EP3597920B1 - Rotor pair for a compressor block of a screw machine - Google Patents

Description

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

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

Screw machines generally have two shafts arranged parallel to one another, on the one hand a main rotor and on the other hand a secondary rotor. Main rotor and secondary rotor engage with each other with appropriate helical gearing. Between the teeth and a In the compressor housing, in which the main and secondary rotors are accommodated, a compression space (working chambers) is formed by the tooth gap volumes. Starting from an intake area, the working chamber is initially closed and then continuously reduced in volume as the rotation of the main and secondary rotors progresses, so that the medium is compressed. Finally, as the rotation progresses, the working chamber opens towards a pressure window and the medium is pushed out into the pressure window. This process of internal compression distinguishes screw machines designed as screw compressors from Roots blowers, which work without internal compression.

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

Typical pressure ratios can range from 1.1 to 20 depending on the tooth count ratio, where pressure ratio is the ratio of discharge pressure to intake pressure. The compaction can take place in one or more stages. Final pressures that can be achieved can be in the range from 1.1 bar to 20 bar, for example. Insofar as reference is made to pressure data in "bar" at this point or later in the present application, such pressure data relate to absolute pressures.

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

Considerable success has been achieved over the past decades in terms of manufacturability, reliability, smooth running and efficiency of screw machines. Improvements or optimizations often relate to optimization of the efficiency depending on the number of teeth, angle of contact and length/diameter ratio of the rotors. The addition of forehead cuts to the optimization process has only recently been found.

Experiments have shown that the front section of the rotors, in particular the front section of the secondary rotor, has a significant impact on energy efficiency. In order to comply with the laws of gearing, the face section of the auxiliary rotor must find its equivalent in the face section of the main rotor. The profile of the rotor in a plane perpendicular to the axis of the rotor is referred to as a front section. Different types of face cut generation, such as rotor-based or rack-based face cut generation methods, are now known from the prior art. Once you have decided on a specific method, a first draft face section is created in a first step. This is conventionally further optimized in several subsequent (revision) steps according to various criteria.

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

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

1 energy efficiency

• Über den Profilspalt haben die druckseitigen Arbeitskammern direkte Verbindung zur Ansaugseite und damit eine größtmögliche Druckdifferenz für Rückströmungen.
• Aufeinanderfolgende Arbeitskammern sind über einen theoretisch nicht notwendigen Durchlass miteinander verbunden, der als Blasloch bezeichnet wird. Zum Teil wird dieser auch als Kopfrundungsöffnung bezeichnet. Dieses Blasloch ergibt sich durch die Kopfrundung der Profile, insbesondere des Profils des Nebenrotors.

Druckseitige Arbeitskammern sind über druckseitige Blaslöcher mit den jeweils benachbarten Arbeitskammern verbunden, saugseitige Arbeitskammern sind über saugseitige Blaslöcher mit den jeweils benachbarten Arbeitskammern verbunden. Soweit nicht anders angegeben ist im Folgenden der Begriff "Blasloch" als "druckseitiges Blasloch" zu verstehen.The energy efficiency of compressor blocks can be advantageously influenced in a known manner by minimizing the internal leakages in the compressor block and in particular by reducing the gaps between the main rotor and the secondary rotor. Specifically, the profile gap and the blow hole must be distinguished here:

• The working chambers on the pressure side have a direct connection to the suction side via the profile gap and thus the greatest possible pressure difference for return flows.
• Successive working chambers are connected via a theoretically unnecessary passageway called a blowhole. Sometimes this is also referred to as the head rounding opening. This blowhole results from the rounding of the head of the profile, in particular the profile of the secondary rotor.

Working chambers on the pressure side are connected to the respective adjacent working chambers via blow holes on the pressure side, working chambers on the suction side are connected to the respective neighboring working chambers via blow holes on the suction side. Unless otherwise stated, the term "blow hole" is to be understood below as "blow hole on the pressure side".

Ideally, to minimize internal leakage, a short profile gap length should be combined with a small (pressure side) blow hole. In principle, however, the two variables behave in opposite directions. This means that the smaller the blowhole is modeled, the larger the profile gap length will inevitably be. Conversely, the shorter the profile gap length, the larger the blowhole becomes. This is explained, for example, by Helpertz in his dissertation "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003 on page 162.

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

Very flat profiles accordingly have a poor utilization of the construction volume, i.e. they lead to large compressor blocks with comparatively high material expenditure or comparatively high production costs.

As described above, blow holes on the pressure side must not be made too large in order to minimize the backflow of already compressed medium into previous working chambers (i.e. in working chambers with lower pressure). Such backflows increase the energy expenditure for the total flow rate achieved and lead to an undesirable increase in the temperature and pressure level during compression, which reduces the overall efficiency. The area of the blow hole (blow hole area) can be kept small by making the head curves of the profiles small in the front section. Specifically, this can be caused by a strong curvature in the tip area of the leading tooth flank of the secondary rotor and in the tip area of the trailing tooth flank of the main rotor. However, the greater this curvature, the more likely it is that you will end up in production-related border areas, since this leads, for example, to high wear on profile milling cutters and profile grinding wheels in the production of the main rotor and secondary rotor.

On the other hand, large blowholes on the suction side do not have a negative effect on energy efficiency, since these only connect working chambers in the suction area with the same pressure.

Another reason for efficiency-reducing internal leaks is the so-called chamber gusset volume, which can arise when the last working chamber (ie the working chamber in which the highest pressure prevails) is pushed out into the pressure window. From a certain angle of rotation of the rotors, the working chamber is no longer connected to the pressure window. A so-called chamber gusset volume remains between the two rotors and the pressure-side end wall of the housing.

This chamber gusset volume is disadvantageous because the enclosed compressed medium can no longer be pushed out into the pressure window, and as the rotors turn further it is compressed even further, which leads to unnecessarily high power consumption (for overcompression), an unnecessarily high additional heat input, noise development and a reduction the service life, in particular of the roller 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 overcompression and is therefore not available to the compressed air user. In the case of oil-injected compressors, there is also incompressible oil in the chamber gusset and is being squeezed.

2 smoothness

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

In addition to good flank osculation and low relative speeds 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 smooth running. As is well known, an unfavorable distribution often leads to the so-called rotor chatter of the auxiliary rotor, in which the auxiliary rotor has undefined flank contact with the main rotor and the auxiliary rotor consequently has alternating contact with the leading and trailing flanks of the main rotor. If the two rotors are kept at a distance by a synchro-gear, the above-mentioned rotor clatter is inevitably shifted to the synchro-gear. Quiet 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 for the roller bearings and low wear in the gearing of the rotors.

3 costs

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

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

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

The more you increase the relative profile depth, the higher the construction volume utilization you achieve, but at the same time the higher the risk of problems with the runnability and manufacturability:

• With increasing profile depth, in particular the tooth profiles of the secondary rotor inevitably become ever thinner and consequently ever more flexible. This makes the rotors increasingly temperature-sensitive and, viewed overall, has an unfavorable effect on the gaps in the compressor block. The gaps have a significant impact on internal leakage, ie backflow from compression chambers with higher pressure in the direction of the suction side, and can therefore impair the energy efficiency of the compressor block.
• Furthermore, the difficulties in rotor production increase with flexible teeth.
  • ∘ For example, there is an increased risk that the already high requirements, particularly with regard to shape tolerances, cannot be met during profile grinding.
  • ∘ Furthermore, flexible teeth require lower feed and cutting speeds for both profile milling and subsequent profile grinding, thereby increasing the machining time and consequently the manufacturing costs.
• An increasing profile depth also means that the rotor itself becomes more flexible. The more flexible the rotors are made, the greater the risk that the rotors will collide with one another or in the compressor housing. To ensure operational safety even at high temperatures or at high pressures, the gaps must therefore be 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 is not very effective on its own, but for a good overall result, a compromise between the different (and sometimes contradictory) requirements has to be found.

In the literature, the theoretical calculation bases for the generation of screw rotor profiles are already dealt with in many cases and general criteria for good cross-section profiles are also described. The computer program developed by Grafinger can be used, for example, to create and modify rotor profiles (Habilitation "The computer-aided development of flank profiles for special gearing of screw compressors", Vienna, 2010).

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

Accordingly, the object of the present invention consists in specifying a pair of rotors for a compressor block of a screw machine, which is characterized by high operational reliability and reasonable production costs by very smooth running and a particular energy efficiency.

This object is achieved with a pair of rotors according to the features of claim 1, 9 or 14. Advantageous configurations are specified in the dependent claims. The object is also achieved with a compressor block that includes a correspondingly designed pair of rotors.

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

In a cross-sectional view, the secondary rotor or main rotor has a predetermined, often different number of teeth of the same design per rotor. The outermost circle drawn through the axis C1 or C2 over the crests of the teeth is referred to as the tip circle. A base circle is defined in the face section by the points of the outer surface of the rotors closest to the axis. The ribs are called the teeth of the rotor. The grooves (or recesses) are accordingly referred to as tooth gaps. The area of the tooth at and above the root circle defines the tooth profile. The contour of the ribs defines the course of the tooth profile. Base points F1 and F2 and a vertex F5 are defined for the tooth profile. The 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 point defined by the axis C1 or C2, i.e. the tooth profile follows an arc of a circle on the addendum circle at its radially outer end, then the vertex F5 lies exactly in the middle of this arc of a circle. A tooth gap is defined between two adjacent vertices F5.

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

Finally, due to the meshing of the main rotor and the secondary rotor, a pitch circle is defined for both the secondary rotor and the main rotor. With screw machines as well as with gear wheels or friction wheels, there are always two circles in the front section of the toothing, which roll off each other during movement. These circles, on which in the present case the main rotor and the 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 ratio.

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

Finally, tooth gap areas between the teeth and the respective addendum circle KK are defined, namely tooth gap area A6 between the profile of the secondary rotor NR between two adjacent vertices F5 and the addendum circle KK ₁ or an area A7 as a tooth gap area between the profile of the main rotor (HR) between two neighboring vertices H5 and the tip circle KK ₂ .

The tooth profile of the secondary rotor (but also of the main rotor) has a tooth flank that leads in the direction of rotation and a tooth flank that trails in the direction of rotation. In the case of the secondary rotor (NR), the leading tooth flank is referred to below as F _v , the trailing tooth flank as F _N .

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

In addition to the pure face section, the following terms and parameters for a rotor, in particular the secondary rotor, are also relevant for the three-dimensional design: First, a wrap angle Φ is defined. This angle of wrap is the angle by which the face section is twisted from the suction-side to the pressure-side rotor face, see also the detailed explanations in connection with figure 8 .

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

The line of action or the profile gap is created by the interaction of the main rotor and the secondary rotor with one another. The line of action is as follows: The tooth flanks of the main rotor and secondary rotor touch each other with backlash-free gearing depending on the rotational angle position of the rotors specific points. These points are called engagement points. The geometric location of all points of action is called the line of action and can already be calculated in two dimensions using the face section of the rotors, cf. Figure 7j .

The line of action is divided into two sections in the face section view by the connecting line between the two centers C1 and C2, specifically into a (comparatively short) suction-side section and a (comparatively long) pressure-side section.

If the angle of wrap and the rotor length (= distance between the suction-side end face and the pressure-side end face) are also specified, the line of action can also be extended three-dimensionally and corresponds to the contact line of the main rotor and auxiliary rotor. The axial projection of the three-dimensional line of action onto the front section plane results in turn from Figure 7j illustrated two-dimensional line of action. The term "line of action" is used in the literature for both two-dimensional and three-dimensional considerations. In the following, unless otherwise stated, "line of action" is to be understood as meaning the two-dimensional line of action, ie the projection onto the face section.

The profile contact gap is defined as follows: In the real compressor block of a screw machine, there is play between the two rotors when the main rotor and secondary rotor are installed axially apart. The gap between the main rotor and the slave rotor is called the profile engagement gap and is the locus of all points where the two paired rotors touch each other or are closest to each other. Through the profile engagement gap, the compressing and ejecting working chambers are connected to chambers that are still in contact with the suction side. The entire maximum pressure ratio is therefore present at the profile engagement gap. Already compressed working fluid is transported back to the suction side through the profile engagement gap and thus reduces the efficiency of the compression. Since the profile engagement gap would be the line of action in the case of backlash-free gearing, the profile engagement gap is also referred to as the “quasi line of action”.

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

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

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

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

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

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

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 pair of rotors with 3 teeth on the main rotor and 4 teeth on the secondary rotor, a geometry with the following specifications is required, which is to be regarded as particularly energy-efficient:
A relative profile depth of the secondary rotor is formed with $${\mathrm{pt}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1},$$

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

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

is at least 1.636 and at most 1.8, preferably at most 1.733, with the main rotor preferably being designed with a wrap angle Φ _HR for which 240°≦Φ _HR ≦360° applies, and with the following preferably applying for a rotor length ratio L _HR/ a: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.4,$$

where the rotor length ratio is formed from the ratio of the rotor length L _HR of the main rotor and the center distance a and the rotor length L _HR of the main rotor is formed by the distance between a suction-side main rotor rotor face and 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: $$\mathrm{1,4}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{3,3},$$

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 pair of rotors with four teeth on the main rotor and five teeth on the secondary rotor, a geometry with the following specifications is required, which can be regarded as particularly energy-efficient: A relative profile depth of the secondary rotor is formed with $${\mathrm{pt}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1},$$

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

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

is at least 1.683 and at most 1.836, preferably at most 1.782, with the main rotor preferably being designed with a wrap angle Φ _HR for which 240° ≤ Φ _HR ≤ 360° applies, and with the following preferably applying for a rotor length ratio L _HR/ a: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.3,$$

where the rotor length ratio is formed from the ratio of the rotor length L _HR of the main rotor and the center distance a and the rotor length L _HR of the Main rotor is formed by the distance 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: $$\mathrm{1,4}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{3,2},$$

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 pair of rotors with five teeth on the main rotor and six teeth on the secondary rotor, a geometry with the following specifications is required, which is to be regarded as particularly energy-efficient:
A relative profile depth of the secondary rotor is formed with $${\mathrm{pt}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1},$$

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

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

at least 1.74, preferably at least 1.75 and at most 1.8, preferably at most 1.79, the main rotor preferably being designed with a wrap angle Φ _HR for which 240°≦Φ _HR ≦360° applies, and where preferably for a rotor length ratio L _HR/ a the following applies: $$1.4\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 3.2,$$

where the rotor length ratio is formed from the ratio of the rotor length L _HR of the main rotor and the center distance a and the rotor length L _HR of the main rotor is formed by the distance between a suction-side main rotor rotor face and an opposite pressure-side main rotor rotor face.

mit $${\mathrm{PT}}_1={\mathrm{rk}}_1-{\mathrm{rf}}_1\mathrm{und}{\mathrm{rf}}_1=\mathrm{a}-{\mathrm{rk}}_2$$

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

with $${\mathrm{<figure-callout\; id="1"\; label="pt"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">pt</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1\mathrm{and}{\mathrm{rf}}_1=\mathrm{a}-{\mathrm{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0010.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2$$

, Achsabstand a zum Nebenrotor-Kopfkreisradius rk₁.In this respect, there is a connection with the relationship between $\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0007.png,imgf0009.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$

, center distance a to the auxiliary rotor tip circle radius rk ₁ .

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

1. Preferred configurations for a pair of rotors with a tooth ratio of 3/4

Preferred configurations for a pair of rotors with a tooth ratio of 3/4, i.e. for a pair of rotors in which the main rotor has 3 teeth and the secondary rotor has 4 teeth, are presented below:
A first preferred embodiment provides that arcs B ₂₅ , B ₅₀ , B ₇₅ running within an auxiliary rotor tooth are defined in a face section view, the common center point of which is given by the axis C1, with the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 * (rk ₁ - rf ₁ ), the radius r ₅₀ of B ₅₀ has the value r ₅₀ = rf ₁ + 0.5 * (rk ₁ - rf ₁ ) and the radius r ₇₅ of B ₇₅ has the value r ₇₅ = rf ₁ + 0.75 * (rk ₁ - rf ₁ ), and the circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each delimited by the leading tooth flank F _v and the trailing tooth flank F _N , where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b ₇₅ of the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ /b ₂₅ and ε ₂ = b ₇₅ /b ₂₅ and the following dimensioning is observed :
0.65≦ε ₁ <1.0 and/or 0.50≦ε ₂ ≦0.85, preferably 0.80≦ε ₁ <1.0 and/or 0.50≦ε ₂ ≦0.79.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the larger the length of the profile contact gap will inevitably be. Conversely, the shorter the length of the profile-engaging gap, the larger the blowhole becomes. A particularly favorable combination of the two parameters is achieved in the stressed areas. At the same time, a sufficiently high flexural rigidity of the secondary rotor is ensured. In addition, there are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, reference is also made to the Figure 7c referred.

A further preferred embodiment provides that in a face section consideration between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 are defined on the root circle and on the radially outermost point of the tooth an apex F5, with F1, F2 and F5, a triangle D _z is defined and in a radially outer area the tooth with its leading tooth flank F _v formed between F5 and F2 has an area A1 and with its trailing tooth flank F _N formed between F1 and F5 has an area A2 the triangle _Dz protrudes and where 8≦A2/A1≦60 is observed.

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

In a further preferred embodiment, the pair of rotors has a secondary rotor, in which, in a face section view, between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the Sub-rotor base points F1 and F2 and at the radially outermost point of the tooth an apex F5 are defined, with a triangle _Dz being defined by F1, F2 and F5 and with the leading tooth flank _Fv formed between F5 and F2 in a radially outer region of the tooth with an area A1 protrudes beyond the triangle D _z and recedes in a radially inner region with respect to the triangle D _z with an area A3 and where 7.0≦A3/A1≦35 is observed. With regard to the illustration of the parameters, reference is also made to the Figure 7d referred.

Furthermore, with regard to the design of the secondary rotor, it is considered advantageous if, in a cross-sectional view, base points F1 and F2 are defined between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the secondary rotor (NR) and a vertex F5 is defined at the radially outermost point of the tooth are, wherein a triangle D _z is defined by F1, F2 and F5 and wherein the leading tooth flank F _v formed between F5 and F2 protrudes in a radially outer region of the tooth with an area A1 over the triangle D _z , the tooth itself having a has a cross-sectional area A0 delimited by the arc of a circle B running between F1 and F2 around the center point defined by the axis C1, and where 0.5%≦A1/A0≦4.5% is observed. With regard to the illustration of the parameters, reference is also made to the Figures 7d as well as 7e.

.A further preferred embodiment provides that in a face section consideration between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR) base points F1 and F2 and at the radially outermost point of the tooth an apex F5 are defined, with the between F1 and F2 arcs B running around the center point defined by the axis C1 defines a tooth pitch angle γ corresponding to 360°/number of teeth of the secondary rotor (NR), with a point F11 being defined on half the arc B between F1 and F2, with a dated The radial ray R drawn through the center point of the secondary rotor (NR) defined by the axis C1 through the vertex F5 intersects the circular arc B at a point F12, with an offset angle β being defined by the offset from F11 to F12 viewed in the direction of rotation of the secondary rotor (NR) and where 14% ≤ δ ≤ 25% is met, with $\delta =\frac{\beta }{g}\ast 100\left[\%\right]$

.

First of all, it is clarified again that the offset angle is preferably always positive, ie always the offset in the direction of the direction of rotation is given and not against. In this respect, the tooth of the secondary rotor is curved towards the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blowhole area, the shape of the line of action, the length and shape of the profile engagement gap, the auxiliary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, reference is also made to Figure 7f referred.

It is considered advantageous if the trailing tooth flank F _N of a tooth of the secondary rotor (NR) formed between F1 and F5 has a convex length portion of at least 45% to at most 95% in a face section consideration.

The relatively long, convex length portion of the trailing tooth flank F _N of a tooth of the secondary rotor, which is defined by the area, allows a good compromise between the length of the profile engagement gap, chamber extension, secondary rotor torque on the one hand and the flexural rigidity of the secondary rotor on the other. With regard to the illustration of the parameters, it is also added Figure 7g referred.

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

is complied with. It should be pointed out once again at this point that the tooth profile is delimited radially inwards towards the axis C1 by the root circle _FK1 . It can happen that the radial ray R divides the tooth profile in such a way that two disjoint surface portions with a total surface portion A5, which are assigned to the leading tooth flank _Fv , arise, cf. Figure 7g . If the vertex F5 were to be offset in relation to the leading tooth flank in such a way that the radial ray R not only touches the leading tooth flank F _v but intersects it at two points, then there are again two of the leading tooth flank associated disjunctive areas defined with a total area A5. The area portion A4 assigned to the trailing tooth flank F _N is then limited on the one hand by the radial ray R and in sections, namely between the two intersection points of the leading tooth flank F _v with the radial ray R, on the other hand also by the leading tooth flank F _v .

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

With an increasing angle of wrap, the pressure window area can be made larger with the same built-in volume ratio. In addition, the axial extent of the working chamber to be pushed out, the so-called profile pocket depth, is also shortened as a result. This reduces the exhaust throttling losses, especially at higher speeds, and thus enables better specific power. However, an angle of wrap that is too large has a negative effect on the construction volume and leads to larger rotors.

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

and where A _Bl denotes an absolute blow hole area on the pressure side and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, with the area A6 in a cross-sectional view being the area between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the Addendum circle KK ₁ area enclosed and the area A7 in a front section view the area enclosed between the profile of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ .

While the absolute size of the blowhole on the pressure side alone does not allow any meaningful statement about the effect on the leakage mass flows, a ratio of the absolute blowhole area A _Bl on the pressure side to the sum of the Tooth gap area A6 of the secondary rotor and tooth gap area A7 of the main rotor are significantly more meaningful. With regard to the further illustration of the parameters, it is also added here Figure 7b referred. The smaller the numerical value μ _Bl , the smaller the influence of the blow hole on the operating behavior. This allows a comparison of different profile shapes. The blow hole area on the pressure side can thus be represented independently of the size of the screw machine.

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

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 $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}\ast 100\left[\%\right]$$

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 pair of rotors is designed and matched to one another in such a way that for a blow hole/profile gap length factor µ _l - µ _Bl $$0.1\%\le {\mathrm{\mu }}_{\mathrm{l}}*{\mathrm{\mu }}_{\mathrm{Bl}}\le 1.72\%$$

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

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

where A _Bl denotes an absolute blow hole area on the pressure side and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, with the area A6 in a cross-sectional view being that between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the addendum circle KK ₁ enclosed area and the area A7 in a front section view the area enclosed between the profile of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ .

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

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and coordinated in such a way that 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 achievable, the pressure ratio being the ratio of the compression end pressure to the intake pressure.

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

$$\mathrm{1,145}\le D_v\le \mathrm{1,30}$$

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

$$1.145\le D_v\le 1.30$$

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

2. Preferred configurations for a pair of rotors with a tooth number ratio of 4/5

Preferred configurations for a pair of rotors with a tooth ratio of 4/5, i.e. for a pair of rotors in which the main rotor has four teeth and the secondary rotor has five teeth, are presented below:
A further preferred embodiment provides that, in a face section view, circular arcs B ₂₅ , B ₅₀ , B ₇₅ , whose common center is given by the axis C1, where 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 where the circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each delimited by the leading tooth flank F _v and the trailing tooth flank F _N , and 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 are defined with ε ₁ = b ₅₀ /b ₂₅ and ε ₂ = b ₇₅ /b ₂₅ and the following design is observed:
0.75 ≤ ε ₁ ≤ 0.85 and/or 0.65 ≤ ε ₂ ≤ 0.74.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the larger the length of the profile contact gap will inevitably be. Conversely, the shorter the length of the profile-engaging gap, the larger the blowhole becomes. A particularly favorable combination of the two parameters is achieved in the stressed areas. At the same time, a sufficiently high flexural rigidity of the secondary rotor is ensured. In addition, there are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, reference is also made to the Figure 7c referred.

A further preferred embodiment provides that in a face section consideration between the considered tooth of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR) base points F1 and F2 are defined at the root circle and at the radially outermost point of the tooth an apex F5, where a triangle D _z is defined by F1, F2 and F5 and in a radially outer area the tooth with its leading tooth flank F _v formed between F5 and F2 has an area A1 and with its trailing tooth flank F _N formed between F1 and F5 has a Area A2 protrudes beyond the triangle D _z and where 6 ≤ A2/A1 ≤ 15 is observed.

The partial tooth surface A1 on the leading tooth flank F _v of the secondary rotor has a significant influence on the blow hole surface. The partial tooth surface A2 on the trailing tooth flank F _N of the auxiliary rotor, on the other hand, has a significant influence on the length of the profile engagement gap, the chamber extension and the auxiliary rotor torque. There is an advantageous range for the tooth surface area ratio A2/A1, which offers a good compromise between the length of the Profile engagement gap on the one hand and blow hole on the other hand allows. With regard to the illustration of the parameters, it is also added Figure 7d referred.

In a further embodiment, the pair of rotors has a secondary rotor in which, in a face section view, base points F1 and F2 are defined between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the secondary rotor (NR) and an apex F5 is defined at the radially outermost point of the tooth A triangle D _z is defined by F1, F2 and F5 and the leading tooth flank F _v formed between F5 and F2 protrudes with an area A1 over the triangle D _z in a radially outer area of the tooth and in a radially inner area compared to the triangle D _z with an area A3 and where 9.0≦A3/A1≦18 is observed. With regard to the illustration of the parameters, reference is also made to the Figure 7d referred.

Furthermore, with regard to the design of the secondary rotor, it is considered advantageous if, in a cross-sectional view, base points F1 and F2 are defined between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the secondary rotor (NR) and a vertex F5 is defined at the radially outermost point of the tooth are, wherein a triangle D _z is defined by F1, F2 and F5 and wherein the leading tooth flank F _v formed between F5 and F2 protrudes in a radially outer region of the tooth with an area A1 over the triangle D _z , the tooth itself having a has a cross-sectional area A0 delimited by the arc of a circle B running between F1 and F2 around the center point defined by the axis C1, and where 1.5%≦A1/A0≦3.5% is observed.

With regard to the definition of the parameters, refer to the Figures 7d as well as 7e.

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

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

is complied with $$\delta =\frac{\beta }{g}\ast 100\left[\%\right].$$

First of all, it is clarified again that the offset angle is preferably always positive, ie the offset is always in the direction of the direction of rotation and not in the opposite direction. In this respect, the tooth of the secondary rotor is curved towards the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blowhole area, the shape of the line of action, the length and shape of the profile engagement gap, the auxiliary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, reference is also made to Figure 7f referred.

It is also considered advantageous if the trailing tooth flank F _N formed between F1 and F5 of a tooth of the secondary rotor (NR) has a convex length portion of at least 55% to at most 95% in a face section consideration.

The relatively long, convex length portion of the trailing tooth flank F _N of a tooth of the secondary rotor, which is defined by the area, allows a good compromise between the length of the profile engagement gap, chamber extension, secondary rotor torque on the one hand and the flexural rigidity of the secondary rotor on the other. With regard to the illustration of the parameters, it is also added Figure 7g referred.

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

is complied with. It should be pointed out once again at this point that the tooth profile is delimited radially inwards towards the axis C1 by the root circle _FK1 . It can happen that the radial ray R divides the tooth profile in such a way that two disjoint surface portions with a total surface portion A5, which are assigned to the leading tooth flank _Fv , arise, cf. Figure 7g . If the vertex F5 were offset towards the leading tooth flank in such a way that the radial ray R not only touches the leading tooth flank F _v but intersects it at two points, then two disjoint surface portions assigned to the leading tooth flank are defined with a total surface portion A5. The area portion A4 associated with the trailing tooth flank F _N is then delimited in sections by the radial ray R, namely between the two intersection points 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 designed with a wrap angle Φ _HR for which the following applies: 320°≦Φ _HR ≦360°, preferably 330°≦Φ _HR ≦360°.

With an increasing angle of wrap, the pressure window area can be made larger with the same built-in volume ratio. In addition, the axial extent of the working chamber to be pushed out, the so-called profile pocket depth, is also shortened as a result. This reduces the exhaust throttling losses, especially at higher speeds, and thus enables better specific power. However, an angle of wrap that is too large has a negative effect on the construction volume and leads to larger rotors.

und wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In addition, in an advantageous embodiment, a pair of rotors is provided which is designed and interacts with one another in such a way that a blowhole factor μ _Bl is at least 0.02% and at most 0.4%, preferably at most 0.25%, is maintained, with $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$

and where A _Bl denote an absolute pressure-side blowhole area and A6 and A7 tooth gap areas of the secondary rotor NR and the main rotor (HR), respectively, with the area A6 in a face section view being the area between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the addendum circle KK ₁ and the area A7 in a cross-sectional view denote the area between the profile of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ .

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

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

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 $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}\ast 100\left[\%\right]$$

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 pair of rotors is designed and matched to one another in such a way that for a blowhole/profile gap length factor µ _l ∗ µ _Bl $$0.1\%\le {\mathrm{\mu }}_{\mathrm{I}}*{\mathrm{\mu }}_{\mathrm{BI}}\le 1.72\%$$

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

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

where A _Bl denotes an absolute blow hole area on the pressure side and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, with the area A6 in a face section view being that between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the addendum circle KK ₁ and the area A7 denote the area enclosed between the profile of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ in a cross-sectional view.

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

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and coordinated with one another in such a way that 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 can be achieved with a pressure ratio of up to 16, in particular with a pressure ratio greater than 1 and up to 16, the pressure ratio designating the ratio of the compression end pressure to the intake pressure.

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

$$\mathrm{1,195}\le D_v\le \mathrm{1,33}$$

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

$$1.195\le D_v\le 1.33$$

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

3. Preferred configurations for a pair of rotors with a tooth number ratio of 5/6

Preferred configurations for a pair of rotors with a tooth ratio of 5/6, i.e. for a pair of rotors in which the main rotor has five teeth and the secondary rotor has six teeth, are presented below:
A further preferred embodiment provides that, in a face section view, arcs B ₂₅ , B ₅₀ , B ₇₅ running within an auxiliary rotor tooth are defined, the common center point of which is given by the axis C1, with the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 * (rk ₁ - rf ₁ ), the radius r ₅₀ of B ₅₀ has the value r ₅₀ = rf ₁ + 0.5 * (rk ₁ - rf ₁ ) and the radius r ₇₅ of B ₇₅ has the value r ₇₅ = rf ₁ + 0.75 * (rk ₁ - rf ₁ ), and the circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each delimited by the leading tooth flank F _V and the trailing tooth flank F _N , where tooth thickness ratios are defined as ratios of the arc lengths b ₂₅ , b ₅₀ , b ₇₅ of the circular arcs B ₂₅ , B ₅₀ , B ₇₅ with ε ₁ = b ₅₀ /b ₂₅ and ε ₂ = b ₇₅ /b ₂₅ and the following dimensioning is observed : 0.76 ≤ ε ₁ ≤ 0.86 and/or 0.62 ≤ ε ₂ ≤ 0.72.

The aim is to combine a small blow hole with a short length of the profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the larger the length of the profile contact gap will inevitably be. Conversely, the shorter the length of the profile-engaging gap, the larger the blowhole becomes. A particularly favorable combination of the two parameters is achieved in the stressed areas. At the same time, a sufficiently high flexural rigidity of the secondary rotor is ensured. In addition, there are also advantages in terms of chamber extension and secondary rotor torque. With regard to the illustration of the parameters, reference is also made to the Figure 7c referred.

A further preferred embodiment provides that in a face section consideration between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR) base points F1 and F2 at the root circle and at the radially outermost point of the tooth an apex F5 are defined, wherein a triangle D _Z is defined by F1, F2 and F5 and wherein in a radially outer area the tooth with its leading tooth flank F _v formed between F5 and F2 has an area A1 and with its trailing tooth flank formed between F1 and F5 F _N protrudes with an area A2 over the triangle D _z and where 4≦A2/A1≦7 is observed.

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

In a further preferred embodiment, the pair of rotors has a secondary rotor in which, in a face section view, there are base points F1 and F2 between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the secondary rotor (NR) and an apex F5 at the radially outermost point of the tooth are defined, with a triangle D _z being defined by F1, F2 and F5 and with the leading tooth flank F _V formed between F5 and F2 protruding in a radially outer area of the tooth with an area A1 over the triangle D _Z and in a radially inner area Area opposite the triangle D _Z with an area A3 recedes and where 8≦A3/A1≦14 is maintained. With regard to the illustration of the parameters, reference is also made to the Figure 7d referred.

Furthermore, with regard to the design of the secondary rotor, it is considered advantageous if, in a cross-sectional view, base points F1 and F2 are defined between the tooth of the secondary rotor (NR) under consideration and the respective adjacent tooth of the secondary rotor (NR) and a vertex F5 is defined at the radially outermost point of the tooth are, wherein a triangle D _z is defined by F1, F2 and F5 and wherein the leading tooth flank F _v formed between F5 and F2 protrudes in a radially outer region of the tooth with an area A1 over the triangle D _z , the tooth itself having a has a cross-sectional area A0 bounded by the arc of a circle B running between F1 and F2 around the center point defined by the axis C1 and where 1.9% ≤ A1/A0 ≤ 3.2% is complied with. With regard to the illustration of the parameters, reference is also made to the Figures 7d as well as 7e.

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

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

is complied with $$\delta =\frac{\beta }{g}\ast 100\left[\%\right].$$

First of all, it is clarified again that the offset angle is preferably always positive, ie the offset is always in the direction of the direction of rotation and not in the opposite direction. In this respect, the tooth of the secondary rotor is curved towards the direction of rotation of the secondary rotor. However, the offset should remain within the range specified as advantageous in order to enable a favorable compromise between the blow hole area, the shape of the line of action, the profile gap length and shape, the auxiliary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. With regard to an illustration of the parameters, reference is also made to Figure 7f referred.

A further preferred embodiment has a pair of rotors which is characterized in that the main rotor HR is designed with a wrap angle Φ _HR for which the following applies: 320° ≤ Φ _HR ≤ 360°, preferably 330° ≤ Φ _HR ≤ 360° With an increasing angle of wrap, the pressure window area can be made larger with the same built-in volume ratio. In addition, this also shortens the axial extension of the to be pushed out Working chamber, the so-called profile pocket depth. This reduces the exhaust throttling losses, especially at higher speeds, and thus enables better specific power. However, an angle of wrap that is too large has a negative effect on the construction volume and leads to larger rotors.

und wobei A_Bl eine absolute druckseitige Blaslochfläche und A6 und A7 Zahnlückenflächen des Nebenrotors NR bzw. des Hauptrotors (HR) bezeichnen, wobei die Fläche A6 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Nebenrotors (NR) zwischen zwei benachbarten Scheitelpunkten F5 und dem Kopfkreis KK₁ eingeschlossene Fläche und die Fläche A7 in einer Stirnschnittbetrachtung die zwischen dem Profilverlauf des Hauptrotors (HR) zwischen zwei benachbarten Scheitelpunkten H5 und dem Kopfkreis KK₂ eingeschlossene Fläche bezeichnen.In addition, in an advantageous embodiment, a pair of rotors is provided which is designed and interacts with one another in such a way that a blow hole factor μ _Bl is at least 0.03% and at most 0.25%, preferably at most 0.2%, with $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$

and where A _Bl denotes an absolute blow hole area on the pressure side and A6 and A7 denote tooth gap areas of the secondary rotor NR and the main rotor (HR), respectively, with the surface A6 in a cross-sectional view being that between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the addendum circle KK ₁ enclosed area and the area A7 denote the area enclosed between the profile progression of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ in a cross-sectional view.

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

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

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 $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}\ast 100\left[\%\right]$$

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 pair of rotors is designed and matched to one another in such a way that for a blowhole/profile gap length factor µ _l ∗ µ _Bl $$0.1\%\le {\mathrm{\mu }}_{\mathrm{l}}*{\mathrm{\mu }}_{\mathrm{Bl}}\le 1.26\%$$

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

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

where A _Bl denotes an absolute blow hole area on the pressure side and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, with the area A6 in a cross-sectional view being that between the profile of the secondary rotor (NR) between two adjacent vertices F5 and the addendum circle KK ₁ enclosed area and the area A7 in a front section view the area enclosed between the profile of the main rotor (HR) between two adjacent vertices H5 and the addendum circle KK ₂ .

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

It is also considered advantageous if the main rotor (HR) and secondary rotor (NR) are designed and coordinated with one another in such a way that 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, can be achieved where the pressure ratio is the ratio of the compression end pressure to the intake pressure.

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

$$\mathrm{1,19}\le D_v\le \mathrm{1,26}$$

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

$$\mathrm{1:19}\le D_v\le 1.26$$

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

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

In general, it is considered preferable that the teeth of the auxiliary rotor taper outwards in a cross-sectional view, i.e. all circular arcs running perpendicularly to a radial ray emanating from the center point defined by the axis C1 and drawn through the point F5 from the trailing tooth flank F _N to the leading tooth flank F _V starting from F1 to F2 in the sequence radially outward decrease (or at least remain the same in sections). In other words, in a face section consideration, for all arc lengths b(r) running within a tooth of the secondary rotor of the associated concentric circular arcs with the radius rf ₁ < r < rk ₁ and the common center defined by the axis C1, the leading tooth flank F _v and the trailing tooth flank F _N are limited so that the arc lengths b(r) decrease monotonically with increasing radius r.

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

Advantageously, the face section design of the secondary rotor (NR) is such that the effective direction of the torque, which results from a reference pressure on the partial surface of the secondary rotor delimiting a working chamber, is directed counter to the direction of rotation of the secondary rotor.

Such an end section design has the effect that the entire torque from the gas forces on the secondary rotor is directed counter to the direction of rotation of the secondary rotor. This achieves a defined flank contact between the trailing secondary rotor flank F _N and the leading main rotor flank. This contributes to avoiding the problem of so-called rotor rattling, which can occur in unfavorable, in particular non-stationary, operating situations. Rotor rattling is understood to mean a leading and lagging of the secondary rotor about its axis of rotation superimposed on the uniform rotational movement, which is accompanied by a rapidly alternating impact of the trailing secondary rotor flanks on the leading main rotor flanks and then the leading secondary rotor flanks on the trailing main rotor flanks, etc. This problem occurs in particular when the moment from the gas forces together with other moments (eg from bearing friction) on the secondary rotor is undefined (eg close to zero), which is effectively avoided by the advantageous front section design.

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

Preferably, the profile of a tooth of the secondary rotor is asymmetrically formed in a face section view with respect to the radial ray R drawn from the center point, which is defined by the axis C1, through the apex F5. In the case of the secondary rotor, the leading tooth flank and trailing tooth flank of each tooth are therefore asymmetrical in relation to one another. This asymmetrical design is already known per se for screw compressors. However, it makes a significant contribution to efficient compaction.

mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR).A further preferred embodiment provides that a point C on the connecting section is viewed in a cross section C1 C2 is defined between the first axis C1 and the second axis C2, where the pitch circles WK ₁ of the secondary rotor (NR) and WK ₂ of the main rotor (HR) touch, that K5 is the intersection of the root circle FK ₁ of the secondary rotor (NR) with the connecting section C1 C2 where r ₁ measures the distance between K5 and C, and that K4 denotes the point of the suction-side part of the line of action furthest from the connecting line C1 C2 is spaced between C1 and C2, where r ₂ measures the distance between K4 and C and where: $$0.9\le \frac{{\mathrm{right}}_1}{{\mathrm{right}}_2}\le 0.875\times \frac{{\mathrm{e.g}}_1}{{\mathrm{e.g}}_2}+0.22$$

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

Over the course of the suction-side part of the line of action between the straight section C1 C2 and the suction-side intersection edge, the secondary rotor torque (= torque on the secondary rotor) and the chamber extension into the pressure window can be influenced, among other things. Characteristic features of the above-mentioned course of the suction-side part of the line of action can be described using the radius ratio r ₁ /r ₂ of two concentric circles around point C (= contact point of pitch circle WK ₁ of the auxiliary rotor and pitch circle WK ₂ of the main rotor). If the radius ratio r ₁ /r ₂ is in the specified range, the working chamber is pushed out essentially completely into the pressure window.

$$\mathrm{bevorzugt}\mathrm{0,89}*\left({\mathrm{z}}_1/{\mathrm{z}}_2\right)+\mathrm{0,94}\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le \mathrm{1,05}*\left({\mathrm{z}}_1/{\mathrm{z}}_2\right)+\mathrm{1,22},$$

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 pair of rotors is constructed and designed in such a way that the following applies for a rotor length ratio L _HR/ a: $$0.85*\left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+0.67\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 1.26*\left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+\mathrm{1:18},$$

$$\mathrm{preferred}0.89*\left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+0.94\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 1.05*\left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+1.22,$$

with z ₁ : number of teeth in the secondary rotor (NR) and z ₂ : number of teeth in the main rotor (HR), the rotor length ratio L _HR/ a the ratio of Rotor length L _HR indicates the center distance a and rotor length L _HR is the distance from 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 (with the same displacement) the flexural rigidity of the rotors. In the stressed area, the flexural rigidity of the rotors is sufficiently high so that the rotors do not deflect significantly during operation and the gaps (between the rotors or between the rotors and the compressor housing) can therefore be made relatively narrow without the risk of that under unfavorable operating conditions (high temperatures and/or high pressures) the rotors collide or collide in the compressor housing. Narrow gaps offer the advantage of low backflow and thus contribute to energy efficiency. At the same time, operational safety is guaranteed despite the small gap dimensions. A high flexural rigidity of the rotors is also advantageous in rotor production in order to comply with the high requirements for shape tolerances.

On the other hand, the ratio of L _HR/ a is dimensioned so large that the center distance a is not excessively large in relation to the rotor length L _HR . This is advantageous because, as a consequence, the rotor diameter and, quite specifically, the end faces of the rotors are not excessively large. As a result, on the one hand, the gap lengths can be kept small; this reduces the backflow into the previous working chambers and this in turn improves energy efficiency. On the other hand, the axial forces resulting from the pressure-loaded, pressure-side end faces of the rotors can also be advantageously kept small through small-dimensioned end faces; these axial forces act on the rotors and in particular on the rotor bearings during operation. By minimizing these axial forces, the load on the (roller) bearings can be minimized or the bearings can be dimensioned smaller.

• 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 vordere Zahnflanke F_v in mindestens einem Punkt berührt oder in zwei Punkten schneidet, vgl. insbesondere die Veranschaulichung in Fig. 7h.

Advantageously, provision can also be made for the tooth profile of the secondary rotor (NR) on its radially outer section to follow an arc of a circle with a radius rk ₁ in sections in a face section view, i.e. several points of the leading tooth flank F _v and the trailing tooth flank F _N on the arc of the circle Radius rk ₁ lie around the center point defined by the axis C1, with preferably the circular arc ARC ₁ encloses an angle relative to the axis C1 of between 0.5° and 5°, more preferably between 0.5° and 2.5°,

• where F10 is the point farthest from F5 on the leading tooth flank on that arc and
• wherein the radial ray R ₁₀ drawn between F10 and the center point of the secondary rotor (NR) defined by the axis C1 touches the front tooth flank F _v at at least one point or intersects it at two points, cf. in particular the illustration in Fig. 7h .

The configuration of the tooth profile of the secondary rotor described above is relevant above all for a tooth number ratio of 3/4 or 4/5. With such a number of teeth ratio, the blow hole area can be reduced by complying with the condition given above. With a tooth number ratio of 5/6, however, an aforementioned point of contact or aforementioned points of intersection with the leading tooth flank F _V does not appear to be 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 is claimed as being according to the invention, the pair of rotors comprising 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 in such a way that the front section is designed in such a way that the working chamber formed between the tooth profiles of the main rotor (HR) and secondary rotor (NR) can be pushed out essentially completely into the pressure window.

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

The front section design of the two rotors advantageously ensures that no chamber gusset volume forms between the two rotors when the working chamber is pushed out into the pressure window. The compression can take place particularly efficiently, since no backflow of already compressed medium takes place on the suction side, and herewith none additional heat input occurs. In addition, the entire compressed volume can be used by downstream compressed air consumers. Because overcompression is avoided, there are advantages in terms of energy efficiency, the smooth running of the compressor block and the service life of the rotor bearings. With oil-injected compressors, squeezing of the oil is prevented, thus improving the smooth running 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 guided out of the compressor housing and designed for connection to a drive, with both shaft ends of the secondary rotor preferably being completely accommodated within the compressor housing.

Figur 1

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

Figur 2

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

Figur 3

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

Figur 4

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

Figur 5

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

Figur 6

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

Figur 7a - 7k

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

Figur 8

eine Veranschaulichung des Umschlingungswinkels beim Hauptrotor.

Figur 9

eine schematische Schnittzeichnung einer Ausführungsform eines Verdichterblocks.

Figur 10

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

Figur 11

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

Figuren 12a, 12b

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

Figur 13

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

Figur 14

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

Figur 15

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

Figur 16

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

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

figure 1

a front section of a first embodiment with a tooth number ratio 3/4.

figure 2

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

figure 3

a face section of a third embodiment with a tooth ratio 4/5.

figure 4

a fourth embodiment in a face section consideration with a tooth number ratio 5/6.

figure 5

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

figure 6

an illustration of the isentropic block efficiency for the fourth embodiment at 5/6 tooth ratio compared to the prior art.

Figure 7a - 7k

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

figure 8

an illustration of the wrap angle on the main rotor.

figure 9

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

figure 10

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

figure 11

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

Figures 12a, 12b

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

figure 13

the front section according to the embodiment figure 1 to explain the profile of the main and secondary rotors in this embodiment.

figure 14

the front section according to the embodiment figure 2 to explain the profile of the main and secondary rotors in this embodiment.

figure 15

the front section according to the embodiment figure 3 to explain the profile of the main and secondary rotors in this embodiment.

figure 16

the front section according to the embodiment figure 4 to explain the profile of the main and secondary rotors in this embodiment.

In the following, the exemplary embodiments according to the Figures 1 to 4 be explained. All four exemplary embodiments represent suitable profiles within the meaning 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 below. <u>Table 1</u> Example 1 Example 2 Example 3 Example 4 Number of teeth HR z ₂ 3 3 4 5 Number of teeth NR z ₁ 4 4 5 6 _PTrel [-] 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: Example 1 Example 2 Example 3 Example 4 Center distance a[mm] 127 111 This results in the following cross section main dimensions: Example 1 Example 2 Example 3 Example 4 Dk ₂ [mm] 191 186.1 186 154 Dk ₁ [mm] 153 147.7 144 124.7 bw ₂ [mm] 54.4 56.4 50.5 bw ₁ [mm] 72.6 70.6 60.5 Other main dimensions of the rotors: Example 1 Example 2 Example 3 Example 4 Rotor length L _HR [mm] 307 293 235.5

The following features and parameters according to the invention result from the illustrated exemplary embodiments, which are compiled in Table 5: <u>Table 5</u> Compilation of the other features and parameters: characteristic Example 1 Example 2 Example 3 Example 4 Tooth thickness ratio ε ₁ [-] 0.85 0.82 0.80 0.79 Tooth thickness ratio ε ₂ [-] 0.74 0.64 0.69 0.65 Area ratio A2/A1 [-] 15.7 37.8 10.0 6.2 Area ratio A1/A0 [%] 2.3 1.1 2.2 2.3 Area ratio A3/A1 [-] 9.9 19.6 12.6 11.6 Tooth curvature ratio δ [%] 18.5 21:1 15.7% 15.2 Convex length portion [%] 66.9% 71.2% 62.7% - Radial tooth thickness progression The tooth thickness of the secondary rotor teeth decreases monotonously from the root circle radius rf ₁ to the tip circle radius rk ₁ . Radial R ₁₀ Radial ray R ₁₀ has 2 points of intersection with the leading tooth flank F _V - Area ratio A4/A5 [-] 7.5 10.1 5.5 - wrap angle Φ _HR 334.7 degrees 330.3 330.3 µBI [%] 0.159 0.086 0.106 0.18 µBI*µl [%] 0.94 0.53 0.631 1,058 Profile front section design with regard to chamber extension The working chamber can essentially be completely pushed out into the pressure window. Profile face section design with regard to secondary rotor torque The effective direction of the NR torque resulting from the gas forces is directed against the direction of rotation of the secondary rotor. Shape of the line of action 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 tooth number ratio in figure 5 illustrated. Two curves of the same pressure ratio are shown there.

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

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

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

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

Figure 7a shows an embodiment for secondary rotor NR and main rotor HR with the centers given by the corresponding axes C1 and C2 in a front section view. Furthermore, the main geometric dimensions and main parameters of the front section consideration are shown:

• Addendum circle KK ₁ of the secondary rotor with associated addendum circle radius rk ₁ or addendum circle diameter Dk ₁
• Tip circle KK ₂ of the main rotor with associated tip circle radius rk ₂ or tip circle diameter Dk ₂
• Root circle FK ₁ of the secondary rotor with associated root circle radius rf ₁ or root circle diameter Df ₁
• Root circle FK ₂ of the main rotor with associated root circle radius rf ₂ or root circle diameter Df ₂
• Center distance a between the first axis C1 and the second axis C2
• Pitch circle WK ₁ of the secondary rotor with associated pitch circle radius rw ₁ or pitch circle diameter Dw ₁
• Pitch 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 necessarily resulting direction of rotation of the main rotor when operating as a compressor.

Representing all the teeth of the secondary rotor, the leading tooth flank F _v and the trailing tooth flank F _N are marked on a secondary rotor tooth. A tooth gap 23 is marked as representative of all tooth gaps of the secondary rotor. The based on Figure 7a shown profile course of the leading tooth flank F _v and the trailing tooth flank F _N corresponds to the basis of figure 4 for a gear ratio of 5/6 explained embodiment.

Figure 7b shows the tooth gap surfaces A6 and A7 as well as a side view of a blowhole in a cross-sectional view. In the Figure 7b The profile curves shown to explain the tooth gap areas A6 and A7 correspond to that for a tooth number ratio of 3/4 based on figure 1 illustrated embodiment.

Furthermore shows Figure 7b the position of the coordinate system of the in Figure 7k illustrated blow hole area A _Bl in relation to the rotor pair.

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

The blow hole on the pressure side lies in the coordinate system described and quite concretely in a plane perpendicular to the rotor end faces between the pressure side intersection edge 11 and a line of action point K2 of the part of the line of action on the pressure side.

In a front section view, the line of action 10 is divided into two sections by the connecting line between the two centers C1 and C2: the suction-side part of the line of action is shown below, the pressure-side part above the connecting line.

K2 designates the point of the pressure-side part of the line of action 10 which is spaced farthest from the straight line through C1 and C2. The intersection of the tip circles of the two rotors creates an intersection edge 11 on the pressure side and an intersection edge 12 on the suction side Figure 7b is the pressure-side intersection edge 11 in one Forehead view shown as a point. The same applies to the representation of the suction-side intersection edge 12.

The u-axis is parallel to the rotor faces and corresponds to the vector from the line of action point K2 to the pressure-side intersection edge 11 in a face section view.

Further details on the blow hole area A _BI on the pressure side can be found in Figure 7k .

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

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

Figure 7d shows base points F1 and F2 on the root circle and at the radially outermost point of the tooth an apex F5 in a face section view between the considered tooth of the secondary rotor and the respectively adjacent tooth of the secondary rotor. Furthermore, the triangle D _Z defined by the points F1, F2 and F5 is shown.

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

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

Area A3 corresponds to the area with which the tooth in question, with its leading tooth flank formed between F5 and F2, recedes in relation to triangle D _z .

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

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

Figure 7f shows the offset angle β in a front section view. This is defined by the offset from point F11 to point F12 viewed in the direction of rotation of the auxiliary rotor. F11 is a point on half the circular arc B between F1 and F2 around the center C1 and therefore corresponds to the intersection of the bisector of the tooth pitch angle γ with the circular arc B.

F12 results from the intersection of the radial ray R drawn from the center C1 to the vertex F5 with the arc of a circle B. The basis of Figure 7f shown profile course of the leading tooth flank F _v and the trailing tooth flank F _N corresponds to the basis of figure 4 for a gear ratio of 5/6 explained embodiment.

Figure 7g shows the inflection point F8 on the trailing tooth flank F _N of the secondary rotor, in which the curvature of the course of the tooth profile changes between the addendum and root circle, in a cross-sectional view.

The trailing tooth flank F _N of the auxiliary rotor is divided by point F8 into a substantially convexly curved portion between F8 and the apex F5 and a substantially concavely curved portion between F8 and the base point F1.

Figure 7h shows two points of intersection of the radial ray R ₁₀ from C1 to F10 with the leading tooth flank F _v of the secondary rotor in a cross-sectional view, with point F10 designating that point on the leading tooth flank F _v which lies on the addendum circle KK ₁ with rk ₁ and is furthest from F5 is spaced. The tooth flank follows a circular arc ARC ₁ with radius rk ₁ radially on the outside over a defined section around the center point of the auxiliary rotor defined by the axis C1. The based on Figure 7h The profile curves of the leading tooth flank F _v and the trailing tooth flank F _N explained above correspond to the exemplary embodiment described for a tooth number ratio of 3/4 figure 1 .

Figure 7i shows the tooth profile divided by the radial ray R drawn from C1 to F5 in a face section view.

Specifically, in the illustrated embodiment, the tooth profile is divided into a surface portion A4 associated with the trailing tooth flank F _N and a surface portion A5 associated with the leading tooth flank F _v . The based on Figure 7i The profile curves of the leading tooth flank F _V and the trailing tooth flank F _N explained above correspond to the exemplary embodiment described for a tooth number ratio of 5/6 figure 4 .

Figure 7j shows the line of action 10 between the main and auxiliary rotor and the two concentric circles around the point C with the radii r ₁ and r ₂ for describing the characteristic features of the course of the suction-side part of the line of action.

The line of action 10 is divided into two sections by the connecting distance between the first axis C1 and the second axis C2: the suction-side part of the line of action is below, the pressure-side part is above the connecting distance C1 C2 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 designates the point of the suction-side part of the line of action which is farthest from the connecting section between C1 and C2.

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

Figure 7k:

Figure 7k shows a pressure-side blow hole area A _Bl of a working chamber, specifically in a sectional view perpendicular to the rotor end faces. The delimitation of the blow hole area A _Bl arises from the intersection line 27 of the imaginary flat surface described above with the leading side rotor flank F _v , the intersection line 26 of the plane with the trailing HR flank and a straight section [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 blowhole on the pressure side lies in the in Figure 7b described flat surface and is spanned by

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

In figure 8 the angle of wrap Φ, which has already been mentioned several times, is illustrated again in pictures. In concrete terms, this is the angle Φ by which the face section is twisted from the suction-side to the pressure-side rotor face. This is illustrated here by the twisting of the profile between a pressure-side end face 13 and a suction-side end face 14 by the angle Φ _HR in the case of the main rotor HR.

figure 9 shows a schematic sectional view of a compressor block 19 comprising a housing 15 and mounted therein two rotors geared to one another in pairs, namely a main rotor HR and a secondary rotor NR. The main rotor HR and the secondary rotor NR are each rotatably mounted 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 clutch 18 .

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

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

In figure 10 a main rotor HR interlocked with one another and a secondary rotor NR are also shown in a perspective view.

figure 11 shows the spatial line of action 10 of exactly one tooth gap 23. The profile gap length l _sp is the length of the spatial line of action of exactly one tooth gap 23. This corresponds accordingly to the profile gap length of exactly one tooth division.

The total torque from the gas forces on the secondary rotor is made up of the sum of the torque effects of the gas pressures in all working chambers on the sub-surfaces of the secondary rotor that delimit the respective working chambers. In 12a such a partial surface (22) of the secondary rotor delimiting a working chamber is shown hatched as an example.

Figure 12b shows the division of the in Figure 12a partial surface (22) delimiting a working chamber into an area (28) shown with dots and an area (29) shown with cross-hatching. Only the cross-hatched area (29) contributes to the torque.

The partial surface (22) results from the specific face section design and the pitch of the secondary rotor. The pitch of the slave rotor refers to the pitch of the helical splines of the slave rotor. In the 12a The three-dimensional line of action (10) which is also shown and delimits the partial surface is also defined by the design of the face section of the secondary rotor and the pitch.

Partial surface (22) is also bounded by intersection line (27). Details of cutting line (27) have already been included in the figures 7b and 7k shown and described. The same applies to the line of action point K2.

The specific length of a working chamber in the direction of the rotor axis between the front face (20) of the secondary rotor, on the one hand, and the limitation by the three-dimensional line of action (10) and line of intersection (27), on the other hand, which is dependent on the angular position of the secondary rotor in relation to the main rotor, does not play a significant role here, because - as in as described in the relevant literature - the gas pressures on areas of the rotor surface corresponding to complete tooth gaps in a sectional plane perpendicular to the axis of the rotor (in Figure 12b shown dotted), make no contribution to the torque. The pitch of the slave rotor only affects the amount, but not the effective direction of the torque.

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

only the in Figure 12b Cross-hatched area (29) contributes to the torque.

Thus, in each working chamber, the effective direction of the torque that the gas pressure in the working chamber (or any reference pressure) causes on the partial surface of the secondary rotor delimiting the working chamber is determined by the design of the front section of the secondary rotor.

The above-described advantageous front section design of the secondary rotor (NR) therefore leads to an effective direction (25) of the torque from the gas forces for each partial surface (22) of the secondary rotor that delimits a working chamber and thus for the entire secondary rotor, which is opposite to the direction of rotation (24) of the secondary rotor is directed, whereby the rotor clatter is effectively avoided.

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

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

Although it will be possible for a person skilled in the art to generate suitable profile profiles using the specified parameter values without further ado using the methods customary in the prior art, the profile profiles in the exemplary embodiments discussed above according to FIGS Figures 1 to 4 explained in more detail. To generate profile profiles, profile profiles can also be generated using publicly accessible computer programs—as is well known to those skilled in the art.

• http://www.staff.city.ac.uk/~ra600/DISCO/DISCO/Instalation%20instructions.pdf. Ein Preview zur DISCO-Software kann unter
• http://www.staff.city.ac.uk/~ra600/DISCO/DISCO%20Preview.htm gefunden werden.

SV_Win, a project of the Vienna University of Technology, is mentioned purely as an example in this context, whereby this software is described in great detail in Grafinger's habilitation thesis mentioned at the beginning. An alternative, publicly accessible computer program is the DISCO software and in particular the SCORPATH module from City University London (Centre for Positive Displacement Compressor Technology). General information on this can be found at http://www.city-compressors.co. UK/. Information on installing the software can be found in

• http://www.staff.city.ac.uk/~ra600/DISCO/DISCO/Installation%20instructions.pdf. A preview of the DISCO software can be found at
• http://www.staff.city.ac.uk/~ra600/DISCO/DISCO%20Preview.htm can be found.

Another alternative software is the ScrewView software, which is also mentioned in the dissertation "Directed Evolutionary Algorithms" by Stefan Berlik, Dortmund 2006 (p. 173 f.). The ScrewView software is described in more detail on the website http://pi.informatik.unisiegen.de/Employees/berlik/projects/ in connection with the project "Method for designing dry-running rotary displacement machines".

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

The section S5 to S6 is defined by an arc of a circle around the center point C1. The subsequent section S6 to S7 is specified by an arc of a circle around the center point M3. Finally, the section S7 to S1 is specified by an envelope curve to form a trochoid, generated by the circular arc section T7 to T1 around the center point M5 on the main rotor HR. The sections described above follow one another seamlessly in the order given. The tangents at the end of one section and at the beginning of the adjacent section are equal. In this respect, the sections merge directly, steplessly and without kinks.

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

In general, it should be noted that the profile curves of the secondary rotor NR and the main rotor HR are of course coordinated with one another and insofar as the envelope curves of a trochoid correspond to circular arc sections on the counter-rotor. In addition, as already mentioned, a tangential transition from one section to the next is guaranteed. A general The procedure for calculating the profile of the counter-rotor is described, for example, in Helpertz's dissertation, "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003, p. 60 et seq.

Claims (24)

1. 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 (z₂) of the main rotor (HR) is 4 and the number of teeth (z₁) of the secondary rotor (NR) is 5,

   wherein the relative profile depth of the secondary rotor $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{rf}}_1}{{\mathrm{rk}}_1}$$

   

   is at least 0.515 and at most 0.58, wherein rk₁ is a tip radius drawn around the outer circumference of the secondary rotor (NR) and rf₁ is a root radius applied to the profile base of the secondary rotor,

   wherein the ratio of the center distance α of the first axis (C1) to the second axis (C2) and the tip radius rk₁ $$\frac{a}{{\mathit{rk}}_1}$$

   

   is at least 1.683 and at most 1.836, preferably at most 1.782,

   wherein the main rotor is formed with a wrap angle Φ_HR, for which 320°≤Φ_HR≤360° applies, and wherein for a rotor length ratio L_HR/a applies: $$1.4\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 3.3,$$

   

   wherein the rotor length ratio is formed from the ratio of the rotor length L_HR of the main rotor and the center distance a, and the rotor length L_HR of the main rotor is formed by the distance between a suction-side main-rotor rotor end face and an opposite pressure-side main-rotor rotor end face.
2. Rotor pair according to claim 1, characterized in that circular arcs B₂₅, B₅₀, B₇₅, whose common center is C1, are defined in a transverse section view within a secondary rotor tooth, wherein the radius r₂₅ of B₂₅ has the value rf₁+0.25^∗(rk₁-rf₁), the radius r₅₀ of B₅₀ has the value rf₁+0.5^∗(rk₁-rf₁) and the radius r₇₅ of B₇₅ has the value rf₁+0.75^∗(rk₁-rf₁), and wherein the circular arcs B₂₅, B₅₀, B₇₅ are respectively bounded 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 b₂₅, b₅₀,

   b₇₅ of the circular arcs B₂₅, B₅₀, B₇₅ with ε₁=b₅₀/b₂₅ and ε₂=b₇₅/b₂₅ and the following dimensioning is observed:
   0.75≤ε₁≤0.85 and/or 0.65≤ε₂≤0.74.
3. Rotor pair according to claim 1 or 2, characterized in that in a transverse section view between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR), root points F1 and F2 and, at the radially outermost point of the tooth, an apex point F5 are defined, wherein a triangle D_z is defined by F1, F2 and F5, and
   wherein in a radially outer region the tooth projects beyond the triangle D_z with its leading tooth flank F_v formed between F5 and F2 with an area A1 and with its trailing tooth flank F_N formed between F1 and F5 with an area A2, and wherein 6≤A2/A1≤15 is observed.
4. Rotor pair according to one of claims 1 to 3, characterized in that, in a transverse section view between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR), root points F1 and F2 and, at the radially outermost point of the tooth, an apex point F5 are defined,

   wherein a triangle D_z is defined by F1, F2 and F5, 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 an area A1 and recedes from the triangle D_z in a radially inner region with an area A3, and wherein 9.0≤A3/A1≤18 is observed.
5. Rotor pair according to one of claims 1 to 4, characterized in that in a transverse section view between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR), root points F1 and F2 and, at the radially outermost point of the tooth, an apex point F5 are defined,

   wherein a triangle D_z is defined by F1, F2 and F5, 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 an area A1, wherein the tooth itself has a cross-sectional area A0 bounded by the circular arc B extending between F1 and F2 about the center defined by the axis C1, and

   wherein 1.5%≤A1/A0≤3.5% is observed.
6. Rotor pair according to one of claims 1 to 5, characterized in that in a transverse section view between the considered tooth of the secondary rotor (NR) and the respective adjacent tooth of the secondary rotor (NR), root points F1 and F2 and, at the radially outermost point of the tooth, an apex point F5 are defined,

   wherein the circular arc B extending between F1 and F2 defines about the center defined by the axis C1 a tooth pitch angle γ corresponding to 360°/number of teeth of the secondary rotor NR,

   wherein a point F11 is defined on the half circular arc B between F1 and F2, wherein a radial beam R drawn from the center of the secondary rotor (NR) defined by the axis C1 through the apex point F5 intersects the circular arc B at a point F12,

   wherein an offset angle β is defined by the offset from F11 to F12 considered in the direction of rotation of the secondary rotor (NR), and wherein $$14\%\le \mathrm{\delta }\le 18\%$$

   

   is observed, with $$\delta =\frac{\beta }{\gamma }\ast 100\left[\%\right].$$

   
7. Rotor pair according to one of claims 1 to 6, characterized in that, in a transverse section view, the trailing tooth flank F_N of a tooth of the secondary rotor (NR), formed between F1 and F5, has a convex length component of at least 55% to at most 95%.
8. Rotor pair according to one of claims 1 to 7, characterized in that, in a transverse section view, the radial beam drawn from the axis C1 of the secondary rotor (NR) through F5 divides the tooth profile into a surface portion A5 associated with the leading tooth flank F_v and a surface portion A4 associated with the trailing tooth flank F_N, and
   wherein $$4\le \mathrm{A}4/\mathrm{A}5\le 9$$

   

   is observed.
9. Rotor pair according to one of claims 1 to 8, characterized in that the main rotor HR is formed with a wrap angle Φ_HR, for which applies: 330°≤Φ_HR≤360°.
10. Rotor pair according to one of claims 1 to 9, characterized in that a blowhole factor µ_Bl is at least 0.02% and at most 0.4%, preferably at most 0.25%, wherein $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}\ast 100\left[\%\right],$$

    

    and
    wherein A_Bl designates an absolute pressure-side blowhole area and A6 and A7 designate tooth gap areas of the secondary rotor NR or of the main rotor (HR), wherein the area A6 in a transverse section view designates the area enclosed between the profile run of the secondary rotor (NR) between two adjacent apex points F5 and the tip circle KK₁ and the area A7 in a transverse section view designates the area enclosed between the profile run of the main rotor (HR) between two adjacent apex points H5 and the tip circle KK₂.
11. Rotor pair according to one of claims 1 to 10, characterized in that for a blowhole/profile gap length factor µ_l ^∗µ_Bl $$0.1\%\le {\mathrm{\mu }}_{\mathrm{l}}*{\mathrm{\mu }}_{\mathrm{Bl}}\le 1.72\%$$

    

    is observed with $${\mu }_l=\frac{l_{\mathit{sp}}}{{\mathit{PT}}_1},$$

    

    wherein l_sp designates the length of the profile engagement gap of a tooth gap of the secondary rotor and PT₁ designates the profile depth of the secondary rotor with PT₁=rk₁-rf₁

    and $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{Bl}}}{A6+A7}\ast 100\left[\%\right],$$

    

    wherein A_Bl designates an absolute blowhole area and A6 and A7 designate profile areas of the secondary rotor (NR) or the main rotor (HR), wherein the area A6 in a transverse section view designates the area enclosed between the profile run of the secondary rotor (NR) between two adjacent apex points F5 and the tip circle KK₁ and the area A7 in a transverse section view designates the area enclosed between the profile run of the main rotor (HR) between two adjacent apex points H5 and the tip circle KK₂.
12. Rotor pair according to one of claims 1 to 11, characterized in that main rotor (HR) and secondary rotor (NR) are formed and matched to each other such that dry compression with a pressure ratio Π of up to 5, in particular with a pressure ratio Π of greater than 1 and up to 5, or alternatively a fluid-injected compression with a pressure ratio Π of up to 16, in particular with a pressure ratio Π of greater than 1 and up to 16, is achievable, wherein the pressure ratio is the ratio of final compression pressure to intake pressure.
13. Rotor pair according to one of claims 1 to 12, characterized in that, in the case of dry compression, the main rotor is formed to be operable at a circumferential speed in a range from 20 to 100 m/s relative to a tip circle KK₂ and, in the case of fluid-injected compression, the main rotor is formed to be operable at a circumferential speed in a range from 5 to 50 m/s relative to a tip circle KK₂.
14. Rotor pair according to one of claims 1 to 13, characterized in that, for a diameter ratio defined by the ratio of the tip radii of main rotor (HR) and secondary rotor (NR) $$D_v=\frac{{\mathit{Dk}}_2}{{\mathit{Dk}}_1}=\frac{{\mathit{rk}}_2}{{\mathit{rk}}_1}$$

    

    $$1.195\le D_v\le 1.33$$

    

    is observed, wherein Dk₁ designates the diameter of the tip circle KK₁ of the secondary rotor (NR) and DK₂ designates the diameter of the tip circle KK₂ of the main rotor (HR).
15. Rotor pair according to one of claims 1 to 14, characterized in that, in a transverse section view, the arc lengths b(r), extending within a tooth of the secondary rotor, of the respectively associated concentric circular arcs with the radius rf₁<r<rk₁ and the common center defined by the axis C1 are in each case bounded by the leading tooth flank F_v and the trailing tooth flank F_N and the arc lengths b(r) decrease monotonically as the radius r increases.
16. Rotor pair according to one of claims 1 to 15, characterized in that the transverse section design of the secondary rotor (NR) is carried out in such a way that the effective direction of the torque resulting from a reference pressure on the partial surface of the secondary rotor bounding a working chamber is directed counter to the direction of rotation of the secondary rotor.
17. Rotor pair according to one of claims 1 to 16, characterized in that main rotor (HR) and secondary rotor (NR) are formed for conveying air or inert gases, such as helium or nitrogen, and are matched to each other.
18. Rotor pair according to one of claims 1 to 17, characterized in that, in a transverse section view, the profile of a tooth of the secondary rotor is of asymmetrical design relative to the radial beam R drawn from the center defined by the axis C1 through the apex point F5.
19. Rotor pair according to one of claims 1 to 18, characterized in that in a transverse section view a point C is defined on the connecting path (C1C2) between the first axis (C1) and the second axis (C2), where the pitch circles WK₁ of the secondary rotor (NR) and WK₂ of the main rotor (HR) touch, in that K5 defines the point of intersection of the root circle FK₁ of the secondary rotor (NR) with the connecting path ( C1C2), wherein r₁ is the distance between K5 and C,

    and in that K4 denotes the point on the suction-side part of the line of contact which is furthest from the connecting path C1C2 between C1 and C2, wherein r₂ is the distance between K4 and C, and wherein the following applies: $$0.9\le \frac{r_1}{r_2}\le 0.875\times \frac{z_1}{z_1}+0.22$$

    

    with z₁: number of teeth of the secondary rotor (NR) and z₂: number of teeth of the main rotor (HR).
20. Rotor pair according to one of claims 1 to 19, characterized in that for a rotor length ratio L_HR/a applies: $$0.85*\left({\mathrm{z}}_1/{\mathrm{z}}_2\right)+0.67\le {\mathrm{L}}_{\mathrm{HR}}/\mathrm{a}\le 1.26*\left({\mathrm{z}}_1/{\mathrm{z}}_2\right)+1.18,$$

    

    preferably 0.89^∗(z₁/z₂)+0.94≤L_HR/a≤1.05^∗(z₁/z₂)+1.22,

    with z₁: number of teeth of the secondary rotor (NR) and z₂: number of teeth of the main rotor (HR), wherein the rotor length ratio L_HR/a indicates the ratio of the rotor length L_HR to the center distance a, and rotor length L_HR is the distance between the suction-side main-rotor rotor end face and the pressure-side main-rotor rotor end face.
21. Rotor pair according to one of claims 1 to 14, characterized in that, in a transverse section view, the tooth profile of the secondary rotor (NR) at its radially outer section follows in sections a circular arc ARC₁ with radius rk₁, i.e. a plurality of points of the leading tooth flank F_v and of the trailing tooth flank F_N lie on the circular arc with radius rk₁ about the center defined by the axis C1, wherein preferably the circular arc ARC₁ encloses an angle relative to the axis C1 of between 0.5° and 5°, further preferably between 0.5° and 2.5°, wherein F10 is the point on the leading tooth flank on said circular arc which is furthest away from F5, and
    wherein the radial beam R₁₀ drawn between F10 and the center of the secondary rotor (NR) defined by the axis C1 touches the leading tooth flank F_v in at least one point or intersects it in two points.
22. Compressor block, comprising a compressor housing (15) and a rotor pair according to one of claims 1 to 21, wherein the rotor pair comprises a main rotor (HR) and a secondary rotor (NR) which are each rotatably mounted in the compressor housing (15).
23. Compressor block according to claim 22, characterized in that the transverse section design is made in such a way that the working chamber formed between the tooth profiles of the main rotor (HR) and the secondary rotor (NR) can be pushed out substantially completely into the pressure window.
24. Compressor block according to claim 22 or 23, characterized in that one shaft end of the main rotor is led out of the compressor housing and is formed for connection to a drive, wherein preferably both shaft ends of the secondary rotor are completely accommodated within the compressor housing.

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