Modelling and dynamic analysis of spline-connected multi-span rotor system

Self-excited oscillation induced by the internal frictions of spline joints is a major cause of rotor system instability. In this study, the dynamic equations of spline-connected multi-span rotor systems have been derived by finite element and lumped mass hybrid modelling methods. In this model, the mathematical models of spline joints and rubber sealing rings were deduced in detail. Newmark numerical algorithm was applied to solve differential equations of the coupling system. On this basis, the amplitude–frequency response characteristics of systems without rubber sealing ring as well as the effects of several important parameters, including friction coefficient, transmission torque and unbalance value, on the self-excited vibration of the system were discussed. Then, in the case of rubber sealing ring assembled next to spline joint, the effects of rubber sealing ring on amplitude–frequency response characteristics and self-excited vibrations of the system were analyzed. The obtained results showed that self-excited oscillation occurred in supercritical state when the friction coefficient of spline joint was high enough; however, it merely occurred within a specific speed range. By the increase of friction coefficient or transmission torque, the speed range corresponding to self-excited oscillation became closer to the natural frequency of the system. However, as the unbalance value was increased, the phenomenon of self-excited vibration showed the opposite trend. Rubber sealing ring not only reduced vibration near spline joint, but also suppressed the self-excited vibration of the system induced by internal friction, thus improving system stability. This paper provides a theoretical basis for studying the mechanism and suppression of self-excited oscillation of rotor systems.