An Analytical Approach to Determine Coil Thickness for Magnetically Levitated Planar Motors

This paper proposes an analytical approach to directly determine coil thickness dimension only according to the magnetic pole pitch of magnetic levitation planar motors. Based on modeling of the electromagnetic forces/torques of magnetically levitated planar motors, three normalization functions about coil thickness, which are named the main forces/torques impact factor function, the y-axis attaching torque impact factor function, and the ratio factor function of the main forces/torques to coil mass, respectively, are abstracted and derived. These three normalized functions all are dimensionless and single value functions of coil thickness when magnetic pole pitch is specified. Taking the physical meanings of these three functions into account simultaneously and comparing the varying trends of these three functions synchronously, a narrower value range of coil thickness, which is between 0.318 times and 0.525 times of the magnetic pole pitch, is determined. By this approach, the coil thickness of magnetically levitated planar motors with Halbach permanent magnet array can be determined directly, instead of determining by numerical optimization usually including a few optimization parameters. This approach still allows coil thickness dimension to be fine-tuned to meet other design requirements of magnetic levitation planar motors.