Non-smooth dynamics of spur gears with manufacturing errors

This paper presents a method for analysing nonlinear vibrations of spur gears in presence of manufacturing errors. The approach is based upon the classical one-degree-of-freedom model, with backlash and time varying stiffness. Manufacturing errors are treated stochastically, starting from the knowledge of the gear tolerance class. A random profile error distribution is given for each tooth; then teeth errors are combined in order to span all possible reciprocal teeth contacts. The result is an analytical forcing, in terms of transmission error, which includes statistically the effect of local errors. Finally, a full dynamic analysis is carried out in the case of perfect and imperfect gears, in order to show the effect of profile errors and their variance on the gear vibration.