Analytical computation of magnetic fields and thrusts in a tubular PM linear servo motor

This paper presents a fully analytical study of a tubular linear motor, with surface-mounted permanent magnets (PMs). The study can be applied to both slot and slotless topologies. The magnetic fields due to the PMs and to the currents are computed applying Maxwell's equations. The first one is obtained by introducing a convenient and operative approximation based on a slight alteration of the PM residual magnetisation M. This allows the differential field equations to be solved with a good accuracy in the final solution. The magnetic fields due to the currents, the flux linkages and the motor thrust are then derived, with two different types of stator winding. The results are shown in perfect agreement with those obtained from the commonly used finite element analysis. The comparison brings out many interesting points about the speed and practicality of the analytical study, showing it particularly adapt to be implemented in motor design software.