Technical Brief: Technical Briefs

Influence of the Operating Conditions of Two-Degree-of-Freedom Planetary Gear Trains on Tooth Friction Losses

[+] Author and Article Information
Essam Lauibi Esmail

Department of Mechanical Engineering,
University of Al-Qadisiyah,
Al Diwaniyah 0964, Iraq
e-mail: essam.esmail@qu.edu.iq

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 16, 2017; final manuscript received February 16, 2018; published online March 23, 2018. Assoc. Editor: Hai Xu.

J. Mech. Des 140(5), 054501 (Mar 23, 2018) (6 pages) Paper No: MD-17-1824; doi: 10.1115/1.4039452 History: Received December 16, 2017; Revised February 16, 2018

In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application.

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Kahraman, A. , Ligata, H. , Kienzle, K. , and Zini, D. M. , 2004, “A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains,” ASME J. Mech. Des., 126(6), pp. 1071–1081. [CrossRef]
White, G. , 1994, “Epicyclic Gears From Early Hoists and Winches—II,” Mech. Mach. Theory, 29(2), pp. 309–325. [CrossRef]
White, G. , 2003, “Derivation of High-Efficiency Two-Stage Epicyclic Gears,” Mech. Mach. Theory, 38(2), pp. 149–159. [CrossRef]
Park, J. J. , Kim, B. S. , and Song, J. B. , 2007, “Double Actuator Unit With Planetary Gear Train for a Safe Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 1146–1151.
Rabindran, D. , and Tesar, D. , 2008, “Power Flow Analysis in Parallel Force/Velocity Actuators (PFVA): Theory and Simulations,” ASME Paper No. DETC2008-49164.
Chen, L. , Yin, C. , Zhu, F. , and Tang, L. , 2010, “Scheme Design and Optimal Selection for Hybrid Electric Vehicle Planetary Gear Mechanism. Zhongguo Jixie Gongcheng/China,” China Mech. Eng., 21(1), pp. 104–109.
Sheu, K. B. , 2007, “Analysis and Evaluation of Hybrid Scooter Transmission Systems,” Appl. Energy, 84(12), pp. 1289–1304. [CrossRef]
Kim, J. , Kim, N. , Hwang, S. , Hori, Y. , and Kim, H. , 2009, “Motor Control of Input-Split Hybrid Electric Vehicles,” Int. J. Automot. Technol., 10(6), pp. 733–742. [CrossRef]
Kim, J. , Kang, J. , Choi, W. , Park, J. , Byun, S. , Jun, Y. , Kim, J. , Ko, J. , and Kim, H. , 2010, “Control Algorithm for a Power Split Type Hybrid Electric Vehicle,” International Symposium on Power Electronics, Electrical Devices, Automation and Motion (SPEEDAM), Pisa, Italy, June 14–16, pp. 1575–1580.
Barman, I. , and Flugrad, D. R. , 1992, “Design of an Epicyclic Transmission for Speed Control of a Turbine-Generator System,” Flexible Mechanisms, Dynamics, and Analysis, Vol. 47, American Society of Mechanical Engineers, New York, pp. 497–504.
Zhao, X. , and Maiber, P. , 2003, “A Novel Power Splitting Drive Train for Variable Speed Wind Power Generators,” Renewable Energy, 28(13), pp. 2001–2011. [CrossRef]
Esmail, E. L. , 2016, “Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains,” ASME J. Mech. Des., 138(8), p. 083301. [CrossRef]
Macmillan, R. H. , 1949, “Epicyclic Gear Efficiencies,” The Engineer, Dec. 23, pp. 727–728.
Chen, C. , and Angeles, J. , 2007, “Virtual-Power Flow and Mechanical Gear-Mesh Tooth Friction Losses of Epicyclic Gear Trains,” ASME J. Mech. Des., 129(1), pp. 107–113. [CrossRef]
Chen, C. , and Liang, T. T. , 2011, “Theoretic Study of Efficiency of Two-DOFs of Epicyclic Gear Transmission Via Virtual Power,” ASME J. Mech. Des., 133(3), p. 031007. [CrossRef]
Davies, K. , Chen, C. , and Chen, B. K. , 2012, “Complete Efficiency Analysis of Epicyclic Gear Train With Two Degrees of Freedom,” ASME J. Mech. Des., 134(7), p. 071006. [CrossRef]
Freudenstein, F. , and Yang, A. , 1972, “Kinematics, and Statics of Coupled Spur-Gear Trains,” Mech. Mach. Theory, 7(2), pp. 263–275. [CrossRef]
Esmail, E. L. , 2013, “Nomographs and Feasibility Graphs for Enumeration of Ravigneaux-Type Automatic Transmissions,” Adv. Mech. Eng., 2013, p. 120324. [CrossRef]
Macmillan, R. H. , and Davies, P. B. , 1965, “Analytical Study of Systems for Bifurcated Power Transmission,” J. Mech. Eng. Sci., 7(1), pp. 40–47. [CrossRef]
Laughlin, H. , Holowenko, A. , and Hall, A. , 1956, “How to Determine Circulating Power in Controlled Epicyclic Gear Systems,” Mach. Des., 28(6), pp. 132–136.
Pennestrì, E. , and Freudenstein, F. , 1993, “The Mechanical Efficiency of Epicyclic Gear Trains,” ASME J. Mech. Des., 115(3), pp. 645–651. [CrossRef]
Sanger, D. , 1972, “The Determination of Power Flow in Multiple-Path Transmission Systems,” Mech. Mach. Theory, 7(1), pp. 103–109. [CrossRef]
Esmail, E. L. , and Hassan, S. S. , 2010, “An Approach to Power-Flow and Static Force Analysis in Multi-Input Multi-Output Epicyclic-Type Transmission Trains,” ASME J. Mech. Des., 132(1), p. 011009. [CrossRef]
Macmillan, R. H. , 1961, “Power Flow and Loss in Differential Mechanisms,” J. Mech. Eng. Sci., 3(1), pp. 37–41. [CrossRef]
Radzimovsky, E. I. , 1956, “A Simplified Approach for Determining Tooth Friction Losses and Efficiency of Epicyclic Gear Drives,” Mach. Des., 9, pp. 101–110.
Radzimovsky, E. I. , 1959, “How to Find Efficiency, Speed and Tooth Friction Losses in Epicyclic Gear Drives,” Mach. Des., 11, pp. 144–153.
Yu, D. , and Beachley, N. , 1985, “On the Mechanical Efficiency of Differential Gearing,” ASME J. Mech., Transm., Autom. Des., 107(1), pp. 61–67. [CrossRef]
del Castillo, J. M. , 2002, “The Analytical Expression of the Efficiency of Epicyclic Gear Trains,” Mech. Mach. Theory, 37(2), pp. 197–214. [CrossRef]
Nelson, C. A. , and Cipra, R. J. , 2005, “Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses,” ASME J. Mech. Des., 127(2), pp. 278–286. [CrossRef]
Mantriota, G. , and Pennestrì, E. , 2003, “Theoretical and Experimental Efficiency Analysis of Multi-Degrees-of-Freedom Epicyclic Gear Trains,” Multibody Syst. Dyn., 9(4), pp. 389–408. [CrossRef]
Hsieh, H. I. , and Tsai, L. W. , 1998, “The Selection of a Most Efficient Clutching Sequences Associated With Epicyclic-Type Automatic Transmission,” ASME J. Mech. Des., 120(4), pp. 514–519. [CrossRef]
Duan, Q. H. , and Yang, S. R. , 2002, “A Study on Power Flow and Meshing Efficiency of 3K Type Epicyclic Gear Train,” Mech. Sci. Technol., 21(3), pp. 360–362.
Hsieh, L.-C. , and Chen, T.-H. , 2011, “The Design and Efficiency Analysis of Epicyclic Gear Reducer,” J. Adv. Mater. Res., 317–319, pp. 2226–2229. [CrossRef]
Hsieh, L. C. , and Chen, T. H. , 2012, “On the Meshing Efficiency of 3K-Type Epicyclic Simple Gear Reducer,” J. Adv. Sci. Lett., 12(1), pp. 34–39. [CrossRef]
Hsieh, L. C. , and Tang, H.-C. , 2013, “On the Meshing Efficiency of 2K-2H Type Epicyclic Gear Reducer,” Adv. Mech. Eng., 2013, p. 686187. [CrossRef]
Ayats, J. G. , Calvet, J. V. , Canela, J. M. , Diego-Ayala, U. , and Artes, F. F. , 2011, “Power Transmitted Through a Particular Branch in Mechanisms Comprising Epicyclic Gear Trains and Other Fixed or Variable Transmissions,” Mech. Mach. Theory, 46(11), pp. 1744–1754.
Tuplin, W. A. , 1957, “Designing Compound Epicyclic Gear Trains for Maximum Speed at High-Velocity Ratios,” Mach. Des., pp. 100–104.
Martin, K. , 1981, “The Efficiency of Involute Spur Gears,” ASME J. Mech. Des., 103(1), pp. 160–169. [CrossRef]
Anderson, N. , and Loewenthal, S. , 1982, “Design of Spur Gears for Improved Efficiency,” ASME J. Mech. Des., 104(4), pp. 767–774. [CrossRef]
Anderson, N. , and Loewenthal, S. , 1983, “Comparison of Spur Gear Efficiency Prediction Methods,” Army Research and Technology Laboratory, Cleveland, OH, Technical Report No. NASA-CP-2210. https://ntrs.nasa.gov/search.jsp?R=19830011870
Petry-Johnson, T. T. , Kahraman, A. , Anderson, N. E. , and Chase, D. R. , 2008, “An Experimental Investigation of Spur Gear Efficiency,” ASME J. Mech. Des., 130(6), p. 062601. [CrossRef]
Vaidyanathan, L. S. , Harianto, A. , and Kahraman, J. , 2009, “Influence of Design Parameters on Mechanical Tooth Friction Losses of Helical Gear Pairs,” J. Adv. Mech. Des., Syst., Manuf., 3(2), pp. 146–158. [CrossRef]
Chiu, Y. P. , 1975, “Approximate Calculation of Tooth Friction Loss in Involute Gears,” Joint ASLE-ASME Lubrication Conference, Fiami, FL, Oct. 21–23, Paper No. 75-PTG-2.
Dorey, R. E. , and McCandlish, D. , 1986, “The Modelling of Losses in Mechanical Gear Trains for the Computer Simulation of Heavy Vehicle Transmission Systems,” International Conference on Integrated Engine Transmission Systems, Bath, UK, July 8–9, pp. 69–82.
Esmail, E. L. , 2012, “Hybrid Transmission for Mobile Robot,” ASME J. Mech. Des., 134(2), p. 021001. [CrossRef]
Maggiore, A. , 1971, “The Efficiency of Epicyclic Two DOF Gear Trains,” Atti I Congresso Nazionale di Meccanica Teorica ed Applicata, Udine, pp. 65–85.
Pennestri, E. , Mariti, L. , Valentini, P. P. , and Mucino, V. H. , 2012, “Efficiency Evaluation of Gearboxes for Parallel Hybrid Vehicles: Theory and Applications,” Mech. Mach. Theory, 49, pp. 157–176. [CrossRef]
Monastero, R. , 1976, “The Efficiency of Series Connected Epicyclic Gear Trains,” Rivista Associazione Tecnica dell'Automobile (ATA), Torino, Italy (in Italian).
Bottiglione, F. , and Mantriota, G. , 2008, “MG-IVT: An Infinitely Variable Transmission With Optimal Power Flows,” ASME J. Mech. Des., 130(11), p. 112603. [CrossRef]
Pennestri, E. , and Freudenstein, F. , 1993, “A Systematic Approach to Power-Flow and Static-Force Analysis in Epicyclic Gear-Trains,” ASME J. Mech. Des., 115(3), pp. 639–644. [CrossRef]
Pennestrì, E. , and Valentini, P. P. , 2003, “A Review of Formulas for the Mechanical Efficiency Analysis of Two Degrees-of-Freedom Epicyclic Gear Trains,” ASME J. Mech. Des., 125(3), pp. 602–608. [CrossRef]
Chen, C. , and Chen, J. , 2015, “Efficiency Analysis of Two Degrees of Freedom Epicyclic Gear Transmission and Experimental Validation,” Mech. Mach. Theory, 87, pp. 115–130. [CrossRef]
Laus, L. P. , Simas, H. , and Martins, D. , 2012, “Efficiency of Gear Trains Determined Using Graph and Screw Theories,” Mech. Mach. Theory, 52, pp. 296–325. [CrossRef]
Esmail, E. L. , 2017, “A Universal Kinematic Analysis of Geared Mechanisms,” J. Braz. Soc. Mech. Sci. Eng., 39(6), pp. 2253–2258. [CrossRef]




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