Numerical simulation of instability conditions in multiple pinion drives

Multiple pinion drives, parallel arrangements of the pinions for large torque transmission, are widely utilized in various heavy-duty industrial applications. For such multi-mesh gear systems, periodic mesh stiffnesses could possibly cause parametric instabilities and server vibrations. Based on the Floquet–Lyapunov theory, numerical simulations are conducted to determine the parametric instability status. For rectangular waveforms assumption of the mesh stiffness variations, the primary, secondary, and combination instabilities of the multiple pinion drives are studied. The effects of mesh stiffness parameters, including mesh frequencies, stiffness variation amplitudes, and mesh phasing, on these instabilities are yielded. Unstable regions are also indicated for different gear pair configurations. Instability conditions of three-pinion drives are obtained and compared with those of the three-stage gear train.