Dynamic modelling and vibration analysis of parallel misaligned shaft system considering the spline time-varying meshing point

Involute spline couplings see extensive use in shaft system connections. In reality, parallel misalignment can cause changes in the meshing point positions of spline teeth. However, most previous works assume that parallel misalignment will not notably change the spline tooth meshing point position. This is unreasonable because the time-varying meshing position (TVMP) will alter the spline meshing force (SMF) and significantly affect the shaft system vibrations. Thus, a TVMP calculation model is derived in this paper. The spline tooth time-varying backlash and pressure angle models considering the TVMP are proposed. Moreover, the spline meshing stiffness (SMS) and deformation models considering TVMP are given. Furthermore, a shaft system dynamic model considering the TVMP is established. Spline meshing characteristics and shaft system vibrations verification experiments are carried out. A comparison of SMFs obtained by the methods with and without considering TVMP is conducted to highlight the importance of considering TVMP. Finally, the influence of parallel misalignment and rotating speed on the shaft system vibrations is evaluated. This paper can provide parallel misalignment control insights for the shaft system.