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.