0
Research Papers

Response Sensitivity and the Assessment of Nonlinear Vibration Using a Nonlinear Lateral–Torsional Coupling Model of Vehicle Transmission System

[+] Author and Article Information
Chang L. Xiang

Vehicle Research Center,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: xiangcl@bit.edu.cn

Yi Huang

Vehicle Research Center,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: porsche9112004@163.com

Hui Liu

Vehicle Research Center,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: lh@bit.edu.cn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 28, 2014; final manuscript received December 15, 2014; published online January 29, 2015. Assoc. Editor: Guilhem Michon.

J. Vib. Acoust 137(3), 031013 (Jun 01, 2015) (11 pages) Paper No: VIB-14-1063; doi: 10.1115/1.4029416 History: Received February 28, 2014; Revised December 15, 2014; Online January 29, 2015

The eigensensitivity analysis does not meet the increasing industrial requirements of the dynamic performance of a vehicle transmission system. To reduce vibration, it is necessary to include response sensitivity in the guideline in the design stage. In this study, we developed a nonlinear lateral–torsional coupling spur gear system model considering the effect of time-varying mesh stiffness, clearance, mass eccentricity, and transmission error. Then the dynamic response sensitivity to system parameters was systematically analyzed by taking the shaft torsional stiffness, for example. The equation of response sensitivity was deduced by a direct method (DM) based on the fitting of the clearance function curve using a polynomial function. In allusion to the characteristic of the aperiodicity of response sensitivity curves of the nonlinear system in the time domain, a novel assessment method—differential sensitivity based on the root mean square (RMS) of response is proposed. This method provides statistical results in a certain range, thus avoiding the inaccuracy of the partial amplitude. The vibrational energy of modified system (MS) can also be estimated. All the abovementioned characteristics make it possible to provide the theoretical support for dynamic modification, model updating, and optimal design.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chen, C. S., Natsiavas, S., and Nelson, H. D., 1998, “Coupled Lateral-Torsional Vibration of a Gear-Pair System Supported by a Squeeze Film Damper,” ASME J. Vib. Acoust., 120(4), pp. 860–867. [CrossRef]
Botman, M., 1976, “Epicyclic Gear Vibrations,” ASME J. Manuf. Sci. Eng., 98(3), pp. 811–815. [CrossRef]
Cunliffe, F., Smith, J. D., and Welbourn, D. B., 1974, “Dynamic Tooth Loads in Epicyclic Gears,” ASME J. Manuf. Sci. Eng., 96(2), pp. 578–584. [CrossRef]
Saada, A., and Velex, P., 1995, “An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains,” ASME J. Mech. Des., 117(2A), pp. 241–247. [CrossRef]
Kahraman, A., 1994, “Dynamic Analysis of a Multi-Mesh Helical Gear Train,” ASME J. Mech. Des., 116(3), pp. 706–712. [CrossRef]
Kahraman, A., 1994, “Natural Modes of Planetary Gear Trains,” J. Sound Vib., 173(1), pp. 125–130. [CrossRef]
Lin, J., and Parker, R. G., 1999, “Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration,” ASME J. Vib. Acoust., 121(3), pp. 316–321. [CrossRef]
Lin, J., and Parker, R. G., 1999, “Sensitivity of Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters,” J. Sound Vib., 228(1), pp. 109–128. [CrossRef]
Guo, Y. C., and Parker, R. G., 2010, “Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters,” ASME J. Vib. Acoust., 132(1), p. 011006. [CrossRef]
Huang, Y., Liu, H., Chen, Y. Q., and Xiang, C. L., 2014, “Response Sensitivity of the Linear Vibration of the Gear System of the Vehicle Transmission,” J. Vib. Eng., 27(3), pp. 333–340.
Petrov, E. P., 2008, “Method for Sensitivity Analysis of Resonance Forced Response of Bladed Disks With Nonlinear Contact Interfaces,” ASME J. Eng. Gas Turbines Power, 131(2), p. 022510. [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]
Walker, D., and Zhang, N., 2014, “Transmission of Engine Harmonics to Synchronizer Mechanisms in Dual Clutch Transmissions,” ASME J. Vib. Acoust., 136(5), p. 051009. [CrossRef]
Özgüven, H. N., 1988, “Mathematical Models Used in Gear Dynamics—A Review,” J. Sound Vib., 121(3), pp. 383–411. [CrossRef]
Munro, R. G., 1962, “The Dynamic Behaviour of Spur Gears,” Ph.D. dissertation, Cambridge University, Cambridge, UK.
Lin, H. H., Huston, R. L., and Coy, J. J., 1988, “On Dynamic Loads in Parallel Shaft Transmissions, Part I—Modelling and Analysis,” ASME J. Mech. Des., 110(2), pp. 221–225. [CrossRef]
Lin, H. H., Huston, R. L., and Coy, J. J., 1988, “On Dynamic Loads in Parallel Shaft Transmissions, Part II—Parameter Study,” ASME J. Mech. Des., 110(2), pp. 226–229. [CrossRef]
Benton, M., and Seireg, A., 1978, “Simulation of Resonances and Instability Conditions in Pinion-Gear Systems,” ASME J. Mech. Des., 100(1), pp. 26–32. [CrossRef]
Benton, M., and Seireg, A., 1981, “Factors Influencing Instability and Resonances in Geared Systems,” ASME J. Mech. Des., 103(2), pp. 372–378. [CrossRef]
Wang, K. L., and Cheng, H. S., 1981, “A Numerical Solution to the Dynamic Load, Film Thickness, and Surface Temperatures in Spur Gears, Part I: Analysis,” ASME J. Mech. Des., 103(1), pp. 177–187. [CrossRef]
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. [CrossRef]
Yang, C., and Adams, D. E., 2009, “Predicting Changes in Vibration Behavior Using First- and Second-Order Iterative Embedded Sensitivity Functions,” J. Sound Vib., 323(1–2), pp. 173–193. [CrossRef]
Yang, C., and Adams, D. E., 2010, “Predicting Changes in Vibration Behavior With Respect to Multiple Variables Using Empirical Sensitivity Functions,” ASME J. Vib. Acoust., 132(6), p. 061004. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Dynamic model of gear pair

Grahic Jump Location
Fig. 2

Geometric model of gear pair

Grahic Jump Location
Fig. 3

Schematic diagram of the projection of sun gear equivalent error. (a) Manufacturing error and (b) assembly error.

Grahic Jump Location
Fig. 4

Comparison between the piecewise curve and the fitting curve of the backlash function of spur gear pair. L is the length of the action line and f(L) is the mesh deflection.

Grahic Jump Location
Fig. 5

An example of the effect of phase on response sensitivity. (a) Response curves and (b) differential sensitivity curves.

Grahic Jump Location
Fig. 6

Procedure flow chart of calculating sensitivity. (IS means the initial system; MS means the modified system).

Grahic Jump Location
Fig. 7

Dynamic model of the example system

Grahic Jump Location
Fig. 8

Input torque of engine for the example system

Grahic Jump Location
Fig. 9

The comparison of additional torque among segments of shaft

Grahic Jump Location
Fig. 10

Sensitivity of the additional torque of SE 25-26 with respect to torsional shaft stiffnesses when input speed being 4200 rpm. (a) Result of the TM and (b) relative sensitivity based on the RMS response.

Grahic Jump Location
Fig. 11

Frequency spectra of the additional torque Tt25-26 of (a) the IS and (b) the MS

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In