Simulation study of active vibration control of planetary gear: Theoretical and numerical analysis using pole placement

Abstract

This paper presents analytical and numerical studies on the active assignment of poles to a planetary gear system for vibration control in order to avoid resonance. This involves feeding back the displacement and velocity to add active stiffness and damping, respectively. A rotating frame of reference has been adopted in order to describe the dynamics over a broad range of rotational speed. As an illustration, the closed loop poles were assigned to the translational directions of the sun gear first and thereafter the carrier. This can be achieved by placing the actuators on the outer race of their bearings mounted onto their shafts. The controller was designed such that the closed loop poles can be assigned considering the rotational speed. In this way, it is possible to apply a robust pole-placement that is insensitive to the rotational speed. Numerical examples, where sensors and actuators were collocated, are presented to demonstrate the feasibility of the method when applied to a physical system. The results shows that the active control force and power required for the system, when rotating, can be determined using a rotating frame of reference and transformed for practical implementation. In addition, the same conjugate poles were assigned to the carrier and sun gear and the optimal place to apply control forces was discovered. This depends upon the control power required to shift the poles from one location to another. The results show that more control power will be required to shift the poles of the system when poles were assigned to the sun gear, where higher active bearing stiffness was required. Therefore, the optimal place to assign poles in this case is the carrier due to lower control power required to shift the system poles.