Parametric Excitations of Multi-step Gear System

Parametric excitations caused by mesh stiffness variation of multi-step gear system are analyzed using multiple time scales method and numerical analysis method based on fundamental solution matrix. As a result, the followings were made clear. (1) Influence of viscous damping was investigated, and it was pointed out that the analysis considering viscous damping was very important. (2) The differences of the results obtained by multiple time scales method and those by the numerical analysis method were large in the regions of combination instabilities which generate when the sum of natural frequencies is close to mesh stiffness variation frequency. On the other hand, in the primary resonances and secondary ones, the differences of those results were small generally. (3) In four-gear system, adding to primary, secondary, and combination parametric excitations, when difference of two mesh stiffness variation frequencies is close to natural frequency, or its twice, or the sum of natural frequencies, parametric resonance occur.