Analysis of the non-linear vibration characteristics of a belt-driven system

In this paper, a mathematical model for a belt-driven system is proposed to analyze vibration characteristics of driving units having belts, and free and forced vibration analyses are carried out. The mathematical model for a belt-driven system includes belts, pulleys, spindle and bearings. The material properties of each belt and the equivalent stiffnesses supported by pulleys, bearings and a spindle are calculated through experiments. By using Hamilton's principle, four non-linear governing equations and twelve non-linear boundary conditions are derived. To linearize and discretize the non-linear governing equations and boundary conditions, the perturbation and Galerkin methods are used. Also, the free vibration analyses for various parameters of a belt driven system are made, including the tension of a belt, the length of a belt, the material properties of belts, the belt velocity and the pulley mass. Forced vibration analyses of the system are performed, and the dynamic responses for the main parameters are analyzed for a belt driven system.