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According to the meshing characteristics of spur gears and helical gears, calculation formulas of time varying friction stiffness and friction torque coefficient are derived. Based on the theory of the concentrated parameter, considering the influence of the time-varying coefficient of friction, time-varying meshing stiffness and the integrated error of the integrated, a three-dimensional dynamic model for a double power input transmission system with multi degrees of freedom and variable parameters was developed, including the flexional, torsional and axial motions. The Fourier series method is used to solve the equations by transforming the time varying system into a linear time invariant system, and the total system response of the system is obtained after the superposition of each order excitation response. The change law of friction torque coefficient and friction stiffness is obtained too. The results show that the friction stiffness curve of herringbone gear changes gently without mutations, and the direction is constant which what makes the resultant friction force direction be of the friction no unchanged. The tooth surface roughness has a certain influence on the dynamic transmission error. The first and second harmonic order frequencies of the split torque stage gears have an important influence on the dynamic transmission errors.

Tooth surface friction and its influence on dynamic transmission error of double power input transmission system