Nonlinear dynamics of spur gear systems with time-varying misalignment errors

Abstract

The mesh stiffness excitation of conventional dynamic models for misaligned spur gear systems is obtained under constant misalignment errors, which inevitably neglects the additional fluctuation of mesh stiffness caused by the influence of dynamic response on misalignment errors. The uneven load distribution and contact state alteration resulting from misalignment errors will produce nonlinear tilting moments that cause pendular vibration in gears. The pendular vibration of the gears, in turn, contributes to the time-varying property of misalignment errors. In this study, misalignment errors consist of an initial constant component that may originate from mounting errors and a time-varying component caused by the pendular vibration of gears. Subsequently, a nonlinear coupled lateral-torsional-axial-pendular vibration model for spur gear systems with time-varying misalignment errors (TVME) is constructed. Parametric analyses reveal that the dynamic behavior of the proposed TVME model and the conventional model differ due to the presence of an initial misalignment error. In contrast to the conventional model, the proposed model exhibits richer nonlinear characteristics, mainly in the high-speed zone, and is more prone to sub-harmonic resonance and contact loss owing to the time-varying property of misalignment errors. At 11,400 r/min, the proposed model undergoes sub-harmonic resonance, and its root-mean-square (RMS) value of dynamic transmission error (DTE) increases from 0.27 to 1.15 and 2.96 as the initial misalignment error increases from 0 to $0.005°$ and $0.01°$ , whereas the corresponding values of the conventional model remain almost unchanged at 0.27.