Complex modal analysis of serpentine belt drives based on beam coupling model

Serpentine belt drive system is widely used as engine front end accessory drive system in automotive industry. It is a complex hybrid discrete-continuous system whose vibrations are mainly composed of rotational vibrations of pulleys and the tensioner arm, and transverse vibrations of continuum belt spans. In this paper, an efficient method to evaluate the natural vibration characteristics of serpentine belt drives is proposed and investigated. The equations of motion of an actual multiple pulley serpentine belt drive are established and reformulated into an extended operator form, in which belt spans are modeled as axial moving beams with bending stiffness so that the belt-pulley coupling is comprehensively quantified. The natural frequencies and modes of the system are comprehensively calculated. The model is verified by a real example. Furthermore, the influences of some parameters such as belt bending stiffness and belt axial speed on natural vibration characteristics and degree of coupling are investigated, and the applicability of the traditional single beam model is discussed. The proposed method can also be used to efficiently solve eigenvalue problems of other hybrid systems composed of continuums and discrete bodies.