Time-varying dynamic analysis for a helical gear pair system with three-dimensional motion due to bearing deformation

Ying-Chung Chen

doi:10.1177/1687814020918128

Abstract

The dynamic response of a helical gear pair system is investigated. A new dynamic model for a helical gear pair system, considering three-dimensional motion due to bearing deformation, is proposed. The proposed model considers the helix angle, gear pair center distance, transverse pressure angle, and the contact ratio as time-dependent variables, which are considered as constants in other models. In fact, three-dimensional motion due to bearing deformation will lead to the changes in a series of dynamic responses. The system equations of motion were obtained by applying Lagrange’s equation and the dynamic responses are computed by the fourth-order Runge–Kutta method. The time-varying dynamic displacements, helix angle, gear pair center distance, transverse pressure angle, and the contact ratio are investigated with bearing deformation, different radial bear stiffness, different axial bear stiffness, and gear eccentricity. The results show that, due to the time-varying effect, this new helical gear pair model provides more accurate dynamic responses than those previous models which are considered as constant. In the future, this study can provide some useful information for the time-varying dynamic design of a helical gear pair system.

Highlights

With the advancement of technology, the gear system is one of the most important components and commonly used in many industrial applications, such as automotive, wind turbines, aircraft, generator, and robotic arms
Umezawa et al.[1] proposed a simulator which solves a differential equation with 1 degree of freedom (DOF) in consideration of the behavior of the stiffness around tooth tip meshing and makes easier on the profile of a spur gear which decreases the vibration
Kim et al.[12] developed a new dynamic model which analyzed the dynamic response of a spur gear pair by considering the pressure angle and the contact ratio as time-dependent variables, as well as gear set translational motion due to bearing deformation

Summary

Introduction

With the advancement of technology, the gear system is one of the most important components and commonly used in many industrial applications, such as automotive, wind turbines, aircraft, generator, and robotic arms. Kim et al.[12] developed a new dynamic model which analyzed the dynamic response of a spur gear pair by considering the pressure angle and the contact ratio as time-dependent variables, as well as gear set translational motion due to bearing deformation.

Results

Conclusion