A Dynamic Model for Six-Degree-of-Freedom Bearingless Linear Motor Systems

This article develops a dynamic model for six-degree-of-freedom bearingless linear motor systems by means of lumped-element modeling. A four-sided motor system, containing eight three-phase motor units fed by their own inverters, is considered as an example system, but the modeling approach can be applied to other motor systems as well. The mechanical subsystem of the model comprises the rigid-body dynamics. The electromagnetic subsystem governs the electrical dynamics of the motor units and the production of the resultant electromagnetic force and its associated torque. In order to model the unbalanced magnetic torque due to tilting of the mover, the motor units are spatially discretized into a number of identical submotor models having a uniform air gap. The submotor models of each motor unit are electrically connected in series, i.e., they share the same current, but their flux linkages and forces differ in tilted positions. The electromagnetic subsystem can be parameterized based on simple static two-dimensional finite-element method computations at a range of uniform air-gap and current values. The developed model is validated through a comparison between the time-domain simulation results and the experimental results. The model can be applied to time-domain simulations, real-time control system development, and various analyses of the system.