Analytical modeling of the lateral stiffness of a spline coupling considering teeth engagement and influence on rotor dynamics

Spline couplings are widely used to transfer rotary motion in rotatory machinery. The local stiffness nonlinearity caused by spline engaging teeth may significantly affect rotordynamics; however, it is usually ignored in most analyses. In this paper, a fully analytical model that can comprehensively account for engaging teeth is first proposed to fast determine the nonlinear stiffness of the spline coupling. Compared with the results of the finite element (FE) model, the results of the proposed model show good agreement but have higher computational efficiency. In addition, the nonlinear mechanism of the spline coupling is revealed, and the effects of the spline length and torque are studied. By introducing the proposed analytical model, a dynamic model of splined rotors is developed. To address the modal solving problem of splined rotors, a modal analysis strategy is proposed based on the Newton-Raphson iteration method. Finally, the modal frequencies, modal shapes and resonance responses of the splined rotor are investigated. The energy-dependent characteristics and softening nonlinearity of splined rotors are highlighted through rotordynamics analysis.