Abstract
A coupled torsional-transition nonlinear dynamic model of a two-stage helical gear (TSHG) reduction system for electric vehicles (EVs) is presented in this paper. The model consists of 16 degrees of freedom (DOF), which includes factors such as the nonlinearity of backlash, time-varying mesh stiffness (TVMS), mesh damping, supporting bearings, static transmission error (STE), and the torsional damping and stiffness of the intermediate shaft, in which the fourth-order Runge–Kutta numerical integration method was applied to solve the differential equations. With the help of bifurcation diagrams, time-domain histories diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps, root-mean-square (RMS) curves, peak-peak values (PPVs), and Lyapunov exponents, the effects of pinion rotational speed, backlash, torsional stiffness, and torque fluctuation on the dynamic behavior of TSHG system are investigated. The stability properties of steady-state responses are investigated using Lyapunov exponents. The results reveal various types of dynamic evolution mechanisms and nonlinear phenomena such as periodic-one responses, quasiperiodic responses, jumps phenomena, and chaotic responses. The research presents useful results and information to vibration control and dynamic design of the TSHG transmission system used in EVs.
Highlights
It is known that the power mechanism of electric vehicles (EVs) is composed of a power coupling system, electrical control systems, motor, and other subsystems
As gear pairs are one of the main parts of EV power coupling system, the dynamic behavior of the gear pairs mechanism has a significant influence on power transmission and even the whole vehicle [1]. erefore, the analysis of the dynamic characteristics of gear pairs is becoming essential in power transmission systems
A dynamic model of a helical gear multiple-shafts reduction box was presented by Kubur et al in [4, 5], which consists of a finite-element model of shaft structures combined with another three-dimensional discrete model of gear pairs
Summary
It is known that the power mechanism of EVs is composed of a power coupling system (transmission shafts, gear pairs, bearings, etc.), electrical control systems, motor, and other subsystems. Considering the effects of TVMS and nonlinear characteristics of bearing, a dynamical model of a TSHG box including the motion of housing was established by Xu et al [12], and steady-state vibration response of the gearbox has been obtained based on the coupling gear-rotor-bearing dynamic model. In order to investigate the nonlinear dynamic response of the TSHG system coupled with an automotive clutch, Walha et al [27] proposed a dynamic model of 27 DOF considering spline clearance, double-stage stiffness, and dry friction path, in which the equation of motion was solved by Runge–Kutta method. Teeth number Base circle radius (mm) Mass (kg) Working face width (mm) Helix angle (°) Pressure angle (°) Modulus (mm)
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