Kinematic analysis of a semi-rigid-elastic multi-body torsional vibration model of gears system

Kinematic analysis of a semi-rigid-elastic multi-body torsional vibration model of gears system is studied by using the state-space model. Equation of motion of gears system is obtained. A four-degree-of-freedom model of the pinion gear-wheel gear system is considered for simplicity. The pinion gear body and wheel gear body are assumed to be rigid. The teeth are assumed to be elastic and parallel spring-damper combinations are assumed to exist between the teeth and the gear body. Differential equations are obtained from equation of motion of gears system. Differential equations are arranged in the state-space form. Rotational positions and rotational velocities are considered as state-variables. The state-space equations of system are solved by MATLAB program. Transmission error of gears system is calculated depending on state-variables. Rotational positions, rotational velocities and transmission error are shown as graphically. It is shown in numerical study that transmission error deepens on various gear parameters and operating conditions. Moreover, it is shown in numerical study that transmission error deepens on elasticity of teeth.