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Dynamic Modeling of the Belt Drive System with an Equivalent Tensioner Model

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Abstract

Background

In the existing studies, the hysteretic model of tensioner is applied in analysis of a belt drive system which can improve the computational accuracy. But the computational efficiency is low and not suitable for system optimization.

Purpose

In this paper, an approach is presented to simplify the tensioner’s hysteretic model into an equivalent stiffness and damping which is used for improving the computational efficiency of vibration responses of the belt drive system.

Method

A simplified model and computation method of a belt drive system is established. The hysteretic model of a belt tensioner consists of a linear stiffness and viscous damping based on the averaging energy method to simplify the hysteretic parameters and improve the computational efficiency. The equivalent linear stiffness and damping of the tensioner are estimated using an iterative technique. A timing belt drive system is considered as a case study. The belt system's vibration responses are obtained and compared with the measured results to evaluate the performance of the presented approach.

Results and conclusion

The computational results are compared with a previously published method, and the difference between the proposed method (Method I) and the previously published method (Method II) is discussed. The presented method has the following merits: (1) The linearization of tensioner’s hysteretic model can improve the computational efficiency greatly with an acceptable computational accuracy. (2) The semi-analytic method which is used to derive the system equations can further reduce the amount of computation. It is suitable for parameter optimization of system.

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Acknowledgements

The paper is supported by the National Natural Science Foundation of China (No. 51775122).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Shangbin Long, Wenlong Wang, Xia Yue & Chunliang Zhang

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  1. Shangbin Long
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  2. Wenlong Wang
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  3. Xia Yue
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  4. Chunliang Zhang
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Correspondence to Chunliang Zhang.

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Appendix

Appendix

See Tables 3, 4, 5 and Figs. 22, 23.

Table 3 The tensioner’s parameters
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Table 4 The coordinate, radius, moment of inertial and damping for all pulley
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Table 5 The timing belt parameters
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Fig. 22
figure 22

The torsional vibration amplitude for the crankshaft versus speed

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Fig. 23
figure 23

The transmitted torque versus the camshaft phase for various crankshaft speed

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Long, S., Wang, W., Yue, X. et al. Dynamic Modeling of the Belt Drive System with an Equivalent Tensioner Model. J. Vib. Eng. Technol. 10, 511–525 (2022). https://doi.org/10.1007/s42417-021-00389-5

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  • DOI: https://doi.org/10.1007/s42417-021-00389-5

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