Modeling and analysis of reluctance motion system with asymmetrical air gaps

To achieve high throughput and efficiency, semiconductor photolithography machines need an actuation system that can meet high acceleration and precision demands on the nanoscale. One available solution is the reluctance actuator, which provides higher acceleration and force output than the standard Lorentz actuator. A floating stage with air-bearings is used to eliminate friction in the photolithography process; however, vibration transfer is not entirely eliminated, leading to potential misalignment and asymmetries between the actuator elements. With asymmetrical offsets between mover elements, the output force can be greatly affected. This paper shows a method for estimating the force of various asymmetrical cases for the C-core reluctance actuator. Analytical models are developed and further improved through polynomial curve fitting using precomputed finite element simulation results from Comsol Multiphysics (COMSOL) to achieve more optimal solutions. An experiment verified the results of the force estimation equations, which were within ∼11% for different cases of asymmetric air gaps. This contribution will lead to a design for a control system that will overcome the issue of asymmetries or other altered states.