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Research Papers

Multiphysics Investigations on the Dynamics of Differential Hypoid Gears

[+] Author and Article Information
M. Mohammadpour, H. Rahnejat

Wolfson School of Mechanical &
Manufacturing Engineering,
Loughborough University,
Loughborough LE113TU, UK

S. Theodossiades

Wolfson School of Mechanical &
Manufacturing Engineering,
Loughborough University,
Loughborough LE113TU, UK
e-mail: s.theodossiades@lboro.ac.uk

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 5, 2013; final manuscript received April 3, 2014; published online April 30, 2014. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 136(4), 041007 (Apr 30, 2014) (3 pages) Paper No: VIB-13-1420; doi: 10.1115/1.4027403 History: Received May 12, 2013

Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

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References

Tangasawi, O., Theodossiades, S., and Rahnejat, H., 2007, “Lightly Loaded Lubricated Impacts: Idle Gear Rattle,” J. Sound Vib., 308(3), pp. 418–430. [CrossRef]
Koronias, G., Theodossiades, S., Rahnejat, H., and Saunders, T., 2011, “Axle Whine Phenomenon in Light Trucks: A Combined Numerical and Experimental Investigation,” Proc. Inst. Mech. Eng., Part D, 225(7), pp. 885–894. [CrossRef]
Ozguven, H. N., and Houser, D. R., 1988, “Mathematical Models Used in Gear Dynamics—A Review,” J. Sound Vib., 121(3), pp. 383–411. [CrossRef]
Kahraman, A., and Singh, R., 1991, “Interactions Between the Time Varying Mesh Stiffness and Clearance Nonlinearities in a Geared System,” J. Sound Vib., 146(1), pp. 135–156. [CrossRef]
Amabili, M., and Rivola, A., 1997, “Dynamic Analysis of Spur Gear Pairs: Steady-State Response and Stability of the SDOF Model With Time Varying Mesh Damping,” Mech. Syst. Signal Process., 11(3), pp. 375–390. [CrossRef]
Remmers, E. P., 1971, “Dynamics of Automotive Rear Axle Gear Noise,” SAE Paper No. 710114. [CrossRef]
Kiyono, S., Fujii, Y., and Suzuki, Y., 1981, “Analysis of Vibration of Bevel Gears,” Bull. Jpn. Soc. Mech. Eng., 24(188), pp. 441–446. [CrossRef]
Abe, E., and Hagiwara, H., 1990, “Advanced Method for Reduction in Axle Gear Noise,” Gear Design, Manufacturing and Inspection Manual, SAE Paper No. 750150. [CrossRef]
Hirasaka, N., Sugita, H., and Asai, M., 1991, “A Simulation Method of Rear Axle Gear Noise,” SAE Paper No. 911041. [CrossRef]
Donley, M. G., Lim, T. C., and Steyer, G. C., 1992, “Dynamic Analysis of Automotive Gearing Systems,” SAE Paper No. 920762. [CrossRef]
Cheng, Y., and Lim, T. C., 1998, “Dynamic Analysis of High Speed Hypoid Gears With Emphasis on Automotive Axle Noise Problem,” ASME Paper No. DETC98/PTG-5784.
Cheng, Y., and Lim, T. C., 2000, “Dynamics of Hypoid Gear Transmission With Time-Varying Mesh,” ASME Paper No. 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. [CrossRef]
Jiang, X., 2002, “Non-Linear Torsional Dynamic Analysis of Hypoid Gear Pairs,” M.Sc. thesis, The University of Alabama, Tuscaloosa, AL.
Wang, H., 2002, “Gear Mesh Characteristics and Dynamics of Hypoid Geared Rotor System,” Ph.D. thesis, The University of Alabama, Tuscaloosa, AL.
Wang, J., Lim, T. C., and Li, M., 2007, “Dynamics of a Hypoid Gear Pair Considering the Effects of Time-Varying Mesh Parameters and Backlash Nonlinearity,” J. Sound Vib., 229(2), pp. 287–310. [CrossRef]
Dareing, D. W., and Johnson, K. L., 1975, “Fluid Film Damping of Rolling Contact Vibrations,” J. Mech. Eng. Sci., 17(4), pp. 214–218. [CrossRef]
Mehdigoli, H., Rahnejat, H., and Gohar, R., 1990, “Vibration Response of Wavy Surfaced Disc in Elastohydrodynamic Rolling Contact,” Wear, 139(1), pp. 1–15. [CrossRef]
Virlez, G., Bruls, O., Duysinx, P., and Poulet, N., 2011, “Simulation of Differentials in Four-Wheel Drive Vehicles Using Multi-Body Dynamics,” ASME Paper No. DETC2011-48313. [CrossRef]
Karagiannis, I., and Theodossiades, S., 2013, “An Alternative Formulation of the Dynamic Transmission Error to Study the Oscillations of Automotive Hypoid Gears,” ASME J. Vib. Acoust., 136(1), p. 011001. [CrossRef]
Xu, H., and Kahraman, A., 2007, “Prediction of Friction-Related Power Losses of Hypoid Gear Pairs,” J. Multi-Body Dyn., 221(3), pp. 387–400. [CrossRef]
Kolivand, M., Li, S., and Kahraman, A., 2010, “Prediction of Mechanical Gear Mesh Efficiency of Hypoid Gear Pairs,” Mech. Mach. Theory, 45(11), pp. 1568–1582. [CrossRef]
Snidle, R. W., and Archard, J. F., 1968, “Lubrication at Elliptical Contacts,” Proc. Inst. Mech. Eng., 183(16), pp. 138–146. [CrossRef]
Simon, V., 1998, “The Influence of Misalignments on Mesh Performances of Hypoid Gears,” Mech. Mach. Theory, 33(8), pp. 1277–1291. [CrossRef]
Simon, V., 2009, “Influence of Machine Tool Setting Parameters on EHD Lubrication in Hypoid Gears,” Mech. Mach. Theory, 44(5), pp. 923–937. [CrossRef]
Ito, N., and Takahashi, K., 2000, “Differential Geometrical Conditions of Hypoid Gears With Conjugate Tooth Surfaces,” ASME J. Mech. Des., 122(3), pp. 323–330. [CrossRef]
Gohar, R., 1971, “Oil Film Thickness and Rolling Friction in Elastohydrodynamic Point Contact,” ASME J. Lub. Tech., 93(3), pp. 371–382. [CrossRef]
Chittenden, R. J., Dowson, D., Dunn, J. F., and Taylor, C. M., 1985, “A Theoretical Analysis of the Isothermal Elastohydrodynamic Lubrication of Concentrated Contacts. I. Direction of Lubricant Entrainment Coincident With the Major Axis of the Hertzian Contact Ellipse,” Proc. R. Soc., London, Ser. A, 397(1813), pp. 245–269. [CrossRef]
Chittenden, R. J., Dowson, D., Dunn, J. F., and Taylor, C. M., 1985, “A Theoretical Analysis of the Isothermal Elastohydrodynamic Lubrication of Concentrated Contacts. II. General Case, With Lubricant Entrainment Along Either Principal Axis of the Hertzian Contact Ellipse or at Some Intermediate Angle,” Proc. R. Soc., London, Ser. A, 397(1813), pp. 271–294. [CrossRef]
Jalali-Vahid, D., Rahnejat, H., Gohar, R., and Jin, Z. M., 2000, “Prediction of Oil-Film Thickness and Shape in Elliptical Point Contacts Under Combined Rolling and Sliding Motion,” Proc. Inst. Mech. Eng., Part J, 214(5), pp. 427–437. [CrossRef]
Mohammadpour, M., Theodossiades, S., and Rahnejat, H., 2012, “Elastohydrodynamic Lubrication of Hypoid Gears at High Loads,” Proc. Inst. Mech. Eng., Part J, 226(3), pp. 183–198. [CrossRef]
De la Cruz, M., Chong, W. W. F., Teodorescu, M., Theodossiades, S., and Rahnejat, H., 2012, “Transient Mixed Thermo-Elastohydrodynamic Lubrication in Multi-Speed Transmissions,” Tribol. Int., 49, pp. 17–29. [CrossRef]
Fujii, M., Nagasaki, Y., and Nohara, M., 1997, “Differences in Dynamic Behavior Between Straight and Skew Bevel Gears,” Trans. Jpn. Soc. Mech. Eng., Part C, 63(613), pp. 3229–3234. [CrossRef]
Yinong, L., Guiyan, L., and Ling, Z., 2010, “Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System,” Math. Prob. Eng., 2010, p. 124148. [CrossRef]
Yang, J., and Lim, T., 2011, “Dynamics of Coupled Nonlinear Hypoid Gear Mesh and Time-Varying Bearing Stiffness Systems,” SAE Int. J. Passeng. Cars, 4(2), pp. 1039–1049. [CrossRef]
Karagiannis, Y., Theodossiades, S., and Rahnejat, H., 2012, “On the Dynamics of Lubricated Hypoid Gears,” Mech. Mach. Theory, 48, pp. 94–120. [CrossRef]
Theodossiades, S., and Natsiavas, S., 2001, “On Geared Rotordynamic Systems With Oil Journal Bearings,” J. Sound Vib., 243(4), pp. 721–745. [CrossRef]
Caughey, T. K., 1960, “Classical Normal Modes in Damped Linear Dynamic Systems,” ASME J. Appl. Mech., 27(2), pp. 269–271. [CrossRef]
Harris, T., and Kotzalas, M. N., 2007, Advanced Concepts of Bearing Technology, Taylors and Francis, London.
Gillespie, T. D., 1992, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Warrendale, PA.
Rahnejat, H., 1998, “Multi-Body Dynamics: Vehicles, Machines and Mechanisms,” Professional Engineering Publishing, Bury St. Edmunds, UK.
Evans, C. R., and Johnson, K. L., 1986, “Regimes of Traction in Elastohydrodynamic Lubrication,” Proc. Inst. Mech. Eng., 200(C5), pp. 313–324. [CrossRef]
Greenwood, J. A., and Tripp, J. H., 1970, “The Contact of Two Nominally Flat Rough Surfaces,” Proc. Inst. Mech. Eng., 185(1), pp. 625–633. [CrossRef]
Teodorescu, M., Balakrishnan, S., and Rahnejat, H., 2005, “Integrated Tribological Analysis Within a Multi-Physics Approach to System Dynamics,” Tribol. Interface Eng. Ser., 48, pp.725–737. [CrossRef]
Mohammadpour, M., Theodossiades, S., Rahnejat, H., and Kelly, P., 2013, “Transmission Efficiency and Noise, Vibration and Harshness Refinement of Differential Hypoid Gear Pairs,” Proc. Inst. Mech. Eng., Part K, 228(1), pp. 19–33. [CrossRef]
Litvin, F. L., and Fuentes, A., 2004, “Gear Geometry and Applied Theory,” 2nd ed., Cambridge University Press, New York.
Yamada, T., and Mitsui, J., 1979, “A Study on the Unstable Vibration Phenomena of a Reduction Gear System, Including the Lightly Loaded Journal Bearings, for a Marine Steam Turbine,” Bull. JSME, 22(163), pp. 98–106. [CrossRef]
Kahraman, A., and Singh, R., 1990, “Non-Linear Dynamics of a Spur Gear Pair,” J. Sound Vib., 142(1), pp. 49–75. [CrossRef]
Cheng, Y., and Lim, T. C., 2003, “Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics,” ASME J. Mech. Des., 125(2), pp. 373–382. [CrossRef]

Figures

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Fig. 1

(a) The multibody dynamics model and (b) the corresponding free body diagrams

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Fig. 2

Frequency spectra of the maximum and minimum DTE amplitudes (nominal case)

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Fig. 3

One meshing cycle (time period = 0.005 s) of the DTE variation of section A-A (Fig. 2)

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Fig. 4

Magnified views of the first and the second resonance regions of Fig. 2

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Fig. 5

Frequency spectra of the maximum and minimum DTE amplitudes (low damping)

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Fig. 6

Frequency spectra of the maximum and minimum DTE amplitudes (high bearing stiffness)

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Fig. 7

Frequency spectra of the maximum and minimum DTE amplitudes (torsional model)

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Fig. 8

Frequency spectra of the lateral motion maximum and minimum amplitudes (nominal case)

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Fig. 9

Frequency spectra of the axial motion maximum and minimum amplitudes (nominal case)

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Fig. 10

Frequency spectra of the maximum and minimum radial transmitted force amplitudes

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Fig. 11

Frequency spectra of the maximum and minimum axial transmitted force amplitudes

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Fig. 12

Frequency spectra of the maximum and minimum pinion friction torque

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Fig. 13

One meshing cycle of the friction torque variation (position A in Fig. 12)

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Fig. 14

One meshing cycle of the friction torque variation (position B in Fig. 12)

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Fig. 15

Input pinion torque for the considered case study

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