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.

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Fig. 3

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

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Fig. 2

Geometric model of gear pair

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Fig. 1

Dynamic model of gear pair

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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.

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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.

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Fig. 5

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

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Fig. 6

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

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Fig. 8

Input torque of engine for the example system

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Fig. 9

The comparison of additional torque among segments of shaft

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Fig. 11

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

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Fig. 7

Dynamic model of the example system




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