Abstract:

：No considering the damping and external forces the pure torsional freedom vibration equation of encased differential planetary train is established and this equation is converted to regular modal equation. The multi-scale method is applied to derive the stability conditions of summation resonance frequencies caused by the meshing stiffness fluctuations for this train and the dynamic stability is analyzed. The research results show that the bigger the absolute value of the coefficient matrix element of the first harmonic of the meshing stiffness fluctuations for this regular modal equation, the greater the vibration frequency instability interval caused by the corresponding combination resonance frequency or second harmonic of this coefficient matrix element. The instability is bigger with the increase of the meshing stiffness volatility while the meshing frequency is close to the resonance combination frequency and twice harmonic frequency. The resonance points of the combination resonance frequency and second harmonic frequency of this train caused by the mesh frequency of the encased stage is far more than that of the differential stage. The point in the undulating surface of the unstable three-dimensional map to the integer of internal and external mesh overlap is the bottom and it has a high stability.

Key words: instability, meshing stiffness, multi-scale method, encased differential planetary train