Improved method for analysing the dynamic response of gear transmission systems
ISSN: 0264-4401
Article publication date: 3 October 2022
Issue publication date: 15 November 2022
Abstract
Purpose
The purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.
Design/methodology/approach
An improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.
Findings
The calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.
Originality/value
The proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.
Keywords
Acknowledgements
The project was supported as part of the Research Project of National Innovation Center of High Speed Train (CXKY-02-01-01(2020)) and the National Key Research and Development Program of China (Grant No. 2017YFB1300700).
Citation
Li, X., Liu, X., Li, X., He, W. and Guo, H. (2022), "Improved method for analysing the dynamic response of gear transmission systems", Engineering Computations, Vol. 39 No. 9, pp. 3232-3254. https://doi.org/10.1108/EC-08-2021-0500
Publisher
:Emerald Publishing Limited
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