Dynamic behaviors of a geared rotor system under time-periodic base angular motions

The dynamic behaviors of a geared rotor system under time-periodic base motions are studied in this paper. The equations of motion for a spur gear pair system are derived based on the energy theorem and Lagrangeʹs principle. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Considering the time-varying base movements and gear meshing, the second order differential equations of the system will not only have time-periodic gyroscopic and stiffness coefficients, but also the multi-frequency external excitations. Numerical method is utilized to obtain the lateral and torsional responses of the geared system under transmission error and unbalanced mass excitations. The effects of various base angular motions on both frequency response and response spectra are discussed in detail. Compared with the other two types of periodic base motions, the rolling base motion has the greatest impact on the dynamic behaviors of the geared system. The transient response of the geared rotor system is always greatly enhanced no matter which type of base angular motion is in operation.