A Review of Gerotor Technology in Hydraulic Machines
Abstract
:1. Introduction
1.1. The Aim of this Article
- Provide a complete literature review of the last decade, while paying more attention articles published in the last five years by journals in the English language;
- Identify the state-of-the-art in gerotor pumps and orbital-motors;
- Grasp the current mainstream of this technology;
- Be a guide and a directory of gerotor technology for inexperienced engineers working with hydraulic machines;
- Promote this fascinating research field to young researchers and PhD students;
- Disseminate the works of the researchers and investigators employing gerotor technology around the world;
- Provide a scenario for future international collaboration and projects by bringing together the researchers working in the field;
- Collect recommendations that combine academia and industry expertise to make better use of these extensive studies;
- Be a catalogue of guidelines;
- Focus the attention of readers on this technology.
1.2. What the Article is Not
- A systematic review or a meta-analysis report. The article intends to follow the PRISMA checklist and its flow diagram within reasonable bounds;
- It is not a bibliometric analysis;
- It is not a survey, or review, of patents, a collection of commercial catalogues or a summary of technical reports;
- It is not a study of PhD or Masters theses;
- It is not an in-depth reading and a totally-in-detail study of all the references included in it.
1.3. The Limitations of this Article
- Being a document than comprises published, open and available articles, as well as papers and texts from the own authors’ collection, archived over the past years;
- Citing and quoting, when required, definitions, keywords, nomenclature and sentences of the researchers;
- Keeping the trochoidal-envelope denomination as the researchers originally named them. We are not able to standardize the published nomenclature in this article, and we do not want to increase the misunderstanding either;
- Not differentiating between articles. Out of context, figures and specific results tend to lose significance. Then, this article undertakes a thorough and objective the search of the figures to be selected and referenced from relevant articles to gain in readability. Nevertheless, we recommend going to the sources referenced. Moreover, we believe we are not eligible to distinguish between published works, since all of them are presumed to come from great effort, resources and time. This report expects not to be subject of bias.
1.4. The Structure of this Article
2. Analysis of this Literature Review
2.1. The Gear Set
2.2. The Background of this Analysis
2.2.1. Distribution of Articles
- Last five years, 2014–2018: 78 items—54%;
- Last decade, 2009–2018: 122 items—84%;
- Current 21st century, 2000–2018: 145 items—100%.
2.2.2. Keywords
3. Historical Background
4. Current Approaches to Gerotor Pumps
4.1. Geometric Approach
- Conventional profiles: Circular-tooth profiles (conventional-toothed gerotor);
- Unconventional profiles: Circular, polycircular and geometrical non-circular-tooth disposition (elliptic, involute, asymmetric) profiles (unconventional-toothed gerotor);
- High Efficiency Profiles: Tailored-tooth profiles (tailored-toothed gerotor).
4.1.1. Conventional Profiles
4.1.2. Unconventional Profiles
4.1.3. High Efficiency Profiles
4.1.4. Geometric Approach: Selected Contributions
- The work of Bonandrini, Mimmi and Rottenbacher [25] is selected as the starting point for a novel engineer in conventional profiles based on the accurate description, the synthetic equations and the geometry defined by the choice of four non-dimensional parameters. A natural step forward is the work of Hsieh [31] where the influence of geometric configuration in conjunction with the performance characteristics (kinematic, sealing and stress) leads to the flow rate and the volumetric efficiency evaluation.
4.2. Performance Approach
4.2.1. Energy, Flow, Friction and Stress Index Evaluation
4.2.2. Manufacturing, Clearances and Porting
4.2.3. Materials
4.2.4. Optimization Techniques
4.2.5. Software Techniques
4.2.6. Visualization Techniques
4.2.7. Variable Flow Development
4.2.8. Performance Approach: Selected Contributions
- Jacazio and De Martin presented a comparison of the performance indexes of circular, elliptic and asymmetric tooth profiles. Reference [56] is a significant summary of profile characterization;
- The knowledge of the influence of the clearance design and porting in the leakage rates is mandatory in gerotor pumps, and the work of Hsieh [64] is a key contribution. If the manufacturing of a new-born gerotor pump is the objective, the work of Gamez-Montero et al. [72] will guide the designer by following a catalogue of best practice rules;
- Without a doubt, the works of Stryczek and the colleagues are fundamental in the learning of fluid power elements with non-metallic materials, and it is recommended to start with Stryczek et al. [80];
- Regarding optimization techniques, Robinson and Vacca [86] presented the most comprehensive work with circular-toothed gerotor, being the scatter matrix of feasible designs an extraordinary contribution;
- The software techniques contribute to the design of a gerotor pump with different strategies, and it is difficult and inadvisable to highlight a specific one. The researcher has to approach each of them based on its characteristics (open access, platform, features, user-friendliness, etc.);
- If the attention of the research is the visualization of the cavitation phenomenon, the selected work is Antoniak and Stryczek [103]. If the attention of the research is focused on the measurement of the instantaneous flow of a gerotor pump without altering its behavior, the experimental study in Garcia-Vilchez et al. [100] is worth to be read;
4.3. Modelling and Numerical Simulation
4.3.1. Analytical Methods
4.3.2. Integrated Methods
4.3.3. CAD Methods
4.3.4. Fluid-dynamic Methods
4.3.5. Modelling and Numerical Simulation: Selected Contributions
- Since integrated methods are widely used, the works presented are complex. Nevertheless, the selected contributions to the integrated approaches are Altare and Rundo [116] (the most comprehensive integrated method regarding the analysis of three commercial tools) and Pellegri et al. [118] (the best integrated method regarding the comparison with experimental work). If a modelling of the cavitation phenomenon is pursued, the works of Buono et al. [122] and Shah et al. [124] have to be studied. Finally, the work of Pellegri and Vacca [121] is the successful contribution of considering the actual position of contact points between gears, as a function of the real geometric tolerances. The experimental validation with a prototype gerotor pump probably makes this work the best contribution to the field in the last five years;
- Up to date, the work of Gherardini et al. [131] uses innovative CAD-based methods, since the geometrical data of three types of positive displacement machines, including gerotor pump, are automatically extrapolated to fluid dynamic analyses;
- With regard to the numerical simulation by using a commercial CFD software, the paper of Altare and Rundo [140] is the most comprehensive work, because it presents the compendium of main geometric characteristics influencing the volumetric performance of a gerotor pump. By using an open source CFD tool, the work of Castilla et al. [141] is the cutting-edge work by numerically simulating contact points between rotors in conjunction with an innovative deforming mesh strategy in gerotor pumps.
5. Hydraulic Orbital Motors
6. New Scales and Concepts in Gerotor Technology
7. Discussion
8. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Decade | Year | Contribution | Ref. |
---|---|---|---|
1960–1969 | |||
1968 | Historical Background | Ansdale and Lockley [5] | |
1970–1979 | |||
1974 | Historical Background | Colbourne [6] | |
1976 | Historical Background | Colbourne [7] | |
Robinson and Lyon [8] | |||
1980–1989 | |||
1988 | Historical Background | Maiti and Sinha [12] | |
1990–1999 | |||
1990 | Historical Background | Maiti and Sinha [13] | |
1992 | Historical Background | Beard et al. [9] | |
1993 | Historical Background | Maiti [14] | |
1994 | Historical Background | Shung and Pennock [10] | |
1996 | Historical Background | Stryczek [11] | |
Dasgupta et al. [15] | |||
1999 | Historical Background | Fabiani et al. [17] | |
New Scales and Concepts | Harada et al. [156] | ||
2000–2009 | |||
2000 | Historical Background | Mimmi and Pennacchi [16] | |
Manufacturing, Clearances and Porting | Mancò et al. [61] | ||
2001 | Historical Background | Vecchiato et al. [19] | |
2002 | Historical Background | Mancò et al. [18] | |
Demenego et al. [20]. | |||
Ivantysyn and Ivantysynova [24] | |||
New Scales and Concepts | Harada et al. [157] | ||
Mancò et al. [158] | |||
2003 | Historical Background | Paffoni [21] | |
New Scales and Concepts | Huber and Aktaa [160] | ||
2004 | Historical Background | Paffoni et al. [22] | |
Litvin [23] | |||
Variable Flow Development | Mancò et al. [106] | ||
2006 | Manufacturing, Clearances and Porting | Kim et al. [62] | |
Visualization Techniques | Itoh et al. [97] | ||
New Scales and Concepts | Maruo and Inoue [162] | ||
2007 | Conventional Profiles | Hwang and Hsieh [28] | |
Hsieh and Hwang [29] | |||
Manufacturing, Clearances and Porting | Chen et al. [67] | ||
Software Techniques | Chang et al. [89] | ||
2008 | High Efficiency Profiles | Sasaki et al. [41] | |
Energy, Flow, Friction and Stress Indexes Evaluation | Kwon et al. [50] | ||
Variable Flow Development | Toyoda et al. [105] | ||
2009 | Conventional Profiles | Bonandrini et al. [25] | |
Hsieh [31] | |||
2009 | Unconventional Profiles | Tong et al. [34] | |
Yan et al. [35] | |||
Software Techniques | Gamez-Montero et al. [91] | ||
Gamez-Montero et al. [92] | |||
Fluid-dynamic Methods | Elayaraja et al. [132] | ||
Hydraulic Orbital Motors | Michael et al. [150] | ||
2010–2014* | |||
2010 | Conventional Profiles | Known et al. [30] | |
Bonandrini et al. [26] | |||
Energy, Flow, Friction and Stress Indexes Evaluation | Rundo [44] | ||
Ivanović et al. [51] | |||
Manufacturing, Clearances and Porting | Hsieh [63] | ||
Materials | Biernacki and Stryczek [73] | ||
Visualization Techniques | Antoniak [98] | ||
Fluid-dynamic Methods | Suresh Kumar and Manonmani [133] | ||
2011 | Unconventional Profiles | Yang et al. [36] | |
Jung et al. [37] | |||
Energy, Flow, Friction and Stress Indexes Evaluation | Meira et al. [45] | ||
Inaguma [46] | |||
Karamooz Ravari [55] | |||
Optimization Techniques | Kwon et al. [82] | ||
Software Techniques | Schweiger et al. [94] | ||
CAD Methods | Kim et al. [127] | ||
Fluid-dynamic Methods | Ruvalcaba and Hu [134] | ||
Hydraulic Orbital Motors | Garcia [144] | ||
2012 | Conventional Profiles | Bonandrini et al. [27] | |
Hsieh [32] | |||
Unconventional Profiles | Choi et al. [38] | ||
High Efficiency Profiles | Yoshida et al. [42] | ||
Energy, Flow, Friction and Stress Indexes Evaluation | Inaguma [47] | ||
Optimization Techniques | Karamooz Ravari et al. [83] | ||
Software Techniques | Gamez-Montero et al. [93] | ||
Analytical Methods | Ivanović et al. [110] | ||
CAD Methods | Carconi et al. [128] | ||
Fluid-dynamic Methods | Gamez-Montero et al. [135] | ||
Hydraulic Orbital Motors | Ding et al. [145] | ||
2013 | Energy, Flow, Friction and Stress Indexes Evaluation | Inaguma [48] | |
Manufacturing, Clearances and Porting | Jamadar et al. [65] | ||
Analytical Methods | Ivanović et al. [111] | ||
Ivanović et al. [112] | |||
Fluid-dynamic Methods | Frosina et al. [136] | ||
Hydraulic Orbital Motors | Nag and Maiti [146] | ||
New Scales and Concepts | O’Sea et al. [165] | ||
2014 | Conventional Profiles | Liu et al. [33] | |
Materials | Biernacki [74] | ||
Stryczek et al. [75] | |||
Stryczek et al. [77] | |||
Krawczyk and Stryczek [78] | |||
CAD Methods | Jeong et al. [126] | ||
Prakash and Manjula [129] | |||
Fluid-dynamic Methods | Frosina et al. [137] | ||
New Scales and Concepts | Leester-Schädel et al. [161] | ||
Malvasi et al. [163] | |||
Heisel and Mishev [164] | |||
2015–2019* | |||
2015 | Unconventional Profiles | Bae and Kim [39] | |
Manufacturing, Clearances and Porting | Hsieh [64] | ||
Materials | Biernacki [76] | ||
Software Techniques | Klopsch et al. [95] | ||
Visualization Techniques | Stryczek et al. [99] | ||
Garcia-Vilchez et al. [100] | |||
Variable Flow Development | Avery and Johnston [109] | ||
Integrated Methods | Frosina et al. [114] | ||
Hussain et al. [115] | |||
CAD Methods | Moetakef and Zouani [130] | ||
Fluid-dynamic Methods | Hsieh [138] | ||
Sang et al. [139] | |||
Hydraulic Orbital Motors | Maiti et al. [147] | ||
Furustig et al. [149] | |||
2016 | Unconventional Profiles | Hao et al. [40] | |
High Efficiency Profiles | Arinaga et al. [43] | ||
Energy, Flow, Friction and Stress Indexes Evaluation | Kamal et al. [49] | ||
Ivanović [52] | |||
Ivanović et al. [53] | |||
Ivanović et al. [54] | |||
Jacazio et al. [56] | |||
Kwak et al. [57] | |||
O’Shea [59] | |||
Manufacturing, Clearances and Porting | Harrison et al. [66] | ||
Kwak et al. [70] | |||
Materials | Krawczyk and Stryczek [79] | ||
Software Techniques | Bae et al. [90] | ||
Visualization Techniques | Sahoo et al. [102] | ||
Integrated Methods | Pellegri et al. [118] | ||
Pellegri et al. [119] | |||
Buono et al. [122] | |||
CAD Methods | Gherardini et al. [131] | ||
Fluid-dynamic Methods | Altare and Rundo [140] | ||
Gamez-Montero et al. [142] | |||
Hydraulic Orbital Motors | Bigliardi et al. [148] | ||
Furustig et al. [151] | |||
2017 | Energy, Flow, Friction and Stress Indexes Evaluation | Siano et al. [60] | |
Manufacturing, Clearances and Porting | Kwak et al. [71] | ||
Materials | Stryczek et al. [80] | ||
Mancini et at. [81] | |||
Optimization Techniques | Ivanović et al. [84] | ||
Ivanović et al. [85] | |||
Software Techniques | Zhang et al. [96] | ||
Visualization Techniques | Raush et al. [101] | ||
Variable Flow Development | Yamamoto et al. [107] | ||
Integrated Methods | Altare and Rundo [116] | ||
Fangwei et al. [117] | |||
Pellegri and Vacca [120] | |||
Pellegri and Vacca [121] | |||
Buono et al. [123] | |||
Shah et al. [124] | |||
Fluid-dynamic Methods | Castilla et al. [141] | ||
New Scales and Concepts | Gamez-Montero et al. [159] | ||
Gamez-Montero et al. [166] | |||
2018 | Energy, Flow, Friction and Stress Indexes Evaluation | Lee et al. [58] | |
Manufacturing, Clearances and Porting | Ham et al. [68] | ||
Sung et al. [69] | |||
Gamez-Montero et al. [72] | |||
Optimization Techniques | Robinson and Vacca [86] | ||
Visualization Techniques | Antoniak and Stryczek [103] | ||
Antoniak et al. [104] | |||
Variable Flow Development | Nishida et al. [108] | ||
Analytical Methods | Ivanović et al. [113] | ||
Fluid-dynamic Methods | Gamez-Montero et al. [143] | ||
Hydraulic Orbital Motors | Bates et al. [152] | ||
Strmčnik and Majdič [153,154] | |||
Zardin et al. [155] | |||
2019 | Optimization Techniques | Robinson and Vacca [87] | |
De Martin et al. [88] | |||
Integrated Methods | Singh et al. [125] |
Approach | Contribution | Year | Ref. |
---|---|---|---|
Historical | |||
Historical Background | 1968 | Ansdale and Lockley [5] | |
1974 | Colbourne [6] | ||
1976 | Colbourne [7] | ||
Robinson and Lyon [8] | |||
1988 | Maiti and Sinha [12] | ||
1990 | Maiti and Sinha [13] | ||
1992 | Beard et al. [9] | ||
1993 | Maiti [14] | ||
1994 | Shung and Pennock [10] | ||
1996 | Stryczek [11] | ||
Dasgupta et al. [15] | |||
1999 | Fabiani et al. [17] | ||
2000 | Mimmi and Pennacchi [16] | ||
2001 | Vecchiato et al. [19] | ||
2002 | Mancò et al. [18] | ||
Demenego et al. [20]. | |||
Ivantysyn and Ivantysynova [24] | |||
2003 | Paffoni [21] | ||
2004 | Paffoni et al. [22] | ||
Litvin [23] | |||
Geometric | |||
Conventional Profiles | 2007 | Hwang and Hsieh [28] | |
Hsieh and Hwang [29] | |||
2009 | Bonandrini et al. [25] | ||
Hsieh [31] | |||
2010 | Known et al. [30] | ||
Bonandrini et al. [26] | |||
2012 | Bonandrini et al. [27] | ||
Hsieh [32] | |||
2015 | Liu et al. [33] | ||
Unconventional Profiles | 2009 | Tong et al. [34] | |
Yan et al. [35] | |||
2011 | Yang et al. [36] | ||
Jung et al. [37] | |||
2012 | Choi et al. [38] | ||
2015 | Bae and Kim [39] | ||
2016 | Hao et al. [40] | ||
High Efficiency Profiles | 2008 | Sasaki et al. [41] | |
2012 | Yoshida et al. [42] | ||
2016 | Arinaga et al. [43] | ||
Performance | |||
Energy, Flow, Friction and Stress Indexes Evaluation | 2008 | Kwon et al. [50] | |
2010 | Rundo [44] | ||
Ivanović et al. [51] | |||
2011 | Meira et al. [45] | ||
Inaguma [46] | |||
Karamooz Ravari [55] | |||
2012 | Inaguma [47] | ||
2013 | Inaguma [48] | ||
2016 | Kamal et al. [49] | ||
Ivanović [52] | |||
Ivanović et al. [53] | |||
Ivanović et al. [54] | |||
Jacazio et al. [56] | |||
Kwak et al. [57] | |||
O’Shea [59] | |||
2017 | Siano et al. [60] | ||
2018 | Lee et al. [58] | ||
Manufacturing, Clearances and Porting | 2000 | Mancò et al. [61] | |
2006 | Kim et al. [62] | ||
2007 | Chen et al. [67] | ||
2010 | Hsieh [63] | ||
2013 | Jamadar et al. [65] | ||
2015 | Hsieh [64] | ||
2016 | Harrison et al. [66] | ||
Kwak et al. [70] | |||
2017 | Kwak et al. [71] | ||
2018 | Ham et al. [68] | ||
Sung et al. [69] | |||
Gamez-Montero et al. [72] | |||
Materials | 2010 | Biernacki and Stryczek [73] | |
2014 | Biernacki [74] | ||
Stryczek et al. [75] | |||
Stryczek et al. [77] | |||
Krawczyk and Stryczek [78] | |||
2015 | Biernacki [76] | ||
2016 | Krawczyk and Stryczek [79] | ||
2017 | Stryczek et al. [80] | ||
Mancini et at. [81] | |||
Optimization Techniques | 2011 | Kwon et al. [82] | |
2012 | Karamooz Ravari et al. [83] | ||
2017 | Ivanović et al. [84,85] | ||
2018 | Robinson and Vacca [86] | ||
2019 | Robinson and Vacca [87] | ||
De Martin et al. [88] | |||
Software Techniques | 2007 | Chang et al. [89] | |
2009 | Gamez-Montero et al. [91] | ||
Gamez-Montero et al. [92] | |||
2011 | Schweiger et al. [94] | ||
2012 | Gamez-Montero et al. [93] | ||
2015 | Klopsch et al. [95] | ||
2016 | Bae et al. [90] | ||
2017 | Zhang et al. [96] | ||
Visualization Techniques | 2006 | Itoh et al. [97] | |
2010 | Antoniak [98] | ||
2015 | Stryczek et al. [99] | ||
Garcia-Vilchez et al. [100] | |||
2017 | Raush et al. [101] | ||
2016 | Sahoo et al. [102] | ||
2018 | Antoniak and Stryczek [103] | ||
Antoniak et al. [104] | |||
Variable Flow Development | 2004 | Mancò et al. [106] | |
2008 | Toyoda et al. [105] | ||
2015 | Avery and Johnston [109] | ||
2017 | Yamamoto et al. [107] | ||
2018 | Nishida et al. [108] | ||
Modelling and Numerical Simulation | |||
Analytical Methods | 2012 | Ivanović et al. [110] | |
2013 | Ivanović et al. [111,112] | ||
2018 | Ivanović et al. [113] | ||
Integrated Methods | 2015 | Frosina et al. [114] | |
Hussain et al. [115] | |||
2016 | Pellegri et al. [118,119] | ||
Buono et al. [122] | |||
2017 | Altare and Rundo [116] | ||
Fangwei et al. [117] | |||
Pellegri and Vacca [120,121] | |||
Buono et al. [123] | |||
Shah et al. [124] | |||
2019 | Singh et al. [125] | ||
CAD Methods | 2011 | Kim et al. [127] | |
2012 | Carconi et al. [128] | ||
2014 | Jeong et al. [126] | ||
Prakash and Manjula [129] | |||
2015 | Moetakef and Zouani [130] | ||
2016 | Gherardini et al. [131] | ||
Fluid-dynamic Methods | 2009 | Elayaraja et al. [132] | |
2010 | Suresh Kumar and Manonmani [133] | ||
2011 | Ruvalcaba and Hu [134] | ||
2012 | Gamez-Montero et al. [135] | ||
2013 | Frosina et al. [136] | ||
2014 | Frosina et al. [137] | ||
2015 | Hsieh [138] | ||
Sang et al. [139] | |||
2016 | Altare and Rundo [140] | ||
Gamez-Montero et al. [142] | |||
2017 | Castilla et al. [141] | ||
2018 | Gamez-Montero et al. [143] | ||
Hydraulic Orbital Motors | Hydraulic Orbital Motors | 2009 | Michael et al. [150] |
2011 | Garcia [144] | ||
2012 | Ding et al. [145] | ||
2013 | Nag and Maiti [146] | ||
2015 | Maiti et al. [147] | ||
Furustig et al. [149] | |||
2016 | Bigliardi et al. [148] | ||
Furustig et al. [151] | |||
2018 | Bates et al. [152] | ||
2018 | Strmčnik and Majdič [153,154] | ||
Zardin et al. [155] | |||
New Scales and Concepts | New Scales and Concepts | 1999 | Harada et al. [156] |
2002 | Harada et al. [157] | ||
Mancò et al. [158] | |||
2003 | Huber and Aktaa [160] | ||
2006 | Maruo and Inoue [162] | ||
2013 | O’Sea et al. [165] | ||
2014 | Leester-Schädel et al. [161] | ||
2014 | Malvasi et al. [163] | ||
Heisel and Mishev [164] | |||
2017 | Gamez-Montero et al. [159] | ||
Gamez-Montero et al. [166] |
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Keywords (1 to 10) | Times | Keywords (11 to 20) | Times | Keywords (21 to 30) | Times |
---|---|---|---|---|---|
pump | 83 | power | 13 | teeth | 10 |
gerotor | 60 | pressure | 13 | profile | 9 |
gear | 37 | cycloidal | 12 | analysis | 9 |
flow | 28 | clearance | 12 | internal | 8 |
trochoidal | 19 | port | 11 | wear | 7 |
hydraulic | 17 | oil | 10 | system | 7 |
design | 17 | motor | 10 | rotary | 6 |
CFD | 17 | simulation | 10 | lubrication | 6 |
contact | 15 | efficiency | 10 | leakage | 6 |
stress | 14 | method | 10 | modelling | 6 |
Manufacturing | Part | Tolerance |
---|---|---|
Radial clearance | Inner to outer profile | 25–80 × 10−6 m |
External gear to housing | 25–80 × 10−6 m | |
Side clearance | Internal gear | 2–4 × 10−6 m |
External gear | 2–4 × 10−6 m | |
Flatness | Housing | 25 × 10−6 m |
Cover | 25 × 10−6 m | |
Internal gear | 1 × 10−6 m | |
External gear | 1 × 10−6 m | |
Surface finishing | Housing | 60 × 10−6 m |
Cover | 15–20 × 10−6 m | |
Internal gear | 15–20 × 10−6 m | |
External gear | 15–20 × 10−6 m |
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Gamez-Montero, P.J.; Codina, E.; Castilla, R. A Review of Gerotor Technology in Hydraulic Machines. Energies 2019, 12, 2423. https://doi.org/10.3390/en12122423
Gamez-Montero PJ, Codina E, Castilla R. A Review of Gerotor Technology in Hydraulic Machines. Energies. 2019; 12(12):2423. https://doi.org/10.3390/en12122423
Chicago/Turabian StyleGamez-Montero, Pedro Javier, Esteve Codina, and Robert Castilla. 2019. "A Review of Gerotor Technology in Hydraulic Machines" Energies 12, no. 12: 2423. https://doi.org/10.3390/en12122423