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This paper proposes an approach to design the length, width, and bundlewidth dimensions of rectangular ironless coils for magnetically levitated planar motors. Firstly, a model for the propulsion and levitation forces generated from a single coil in Halbach permanent magnetic field by using Lorenz force volume integral method is developed. Then, a dimensionless factor named coil width dependent factor,    $K_{\mathrm {c}}$   , which can define the amplitudes of propulsion and levitation forces, is formulated. In order to maximize the value of    $K_{\mathrm {c}}$   , the optimal coils number,    $n$   , of a square forcer is derived to be    $m/2+1$   , where    $m$    is the multiples of coil length    $L_{\mathrm {c}}$    to magnetic pole pitch    $\tau $   . Thereafter, the coil width    $W_{\mathrm {c}}$    and bundlewidth    $B_{\mathrm {c}}$    are determined considering the given magnetic pole pitch    $\tau $   . The comparison between the proposed approach and other formulations verifies that if such designed coils is utilized in a forcer, the average amplitude and the quadratic sum of all coil currents are both minimal when the forcer is desired to generate the identical driving forces. The proposed approach can be used to design the dimensions of a single coil and also to configure the high power density forcers or coil arrays for magnetically levitated planar motors.

Optimal Matching Design of Length and Width of Rectangular Ironless Coils for Magnetically Levitated Planar Motors