ratio A2 / A1, there is an advantageous range that makes a good compromise between the length of the Profile engaging gap on the one hand and blow hole on the other hand allows. With regard to the illustration of the parameters is also on FIG. 7d directed.

In a further embodiment, the rotor pair has a secondary rotor in which, in an end-sectional view, between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR), foot points F1 and F2 are defined and at the radially outermost point of the tooth a vertex F5 , said by F1, F2 and F5 D _Z is defined a triangle and wherein said formed between F5 and F2 leading tooth flank F _V protrudes in a radially outer region of the tooth with an area A1 on the triangle D _Z and in a radially inner region with respect to the triangle D _{Z recedes} with an area A3 and wherein 9.0 ≤ A3 / A1 ≤ 18 is maintained. With regard to the illustration of the parameters, reference is also made to the FIG. 7d directed.

Furthermore, it is considered advantageous with respect to the design of the secondary rotor, when in an end-sectional view defined between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) feet F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined by F1, F2 and F5 a triangle D _Z and wherein the leading tooth flank formed between F5 and F2 F _V in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z , the tooth itself a by the circular arc B extending between F1 and F2 around the center defined by the axis C1 has limited cross-sectional area A0 and wherein 1.5% ≤ A1 / A0 ≤ 3.5% is maintained.

With regard to the definition of the parameters is on the FIGS. 7d and 7e referenced.

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

A further preferred embodiment provides that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) feet F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined, the between F1 and F2 arc extending around the defined by the axis C1 center a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR defined, wherein on the half circular arc B a point F11 is defined between F1 and F2, wherein a radial ray R drawn from the center point of the sub rotor (NR) defined by the axis C1 intersects the arc B at a point F12, wherein an offset angle β is determined by the rotational direction of the sub rotor (NR) is considered to be offset from F11 to F12 and where $$14\%\le \mathrm{\delta }\le 18\%$$

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

First of all, it is again made clear that the offset angle is always always positive, that is to say always the offset in the direction of the direction of rotation is given and not contrary. The tooth of the secondary rotor is curved in this respect to the direction of rotation of the secondary rotor. However, the offset should be in the range indicated to be favorable to allow a favorable compromise between the blow hole area, the shape of the line of action, the length and shape of the profile engagement gap, the minor rotor torque, the flexural stiffness of the rotors, and the chamber thrust into the pressure window. With regard to an illustration of the parameters is in addition to Figure 7f directed.

It is furthermore considered advantageous if, in a front-sectional view, the trailing tooth flank FN of a tooth of the secondary rotor (NR) formed between F1 and F5 has a convex length portion of at least 55% to at most 95%.

The fixed with the area, relatively long convex length portion of the trailing tooth face FN of a tooth of the secondary rotor allows a good compromise between length of the profile engagement gap, chamber thrust, secondary rotor torque on the one hand and flexural rigidity of the secondary rotor on the other. With regard to the illustration of the parameters is also on FIG. 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.Preferred dimensions of the secondary rotor is designed so that in a cross-sectional view of the axis C1 of the sub rotor (NR) by F5 drawn radial beam R divides the tooth profile in a leading edge of the tooth F _V associated surface portion A5 and the trailing tooth flank F _N associated surface portion A4 and in which $$4\le \mathrm{A}4/\mathrm{A}5\le 9$$

is complied with. It should be pointed out again at this point that the tooth profile is limited radially inward toward the axis C1 through the root circle FK ₁ . In this case, it may occur that the radial ray R divides the tooth profile in such a way that two disjoint surface portions with a total surface area A5, which are assigned to the leading tooth flank F _V , arise, cf. FIG. 7g , If the vertex F5 were offset from the leading tooth flank in such a way that the radial ray R not only touches the leading tooth flank F _V but intersects at two points, then two disjoint surface fractions associated with the leading tooth flank are defined with a total area fraction A 5. The surface portion A4 associated with the trailing tooth flank F _N is then limited in part by the radial ray R in sections, namely between the two intersections of the leading tooth flank F _V with the radial ray R, and 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 formed with a wrap angle φ _HR , for which applies: 320 ° ≤ φ _HR ≤ 360 °, preferably 330 ° ≤ φ _HR ≤ 360 °.

With increasing wrap angle, the pressure window area can be made larger with the same volume ratio built-in. In addition, thereby shortening the axial extent of auszuschiebenden working chamber, the so-called. Profile pocket depth. This reduces the Ausschiebedrosselverluste especially at higher speeds and thus allows a better specific performance. However, too great a wrap angle has a disadvantageous effect on the overall 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, in an advantageous embodiment, a rotor pair is provided, which is designed and cooperates with each other such that a blow hole factor μ _{Bl is} at least 0.02% and at most 0.4%, preferably at most 0.25%,
is complied with, ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
where A _Bl denote an absolute pressure side blow hole surface and A6 and A7 tooth space surfaces of the secondary rotor NR and the main rotor (HR), wherein the surface A6 in an end-sectional 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 surface A7 in a cross-sectional view denote between the profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.

While the absolute size of the pressure-side blow hole alone does not make any meaningful statement about the effect on the leakage mass flows, a ratio of absolute pressure side blow hole 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 is much more meaningful. With regard to the illustration of the parameters, this is supplemented by FIG. 7b directed. The smaller the numerical value μ _Bl , the lower the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole surface can thus be displayed independently of the size of the screw machine.

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

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

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 rotor pair is designed and matched to one another such that for a blow hole / profile gap length factor μ ₁ * 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 l _{sp is} the length of the spatial, ie three-dimensional profile engagement gap of a tooth space of the secondary rotor and PT _{1 is} the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
and $${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$$

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

μ _l denotes a profile gap length factor, wherein the length of the profile engagement gap of a tooth gap is set in relation to the profile depth PT ₁ . This can be a measure of the length of the profile engagement gap set regardless of the size of the screw machine. The smaller the numerical value of the characteristic μ _l is, the shorter is the profile gap at the same profile depth and thus the lower the leakage volume flow back to the suction side. From the factor μ _l * μ _Bl , the goal is to combine a small pressure-side blow hole with a short profile gap. However, the two ratios behave, as already mentioned, but in opposite directions.

It is also considered advantageous if main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that a dry compression with a pressure ratio of up to 5, in particular with a pressure ratio Π of greater than 1 and up to 5, 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, is achievable, wherein the pressure ratio is the ratio of compression end pressure to suction pressure.

A further preferred embodiment provides a pair of rotors, such that in the case of a dry compression of 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 of the main rotor with a peripheral speed in a range of 5 to 50 m / s is operable.

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

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 rotor pair, which is characterized in that a diameter ratio defined by the ratio of the head circle radii of the main rotor (HR) and secondary rotor (NR) $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

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

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

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

Hereinafter, preferred embodiments for a rotor pair with teeth number ratio 5/6, ie for a pair of rotors, in which the main rotor has five teeth and the secondary rotor has six teeth, set out:
A further preferred embodiment provides that, in an end-face view within a secondary rotor tooth, circular arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is given by the axis C 1 are defined, wherein the radius r ₂₅ of B _{25 is} 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} respectively bounded by the leading tooth flank F _V and the trailing tooth flank FN, wherein 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 design is observed: 0.76 ≤ ε ₁ ≤ 0.86 and / or 0.62 ≤ ε ₂ ≤ 0.72.

The goal 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 inevitable length of the profile engagement gap. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole becomes. In the claimed areas, a particularly favorable combination of the two parameters is achieved. At the same time a sufficiently high bending stiffness of the secondary rotor is ensured. In addition, there are also advantages in terms of the chamber ejection, and the side rotor torque. With regard to the illustration of the parameters, the following is added to the FIG. 7c directed.

A further preferred embodiment provides that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR), foot points F1 and F2 at the root circle and at the radially outermost point of the tooth a vertex F5 are defined by F1, F2 and F5, a triangle D _Z and wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V having a surface A1 and with its trailing formed between F1 and F5 tooth flank F _N with a surface A2 over the triangle D _Z survives and wherein 4 ≤ A2 / A1 ≤ 7 is maintained.

The tooth part surface A1 on the leading tooth flank F _{V of} the secondary rotor has a significant influence on the blow hole surface. The tooth part surface A2 on the trailing tooth flank FN 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. For the tooth area ratio A2 / A1, there is an advantageous range that allows 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 will be supplementary FIG. 7d directed.

In a further preferred embodiment, the rotor pair has a secondary rotor, in which, in an end-sectional view, between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR), foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined by F1, F2 and F5, a triangle D _{Z is} defined and wherein the leading tooth flank formed between F5 and F2 F _V in a radially outer region of the tooth with a surface A1 over the triangle D _Z and in a radially inner Area with respect to the triangle D _{Z recedes} with an area A3 and wherein 8 ≤ A3 / A1 ≤ 14 is complied with. With regard to the illustration of the parameters, reference is also made to the FIG. 7d directed.

Furthermore, it is considered advantageous with respect to the design of the sub-rotor, when in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) defines foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined by F1, F2 and F5 a triangle D _Z and wherein the leading tooth flank formed between F5 and F2 F _V in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z , the tooth itself a by the circular arc B running between F1 and F2 around the center point defined by the axis C1, and having 1.9% ≤ A1 / A0 ≤ 3.2% is complied with. With regard to the illustration of the parameters, reference is also made to the FIGS. 7d and 7e referenced.

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

A further preferred embodiment provides that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) feet F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined, the between F1 and F2 extending arc B around the center defined by the axis C1 a tooth pitch angle γ corresponding to 360 ° / number of teeth of the minor rotor NR defined on the half arc B between F1 and F2 a point F11 is defined, one of the through Axis C1 defined center of the secondary rotor (NR) by the vertex F5 radial beam R intersects the arc B at a point F12, wherein an offset angle β by the in the direction of rotation of the secondary rotor (NR) considered offset from F11 to F12 is defined and $$13.5\%\le \mathrm{\delta }\le 18\%$$

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

First of all, it is again made clear that the offset angle is always always positive, that is to say always the offset in the direction of the direction of rotation is given and not contrary. The tooth of the secondary rotor is curved in this respect to the direction of rotation of the secondary rotor. However, the offset should be in the range indicated to be advantageous in order to allow a favorable compromise between the blow hole area, the shape of the line of action, the profile gap length and shape, the minor 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 in addition to Figure 7f directed.

A further preferred embodiment has a pair of rotors, which is characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 320 ° ≤ φ _HR ≤ 360 °, preferably 330 ° ≤ φ _HR ≤ 360 ° .Mit increasing wrap angle can be made larger with the same built volume ratio, the pressure window area. In addition, this also shortens the axial extension of the auszuschiebenden Working chamber, the so-called profile pocket depth. This reduces the Ausschiebedrosselverluste especially at higher speeds and thus allows a better specific performance. However, too great a wrap angle has a disadvantageous effect on the overall 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, in an advantageous embodiment, a rotor pair is provided, which is designed and cooperates with one another such that a blow hole factor μ _{Bl is} at least 0.03% and at most 0.25%, preferably at most 0.2%,
in which ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$

and
wherein A _Bl an absolute pressure side Blaslochfläche and A6 and A7 gullet areas of the sub-rotor NR or of the main rotor (HR) denote, wherein the area A6 in an end sectional view between the profile curve of the slave 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 between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.

While the absolute size of the pressure-side blow hole alone does not make any meaningful statement about the effect on the leakage mass flows, a ratio of absolute pressure side blow hole 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 is much more meaningful. With regard to the illustration of the parameters, this is supplemented by FIG. 7b directed. The smaller the numerical value μ _Bl , the lower the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The pressure-side blow hole surface can thus be independent of the size of the screw compressor.

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

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

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 rotor pair is designed and matched to one another such that for a blow hole / profile gap length factor μ ₁ * μ _Bl $$\mathrm{0}.\mathrm{1}\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le \mathrm{1}.\mathrm{16}\%$$

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

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

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

μ _l denotes a profile gap length factor, wherein the length of the profile engagement gap of a tooth gap is set in relation to the profile depth PT ₁ . This can be a measure of the length of the profile engagement gap set regardless of the size of the screw machine. The smaller the numerical value of the characteristic μ _l is, the shorter is the profile gap at the same profile depth and thus the lower the leakage volume flow back to the suction side. From the factor μ _l * μ _Bl , the goal is to combine a small pressure-side blow hole with a short profile gap. However, the two ratios behave, as already mentioned, but in opposite directions.

It is also considered advantageous if main rotor (HR) and secondary rotor (NR) are designed and matched to one another such that a dry compression with a pressure ratio 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 of up to 20, in particular with a pressure ratio Π of greater than 1 and up to 20, achievable where the pressure ratio is the ratio of the discharge pressure to the suction pressure.

A further preferred embodiment provides a rotor pair, such that the main rotor (HR) with respect to a tip circle KK ₂ in the case of a dry compression at a peripheral speed in a range of 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 of 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 rotor pair, which is characterized in that a diameter ratio defined by the ratio of the head circle radii of the main rotor (HR) and 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 maintained, where Dk ₁ denotes the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ the diameter of the top circle KK _{2 of} the main rotor (HR).

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

In general, it is considered preferable that, in an end-sectional view, the teeth of the secondary rotor taper outwards, ie all circular arcs extending from the trailing tooth flank F _N towards a radial beam drawn from the center defined by the axis C 1 and drawn through the point F ₅ leading edge F _V starting from F1 to F2 in the sequence to remove radially outward (or at least in sections remain constant). In other words, in an end-sectional view, for all arc lengths b (r) of the respectively associated concentric circular arcs with the radius rf ₁ <r <rk ₁ and the common center defined by the axis C1 within each tooth of the auxiliary rotor, the respective concentric arcs apply leading tooth flank F _V and the trailing tooth flank F _{N are} limited so that the arc lengths b (r) monotonously decrease with increasing radius r.

The teeth of the secondary rotor are thus formed in this preferred embodiment so that no constrictions arise, so the width of a tooth of the secondary rotor increases at any point, but decreases radially outward or remains the same maximum. This is considered useful in order to achieve on the one hand a small pressure-side blowing hole with a short profile engagement gap length.

Advantageously, the front section design of the secondary rotor (NR) is made such that the effective direction of the torque, which results from a reference pressure on the working chamber limiting partial surface of the secondary rotor, is directed against the direction of rotation of the secondary rotor.

Such an endcut design causes the entire torque from the gas forces on the secondary rotor to be directed counter to the direction of rotation of the secondary rotor. As a result, a defined edge contact between the trailing secondary rotor edge F _N and the leading main rotor edge is achieved. This helps to avoid the problem of so-called rotor flapper, which can occur in unfavorable, in particular transient operating situations. Rotorklappern is understood to mean a uniform rotational movement superimposed advancing and lagging the secondary rotor about its axis of rotation, which is accompanied by a fast-changing impact of the trailing secondary rotor edges on the leading main rotor edges and then the leading secondary rotor edges on the trailing main rotor edges and so on. 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 endcut design.

In a concretely possible, optional embodiment, 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.

Preferably, in an end-face view, the profile of a tooth of the sub-rotor is asymmetrical with respect to the radial ray R drawn from the center defined by the axis C1 through the vertex F5. In the secondary rotor thus leading tooth flank and trailing tooth flank of each tooth are formed asymmetrically to each other.

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

mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR).A further preferred embodiment provides that, in an end-sectional view, a point C on the connecting path 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 where r _{1 is} the distance between K5 and C, and K4 is the point on the suction side of the line of action that is furthest from the link C 1 C 2 between C1 and C2, wherein 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 engagement line between the straight line section C 1 C 2 and the suction-side intersection edge can be influenced, among other things, the secondary rotor torque (= torque on the secondary rotor) and the Kammerausschub in the pressure window.
Characteristic features of the above course of the suction-side part of the engagement line 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 radii ratio r ₁ / r _{2 is} in the specified range, the working chamber is pushed out substantially completely into the pressure window.

bevorzugt 0,89 * (z₁/z₂) + 0,94 ≤ LHR/a ≤ 1,05 * (z₁/z₂) + 1,22, 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 rotor pair is designed and configured such that the following applies for a rotor length ratio L _HR / a: $$\mathrm{0}.\mathrm{85}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{0}.\mathrm{67}\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le \mathrm{1}.\mathrm{26}*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{1}}/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_{\mathrm{2}}\right)+\mathrm{1}.\mathrm{18}.$$

preferably 0.89 * (z ₁ / z ₂ ) + 0.94 ≤ LHR / a ≤ 1.05 * (z ₁ / z ₂ ) + 1.22, with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth in the main rotor (HR), where the rotor length ratio L _HR / a is the ratio of the Rotor length L _HR to the center distance a indicates and rotor length L _{HR is} the distance of the suction side main rotor rotor face to the pressure side main rotor rotor face.

The smaller the value of L _HR / a, the higher the bending stiffness of the rotors (with the same absorption volume). In the claimed range, the flexural rigidity of the rotors is sufficiently high that the rotors do not appreciably deflect during operation and therefore the gaps (between the rotors or between the rotors and the compressor housing) can be made relatively narrow without risking that the rotors start under unfavorable operating conditions (high temperatures and / or high pressures) together or start in the compressor housing. Narrow gaps offer the advantage of low backflow and thus contribute to energy efficiency. At the same time, the operational reliability is guaranteed despite small gaps. Also in the rotor manufacturing a high bending stiffness of the rotors to comply with the high demands on the shape tolerances is advantageous.

On the other hand, however, the ratio of L _HR / a is so large that the axial 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 concretely, the end faces of the rotors are not excessively large. As a result, on the one hand, the gap lengths can be kept small; thereby reducing backflow into previous working chambers and thereby improving energy efficiency. On the other hand, the axial forces resulting from the pressure-loaded end faces of the rotors can advantageously be kept small by small-sized end faces, these axial forces act in operation on the rotors and in particular on the rotor bearing. By minimizing these axial forces, the load on the (rolling) bearings can be minimized, or the bearings can be made smaller.

It can be advantageously further provided that in a front section view the tooth profile of the secondary rotor (NR) at its radially outer portion sections a circular arc with radius rk ₁ follows, ie several points of the leading tooth flank F _V and the trailing tooth flank F _N on the arc with Radius rk ₁ lie around the center defined by the axis C1, wherein preferred circular arc ARC ₁ 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 farthest point on the leading tooth flank of F5 on this arc and F5
wherein the radial ray R ₁₀ drawn between F10 and the midpoint of the minor rotor (NR) defined by the axis C1 contacts the front tooth flank F _V at at least one point or intersects at two points, cf. in particular the illustration in Fig. 7h ,

The above-described embodiment of the tooth profile of the secondary rotor is relevant above all for a tooth-number ratio of 3/4 or 4/5. With such a teeth number ratio, by keeping to the above-mentioned condition, the blow hole area can be reduced. When teeth number ratio 5/6 an aforementioned point of contact or aforementioned intersections with the leading tooth flank F _V, however, not desirable, since the teeth of the secondary rotor may then be too thin and consequently too flexible.

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

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

In general, it is also considered advantageous that in the propagated here selection of the profiles of secondary rotor and main rotor, it is possible to dispense with a Entlastungsnut / noise completely or make them smaller.

Due to the cross-sectional design of the two rotors is advantageously achieved that forms no chamber gusset volume between the two rotors when pushing out of the working chamber in the pressure window. The compression can be particularly efficient, since there is no backflow of already compressed medium on the suction side, and hereby no additional heat input is required. In addition, the entire compressed volume of downstream compressed air consumers can be used. The avoidance of overcompaction results in advantages for energy efficiency, for the smooth running of the compressor block and for the service life of the rotor bearings. Oil-injected compressors prevent squeezing of the oil, thus improving the smoothness of the compressor, reducing the load on the rotor bearings and reducing the stress on the oil.

In a further preferred embodiment, a shaft end of the main rotor is led out of the compressor housing and formed for connection to a drive, wherein preferably both shaft ends of the secondary rotor are 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 will be explained in more detail below with regard to further features and advantages with reference to the description of exemplary embodiments. Hereby show:

FIG. 1

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

FIG. 2

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

FIG. 3

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

FIG. 4

a fourth embodiment in an end-sectional view with a teeth number ratio 5/6.

FIG. 5

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

FIG. 6

FIG. 4 is an illustration of the isentropic block efficiency for the fourth embodiment for the 5/6 teeth pay ratio as compared to the prior art. FIG.

Figure 7a - 7k

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

FIG. 8

an illustration of the wrap angle at the main rotor.

FIG. 9

a schematic sectional view of an embodiment of a compressor block.

FIG. 10

an embodiment of an intermeshed rotor pair consisting of a main rotor and a side rotor in three-dimensional representation.

FIG. 11

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

Figures 12a, 12b

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

FIG. 13

the end section of the embodiment according to FIG. 1 to explain the profile profile of the main and secondary rotor in this embodiment.

FIG. 14

the end section of the embodiment according to FIG. 2 to explain the profile profile of the main and secondary rotor in this embodiment.

FIG. 15

the end section of the embodiment according to FIG. 3 to explain the profile profile of the main and secondary rotor in this embodiment.

FIG. 16

the end section of the embodiment according to FIG. 4 to explain the profile profile of the main and secondary rotor in this embodiment.

In the following, the embodiments according to the FIGS. 1 to 4 be explained. All four embodiments represent suitable profiles in the context 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 reproduced 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 cross-sectional main 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 illustrated exemplary embodiments: <u> Table 5 </ u> Compilation of further features and characteristics: feature 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 Toothburn ratio δ [%] 18.5 21.1 15.7% 15.2 Convex length fraction [%] 66.9% 71.2% 62.7% - Radial tooth thickness progression The tooth thickness of the slave rotor teeth decreases monotonously from the root radius rf ₁ to the tip circle 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 μ _Bl [%] 0,159 0.086 0.106 0.18 μBl * μl [%] 0.94 0.53 0.631 1,058 Profilstirnschnittgest tion with respect to chamber extension The working chamber can essentially be pushed out completely into the printing window. Profilstirnschnittgest ment with respect. In addition to rotor torque The effective direction of the resulting from the gas forces NR torque is directed counter to the direction of rotation of the secondary rotor. Shape of the intervention line 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 compared to the prior art is for the second embodiment to 3/4 teeth number ratio in FIG. 5 illustrated. There are two curves with the same pressure ratio.

The concrete reproduced pressure ratio is 2.0 (ratio of outlet pressure to inlet pressure). The isentropic block efficiency was significantly improved over the values achievable with the prior art.

In FIG. 6 Fig. 13 illustrates the isentropic block efficiency as compared with the prior art in the fourth embodiment (5/6 teeth number ratio). Again, two curves of equal pressure ratio are shown. The pressure ratio shown here is 9.0 (ratio of outlet pressure to inlet pressure). Here, too, the isentropic blocking efficiency could be significantly improved compared to the values obtainable with the prior art.

The in the Figures 5 and 6 each specified delivery quantity corresponds to the delivery volume flow of the compressor block based on the intake state.

• 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 given by the corresponding axes C1 and C2 centers. Furthermore, the main geometrical dimensions and main parameters of the front view are shown:

• Tip circle KK _{1 of} the secondary rotor with associated tip circle radius rk ₁ or tip circle diameter Dk ₁
• Head circle KK _{2 of} the main rotor with associated head circle radius rk ₂ or tip circle diameter Dk ₂
• Base circle FK _{1 of} the secondary rotor with associated root radius rf ₁ or root circle diameter Df ₁
• Base circle FK _{2 of} the main rotor with associated root radius rf ₂ or root 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 associated pitch circle radius rw ₁ or pitch circle diameter Dw ₁
• Rolling circle WK _{2 of} the main rotor with associated pitch circle radius rw ₂ or pitch circle diameter Dw ₂

Also shown are the direction of rotation 24 of the secondary rotor and the inevitably resulting direction of rotation of the main rotor 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. Representing all tooth spaces of the secondary rotor, a tooth gap 23 is marked. The basis of Figure 7a shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to the basis of the FIG. 4 for a teeth ratio of 5/6 explained embodiment.

FIG. 7b shows in a cross-sectional view, the tooth space surfaces A6 and A7 and a side view of a blow hole. In the FIG. 7b to illustrate the tooth gap surfaces A6 and A7 profiles shown correspond to that for a teeth ratio of 3/4 based on FIG. 1 illustrated embodiment.

Further shows Fig. 7b the location of the coordinate system of Fig. 7k illustrated Blaslochfläche 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 pressure-side intersection edge 11.

The pressure-side blowing hole lies in the described coordinate system and quite concretely 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 engagement line 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 connection line.

K2 denotes the point of the pressure-side part of the engagement line 10 which is furthest from the straight line through C1 and C2.
The intersection of the head circles of the two rotors creates a pressure-side intersection edge 11 and a suction-side intersection edge 12 Fig. 7b is the pressure-side intersection edge 11 in one Foresight view shown as a point. The same applies to the representation of the suction-side intersection edge 12th

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

FIG. 7c shows in a cross-sectional view, a tooth of the sub-rotor with the running inside the rotor tooth concentric arcs B ₂₅ , B ₅₀ , B ₇₅ 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 bounded by the leading tooth flank F _V and the trailing tooth flank F _N. The basis of FIG. 7c shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to the basis of the FIG. 4 for a teeth ratio of 5/6 explained embodiment.

FIG. 7d shows in an end-sectional view between the considered tooth of the sub rotor and the adjacent tooth of the sub rotor foot points F1 and F2 at the root circle and at the radially outermost point of the tooth apex F5. Furthermore, the defined by the points F1, F2 and F5 triangle D _{Z is} shown.

• Zahnteilfläche A1 entspricht der Fläche, mit der der betrachtete Zahn mit seiner zwischen F5 und F2 ausgebildeten vorlaufenden Zahnflanke F_V über das Dreieck D_Z in einem radial äußeren Bereich übersteht.
• Zahnteilfläche A2 entspricht der Fläche, mit der der betrachtete Zahn mit seiner zwischen F5 und F1 ausgebildeten nachlaufenden Zahnflanke F_N über das Dreieck D_Z in einem radial äußeren Bereich übersteht.
• Fläche A3 entspricht der Fläche, mit der der betrachtete Zahn mit seiner zwischen F5 und F2 ausgebildeten vorlaufenden Zahnflanke gegenüber dem Dreieck D_Z zurücktritt.

FIG. 7d shows the following (tooth part) surfaces:

• Part of tooth surface A1 corresponds to the area with which the considered tooth, with its leading tooth flank F _V formed between F5 and F2, projects beyond the triangle D _Z in a radially outer area.
• Part of tooth surface A2 corresponds to the surface with which the considered tooth, with its trailing tooth flank F _N formed between F5 and F1, projects beyond the triangle D _Z in a radially outer region.
• Area A3 corresponds to the area with which the tooth in question with its leading tooth flank formed between F5 and F2 recedes with respect to the triangle D _Z.

Also shown is the tooth pitch angle γ corresponding to 360 ° / number of teeth of the sub rotor. The basis of FIG. 7d shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to the basis of the FIG. 4 for a teeth ratio of 5/6 explained embodiment.

Figure 7e shows in a cross-sectional view, the cross-sectional area A0 of a tooth of the sub-rotor, which is bounded by the running between F1 and F2 circular arc B around the center C1. The basis of Figure 7e shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to the basis of the FIG. 4 for a teeth ratio of 5/6 explained embodiment.

Figure 7f shows in an end-sectional view the offset angle β. This is defined by the offset from point F11 to point F12 considered in the direction of rotation of the secondary rotor. F11 is a point on the half circular arc B between F1 and F2 around the center point C1 and accordingly 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 ray R drawn from the center C1 to the vertex F5 with the arc B. The basis of FIG Figure 7f shown profile profile of the leading tooth flank F _V and the trailing tooth flank F _N corresponds to the basis of the FIG. 4 for a teeth ratio of 5/6 explained embodiment.

FIG. 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 between the head and root circle changes.

The trailing tooth flank F _{N of} the sub rotor is subdivided by the point F8 into a substantially convexly curved portion between F8 and the vertex F5 and a substantially concavely curved portion between F8 and the root F1.

FIG. 7h shows in a cross-sectional view two intersections of the radial beam R ₁₀ from C1 to F10 with the leading tooth flank F _{V of} the sub rotor, the point F10 that point of the leading tooth flank F _V , which lies on the head circle KK ₁ with rk ₁ and furthest from F5 is spaced. The tooth flank follows radially outside so over a defined section of a circular arc ARC ₁ with radius rk ₁ to the defined by the axis C1 center of the secondary rotor. The basis of FIG. 7h explained profile curves of the leading tooth flank F _V and the trailing tooth flank F _N correspond to the embodiment described for a tooth ratio of 3/4 FIG. 1 ,

FIG. 7i shows in a cross-sectional view the tooth profile divided by the radial beam R drawn from C1 to F5.

Specifically, in the illustrated embodiment, the tooth profile is divided into an area portion A4 associated with the trailing tooth flank FN and an area portion A5 associated with the leading tooth flank F _V. The basis of FIG. 7i explained profile curves of the leading tooth flank F _V and the trailing tooth flank F _N correspond to the embodiment described for a teeth ratio of 5/6 FIG. 4 ,

FIG. 7j shows in an end-sectional view, the engagement line 10 between the main and secondary rotor 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 engagement line.

The engagement line 10 is divided into two sections by the connection path between the first axis C1 and the second axis C2: the suction-side part of the engagement line is below, the pressure-side part above the connection path 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 engagement line which is farthest from the connection path between C1 and C2.

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

FIG. 7k:

FIG. 7k shows a pressure-side Blaslochfläche A _{Bl of} a working chamber in a sectional view perpendicular to the rotor end faces. The limitation of the Blaslochfläche A _Bl arises here from the cut line 27 of the imaginary planar surface as described above with the leading female rotor flank F _v, the cut line 26 of the plane with the trailing HR-edge and a line segment [K1 K3] of the pressure side intersection edge. 11

• 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 discharge-side blow hole is located in the Fig. 7b described flat surface and is spanned by

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

In FIG. 8 is the repeatedly addressed wrap φ again illustrated. Specifically, it is the angle φ, around which the endcut is twisted from the suction side to the pressure side rotor end face. This is illustrated 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.

FIG. 9 shows a schematic sectional view of a compressor block 19 comprising a housing 15 and stored therein two mutually paired rotors, 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. A drive power can be applied to a shaft 17 of the main rotor HR, for example with a motor (not shown) via a coupling 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 over the rotor flanks. In contrast to can be avoided in a dry screw compressor touching the rotor edges by means of a synchronization gear (not shown).

Also not shown are an intake for sucking the medium to be compressed and an outlet for the compressed medium.

In FIG. 10 are still a toothed main rotor HR and side rotor NR shown in a perspective view.

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

The total torque from the gas forces on the secondary rotor is composed of the sum of the torque effects of the gas pressures in all working chambers on the sub-surfaces of the sub-rotor which delimit the respective working chambers. In Fig. 12a is such, a working chamber limiting partial surface (22) of the secondary rotor shown by hatching example.

FIG. 12b shows the breakdown of in FIG. 12a illustrated a working chamber limiting part surface (22) in a dotted surface (28) and a cross-hatched surface (29). Only the cross-hatched area (29) contributes to the torque.

The sub-surface (22) results from the actual Stirnschnittgestaltung and the slope of the secondary rotor. The slope of the secondary rotor refers to the pitch of the helical toothing of the secondary rotor. In the Fig. 12a Also shown, the partial surface limiting three-dimensional engagement line (10) is also determined by the front section design of the secondary rotor and the slope.

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

The dependent on the angular position of the secondary rotor to the main rotor concrete length of a working chamber in the direction of the rotor axis between the Nebenrotorstirnfläche (20) on the one hand and the boundary by the three-dimensional line of action (10) and cutting line (27) on the other hand does not play an essential role, 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 shown dotted), make no contribution to the torque. The slope of the secondary rotor affects only the amount, but not on the effective direction of the torque.

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

Only the in Fig. 12b crosshatched surface (29) contributes to the torque.

Thus, in each working chamber, the effective direction of the torque, which causes the gas pressure in the working chamber (or any reference pressure) on the working chamber limiting partial surface of the secondary rotor, determined by the Stirnschnittgestaltung the secondary rotor.

The above-described advantageous front section design of the secondary rotor (NR) therefore leads for each working chamber limiting part surface (22) of the secondary rotor and thus for the entire secondary rotor to a direction of action (25) of the torque from the gas forces, which counter to the direction of rotation (24) of the secondary rotor is directed, whereby the Rotorklappern is effectively avoided.

The illustrated embodiments show that with the present invention, a considerable increase in efficiency for a rotor pair used in screw machines consisting of main rotor and secondary rotor could be achieved with a corresponding profile geometry.

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

Although it will be readily possible for the person skilled in the art on the basis of the specified parameter values to produce suitable profile profiles with the methods customary in the prior art, the profile profiles in the exemplary embodiments discussed above will be described below purely by way of example FIGS. 1 to 4 explained in more detail. To generate profile profiles, profile profiles can also be generated by means of publicly available computer programs, as is well known to the person skilled in the art.

By way of example, SV_Win, a project of the Vienna University of Technology, is described in this context, this software being described in great detail in the abovementioned Habilitationsschrift by Grafinger. An alternative, publicly available computer program also includes the DISCO software and, in particular, the SCORPATH module of the City University of London (Center for Positive Displacement Compressor Technology). For general information, see http://www.city-compressors.co. uk /. Information about 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 software ScrewView, which is also available in the Dissertation "Directed Evolutionary Algorithms" by Stefan Berlik, Dortmund 2006 (p. 173 f .) mentioned. The ScrewView software is described in more detail on the website http://pi.informatik.unisiegen.de/Mitarbeiter/berlik/projekte/ in connection with the project "Method for designing dry-running rotary displacement machines".

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

The section S5 to S6 is defined by a circular arc about the center C1. The subsequent section S6 to S7 is given by a circular arc around the center M3. Finally, the section S7 to S1 is defined by an envelope to a trochoid generated by the circular arc section T7 to T1 around the center M5 on the main rotor HR. The above-described sections seamlessly join each other in the given order. The tangents at the end of each section and at the beginning of the adjacent section are the same. The sections go so far directly, stepless and kink-free into each other.

The profile profile of the teeth of the main rotor HR is for the embodiment of the FIGS. 1 to 4 also on the basis of FIGS. 13 to 16 briefly explained below. The section T1-T2 results from a circular arc on the main rotor HR about the center C2 on the main rotor HR. The section T2-T3 is defined by the 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 sub rotor NR. The section T4-T5 is given by an envelope to a trochoid generated by the section S4-S5 on the sub rotor. The section T5-T6 is defined by a circular arc around the center point C2 generated by the circular arc section S5-S6 about the center point C1 on the sub rotor NR. The section T6-T7 results from an envelope to a trochoid generated from the section S6-S7 on the sub rotor NR. Finally, the section T7-T1 is defined by a circular arc around the center point M5. Here too, the above-mentioned sections seamlessly connect to each other in the given order. The tangents at the end of each section and at the beginning of the adjacent section are the same. The sections go so far directly, stepless and kink-free into each other.

In general, it should be noted that the profile curves of secondary rotor NR and main rotor HR are of course matched to one another and inasmuch as the envelopes correspond to a trochoid each circular arc sections on the counter rotor. In addition, as already mentioned, a tangential transition from one section to the next is ensured. A general Procedure in the calculation of the profile profile of the counter-rotor is for example in the Dissertation by Helpertz, "Method for 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 $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
   
   mindestens 0,5, bevorzugt mindestens 0,515, und höchstens 0,65, 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 $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
   
   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 FN 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 FN 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 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 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 $\delta =\frac{\beta }{\gamma }\ast 100\left[\%\right]\mathrm{.}$
   
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 FN zugeordneten Flächenanteil A4 teilt und
   wobei $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{14}$$
   
   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 ${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$
    
    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 l_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und $${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
    
    wobei A_BI 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: $$\mathrm{0},\mathrm{75}\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{1}}\le \mathrm{0},\mathrm{85}\mathrm{und}/\mathrm{<figure-callout\; id="0"\; label="oder"\; filenames="imgf0004.png"\; state="\{\{state\}\}">oder</figure-callout>}\mathrm{0},\mathrm{65}\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{2}}\le \mathrm{0},\mathrm{74.}$$
    
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 FN 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 $\delta =\frac{\beta }{\gamma }\ast 100\left[\%\right]\mathrm{.}$
    
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 ${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$
    
    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 l_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und $${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
    
    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: $$\mathrm{0},\mathrm{76}\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{1}}\le \mathrm{0},\mathrm{86}\mathrm{und}/\mathrm{<figure-callout\; id="0"\; label="oder"\; filenames="imgf0004.png"\; state="\{\{state\}\}">oder</figure-callout>}\mathrm{0},\mathrm{62}\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{2}}\le \mathrm{0},\mathrm{72.}$$
    
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 F1 und 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 $\delta =\frac{\beta }{\gamma }\ast 100\left[\%\right]\mathrm{.}$
    
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 ${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$
    
    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 l_sp die Länge des Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnet
    und $${\mathit{\mu }}_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
    
    
    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: $$0,9\le \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\le 0,875\times \frac{z_1}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2}+0,22$$
    
    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: $$0,85*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_1/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right)+0,67\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 1,26*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_1/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right)+1,18,$$
    
    bevorzugt 0,89 * (z₁/z₂) + 0,94 ≤ LHR/a ≤ 1,05 * (z₁/z₂) + 1,22,
    mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR), wobei das Rotorlängenverhältnis LHR/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. A rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
   wherein the number of teeth (z ₂ ) in the main rotor (HR) 3 and the number of teeth (z ₁ ) in the secondary rotor (NR) is 4,
   the relative tread 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 0.65, preferably at most 0.595, wherein it is at rk ₁ to a drawn around the outer circumference of the secondary rotor (NR) tip radius and at rf ₁ by a profile base of the secondary rotor attaching Root radius,
   wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the tip circle 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 1.636, and at most 1.8, preferably at most 1.733, wherein preferably the main rotor is formed with a wrap angle φ _HR , for which applies 240 ° ≤ φ _HR ≤ 360 °, and preferably applies to a rotor length ratio L _HR / a : $$1.4\le L_{\mathit{MR}}/a\le 3.4.$$
   
   wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face.
2. 2. rotor pair according to aspect 1, characterized
   that in a cross-sectional view within a secondary rotor tooth extending circular arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is given by the axis C1, are defined, wherein the radius r ₂₅ of B _{25 is} 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 wherein the circular arcs B ₂₅ , B ₅₀ , B _{75 are} each bounded by the leading tooth flank F _V and trailing tooth flank FN, wherein tooth thickness ratios 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 are} defined and the following dimensioning is complied with:
   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. pair of rotors according to aspect 1 or 2, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the respective adjacent tooth of the sub rotor foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
   where by F1, F2 and F5 a triangle D _{Z is} defined and
   wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank FN with an area A2 on the triangle D _Z and
   where 8 ≤ A2 / A1 ≤ 60 is maintained.
4. 4. pair of rotors according to one of the aspects 1 to 3, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the respective adjacent tooth of the sub rotor feet F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined .
   where by F1, F2 and F5 a triangle D _{Z is} defined and
   wherein 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 _recedes with a surface A3 in a radially inner region opposite to the triangle D _Z , and wherein 7.0 ≤ A3 / A1 ≤ 35 are complied with.
5. Rotor pair according to one of the aspects 1 to 4, characterized in that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
   where by F1, F2 and F5 a triangle D _{Z is} defined and
   wherein 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,
   the tooth itself has a cross-sectional area A0 bounded by the arc B running between F1 and F about the center defined by the axis C1, and
   where 0.5% ≤ A1 / A0 ≤ 4.5% is maintained.
6. 6. pair of rotors according to one of aspects 1 to 5, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex 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 minor rotor (NR) about the center defined by the axis C1,
   wherein a point F11 is defined on the half circular arc B between F1 and F2,
   wherein a radial ray R drawn from the midpoint of the sub rotor (NR) defined by the axis C1 through the vertex F5 intersects the arc B at a point F12,
   wherein an offset angle β is defined by the offset of F11 to F12 considered in the direction of rotation of the sub rotor (NR), and
   in which $$14\%\le \mathrm{\delta }\le 25\%$$
   
   is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$
   
7. 7. Rotor pair according to one of the aspects 1 to 6, characterized in that in a front view section formed between F1 and F5 trailing tooth flank F _{N of} a tooth of the sub rotor (NR) has a convex length portion of at least 45% to at most 95%.
8. 8. rotor pair according to one of aspects 1 to 7, characterized in that in a front section view of the axis C1 of the sub rotor (NR) by F5 drawn radial beam, the tooth profile in a leading edge of the tooth F _V associated surface portion A5 and one of the trailing tooth flank FN assigned area share A4 shares and
   in which $$\mathrm{5}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{14}$$
   
   is complied with.
9. 9. rotor pair according to one of aspects 1 to 8, characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 290 ° ≤ φ _HR ≤ 360 °, preferably 320 ° ≤ φ _HR ≤ 360 °.
10. 10. Rotor pair according to one of 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 ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    where A _Bl denotes an absolute pressure-side blow hole area and A6 and A7 tooth spaces of the secondary rotor (NR) and the main rotor (HR), wherein the area A6 in an end-sectional view between the profile profile of the secondary rotor (NR) between two adjacent vertices F5 and the top circle KK ₁ enclosed area and the area A7 in an end-sectional view denote between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
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 l _sp denotes 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 $${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$$
    
    where A _{BI is} an absolute blow hole area and A6 and A7 profile surfaces of the secondary rotor (NR) and the main rotor (HR), wherein the surface A6 in an end-sectional view 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 between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
12. 12. rotor pair according to one of aspects 1 to 11, characterized in that the main rotor (HR) and secondary rotor (NR) are designed and matched to one another that a dry compression with a pressure ratio Π of up to 3, in particular with a pressure ratio Π greater can be achieved as 1 and up to 3, wherein the pressure ratio is the ratio of compression end pressure to suction pressure, is achievable.
13. 13. Rotor pair according to one of the aspects 1 to 12, characterized in that the main rotor (HR) based on a tip circle KK ₂ with a peripheral speed in a range of 20 to 100 m / s is operable.
14. 14. Rotor pair according to one of the aspects 1 to 13, characterized in that for a by the ratio of the head circle radii of main rotor (HR) and secondary rotor (NR) defined diameter ratio $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.145\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.30$$
    
    is complied with, wherein Dk ₁ the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denote the diameter of the top circle KK _{2 of} the main rotor (HR).
15. 15 rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a about a first axis (C1) rotating secondary rotor (NR) and about a second axis (C2) rotating main rotor (HR),
    wherein the number of teeth (z ₂ ) in the main rotor (HR) 4 and the number of teeth (z ₁ ) in the secondary rotor (NR) is 5,
    the relative tread 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 radius beginning at the base of the profile of the secondary rotor,
    wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the head radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    at least 1.683, and at most 1.836, preferably at most 1.782,
    wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which 240 ° ≤ φ _HR ≤ 360 °, and where preferably for a rotor length ratio L _HR / a, the following applies: $$1.4\le L_{\mathit{MR}}/a\le 3.3.$$
    
    wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face.
16. 16. Rotor pair according to aspect 15, characterized
    that in an end-face view within a sub rotor tooth extending arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is C1, where the radius r ₂₅ of B ₂₅ is 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 limited in each case by the leading tooth flank F _V and trailing tooth flank F _N ,
    wherein 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 design is observed: $$\mathrm{0}.\mathrm{75}\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{1}}\le \mathrm{0}.\mathrm{85}\mathrm{and}/\mathrm{or}\mathrm{0}.\mathrm{65}\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{2}}\le \mathrm{0}.\mathrm{74th}$$
    
17. 17 rotor pair according to aspect 15 or 16, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the respective adjacent tooth of the sub rotor (NR) foot points F1 and F2 and defined at the radially outermost point of the tooth a vertex F5 are,
    where by F1, F2 and F5 a triangle D _{Z is} defined and
    wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank FN with an area A2 on the triangle D _Z and
    where 6 ≤ A2 / A1 ≤ 15 is maintained.
18. 18. Rotor pair according to one of the aspects 15 to 17, characterized in that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    where by F1, F2 and F5 a triangle D _{Z is} defined 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 _recedes with a surface A3 in a radially inner region opposite to the triangle D _Z and wherein 9.0 ≤ A3 / A1 ≤ 18 is complied with.
19. 19 rotor pair according to one of the aspects 15 to 18, characterized in that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR) feet F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    where by F1, F2 and F5 a triangle D _{Z is} defined and
    wherein 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,
    the tooth itself has a cross-sectional area A0 bounded by the arc B running between F1 and F about the center defined by the axis C1, and
    where 1.5% ≤ A1 / A0 ≤ 3.5% is maintained.
20. Rotor pair according to one of the aspects 15 to 19, characterized in that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of the teeth of the minor rotor NR about the center defined by the axis C1,
    wherein a point F11 is defined on the half circular arc B between F1 and F2,
    wherein a radial ray R drawn from the midpoint of the sub rotor (NR) defined by the axis C1 through the vertex F5 intersects the arc B at a point F12,
    wherein an offset angle β is defined by the offset of F11 to F12 considered in the direction of rotation of the sub rotor (NR), and
    in which $$14\%\le \mathrm{\delta }\le 18\%$$
    
    is complied with $\delta =\frac{\beta }{\gamma }*100\left[\%\right]\mathrm{,}$
    
21. 21. Rotor pair according to one of the aspects 15 to 20, characterized in that in an end-sectional view formed between F1 and F5 trailing tooth flank F _{N of} a tooth of the secondary rotor (NR) has a convex length portion of at least 55% to at most 95%.
22. 22. Rotor pair according to one of the aspects 15 to 21, characterized in that in an end-sectional view of the axis C1 of the secondary rotor (NR) radial line drawn by F5 divides the tooth profile into a surface portion A5 assigned to the leading tooth flank F _V and an area portion A4 assigned to the trailing tooth flank F _N , and wherein $$\mathrm{4}\le \mathrm{A}\mathrm{4}/\mathrm{A}\mathrm{5}\le \mathrm{9}$$
    
    is complied with.
23. 23 rotor pair according to one of the aspects 15 to 22, characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 320 ° ≤ φ _HR ≤ 360 °, preferably 330 ° ≤ φ _HR ≤ 360 °.
24. 24. 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 ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    wherein A _Bl an absolute pressure side Blaslochfläche and A6 and A7 gullet areas of the sub-rotor NR or of the main rotor (HR) denote, wherein the area A6 in an end sectional view between the profile curve of the slave 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 between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
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 l _sp denotes 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 $${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$$
    
    where A _{Bl is} an absolute blow hole area and A6 and A7 profile surfaces of the secondary rotor (NR) and the main rotor (HR), wherein the surface A6 in an end-sectional view 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 between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
26. 26 rotor pair 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 that a 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, is achievable, wherein the pressure ratio is the ratio of compression end pressure to suction pressure.
27. 27 rotor pair according to one of the aspects 15 to 26, characterized in that in the case of a dry compression of 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 of the main rotor formed on a top circle KK ₂ with a peripheral speed in a range of 5 to 50 m / s operable.
28. 28 rotor pair according to one of the aspects 15 to 27, characterized in that for a defined by the ratio of the head circle radii of main rotor (HR) and secondary rotor (NR) diameter ratio $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.195\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.33$$
    
    is complied with, where Dk ₁ denote the diameter of the top circle KK _{1 of} the secondary rotor (NR) and DK ₂ the diameter of the top circle KK _{2 of} the main rotor (HR).
29. 29. 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),
    wherein the number of teeth (z ₂ ) in the main rotor (HR) is 5 and the number of teeth (z ₁ ) in the secondary rotor (NR) is 6,
    the relative tread depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    at least 0.44 and at most 0.495, preferably at most 0.48, wherein rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is a root radius starting at the base of the profile of the secondary rotor,
    wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the head radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    at least 1.74, preferably at least 1.75, and at most 1.8, preferably at most 1.79, is,
    wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which 240 ° ≤ φ _HR ≤ 360 °, and where preferably for a rotor length ratio L _HR / a, the following applies: $$1.4\le L_{\mathit{MR}}/a\le 3.2.$$
    
    wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face.
30. 30. Rotor pair according to aspect 29, characterized
    in that a circular cross-section B ₂₅ , B ₅₀ , B ₇₅ whose common center point is C ₁ is defined in an end-face view within a secondary rotor tooth, wherein the radius r ₂₅ of B _{25 has} 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 Circular arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and trailing tooth flank F _N ,
    wherein 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 design is observed: $$\mathrm{0}.\mathrm{76}\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{1}}\le \mathrm{0}.\mathrm{86}\mathrm{and}/\mathrm{or}\mathrm{0}.\mathrm{62}\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_{\mathrm{2}}\le \mathrm{0}.\mathrm{72nd}$$
    
31. 31 rotor pair according to aspect 29 or 30, characterized in that defined in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are,
    where by F1, F2 and F5 a triangle D _{Z is} defined and
    wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank F _N with a surface A2 on the triangle D _Z and
    where 4 ≤ A2 / A1 ≤ 7 is maintained.
32. 32. rotor pair according to one of the aspects 29 to 31, characterized in that in an end-sectional view between the considered tooth of the secondary rotor (NR) and the adjacent tooth of the secondary rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    where by F1, F2 and F5 a triangle D _{Z is} defined 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 recedes in a radially inner region opposite to the triangle D _Z with an surface A3 and wherein 8 ≤ A3 / A1 ≤ 14 is complied with.
33. 33. rotor pair according to one of the aspects 29 to 32, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    where by F1, F2 and F5 a triangle D _{Z is} defined and
    wherein 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,
    the tooth itself has a cross-sectional area A0 bounded by the arc B running between F1 and F about the center defined by the axis C1, and
    where 1.9% ≤ A1 / A0 ≤ 3.2% is maintained.
34. 34. rotor pair according to one of the aspects 29 to 33, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are defined,
    wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of the teeth of the minor rotor NR about the center defined by the axis C1,
    wherein a point F11 is defined on the half circular arc B between F1 and F2,
    wherein a radial ray R drawn from the midpoint of the sub rotor (NR) defined by the axis C1 through the vertex F5 intersects the arc B at a point F12,
    wherein an offset angle β is defined by the offset of F11 to F12 considered in the direction of rotation of the sub 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. rotor pair according to one of the aspects 29 to 34, characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 320 ° ≤ φ _HR ≤ 360 °, preferably 330 ° ≤ φ _HR ≤ 360 °.
36. 36. Rotor pair 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 ${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$
    
    and
    wherein A _Bl an absolute pressure side Blaslochfläche and A6 and A7 gullet areas of the sub-rotor NR or of the main rotor (HR) denote, wherein the area A6 in an end sectional view between the profile curve of the slave 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 between the profile profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
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 l _sp denotes 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 $${\mathit{\mu }}_{\mathit{bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">bl\; </figure-callout>}}}{A}*100\left[\%\right]$$
    
    
    where A _{Bl is} an absolute blow hole area and A6 and A7 profile surfaces of the secondary rotor (NR) and the main rotor (HR), wherein the surface A6 in an end-sectional view 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 profile of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ enclosed area.
38. 38. rotor pair according to one of the aspects 29 to 37, characterized in that the main rotor (HR) and secondary rotor (NR) are designed and matched to one another that a 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 20, in particular with a pressure ratio Π of greater than 1 and up to 20, can be achieved, wherein the pressure ratio is the ratio of compression end pressure to suction pressure.
39. 39. rotor pair 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 at a peripheral speed in a range of 20 to 100 m / s and in the case of a fluid-injected compression is designed operable with a peripheral speed in a range of 5 to 50 m / s.
40. 40. Rotor pair according to one of the aspects 29 to 39, characterized in that for a by the ratio of the head circle radii of the main rotor (HR) and secondary rotor (NR) defined diameter ratio $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="dk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="dk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$
    
    $$1.19\le {\mathrm{<figure-callout\; id="1"\; label="D\; v\; \le "\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">D\; </figure-callout>}}_v\le 1.26$$
    
    is complied with, wherein Dk ₁ the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denote the diameter of the top circle KK _{2 of} the main rotor (HR).
41. 41. rotor pair according to one of the aspects 1 to 40, characterized in that in an end-sectional view extending within a tooth of the sub-rotor arc lengths b (r) of each associated concentric circular arcs with the radius rf ₁ <r <rk ₁ and the common, by the axis C1 defined center are each bounded by the leading tooth flank F _V and the trailing tooth flank F _N and decrease the arc lengths b (r) monotonously with increasing radius r.
42. 42. rotor pair according to one of the aspects 1 to 41, characterized in that the Stirnschnittgestaltung the sub rotor (NR) is made such that the effective direction of the torque, which results from a reference pressure on a working chamber delimiting part surface of the sub rotor opposite to the direction of rotation of Side rotor is directed.
43. 43. rotor pair according to one of aspects 1 to 42, characterized in that the main rotor (HR) and secondary rotor (NR) for conveying air or inert gases, such as helium or nitrogen, are formed and matched.
44. 44. rotor pair according to one of the aspects 1 to 43, characterized in that in an end-sectional view, the profile of a tooth of the sub-rotor with respect to the center of the axis defined by the axis C1, through the apex F5 drawn radial beam R is formed asymmetrically.
45. 45. rotor pair according to one of the aspects 1 to 44, characterized in that in a cross-sectional view, a point C on the link ( 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 link ( C 1 C 2 ), where r ₁ measures the distance between K5 and C,
    and K4 denotes the point of the suction-side part of the engagement line furthest from the connection path C 1 C 2 between C1 and C2, wherein 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).
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: $$0.85*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_1/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right)+0.67\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 1.26*\left({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">z</figure-callout>}}_1/{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}_2\right)+1.18.$$
    
    preferably 0.89 * (z ₁ / z ₂ ) + 0.94 ≤ LHR / a ≤ 1.05 * (z ₁ / z ₂ ) + 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 LHR / a indicates the ratio of the rotor length L _HR to the center distance a and rotor length L _HR the distance between the main rotor on the intake side Rotor end face to the pressure side main rotor rotor face is.
47. 47. Rotor pair according to one of the aspects 1 to 28, characterized in that in a cross-sectional view, the tooth profile of the secondary rotor (NR) at its radially outer portion sections a circular arc ARC ₁ with radius rk ₁ follows, ie several points of the leading tooth flank F _V and the trailing tooth flank F _N lie on the circular arc of radius rk ₁ about the center defined by the axis C1, wherein preferably the circular arc ARC ₁ 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 farthest point on the leading tooth flank of F5 on this arc and F5
    wherein the radial ray R ₁₀ drawn between F10 and the midpoint of the minor rotor (NR) defined by the axis C1 contacts the leading tooth flank F _V at at least one point or intersects at two points.
48. 48. compressor block comprising a compressor housing (15) and a pair of rotors according to one of aspects 1 to 47, wherein the pair of rotors comprises a main rotor (HR) and a secondary rotor (NR), each rotatably mounted in the compressor housing (15).
49. 49. compressor block according to aspect 48, characterized in that the Stirnschnittgestaltung is made such that between the tooth profiles of the main rotor (HR) and secondary rotor (NR) formed working chamber can be pushed out substantially 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 (21)

Rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
wherein the number of teeth (z ₂ ) in the main rotor (HR) 3 and the number of teeth (z ₁ ) in the secondary rotor (NR) is 4,
the relative tread depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{rf}}_1}{{\mathrm{rk}}_1}$$

is at least 0.5, preferably at least 0.515, and at most 0.65, preferably at most 0.595, wherein it is at rk ₁ to a drawn around the outer circumference of the secondary rotor (NR) tip radius and at rf ₁ by a profile base of the secondary rotor attaching Root radius,
wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the tip circle radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{rk}}_1}$$

is at least 1.636, and at most 1.8, preferably at most 1.733, wherein preferably the main rotor is formed with a wrap angle φ _HR , for which applies 240 ° ≤ φ _HR ≤ 360 °, and wherein in a Foresight view a point C on the link ( 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 link ( C 1 C 2 ), where r ₁ measures the distance between K5 and C,
and K4 denotes the point of the suction-side part of the engagement line furthest from the connection path C 1 C 2 between C1 and C2, wherein 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 claim 1, characterized in that 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 of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face. Rotor pair according to claim 1 or 2, characterized
that in a cross-sectional view within a secondary rotor tooth extending circular arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is given by the axis C1, are defined, wherein the radius r ₂₅ of B _{25 is} 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 wherein the arcs B ₂₅ , B ₅₀ , B _{75 are} each bounded by the leading tooth flank F _V and trailing tooth flank F _N , wherein tooth thickness ratios 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 are} defined and the following dimensioning is complied with:
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. Pair of rotors according to any of claims 1 to 3, characterized in that in an end-sectional view between the observed tooth of the slave rotor (NR) and the respective adjacent tooth of the slave rotor base points F1 and F2 and at the radially outermost point of the tooth, a vertex defined F5
where by F1, F2 and F5 a triangle D _{Z is} defined and
wherein in a radially outer region of the tooth with its formed between F5 and F2 leading tooth flank F _V with a surface A1 and with its trailing formed between F1 and F5 tooth flank F _N with a surface A2 on the triangle D _Z and
where 8 ≤ A2 / A1 ≤ 60 is maintained. Rotor pair defines a vertex F5 according to any one of claims 1 to 4, characterized in that in an end-sectional view between the observed tooth of the slave rotor (NR) and the respective adjacent tooth of the slave rotor (NR) base points F1 and F2 and at the radially outermost point of the tooth 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 minor rotor (NR) about the center defined by the axis C1,
wherein a point F11 is defined on the half circular arc B between F1 and F2,
wherein a radial ray R drawn from the midpoint of the sub rotor (NR) defined by the axis C1 through the vertex F5 intersects the arc B at a point F12,
wherein an offset angle β is defined by the offset of F11 to F12 considered in the direction of rotation of the sub rotor (NR), and
in which $$14\%\le \mathrm{\delta }\le 25\%$$

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

Rotor pair according to one of claims 1 to 5, characterized in that in an end-sectional view the formed between F1 and F5 trailing tooth flank F _{N of} a tooth of the secondary rotor (NR) has a convex length portion of at least 45% to at most 95%. Rotor pair according to one of claims 1 to 6, characterized in that for a by the ratio of the head circle radii of main rotor (HR) and secondary rotor (NR) defined diameter ratio $$D_v=\frac{{\mathit{dk}}_2}{{\mathit{dk}}_1}=\frac{{\mathit{rk}}_2}{{\mathit{rk}}_1}$$

$$1.145\le D_v\le 1.30$$

is complied with, wherein Dk ₁ the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denote the diameter of the top circle KK _{2 of} the main rotor (HR). Rotor pair according to one of claims 1 to 7, characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 290 ° ≤ φ _HR ≤ 360 °, preferably 320 ° ≤ φ _HR ≤ 360 °. Rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
wherein the number of teeth (z ₂ ) in the main rotor (HR) 4 and the number of teeth (z ₁ ) in the secondary rotor (NR) is 5,
the relative tread depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{rf}}_1}{{\mathrm{rk}}_1}$$

at least 0.5, preferably at least 0.515 and at most 0.58, is, which is ₁ drawn to an around the outer circumference of the secondary rotor (NR) tip circle radius and rf ₁ is a accreting on the basic profile of the female rotor root circle radius at rk,
wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the head radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{rk}}_1}$$

at least 1.683, and at most 1.836, preferably at most 1.782,
wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which 240 ° ≤ φ _HR ≤ 360 °, and wherein in a front-sectional view a point C on the connecting path (FIG. 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 link ( C 1 C 2 ), where r ₁ measures the distance between K5 and C,
and K4 denotes the point of the suction-side part of the engagement line furthest from the connection path C 1 C 2 between C1 and C2, wherein 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 claim 9, characterized
that applies to a rotor length ratio LHR / a: $$1.4\le L_{\mathit{MR}}/a\le 3.3.$$

wherein the rotor length ratio is formed of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face. Rotor pair according to claim 9 or 10, characterized
that in an end-face view within a secondary rotor tooth extending circular arcs B ₂₅ , B ₅₀ , B ₇₅ whose common center is C1, are defined, wherein the radius r ₂₅ of B _{25 has} 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 Arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and trailing tooth flank F _N ,
wherein 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 design is observed: $$\mathrm{0}.\mathrm{75}\le {\mathrm{\epsilon }}_{\mathrm{1}}\le \mathrm{0}.\mathrm{85}\mathrm{and}/\mathrm{or}\mathrm{0}.\mathrm{65}\le {\mathrm{\epsilon }}_{\mathrm{2}}\le \mathrm{0}.\mathrm{74th}$$

Rotor pair according to one of claims 9 to 11, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) defines foot points F1 and F2 and at the radially outermost point of the tooth a vertex F5 are,
where by F1, F2 and F5 a triangle D _{Z is} defined 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 _recedes with a surface A3 in a radially inner region opposite to the triangle D _Z and wherein 9.0 ≤ A3 / A1 ≤ 18 is complied with. Rotor pair according to one of claims 9 to 12, characterized in that in an end-sectional view, formed between F1 and F5 trailing tooth flank F _{N of} a tooth of the sub rotor (NR) has a convex length portion of at least 55% to at most 95%. Rotor pair for a compressor block of a screw machine, wherein the rotor pair consists of a secondary rotor (NR) rotating about a first axis (C1) and a main rotor (HR) rotating about a second axis (C2),
wherein the number of teeth (z ₂₎ in the main rotor (HR) 5 and the number of teeth (z ₁₎ at the slave rotor (NR) is 6,
the relative tread depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{rf}}_1}{{\mathrm{rk}}_1}$$

at least 0.44 and at most 0.495, preferably at most 0.48, wherein rk ₁ is a tip circle radius drawn around the outer circumference of the secondary rotor (NR) and rf ₁ is a root radius starting at the base of the profile of the secondary rotor,
wherein the ratio of the axial distance α of the first axis (C1) to the second axis (C2) and the head radius rk ₁ $$\frac{\mathrm{a}}{{\mathrm{rk}}_1}$$

is at least 1.74, preferably at least 1.75, and at most 1.8, preferably at most 1.79, wherein preferably the main rotor is formed with a wrapping angle φ _HR , for which 240 ° ≤ φ _HR ≤ 360 °, and wherein in a cross-sectional view a point C on the connecting path ( 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 link ( C 1 C 2 ), where r ₁ measures the distance between K5 and C,
and K4 denotes the point of the suction-side part of the engagement line furthest from the connection path C 1 C 2 between C1 and C2, wherein 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 claim 14, characterized
that 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 of 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 of a suction-side main rotor rotor face to an opposite pressure-side main rotor rotor face. Rotor pair according to claim 14 or 15, characterized
in that a circular cross-section B ₂₅ , B ₅₀ , B ₇₅ whose common center point is C ₁ is defined in an end-face view within a secondary rotor tooth, wherein the radius r ₂₅ of B _{25 has} 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 Circular arcs B ₂₅ , B ₅₀ , B _{75 are} each limited by the leading tooth flank F _V and trailing tooth flank F _N ,
wherein 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 design is observed: $$\mathrm{0}.76\le {\mathrm{\epsilon }}_{\mathrm{1}}\le \mathrm{0}.\mathrm{86}\mathrm{and}/\mathrm{or}\mathrm{0}.\mathrm{62}\le {\mathrm{\epsilon }}_{\mathrm{2}}\le \mathrm{0}.\mathrm{72nd}$$

Rotor pair according to one of claims 14 to 16, characterized in that in an end-sectional view between the considered tooth of the sub rotor (NR) and the adjacent tooth of the sub rotor (NR) foot points F1 and F2 and defined at the radially outermost point of the tooth a vertex F5 are,
wherein the circular arc B running between F1 and F2 defines a tooth pitch angle γ corresponding to 360 ° / number of the teeth of the minor rotor NR about the center defined by the axis C1,
wherein a point F11 is defined on the half circular arc B between F1 and F2,
wherein a radial ray R drawn from the midpoint of the sub rotor (NR) defined by the axis C1 through the vertex F5 intersects the arc B at a point F12,
wherein an offset angle β is defined by the offset of F11 to F12 considered in the direction of rotation of the sub rotor (NR), and
in which $$13.5\%\le \mathrm{\delta }\le 18\%$$

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

Rotor pair according to one of claims 14 to 17, characterized in that for a by the ratio of the head circle radii of main rotor (HR) and secondary rotor (NR) defined diameter ratio $$D_v=\frac{{\mathit{dk}}_2}{{\mathit{dk}}_1}=\frac{{\mathit{rk}}_2}{{\mathit{rk}}_1}$$

$$1.19\le D_v\le 1.26$$

is complied with, wherein Dk ₁ the diameter of the top circle KK _{1 of} the secondary rotor (NR) and Dk ₂ denote the diameter of the top circle KK _{2 of} the main rotor (HR). Rotor pair according to one of claims 1 to 18, characterized in that in an end-sectional view extending within a tooth of the sub-rotor arc lengths b (r) of the respective associated concentric circular arcs with the radius rf ₁ <r <rk ₁ and the common, through the axis C1 defined center are each bounded by the leading tooth flank F _V and the trailing tooth flank F _N and decrease the arc lengths b (r) monotonously with increasing radius r. Pair of rotors according to one of claims 1 to 13, characterized in that the tooth profile of the secondary rotor (NR) at its radially outer portion sections follows a circular arc ARC ₁ with radius rk ₁ in an end-sectional view, ie several points of the leading tooth flank F _V and the trailing Tooth flank F _N on the arc of radius rk ₁ lie around the center defined by the axis C1, wherein preferably the arc ARC ₁ 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 farthest point on the leading tooth flank of F5 on this arc and F5
wherein the radial ray R ₁₀ drawn between F10 and the midpoint of the minor rotor (NR) defined by the axis C1 contacts the leading tooth flank F _V at at least one point or intersects at two points. Rotor pair according to one of claims 9 to 20, characterized in that the main rotor HR is formed with a wrap angle φ _HR , for which applies: 320 ° ≤ φ _HR ≤ 360 °, preferably 330 ° ≤ φ _HR ≤ 360 °.

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