Effect of gear topology discontinuities on the nonlinear dynamic response of a multi-degree-of-freedom gear train

Adrien Mélot,Youness Benaïcha,Emmanuel Rigaud,Joël Perret-Liaudet,Fabrice Thouverez

doi:10.1016/j.jsv.2021.116495

Abstract

Weight reduction is a recurring concern in the design of modern mechanical systems. This search may lead engineers to resort to using gears with holes in order to meet their requirements. This paper presents a methodology to carry out nonlinear dynamic analyses of a gear transmission with holes in the gear blanks subjected to a multiharmonic internal excitation. This work investigates the influence of these holes on the vibration levels, occurrence of contact loss and possible bifurcations. The numerical model features two flexible shafts coupled by a spur gear pair with holes. The gear model consists in two lumped masses and inertias and includes the gear backlash as well as the internal excitation sources that are the time-varying stiffness and the static transmission error (STE). The resulting mechanical system is solved in the frequency domain by the Harmonic Balance Method (HBM) coupled with an arc-length continuation algorithm and its stability is evaluated with Hill’s method. Results show that adding holes not only impacts the STE but also the mesh stiffness. The interactions of these two quantities has a substantial influence on the bifurcation structure along the main solution branch and leads to a decrease of the span of vibro-impact regions. As the applied static torque is increased, it is found that using holed gear blanks can effectively prevent contact loss and lead to a linear response.

Highlights

Geared systems are known to be prone to unwanted noise and vibrations stemming from the meshing process and possible contact loss between gear teeth
The paper is structured as follows: first, we introduce the dynamic model of the whole transmission and the computational procedure used to compute the static transmission error and mesh stiffness
Gears are a central part of many mechanical systems and engineering applications

Summary

Introduction

Geared systems are known to be prone to unwanted noise and vibrations stemming from the meshing process and possible contact loss between gear teeth These vibrations have motivated many studies over the last few decades. Under particular loading conditions, tooth separation can occur due to the gear backlash necessary to allow for assembly and operation [1, 2, 26, 33] These events induce nonlinear vibrations which generate a noise that can be classified into two categories depending on the loading scenario: rattling noise in case of lightly loaded gears [27, 46, 25] and hammering noise in case of a high static torque [43]

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