Research On Nolinear Dynamics Of The Belt Driver Mechanism

Regarding electric motor, belt,pulleys and theirs coupling system as objects, we study nonlinear dynamics problems of the belt driver mechanism system by means of electromechanical analysis dynamics, nonlinear vibration theory and numerical analysis method.The nonlinear differential equation with quadratic and cubic nonlinearities for vibration analysis of the belt driver mechanism is derived by means of Lagrange equation. Applying the method of multiple scales for the nonlinear vibration the approximate solutions of primary resonance of the system are obtained. Numerical results on the influences of length, cross section area of the belt, excitation, detuning and damping on the system are analyzed in detail. The first approximate solution for amplitude frequency response curve of the primary resonance of the system has hard stiffness characteristic; The second approximate solution for amplitude frequency response curve of the primary resonance of the system has soft stiffness characteristic.The approximate solution of 1/2,1/3 subharmonic resonance and 2,3 superharmonic resonance are obtained. Numerical analysis on the influences of the length, cross section area, external excitation, detuning, and damping on the system is carried out.Based on Coriolis acceleration and Lagrangian strain formula, the transverse vibration system of convection belts equation generalized is derived by Newton's second law in this paper. The method of multiple scales is applied directly to the governing equations, and approximate solution of primary parameter resonance and the parametric with forced resonance of the system are obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, an axial moving speed has a significant effect on the amplitudes of steady-state response and their existence boundaries.The nonlinear differential equation for vibration analysis of the belt driver mechanism excited on thedirection of lateral and axial is derived by means of Lagrange equation, function.The method of multiple scales is applied directly to the governing equations, and approximate solution is obtained. The characteristics of the lateral and axial vibration are obtained based on numerical method. The influences of the torsion vibration of lateral and axial vibration are analyzed. According to generalized Lagrange-Maxwell's equation, the differential equations are established considering the nonlinear elasticity and electromagnetism of the belt driver mechanism. Using the numerical method analyzes the influences of the electric motor for the belt driver mechanism.