Multiphysical modeling of high-precision electromechanical devices : towards nanometer-accurate planar motors

The semiconductor lithographic industry demands increasingly higher accelerations and accuracies. Present day wafer stages offer positioning accuracies of about one nanometer, and accelerations of several tens of m/s2. This is achieved by a stack of two motor types, i.e. a planar motor for long-stroke motion, and short-stroke actuators for accuracy. As the power dissipation is quadratically proportional to the acceleration values, increasing the acceleration performance quadratically increases the dissipated power. The power dissipation can be minimized by minimizing the weight of the moving member. The weight of the moving member can be decreased by decreasing its complexity. The goal of this thesis is to investigate the possibility of achieving the required acceleration, accuracy and stroke with a single planar motor. The planar motor under research is a movingmagnet planar motor with no cables to the moving member. It consists of a moving magnet array (the translator), and a stationary coil set (the stator). The translator is magnetically levitated and stabilized, and capable of long-stroke motion in the xy-plane. To investigate the applicability of such devices as a wafer scanner in the semiconductor lithographic industry, the multiphysical behavior of such planar motors is researched using an electromagnetic model, a mechanical model and a thermal model, constituting a multiphysical model. The electromagnetic model is based on existing models which make use of a magnetic surface charge density description of the magnetization of permanent magnets. The accuracy of such existing models is increased by proper incorporation of the relative permeability of the magnetic material, and by increasing the accuracy of the implementation using lookup tables. To optimize the acceleration, the weight of the translator should be as low as possible. This limits the stiffness of the translator, increasing its deformation during levitation and acceleration. The electromagnetic model offers the force and torque acting on each individual permanent magnet, yielding a force and torque distribution on the translator. A mechanical model of the translator is extracted from a finite element model. It calculates the deformation of the translator based on the force and torque distribution, which is varying with position and desired acceleration. This mechanical model allows to actively limit the deformation of the translator. The stator temperature is calculated using the current distribution in the coil set. To this end, firstly, using the finite element method, the thermal paths are identified. From this, a thermal equivalent circuit model of the stator is extracted, which is suitable for real-time implementation in state-space form. The thermal model can be used to actively limit the maximum temperature of the coil set, Using these models, the multiphysical behavior of moving-magnet planar motor topologies is analyzed in terms of the dissipated power and resulting temperatures, deformation of the translator, and the positioning accuracy. A novel planar motor topology is synthesized and optimized to the aforementioned performance criteria. Its stator consists of two coil layers, and it is referred to as the Double Layer Planar Motor (DLPM). The coils in one layer are placed orthogonal to the coils in the other layer. This way, both layers provide levitation force, besides which one coil layer provides an acceleration force along the x-direction, the other coil layer provides an acceleration force in the y-direction. A prototype of the Double Layer Planar Motor topology is built. It consists of 160 coils in the stator and 281 permanent magnets arranged in a quasi-Halbach pattern and glued to the translator. The coils are powered using 40 amplifiers. The active coil set is switched using multiplexers. The manufacturing tolerances of the permanent magnets and the coils are decreased with respect to previous prototypes, to improve the positioning accuracy. The position is measured using a 9-DOF laser interferometer system. Furthermore, a novel cooling topology is built to achieve the desired acceleration values. The mean dissipated power during a representative trajectory is estimated at just over 1 kW, yielding a temperature increase of less than 30 degrees. Measurement on a previous planar motor prototype using the same measurement system show a tracking error of 900 nm. Measurements on the DLPM prototype are yet to be performed, however, based on measurements of the magnetic field of the magnet array, and the measured variations in the dimensions and properties of the permanent magnets and the coils, a tracking error of approximately 150 nm is expected