Modeling hysteresis behavior of spline coupling and its application in rotodynamic prediction

Abstract

In aeronautical applications, spline couplings are widely used and often exhibit hysteretic behavior under non-synchronous whirl conditions. This behavior significantly influences the vibration characteristics of rotor systems. However, existing research has paid insufficient attention to the hysteretic mechanisms of spline couplings and lacks a deep understanding of the dynamic characteristics of spline rotor systems with complex structural features. In this paper, we propose a novel analytical model that accounts for the contact-slip behavior of engaging teeth to predict the nonlinear hysteretic characteristics of spline couplings. Model’s high accuracy and computational efficiency are validated through comparison with the finite element (FE) results. Based on this analytical model, the nonlinear stiffness, damping, and contact characteristics of spline couplings are further revealed. Subsequently, a dynamic model and analysis process for spline rotor systems are developed by incorporating the nonlinear stiffness and damping of spline couplings. Finally, the nonlinear vibrations of spline rotor systems are discussed. Results indicate that as lateral load increases, the stiffness of spline coupling decreases while its loss factor increases. This behavior is closely related to the normal contact and tangential slip of engaging teeth. Due to the nonlinearity of spline coupling, splined rotor systems exhibit phenomena such as leftward shifts in critical speeds, complex frequency contents, and self-excited vibrations.