Optimization of design parameters to improve performance of a planar electromagnetic actuator

Electromagnetic actuators based on passively levitating planar magnetic platforms driven by co-planar current-carrying coils find widespread use in precision positioning applications. While these actuators provide nanometer scale positioning resolution, their in-plane actuation bandwidth is limited to a few tens of hertz due to the small in-plane electromagnetic stiffness. In this study, we optimize the design parameters of the electromagnetic coil and the magnetic platform to maximize the in-plane electromagnetic force and trapping stiffness per unit volume of the magnetic platform. Our approach utilizes closed-form expressions for electromagnetic forces and stiffness, derived in terms of the actuation currents, the pitch of the electromagnetic coil, and the dimensions, position, and magnetization of the magnetic platform. Notably, our investigation reveals that by reducing the pitch of the electromagnetic coil by a factor of 10, the in-plane forces and stiffness per unit volume of the magnetic platform can be increased by two and three orders of magnitude, respectively. Experimental validation using a precision force sensor demonstrates close agreement with the analytical values, with an error of less than 15%.