Investigation on nonlinear vibration of a gear transmission system considering time-varying mesh stiffness and time-varying supporting stiffness

Abstract

Nonlinear vibration of a gear transmission system considering time-varying mesh stiffness (TVMS) and time-varying supporting stiffness (TVSS) caused by variable numbers of engaged teeth of gears and contacted rolling elements of bearings, respectively, is investigated in detail in this work. The lumped mass method is employed to simplify the gear transmission system as a three degree-of-freedom (DOF) model system with piecewise linear stiffness caused by backlashes and clearances of bearings under forced excitations and parametric excitations due to TVMS and TVSS. To obtain nonlinear vibration of the gear transmission system, ordinary differential equations that represent a three-DOF model system are established by employing the Newton’s second law. An incremental harmonic balance (IHB) method is proposed to determine periodic responses of the gear transmission system. The modified Floquet theory is applied to examine stability of periodic responses of the gear transmission system. Some interesting phenomena that exist in periodic responses including softening-spring characteristics, resonances, and bifurcations are revealed. In particular, effects of TVMS and TVSS can generate different types of resonances. Increased responses are obtained in this case, as compared to the case without TVMS and TVSS. Analytical results obtained by the IHB method are in agreement with those from numerical integration.