On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

Jun Wang,Teik C Lim

doi:10.1155/2011/583678

Jun Wang, Teik C Lim

Open Access

https://doi.org/10.1155/2011/583678

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Abstract

A nonlinear time‐varying (NLTV) dynamic model of a hypoid gear pair system with time‐dependent mesh point, line‐of‐action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high‐speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

Highlights

Gear dynamics have been studied intensively as evident from the discussions in [1,2,3,4,5]
Kahraman, and Singh examined the nonlinear dynamics of a spur gear pair [2] as well as a geared rotor-bearing system [3] and studied the interaction between mesh stiffness and clearance nonlinearities [4]
Cheng and Lim studied the vibratory response of a hypoid geared rotor system with nonlinear time-varying mesh characteristics [5]

Summary

Introduction

Gear dynamics have been studied intensively as evident from the discussions in [1,2,3,4,5]. Cheng and Lim studied the vibratory response of a hypoid geared rotor system with nonlinear time-varying mesh characteristics [5]. From those studies, it is well known that nonlinear phenomena like jump discontinuity frequently occurs for lightly loaded gear pairs. Different levels of torques and damping ratios are applied so that the transition condition between linear and nonlinear responses can be located. If the dynamic mesh force is smaller in value than the mean mesh force, the jump behavior tends to disappear making the response appearing to be quite linear

Mathematical Model

Dynamic Analysis

Concluding Remarks