Spiral Bevel Gears Nonlinear Vibration Having Radial and Axial Misalignments Effects

Moslem Molaie,Farhad S Samani,Francesco Pellicano

doi:10.3390/vibration4030037

Moslem Molaie, Farhad S Samani + Show 1 more

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https://doi.org/10.3390/vibration4030037

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Abstract

In gear transmissions, vibration causes noise and malfunction. In actual applications, misalignments contribute to intensifying the destructive effect of vibrations. In this paper, the nonlinear dynamics of a spiral bevel gear pair, with small helix angle, considering different misalignments, are deeply investigated. Axial misalignment, radial misalignment, and the combination of these two types are considered in this study. The governing equation is numerically solved through an implicit Runge–Kutta scheme. Since the main goal of this study is the analysis of the dynamic scenario, the mesh stiffness of the gear pair is obtained from the literature. The dynamical system is nonlinear and time-varying; it is analyzed through time responses, phase portraits, Poincaré maps, and bifurcation diagrams. Results show that, among the considered three cases with different types of misalignments, the spiral bevel gear with axial misalignment is the worst destructive case; aperiodic, subharmonic, and multiperiod responses are observable for this case. It is interesting that the chaotic responses for the case, having both types of misalignments, are less likely for the case with axial misalignment, only.

Highlights

The overall objective of the present paper is to investigate the nonlinear dynamics of an spiral bevel gears (SBG) pair with small helix angle, which is based on the influence of misalignment in actual SBG manufacturing
It is to be noted that gear pairs with small helix angle are used in power transmission gearbox in aerospace applications, due to its high loaded tooth contact performance [1,27]
This paper investigates the effect of misalignments on the dynamics of spiral bevel This paper investigates the effect of misalignments on the dynamics of spiral bevel gears with small helix angle

Summary

Introduction

Among the considered three cases with different types of misalignments, the spiral bevel gear with axial misalignment is the worst destructive case; aperiodic, subharmonic, and multiperiod responses are observable for this case. The nonlinear behavior of SBG is worthy of investigation; see, e.g., [1] Various parameters, such as backlash and time-varying mesh stiffness, exert a prominent influence on the nonlinearity. The nonlinear vibration of actual gear pairs, with some likely faults and conditions, has become the main issue among researchers due to vast ranges of applications of the gear systems. Truncated contacts and edge loading are caused by misalignment, which directly affect the contact pattern It results in the high edge stresses on the teeth flank, which leads to micropitting [8].

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