EP3358189B9 - 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 rotor pair consisting of a main rotor rotating about a first axis and a secondary rotor rotating about a second axis according to the features of claim 1 or 9. The invention further relates to a compressor block with a corresponding pair of rotors .

Screw machines, be it 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, work 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 which a main rotor sits on the one hand and a secondary rotor on the other. The main rotor and secondary rotor mesh with each other with corresponding helical teeth. Between the teeth and one 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 a suction area, as the rotation of the main and secondary rotors progresses, the working chamber is initially closed and then continuously reduced in volume, so that the medium is compressed. Finally, as the rotation progresses, the working chamber is opened to a 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 compaction.

Depending on the number of teeth, typical pressure ratios can be between 1.1 and 20, whereby the pressure ratio is the ratio of the final compression pressure to the intake pressure. The compaction can take place in one or more stages. Achievable final pressures can be in the range 1.1 bar to 20 bar, for example. As far as pressure information in “bar” is referred to at this point or subsequently in the present application, such pressure information refers to absolute pressures.

In addition to the already mentioned function as a vacuum pump or as a screw expander, screw machines can be used as a compressor in various 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, although this poses different structural requirements in particular, to use a screw machine to compress refrigerants, for example for air conditioning or refrigeration applications. When compressing gases, especially at higher pressure conditions, fluid-injected compression, in particular oil-injected compression, is usually used; However, it is also possible to operate screw machines based on the principle of dry compression. In the low-pressure range, screw compressors are sometimes also referred to as screw blowers.

In recent decades, considerable success has been achieved in terms of the manufacturability, reliability, smooth running and efficiency of screw machines. Improvements or optimizations often refer to optimizing the efficiency depending on the number of teeth, wrap angle and length/diameter ratio of the rotors. The addition of face cuts to the optimization process has only recently become apparent.

Tests have shown that the face cut of the rotors, especially the face cut of the secondary rotor, has a significant influence on energy efficiency. In order to comply with the gearing laws, the face cut of the secondary rotor must correspond to the face cut of the main rotor. The profile of the rotor in a plane perpendicular to the axis of the rotor is referred to as the end section. Different types of end cut generation, such as rotor or rack-based end cut generation methods, are now known from the prior art. If you have decided on a specific process, the first step is to create an initial draft front section. 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.

As an example, some optimization approaches that are known in the state of the art with regard to improving energy efficiency, smooth running and costs will be explained below. Furthermore, problems that can arise should be identified.

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 internal leaks in the compressor block and in particular by reducing the gap between the main rotor and secondary rotor. Specifically, a distinction must be made between the profile gap and the blow hole:

• The pressure-side working chambers have a direct connection to the suction side via the profile gap and thus the greatest possible pressure difference for backflow.
• Successive working chambers are connected to each other via a theoretically unnecessary passage called a blowhole. This is sometimes also referred to as a head rounding opening. This blow hole results from the top rounding of the profiles, in particular the profile of the secondary rotor.
  Pressure-side working chambers are connected to the respective neighboring working chambers via pressure-side blow holes, suction-side working chambers are connected to the respective neighboring working chambers via suction-side blow holes. Unless otherwise stated, the term “blow hole” is to be understood below as “pressure-side blow hole”.

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

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

Very flat profiles therefore have poor utilization of the construction volume, i.e. they lead to large compressor blocks with comparatively high material costs and comparatively high manufacturing costs.

As described above, pressure-side blowholes must not be made too large in order to minimize the backflow of already compressed medium into previous working chambers (i.e. in lower pressure working chambers). Such backflows increase the energy expenditure for the total delivery volume achieved and lead to an undesirable increase in the temperature and pressure levels 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 end cut. Specifically, this can be caused by a strong curvature in the head area of the leading tooth flank of the secondary rotor and in the head area of the trailing tooth flank of the main rotor. However, the stronger this curvature is, the more likely you are to reach production limits, as this leads, for example, to high levels of wear on profile milling cutters and profile grinding wheels during the production of the main rotor and secondary rotor.

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

Another cause of internal leaks that reduce efficiency is the so-called chamber gusset volume, which can arise when the last working chamber (i.e. the working chamber in which the highest pressure prevails) is pushed out into the pressure window. Once the rotors reach a certain angle of rotation, the working chamber no longer has a connection to the pressure window. A so-called chamber gusset volume remains between the two rotors and the pressure-side housing end wall.

This chamber gusset volume is disadvantageous because the enclosed compressed medium can no longer be pushed out into the pressure window The further rotation of the rotors is further compressed, which leads to unnecessarily high power consumption (for over-compression), an unnecessarily high additional heat input, noise development and a reduction in the service life, especially of the roller bearings of the rotors. In addition, the specific performance is impaired because 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 oil-injected compressors, there is also incompressible oil in the chamber gusset and is squeezed.

2 Smooth running

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

In addition to good flank oscillation and low relative speeds between the tooth flanks of the main and secondary rotors, the distribution of the drive torque between the two rotors has a significant effect on smooth running. It is known that an unfavorable distribution often leads to the so-called rotor chatter of the secondary rotor, in which the secondary rotor has undefined flank contact with the main rotor, and as a consequence the secondary rotor alternately has contact with the leading and trailing main rotor flanks. If the two rotors are kept at a distance via a synchronous gear, the above-mentioned rotor chatter is inevitably transferred to the synchronous gear. Good running smoothness not only ensures low noise emissions from the compressor block, but also ensures, for example, that the compressor block is less susceptible to vibration, a long service life for the rolling bearings and low wear in the teeth of the rotors.

3 costs

The material and manufacturing costs of screw compressor blocks are particularly influenced by the manufacturability and the degree of utilization of the construction volume.

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

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

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

• As the profile depth increases, the tooth profiles of the secondary rotor in particular inevitably become thinner and therefore more and more flexible. This makes the rotors increasingly more sensitive to temperature and, overall, has an unfavorable effect on the gaps in the compressor block. The gaps have a significant influence on internal leaks, ie backflows from compression chambers at higher pressure towards the suction side, and can therefore worsen the energy efficiency of the compressor block.
• Furthermore, the difficulties in rotor production increase with flexible teeth.
  • ∘ For example, the risk increases that the already high requirements, particularly in terms of shape tolerances, cannot be met during profile grinding.
  • ∘ Furthermore, flexible teeth require lower feed and cutting speeds both during profile milling and subsequent profile grinding and thereby increase the processing time and, as a result, the manufacturing costs.
• Increasing profile depth also means that the rotor itself becomes more flexible. The more flexible the rotors are, the greater the risk that the rotors will start touching each other or in the compressor housing. To ensure operational safety even at high temperatures or at high pressures, the gaps must be dimensioned 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 optimizing the individual parameters is not very effective on its own, but rather for one good overall result, a compromise must be found between the different (and sometimes contradictory) requirements.

The theoretical calculation bases for generating screw rotor profiles are already often discussed in the literature and general criteria for good end-cut profiles are also described. For example, rotor profiles can be created and modified using the computer program developed by Grafinger ( Habilitation "The computer-aided development of flank profiles for special gearing of screw compressors", Vienna, 2010 ).

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

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

This task is achieved with a pair of rotors according to the features of claim 1 or 9. Advantageous refinements are specified in the subclaims. The task is also solved with a compressor block that includes a correspondingly designed pair of rotors.

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

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

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

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

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

Finally, tooth gap areas are defined between the teeth and the respective tip circle KK, namely tooth gap area A6 between the profile of the secondary rotor NR between two adjacent vertices F5 and the tip 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 head circle KKz.

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

The trailing tooth flank F _N forms a point in its section between the tip circle and the root circle in which the curvature of the course of the tooth profile changes. This point is referred to below as F8 and divides the trailing tooth flank F _N into a convexly curved portion between F8 and the tip circle and a concavely curved portion between the root circle and F8. Small-scale profile changes, such as those caused by 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 front cut, the following terms or parameters for a rotor, in particular the secondary rotor, are crucial for the three-dimensional design: First, a wrap angle Φ is defined. This wrap angle is the angle by which the end section is rotated from the suction-side to the pressure-side rotor end face, see also the more detailed explanations in connection with Figure 8 .

The main rotor has a rotor length L _HR , which is defined as the distance from a main rotor rotor end face on the suction side to a main rotor rotor end face on the pressure side. The distance between the parallel first axis C1 of the secondary rotor and the second axis C2 of the main rotor is referred to below as the axis distance a. It should be noted that in most cases the length of the main rotor L _HR corresponds to the length of the secondary rotor L _NR , with the length of the secondary rotor also being understood as the distance between a suction-side secondary rotor rotor end face and a pressure-side secondary rotor rotor end 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. The ratio L _HR /a is therefore a measure of 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 secondary rotor. 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 rotation angle position of the rotors certain points. These points are called engagement points. The geometric location of all engagement points is called the engagement line and can be calculated in two dimensions using the front section of the rotors, cf. Figure 7j .

When viewed from the front section, the line of engagement is divided into two sections by the connecting line between the two center points C1 and C2, namely a (comparatively short) suction-side section and a (comparatively long) pressure-side section.

If the wrap angle and the rotor length are also specified (= distance between the suction-side end face and the pressure-side end face), the contact line can also be expanded three-dimensionally and corresponds to the contact line of the main rotor and secondary rotor. The axial projection of the three-dimensional line of action onto the frontal cutting plane in turn results in the following Figure 7j illustrated two-dimensional line of action. The term “interference line” is used in the literature for both two-dimensional and three-dimensional considerations. In the following, unless otherwise stated, the term “intervention line” is to be understood as the two-dimensional intervention line, i.e. the projection onto the forehead cut.

The profile engagement gap is defined as follows: In the real compressor block of a screw machine, there is play between both rotors at the installation center distance of the main rotor and secondary rotor. The gap between the main rotor and the secondary rotor is called the profile engagement gap and is the geometric location of all points at which the two paired rotors touch each other or are at the shortest distance from each other. Through the profile engagement gap, the compressing and expanding 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. Working fluid that has already been compressed is transported back to the suction side through the profile engagement gap, thereby reducing the efficiency of the compression. Since the profile engagement gap would be the line of engagement in the case of backlash-free gearing, the profile engagement gap is also referred to as a “quasi-engagement line”.

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

Furthermore, it is known that certain tooth pairings are common in screw machines, for example a rotor pair in which the main rotor 3 and the secondary rotor have 4 teeth or a rotor pairing in which the main rotor has 4 teeth and the secondary rotor 5 teeth or furthermore a rotor pair geometry in which the main rotor has 5 teeth and the secondary rotor has 6 teeth. For different areas of application or purposes, rotor pairs or screw machines with different tooth ratios may be used. For example, rotor pair arrangements with a tooth ratio of 4/5 (main rotor with 4 teeth, secondary 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 specifies different types of rotor pairings and, as a result, different types of screw machines, in particular screw compressors.

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, this creates the basic requirements for a good secondary rotor profile or a good interaction between the secondary rotor profile and the main rotor profile , in particular, this enables a particularly favorable ratio of blow hole area to profile gap length. With regard to the decisive parameters for all the tooth number ratios mentioned, the illustration in Figure 7a referred. The relative profile depth of the secondary rotor is a measure of how deep the profiles are cut. For example, as the profile depth increases, the volume utilization increases, but at the expense of the bending rigidity of the secondary rotor. The following applies to the relative profile depth of the secondary rotor: $${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="1"\; label="PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">PT</figure-callout>}}_1}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-\left(a-{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2\right)}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}=1-\frac{a-{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

with $${\mathrm{<figure-callout\; id="1"\; label="PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">PT</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1-{\mathrm{<figure-callout\; id="1"\; label="rf"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rf</figure-callout>}}_1\mathrm{and}{\mathrm{rf}}_1=\mathrm{a}-{\mathrm{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2$$

, Achsabstand a zum Nebenrotor-Kopfkreisradius rk₁.In this respect there is a connection with the relationship of $\frac{\mathrm{a}}{{\mathrm{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$

, center distance a to the secondary 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 determine an advantageous rotor pairing in the axial dimension.

1, Preferred embodiments for a pair of rotors with a tooth ratio of 3/4

Preferred embodiments 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 circular arcs B ₂₅ , B ₅₀ , B ₇₅ running within a secondary rotor tooth, whose common center is given by the axis C1, are defined in a face section view, the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 ^∗ (rk ₁ - rf ₁ ), the radius r ₅₀ of B ₅₀ has the value r ₅₀ = rf ₁ + 0.5 ^∗ (rk ₁ - rf ₁ ) and the radius r ₇₅ of B ₇₅ has the value r ₇₅ = rf ₁ + 0.75 ^∗ (rk ₁ - rf ₁ ), and where the circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each limited by the leading tooth flank F _V and the trailing tooth flank F _N , 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 profile engagement gap. However, the two parameters behave in opposite directions, ie the smaller the blow hole is modeled, the longer the length of the profile engagement gap inevitably becomes. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole becomes. A particularly favorable combination of the two parameters is achieved in the stressed areas. At the same time, a sufficiently high bending rigidity of the secondary rotor is ensured. 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 view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor, base points F1 and F2 are defined on the base circle and a vertex F5 at the radially outermost point of the tooth, whereby F1, F2 and F5 a triangle D _Z is defined and wherein in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 has a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a surface A2 the triangle D protrudes _Z and where 8 ≤ A2/A1 ≤ 60 is maintained.

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

In a further preferred embodiment, the rotor pair has a secondary rotor, in which base points F1 and F2 and a vertex F5 are defined at the radially outermost point of the tooth in a face section view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor, wherein a triangle D _Z is defined by F1, F2 and F5 and the leading tooth flank F _V formed between F5 and F2 projects in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z and in a radially inner region opposite the Triangle D _Z with an area A3 recedes and where 7.0 ≤ A3/A1 ≤ 35 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 base points F1 and F2 and a vertex F5 are defined at the radially outermost point of the tooth in a face section view between the tooth of the secondary rotor (NR) under consideration and the adjacent tooth of the secondary rotor (NR). are, where F1, F2 and F5 form a triangle D _Z is defined and wherein the leading tooth flank F _V formed between F5 and F2 projects in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z , the tooth itself having a circular arc B running through the between F1 and F2 Axis C1 has a limited cross-sectional area A0 and where 0.5% ≤ A1/A0 ≤ 4.5% is maintained. 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 base points F1 and F2 and a vertex F5 are defined at the radially outermost point of the tooth between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), the between F1 and F2 extending circular arc B around the center defined by the axis C1 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor (NR), a point F11 being defined on half the circular arc B between F1 and F2, whereby one of The center point of the secondary rotor (NR) defined by the axis C1, the radial beam R drawn through the apex F5 intersects the circular arc B at a point F12, an offset angle β being defined by the offset from F11 to F12 viewed in the direction of rotation of the secondary rotor (NR) and where 14% ≤ δ ≤ 25% is complied with $\delta =\frac{\beta }{\gamma }\ast 100\left[\%\right]$

.

First of all, it is once again made clear that the offset angle is preferably always positive, i.e. the offset is always in the direction of the direction of rotation and not in the opposite direction. The tooth of the secondary rotor is therefore 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 engagement, the length and shape of the profile engagement gap, the secondary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. For an illustration of the parameters, see additional information Figure 7f referred.

It is considered advantageous if, in an end-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 45% to at most 95%.

The relative long convex length component 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 bending stiffness of the secondary rotor on the other hand. With regard to the illustration of the parameters, additional information is also provided 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 an end-section view, the radial beam R drawn from the axis C1 of the secondary rotor (NR) through F5 divides the tooth profile into an area portion A5 assigned to the leading tooth flank F _V and an area 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 noted again at this point that the tooth profile is limited radially inward towards the axis C1 by the root circle FK ₁ . It can happen here that the radial beam 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 F _V , 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 also 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 assigned to the trailing tooth flank F _N is then limited on the one hand by the radial beam R and in sections, namely between the two intersection points of the leading tooth flank F _V with the radial beam R, and on the other hand also by the leading tooth flank F _V.

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

As the wrap angle increases, the pressure window area can be made larger with the same built-in volume ratio. In addition, this also shortens the axial extent of the one to be pushed out Working chamber, the so-called profile pocket depth. This reduces the exhaust throttle losses, especially at higher speeds, and thus enables better specific performance. However, a wrap angle that is too large has a negative impact on the construction volume and leads to larger rotors.

und
wobei A_BI 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 _BI is at least 0.02% and at most 0.4%, preferably at most 0.25%, where $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$

and
where A _BI denotes an absolute pressure-side blow hole area and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, whereby the area A6 in a face section view is between the profile course of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in a face section view denote the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

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

• eingehalten ist mit $${\mu }_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
  
• wobei I_sp die Länge des räumlichen, also dreidimensionalen Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnen
  und $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
• wobei A_BI eine absolute 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 coordinated with one another in such a way that for a blow hole/profile gap length factor µ _I ^∗ µ _BI $$0.1\%\le {\mathrm{\mu }}_{\mathrm{l}}\ast {\mathrm{\mu }}_{\mathrm{Bl}}\le 1.72\%$$

• is complied with $${\mu }_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
  
• where I _sp denotes the length of the spatial, i.e. three-dimensional profile engagement gap of a tooth gap of the secondary rotor and PT ₁ denotes the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
  and $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
• where A _BI denotes an absolute pressure-side blow hole area and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, whereby the area A6 in a face section view is between the profile course of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in a face section view denote the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

µ _I 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 you to set a dimension for the length of the profile engagement gap, regardless of the size of the screw machine. The smaller the numerical value of the characteristic number µ _I , the shorter the profile gap of a tooth pitch is with the same profile depth and thus the lower the leakage volume flow back to the suction side. From the factor µ _I ^∗ µ _BI , the goal is to combine a small pressure-side blow hole with a short profile gap. However, 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 Π of up to 3, in particular with a pressure ratio Π of greater than 1 and up to 3 , can be achieved, whereby the pressure ratio refers to the ratio of final compression pressure to intake pressure.

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

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

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 secondary rotor (NR). $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="Dk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="Dk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

$$\mathrm{1,145}\le D_v\le 1.30$$

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 embodiments for a pair of rotors with a tooth ratio of 4/5

Preferred embodiments 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 circular arcs B ₂₅ , B ₅₀ , B ₇₅ running within a secondary rotor tooth, whose common center is given by the axis C1, are defined in a face section view, the radius r ₂₅ of B ₂₅ having the value r ₂₅ = rf ₁ + 0.25 ^∗ (rk ₁ - rf ₁ ), the radius r ₅₀ of B ₅₀ has the value r ₅₀ = rf ₁ + 0.5 ^∗ (rk ₁ - rf ₁ ) and the radius r ₇₅ of B ₇₅ has the value r ₇₅ = rf ₁ + 0.75 ^∗ (rk ₁ - rf ₁ ), and where the circular arcs B ₂₅ , B ₅₀ , B ₇₅ are each limited by the leading tooth flank F _V and the trailing tooth flank F _N , and 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 is: $$0.75\le {\mathrm{<figure-callout\; id="1"\; label="\epsilon "\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_1\le 0.85\mathrm{and}/\mathrm{or}0.65\le {\mathrm{<figure-callout\; id="2"\; label="\epsilon "\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_2\le 0.74.$$

The aim is to combine a small blow hole with a short length of profile engagement gap. However, the two parameters behave in opposite directions, i.e. the smaller the blowhole is modeled, the longer the length inevitably becomes of the profile engagement gap. Conversely, the shorter the length of the profile engagement gap, the larger the blow hole becomes. A particularly favorable combination of the two parameters is achieved in the stressed areas. At the same time, a sufficiently high bending rigidity of the secondary rotor is ensured. 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 view between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), base points F1 and F2 are defined on the base circle and a vertex F5 is defined at the radially outermost point of the tooth, where a triangle D _Z is defined by F1, F2 and F5 and wherein in a radially outer region the tooth with its leading tooth flank F _V formed between F5 and F2 has a surface A1 and with its trailing tooth flank F _N formed between F1 and F5 with a Area A2 protrudes beyond the triangle D _Z and where 6 ≤ A2/A1 ≤ 15 is maintained.

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

In a further embodiment, the pair of rotors has a secondary rotor, in which base points F1 and F2 are defined in a face section view between the tooth of the secondary rotor (NR) under consideration and the adjacent tooth of the secondary rotor (NR) and a vertex F5 is defined at the radially outermost point of the tooth are, where a triangle D _Z is defined by F1, F2 and F5 and where the leading tooth flank F _V formed between F5 and F2 projects in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z and in a radially inner region recedes from the triangle D _Z with an area A3 and where 9.0 ≤ A3/A1 ≤ 18 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 base points F1 and F2 and a vertex F5 are defined at the radially outermost point of the tooth in a face section view between the tooth of the secondary rotor (NR) under consideration and the adjacent tooth of the secondary rotor (NR). are, where a triangle D _Z is defined by F1, F2 and F5 and where the leading tooth flank F _V formed between F5 and F2 projects in a radially outer region of the tooth with a surface A1 beyond the triangle D _Z , the tooth itself having a has a cross-sectional area A0 limited by the circular arc B running between F1 and F2 around the center defined by the axis C1 and where 1.5% ≤ A1/A0 ≤ 3.5% is maintained.

Regarding the definition of the parameters, reference is 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 base points F1 and F2 and a vertex F5 are defined at the radially outermost point of the tooth between the tooth of the secondary rotor (NR) under consideration and the respectively adjacent tooth of the secondary rotor (NR), the between F1 and F2 extending circular arc B around the center defined by the axis C1 defines a tooth pitch angle γ corresponding to 360 ° / number of teeth of the secondary rotor NR, with a point F11 being defined on half the circular arc B between F1 and F2, whereby a point F11 is defined by the Axis C1 defined center of the secondary rotor (NR) drawn through the apex F5 radial beam R intersects the circular arc B at a point F12, 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 $$14\%\le \mathrm{\delta }\le 18\%$$

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

First of all, it is once again made clear that the offset angle is preferably always positive, i.e. the offset is always in the direction of the direction of rotation and not in the opposite direction. The tooth of the secondary rotor is therefore curved towards the direction of rotation of the secondary rotor. However, the offset should stay within the range specified as advantageous in order to enable a favorable compromise between the blow hole area, the shape of the line of engagement, the length and shape of the profile engagement gap, the secondary rotor torque, the bending stiffness of the rotors and the chamber extension into the pressure window. For an illustration of the parameters, see additional information Figure 7f referred.

It is also considered advantageous if, in a face-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%.

The relative long convex length component 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 bending stiffness of the secondary rotor on the other hand. With regard to the illustration of the parameters, additional information is also provided 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 secondary rotor is preferably designed in such a way that, in an end-section view, the radial beam R drawn from the axis C1 of the secondary rotor (NR) through F5 divides the tooth profile into an area portion A5 assigned to the leading tooth flank F _V and an area portion A4 assigned to the trailing tooth flank F _N and where $$4\le \mathrm{A}4/\mathrm{A}5\le 9$$

is complied with. It should be noted again at this point that the tooth profile is limited radially inward towards the axis C1 by the root circle FK ₁ . It can happen here that the radial beam 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 F _V , 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 also 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 assigned to the trailing tooth flank F _N is then limited in sections by the radial beam R, namely between the two intersection points of the leading tooth flank F _V with the radial beam 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°.

As the wrap angle increases, the pressure window area can be made larger with the same built-in volume ratio. In addition, this also shortens the axial extent of the working chamber to be pushed out, the so-called profile pocket depth. This reduces the exhaust throttle losses, especially at higher speeds, and thus enables better specific performance. However, a wrap angle that is too large has a negative impact on the construction volume and leads to larger rotors.

• eingehalten ist, wobei $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
  und
• wobei A_BI 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 _BI is at least 0.02% and at most 0.4%, preferably at most 0.25%,

• is complied with, whereby $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
  and
• where A _BI denotes an absolute pressure-side blow hole area and A6 and A7 denote tooth gap areas of the secondary rotor NR and the main rotor (HR), respectively, whereby the area A6 in a face section view is the one between the profile course of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in a face section view denote the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

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

• eingehalten ist mit $${\mu }_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
  
• wobei I_sp die Länge des räumlichen, also dreidimensionalen Profileingriffspalts einer Zahnlücke des Nebenrotors und PT₁ die Profiltiefe des Nebenrotors mit PT₁ = rk₁ - rf₁ bezeichnen
  und $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
• wobei A_BI eine absolute 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 coordinated with one another in such a way that for a blow hole/profile gap length factor µ _I ^∗ µ _BI $$0.1\%\le {\mathrm{\mu }}_{\mathrm{l}}\ast {\mathrm{\mu }}_{\mathrm{Bl}}\le 1.72\%$$

• is complied with $${\mu }_l=\frac{{\mathrm{<figure-callout\; id="1"\; label="l\; sp\; PT"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">l</figure-callout>}}_{\mathit{sp}}}{{\mathit{PT}}_{}},$$
  
• where I _sp denotes the length of the spatial, i.e. three-dimensional profile engagement gap of a tooth gap of the secondary rotor and PT ₁ denotes the profile depth of the secondary rotor with PT ₁ = rk ₁ - rf ₁
  and $${\mu }_{\mathit{Bl}}=\frac{A_{\mathit{<figure-callout\; id="6"\; label="Bl\; A"\; filenames="imgf0004.png,imgf0017.png"\; state="\{\{state\}\}">Bl</figure-callout>}}}{A}\ast 100\left[\%\right]$$
  
• where A _BI denotes an absolute pressure-side blowhole area and A6 and A7 denote tooth gap areas of the secondary rotor (NR) and the main rotor (HR), respectively, whereby the area A6 in a face section view is between the profile course of the secondary rotor (NR) between two adjacent vertices F5 and the tip circle KK ₁ enclosed area and the area A7 in a face section view denote the area enclosed between the profile course of the main rotor (HR) between two adjacent vertices H5 and the tip circle KK ₂ .

µ _I 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 you to set a dimension for the length of the profile engagement gap, regardless of the size of the screw machine. The smaller the numerical value of the characteristic figure µ _I , the shorter the profile gap is for the same profile depth and therefore the lower the leakage volume flow back to the suction side. The factor µ _I ^∗ µ _BI gives the goal of a small pressure-side blowhole with a short profile gap. However, 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 denoting the ratio of the final compression pressure to the intake pressure.

A further preferred embodiment provides a pair of rotors such that in the case of dry compression the main rotor has a peripheral speed in a range of 20 to 100 m/s in relation to a tip circle KK ₂ and in the case of fluid-injected compression the main rotor has a peripheral speed in is designed to be operable 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 secondary rotor (NR). $$D_v=\frac{{\mathit{<figure-callout\; id="2"\; label="Dk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="Dk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">Dk</figure-callout>}}_1}=\frac{{\mathit{<figure-callout\; id="2"\; label="rk"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">rk</figure-callout>}}_2}{{\mathit{<figure-callout\; id="1"\; label="rk"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">rk</figure-callout>}}_1}$$

$$\mathrm{1,195}\le D_v\le 1.33$$

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 design for a pair of rotors with a tooth ratio of 3/4 or 45

In general, it is considered to be preferred that, when viewed from an end-section perspective, the teeth of the secondary rotor taper outwards, that is, all circular arcs extending perpendicularly from the trailing tooth flank F _N to a radial beam emanating from the center defined by the axis C1 and drawn through the point F5 leading tooth flank F _V starting from F1 to F2 in the sequence radially outwards (or in sections at least stay the same). In other words, in a face section view, the following applies to all arc lengths b(r) of the associated concentric circular arcs with the radius rf ₁ < r < rk ₁ and the common center defined by the axis C1, which are defined by the axis C1, which run within a tooth of the secondary rotor leading tooth flank F _V and the trailing tooth flank F _N are limited so that the arc lengths b(r) decrease monotonically with increasing radius r.

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

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

Such a face cut design causes the entire torque from the gas forces on the secondary rotor to be directed in the opposite direction to the direction of rotation of the secondary rotor. This results in a defined flank contact between the trailing secondary rotor flank F _N and the leading main rotor flank. This helps to avoid the problem of so-called rotor chatter, which can occur in unfavorable, especially unsteady, operating situations. Rotor chatter 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 changing impact of the trailing secondary rotor flanks on the leading main rotor flanks and then of 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 cut design.

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

Preferably, in an end-section view, the profile of a tooth of the secondary rotor is asymmetrically designed with respect to the radial beam R drawn from the center point, which is defined by the axis C1, through the apex F5. In the secondary rotor, the leading tooth flank and trailing tooth flank of each tooth are designed to be asymmetrical to one another. This asymmetrical design is already known per se for screw compressors. However, it contributes significantly to efficient compaction.

mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR).A further preferred embodiment provides that in a front section view a point C on the connecting route C1C2 _ 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 C1C2 _ defined, where r ₁ measures the distance between K5 and C, and that K4 denotes the point of the suction-side part of the line of action that is furthest from the connecting section C1C2 _ is spaced between C1 and C2, where r ₂ measures the distance between K4 and C and where: $$0.9\le \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0004.png,imgf0006.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}\le 0.875\times \frac{{\mathrm{e.g}}_1}{{\mathrm{e.g}}_2}+0.22$$

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

About the course of the suction-side part of the line of action between the straight section C1C2 _ and the intersection edge on the suction side, 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 secondary rotor and pitch circle WK ₂ of the main rotor). If the radius ratio r ₁ /r ₂ is in the specified range, the working chamber is essentially completely pushed out into the pressure window.

• bevorzugt 0,89 ^∗ (z₁z₂) + 0,94 ≤ L_HR/a ≤ 1,05 ^∗ (z₁/z₂) + 1,22,
• mit z₁: Zahl der Zähne beim Nebenrotor (NR) und z₂: Zahl der Zähne beim Hauptrotor (HR), wobei das Rotorlängenverhältnis L_HR/a das Verhältnis der Rotorlänge L_HR zum Achsabstand a angibt und Rotorlänge L_HR der Abstand der saugseitigen Hauptrotor-Rotorstirnfläche zur druckseitigen Hauptrotor-Rotorstirnfläche ist.

In a preferred embodiment, the rotor pair is designed and designed in such a way that the following applies to a rotor length ratio L _HR /a: $$0.85\ast \left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+0.67\le {\mathrm{L}}_{\mathrm{MR}}/\mathrm{a}\le 1.26\ast \left({\mathrm{e.g}}_1/{\mathrm{e.g}}_2\right)+1.18,$$

• preferably 0.89 ^∗ (z ₁ z ₂ ) + 0.94 ≤ L _HR /a ≤ 1.05 ^∗ (z ₁ /z ₂ ) + 1.22,
• with z ₁ : number of teeth on the secondary rotor (NR) and z ₂ : number of teeth on the main rotor (HR), where the rotor length ratio L _HR /a indicates the ratio of the rotor length L _HR to the center distance a and rotor length L _HR the distance between the suction side Main rotor rotor end face is to the pressure side main rotor rotor end face.

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

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

It can advantageously also be provided that, in an end-section view, the tooth profile of the secondary rotor (NR) follows a circular arc with radius rk ₁ in sections on its radially outer section, i.e. several points of the leading tooth flank F _V and the trailing tooth flank F _N on the circular arc Radius rk ₁ lies around the center defined by the axis C1, the circular arc ARC ₁ preferably enclosing an angle with respect to the axis C1 between 0.5° and 5°, more preferably between 0.5° and 2.5°,

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

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

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

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

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

The face cut design of the two rotors advantageously ensures that no chamber gusset volume is formed between the two rotors when the working chamber is pushed out into the pressure window. The compression can be carried out particularly efficiently because there is no backflow of already compressed medium onto the suction side, and therefore no additional heat input occurs. In addition, the entire compressed volume can be used by downstream compressed air consumers. The fact that overcompression is avoided results in advantages for energy efficiency, for the smooth running of the compressor block and for the service life of the rotor bearings. With oil-injected compressors, 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 led out of the compressor housing and designed for connection to a drive, with preferably both shaft ends of the secondary rotor being completely accommodated within the compressor housing.

Figur 1

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

Figur 2

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

Figur 3

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

Figur 4

ein nicht erfindungsgemäßes Veranschaulichungsbeispiel 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 nicht erfindungsgemäßes Veranschaulichungsbeispiel zum 5/6 Zähne-Zahlverhältnis im Vergleich zum Stand der Technik.

Figur 7a - 7k

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

Figur 8

eine Veranschaulichung des Umschlingungswinkels beim Hauptrotor.

Figur 9

eine schematische Schnittzeichnung einer Ausführungsform eines Verdichterblocks.

Figur 10

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

Figur 11

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

Figuren 12a, 12b

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

Figur 13

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

Figur 14

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

Figur 15

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

Figur 16

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

The invention will be explained in more detail below with regard to further features and advantages based on the description of exemplary embodiments. Show here:

Figure 1

a face cut of a first embodiment with a tooth ratio of 3/4.

Figure 2

a face cut of a second embodiment with a tooth ratio of 3/4.

Figure 3

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

Figure 4

an illustrative example not according to the invention in a face cut view with a tooth number ratio of 5/6.

Figure 5

an illustration of the isentropic block efficiency for the second exemplary embodiment with a 3/4 tooth number ratio in comparison to the prior art.

Figure 6

an illustration of the isentropic block efficiency for the illustrative example not according to the invention for the 5/6 tooth number ratio in comparison to the prior art.

Figure 7a - 7k

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

Figure 8

an illustration of the wrap angle of the main rotor.

Figure 9

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

Figure 10

an embodiment for a pair of interlocking 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 forehead cut according to the embodiment Figure 1 to explain the profile of the main and secondary rotors in this embodiment.

Figure 14

the forehead cut according to the embodiment Figure 2 to explain the profile of the main and secondary rotors in this embodiment.

Figure 15

the forehead cut according to the embodiment Figure 3 to explain the profile of the main and secondary rotors in this embodiment.

Figure 16

the forehead cut according to the embodiment Figure 4 to explain the profile of the main and secondary rotors in this embodiment.

The following are the exemplary embodiments Figures 1 to 3 be explained. All three exemplary embodiments represent suitable profiles in the sense of the present invention.

The corresponding geometric default values for the main rotor HR and the secondary rotor NR are given in Tables 1 to 4 below. <u>Table 1</u> Example 1 Example 2 Example 3 Illustrative 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 Illustrative example 4 Center distance a[mm] 127 111 This results in the following main face cut dimensions: Example 1 Example 2 Example 3 Illustrative example 4 Dk ₂ [mm] 191 186.1 186 154 Dk ₁ [mm] 153 147.7 144 124.7 rw2 [mm] 54.4 56.4 50.5 rw ₁ [mm] 72.6 70.6 60.5 Other main dimensions of the rotors: Example 1 Example 2 Example 3 Illustrative example 4 Rotor length L _HR [mm] 307 293 235.5

The exemplary embodiments shown result in the following features and parameters according to the invention, which are summarized in Table 5: <u>Table 5</u> Compilation of other features and parameters: characteristic Example 1 Example 2 Example 3 Illustrative 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 component [%] 66.9% 71.2% 62.7% - Radial tooth thickness progression The tooth thickness of the secondary rotor teeth decreases monotonically from the root radius rf ₁ to the tip radius rk ₁ . Radial jet R ₁₀ Radial beam R ₁₀ has 2 intersection points with the leading tooth flank F _V - characteristic Example 1 Example 2 Example 3 Illustrative example 4 Area ratio A4/A5 [-] 7.5 10.1 5.5 - Wrap angle Φ _HR 334.7° 330.3 330.3 µBI [%] 0.159 0.086 0.106 0.18 µBI ^∗ µl [%] 0.94 0.53 0.631 1,058 Profile end section design q regarding chamber extension The working chamber can essentially be completely pushed out into the pressure window. Profile end section design with regard to secondary rotor torque The effective direction of the NR torque resulting from the gas forces is directed opposite to 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 in comparison to the prior art is for the second exemplary embodiment at the 3/4 tooth number ratio in Figure 5 illustrated. Two curves with the same pressure ratio are shown there. The specific pressure ratio shown is 2.0 (ratio of outlet pressure to inlet pressure). The isentropic block efficiency could be significantly improved compared to the values achievable with the state of the art.

In Figure 6 The isentropic block efficiency is illustrated in comparison to the prior art in the illustrative example not according to the invention (5/6 tooth number ratio). Here too, two curves with the same pressure ratio are shown. The pressure ratio shown here is 9.0 (ratio of outlet pressure to inlet pressure).

The ones in the Figures 5 and 6 The specified delivery quantity corresponds to the delivery volume flow of the compressor block based on the intake 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 end-section view of an embodiment for secondary rotor NR and main rotor HR with the center points given by the corresponding axes C1 and C2. Furthermore, the main geometric dimensions or main parameters of the end section analysis are shown:

• Tip circle KK ₁ of the secondary rotor with the associated tip circle radius rk ₁ or tip circle diameter Dk ₁
• Tip circle KK ₂ of the main rotor with the associated tip circle radius rk ₂ or tip circle diameter Dk ₂
• Root circle FK ₁ of the secondary rotor with the associated root circle radius rf ₁ or root circle diameter Df ₁
• Root circle FK ₂ of the main rotor with the associated root circle radius rf ₂ or root circle diameter Df ₂
• Axis distance a between the first axis C1 and the second axis C2
• Pitch circle WK ₁ of the secondary rotor with the associated pitch circle radius rw ₁ or pitch circle diameter Dw ₁
• Pitch circle WK ₂ of the main rotor with the associated pitch circle radius rw ₂ or pitch circle diameter Dw ₂

Also shown are the direction of rotation 24 of the secondary rotor and the inevitably resulting direction of rotation of the main rotor when operating as a compressor.

Representing all 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 a representative of all tooth gaps in the secondary rotor. The based on Figure 7a The profile course of the leading tooth flank F _V and the trailing tooth flank F _N shown corresponds to that based on Figure 4 for a tooth number ratio of 5/6 explained embodiment.

Figure 7b shows the tooth gap surfaces A6 and A7 in a front section view as well as a side view of a blow hole. In the Figure 7b The profile curves shown to explain the tooth gap surfaces A6 and A7 correspond to that for a tooth number ratio of 3/4 based on Figure 1 illustrated embodiment.

Continues to show Fig. 7b the position of the coordinate system of the in Fig. 7k shown blow hole area A _BI in relation to the rotor pair.

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

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

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

K2 denotes the point of the pressure-side part of the line of action 10 which is furthest away from the straight line through C1 and C2.

The intersection of the tip circles of the two rotors creates a pressure-side intersection edge 11 and a suction-side intersection edge 12. In Fig. 7b the pressure-side intersection edge 11 is shown as a point in an end-section view. The same applies to the representation of the suction-side intersection edge 12.

The u-axis is parallel to the rotor end faces and, when viewed from the end face, corresponds to the vector from the line of action point K2 to the pressure-side intersection edge 11.

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

Figure 7c shows a face sectional view of a tooth of the secondary rotor with the concentric circular arcs B ₂₅ , B ₅₀ , B ₇₅ running within the rotor tooth around the center point C1 with the associated radii r ₂₅ , r ₅₀ , r ₇₅ and the associated arc lengths b ₂₅ , b ₅₀ , _b75 .

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

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

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

Tooth partial surface A2 corresponds to the surface 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 region.

Area A3 corresponds to the area with which the tooth under consideration with its leading tooth flank formed between F5 and F2 recedes from the 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 The profile course of the leading tooth flank F _V and the trailing tooth flank F _N shown corresponds to that based on Figure 4 for a tooth number ratio of 5/6 explained embodiment.

Figure 7e shows, in an end-section view, the cross-sectional area A0 of a tooth of the secondary rotor, which is limited by the circular arc B running between F1 and F2 around the center point C1. The based on Figure 7e The profile course of the leading tooth flank F _V and the trailing tooth flank F _N shown corresponds to that based on Figure 4 for a tooth number 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 secondary rotor. F11 is a point on half the circular arc B between F1 and F2 around the center point 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 circular arc B. The point based on Figure 7f The profile course of the leading tooth flank F _V and the trailing tooth flank F _N shown corresponds to that based on Figure 4 for a tooth number ratio of 5/6 explained embodiment.

Figure 7g shows, in a face section view, the turning point F8 on the trailing tooth flank F _N of the secondary rotor, in which the curvature of the course of the tooth profile between the tip and root circles changes.

The trailing tooth flank F _N of the secondary rotor is divided by the 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, in an end-section view, two intersection points of the radial beam R ₁₀ from C1 to F10 with the leading tooth flank F _V of the secondary rotor, where the point F10 denotes the point of the leading tooth flank F _V which lies on the tip 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 around the center of the secondary rotor defined by the axis C1 over a defined section on the radial outside. The based on Figure 7h The profile curves of the leading tooth flank F _V and the trailing tooth flank F _N explained correspond to the exemplary embodiment described for a tooth number ratio of 3/4 Figure 1 .

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

Specifically, in the embodiment shown, the tooth profile is divided into an area portion A4 assigned to the trailing tooth flank F _N and an area portion A5 assigned to 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 correspond to the exemplary embodiment described for a tooth number ratio of 5/6 Figure 4 .

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

The line of action 10 is divided into two sections by the connecting section 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 section C1C2 _ shown.

Point C is the contact point 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 that is furthest away from the connecting section between C1 and C2. Radius r ₁ is the distance between K5 and C, radius r ₂ is the distance between K4 and C.

Figure 7k:

Figure 7k shows a pressure-side blow hole surface A _BI of a working chamber in a sectional view perpendicular to the rotor end faces. The boundary of the blow hole area A _BI arises from the intersection line 27 of the imaginary flat surface described above with the leading secondary rotor flank F _V , the intersection line 26 of the plane with the trailing HR flank and a straight 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 pressure-side blow hole is in Fig. 7b flat surface described and is clamped by

• the u-axis parallel to the rotor end 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 wrap angle Φ, which has already been mentioned several times, is illustrated again. Specifically, this is the angle Φ by which the face cut is rotated from the suction-side to the pressure-side rotor face. In this case, this is due to the rotation of the profile between one pressure-side end face 13 and a suction-side end face 14 illustrated by the angle Φ _HR in the main rotor HR.

Figure 9 shows a schematic sectional view of a compressor block 19 comprising a housing 15 and two rotors mounted in pairs, namely a main rotor HR and a secondary rotor NR. The main rotor HR and 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 secondary rotor NR directly via the rotor flanks. In contrast, in a dry screw compressor, contact with 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 An interlocking main rotor HR and secondary rotor NR are shown in a perspective view.

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

The total torque from the gas forces on the secondary rotor is composed of the sum of the torque effects of the gas pressures in all working chambers on the partial surfaces of the secondary rotor delimiting the respective working chambers. In Fig. 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 shown a partial surface (22) delimiting the working chamber into an area (28) shown in dotted lines and an area (29) shown cross-hatched. Only the cross-hatched area (29) contributes to the torque.

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

Partial surface (22) is also limited by cutting line (27). Details on cutting line (27) have already been discussed as part of 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 secondary rotor end face (20) on the one hand and the boundary caused by the three-dimensional engagement line (10) and cutting line (27) on the other hand, which depends on the angular position of the secondary rotor to the main rotor, does not play a significant role here because - as in the relevant literature - the gas pressures on areas of the rotor surface that correspond to complete tooth gaps in a section plane perpendicular to the axis of the rotor (in Fig. 12b shown dotted), make no contribution to the torque. The pitch of the secondary rotor only affects the amount, but not the effective direction, of the torque.

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

Only the ones in Fig. 12b The 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 front section design of the secondary rotor.

The advantageous front section design of the secondary rotor (NR) described above therefore leads to an effective direction (25) of the torque from the gas forces for each partial surface (22) of the secondary rotor delimiting 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, which effectively prevents rotor chatter.

The exemplary embodiments shown demonstrate that with the present invention a significant 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, regardless of a specifically claimed profile definition.

Although it will be easily possible for a person skilled in the art to generate suitable profile curves using the methods customary in the prior art based on the specified parameter values, the profile curves in the exemplary embodiments discussed above are described below purely as an example Figures 1 to 4 explained in more detail. To generate profile histories, profile histories can also be generated using publicly accessible computer programs - as is well known to those skilled in the art in the present field.

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

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

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 point C1, generated by the circular arc section T1 to T2 around the center point C2 on the Main rotor HR. The section S2 to S3 results from an envelope curve to a trochoid, generated by the circular arc section T2 to T3 around the center point M4 on the main rotor HR. The section S3 to S4 is defined by a circular arc around the center M1. The section S4 to S5 is defined by a circular arc around the center M2.

The section S5 to S6 is defined by a circular arc around the center point C1. The subsequent section S6 to S7 is defined by a circular arc around the center point M3. Finally, the section S7 to S1 is predetermined by an envelope to 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 each other seamlessly in the order given. The tangents at the end of a section and at the beginning of the adjacent section are the same. The sections merge into one another directly, smoothly and without kinks.

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

In general, it should be noted that the profile curves of the secondary rotor NR and main rotor HR are of course coordinated with one another and in this respect 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 procedure for calculating the profile of the counter rotor is, for example, in Dissertation by Helpertz, "Method for the stochastic optimization of screw rotor profiles", Dortmund, 2003, p. 60 ff . described.

Claims (14)

1. Rotor pair for a compressor block of a screw machine, wherein the rotor pair is comprised of a secondary rotor (NR) that rotates about a first axis (C1) and a main rotor (HR) that rotates about a second axis (C2),

   wherein the number of teeth (z₂) in the main rotor (HR) is 3 and the number of teeth (z₁) in the secondary rotor (NR) is 4, wherein the relative profile depth of the secondary rotor $${\mathit{PT}}_{\mathit{rel}}=\frac{{\mathit{rk}}_1-{\mathit{rf}}_1}{{\mathit{rk}}_1}$$

   

   is at least 0.5, preferably at least 0.515, and at most 0.65, preferably at most 0.595, wherein rk₁ is an addendum circle radius drawn around the outer circumference of the secondary rotor (NR) and rf₁ is a dedendum circle radius starting at the profile base of the secondary rotor,

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

   

   is at least 1.636 and at most 1.8, preferably at most 1.733, wherein preferably the main rotor is configured with a wrap-around angle Φ_HR, for which it holds that 240° ≤ Φ_HR ≤ 360°, and wherein, in a transverse sectional view, a point C is defined on the connecting line ( C1C2 ) between the first axis (C1) and the second axis (C2), at which the pitch circles WK₁ of the secondary rotor (NR) and WK₂ of the main rotor (HR) touch, that K5 defines the point of intersection of the dedendum circle FK₁ of the secondary rotor (NR) with the connecting line ( C1C2 ), wherein r₁ is the distance between K5 and C,

   and that K4 designates the point of the suction-side part of the line of engagement which lies farthest spaced apart from the connecting line ( C1C2 ) between C1 and C2, wherein r₂ is the distance between K4 and C, and wherein it holds that: $$0.9\le \frac{r_1}{r_2}\le 0.875\times \frac{z_1}{z_2}+0.22$$

   

   with z₁: number of teeth in the secondary rotor (NR) and z₂: number of teeth in the main rotor (HR), and wherein, in a transverse sectional view, circular arcs B₂₅, B₅₀, B₇₅ extending within a secondary rotor tooth are defined, the common center point of which is given by the axis C1, wherein the radius r₂₅ of B₂₅ has the value r₂₅ = rf₁+0.25*(rk₁-rf₁), the radius r₅₀ of B₅₀ has the value r₅₀ = 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 each delimited 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 rating is satisfied: 0.65 ≤ ε₁ < 1.0 and/or 0.50 ≤ ε₂ ≤ 0.85, preferably 0.80 ≤ ε₁ < 1.0 and/or 0.50 ≤ ε₂ ≤ 0.79.
2. Rotor pair according to claim 1, characterized in that, for a rotor length ratio L_HR/a, it holds that: $$1.4\le L_{\mathit{HR}}/a\le 3.4$$

   

   wherein the rotor length ratio is formed from the ratio of the rotor length L_HR of the main rotor and the axis distance a, and the rotor length L_HR of the main rotor is formed by the distance of a suction-side main-rotor rotor end face to an opposite pressure-side main-rotor rotor end face.
3. Rotor pair according to any one of claims 1 or 2, characterized in that, in a transverse sectional view, foot points F1 and F2 are defined between the tooth in question of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor, and an apex point F5 is defined at the radially outermost point of the tooth,

   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 by an area A1 with its leading tooth flank F_V formed between F5 and F2 and by an area A2 with its trailing tooth flank F_N formed between F1 and F5, and

   wherein 8 ≤ A2/A1 ≤ 60 is satisfied.
4. Rotor pair according to any one of claims 1 to 3, characterized in that, in a transverse sectional view, foot points F1 and F2 are defined between the tooth in question of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR), and an apex point F5 is defined at the radially outermost point of the tooth,

   wherein the circular arc B extending between F1 and F2 around the center point defined by the axis C1 defines a tooth partition 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 line R drawn from the center point of the secondary rotor (NR) defined by the first 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 of F11 to F12 viewed in the direction of rotation of the secondary rotor (NR), and

   wherein $$14\%\le \delta \le 25\%$$

   

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

   
5. Rotor pair according to any one of claims 1 to 4, characterized in that, in a transverse sectional view, the trailing tooth flank F_N of a tooth of the secondary rotor (NR) formed between F1 and F5 has a convex length component of at least 45% to at most 95%.
6. Rotor pair according to any one of claims 1 to 5, characterized in that, for a diameter ratio defined by the ratio of the addendum circle radii of main rotor (HR) and secondary rotor (NR), $$D_v=\frac{{\mathit{Dk}}_2}{{\mathit{Dk}}_1}=\frac{{\mathit{rk}}_2}{{\mathit{rk}}_1}$$

   

   $$1.145\le D_v\le 1.30$$

   

   is satisfied, wherein Dk₁ designates the diameter of the addendum circle KK₁ of the secondary rotor (NR) and Dk₂ designates the diameter of the addendum circle KK₂ of the main rotor (HR).
7. Rotor pair according to any one of claims 1 to 6, characterized in that the main rotor HR is formed with a wrap-around angle Φ_HR, for which it holds that: 290° ≤ Φ_HR ≤ 360°, preferably 320° ≤ Φ_HR ≤ 360°.
8. Rotor pair for a compressor block of a screw machine, wherein the rotor pair is comprised of a secondary rotor (NR) that rotates about a first axis (C1) and a main rotor (HR) that rotates about a second axis (C2),

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

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

   

   is at least 0.5, preferably at least 0.515, and at most 0.58, wherein rk₁ is an addendum circle radius drawn around the outer circumference of the secondary rotor (NR) and rf₁ is a dedendum circle radius starting at the profile base of the secondary rotor,

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

   

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

   wherein preferably the main rotor is configured with a wrap-around angle Φ_HR, for which it holds that 240° ≤ Φ_HR ≤ 360°, and wherein, in a transverse sectional view, a point C is defined on the connecting line ( C1C2) between the first axis (C1) and the second axis (C2), at which the pitch circles WK₁ of the secondary rotor (NR) and WK₂ of the main rotor (HR) touch, that K5 defines the point of intersection of the dedendum circle FK₁ of the secondary rotor (NR) with the connecting line ( C1C2), wherein r₁ is the distance between K5 and C,

   and that K4 designates the point of the suction-side part of the line of engagement which lies farthest spaced apart from the connecting line ( C1C2) between C1 and C2, wherein r₂ is the distance between K4 and C, and wherein it holds that: $$0.9\le \frac{r_1}{r_2}\le 0.875\times \frac{z_1}{z_2}+0.22$$

   

   with z₁: number of teeth in the secondary rotor (NR) and z₂: number of teeth in the main rotor (HR), and wherein, in a transverse sectional view, circular arcs B₂₅, B₅₀, B₇₅ extending within a secondary rotor tooth are defined, the common center point of which is C1, 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 each delimited 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 rating is satisfied: 0.75 ≤ ε₁ ≤ 0.85 and/or 0.65 ≤ ε₂ ≤ 0.74.
9. Rotor pair according to claim 8, characterized in that, for a rotor length ratio L_HR/a, it holds that: $$1.4\le L_{\mathit{HR}}/a\le 3.3$$

   

   
   wherein the rotor length ratio is formed from the ratio of the rotor length L_HR of the main rotor and the axis distance a, and the rotor length L_HR of the main rotor is formed by the distance of a suction-side main-rotor rotor end face to an opposite pressure-side main-rotor rotor end face.
10. Rotor pair according to any one of claims 8 or 9, characterized in that, in a transverse sectional view, foot points F1 and F2 are defined between the tooth in question of the secondary rotor (NR) and the respectively adjacent tooth of the secondary rotor (NR), and an apex point F5 is defined at the radially outermost point of the tooth,

    wherein a triangle D_Z is defined by F1, F2 and F5, and

    wherein, in a radially outer region of the tooth, the leading tooth flank F_V formed between F5 and F2 projects beyond the triangle D_Z by an area A1, and in a radially inner region is set back with respect to the triangle D_Z by an area A3, and wherein 9.0 ≤ A3/A1 ≤ 18 is satisfied.
11. Rotor pair according to any one of claims 8 to 10, characterized in that, in a transverse sectional view, the trailing tooth flank F_N of a tooth of the secondary rotor (NR) formed between F1 and F5 has a convex length component of at least 55% to at most 95%.
12. Rotor pair according to any one of claims 1 to 11, characterized in that, in a transverse sectional view, the arc lengths b(r), extending inside a tooth of the secondary rotor, of the respective associated concentric circular arcs having the radius rf₁ < r < rk₁ and the common center point defined by the axis C1 are each delimited 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.
13. Rotor pair according to any one of claims 1 to 11, characterized in that, in a transverse sectional view, the tooth profile of the secondary rotor (NR), on its radially outer section, follows in part a circular arc ARC₁ having a radius rk₁, thus a plurality of points of the leading tooth flank F_V and of the trailing tooth flank F_N lie on the circular arc having the radius rk₁ around the center point 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°, more preferably of between 0.5° and 2.5°,

    wherein F10 is the point on the leading tooth flank on this circular arc that is farthest spaced apart from F5, and

    wherein the radial line R₁₀ drawn between F10 and the center point of the secondary rotor (NR) defined by the axis C1 touches the leading tooth flank F_V at least at one point or intersects it at two points.
14. Rotor pair according to any one of claims 8 to 13, characterized in that the main rotor HR is formed with a wrap-around angle Φ_HR, for which it holds that: 320° ≤ Φ_HR ≤ 360°, preferably 330° ≤ Φ_HR ≤ 360°.

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