Development and Simulation of Non-Linear Gear Dynamics Model

Abstract

With the development of high-speed mechanical transmission, the dynamic characteristics of gear transmission require continuous improvement and more accurate prediction of the gear system dynamics becomes more and more important. The literature revealed that the gear pair transmission system is inherently non-linear which exhibits complex behavior and it is significant to study its vibration characteristics in detail and to analyze the influencing factors. A nonlinear dynamic model of gear transmission is developed using lumped mass parameter approach. The equations of torsional motion of the mathematical model of gear pair system was developed based on the Newton’s Second law of motion/D’ Alembert’s principle, and the gear backlash was included in the mathematical model which is a discontinuous and non-differentiable function. The numerical simulation of the non-linear second order ordinary differential equation was carried out in MATLAB using Runge-Kutta method (6^th–8^thorder). The aim of this paper is to compare the dynamic behaviour of lightly loaded and heavily loaded gears and to analyze the effect of force ratio, damping ratio and excitation frequency on gear dynamics which provides a theoretical basis for in-depth studying of the gear dynamics. Clearly, the study showed that if a suitable load ratio is chosen and the damping parameter is increased, the chaotic motion can be controlled and can avoid the unstable motion in order to decay the vibration and noise of the gear-pair system.

Keywords: Mathematical model, gear dynamic, non-linear, differential equation, Runge-Kutta, phase-plane, chaos