Analytical investigation on unstable vibrations of single-mesh gear systems with velocity-modulated time-varying stiffness

• Parametric instability due to velocity-modulated mesh stiffness is studied.
• Two types of speed fluctuation model are considered.
• Operating conditions leading to parametric instability are analytically obtained.
• Effects of various parameters on instability regions are systematically discussed.
• Modulation impact factor is defined to roughly estimate the perturbation order.

Time-varying mesh stiffness parametrically excites gear systems and causes severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and more complex instabilities might arise. Considering two different speed fluctuation models, parametric instability associated with velocity-modulated time-varying stiffness is analytically investigated using a typical single-mesh gear system model. Closed-form approximations are obtained by perturbation analysis, and verified by numerical analysis. The effects of the amplitude of the mesh stiffness variation, the characteristics of speed fluctuations and damping on parametric instability are systematically examined.