Rotor pair for a compression block of a screw machine

Abstract

A rotor pair for a compressor block of a screw machine includes a secondary rotor that rotates about a first axis and a main rotor that rotates about a second axis. The number of teeth of the main rotor is 3 and the number of teeth of the secondary rotor is 4. The relative profile depth of the secondary rotor is at least 0.5 rk1 is an addendum circle radius drawn around the outer circumference of the secondary rotor and rf1 is a dedendum circle radius starting at the profile base of the secondary rotor. The ratio of the axis distance of the first axis from the second axis and the addendum circle radius rk1 is at least 1.636.

Claims

1. A rotor pair for a compressor block of a screw machine, wherein the rotor pair comprises a secondary rotor that rotates about a first axis and a main rotor that rotates about a second axis, wherein a number of teeth of the main rotor is 4 and the number of teeth of the secondary rotor is 5, wherein a relative profile depth of the secondary rotor ${\mathrm{PT}}_{\mathrm{rel}}=\frac{{\mathrm{rk}}_1-{\mathrm{rf}}_1}{{\mathrm{rk}}_1}$ is at least 0.515, and at most 0.58 wherein rk.sub.1 is an addendum circle radius drawn around an outer circumference of the secondary rotor and rf.sub.1 is a dedendum circle radius starting at a profile base of the secondary rotor, wherein a ratio of an axis distance a of the first axis from the second axis and the addendum circle radius rk.sub.1 $\frac{a}{{\mathrm{rk}}_1}$ is between 1.683 to 1.836, wherein the main rotor is configured with a wrap-around angle ΦHR for which it holds that 320°<ΦHR <360°, and wherein optionally for a rotor length ratio L.sub.HR/a:
1.4≤L.sub.HR/a≤3.2, wherein the rotor length ratio is formed from a ratio of the rotor length L.sub.HR of the main rotor and the axis distance a and the rotor length L.sub.HR of the main rotor is formed by a distance of a suction-side main-rotor rotor end face to an opposite pressure-side main-rotor rotor end face.

2. The rotor pair according to claim 1, wherein in a transverse sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running within a secondary rotor tooth are defined, a common centre point of which is the first axis, wherein a radius r.sub.25 of B.sub.25 has a value r.sub.25=rf.sub.1+0.25* (rk.sub.1-rf.sub.1), a radius r.sub.50 of B.sub.50 has a value r.sub.50=rf.sub.1+0.5* (rk.sub.1-rf.sub.1), and a radius r.sub.75 of B.sub.75 has the value r.sub.75=rf.sub.1+0.75* (rk.sub.1-rf.sub.1), and wherein the circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by a leading tooth flank F.sub.v and trailing tooth flank F.sub.N relative to a direction of rotation of the secondary rotor, wherein tooth thickness ratios are defined as ratios of arc lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25, B.sub.50, B.sub.75 with ε.sub.l=b.sub.50/b.sub.25 and 0.75<ε.sub.1<0.85.

3. The rotor pair according to claim 1, wherein in a transverse sectional view, foot points F1 and F2 are defined between an observed tooth of the secondary rotor and a 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.sub.z is defined by F1, F2 and F5 and wherein in a radially outer region, the tooth projects beyond the triangle D.sub.z with its leading tooth flank Fv formed between F5 and F2 with an area A1 and with its trailing tooth flank F.sub.N formed between F1 and F5 with an area A2 and wherein 6<A2/A1<15.

4. The rotor pair according to claim 1, wherein in a transverse sectional view, foot points F1 and F2 are defined between an observed tooth of the secondary rotor and a respectively adjacent tooth of the secondary rotor and an apex point F5 is defined at a radially outermost point of the tooth, wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein in a radially outer region of the tooth, a leading tooth flank Fv formed between F5 and F2 projects with an area A1 beyond the triangle Dz and in a radially inner region is set back with respect to the triangle D.sub.z with an area A3 and wherein 9.0<A3/A1<18.

5. The rotor pair according to claim 1, wherein in a transverse sectional view, foot points F1 and F2 are defined between an observed tooth of the secondary rotor and the respectively adjacent tooth of the secondary rotor and an apex point F5 is defined at a radially outermost point of the tooth, wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein in a radially outer region of the tooth, a leading tooth flank Fv formed between F5 and F2 projects with an area A1 beyond the triangle D.sub.z, wherein the tooth itself has a cross-sectional area A0 delimited by a circular arc B running between F1 and F2 about the centre point defined by the first axis and wherein 1.5%<A1/A0<3.5%.

6. The rotor pair according to claim 1, wherein in a transverse sectional view, foot points F1 and F2 are defined between an observed tooth of the secondary rotor and a respectively adjacent tooth of the secondary rotor and an apex point F5 is defined at a radially outermost point of the tooth, wherein a circular arc B running between F1 and F2 defines a tooth partition angle γ corresponding to 360°/number of teeth of the secondary rotor about a centre point defined by the first axis, wherein a point F11 is defined on a half circular arc B between F1 and F2, wherein a radial half-line R drawn from a centre point of the secondary rotor defined by the first axis through the apex point F5 intersects a circular arc B at a point F12, wherein an offset angle θ is defined by an offset of F11 to F12 viewed in a direction of rotation of the secondary rotor and wherein $14\%\le \delta \le 18\%$ $\mathrm{where}$ $\delta =\frac{\beta }{\gamma }*100\left[\%\right].$

7. The rotor pair according to claim 1, wherein in a transverse sectional view, a trailing tooth flank F.sub.N of a tooth of the secondary rotor formed between a foot point F1 and an apex point F5 has a convex length component of at least 55% to at most 95%.

8. The rotor pair according to claim 1, wherein in a transverse sectional view, a radial half-line drawn from the first axis of the secondary rotor through an apex point F5 divides a tooth profile into an area component A5 assigned to a leading tooth flank Fv and an area component A4 assigned to a trailing tooth flank F.sub.N and wherein
4≤A4/A5≤9.

9. The rotor pair according to claim 1, wherein the main rotor HR is formed with the wrap-around angle Φ.sub.HR for which 330°<Φ.sub.HR<360°.

10. The rotor pair according to claim 1, wherein a blow hole factor μ.sub.B1 is at least 0.02% and at most 0.4%, wherein ${\mu }_{\mathrm{Bl}}=\frac{A_{\mathrm{Bl}}}{A6+A7}*100\left[\%\right]$ wherein A.sub.B1 designates an absolute pressure-side blow hole area and A6 and A7 designate tooth gap areas of the secondary rotor or the main rotor, wherein an area A6 in a transverse sectional view is an area enclosed between a profile course of the secondary rotor between two adjacent apex points F5 and an addendum circle KK.sub.1 and an area A7 in a transverse sectional view is the area enclosed between a profile course of the main rotor between two adjacent apex points H5 and the addendum circle KK.sub.2.

11. The rotor pair according to claim 1, wherein that for a blow hole/profile gap length factor μ.sub.1* μ.sub.B1 $0.1\%\le {\mu }_l*{\mu }_{\mathrm{Bl}}\le 1.72\%$ $\mathrm{where}$ ${\mu }_l=\frac{l_{\mathrm{sp}}}{{\mathrm{PT}}_1},$ where 1.sub.sp designates a length of the profile engagement gap of a tooth gap of the secondary rotor and PT.sub.1 designates a profile depth of a secondary rotor where PT.sub.1=rk.sub.1-rf.sub.1 and ${\mu }_{\mathrm{Bl}}=\frac{A_{\mathrm{Bl}}}{A6+A7}*100\left[\%\right]$ where A.sub.B1 designates an absolute blow hole area and A6 and A7 designate the profile areas of the secondary rotor or the main rotor, wherein an area A6 in a transverse sectional view designates an area enclosed between a profile course of the secondary rotor between two adjacent apex points F5 and an addendum circle KK.sub.1, and an area A7 in a transverse sectional view designates an area enclosed between the profile course of the main rotor between two adjacent apex points H5 and an addendum circle KK.sub.2.

12. The rotor pair according to claim 1, wherein the main rotor and secondary rotor are configured and tuned to one another in such a manner that a dry compression with a pressure ratio Π of up to 5 is achieved, or alternatively a fluid-injected compression with a pressure ratio Π of up to 16 where the pressure ratio is a ratio of compression end pressure to suction pressure.

13. The rotor pair according to claim 12, wherein in the case of a dry compression, the main rotor is configured to be operated relative to an addendum circle KK.sub.2 at a circumferential speed in a range from 20 to 100 m/s and for a fluid-injected compression, the main rotor is configured to be operated relative to an addendum circle KK.sub.2 at a circumferential speed in a range from 5 to 50 m/s.

14. The rotor pair according to claim 1, wherein for a diameter ratio defined by a ratio of an addendum circle radii of the main rotor and the secondary rotor $D_v=\frac{{\mathrm{Dk}}_2}{{\mathrm{Dk}}_1}=\frac{{\mathrm{rk}}_2}{{\mathrm{rk}}_1}$ $1.195\le D_v\le 1.33$ where Dk.sub.1 designates a diameter of an addendum circle KK.sub.1 of the secondary rotor and DK.sub.2 designates a diameter of an addendum circle KK.sub.2 of the main rotor.

15. The rotor pair according to claim 1, wherein a transverse sectional view arc lengths b(r), running inside a tooth of the secondary rotor, of a respectively appurtenant concentric circular arcs having a radius rf.sub.1<r<rk.sub.1 and a common central point defined by the first axis are each delimited by a leading tooth flank F.sub.v and a trailing tooth flank F.sub.N and the arc lengths b(r) decrease monotonically with increasing radius r.

16. The rotor pair according to claim 1, wherein a transverse sectional configuration of the secondary rotor is executed in such a manner that a direction of action of torque which results from a reference pressure on a partial surface of the secondary rotor delimiting a working chamber is directed contrary to the direction of rotation of the secondary rotor.

17. The rotor pair according to claim 1, wherein the main rotor and secondary rotor are configured and tuned to one another for conveying air or inert gases.

18. The rotor pair according to claim 1, wherein in a transverse sectional view, a profile of a tooth of the secondary rotor relative to a radial half-line R drawn from a centre point defined by the first axis C1 through an apex point F5 is configured to be asymmetrical.

19. The rotor pair according to claim 1, wherein in a transverse sectional view a point C is defined on a connecting section between the first axis and the second axis where a pitch circles WK.sub.1 of the secondary rotor and WK.sub.2 of the main rotor contact, that K5 defines a point of intersection of a dedendum circle FK.sub.1 of the secondary rotor with the connecting section where r.sub.1 determines the distance between K5 and C and that K4 designates a point of a suction-side part of a line of engagement which lies at a greatest distance from the connecting section between the first and second axis, where r.sub.2 determines a distance between K4 and C and where: $0.9\le \frac{r_1}{r_2}\le 0.875\times \frac{z_1}{z_2}+0.22$ where z.sub.1 is a number of teeth of the secondary rotor and z.sub.2 is a number of teeth of the main rotor.

20. The rotor pair according claim 1, wherein for the rotor length ratio L.sub.HR/a it holds: 0.85* (z.sub.1/z.sub.2)+0.67<L.sub.HR/a <1.26* (z.sub.1/z.sub.2)+1.18 where z.sub.1 is a number of teeth of the secondary rotor and z.sub.2 is a number of teeth of the main rotor, wherein the rotor length ratio L.sub.HR/a denotes a ratio of the rotor length L.sub.HR to the axial distance a and the rotor length L.sub.HR is the distance of the suction-side main-rotor rotor end face to the pres sure-side main-rotor rotor end face.

21. The rotor pair according to claim 1, wherein in a transverse sectional view a tooth profile of the secondary rotor on its radially outer section in sections follows a circular arc ARC.sub.1 having a radius rk.sub.1, such that a plurality of points of a leading tooth flank Fv and a trailing tooth flank F.sub.N lie on the circular arc having the radius rk.sub.1 around a centre point defined by the first axis, wherein the circular arc ARC.sub.1 encloses an angle relative to the first axis between 0.5° and 5°, wherein F10 is a point at a furthest distance from an apex point F5 on a leading tooth flank on a circular arc and wherein a radial half-line R10 drawn between F10 and a centre point of the secondary rotor defined by the first axis contacts the leading tooth flank Fv at least at one point or intersects the leading tooth flank F.sub.v in two points.

22. A compressor block comprising a compressor housing and a rotor pair according to claim 1, wherein the rotor pair comprises the main rotor and the secondary rotor, which are each mounted rotatably in the compressor housing.

23. The rotor pair according to claim 1, wherein the ratio of the axis distance a of the first axis from the second axis and the addendum circle radius rk.sub.1 $\frac{a}{{\mathrm{rk}}_1}$ is at most 1.782.

24. The rotor pair according to claim 1, wherein in a transverse sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running within a secondary rotor tooth are defined, a common centre point of which is the first axis, wherein a radius r.sub.25 of B.sub.25 has a value r.sub.25=rf.sub.1+0.25* (rk.sub.1-rf.sub.1), a radius r.sub.50 of B.sub.50 has a value r.sub.50=rf.sub.1+0.5* (rk.sub.1-rf.sub.1), and a radius r.sub.75 of B.sub.75 has the value r.sub.75=rf.sub.1+0.75* (rk.sub.1-rf.sub.1), and wherein the circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by a leading tooth flank Fv and trailing tooth flank F.sub.N relative to a direction of rotation of the secondary rotor, wherein tooth thickness ratios are defined as ratios of arc lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25, B.sub.50, B.sub.75 with ε.sub.2=b.sub.75/b.sub.25 and 0.65<ε.sub.2<0.74.

25. The rotor pair according to claim 1, wherein in a transverse sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running within a secondary rotor tooth are defined, a common centre point of which is the first axis, wherein a radius r.sub.25 of B.sub.25 has a value r.sub.25=rf.sub.1+0.25* (rk.sub.1-rf.sub.1), a radius r.sub.50 of B.sub.50 has a value r.sub.25=rf.sub.1+0.5* (rk.sub.1-rf.sub.1), and a radius r.sub.75 of B.sub.75 has the value r.sub.75=rf.sub.1+0.75* (rk.sub.1-rf.sub.1), and wherein the circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by a leading tooth flank Fv and trailing tooth flank F.sub.N relative to a direction of rotation of the secondary rotor, wherein tooth thickness ratios are defined as ratios of arc lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25, B.sub.50, B.sub.75 with ε.sub.1=b.sub.50/b.sub.25 and ε.sub.2 b.sub.75/b.sub.25 and 0.75<ε.sub.1<0.85 and 0.65<ε.sub.2<0.74.

26. The rotor pair according to claim 10, wherein the blow hole factor μ.sub.BL is at most 0.25%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention is explained in further detail hereinafter with regard to further features and advantages by reference to the description of exemplary embodiments. In the figures:

(2) FIG. 1 shows a transverse section of a first embodiment with a tooth-number ratio of 3/4.

(3) FIG. 2 shows a transverse section of a second embodiment with a tooth-number ratio of 3/4.

(4) FIG. 3 shows a transverse section of a third embodiment with a tooth-number ratio of 4/5.

(5) FIG. 4 shows a fourth exemplary embodiment in a transverse sectional view with a tooth number ratio of 5/6.

(6) FIG. 5 shows an illustration of the isentropic block efficiency for the second exemplary embodiment for the 3/4 tooth-number ratio compared with the prior art.

(7) FIG. 6 shows an illustration of the isentropic block efficiency for the fourth exemplary embodiment for the 5/6 tooth-number ratio compared with the prior art.

(8) FIG. 7a-7k shows illustration diagrams for the various parameters of the geometry of the secondary rotor or the rotor pair consisting of main rotor and secondary rotor.

(9) FIG. 8 shows an illustration of the wrap-around angle at the main rotor.

(10) FIG. 9 shows a schematic sectional drawing of an embodiment of a compressor block.

(11) FIG. 10 shows an embodiment for an intermeshed rotor pair consisting of a main rotor and a secondary rotor in three-dimensional view.

(12) FIG. 11 shows a perspective view of one embodiment of a secondary rotor to illustrate the spatial line of engagement.

(13) FIG. 12a, 12b shows an illustration of the areas or subareas of a working chamber of one embodiment of the secondary rotor which are relevant for the torque effects.

(14) FIG. 13 shows the transverse section of the embodiment according to FIG. 1 to explain the profile course of main and secondary rotor in this embodiment.

(15) FIG. 14 shows the transverse section of the embodiment according to FIG. 2 to explain the profile course of main and secondary rotor in this embodiment.

(16) FIG. 15 shows the transverse section of the embodiment according to FIG. 3 to explain the profile course of main and secondary rotor in this embodiment.

(17) FIG. 16 shows the transverse section of the embodiment according to FIG. 4 to explain the profile course of main and secondary rotor in this embodiment.

DETAILED DESCRIPTION

(18) The exemplary embodiments according to FIGS. 1 to 4 will be explained hereinafter. All four exemplary embodiments represent suitable profiles in the sense of the present invention.

(19) The corresponding geometrical specifications for the main rotor HR or the secondary rotor NR are given in Tables 1 to 4 reproduced hereinafter.

(20) TABLE-US-00001 TABLE 1 Exemplary Exemplary Exemplary Exemplary embodiment embodiment embodiment embodiment 1 2 3 4 Teeth number 3 3 4 5 HR z.sub.2 Teeth number 4 4 5 6 NR z.sub.1 PT.sub.rel [—] 0.588 0.54 0.528 0.455 a/rk.sub.1 [—] 1.66 1.72 1.764 1.78

(21) TABLE-US-00002 TABLE 2 The profiles were created with the following axial distances a: Exemplary Exemplary Exemplary Exemplary embodiment embodiment embodiment embodiment 1 2 3 4 Axial distance 127 111 a [mm]

(22) TABLE-US-00003 TABLE 3 Thus the following transverse-section principal dimensions are obtained: Exemplary Exemplary Exemplary embodiment Exemplary embodiment embodiment 1 2 embodiment 3 4 Dk.sub.2 [mm] 191 186.1 186 154 Dk.sub.1 [mm] 153 147.7 144 124.7 rw.sub.2 [mm] 54.4 56.4 50.5 rw.sub.1 [mm] 72.6 70.6 60.5

(23) TABLE-US-00004 TABLE 4 Further principal dimensions of the rotors: Exemplary Exemplary Exemplary embodiment embodiment embodiment Exemplary 1 2 3 embodiment 4 Rotor length 307 293 235.5 L.sub.HR [mm]

(24) In the exemplary embodiments presented, the following features and characteristics according to the invention are obtained, which are presented in Table 5:

(25) TABLE-US-00005 TABLE 5 Compilation of the further features and characteristics: Exemplary Exemplary Exemplary Exemplary Feature embodiment 1 embodiment 2 embodiment 3 embodiment 4 Tooth thickness 0.85 0.82 0.80 0.79 ratio ε.sub.1 [—] Tooth thickness 0.74 0.64 0.69 0.65 ratio ε.sub.2 [—] 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 18.5 21.1 15.7% 15.2 ratio δ [%] Convex length 66.9% 71.2% 62.7% — component [%] Radial tooth The tooth thickness of the secondary rotor teeth decreases thickness profile monotonically from the addendum circle radius rf.sub.1 to the dedendum circle radius rk.sub.1 Radial half-line Radial half-line R.sub.10 has two points of intersection with the leading R.sub.10 tooth flank FV Area ratio A4/A5 7.5 10.1 5.5 — [—] Wrap-around angle 334.7° 330.3 330.3 Φ.sub.HR μ.sub.B1 [%] 0.159 0.086 0.106 0.18 μ.sub.B1 * μ.sub.1 [%] 0.94 0.53 0.631 1.058 Profile transverse The working chamber can be expelled substantially completely sectional into the pressure window configuration in relation to chamber expulsion Profile transverse The direction of action of the NR torque resulting from the gas sectional forces is directed contrary to the direction of rotation of the configuration in secondary rotor relation to secondary rotor torque Shape of 1.037 1.044 0.984 1.0 engagement line r.sub.1/r.sub.2 Diameter ratio D.sub.V 1.248 1.26 1.292 1.235 Rotor length ratio 2.42 2.42 2.31 2.12 L.sub.HR/a

(26) The isentropic block efficiency compared to the prior art is illustrated for the second exemplary embodiment for the 3/4 tooth-number ratio in FIG. 5. Two curves for the same pressure ratio are reproduced there. The specifically reproduced pressure ratio is 2.0 (ratio of output pressure to input pressure). The isentropic block efficiency could be improved significantly compared with the values attainable with the prior art.

(27) FIG. 6 shows the isentropic block efficiency compared to the prior art for the fourth exemplary embodiment (5/6 tooth-number ratio). Two curves for the same pressure ratio are also reproduced here. The specifically reproduced pressure ratio is 9.0 (ratio of output pressure to input pressure). Here also the isentropic block efficiency could be improved significantly compared with the values attainable with the prior art.

(28) The quantity delivered specified in each case in FIGS. 5 and 6 corresponds to the conveyed volume flow of the compressor block relative to the suction state.

(29) FIG. 7a shows in a transverse sectional view one embodiment for secondary rotor NR and main rotor HR with the centre points given by the corresponding axes C1 and C2. Furthermore, the geometrical principal dimensions or principal parameters of the transverse sectional view are shown: Addendum circle KK.sub.1 of the secondary rotor with appurtenant addendum circle radius rk.sub.1 or addendum circle diameter Dk.sub.1 Addendum circle KK.sub.2 of the main rotor with appurtenant addendum circle radius rk.sub.2 or addendum circle diameter Dk.sub.2 Dedendum circle FK.sub.1 of the secondary rotor with appurtenant dedendum circle radius rf.sub.1 or dedendum circle diameter Df.sub.1 Dedendum circle FK.sub.2 of the main rotor with appurtenant dedendum circle radius rf.sub.2 or dedendum circle diameter Df.sub.2 Axial distance a between the first axis C1 and the second axis C2 Pitch circle WK.sub.1 of the secondary rotor with appurtenant pitch circle radius rw.sub.1 or pitch circle diameter Dw.sub.1 Pitch circle WK.sub.2 of the main rotor with appurtenant pitch circle radius rw.sub.2 or pitch circle diameter Dw.sub.2

(30) Also shown are the direction of rotation 24 of the secondary rotor and the necessarily resulting direction of rotation of the main rotor during operation as a compressor.

(31) The leading tooth flank F.sub.V and the trailing tooth flank F.sub.N are characterized on a secondary rotor tooth as representative for all teeth of the secondary rotor. A tooth gap 23 is characterized as representative of all tooth gaps of the secondary rotor. The profile course of the leading tooth flank F.sub.V and of the trailing tooth flank F.sub.N shown by reference to FIG. 7a corresponds to the exemplary embodiment for a tooth-number ratio of 5/6 illustrated by reference to FIG. 4.

(32) FIG. 7b shows in a transverse sectional view the tooth gap areas A6 and A7 as well as a side view of a blow hole. The profile courses shown in FIG. 7b to explain the tooth gap areas A6 and A7 correspond to the exemplary embodiment for a tooth number ratio of 3/4 illustrated by reference to FIG. 1.

(33) Furthermore, FIG. 7b shows the position of the coordinate system of the blow hole area A.sub.Bl shown in FIG. 7k in relation to the rotor pair.

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

(35) The pressure-side blow hole lies in the described coordinate system and quite 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 line of engagement.

(36) In a transverse sectional view the line of engagement 10 is divided into two sections by the connecting line between the two centre points C1 and C2: the suction-side part of the line of engagement is shown below, the pressure-side part is shown above the connecting line.

(37) K2 designates the point of the pressure-side part of the line of engagement 10 which lies at the furthest distance from the straight lines through C1 and C2. As a result of the intersection of the addendum circles of the two rotors, a pressure-side intersection edge 11 and a suction-side intersection edge 12 are formed. In FIG. 7b the pressure-side intersection edge 11 is shown as a point in a transverse sectional view. The same applies to the depiction of the suction-side intersection edge 12.

(38) The u-axis is a parallel to the rotor end faces and in a transverse sectional view corresponds to the vector from the engagement line point K2 to the pressure-side intersection edge 11. Further details on the pressure-side blow hole area A.sub.Bl are obtained from FIG. 7k.

(39) FIG. 7c shows in a transverse sectional view a tooth of the secondary rotor with the concentric circular arcs B.sub.25, B.sub.50, B.sub.75 running inside the rotor tooth around the centre point C1 with the appurtenant radii R.sub.25, r.sub.50, r.sub.75 and the appurtenant arc lengths b.sub.25, b.sub.50, b.sub.75.

(40) The circular arcs B.sub.25, B.sub.50, B.sub.75 are in each case delimited by the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N. The profile course of the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N shown by reference to FIG. 7c corresponds to the exemplary embodiment explained by reference to FIG. 4 for a tooth-number ratio of 5/6.

(41) FIG. 7d shows in a transverse sectional view foot points F1 and F2 on the addendum circle between the observed tooth of the secondary rotor and the respectively adjacent tooth of the secondary rotor and an apex point F5 at the radially outermost point of the tooth. Furthermore, the triangle D.sub.z defined by the points F1, F2 and F5 is shown.

(42) FIG. 7d shows the following (tooth sub-)areas:

(43) Tooth sub-area A1 corresponds to the area with which the observed tooth projects with its leading tooth flank F.sub.V formed between F5 and F2 beyond the triangle D.sub.z in a radially outer region.

(44) Tooth sub-area A2 corresponds to the area with which the observed tooth projects with its trailing tooth flank F.sub.N formed between F5 and F1 beyond the triangle D.sub.z in a radially outer region.

(45) Area A3 corresponds to the area with which the observed tooth is set back with its leading tooth flank formed between F5 and F2 with respect to the triangle D.sub.z.

(46) Also shown is the tooth partition angle γ corresponding to 360°/number of teeth of the secondary rotor. The profile course of the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N shown by reference to FIG. 7d corresponds to the exemplary embodiment explained by reference to FIG. 4 for a tooth-number ratio of 5/6.

(47) FIG. 7e shows in a transverse sectional view the cross-sectional area A0 of a tooth of the secondary rotor which is delimited by the circular arc B running between F1 and F2 about the centre point C1. The profile course of the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N shown by reference to FIG. 7e corresponds to the exemplary embodiment explained by reference to FIG. 4 for a tooth-number ratio of 5/6.

(48) FIG. 7f shows in a transverse sectional view the offset angle β. This is defined by the offset from point F11 to point F12 observed in the direction of rotation of the secondary rotor. F11 is a point on the half circular arc B between F1 and F2 about the centre point C1 and consequently corresponds to the point of intersection of the angle bisector of the tooth partition angle γ with the circular arc B.

(49) F12 is obtained from the point of intersection of the radial half-line R drawn from the centre point C1 to the apex point F5 with the circular arc B. The profile course of the leading tooth flank F.sub.V and the trailing tooth flank FN shown by reference to FIG. 7f corresponds to the exemplary embodiment explained by reference to FIG. 4 for a tooth-number ratio of 5/6.

(50) FIG. 7g shows in a transverse sectional view the turning point F8 on the trailing tooth flank F.sub.N of the secondary rotor at which the curvature of the course of the tooth profile changes between addendum and dedendum circle.

(51) The trailing tooth flank F.sub.N of the secondary rotor is divided by the point F8 into a substantially convexly curved component between F8 and the apex point F5 and a substantially concavely curved component between F8 and the foot point F1.

(52) FIG. 7h shows in a transverse sectional view two points of intersection of the radial half-line R.sub.10 from C1 to F10 with the leading tooth flank F.sub.V of the secondary rotor, wherein the point F10 designates that point of the leading tooth flank F.sub.V which lies on the addendum circle KK.sub.1 and is at the furthest distance from F5. The tooth flank therefore radially outwards over a defined section follows a circular arc ARC1 with radius rk.sub.1 about the centre point of the secondary rotor defined by the axis C1. The profile courses of the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N explained by reference to FIG. 7h correspond to the exemplary embodiment according to FIG. 1 for a tooth-number ratio of 3/4.

(53) FIG. 7i shows in a transverse sectional view the tooth profile divided by the radial half-line drawn from C1 to F5.

(54) Specifically in the embodiment shown, the tooth profile is divided into an area component A4 assigned to the trailing tooth flank F.sub.N and an area component A5 assigned to the leading tooth flank F.sub.V. The profile courses of the leading tooth flank F.sub.V and the trailing tooth flank F.sub.N explained by reference to FIG. 7i correspond to the exemplary embodiment according to FIG. 4 described for a tooth-number ratio of 5/6.

(55) FIG. 7j shows in a transverse sectional view the line of engagement 10 between main and secondary rotor as well as the two concentric circles about the point C having the radii r.sub.1 and r.sub.2 to describe the characteristic features of the course of the suction-side part of the line of engagement.

(56) The line of engagement 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 engagement is shown below, the pressure-side part is shown above the connecting section C1C2.

(57) Point C is the point of contact of the pitch circle WK1 of the secondary rotor with the pitch circle WK.sub.2 of the main rotor.

(58) K4 designates the point of the suction-side part of the line of engagement which lies at the greatest distance from the connecting section between C1 and C2.

(59) Radius r.sub.1 is the distance between K5 and C, radius r.sub.2 designates the distance between K4 and C.

(60) FIG. 7k:

(61) FIG. 7k shows a pressure-side blow hole area A.sub.Bl of a working chamber and specifically in a sectional view perpendicular to the rotor end faces. The delimitation of the blow hole area A.sub.B1 is formed here from the line of intersection 27 of the above-described imaginary flat surface with the leading secondary-rotor tooth flank F.sub.v, the line of intersection 26 of the plane with the trailing HR flank and a straight line section [K1 K3] of the pressure-side intersection edge 11.

(62) The coordinate system of the pressure-side blow hole lies in the flat surface described in FIG. 7b and is spanned by the u-axis parallel to the rotor end faces (vector from the engagement line point K2 to the pressure-side intersection edge 11) and the pressure-side intersection edge 11.

(63) In FIG. 8 the wrap-around angle Φ already discussed several times is illustrated once again. Specifically this is the angle Φ through which the transverse section is turned from the suction-side to the pressure-side rotor end face. This is illustrated in the present case by the turning of the profile between a pressure-side end face 13 and a suction-side end face 14 through the angle Φ.sub.HR at the main rotor HR.

(64) FIG. 9 shows a schematic sectional view of a compressor block 19 comprising a housing 15 as well as two rotors toothed with one another in pairs, mounted therein, namely a main rotor HR and a secondary rotor NR. Main rotor HR and secondary rotor NR are each mounted rotatably in a housing 15 by means of suitable bearings 16. A drive power can be applied to a shaft 17 of the main rotor HR, for example with a motor (not shown) via a coupling 18.

(65) The compressor block shown is an oil-injected screw compressor in which the torque transmission between main rotor HR and secondary rotor NR is accomplished directly by means of the rotor flanks. In contrast to this in a dry screw compressor any contact of the rotor flanks can be avoided by means of a synchronization transmission (not shown).

(66) Also not shown are a suction connection for suction of the medium to be compressed and an outlet for the compressed medium.

(67) FIG. 10 shows intermeshed main rotor HR and secondary rotor NR in a perspective view.

(68) FIG. 11 shows the spatial line of engagement 10 of precisely one tooth gap 23. The profile gap length I.sub.sp is the length of the spatial line of engagement of precisely one tooth gap 23. This therefore corresponds to the profile gap length of precisely one tooth pitch.

(69) The entire torque of the gas forces on the secondary rotor is composed of the sum of the torque effects of the gas pressures in all working chambers on the sub-surfaces of the secondary rotor delimiting the respective working chambers. In FIG. 12a such a sub-surface (22) of the secondary rotor delimiting a working chamber is shown hatched as an example.

(70) FIG. 12b shows the division of the sub-surface (22) delimiting a working chamber, shown in FIG. 12a into an area (28) shown dotted and an area (29) shown cross-hatched. Only the cross-hatched area (29) makes a contribution to the torque.

(71) The sub-surface (22) is obtained from the specific transverse sectional configuration and pitch of the secondary rotor. The pitch of the secondary rotor relates to the pitch of the screw-shaped toothed structure of the secondary rotor. The three-dimensional line of engagement (10) delimiting the sub-surface, also shown in FIG. 12a is also specified by the transverse sectional configuration of the secondary rotor and the pitch.

(72) Sub-surface (22) is also delimited by line of intersection (27). Details on the line of intersection (27) have already been presented and described within the framework of FIGS. 7b and 7k. The same applies to the engagement line point K2.

(73) The specific length of a working chamber in the direction of the axis of rotation, which is dependent on the angular position of the secondary rotor with respect to the main rotor, between the secondary rotor end face (20) on the one hand and the delimitation by the three-dimensional line of engagement (10) and line of intersection (27) on the other hand does not play any significant role here because—as is described in the relevant literature—the gas pressures on regions of the rotor surface which in a sectional plane perpendicular to the axis of the rotor correspond to complete tooth gaps (shown dotted in FIG. 12b) make no contribution to the torque. The pitch of the secondary rotor only has an effect on the magnitude but not on the direction of action of the torque.

(74) The area (28) shown dotted in FIG. 12b and the area (29) shown cross-hatched in FIG. 12b together form the sub-surface (22).

(75) Only the area (29) shown cross-hatched in FIG. 12b makes a contribution to the torque.

(76) Thus, in each working chamber, the direction of action of the torque which is brought about by the gas pressure in the working chamber (or an arbitrary reference pressure) on the sub-surface of the secondary rotor delimiting the working chamber, is specified by the transverse sectional configuration of the secondary rotor.

(77) The above-described advantageous transverse sectional configuration of the secondary rotor (NR) thus results for each sub-surface (22) of the secondary rotor delimiting a working chamber and thus for the entire secondary rotor in a direction of action (25) of the torque from the gas forces which is directed contrary to the direction of rotation (24) of the secondary rotor, whereby rotor rattling is effectively avoided.

(78) The exemplary embodiments presented confirm that with the present invention a considerable increase in efficiency could be achieved for a rotor pair used in screw machines consisting of main rotor and secondary rotor having a corresponding profile geometry.

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

(80) Although it will easily be possible for the person skilled in the art using the specified parameter values to produce suitable profile courses using conventional methods in the prior art, purely as an example the profile courses in the previously discussed exemplary embodiments according to FIGS. 1 to 4 will be explained in detail hereinafter. As is best known to the person skilled in the art working in the present field, in order to generate profile courses, profile courses can also be generated using publicly accessible computer programs.

(81) Purely as an example in this connection mention is made of SV_Win, a project of Vienna Technical University, where this software is described in great detail in the Grafinger post-doctoral thesis. An alternative, publicly accessible computer program is moreover the DISCO software and in particular the SCORPATH module of the City University London (Centre for Positive Displacement Compressor Technology). General information on this can be obtained from: http://www.city.compressors.co.uk/. Information on installation of the software can be obtained from 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.

(82) Another alternative software is the software ScrewView which is also mentioned in the thesis “Directed Evolutionary Algorithms” by Stefan Berlik, Dortmund 2006 (p. 173 f.). On the internet page http://pi.informatik.uni-siegen.de/Mitarbeiter/berlik/proiekte/ the ScrewView software is described in detail in connection with the project “Method for the design of dry-running rotary compressor machines.”

(83) In FIGS. 13 to 16 a tooth with trailing rotor flank F.sub.N and leading rotor flank F.sub.V is specifically produced as follows: the section S1 to S2 is obtained from a circular arc on the secondary rotor NR about the centre point C1 produced by the circular arc section T1 to T2 about the centre point C2 on the main rotor HR. The section S2 to S3 is obtained from an envelope curve to a trochoid produced by circular arc section T2 to T3 about the centre point M4 on the main rotor HR. The section S3 to S4 is defined by a circular arc about the centre point M1. The section S4 to S5 is predefined by a circular arc about the centre point M2.

(84) The section S5 to S6 is specified by a circular arc about the centre point C1. The adjoining section S6 to S7 is predefined by a circular arc about the centre point M3. The section S7 to S1 is finally predefined by an envelope curve to a trochoid produced by the circular arc section T7 to T1 about the centre point M5 on the main rotor HR. The previously described sections each adjoin one another seamlessly in the specified sequence. The tangents at the end of one section and at the beginning of the adjacent section are each the same. The sections in this respect merge into one another directly, smoothly and free from bends.

(85) The profile course of the teeth of the main rotor HR is explained briefly hereinafter for the exemplary embodiment according to FIGS. 1 to 4 also with reference to FIGS. 13 to 16. The section T1-T2 is obtained by a circular arc on the main rotor HR about the centre point C2 on the main rotor HR. The section T2-T3 is defined by the circular arc on the main rotor HR about the centre point M4. The section T3-T4 is obtained from an envelope curve to a trochoid produced by the section S3-S4 on the secondary rotor NR. The section T4-T5 is predefined by an envelope curve to a trochoid produced by the section S4-S5 on the secondary rotor. The section T5-T6 is defined by a circular arc about the centre point C2 produced by the circular arc section S5-S6 about the centre point C1 on the secondary rotor NR. The section T6-T7 is obtained by an envelope curve to a trochoid produced by the section S6-S7 on the secondary rotor NR. The section T7-T1 finally is specified by a circular arc about the centre point M5. Here it also applies that: the previously described sections each adjoin one another seamlessly in the specified sequence. The tangents at the end of one section and at the beginning of the adjacent section are each the same. The sections in this respect merge into one another directly, smoothly and free from bends.

(86) In general it should be noted that the profile courses of secondary rotor NR and main rotor HR are naturally matched to one another and in this respect the envelope curves to a trochoid each correspond to circular arc sections on the counter-rotor. Furthermore, as already mentioned a tangential transition from one to the next section is ensured. A general procedure for calculating the profile course of the counter rotor is described for example in the Helpertz thesis “Method for stochastic optimization of screw rotor profiles”, Dortmund 2003, p. 60 ff.