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In the last decades, the growing mechatronic sector has promoted the development of more and more compact and efficient gearboxes. The margins of improvement are still big even if, sometimes, finding the optimal solutions is a trial and error procedure. For this reason, the development of dedicated tools for the optimization of the geometry and configuration of gearboxes can significantly increase the development effectiveness and help in reducing design costs. Moreover, having a more efficient solution could also reduce thermal problems during operation and increase the system reliability.
The so-called ‘thermal limit’, i.e. the maximum transmittable power without an overheating of the systems, is particularly critical for high power density and compact solutions. Those relies mainly on planetary, harmonic and cycloidal architectures. While many empirical or analytical prediction models can be found in literature for the prediction of the power losses associated with the gear meshing and the bearing, few reliable models are nowadays available for the losses associated with the interaction with the lubricant, i.e. hydraulic losses. Experimental and computational fluid dynamics studies on parallel axis as well as planetary gear sets have been presented in the past.
The goal of this research is the extension of the applicability range of those numerical approached to cycloidal kinematics for which no studies at all are available with respect to the hydraulic losses.
The main challenge in numerically simulate the lubricant splashing in a cycloidal reduced is related to the topological modification of the computational domain during operation. For this purpose, a specific mesh handling technique, based on a 2.5D mesh, capable to handle the variations of the geometry of the domain was developed in the OpenFOAM® environment. The capability to analytically control the mesh generation at each time step ensures a very high numerical stability and a very high computational efficiency of the solution.
Eventually, the approach was systematically applied to a real geometry and the results compared with those obtained for other gear architectures with comparable performances in terms of dimensions and reduction ratios.
CFD, cycloidal gear, efficiency, lubrication, multiphase, power losses
[1] Sensinger, J. W. & Lipsey, J. H., Cycloid vs. harmonic drives for use in high ratio, singlestage robotic transmissions. 2012 IEEE Int. Conf. Robot. Autom., pp. 4130–4135, 2012.
[2] Gorla, C., Davoli, P., Rosa, F., Longoni, C., Chiozzi, F. & Samarani, A., Theoreticaland experimental analysis of a cycloidal speed reducer. J. Mech. Des. Trans. ASME,130(11), pp. 1126041–1126048, 2008. https://doi.org/10.1115/1.2978342
[3] Blagojevic, M., Marjanovic, N., Djordjevic, Z., Stojanovic, B., Marjanovic, V., Vujanac,R. & Disic, A., Numerical and experimental analysis of the cycloid disc stress state.Tech. Gaz., . 21(2), pp. 337–382, 2014.
[4] H. B. -r. Niemann, G., Winter, H, Maschinenelemente. 2005.
[5] ISO, “6336.” 2006.
[6] Xia, Y., A new topology of CMG for high torque and low loss, 2016 Prog. Electromagn.Res. Symp. PIERS 2016 – Proc., 65(11–12), pp. 78–82, 2016.
[7] Concli, F., Low-loss gears precision planetary gearboxes: reduction of the load dependentpower losses and efficiency estimation through a hybrid analytical-numerical optimizationtool. Forsch. im Ingenieurwesen/Engineering Res., 2017.
[8] Anderson, N. E. & Loewenthal, S. H., Design of spur gears for improved efficiency. J.Mech. Des. Trans. ASME, 104(4), pp. 767–774, 1982.
[9] “www.SKF.com.”.
[10] “www.schaeffler.it.”.
[11] Daily, J. W. & Nece, R. E., Chamber dimension effects on induced flow and frictionalresistance of enclosed rotating disks. J. Fluids Eng. Trans. ASME, 82(1), pp. 217–230,1960. https://doi.org/10.1115/1.3662532
[12] Mann, R. W. & Marston, C. H., Friction drag on bladed disks in housings as a functionof reynolds number, axial and radial clearance, and blade aspect ratio and solidity. J.Fluids Eng. Trans. ASME, 83(4), pp. 719–723, 1961. https://doi.org/10.1115/1.3662308
[13] Ohlendorf, H., Verlustleistung und Erwärmung von Stirnrädern. Verlustleistung undErwärmung von Stirnrädern, 1958.
[14] Richter, W., Stirnradgetriebe, Zahnreibung, Verlustleistung und Erwärmung, 1964.
[15] Terekhov, A. S., Hydraulic Losses In Gearboxes With Oil Immersion. Russ Eng J,55(5), pp. 7–11, 1975.
[16] Walter, P. & Langenbeck, K., Anwendungegrenzen für die Tauchschmierung von Zahnradgetrieben,Plansch- und Quetschverluste bei Tauchschmierung, 1982.
[17] Walter, P., Untersuchung Zur Tauchschmierung Von Stirnrädern Bei UmfangsgeschwindigkeitenBis 60 M/S, 1982.
[18] Mauz, W., Hydraulische Verluste von Strinradgetrieben bei Umfansgsgeschwindigkeitenbis 60 m/s, Hydraul. Verluste von Stirnradgetrieben Bei UmfangsgeschwindigkeitenBis 60 M/s, 1987.
[19] Diab,Y., Ville, F., Velex, P. & Changenet, C., Windage losses in high speed gears-preliminaryexperimental and theoretical results. J. Mech. Des. Trans. ASME, 126(5), pp.903–908, 2004. https://doi.org/10.1115/1.1767815
[20] Höhn, B. R., Michaelis, K. & Otto, H. P., Influence on no-load gear losses. Ecotrib 2011Conf. Proc., 2, pp. 639–644, 2011.
[21] Marchesse, Y., Changenet, C., Ville, F. & Velex, P., Investigations on CFD simulationsfor predicting windage power losses in spur gears. J. Mech. Des. Trans. ASME, 133(2),2011. https://doi.org/10.1115/1.4003357
[22] Gorla, C., Concli, F., Stahl, K., Höhn, B. R., Michaelis, K., Schultheiß, H., & Stemplinger,J. P., Hydraulic losses of a gearbox: CFD analysis and experiments. TribologyInternational, 66, pp. 337–344, 2013. https://doi.org/10.1016/j.triboint.2013.06.005
[23] Stahl, K., Höhn, B. R., Michaelis, K., Schultheiß, H., Stemplinger, J. P., Gorla, C., &Concli, F, CFD Simulations of Splash Losses of a Gearbox. Advances in Trobology, 10,2012. https://doi.org/10.1155/2012/616923
[24] Concli, F., Gorla, C., Stahl, K., Höhn, B. R., Michaelis, K., Schultheiß, H., & Stemplinger,J. P., Load independent power losses of ordinary gears: Numerical and experimentalanalysis. In 5th World Tribology Congress WTC 2013, 2, pp. 1243–1246, 2013.https://doi.org/10.1016/j.triboint.2013.06.005
[25] Concli, F., Gorla, C., Della Torre, A. & Montenegro, G., Windage power losses of ordinarygears: Different CFD approaches aimed to the reduction of the computationaleffort. Lubricants, 2(4), pp. 162–176, 2014. https://doi.org/10.3390/lubricants2040162
[26] Concli, F., Gorla, C., Della Torre, A. & Montenegro, G., Churning power losses ofordinary gears: A new approach based on the internal fluid dynamics simulations. Lubr.Sci., 27(5), 2015. https://doi.org/10.1002/ls.1280
[27] Groenenboom, P. H. L., Mettichi, M. Z. & Gargouri, Y., Simulating Oil Flow for GearboxLubrication using Smoothed Particle Hydrodynamics. Proc. Int. Conf. Gears 2015,2015.
[28] Ji, Z., Stanic, M., Hartono, E. A. & Chernoray, V., Numerical simulations of oil flowinside a gearbox by Smoothed Particle Hydrodynamics (SPH) method, Tribol. Int., 127,pp. 47–58, 2018. https://doi.org/10.1016/j.triboint.2018.05.034
[29] Liu, Z., Shen, Y. & Rinderknecht, S., Theoretical and experimental investigation onpower loss of vehicle transmission synchronizers with spray lubrication. SAE Tech.Pap., 2019, pp. 215–226, 2019.
[30] Rahmatjan I., & Geni, M., SPH algorithm for proper meshing and coupling contact ofgears. Zhendong yu Chongji/Journal Vib. Shock, 34(12), pp. 65–69, 2015.
[31] Shi, Y., Li, S., Chen, H., He, M. & Shao, S., Improved SPH simulation of spilled oilcontained by flexible floating boom under wave–current coupling condition. J. FluidsStruct., 76, pp. 272–300, 2018. https://doi.org/10.1016/j.jfluidstructs.2017.09.014
[32] Imin, R. & Geni, M., Stress analysis of gear meshing impact based on SPH method,Math. Probl. Eng., 2014, 2014. https://doi.org/10.1155/2014/328216
[33] Zhigang, Y., Imin, R. & Geni, M., Study on the gear modeling in SPH analysis. Adv.Mater. Res., 33–37, pp. 773–778, 2008. https://doi.org/10.4028/www.scientific.net/amr.33-37.773
[34] Liu, H., Arfaoui, G., Stanic, M., Montigny, L., Jurkschat, T., Lohner, T., & Stahl, K.,Numerical modelling of oil distribution and churning gear power losses of gearboxes bysmoothed particle hydrodynamics. Proceedings of the Institution of Mechanical Engineers,Part J: Journal of Engineering Tribology, 233(1), pp. 74–86, 2019.
[35] Concli, F. & Gorla, C., Windage, churning and pocketing power losses of gears: differentmodeling approaches for different goals [Wirkungsgrad und Verluste von Zahnradgetrieben:Verschiedene Methoden für verschiedene Anwendungen]. Forsch. imIngenieurwesen/Engineering Res., 80(3–4), pp. 85–99, 2016. https://doi.org/10.1007/s10010-016-0206-9
[36] Concli, F., Maccioni, L. & Gorla, C., Lubrication Of Gearboxes: CFD Analysis Of ACycloidal Gear Set. In WIT Transactions on Engineering Sciences, 123, pp. 101–112,2019.
[37] Concli, F. & Gorla, C., Numerical modeling of the churning power losses in planetarygearboxes: An innovative partitioning-based meshing methodology for the applicationof a computational effort reduction strategy to complex gearbox configurations. LubricationScience, 29(7), pp. 455–474, 2017. https://doi.org/10.1002/ls.1380
[38] Concli, F. & Gorla, C., CFD simulation of power losses and lubricant flows in gearboxes.American Gear Manufacturers Association Fall Technical Meeting, 2017, 2017.
[39] Concli, F., Conrado, E. & Gorla, C., Analysis of power losses in an industrial planetaryspeed reducer: Measurements and computational fluid dynamics calculations.Proc. Inst. Mech. Eng. Part J J. Eng. Tribol., 228(1), 2014. https://doi.org/10.1177/1350650113496980
[40] Concli, F., Thermal and efficiency characterization of a low-backlash planetarygearbox: An integrated numerical-analytical prediction model and its experimentalvalidation. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol., 230(8), 2016. https://doi.org/10.1177/1350650115622363
[41] Drewniak, J., Kopec, J. Zawislak, S., Kinematical and efficiency analysis of planetarygear trains by means of various graph-based approaches. Mech. Mach. Sci., 34, pp.263–284, 2016.
[42] Yin, H. B., Li, S. L., Zhang, H., Zhao, X. Y. & Zhang, J., The power loss and efficiencyanalysis of a 3DOFs planetary gear box. Adv. Mater. Res., 834–836, pp. 1285–1289,2013. https://doi.org/10.4028/www.scientific.net/amr.834-836.1285
[43] Concli, F & Gorla, C., Computational and experimental analysis of the churning powerlosses in an industrial planetary speed reducer. WIT Transactions on Engineering Sciences,74, pp. 287–298, 2012.
[44] Concli, F., & Gorla, C., Influence of lubricant temperature, lubricant level and rotationalspeed on the churning power loss in an industrial planetary speed reducer: computationaland experimental study. Int. J. Comput. Methods Exp. Meas., 1(4), pp. 353–366,2013. https://doi.org/10.2495/cmem-v1-n4-353-366
[45] Concli, F. & Gorla, C., Numerical modeling of the power losses in geared transmissions:Windage, churning and cavitation simulations with a new integrated approachthat drastically reduces the computational effort. Tribol. Int., 103, pp. 58–68, 2016.https://doi.org/10.1016/j.triboint.2016.06.046
[46] Concli, F., Della Torre, A., Gorla, C. & Montenegro, G., A new integrated approach forthe prediction of the load independent power losses of gears: development of a meshhandlingalgorithm to reduce the CFD simulation time. Adv. Tribol., 2016, 2016.
[47] “www.hpfem.jku.at/netgen/.” .
[48] Schöberl, J., An advancing front 2D/3D-mesh generator based on abstract rules. Comput.Vis. Sci., 1(1), pp. 41–52, 1997. https://doi.org/10.1007/s007910050004
[49] Concli, F., Gorla, C., Rosa, F. & Conrado, E., Effect of the static pressure on the powerdissipation of gearboxes. Lubr. Sci., 31(8), pp. 347–355, 2019.
[50] Sensinger, J. W., Unified approach to cycloid drive profile, stress, and efficiency optimization.J. Mech. Des. Trans. ASME, 132(2), pp. 245031–245035, 2010.
[51] Concli, F. & Gorla, C., Oil squeezing power losses in gears: A CFD analysis. WITTransactions on Engineering Sciences, 74, pp. 37–48, 2012.
[52] Concli, F., & Gorla, C., Analysis of the oil squeezing power losses of a spur gear pairby mean of CFD simulations. ASME 2012 11th Biennial Conference on EngineeringSystems Design and Analysis, ESDA 2012, 2, pp. 177–184, 2012.
[53] Concli, F. & Gorla, C., A CFD analysis of the oil squeezing power losses of a gear pair.Int. J. Comput. Methods Exp. Meas., 2(2), pp. 157–167, 2014. https://doi.org/10.2495/cmem-v2-n2-157-167
[54] Rundo, M., Models for flow rate simulation in gear pumps: A review. Energies, 10(9),2017. https://doi.org/10.3390/en10091261
[55] Serov, A. F., Nazarov, A. D., Mamonov, V. N. & Terekhov, V. I., Experimental investigationof energy dissipation in the multi-cylinder Couette-Taylor system with independentlyrotating cylinders. Appl. Energy, 251, 2019.
[56] Fu, X., Liu, G., Tong, R., Ma, S. & Lim, T. C., A nonlinear six degrees of freedomdynamic model of planetary roller screw mechanism. Mech. Mach. Theory, 119, pp.22–36, 2018. https://doi.org/10.1016/j.mechmachtheory.2017.08.014
[57] Burka, E. S. & Ciania, W., An approximate method determining volumetric losses inradial clearance of a gear pump, 1987.