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Contribution of modern rotor profiles to energy efficiency of screw compressors

Contribution of modern rotor profiles to energy efficiency of screw compressors International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Contribution of modern rotor pro les to energy eciency of screw compressors 1;2 1 1 1 2 S Patil , M Davis , N Stosic , A Kovacevic and N Asati Centre for Compressor Technology, City, University of London, Northampton Square, London EC1V 0HB, United Kingdom Department of Research & Development, Kirloskar Pneumatic Co. Ltd., Hadapsar, Pune 411 013, India E-mail: [email protected] Abstract. Screw rotors are the heart of screw compressors. And the energy eciency of industrial machines is a matter of tremendous signi cance now more than ever. Historically, rotor pro le developments have played a key role in making screw compressors energy ecient and commercially viable. Further attention to manufacturing aspects of rotor pro les and the invention of the rack generated rotor pro les led to rotor pro les having good manufacturability. The principles of rotor pro le generation and manufacturing are available in open literature since 1960's. But more and more literature on rotor pro ling has been published since then. Modern screw rotor pro les (patented close to and in the 21st century) have all the principles of a good pro le incorporated in their design. Hence the industry and pro le designers at large are aware of the increasing diculty to further make the twin screw compressor rotor pro les more energy ecient. This paper tries to quantify the contribution of rotor pro le to energy eciency of a typical twin screw compressor by comparing the most recent (hence modern) screw compressor rotor pro les. In order to fairly compare di erent rotor pro les, all are retro tted to a single size, lobe combination, rotor length, and helix angle. Only the curves constituting the pro le, as dictated in the patent documents of the respective pro les, have been changed. Tools such as SCORPATH and SCORG have been used to do the geometric and thermodynamic calculations on the pro les. Keeping the working conditions same for all the retro tted but di erent pro les, a comparison has been made. This comparison sheds some light on how much is the energy eciency of a particular twin screw compressor in uenced by a mere change of pro le. This analysis can be further extended to establish reasonable targets for twin screw compressor manufacturers to improve energy eciency of their machines via improving their rotor pro les. This remains the future scope of this work. 1. Introduction Twin screw compressors have evolved for almost a century since their invention in 1930's. Rotor pro les being an essential element of these machines, have gone through a similar evolution over these years. Advancements in rotor pro le design and manufacturing played crucial role in putting the twin screw compressors on par with the other compression technologies. Energy eciency of compressors could be talked about in terms of either their speci c power which is power consumed to deliver a unit of compressed medium or the adiabatic or isothermal eciencies of compression process evaluated for that machine. Early rotor pro les were not very energy ecient due to large leakage areas between the rotors. This scenario changed Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 with the invention of asymmetric rotor pro les, rst by Lysholm [1] and later with the SRM- A pro le by Schibbye [2] which led to signi cant reduction of internal leakages with respect to total throughput of the rotors. The developments in manufacturing technology for making the helical rotors with precision also played a key role in making screw compressors energy ecient and hence commercially viable. Only by maintaining the tight form of rotor pro les in manufacturing, the internal clearances could be kept to minimum and thereby internal leakages were minimized too. There's a long and interesting history to how these principles of generating viable rotor pro les were discovered, patented and then re-discovered by other manufacturers. It is very well summarized by Stosic et al. [3]. By and large, most of the major screw compressor manufacturers had their own pro le patents by 1980's [4] [5] [6] [7]. All these pro les were based on principles similar to SRM-A pro le, wherein curves of choice were de ned on either rotor to derive the conjugate curves on the other rotor using gearing condition. E orts were put into choosing most suitable curves which would facilitate larger throughput area and minimize the leakage areas keeping manufacturability in consideration. In the period that followed, the principle of rack generation was introduced in rotor pro ling for screw compressors rst by Menssen [8] followed by Rinder [9]. The principle of rack generation had several advantages over previous method such as better manufacturability by design, involute contact and a simplicity in the design. Still, the rack generated pro les had ample scope of improvement which was steadily and incrementally realized in later pro les such as Stosic [10] and as latest as Cavatorta and Tomei [11]. The rack generated pro le by Rinder [9] though ingenious; had a problem of slightly larger blow hole area and poor sealing on the portion of rotors generated by the high pressure side of the rack. This particular shortcoming of the rack generated pro le was overcome by Stosic and Hanjalic [12] through introduction of cycloids in this region of rack which could also be seen as a combined rotor-rack generation method. N- rotors are stronger yet lighter and also facilitate high throughput to leakage area ratio resulting in a higher energy eciency of the machine. Later and more recent contributions to the eld of rotor pro ling came through applications of ner design principles such as variable clearance distributions on rotors, controlling torque characteristics of the gate rotor [13] and an extensive work on optimisation techniques applied to rotor pro le designs [14] [15] [16] [17]. The wealth of all this literature available in modern times has made the principles of good rotor pro ling accessible to the majority of rotor pro le designers. The intent of this paper is to review the more recent or modern rotor pro les from last 25 years. These modern rotor pro les are based on the body of literature and knowledge brie y outlined hereby. The state of the art rotor pro le patents owned by major compressor manufacturers are reviewed in light of their uniqueness and di erences. Their contribution to energy eciency of modern screw compressors is discussed. Based on the review and discussion, a general outline of what may lie in future for the screw rotor pro ling is drawn. 2. Modern screw rotor pro les Fu Sheng's [18], Gardner Denver's [11], City's [19] and Kaeser's [20] are some of the major rotor pro le patents in last 20 years. They are chosen particularly to highlight the features of the state of the art rotor pro les. There are obviously more patents to be found on rotor pro les in this time period but these pro les are assumed to be representatives of good rotor pro ling principles applied in the design of energy ecient screw compressors by the respective assignees. Figures 1, 2 and 3 depict the mentioned modern rotor pro les as represented in their respective patent documents. The patent [19] is mainly about the N-pro led rotors designed for better torque characteristics and reduced noise. Geometrically, the pro le curves in this patent are same as that of [10]. Two of the three pro les depicted herein ( gures 1 and 2) are based on the principle of rotor- 2 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Figure 1. Fu Sheng Pro le [18] Figure 2. Gardner Denver Pro le [11] Figure 3. Kaeser Pro le [20] 3 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 rack generation which is known have several advantages over classical rotor generation or rack generation principle. The racks used to de ne these pro les are very similar to the N-rack [10]. They all di er essentially by the curve used to de ne the low pressure side of the rack. Figure 4 depicts a general rack pro le for rotor-rack generated pro les with nodes representing end points of the constituent curves. Table 1 then lists the individual curves to show how the patents are di erent. The respective conjugates on rotors are simply roulettes of the curves de ned on rack calculated by solving the envelope gearing condition. Main rotor lobe E2 G1 G E Gate rotor lobe H2 E1 F2 Rack profile F1 G2 H1 A A2 A1 B2 C1 B1 D1 C2 E1 D2 E2 Figure 4. A general rack pro le generating main and gate rotor pro les Table 1. The curves constituting rack of the N-pro le, Fu Sheng pro le and the Gardner Denver pro le Rack curve N-pro le Fu Sheng pro le Gardner Denver pro le D-E Vertical straight line Vertical straight line Vertical straight line E-F Circular arc Circular arc Circular arc F-G Straight line Straight line - G-H Cycloid Cycloid Cycloid H-A Cycloid Cycloid Cycloid A-B General arc Elliptic arc Hyperbolic arc B-C Straight line Straight line Straight line C-D Circular arc Circular arc Circular arc Parabolic, Elliptic or Hyperbolic arc, depending upon the arc exponents [10] The key change in the three similar pro les in table 1 is in the curve A-B. This particular portion of the rack determines what would be main and gate rotor lobe thicknesses which in uence the total combined throughput area of the rotor pair. It also a ects the sealing line length of the meshing rotor pair. Hence, the changes in arc to get various conic sections such as ellipse and hyperbola are probably done for striking a good balance between total throughput area and the sealing line leakage area. Curve A-B does not a ect high pressure side blow-hole area but all the curves above horizontal axis do. In this context, it is interesting to note that 4 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 the straight line F-G is omitted in the Gardner Denver pro le. This slight change of directly connecting the cycloid with circular arc on high pressure side helps marginally reduce the blow hole area. Only the Kaeser pro le out of most of the modern pro les is based on the principle of rotor generation. Majority of this pro le's curves are de ned on the gate rotor and the remaining on the main rotor. It is largely based on its predecessor SIGMA pro le by Bammert [4]. The latest pro le has made amendments with the targets of improving gate rotor torque characteristics, minimizing blow-hole area, strengthening gate rotors and optimizing the pro les with respect to multi-objective criteria. Especially the pro le version of Kaeser's new pro le depicted in gure 3 has up to four times smaller blow-hole than an equivalent rack-generated pro le due to slightly negative gate rotor addendum combined with a well designed sharp gate rotor tip. This however comes at a price of relatively lesser throughput area due to smaller pro le depth. Such trade-o s are ubiquitous in rotor pro le design. Therefore, one has to weigh in the role of operating conditions and application of the screw compressor to make the best trade-o s. 3. Contribution of modern pro les to the energy eciency of screw compressors The literature has several clues and reportings of the improvement in energy eciency of screw compressors with the onset of rotor-rack generation method along with the application of ner design principles such as variable clearance distributions and multi-variate optimisation to rotor pro les. That is to say, contribution of the modern screw rotor pro les replacing the older th pro les of late 20 century to the energy eciency of screw compressors can be pinned down with evidence. Stosic et al. [21] presents a case of retro tting old SRM-A pro led rotors in an oil ooded twin screw compressor with the N-pro led rotors and thereby improving the energy eciency of the machine by 2.5%. From a purely geometric point of view, pro le does not solely contribute to the energy eciency of screw machine. Other characteristics of the rotors such as lobe combination, diameter, length, helix angle, speed and also the suction and discharge ports a ect the performance to a signi cant degree. Hence, only a holistic approach to optimum choice of all the geometric and operating parameters would lead to substantially ecient compressors. The combined pro le and geometry optimisation with Kaeser's new pro le [20] is claimed to have improved upon the old SIGMA pro le [4] by up to 3%. Similarly, Fu Sheng's rack generated pro le ( gure 1) is claimed to have improved on their own old rotor generated pro le [22] by 1.32% in terms of the energy eciency [17]. Nevertheless, all three of the presented examples arise from a comparison of the modern pro les with old pro les. But, if one wishes to gauge the contributions of only modern rotor pro les into improvements of energy eciency of screw compressors in last 25 years, only the modern pro les must be compared starting from N-pro le [10]. As elaborated in the previous section, majority of the modern screw rotor pro les have incorporated the principles of designing good pro les. This could be the reason for minimal di erences among their designs. But to what extent do these minimal changes a ect the energy eciency of machines? To answer this, Fu- Sheng pro le [18] and the Gardner Denver pro le [11] can be compared through retro tting and numerical evaluation of their geometric and thermodynamic properties. The pro le with 5/6 lobe combination of rotors as depicted in gure 1 true to Fu Sheng's patent description is generated and taken as a reference for calculation. The Gardner Denver pro le's patent depiction ( gure 2) is in 3/5 lobe combination of rotors. In order to retro t with Fu Sheng pro le, a Gardner Denver pro le with 5/6 lobe combination is generated based on the patent description of curves and other details of the pro le. The two pro les are set at the same centre distance of approximately 100 mm and have a 140 mm main rotor outer diameter. The length to diameter ratio is set to 1.55 and the wrap angle is set to 300 for both rotor pairs. Figure 5 is a representation of these two retro tted pro les. 5 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Figure 5. Retro tted rotor pro les with 5/6 lobe combination-[18] and [11] As elaborated earlier, the high pressure side of these pro les is identical except the absence of straight line in Gardner Denver pro le. A closer look at the leading edge tip of the gate rotors of Gardner Denver pro le shows that it would have a smaller blow hole area compared to Fu Sheng pro le on account of this small change. The low pressure sides of these pro les have Ellipse and a Hyperbola respectively. That makes them look slightly di erent on leading edge of the main rotor. The throughput area and the leakage areas for these two pro les are calculated and given in table 2. It is worth noting that both, FuSheng and Gardner Denver pro les can be generated through the N rotor form by choosing coecients and exponents in its general curve to resemble circles, ellipses, parabolas or hyperbolas. Table 2. Geometric pro le characteristics for retro tted Fu Sheng and Gardner Denver pro les Pro le Characteristic Fu Sheng Pro le Gardner Denver Pro le Throughput area (mm ) 8507 8621 Interlobe sealing area (mm ) 4.693 4.876 Blow hole area (mm ) 1.852 1.191 The Gardner Denver pro le has a slight advantage in throughput area as well as blow hole area on account of the ner details elaborated in previous section. If these pro les are subjected to a thermodynamic simulation for an oil injected screw compressor air application, the di erence in energy eciency of these machines is observed to be of the order of 0.3% to 0.5% only. The simulation was done in SCORG software within the envelope of operating conditions - tip speed 10 m/s to 40 m/s, suction pressure 1 bar absolute (bara) and discharge pressure 6.5 bara to 12.5 bara. The oil injection parameters and other peripheral details were set to practically reasonable values and same for both setups to avoid their in uence on evaluation. The observed order of di erence shows that the modern pro les which are more or less equivalent in application of good 6 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 design principles do not make a big di erence in terms of energy eciency. Even the gap of 0.3% could be minimized if the pro le with larger leakage area is allowed to compensate using other characteristics such as rotor size, sharper tips or rotor speeds, etc. If an N-pro le were designed for similar size, it wouldn't be any di erent because structurally both the pro les in gure 5 are equivalent to it. Either FuSheng or Gardner Denver pro les can be generated through the N rotor patent de nition by changing the curve A-B exponent n [10]. No more than 0.5% of di erence in energy eciency would be observed by only interchanging curves such as-parabola, ellipse and a hyperbola. 4. Conclusion & Future scope Most of the known features of a good rotor pro les are already incorporated in all the modern rotor pro les. Hence, an advantage by a mere change of curves or their placement in a pro le is practically not possible at least in modern pro les. Unlike the leap in energy eciency of screw compressors rst by introduction of asymmetric pro les in 1960's and then through the principle of rotor-rack generation in 1990's, modern pro les are unlikely to come by such leap through only change of pro le curves and shapes. Screw compressor manufacturers already in possession of a good modern pro le should expect improvements from any new pro les only in the order of 1% at maximum. More improvements are only going to come from either innovations in optimisation techniques or a scienti c disruption in the methods of pro le generation and manufacturing. One example of such an innovation which could improve rotor pro les if combined with good optimisation framework is application of topology inspired by path homotopy in pro ling [23]. Since all modern pro les are more or less equally ecient, the weight of designing more ecient screw compressors lies with the ability of pro le designer. Use of the state of the art optimisation algorithms, understanding of the machine application and underlying physics of compression is paramount if one wishes to ne tune any good pro le for the desired duty. Energy eciency of not only operation but also during manufacturing of screw compressors until the end of complete product life-cycle should be the focus for future of rotor pro ling. References [1] Lysholm A 1967 Screw rotor machine US Patent 3,314,598 [2] Schibbye L B 1969 Screw rotor machine and rotors therefor US Patent 3,423,017 [3] Stosic N, Smith I K and Kovacevic A 2003 Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 217 157{170 [4] Bammert K 1982 Intermeshing screw rotor machine with speci c thread pro le US Patent 4,350,480 [5] Bowman J L 1983 Helical screw rotor pro les US Patent 4,412,796 [6] Astberg A 1984 Screw rotor machine and rotor pro le therefor US Patent 4,435,139 [7] Hough D, Morris S J and Barber A D 1987 Screw rotor machines with speci c tooth pro les US Patent 4,636,156 [8] Menssen E 1977 Screw compressor with involute pro led teeth US Patent 4,028,026 [9] Rinder L 1987 Screw rotor pro le and method for generating US Patent 4,643,654 [10] Stosic N R 1997 Plural screw positive displacement machines US Patent 6,296,461 [11] Cavatorta P and Tomei U 2014 Screw compressor having male and female rotors with pro les generated by enveloping a rack pro le US Patent 8,702,409 [12] Stosic N and Hanjalic K 1997 Journal of Fluids Engineering 119 659{664 [13] Stosic N, Smith I and Kovacevic A 2005 Screw compressors: mathematical modelling and performance calculation (Springer Science & Business Media) 7 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 [14] Su S H and Tseng C H 2000 Journal of mechanical design 122 543{552 [15] Kauder K, Helpertz M, Reusch B and Berlik S 2002 VDI BERICHTE 1715 29{50 [16] Stosic N, Smith I K and Kovacevic A 2003 Applied Thermal Engineering 23 1177{1195 [17] Wu Y R and Fong Z H 2009 Mechanism and Machine Theory 44 66{82 [18] Lee H T, Fong Z H and Wu Y R 2006 Mechanism of the screw rotor US Patent App. 10/961,056 [19] Stosic N R 2017 Reduced noise screw machines US Patent 9,714,572 [20] Weih G 2019 Rotor pair for a compression block of a screw machine US Patent 10,400,769 [21] Stosic N, Smith I, Kovacevic A and Venumadhav K 2000 Retro t `n' rotors for ecient oil- ooded screw compressors Proc. of the 2000 International Compressor Engineering Conference at Purdue [22] Lee H T 1990 Screw-rotor machine with an ellipse as a part of its male rotor US Patent 4,890,992 [23] Patil S, Stosic N, Kovacevic A, Smith I and Asati N 2021 Application of path homotopy in twin screw compressor rotor pro le design IOP Conference Series: Materials Science and Engineering vol 1180 (IOP Publishing) p 012004 Acknowledgments Authors would like to thank Kirloskar Pneumatic Company Limited, India for nancially supporting this research. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png IOP Conference Series: Materials Science and Engineering IOP Publishing

Contribution of modern rotor profiles to energy efficiency of screw compressors

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Abstract

International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Contribution of modern rotor pro les to energy eciency of screw compressors 1;2 1 1 1 2 S Patil , M Davis , N Stosic , A Kovacevic and N Asati Centre for Compressor Technology, City, University of London, Northampton Square, London EC1V 0HB, United Kingdom Department of Research & Development, Kirloskar Pneumatic Co. Ltd., Hadapsar, Pune 411 013, India E-mail: [email protected] Abstract. Screw rotors are the heart of screw compressors. And the energy eciency of industrial machines is a matter of tremendous signi cance now more than ever. Historically, rotor pro le developments have played a key role in making screw compressors energy ecient and commercially viable. Further attention to manufacturing aspects of rotor pro les and the invention of the rack generated rotor pro les led to rotor pro les having good manufacturability. The principles of rotor pro le generation and manufacturing are available in open literature since 1960's. But more and more literature on rotor pro ling has been published since then. Modern screw rotor pro les (patented close to and in the 21st century) have all the principles of a good pro le incorporated in their design. Hence the industry and pro le designers at large are aware of the increasing diculty to further make the twin screw compressor rotor pro les more energy ecient. This paper tries to quantify the contribution of rotor pro le to energy eciency of a typical twin screw compressor by comparing the most recent (hence modern) screw compressor rotor pro les. In order to fairly compare di erent rotor pro les, all are retro tted to a single size, lobe combination, rotor length, and helix angle. Only the curves constituting the pro le, as dictated in the patent documents of the respective pro les, have been changed. Tools such as SCORPATH and SCORG have been used to do the geometric and thermodynamic calculations on the pro les. Keeping the working conditions same for all the retro tted but di erent pro les, a comparison has been made. This comparison sheds some light on how much is the energy eciency of a particular twin screw compressor in uenced by a mere change of pro le. This analysis can be further extended to establish reasonable targets for twin screw compressor manufacturers to improve energy eciency of their machines via improving their rotor pro les. This remains the future scope of this work. 1. Introduction Twin screw compressors have evolved for almost a century since their invention in 1930's. Rotor pro les being an essential element of these machines, have gone through a similar evolution over these years. Advancements in rotor pro le design and manufacturing played crucial role in putting the twin screw compressors on par with the other compression technologies. Energy eciency of compressors could be talked about in terms of either their speci c power which is power consumed to deliver a unit of compressed medium or the adiabatic or isothermal eciencies of compression process evaluated for that machine. Early rotor pro les were not very energy ecient due to large leakage areas between the rotors. This scenario changed Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 with the invention of asymmetric rotor pro les, rst by Lysholm [1] and later with the SRM- A pro le by Schibbye [2] which led to signi cant reduction of internal leakages with respect to total throughput of the rotors. The developments in manufacturing technology for making the helical rotors with precision also played a key role in making screw compressors energy ecient and hence commercially viable. Only by maintaining the tight form of rotor pro les in manufacturing, the internal clearances could be kept to minimum and thereby internal leakages were minimized too. There's a long and interesting history to how these principles of generating viable rotor pro les were discovered, patented and then re-discovered by other manufacturers. It is very well summarized by Stosic et al. [3]. By and large, most of the major screw compressor manufacturers had their own pro le patents by 1980's [4] [5] [6] [7]. All these pro les were based on principles similar to SRM-A pro le, wherein curves of choice were de ned on either rotor to derive the conjugate curves on the other rotor using gearing condition. E orts were put into choosing most suitable curves which would facilitate larger throughput area and minimize the leakage areas keeping manufacturability in consideration. In the period that followed, the principle of rack generation was introduced in rotor pro ling for screw compressors rst by Menssen [8] followed by Rinder [9]. The principle of rack generation had several advantages over previous method such as better manufacturability by design, involute contact and a simplicity in the design. Still, the rack generated pro les had ample scope of improvement which was steadily and incrementally realized in later pro les such as Stosic [10] and as latest as Cavatorta and Tomei [11]. The rack generated pro le by Rinder [9] though ingenious; had a problem of slightly larger blow hole area and poor sealing on the portion of rotors generated by the high pressure side of the rack. This particular shortcoming of the rack generated pro le was overcome by Stosic and Hanjalic [12] through introduction of cycloids in this region of rack which could also be seen as a combined rotor-rack generation method. N- rotors are stronger yet lighter and also facilitate high throughput to leakage area ratio resulting in a higher energy eciency of the machine. Later and more recent contributions to the eld of rotor pro ling came through applications of ner design principles such as variable clearance distributions on rotors, controlling torque characteristics of the gate rotor [13] and an extensive work on optimisation techniques applied to rotor pro le designs [14] [15] [16] [17]. The wealth of all this literature available in modern times has made the principles of good rotor pro ling accessible to the majority of rotor pro le designers. The intent of this paper is to review the more recent or modern rotor pro les from last 25 years. These modern rotor pro les are based on the body of literature and knowledge brie y outlined hereby. The state of the art rotor pro le patents owned by major compressor manufacturers are reviewed in light of their uniqueness and di erences. Their contribution to energy eciency of modern screw compressors is discussed. Based on the review and discussion, a general outline of what may lie in future for the screw rotor pro ling is drawn. 2. Modern screw rotor pro les Fu Sheng's [18], Gardner Denver's [11], City's [19] and Kaeser's [20] are some of the major rotor pro le patents in last 20 years. They are chosen particularly to highlight the features of the state of the art rotor pro les. There are obviously more patents to be found on rotor pro les in this time period but these pro les are assumed to be representatives of good rotor pro ling principles applied in the design of energy ecient screw compressors by the respective assignees. Figures 1, 2 and 3 depict the mentioned modern rotor pro les as represented in their respective patent documents. The patent [19] is mainly about the N-pro led rotors designed for better torque characteristics and reduced noise. Geometrically, the pro le curves in this patent are same as that of [10]. Two of the three pro les depicted herein ( gures 1 and 2) are based on the principle of rotor- 2 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Figure 1. Fu Sheng Pro le [18] Figure 2. Gardner Denver Pro le [11] Figure 3. Kaeser Pro le [20] 3 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 rack generation which is known have several advantages over classical rotor generation or rack generation principle. The racks used to de ne these pro les are very similar to the N-rack [10]. They all di er essentially by the curve used to de ne the low pressure side of the rack. Figure 4 depicts a general rack pro le for rotor-rack generated pro les with nodes representing end points of the constituent curves. Table 1 then lists the individual curves to show how the patents are di erent. The respective conjugates on rotors are simply roulettes of the curves de ned on rack calculated by solving the envelope gearing condition. Main rotor lobe E2 G1 G E Gate rotor lobe H2 E1 F2 Rack profile F1 G2 H1 A A2 A1 B2 C1 B1 D1 C2 E1 D2 E2 Figure 4. A general rack pro le generating main and gate rotor pro les Table 1. The curves constituting rack of the N-pro le, Fu Sheng pro le and the Gardner Denver pro le Rack curve N-pro le Fu Sheng pro le Gardner Denver pro le D-E Vertical straight line Vertical straight line Vertical straight line E-F Circular arc Circular arc Circular arc F-G Straight line Straight line - G-H Cycloid Cycloid Cycloid H-A Cycloid Cycloid Cycloid A-B General arc Elliptic arc Hyperbolic arc B-C Straight line Straight line Straight line C-D Circular arc Circular arc Circular arc Parabolic, Elliptic or Hyperbolic arc, depending upon the arc exponents [10] The key change in the three similar pro les in table 1 is in the curve A-B. This particular portion of the rack determines what would be main and gate rotor lobe thicknesses which in uence the total combined throughput area of the rotor pair. It also a ects the sealing line length of the meshing rotor pair. Hence, the changes in arc to get various conic sections such as ellipse and hyperbola are probably done for striking a good balance between total throughput area and the sealing line leakage area. Curve A-B does not a ect high pressure side blow-hole area but all the curves above horizontal axis do. In this context, it is interesting to note that 4 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 the straight line F-G is omitted in the Gardner Denver pro le. This slight change of directly connecting the cycloid with circular arc on high pressure side helps marginally reduce the blow hole area. Only the Kaeser pro le out of most of the modern pro les is based on the principle of rotor generation. Majority of this pro le's curves are de ned on the gate rotor and the remaining on the main rotor. It is largely based on its predecessor SIGMA pro le by Bammert [4]. The latest pro le has made amendments with the targets of improving gate rotor torque characteristics, minimizing blow-hole area, strengthening gate rotors and optimizing the pro les with respect to multi-objective criteria. Especially the pro le version of Kaeser's new pro le depicted in gure 3 has up to four times smaller blow-hole than an equivalent rack-generated pro le due to slightly negative gate rotor addendum combined with a well designed sharp gate rotor tip. This however comes at a price of relatively lesser throughput area due to smaller pro le depth. Such trade-o s are ubiquitous in rotor pro le design. Therefore, one has to weigh in the role of operating conditions and application of the screw compressor to make the best trade-o s. 3. Contribution of modern pro les to the energy eciency of screw compressors The literature has several clues and reportings of the improvement in energy eciency of screw compressors with the onset of rotor-rack generation method along with the application of ner design principles such as variable clearance distributions and multi-variate optimisation to rotor pro les. That is to say, contribution of the modern screw rotor pro les replacing the older th pro les of late 20 century to the energy eciency of screw compressors can be pinned down with evidence. Stosic et al. [21] presents a case of retro tting old SRM-A pro led rotors in an oil ooded twin screw compressor with the N-pro led rotors and thereby improving the energy eciency of the machine by 2.5%. From a purely geometric point of view, pro le does not solely contribute to the energy eciency of screw machine. Other characteristics of the rotors such as lobe combination, diameter, length, helix angle, speed and also the suction and discharge ports a ect the performance to a signi cant degree. Hence, only a holistic approach to optimum choice of all the geometric and operating parameters would lead to substantially ecient compressors. The combined pro le and geometry optimisation with Kaeser's new pro le [20] is claimed to have improved upon the old SIGMA pro le [4] by up to 3%. Similarly, Fu Sheng's rack generated pro le ( gure 1) is claimed to have improved on their own old rotor generated pro le [22] by 1.32% in terms of the energy eciency [17]. Nevertheless, all three of the presented examples arise from a comparison of the modern pro les with old pro les. But, if one wishes to gauge the contributions of only modern rotor pro les into improvements of energy eciency of screw compressors in last 25 years, only the modern pro les must be compared starting from N-pro le [10]. As elaborated in the previous section, majority of the modern screw rotor pro les have incorporated the principles of designing good pro les. This could be the reason for minimal di erences among their designs. But to what extent do these minimal changes a ect the energy eciency of machines? To answer this, Fu- Sheng pro le [18] and the Gardner Denver pro le [11] can be compared through retro tting and numerical evaluation of their geometric and thermodynamic properties. The pro le with 5/6 lobe combination of rotors as depicted in gure 1 true to Fu Sheng's patent description is generated and taken as a reference for calculation. The Gardner Denver pro le's patent depiction ( gure 2) is in 3/5 lobe combination of rotors. In order to retro t with Fu Sheng pro le, a Gardner Denver pro le with 5/6 lobe combination is generated based on the patent description of curves and other details of the pro le. The two pro les are set at the same centre distance of approximately 100 mm and have a 140 mm main rotor outer diameter. The length to diameter ratio is set to 1.55 and the wrap angle is set to 300 for both rotor pairs. Figure 5 is a representation of these two retro tted pro les. 5 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 Figure 5. Retro tted rotor pro les with 5/6 lobe combination-[18] and [11] As elaborated earlier, the high pressure side of these pro les is identical except the absence of straight line in Gardner Denver pro le. A closer look at the leading edge tip of the gate rotors of Gardner Denver pro le shows that it would have a smaller blow hole area compared to Fu Sheng pro le on account of this small change. The low pressure sides of these pro les have Ellipse and a Hyperbola respectively. That makes them look slightly di erent on leading edge of the main rotor. The throughput area and the leakage areas for these two pro les are calculated and given in table 2. It is worth noting that both, FuSheng and Gardner Denver pro les can be generated through the N rotor form by choosing coecients and exponents in its general curve to resemble circles, ellipses, parabolas or hyperbolas. Table 2. Geometric pro le characteristics for retro tted Fu Sheng and Gardner Denver pro les Pro le Characteristic Fu Sheng Pro le Gardner Denver Pro le Throughput area (mm ) 8507 8621 Interlobe sealing area (mm ) 4.693 4.876 Blow hole area (mm ) 1.852 1.191 The Gardner Denver pro le has a slight advantage in throughput area as well as blow hole area on account of the ner details elaborated in previous section. If these pro les are subjected to a thermodynamic simulation for an oil injected screw compressor air application, the di erence in energy eciency of these machines is observed to be of the order of 0.3% to 0.5% only. The simulation was done in SCORG software within the envelope of operating conditions - tip speed 10 m/s to 40 m/s, suction pressure 1 bar absolute (bara) and discharge pressure 6.5 bara to 12.5 bara. The oil injection parameters and other peripheral details were set to practically reasonable values and same for both setups to avoid their in uence on evaluation. The observed order of di erence shows that the modern pro les which are more or less equivalent in application of good 6 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 design principles do not make a big di erence in terms of energy eciency. Even the gap of 0.3% could be minimized if the pro le with larger leakage area is allowed to compensate using other characteristics such as rotor size, sharper tips or rotor speeds, etc. If an N-pro le were designed for similar size, it wouldn't be any di erent because structurally both the pro les in gure 5 are equivalent to it. Either FuSheng or Gardner Denver pro les can be generated through the N rotor patent de nition by changing the curve A-B exponent n [10]. No more than 0.5% of di erence in energy eciency would be observed by only interchanging curves such as-parabola, ellipse and a hyperbola. 4. Conclusion & Future scope Most of the known features of a good rotor pro les are already incorporated in all the modern rotor pro les. Hence, an advantage by a mere change of curves or their placement in a pro le is practically not possible at least in modern pro les. Unlike the leap in energy eciency of screw compressors rst by introduction of asymmetric pro les in 1960's and then through the principle of rotor-rack generation in 1990's, modern pro les are unlikely to come by such leap through only change of pro le curves and shapes. Screw compressor manufacturers already in possession of a good modern pro le should expect improvements from any new pro les only in the order of 1% at maximum. More improvements are only going to come from either innovations in optimisation techniques or a scienti c disruption in the methods of pro le generation and manufacturing. One example of such an innovation which could improve rotor pro les if combined with good optimisation framework is application of topology inspired by path homotopy in pro ling [23]. Since all modern pro les are more or less equally ecient, the weight of designing more ecient screw compressors lies with the ability of pro le designer. Use of the state of the art optimisation algorithms, understanding of the machine application and underlying physics of compression is paramount if one wishes to ne tune any good pro le for the desired duty. Energy eciency of not only operation but also during manufacturing of screw compressors until the end of complete product life-cycle should be the focus for future of rotor pro ling. References [1] Lysholm A 1967 Screw rotor machine US Patent 3,314,598 [2] Schibbye L B 1969 Screw rotor machine and rotors therefor US Patent 3,423,017 [3] Stosic N, Smith I K and Kovacevic A 2003 Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 217 157{170 [4] Bammert K 1982 Intermeshing screw rotor machine with speci c thread pro le US Patent 4,350,480 [5] Bowman J L 1983 Helical screw rotor pro les US Patent 4,412,796 [6] Astberg A 1984 Screw rotor machine and rotor pro le therefor US Patent 4,435,139 [7] Hough D, Morris S J and Barber A D 1987 Screw rotor machines with speci c tooth pro les US Patent 4,636,156 [8] Menssen E 1977 Screw compressor with involute pro led teeth US Patent 4,028,026 [9] Rinder L 1987 Screw rotor pro le and method for generating US Patent 4,643,654 [10] Stosic N R 1997 Plural screw positive displacement machines US Patent 6,296,461 [11] Cavatorta P and Tomei U 2014 Screw compressor having male and female rotors with pro les generated by enveloping a rack pro le US Patent 8,702,409 [12] Stosic N and Hanjalic K 1997 Journal of Fluids Engineering 119 659{664 [13] Stosic N, Smith I and Kovacevic A 2005 Screw compressors: mathematical modelling and performance calculation (Springer Science & Business Media) 7 International Conference on Screw Machines 2022 IOP Publishing IOP Conf. Series: Materials Science and Engineering 1267 (2022) 012006 doi:10.1088/1757-899X/1267/1/012006 [14] Su S H and Tseng C H 2000 Journal of mechanical design 122 543{552 [15] Kauder K, Helpertz M, Reusch B and Berlik S 2002 VDI BERICHTE 1715 29{50 [16] Stosic N, Smith I K and Kovacevic A 2003 Applied Thermal Engineering 23 1177{1195 [17] Wu Y R and Fong Z H 2009 Mechanism and Machine Theory 44 66{82 [18] Lee H T, Fong Z H and Wu Y R 2006 Mechanism of the screw rotor US Patent App. 10/961,056 [19] Stosic N R 2017 Reduced noise screw machines US Patent 9,714,572 [20] Weih G 2019 Rotor pair for a compression block of a screw machine US Patent 10,400,769 [21] Stosic N, Smith I, Kovacevic A and Venumadhav K 2000 Retro t `n' rotors for ecient oil- ooded screw compressors Proc. of the 2000 International Compressor Engineering Conference at Purdue [22] Lee H T 1990 Screw-rotor machine with an ellipse as a part of its male rotor US Patent 4,890,992 [23] Patil S, Stosic N, Kovacevic A, Smith I and Asati N 2021 Application of path homotopy in twin screw compressor rotor pro le design IOP Conference Series: Materials Science and Engineering vol 1180 (IOP Publishing) p 012004 Acknowledgments Authors would like to thank Kirloskar Pneumatic Company Limited, India for nancially supporting this research.

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IOP Conference Series: Materials Science and Engineering – IOP Publishing

Published: Nov 1, 2022

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