Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

Zhong Wang,Yuan-Qing Luo,Chang-Zheng Chen,Lei Zhang

doi:10.1155/2017/1264904

Zhong Wang, Yuan-Qing Luo + Show 2 more

Open Access

https://doi.org/10.1155/2017/1264904

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Abstract

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

Highlights

The first systematic efforts to analyze the gear dynamics were in the 1920s and early 1930s [1]
To reveal the nonlinear dynamic response of the spur gear pair under near-resonance conditions, the internal excitation shown in Figure 6(a) and that shown in Figure 6(b) are applied to the system
The spectrum of internal excitation is shown to contain sidebands because of the modulation timevarying mesh stiffness and modulation transmission errors caused by manufacturing errors and so forth

Summary

Introduction

The first systematic efforts to analyze the gear dynamics were in the 1920s and early 1930s [1]. Shen et al [8] solved the single-DOF model of a spur gear pair considering the time-varying mesh stiffness, backlash, and static transmission error with Incremental Harmonic Balance Method (IHBM) and studied the effect of damping coefficient and excitation amplitude. Liu et al [14] focused on the nonlinear behavior of a spur gear with backlash by a 2 DOF lumped-parameter model, solved the dynamic equations with Runge-Kutta method, and expounded the influence of revolution speed, backlash, and mesh damping coefficient on the dynamic response. To the authors’ knowledge, the internal excitation of the spur gear pair caused by the time-varying meshing stiffness and transmission error was usually regarded as nonmodulated signals.

Dynamic Model of Spur Gear Pair

Numerical Simulation

Experimental Validation

Conclusion