Levitation Force and Lateral Force Analysis of a Large-Load Magnetic Levitation Gravity Compensator with Two-Dimensional Permanent Magnet Array.

Abstract

I. IntroductionMagnetic levitation technologies are widely used in many fields, such as the electromagnetic bearings in high-speed compressor, the maglev in transportation, and the magnetic levitation planar motor in ultra-precision positioning systems. In addition, there are also potential application for magnetic levitation technology in some special fields [1-6]. For instance, the passive magnetic force between permanent magnets could be used to compensate the gravity of the large optical loads to achieve the ground test. Compared with the air bearings or air springs, the magnetic levitation gravity compensator (MLGC) can realize multiple degrees of freedom and vacuum compatibility. Furthermore, the complex air supply system can be removed. According to Earnshaw's theorem, the stable levitation state cannot be realized only with permanent magnets. Therefore, the non-contact actuators are required to achieve the active control. Generally, a constant passive levitation force within effective stroke is expected in order to reduce the active force level and the volume of the actuators. In this paper, a large-load magnetic levitation gravity compensator with two-dimensional permanent magnet array is analyzed in aspects of levitation force and lateral force.II. Topology and ModelThe large-load MLGC composed of three two-dimensional permanent magnet arrays. The middle PM array is the mover. The top PM array and bottom PM array are the stator. The mover is attracted by the top stator and repelled by the bottom stator, so a levitation force can be generated to compensate the load mass [7]. Each PM array are composed of 36 pieces of cuboid PM distributed in a checkerboard pattern. Basically, the passive force between two cuboid PM can be calculated using the magnetic charge model [8-9] or the equivalent current model. However, the relative permeability in both two classical models is assumed to 1.0, which causes a negligible error for MLGC. In [10], the actual working point of PM in magnetic spring is considered, using which the accurate model of the large-load MLGC can be built.III. Levitation Force and Lateral Force AnalysisIn this section, the influence of the parameters on the levitation force level and levitation force variation are analyzed based on the model and FEM. The levitation force level of the large-load MLGC is determined by some structural parameters. Compared with the PM thickness and pole arc coefficient, the pole pitch and air gap length are two critical parameters to decide the levitation force level. When the structural parameters are selected, the levitation force with different vertical and lateral displacement are analyzed. The maximum and minimum levitation force within 2mm vertical displacement is 17282N and 17155N. The maximum and minimum levitation force within 2mm lateral displacement is 17155N and 17108N. The change rate of levitation force is less than 1%. Additionally, the value of the lateral force is also very low. However, it should be noted that the lateral force increases with the increase of the vertical displacement. The maximum lateral force is 102N within 2mm lateral displacement when the vertical displacement is 1mm.IV. ExperimentTo verify the accuracy of the model and the correctness of the related analysis, a prototype of the large-load MLGC is manufactured. In order to maintain the relative position of the PM in each layer, all of the PM are inserted into the slots of aluminum plates. As shown in Fig. 1, the testing platform consists of base plate, adjusting bolts, multimeter, load sensor, sensor transmitter and power supply, in which the adjusting bolts are used to change the vertical displacement of the large-load MLGC. The measurement range of the load sensor is 25000N. To improve test accuracy, the components on the test platform should be made of non-magnetic materials as many as possible. As shown in Fig. 2, the levitation force increases with the vertical displacement, and the test value of the levitation force in the center position is 16860N. the error between the experiment and FEM is less than 2%. The levitation force variation within 2mm vertical displacement is 1.2%.V. ConclusionIn this paper, a large-load magnetic levitation gravity compensator is analyzed and tested. To achieve a high levitation force, the 2-D permanent magnet array are used. To reduce the levitation force variation, the double-sided stator is applied. The ultimate load capacity of the prototype is 16860N (i.e., 1720kg). The testing results match well with the 3D FEM. **