Servomotor control of a coupled elastic shaft–elastic beam system

In this study, a servomotor driven coupled elastic shaft–elastic beam system is analyzed. The model consists of a servomotor, disk, and an elastic beam attached to the disk separated by an elastic shaft. Equations of motion are derived with respect to the generalized coordinates of the elastic shaft, elastic beam and the servomotor rotation. Frequency equations and mode shapes for the elastic beam and elastic shaft are obtained assuming compliant boundary conditions. Nonlinear terms which come from the Coriolis, normal and tangential accelerations retained in the equations. For a chosen example, disk rotation, servomotor rotation and beam vibration are obtained for a desired servomotor input rotation which assumes proportional plus derivative control. Results show that shaft elasticity not only affects the disk motion and beam vibrations but also alters the actual servomotor motion. Beam vibration amplitudes are lower when the shaft elasticity is higher. Nonlinear terms have also a lowering effect on the beam vibration amplitudes.