AU2003257923A1

AU2003257923A1 - Conjugate screw rotor profile

Info

Publication number: AU2003257923A1
Application number: AU2003257923A
Authority: AU
Inventors: James W. Bush; Keshava B. Kumar
Original assignee: Carrier Corp
Current assignee: Carrier Corp
Priority date: 1998-05-29
Filing date: 2003-10-29
Publication date: 2003-11-20
Anticipated expiration: 2019-05-28
Also published as: AU2003257923B2

Description

P001 Section 29 Regulation 3.2(2)

AUSTRALIA

Patents Act 1990 COMPLETE SPECIFICATION STANDARD PATENT Application Number: Lodged: Invention Title: Conjugate screw rotor profile The following statement is a full description of this invention, including the best method of performing it known to me us: CONJUGATE SCREW ROTOR PROFILE While there is some commonality between gears and screw rotors, a major difference is in the fluid sealing requirements of screw rotors. As in the case of gears, screw rotors have pitch circles which represent locations of equal tangential velocity for conjugate pairs of rotors. The spiral grooves in the rotors are the locations of the volumes of gas which are trapped and compressed due to the coaction of a conjugate pair of rotors and an enclosing casing. Accordingly, the volumes of the spiral grooves are a major design consideration with their width, depth, length and number being design variables. The shape of the cross section of the spiral grooves includes the variables of width and depth as well as the shape requirements for the driving/driven coaction between the conjugate pair of rotors. Additionally, the conjugate pair must meet the sealing requirements as the line contact advances along the rotor profile in the driving/driven coaction and as the rotor tips and end faces coact with the enclosing casing. This line contact follows the perimeters of the rotor profiles and is therefore at a varying tangential speed and has significant radial components. Additionally, the shape and cross section of the spiral grooves must meet requirements for ease of manufacture and cutting tool life. One problem associated with conventional screw rotor designs is that the pressure angle and lobe thickness are interrelated. It is desirable to minimize the pressure angle, the angle of contact between the rotors in the contact zone near or at the pitch circle, to provide reduced contact loading. However, the reducing of the pressure angle has an attendant undesirable reduction in lobe thickness such that conventional designs represent a compromise between desired pressure angle and desired lobe thickness.

Assuming that each respective lobe tip of each rotor is in tangential contact with a root of the other rotor during a point in each revolution, the addendum of the lobes of one rotor will be coincident to the dedendum of the lobes of the other rotor as measured along a line connecting the centers of the two rotors. Ignoring running clearances, machining tolerances, wear, thermal expansion, etc. there are three nominal points of tangency between a conjugate pair of rotors, namely between the pitch circles and between the tip circle of each rotor and the root circle of the other rotor.

The present invention is directed to an improved configuration for a conjugate pair of screw rotors. Among the benefits provided by the present invention are: reduced viscous drag through the use of a departure angle; strengthened female lobes by controlling thickness along the pitch circle; opened root of male rotor to enhance manufacturability and tool life; a tortuous flow path for gas leaking from a high pressure thread; better control of root diameter; and control of the pressure angle independently of the other Variables.

It is an object of this invention to increase the efficiency of a screw machine.

It is another object-of-this invention to provide conjugate screw rotor profiles having reduced leakage.

It is a further object of this invention to achieve the disclosed performance based objects while improving the manufacturability of the screw rotor profiles. These objects, and others as will become apparent hereinafter, are accomplished by the present invention.

Basically, the point of tangency of the tip circle of the male rotor and the root circle of the female rotor is used as a starting point in generating the series of curves defining the male and female conjugate rotor profiles. Additionally, the pressure angle is independent o,f the female lobe thickness.

Figure 1 is a transverse suction through a screw machine :employing'the present invention; Figure 2 is a plot of the curve segments making up the female rotor; Figure 3 is a plot of the curve segments making up the male rotor; Figure 4 is an enlarged representation of the departure segment of the rotors of the present invention; Figure 5 is an enlarged representation of the departure segment of the rotors of a PRIOR ART device; Figure 6 is an enlarged portion ofa modified segment of a female rotor; Figure 7 is an enlarged portion of a second modified segment of a female rotor; Figure 8 is an enlarged portion of a third modified segment of a female rotor; Figure 9 is an enlarged portion of a fourth modified segment of a female rotor; Figure 10 is an enlarged portion of a fifth modified segment of a female rotor; Figure 11 is an enlarged portion of a sixth modified segment of a female rotor; Figure 12 is an enlarged portion of a first modified segment of a male rotor; Figure 13 is an enlarged portion of a second modified segment of a male rotor; Figure 14 is an enlarged portion of a seventh modified segment of a female rotor; and Figure 15 is an enlarged portion of a third modified segment of a male rotor which is conjugate to the Figure 14 configuration.

In Figure 1, the numeral 10 generally indicates a screw machine such as a screw compressor. Screw machine 10 has a casing 12 with overlapping bores 12-1 and 12-2 located therein. Female rotor 14 has a pitch circle, PF, and is located in bore 12-1..

Male rotor 16 has a pitch circle, PM, and is located in bore 12-2. The axes indicated by points A and B are perpendicular to the plane of Figure 1 and are parallel to each other and are separated by a distance equal to the sum of the radius, R

F

of the pitch circle, PF, of female rotor 14 and the radius, Rm, of the pitch circle, Pm, of male rotor 16. The axis indicated by point A is the axis of rotation of female rotor 14 and the center, of bore 12-1 whose diameter generally corresponds to the diameter of the tip circle, TF, of female rotor 14. Similarly, the axis indicated by point B is the axis of rotation of male rotor 16 and the center of bore 12-2 whose diameter generally corresponds to the diameter of the tip circle, TM, of male rotor 16. Neglecting operating clearances, the extension of the bore 12-1 through the overlapping portion with bore 12-2 will intersect line A-B at the tangent point with the root circle, RR, of male rotor 16. Similarly, the extension of the bore 12-2 through the overlapping portion with bore 12-1 will intersect line A-B at the tangent point with the root circle, RFR, of female rotor 14 and this common point is labeled F, relative to female rotor 14 and M, relative to male rotor 16.

As illustrated, female rotor 14 has six lands, 14-1, separated by six grooves, 14-2, while male rotor 16 has five lands, 16-1, separated by five grooves 16-2.

Accordingly, the rotational speed of rotor 16 will be 6/5 or 120% of that of rotor 14.

Either the female rotor 14 or the male rotor 16 may be connected to a prime mover (not illustrated) and serve as the driving rotor. Other combinations of the number of female and male lands and grooves may also be used.

The generation of the profiles of rotors 14 and 16 starts with common point, as shown in Figure 1. With reference to Figures 1-3, the curve F,-F 2 on female rotor 14 is generated by point M, on the male tip as it rotates about axis B with both of rotors 14 and 16 having the same pitch circle velocity. Curve extends from the root of female rotor 14 to a point, short of the female pitch circle, P,.

Curve F 2 is a circular arc on female rotor 14 and extends from point F, to the pitch circle PF. The center of curve F,-F 3 is positioned such that curve both intersects curve F,-F 2 and is tangent to curve FI-F, at the point of intersection. The radius of curve F 2

-F

3 is adjusted to provide a desired balance between minimum blow hole area, as it affects the angle at which curve F 3

-F

4 intersects the pitch circle described below, and ease of manufacturing since tool life decreases with a reduction in the radius of curve F,-F 3 Curve F 2 generates curve on male rotor 16. As noted above, point M, generates curve F,-F so that F, is a common point with point M, at one point in the.

rotation of the rotors. Curve M 1

-M

2 represents the path swept out on male rotor 16 by curve F 2

-F

3 as contact advances from F 2 to F 3 while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

The curve F 3

-F

4 is a circular arc on female rotor 14 and its length or angular range is adjusted such that the male portion it generates, M 2 -M3, falls inside the pitch circle, PM, of male rotor 16. The center of curve F 3

-F

4 is positioned such that curve F3-F, both intersects curve and is tangent to curve F 2

-F

3 at the point of intersection.

Curve F 3

-F

4 influences the blow hole area, which is a leakage area defined by the cusp between bores 12-1 and 12-2 and rotors 14 and 16, and by minimizing the blow hole area, the leakage area, and therefore the leakage, is reduced which helps to improve the efficiency of screw machine 10. The radius of curve F 3

-F

4 is adjusted to provide a desired balance between minimum blow hole area and ease of manufacturing.

Curve M 2

-M

3 is generated by curve F3-F 4 on the female rotor 14 and represents the clearance path swept out on male rotor 16 by curve F,-F 4 as contact advances from F 3 to F 4 while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

The curve F 4

-F

5 on female rotor 14 is a circular arc extending from point F 4 to its intersection with the tip circle T F (bore 12-1) at point F 5 The radius and position of curve F 4

-F

5 is adjusted so that curve F 4

-F

5 is both coincident with and tangent to curve at the point of intersection, F 4 and so that it is tangent to the tip circle TF (bore 12-1) at point F,.

Curve M 3

-M

4 on the male rotor is generated by curve. F 4 -F and represents the path swept out on male rotor 16 by curve F 4

-F

5 as contact advances from M 3 to M 4 while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

Curve Fs-Fs is a circular arc extending along the tip circle T, (bore 12-1) of female rotor 14. Curve generates curve M 4

M

5 as contact advances from F 5 to F,' while both of rotors 14 and 16.are rotating at the same pitch circle velocity. Since curve F 5

F

5 is a circular arc on the tip circle T, (bore 12-1) of the female rotor 14 and is thus centered on the female rotor center A, the resulting curve M 4

M

5 is also a circular arc which is centered on the male rotor center B and which is the root circle RMR of male rotor 16. These qualities of M 4

M

5 make it particularly suited for easy generation and inspection and provides better control of the male root for manufacturability.

Points F 5 and Ms' correspond to points F 5 and M 5 respectively, located on an adjacent rotor lobe face and will be used as starting points for describing the other portions of the profiles of rotors 14 and 16. Straight line, or curve of infinite radius, F,"-F 6 extends from F 5 on the tip of female rotor 14 at an angle, with respect to a tangent at female tip circle TF (bore 12-1) at F 5 Line extends to a point short of the female pitch circle The angle A, is the female rotor departure angle and it provides the benefit of reducing viscous drag.

Curve Ms-M, on male rotor 16 is generated by line Fs"-F 6 and represents the path swept out on male rotor 16 by line as contact advances from M' to M 6 while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

Curve F 6

-F

7 is a circular arc on'female rotor 14. Line Fs"-F, and curve F 6 coact to: control the thickness, t, of the lobes of female rotor 14 as measured along the pitch circle, and which is controlled to maintain stiffness of the female lobe tip 14-1 to reduce deflection during machining; to provide sufficient room at the base 16-2 of the male lobe so that a large, strong cutting tool may be used to improve the accuracy and speed of machining; and to make the leak path more tortuous.

Curve M 6 on male rotor 16 is generated by curve F,-F 7 and represents the path swept out on male rotor 16 by curve F,-F 7 as contact advances from M 6 to M 7 while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

Curve M 7 -Mg on male rotor 16 is an involute of a circle at the desired pressure angle.

The male pitch circle, and female pitch circle, PF, meet at a common point called the pitch point and have a common tangent at the pitch point. At any contact point between the male and female rotor profiles, or conjugate profiles, a common normal can be drawn between the contact point and the pitchpoint. The angle between this common normal at the contact point and the common tangent at the pitchpoint is called pressure angle.

Curve F 7 on female rotor 14 is also an involute of a circle at the desired pressure angle. For both rotors, the involute base circle is smaller than but proportional to the pitch circles P, and of the female rotor 14 and the male rotor 16, respectively.

Thus the two involutes are inherently conjugate and one surface need not be generated by the other. Points F, and F, are not on the same side of pitch circle, but one of the points can be located on the pitch circle. The transmission of torque between the driving and driven rotors occurs at, or near, the pitch circle with some sliding but primarily with rolling contact between the rotors. Point F 7 has been illustrated as located on pitch circle P,.

Curve Mg-M, is a circular arc on the tip circle TM (bore 12-2) of male rotor 16. Curve on female rotor 14 is generated by curve Mg-M, and represents the path swept out on female rotor 14 by curve as line contact advances from F, to F, while both rotors 14 and 16 are rotating at the same pitch circle velocity. Since curve M,- M, is a circular arc on the tip circle TM (bore 12-2) of.male rotor 16 and is thus centered on the male rotor center B, the resulting curve is also a circular arc which is centered on the female rotor center A and which is the root circle RFR of the female rotor 14. These qualities of curve F, F, make it particularly suited for easy generation and inspection which provides better control of the female root for manufacturability.

The curve Ms-M,, on male rotor 16 is a curve of variable length and radius which bridges the gap between points M 8 and M 9 while approaching point M, at departure angle A z with respect to a tangent at tip circle TM (bore 12-2) of male rotor 16. Curve Ms-M, may be a generalized involute or made up of two or more curves such as arcs of circles with different radii. Curve F 8 on female rotor 14 is generated by curve Ms-M,, and represents the path swept out on female rotor 14 by curve Ms-M, as line contact advances from F, to while both of rotors 14 and 16 are rotating at the same pitch circle velocity.

Alternatively, the curve on female rotor 14 may be a curve of variable length and radius which bridges the gap between points F, and F, while approaching point F, at an angle which will control departure angle A, with respect to a tangent at tip circle T, (bore 12-2) of male rotor 16 at point Curve may be a generalized involute or made up of two or more curves such as arcs of circles with different radii.

Curve Ms-M, on male rotor 16 is generated by alternative curve and represents the path swept out on male rotor 16 by alternative curve as line contact advances from M 8 to M 9 while both rotors 14 and 16 are rotating at the same pitch velocity.

The curves F,"-F 6 Ms'-M 6

F

6

M

6

M

8 and F,-F 9 coact to provide control of the pressure angle independently of other profile variables such as female and male departure angles A, and respectively, and the female lobe thickness, t, among others.

Referring now to Figure 4, points W and X would correspond to points F, and Fs' of female rotor 14 and points M, and M 9 of male rotor 16, respectively. The departure angle A, for female rotor 14 and A, for male rotor 16 is located between a tangent to curve W-X at point X and the departure segment S which is the portion of rotor 14 or 16 starting at point X and corresponding to line F"-F 6 on female rotor 14 and curve Ms-M, on male rotor 16. It will be noted that departure segment S moves rapidly away from the bore which will be 12-1 for rotor 14 and 12-2 for rotor 16.

Accordingly, since oil film 100 is dependent upon a close distance between adjacent parts, its length is reduced and restricted essentially to the region of small clearance which essentially corresponds to the surface defined between W and X and a little past X. The reduced length of oil film 100 results in a reduced viscous shear stress area and thus reduced overall drag.

Referring now to Figure 5, points Y and Z correspond to points W and X in Figure 4.

Departure segment S' has a PRIOR ART configuration and starts essentially tangent to, and for considerable distance remains close to, the rotor bore 12-1', 12-2'. The oil film 100' which develops is much longer than oil film 100 and results in a greater viscous drag as the rotor tip moves relative to the bore as compared to the configuration of Figure 4.

As noted above, the present invention permits control of the pressure angle independently of other profile variables such as female and male departure angles A, and respectively, and the female lobe thickness, t, among others. Accordingly, the rotor profiles described above may be modified in order to achieve a desired design feature.

Segment of Figure 2 is described above as a straight line or a curve of infinite radius. In reality, taking manufacturing tolerances and the length of into account, there would be no practical difference if is a straight line or a curved segment where the radius is very large, and there would be no perceived difference in the drawings in the absence of distortion at a very greatly magnified scale. Segment Fs"-F, becomes a point where there is tangency with the tip circle at and where A, becomes 0°.

Referring now to Figure 6, straight or very large radius segment Fs'-F has been replaced by large radius segment Fs"-F 6 which is tangent to female rotor tip circle T

F

(bore 12-1) at Curved segment F 6 F, is of a smaller radius than curved segment Fs'-F 6 The advantage of this embodiment is that the female rotor departure angle is made O' while still allowing for independent control of the pressure angle and the female lobe thickness, t. Segments Fs"-Fs, and will generate modified segments corresponding to Ms-M, and M 6 respectively, on male rotor 16 as described with respect to Figures 1-3.

Figure 7 illustrates a second modified female rotor profile. Specifically, points F," and F 7 are connected through three curved segments, rather than two segments.

Segment Fs"-F 6 is a small radius portion intersecting the female rotor tip circle TF (bore 12-1). Segment F 6 2

-F

6 3 is a large radius segment and segment F6 3 is a small radius segment. The angle A, is the female rotor departure angle and is measured between a tangent to point F 6 2 and the female rotor tip circle T F (bore 12-1).

Segments F,.-F 6 3 and F 6 3 will generate modified segments corresponding to the portion between Mv and M, on male rotor 16. The advantage of the embodiment of Figure 7 is the elimination of the sharp comer at F 5 which otherwise might be difficult to produce with certain manufacturing processes such as finish milling or grinding of the lobes and tip diameter in a single operation.

Figure 8 illustrates a third modified female rotor profile. Specifically, points Fs" and F, are connected through three curved segments. Segment is a large radius portion intersecting the female rotor tip circle TF (bore 12-1). Segment F 6 4-F,6- is a curved segment having a smaller radius than segment Fs'-F 64 Segment F 6 is a curved segment having a smaller radius than segment F 64

-F

6 s Segments Fs'-F 6 4

F

6 F.s and F6,-F 7 will generate modified segments corresponding to the portion between Ms' and M 7 on male rotor 16. The advantage of the embodiment of Figure 8 is the increased flexibility in the independent selection of female lobe thickness, pressure angle and the radius of segments F6-F.- and F.s F 7 which replace segment in the Figure 2 embodiment and which may be restricted in certain desired ranges based on manufacturing requirements.

Figure 9 illustrates a fourth modified female rotor profile. Specifically, points and

F

7 are connected through a single varying radius curve, such as an involute, which reduces in radius in going from point F s to point F 7 Segment F5"-F 7 will generate a modified segment corresponding to the portion between and M 7 on male rotor 16.

The advantage of the embodiment of Figure 9 is the extension of the width of the contact band where a constant pressure angle is maintained.

Other variations are the cases where either curve Ms-M, or curve is made up of two or more curves, one of said curves may be located on a portion of curve M 8

-M

9 and another of said curves may be located on curve both of said curves being located so as not to be conjugate with each other.

Figure 10 illustrates a fifth modified female rotor profile. Specifically, points F, and F, are connected through two curves. The two curves are F, F, and.F,' F which are each arcs of circles. Segments F, F' and F' F 9 will coact to generate a modified segment corresponding to segment M 8 M, on male rotor 16. The advantage of the embodiment of Figure 10 is an alternate method of generating curves and M,-M, of Figures 2 and 3, respectively, by substituting simplified arcs of circles on the female rotor in place of the more complex generalized involute.

Figure 11 illustrates a sixth modified female rotor profile. Specifically, points F, and F, are connected through two curves. The two curves are F, F 8 which is a curve of continuously varying radius, such as an involute, and F 8 F, which is an arc of a circle. Segments and coact to generate a modified segment Mg-M, on male rotor 16. The advantage of the embodiment of Figure 11 is an alternate method of generating curves and Ms-M, of Figures 2 and 3 by substituting a simplified arc of a circle and a lower order involute on the female rotor in place of the more complex generalized involute.

Figure 12 illustrates a first modified male rotor profile. Specifically, points M 8 and

M

9 are connected through two curves. Curves M s M' and M, are each arcs of circles tangent at their common point Mg'. The advantage of the embodiment of Figure 12 is an alternate method of generating curves and Ms-M, of Figures 2 and 3 by substituting simplified arcs of circles on the male rotor in place of the more complex generalized involute.

Figure 13 illustrates a second modified male rotor profile. Specifically, points M 8 and M, are connected through two curves. Curve M 8 and is an arc of a circle and curve M 8 M, is a curve of continuously varying radius such as an involute. The two curves are tangent at their common point Ms". The advantage of the embodiment of Figure 13 is an alternate method of generating curves and Ms-M, of Figures 2 and 3 by substituting a simplified arc of a circle and a lower order of involute on the male rotor in place of the more complex generalized involute.

Figures 14 and 15 depict conjugate segments on a female and male rotor, respectively.

The Figure 14 modification differs from the Figure 2 embodiment in that points F 7 and F 9 are connected through a single curve of continuously varying radius, such as a generalized involute. Similarly, the Figure 15 modification differs from the Figure 3 embodiment in that points M7 and M 9 are connected through a single curve of continuously varying radius, such as a generalized involute. The advantage of the embodiments of Figures 14 and 15 is the elimination of the transition at the points F, and M 8 and the associated sudden change in radius of curvature which in some cases might otherwise add complexity to the design.

"Comprises/ccmprising" when used-in this specification is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more features, integers, steps, cmnponents or groups thereof.

Claims

3. The rotors of claim 1 wherein a second portion of 2 each female rotor lobe is located generally between said female rotor pitch 3 circle and said female rotor root circle and characterized by having a varying 4 radius and the conjugate portion on said male rotor is also characterized by having a varying radius (SEGMENT F 7 -F 9 ON FEMALE 6 AND SEGMENT M 7 -M 9 ON MALE). 1 4. The rotors of claim 1 wherein said female rotor is further 2 characterized by: 3 a second segment located inside said female pitch circle and 4 intersecting tangentially with said female root circle and having a varying radius which is selected such that the corresponding conjugate segment on said 6 male lobe also has a varying radius (SEGMENT F 7 ON FEMALE AND 7 SEGMENT M 7 ON MALE). 1 5. A conjugate pair of intermeshing rotors (14, 16) having helical 2 lobes comprising helical crests (14-1, 16-1) and intervening grooves (14-2, 16-2) and 3 adapted for rotation about parallel axes B) within a working space of a screw rotor 4 machine, each rotor has a tip circle (TF, TM), a pitch circle (P F and a root circle (RFR, RMR; one rotor of each pair being a female rotor 14) such that the major portion 6 of each lobe of said female rotor is located inside said pitch circle of said female rotor, 7 the other rotor being a male rotor (16) formed such that the major portion of each lobe 8 of said male rotor is located outside said pitch circle of said male rotor, the lands of 9 one rotor following the grooves of the other rotor to form a continuous sealing line between said pair of rotors, said lobes on said female rotor comprising at least eight 11 segments, said lobes on said male rotor comprising at least eight segments which are 12 conjugate to said female rotor segments, respectively, said female rotor segments 13 starting at a first point coincident with a point on the female root circle and said 14 conjugate male rotor segments starting at a corresponding first point coincident with a point on the male tip circle, said segments being characterized by: 16 a first segment on said male rotor comprising solely said first point 17 only on said tip circle of said male rotor, and a first segment on said female rotor 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 39 41 42 43 44 46 47 extending from said first female point on said female root circle to a second point radially inward of said female pitch circle andwhich is generated by said first point on male rotor when both of said rotors are rotated at the same pitch velocity; (POINT M, ON MALE AND SEGMENT FI-F, ON FEMALE) a second segment on said female rotor comprising a circular arc extending from the said second female rotor point and extending to a third point located radially outward at least to said pitch circle of said female rotor, and a second segment on said male rotor extending between said first male rotor point and a second male rotor point and which is generated by said second female segment when both of said rotors are rotated at the same pitch velocity; (SEGMENT F 2 -F 3 ON FEMALE AND SEGMENT ON MALE) a third segment on said female rotorcdomprisiing' a circular arc extending from said third female rotor point and extending to a fourth point located between said female rotor tip circle and said female'rotor pitch circle and a third segment on said male rotor extending from said second male rotor point to a third male rotor point and which is generated by said third female segment when both of said rotors are rotated at the same pitch circle velocity; ('SEGMENT M,-M 3 ON MALE AND SEGMENT F 3 -F 4 ON FEMALE) a fourth segment on said female rotor comprising a circular arc extending from said fourth female rotor point and extending to a fifth female rotor point which is coincident with a point on said female tip circle, and a fourth segment on said male rotor extending from said third male rotor point to a fourth male rotor point which is coincident with a point on said male root circle, and said fourth male rotor segment which is generated by said fourth female segment when both of said rotors are rotated at the same pitch circle velocity; (SEGMENT F 4 -Fs ON FEMALE AND SEGMENT M 3 -M 4 ON MALE) a fifth segment on said female rotor comprising a circular arc coincident with said female rotor tip circle and extending from said fifth female rotor point to a sixth female rotor point, and a fifth segment on said male rotor extending from said fourth male rotor point to a fifth male rotor point and which is generated by 48 said fifth female segment when both of said rotors are rotated at the same pitch circle 49 velocity; (SEGMENT F 5 -F 5 ON FEMALE AND SEGMENT M 4 -M 5 ON MALE) a sixth segment on said female rotor which extends firom said sixth 51 female rotor point. on said tip circle of said female rotor to a seventh female rotor 52 point located on or radially outward of said female rotor pitch circle,comprising a 53 curve of generally large radius in the outward end nearer said female rotor tip circle 54 and having a generally smaller radius in the inward end nearer said female rotor pitch circle, and a sixth segment on said male rotor extending from said fifth male rotor 56 point to a sixth male rotor point and which is generated by said sixth female segment 57 when both of said rotors are rotated at the same pitch circle velocity; (SEGMENT 58 FS"-F 7 ON FEMALE AND SEGMENT M 5 '-M 7 ON MALE)' 59 a seventh segment on said male rotor which extends from said sixth male rotor point to an seventh male rotor point which is coincident with a point on 61 said tip circle of said male rotor and said seventh male rotor segment comprising a 62 curve characterized by having a varying radius, and a seventh segment on said female 63 rotor which extends from said seventh female rotor point to an eighth female rotor 64 point which is coincident with a point on said female root circle and at least a portion of said eighth female rotor segment being generated by at least a portion of said 66 seventh male rotor segment when both of said rotors are rotated at the same pitch 67 circle velocity; (SEGMENT MT-M 9 ON MALE AND SEGMENT F 7 -F 9 ON 68 FEMALE) 69 an eighth segment on said male rotor comprising a circular arc coincident with said male tip circle and extending from said seventh male rotor point 71 to an eight male rotor point which is coincident with said first male rotor point for the 72 subsequent male lobe, and an eighth segment on said female rotor extending from said 73 eight female rotor point to a ninth female rotor point which is coincident with said 74 first female rotor point for a subsequent female lobe, said eighth female rotor segment being generated by said eighth male rotor segment when both of said rotors are rotated 76 at the same pitch circle velocity. (SEGMENT Mg-M, ON MALE AND SEGMENT 77 F 9 -F ON FEMALE) 1 6. The rotors of claim 5 wherein said seventh male rotor segment 2 contains two or more different arcs of circles. DATED this 29th day of October 2003. CARRIER CORPORATION WATERMARK PATENT TRADEMARK ATTORNEYS 290 BURWOOD ROAD HAWTHORN. VIC. 3122.