FORM 2
The Patents Act 1970
(39 of 1970)
&
The Patent Rules 2003
COMPLETE SPECIFICATION
(See Section 10 and rule 13)
TITLE OF THE INVENTION:
IMPROVED SCREW COMPRESSOR ROTOR WITH HOMOTOPIC
CURVES
APPLICANT:
a) Name: KIRLOSKAR PNEUMATIC COMPANY LIMITED.
b) Nationality: Indian
c) Address: HADAPSAR INDUSTRIAL ESTATE, PUNE 411013
PREAMBLE OF THE DESCRIPTION:
THE FOLLOWING SPECIFICATION PARTICULARLY DESCRIBES THE INVENTION AND THE MANNER IN WHICH IT IS PERFORMED

A) TECHNICAL FIELD
[001] The present invention generally relates to a mechanical apparatus and particularly relates to a compressor rotor with a homotopic teething profiles to improve an adiabatic and an overall compression efficiency.
B) BACKGROUND OF INVENTION
[002] A profile is one side of a tooth in a cross section between the outside circle and the root circle of the rotor. Usually, a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane.
[003] Prior art screw rotor profiles are a composition of different curves such as lines, circles, ellipses, parabolas, cycloids, hyperbolas, and their trochoids. A unique choice and placement of these curves with a purpose to make a shape that is as suitable as possible for the intended application of the screw machine makes a unique rotor profile. Such a unique composition or rotor profile enables the screw compressor designer to exploit particular and specific features of the composite curves. The choice and placement of composite curves is a non-obvious task; one which involves research and development as well as trial and error type of search for the curves offering maximum advantages. Compressor manufacturers with better rotor profiles have competitive advantage in their product's performance, reliability and cost.
[004] Hence, there is a requirement for improved rotor profiles in multiple rotors of a compressor to get maximum displacement and reduce the leakage areas such as

the blow hole area between two consecutive rotors. This leads to more efficient screw compressors in particular.
[005] The above-mentioned shortcomings, disadvantages and problems are addressed herein, as detailed below.
C) OBJECT OF INVENTION
[006] The primary objective of the present invention is to provide an improved
rotor profiles in multiple rotors of a screw compressor to reduce the blow hole area
between two consecutive rotors.
[007] Another objective of the present invention is to provide variable homotopic
profiles to teeth of consecutive rotor assemblies interacting with each other to
improve an adiabatic efficiency of compression further leading to improvement in
the energy efficiency of the compressor.
[008] These and other objects and advantages of the embodiments herein will
become readily apparent from the following detailed description taken in
conjunction with the accompanying drawings.
D) SUMMARY OF INVENTION
[009] The embodiments of the present invention provide a rotor assembly in a screw compressor with a homotopic rack profile comprising a main rotor and a gate rotor. A teeth profile of the leading edge of the main rotor and a trailing edge of the gate profile is created to intersect with the homotopic rack profile.

[0010] According to one embodiment of the present invention, the meshing of the
leading edge of the main rotor and the trailing edge of gate rotor generated from the
homotopic curves on rack improves the inter-teeth area(displacement) to leakage
area ratio by 1 -2%.
[0011 ] According to one embodiment of the present invention, the improvement in
inter-teeth area (displacement) to leakage area ratio by 1-2% results in an increase
in an adiabatic efficiency by 1-2% and a reduction in specific power requirement by
1-2%.
[0012] According to one embodiment of the present invention, the homotopic curve
comprising an elliptical arc and a straight-line interaction between the tips of the
main rotor and the gate rotor reduces the blow-hole leakage area by at least 10-
20%.
[0013] According to one embodiment of the present invention, the reduction in
blow hole area leakage by 10-20% leads to an overall increase in energy efficiency
of the screw compressor by an additional 1-2%.
[0014] These and other aspects of the embodiments herein will be better
appreciated and understood when considered in conjunction with the following
description and the accompanying drawings. It should be understood, however, that
the following descriptions, while indicating preferred embodiments and numerous
specific details thereof, are given by way of illustration and not of limitation. Many
changes and modifications may be made within the scope of the embodiments
herein without departing from the spirit thereof, and the embodiments herein
include all such modifications.

E) BRIEF DESCRIPTION OF DRAWINGS
[0015] The other objects, features and advantages will occur to those skilled in the
art from the following description of the preferred embodiment and the
accompanying drawings in which:
[0016] FIG. 1 illustrates a main rotor against a gate rotor in a screw compressor
and a homotopic rack profile according to which the teeth profile of both main rotor
and gate rotor are determined, according to one embodiment of the present
invention.
[0017] FIG. 2 illustrates an intersection rack (homotopic) profile with conjunction
or map points with the curves in between that are used to create a profile of the
main rotor teeth and gate rotor teeth as shown in FIG. 1, according to one
embodiment of the present invention.
[0018] FIG. 3a and 3b illustrates a rotational interaction between the main rotor
and gate rotor of FIG. 1 within a rotor casing and a projection of a sealing line (3b)
onto an end plane respectively for describing a blow hole area (3a), according to
one embodiment of the present invention.
[0019] FIG. 4 illustrates a rack profile generated by following different homotopy
deformation parameter, according to one embodiment of the present invention.
F) DETAILED DESCRIPTION OF THE EMBODIMENTS
[0020] In the following detailed description, a reference is made to the accompanying drawings that form a part hereof, and in which the specific embodiments that may be practiced is shown by way of illustration. The

embodiments are described in sufficient detail to enable those skilled in the art to practice the embodiments and it is to be understood that the logical, mechanical and other changes may be made without departing from the scope of the embodiments. The following detailed description is therefore not to be taken in a limiting sense. [0021] The present invention works on a principle of path homotopy that allows for continual deformations of analytical curves. Beginning with a set of any two analytical curves, the homotopy enables one to reach the intermediate curves (deformations) with a single parameter variation. Mathematically, the homotopy between two curves Curve_l and Curve_2 with respect to the homotopy parameter or deformation parameter q is written as-[0022] H = (q)(Curve_2) + (1 - q)(Curve_l)
[0023] When q = 0, H = Curve_l; and when q = 1, H = Curve_2. The homotopy parameter "q' continually deforms the Curve_l into the Curve_2 while taking intermediate shapes as 'q' goes smoothly from 0 to 1.
[0024] Homotopic curves were chosen to define certain portions of the rotor profiles over normal analytical curves used in prior arts such as straight lines and conic sections. The additional degree of control that comes with deformation parameter in homotopy allows larger scope for shape optimisation of profiles and leads to generation of multiple profiles having larger profile efficiencies (inter-teeth area to leakage area ratio) than the prior art profiles by at least 2-3%. [0025] The main rotor (2) and the gate rotor (3) of the rotors mapping onto a rack profile (1) shown in FIG. 1 uses the homotopic combination of a pair of analytical curves at two instances in its design (location and particulars of these curves are

elaborated in Fig. 2). The interaction between main rotor and gate rotor is similar to two gears that lead to a compression of a fluid by virtue of their meshing and continually shrinking compression chamber hence created. A higher inter-teeth area combined with smaller leakages during the interaction leads to a high compression efficiency and hence a rack profile (1) of an imaginary rotor with an indefinite radius is considered that leads to very high compression efficiency. Both the main rotor (2) and the gate rotor (3) are made conjugate to the rack profile according to the laws of gearing.
[0026] As shown in FIG. 2, the rack profile (10) provides an indication to design the teeth profile in a manner that the interaction of the main rotor and the gate rotor during a given instance follows a homotopic curve. The instances are primarily focussed around minimizing the leakage areas such as rack profile between 14-15 following a homotopic curve formed by a parabola and a hyperbola and is mapped onto the teeth profile between 24-25 of the main rotor (2) and 34-35 of the gate rotor (3). Further, the same rack profile allows to design the main rotor and the gate rotor with small blow hole areas in such a way that 12-13 and 18-19 rack profile is conjugated on an intersection line created during meshing of the main rotor and the gate rotor (which is a homotopic curve formed by an elliptical arc and a straight line). Each point on rack profile 10 can be associated with respective transformed points on 20 (teeth profile of the main rotor) and 30 (teeth profile of the gate rotor). The rack profile (10) comprises -a) 11-12—> Straight line

b) 12-13 —> Homotopic curve constructed with an elliptical arc and a straight line
c) 13-14 —> Straight line
d) 14-15 —> Homotopic curve constructed with a parabola and a hyperbola
e) 15-16 —> Cycloid
f) 16-17 —>Cycloid
g) 17-18—> Straight line
h) 18-19 —> Homotopic curve constructed with an elliptical arc and a straight line
i) 19-11 —> Straight line [0027] The respective curves on 20 and 30 are roulettes of the above curves generated according to the law of gearing or the Euler's envelope theory. [0028] The homotopic construction used between points 14-15 in 10 with Curve_l as parabola and the Curve_2 as hyperbola is found to be most suitable to generate the corresponding portion of leading edge of the main rotor lobe (24-25) and the trailing edge of the gate rotor lobe (34-35). This particular homotopic curve gives a wider and inclusive search space to optimize the rotor profile w.r.t compressor displacement and leakage area compared to prior arts.
[0029] Another homotopic construction used particularly between the points 12-13 and 18-19 in 10 with the Curve_l as an elliptical arc and the Curve_2 as a straight line is found to be highly suitable to generate the gate rotor tips. Rotor profile tips affect the blow-hole leakage area, sealing line leakage area (elaborated and visualized in Fig 3) and the manufacturability of the profiles. This particular

homotopic curve is found to enable a larger degree of control over the tip shape which results in greater ability of the profile designer to strike a better balance of leakage areas and manufacturability of the profiles. Thus, homotopic curve can also be constructed with an elliptical arc and a straight line. Such curve design is used to generate the tips of the gate rotor that enable to maintain a smaller sealing line leakage area and also a smaller blow-hole leakage area without compromising manufacturability of the resulting profiles. Prior art profiles are prone to compromising manufacturability of rotors due to sharper rotor tips arising in an attempt to minimise the blow-hole leakage area.
[0030] Further as shown in FIG. 3a and 3b, the main rotors (2) and the gate rotor (3) inside a rotor casing (4) during a perpetual rotational interaction where two key leakage areas associated with the rotor profile design are visualized. One of them, the blow hole area (5) is a small curvilinear triangle formed at the cusp of casing between a cusp line and the helical rotor tips as shown in Fig 3a. The shape of rotor tips hence influences the blow hole area (5).
[0031] The other important leakage area is the sealing line (8) projected onto an end plane as shown in FIG. 3b. The sealing line is a path of closest distance between the main rotor and the gate rotor along their length and hence it is a path of leakage too. The sealing line length is again a function of profile curves. The area depicted as 6 and 7 are inter-teeth area between the main rotor lobe and the gate rotor lobe respectively. These areas affect the volume throughput of the screw compressor per revolution (displacement). A higher displacement area (or inter-

teeth area) along with smaller leakage areas ensures higher volumetric efficiency of the compressor and also indicates a higher adiabatic efficiency. [0032] Depending on the shape of curves, the inter-teeth area or displacement of rotors also changes. Due to conjugacy of curves, the effect of increasing the inter-teeth area of the main rotor (6) results in reduction of the inter-teeth area of the gate rotor (7). The leading edge of main rotor (24-25) and trailing edge of gate rotor (34-35) generated by the curve (14-15) on the rack profile majorly affects the displacement of the rotor pair. The said two curves also have a certain sealing line length during meshing of the main rotor and the gate rotor. In order to get an efficient profile, the curve 14-15 must be chosen in such a way that it will have minimum sealing line length while trying to maximise the combined inter-teeth area of both rotors.
[0033] FIG. 4 depicts one exemplar variation of the curve 14-15 to show how the homotopic deformations work. The rack profile 91 as well as 92 has a homo topic curve constructed with a parabola and a hyperbola at the profile curve 14-15. The only difference is that the homotopy deformation parameter 'q is different for the rack profiles 91 and 92. The rack profile 92 is closer to a hyperbola (q<0.5) and the rack profile 91 is closer to a parabola (q>0.5). These two racks generate two different profiles with different shapes. Each has a unique displacement to leakage area but same blow-hole area (14-15 does not affect blow-hole). At certain instances of this homotopic curve's deformation, the ratio of inter-teeth area and leakage area will be optimised. The homotopic curve constructed with a parabola and a hyperbola covers a large range of shapes and it was found that one with q=0.8

gives up to 1% higher volumetric efficiency compared to the conventional rotor profiles.
[0034] Thus, key aspects of the rotor profiles in the present invention are: [0035] 1. Homotopic curves are chosen to represent the shapes on rotor profiles over normal analytical curves used in prior arts such as straight lines and conic sections. The profile change is done for the additional degree of freedom to manipulate shapes on the profile.
[0036] 2. The additional degree of freedom allows larger scope for shape optimisation of profiles which is exploited to try different combinations of commonly known analytical curves to construct homotopic curves and test their performance.
[0037] 3. Multiple pairs of curves such as ellipse-line, circle-parabola, hyperbola-ellipse, etc. were used to construct homotopic curves to generate the leading edge of main rotor and trailing edge of gate rotor lobe. The homotopy between hyperbola and parabola was found to offer the largest range of shapes and generated multiple profiles having larger profile efficiencies than the prior art profiles. [0038] 4. Blow-hole leakage area is an important feature that affects the machine's efficiency as well as rotor's manufacturability. The blow-hole area is inversely proportional to one of the other equally important leakage areas in screw compressors- sealing line leakage area. Smaller blow-hole leads to longer sealing line length. Hence, striking a good balance between these two is a key to a good profile. Rotor profile tips generated with homotopic curves offer this additional degree of freedom to strike a good balance between leakage areas.

[0039] 5. Usually, a smaller blow-hole area demands sharper rotor tips. Sharper tips are tougher and costlier to manufacture. Hence, striking a good balance of blow¬hole area and sealing line length without compromising the manufacturability of profile is also a challenge. A homotopic curve constructed with an elliptical arc and a straight line is found to be the right candidate for this purpose after several digital experiments with several homotopic curves.
G) ADVANTAGES OF THE INVENTION
[0040] The present rotor profile is generated by following a homotopic rack profile which increases the energy efficiency of the screw compressor and simultaneously leads to lower cost of manufacturing rotors bearing this profile due to better manufacturability.
[0041] It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the claims.

Claims: I/We Claim:
1. A rotor assembly in a screw compressor with a homotopic rack profile
comprising a main rotor and a gate rotor, wherein a teeth profile of the main rotor and the gate rotor is created to mesh with the homotopic rack profile.
2. The rotor assembly as claimed in claim 1, wherein the homotopic curve
comprising a hyperbola and a parabola interaction improves the inter-teeth area to leakage area ratio by 1-2%.
3. The rotor assembly as claimed in claim 2, wherein the increase in inter-teeth
area and reduction in leakage area results due in an increase in an adiabatic efficiency by 1-2% and a reduction in specific power requirement by 1-2%.
4. The rotor assembly as claimed in claim 1, wherein the homotopic curve
comprising an elliptical arc and a straight-line interaction between the tips of the rotor profiles reduces the blow-hole leakage area by at least 10-20%.
5. The rotor assembly as claimed in claim 4, wherein the reduction in blow-hole
leakage area results in an increase in the adiabatic efficiency by an additional 1-2% and a reduction in specific power requirement by an additional 1-2%.

6. The rotor assembly as claimed in claim 2 and 4, wherein the use of particular homotopic curves leads to an overall increase in energy efficiency of the screw compressor by 2-3%.