Abstract
The nonlinear equation of the rotational vibration of a pair of spur gear has a restriction that the analytical solution of the equation cannot be obtained. If the nonlinear equation of vibration has not this restriction, it will be very useful. The Linear Approximated Equation (Abbreviate with LAE) of vibration, which has the analytical solution, is derived by converting the varying spring constant of meshing gears to “the equivalent exciting force”. The linear model of vibration, which can be used to analyze the vibration due to any tooth profile error with any shape when the pair of spur gear has any rotational speed, any load and any contact ratio, is presented in this paper. As a result of the investigation of the applicability of the LAE, it has been cleared that the LAE can be applied in wide range of the amplitudes and shapes of the tooth profile errors. The analytical solution of vibration of the LAE, which is derived by analytical method, agreed well with the result numerically calculated by the exact nonlinear equation of the vibration.
