Dynamic characteristics of rotor system with parallel and angular misaligned involute spline coupling

Spline couplings are commonly used to transfer rotary motion in rotating structures, such as low-pressure rotor systems in dual-rotor aero-engines. The misalignment introduced by spline coupling assembly error will seriously affect the safe operation of rotor system. In this paper, a method is proposed to calculate the spline meshing stiffness under arbitrary misalignment conditions, considering the static and dynamic misalignment. The accurate meshing parameters of spline couplings under parallel and angular misalignments were determined by computing the effective meshing region of misaligned spline teeth. Furthermore, a time-varying stiffness-damping spline model is established, considering friction on the spline teeth surfaces, to derive the dynamic model of the spline-rotor system under arbitrary misalignment conditions. The Newmark-β method, in conjunction with the Newton–Raphson method, was used to solve the dynamic response of the system, and the correctness of the model was verified by experiments. Finally, the variation of spline meshing stiffness and force caused by static and dynamic misalignment is described, and the effects of parallel and angular misalignment, as well as the phase difference in unbalance, on the vibration response and self-excited vibrations are also investigated.