Self-balancing characteristics of three self-synchronous linear motion mechanical oscillators

How to restrain the unbalance caused by the manufacturing and installation of parts during the working process of the rotating oscillators is rarely addressed, yet it is very important for evaluating the performance of rotating machines. This paper treats a system comprising three linear motion mechanical oscillators (LMMOs) fixed to a rigid body and clarifies the self-balancing characteristics of the system in the over-resonance state. An electromechanically coupled dynamic model of LMMO is constructed using Lagrange's energy approach. The small parameter average method is used to derive the synchronization conditions among the LMMOs, and the reasonable coupling torque parameter range that the system should be satisfied. The motion stability is analyzed using a linearized matrix of the torque perturbation equation describing the system, and the stability criteria of synchronous linear motion are provided. Subsequently, the necessary conditions are found for implementing selfbalancing among the three LMMOs to eliminate the unbalanced vibration in the system, and the influences of the structural parameters on self-balancing behavior are investigated. The results demonstrate that the structural parameters and phase differences among the three LMMOs can positively reduce the unbalanced vibration of the system, when the necessary condition for the vibrating displacement response nearing to be zero is fully satisfied. This research can provide theoretical guidance for the vibrating isolation of rotating machinery body with several linear motion vibrating sources installed on a common oscillating platform.