A calculation method for natural frequencies and transverse vibration of a belt span in accessory drive systems

A method for modeling and calculation of natural frequencies of a belt span and transverse vibration displacement of a point in the belt span for an accessory drive system is presented in this article. In the model, the belt between two adjacent pulleys is simplified as an axial moving visco-elastic string, and the relation between stress and strain for the belt is modeled with standard visco-elastic constitutive model. The calculated natural frequencies from the axial moving string model are compared with estimated results from the pulley-string belt coupled model. It is shown that the natural frequencies can be obtained directly from axial moving string model. An experiment is carried out for getting the natural frequencies of a belt span and the transverse displacement of a point in a belt span in a generic engine front end accessory drive system. The measured natural frequencies and transverse displacements are compared well with calculated results, which validate the modeling and calculation methods presented in this article. Based on the axial moving visco-elastic string model, the influences of elastic stiffness and damping of a belt on the transverse deflections of a point in one belt span are investigated. It is shown that the transverse deflections of the belt decrease with the increasing of the elastic stiffness and damping of belt.