Modeling and analysis of a new cylindrical magnetic levitation gravity compensator with low stiffness for the 6-DOF fine stage

A novel cylindrical magnetic levitation gravity compensator (MLGC) with low-stiffness and vacuum-compatible characteristics is proposed in this paper. This compensator can be used as the out-of-plane electromagnetic actuator for the 6-DOF fine stage in certain high-precision positioning applications, for example, the wafer stage in a lithography machine. Compared with conventional actuators such as the electromagnet and voice coil motor, the heat and the resulting temperature rise that degrade the stage positioning accuracy can be reduced by using passive magnetic gravity compensation. Based on the equivalent current method, the analytical equations for the magnetic field, static levitation force, vertical stiffness, and dynamic levitation force are derived. However, the static levitation force-vertical displacement characteristic from the traditional analytical model is not sufficiently accurate for the low-stiffness applications when compared with the finite-element model. Therefore, the main reason for the model error is analyzed, and an improved semianalytical method based on a single-point magnetostatic field simulation is proposed. This method offers a theoretical basis for the analysis and design of the low-stiffness MLGC.