Electromagnetic-Mechanical Modeling and Evaluation of a 2-DoF Parallel-Kinematic Compliant Nano-Positioning Stage Based on Normal-Stressed Electromagnetic Actuators

The normal-stressed electromagnetic actuators (NSEAs) have emerged as a promising actuation technology for developing high-performance compliant nano-positioning stages. But less attention was devoted to the modeling of the multi degrees-of-freedom (DoF) NSEA-based stages. This paper aims to improve the modeling accuracy of the stages’ static and dynamic performances by introducing a novel electromagnetic-mechanical modeling method. Unlike the previous studies, the proposed modeling method considers the effects of the NSEAs’ negative stiffnesses along both its actuation direction and the vertical-to-actuation direction in the electromagnetic modeling step. Together with the model of the mechanisms, the coupled electromagnetic-mechanical model is analytically derived. As an application case, the working stroke and resonant frequency of a NSEA-based parallel-kinematic 2-DoF compliant nano-positioning stage are evaluated with the proposed model. It is demonstrated by numerical, simulation, and experimental studies, that the proposed modeling method is accurate for predicting the performances of the NSEA-based nano-positioning stages. This is significant for the future development and applications of NSEA-based mechatronic systems.
Note to Practitioners
—The multi-DoF NSEA-based nano-positioning stages are the promising choice to develop long stroke, high natural frequency nano-positioning stages. However, some inherent electromagnetic-mechanical coupling effects are ignored in previous study when modeling the multi-DoF NSEA-based stages, which leads to a significant prediction error. By considering the electromagnetic characteristics both along and vertical to actuation direction, this study proposed an electromagnetic-mechanical model for the 2-DoF NSEA-based stages. The proposed model shows a higher accuracy to evaluate the static and dynamic performances of the NSEA-based stages, which are beneficial to practical applications such as trajectories tracking.