Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics

[+] Author and Article Information
Yuping Cheng

Ford Motor Company, Livonia, MI 48150

Teik C. Lim

Department of Mechanical, Industrial & Nuclear Engineering, The University of Cincinnati, Cincinnati, OH 45221-0072

J. Mech. Des 125(2), 373-382 (Jun 11, 2003) (10 pages) doi:10.1115/1.1564064 History: Received July 01, 2001; Revised July 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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Litvin,  F. L., and Gutman,  Y., 1981, “Method of Synthesis and Analysis for Hypoid Gear-drives of Format and Helixform,” ASME J. Mech. Des., 103, pp. 83–113.
Litvin, F. L., and Zhang, Y., 1991, “Local Synthesis and Tooth Contact Analysis of Face-milled Spiral Bevel Gear,” NASA Technical Report 4342 (AVSCOM 90-C-028).
Litvin,  F. L., Wang,  A. G., and Handschuh,  R. F., 1998, “Computerized Generation and Simulation of Meshing and Contact of Spiral Bevel Gears with Improved Geometry,” Comput. Methods Appl. Mech. Eng., 158, pp. 35–64.
Gosselin, C., Cloutier, L., and Sankar, S., 1989, “Effects of the Machine Settings on the Transmission Error of Spiral Bevel Gears Cut by the Gleason Method,” Proc. International Power Transmission and Gearing Conference: New Technologies for Power Transmissions of the 90’s, Chicago, Illinois, pp. 705–712.
Fong,  Z. H., and Tsay,  C. B., 1992, “Kinematical Optimization of Spiral Bevel Gears,” ASME J. Mech. Des., 114, pp. 498–506.
Kubo,  A., Tarutani,  I., Gosselin,  C., Nonaka,  T., Aoyama,  N., and Wang,  Z., 1997, “Computer Based Approach for Evaluation of Operating Performances of Bevel and Hypoid Gears,” JSME Int. J., Ser. III, 40, pp. 749–758.
Remmers, E. P., 1971, “Dynamics of Automotive Rear Axle Gear Noise,” SAE Paper 710114.
Pitts, L. S., 1972, “Bevel and Hypoid Gear Noise Reduction,” SAE Paper 720734.
Kiyono,  S., Fujii,  Y., and Suzuki,  Y., 1981, “Analysis of Vibration of Bevel Gears,” Bull. JSME, 24, pp. 441–446.
Nakayashiki, A., 1983, “One Approach on the Axle Gear Noise Generated from the Torsional Vibration,” Proc. Japanese Society of Automotive Engineers, P-139, 2 , Tokyo, Japan, pp. 571–580.
Abe, E., and Hagiwara, H., 1990, “Advanced Method for Reduction in Axle Gear Noise,” Gear Design, Manufacturing and Inspection Manual, Society of Automotive Engineers, Warrendale, PA, pp. 223–236.
Özgüven,  H. N., and Houser,  D. R., 1988, “Mathematical Models Used in Gear Dynamic-a Review,” J. Sound Vib., 121(3), pp. 383–411.
Özgüven,  H. N., and Houser,  D. R., 1988, “Dynamic Analysis of High Speed Gears By Using Loaded Static Transmission Error,” J. Sound Vib., 125, pp. 71–83.
Kahraman,  A., and Singh,  R., 1990, “Non-linear Dynamics of a Spur Gear Pair,” J. Sound Vib., 142(1), pp. 49–75.
Kahraman,  A., and Singh,  R., 1991, “Non-linear Dynamics of a Geared Rotor-Bearing System With Multiple Clearances,” J. Sound Vib., 144(3), pp. 469–505.
Kahraman,  A., and Singh,  R., 1991, “Interactions Between Time-varying Mesh Stiffness and Clearance Non-linearities in a Geared System,” J. Sound Vib., 146(1), pp. 135–156.
Blankenship,  G. W., and Kahraman,  A., 1996, “Torsional Gear Pair Dynamics, Part-I: Characterization of Forced Response,” Proc. International Power Transmission and Gearing Conference, ASME, San Diego, CA DE-88, pp. 373–380.
Blankenship,  G. W., and Singh,  R., 1995, “Dynamic Force Transmissibility in Helical Gear Pairs,” Mech. Mach. Theory, 30, pp. 323–339.
Velex,  P., and Maatar,  M., 1996, “A Mathematical Model For Analyzing The Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behavior,” J. Sound Vib., 191(5), pp. 629–660.
Donley,  M. G., Lim,  T. C., and Steyer,  G. C., 1992, “Dynamic Analysis of Automotive Gearing Systems,” Journal of Passenger Cars, 101(6), pp. 77–87.
Cheng, Y., and Lim, T. C., 1998, “Dynamic Analysis of High Speed Hypoid Gears With Emphasis on Automotive Axle Noise Problem,” Proc. 7th International Power Transmission and Gearing Conference, ASME, Atlanta, Georgia, DETC98/PTG-5784.
Cheng, Y., and Lim, T. C., 2000, “Hypoid Gear Transmission with Non-linear Time-varying Mesh,” Proc. 8th International Power Transmission and Gearing Conference, ASME, Baltimore, Maryland, DETC2000/PTG-14432.
Cheng,  Y., and Lim,  T. C., 2001, “Vibration Analysis of Hypoid Transmissions Applying an Exact Geometry-based Gear Mesh Theory,” J. Sound Vib., 240(3), pp. 519–543.
Hochmann, D., 1997, “Friction Force Excitation in Spur and Helical Involute Parallel Axis Gearing,” Ph.D. thesis, The Ohio State University, Columbus, Ohio.
Lida,  H., Tamura,  A., and Yamada,  Y., 1985, “Vibrational Characteristics of Friction Between Gear Teeth,” Bull. JSME, 28(241), pp. 1512–1519.
Handschuh,  R. F., and Kicher,  T. P., 1996, “A Method for Thermal Analysis of Spiral Bevel Gears,” ASME J. Mech. Des., 118, pp. 580–585.
Gosselin,  C., Cloutier,  L., and Nguyen,  Q. D., 1995, “A General Formulation For the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears,” Mech. Mach. Theory, 30, pp. 433–450.
Tavakoli,  M. S., and Houser,  D. R., 1986, “Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears,” ASME J. Mech. Des., 108, pp. 86–94.
Krenzer, T. J., 1981, “Tooth Contact Analysis of Spiral Bevel and Hypoid Gears Under Load,” SAE Paper 810688.
Vijayakar, S., 1987, “Finite Element Methods for Quasi-prismatic Bodies With Application To Gears,” Ph.D thesis, The Ohio State University, Columbus, Ohio.
Vijayakar,  S., 1991, “A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem,” Int. J. Numer. Methods Eng., 31, pp. 525–545.
Lim,  T. C., and Singh,  R., 1990, “Vibration Transmission Through Rolling Element Bearings. Part I: Bearing Stiffness Formulation,” J. Sound Vib., 139(2), pp. 179–199.
Lim,  T. C., and Cheng,  Y., 1999, “A Theoretical Study of the Effect of Pinion Offset on the Dynamics of Hypoid Geared Rotor System,” ASME J. Mech. Des., 121, pp. 594–601.


Grahic Jump Location
Illustrations of (a) hypoid gear setup, (b) contact cells and three coordinate systems denoted by S0,S1 and S2, and (c) load distributions on the tooth surface for a specific gear angular position
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A multi-degree-of-freedom lumped parameter model of a hypoid geared rotor system
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Flowchart of the proposed computational approach
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Loaded transmission error and corresponding Fourier coefficients for two different pinion torques: (a) effect of load; (b) 113 Nm; and (c) 509 Nm
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Effect of mean pinion torque load on averaged mesh stiffness
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Quasi-static multi-tooth contact analysis results of (a) load sharing characteristic within one mesh cycle at 509 Nm pinion input torque; and (b) load distributions for two different mesh positions
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Predicted dynamic mesh loads for one mesh cycle at the resonant frequency of 340 Hz for the case of time-varying (TV) and time-invariant (TI) mesh vectors at 509 Nm of applied pinion torque load (friction coefficient μ=0)
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Mesh load FFT spectra of the time response shown in Fig. 8
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Comparison of the frequency response functions of the non-linear time-varying (NLTV) and time invariant (NLTI) cases for 509 Nm of pinion torque. Note that the linear time-invariant response (LTI) is also plotted (friction coefficient μ=0)
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Effect of applied pinion torque load on the dynamic mesh force assuming the same mesh stiffness of 3×108N/m for all 3 cases shown (friction coefficient μ=0)
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Effect of applied pinion torque load on dynamic mesh force with load-dependent averaged mesh stiffness (no friction effect)
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Effect of applied pinion torque load on the pinion bearing force with load-dependent averaged mesh stiffness (no friction effect)
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Time-history response of the dynamic mesh force near the jump frequency under light load condition (113 Nm)
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Dynamic mesh force and pinion bearing force due to the fundamental harmonic of LTE compared to that of the first three harmonics of LTE. These cases assume 509 Nm of pinion torque, time-varying mesh vector, time-invariant mesh stiffness, and no friction effect.
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Dynamic transmission error for 2 different pinion torque loads assuming constant mesh stiffness with time-varying mesh vector and no friction effect. The corresponding linear time-invariant solutions are also shown. The super-harmonics indicated are due to the 3rd harmonic of the LTE excitation.
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Frequency spectrum of DTE (μm) at operating frequency of 580 Hz for the case of 226 Nm of input pinion torque
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Waterfall plots of the dynamic response at 509 Nm of input pinion torque. (a) Pinion bearing force; (b) Dynamic mesh force




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