Series solution for relative-rotation motion equation

For solving the difficult calculation problem of nonlinear differential equation of motion of complex revolving shaft in relative rotation, a new decoupled equation was proposed by using series method, which expands the nonlinear differential equation into a series of algebraic equations and the series solution is obtained. Based on the result of the research, the veracious speed fluctuation of revolving shaft in relative rotation in practice can be calculated for the steady state. The method also provides a technology for error detachment of measuring apparatus calibration and a highly effective algorithm for torsional vibration real-time on-line monitor of heavy-duty and complex revolving shaft.