  In this paper, Amperian current and magnetic charge models of permanent
magnets are integrated into a hybrid approach to develop a comprehensive
analytical modeling for designing a slotless double-sided linear motor with an
arbitrary Halbach array. Unlike the conventional methods that treat magnets as
sources for Poisson's equations, the solution is reduced to Laplace's
equations, with magnets being represented as boundary conditions. The proposed
hybrid approach reduces the complexity of of the problem, requiring the
solution for only two or three regions compared to a large number of regions if
either Amperian currents or magnetic charges were utilized. The magnetic fields
and potentials within distinct regions, along with machine quantities such as
shear stress, force-angle characteristics, torque profile, attraction force,
misalignment force, and back-EMF, are derived, comprehensively analyzed, and
compared to FEM results for accuracy validation. Finally, a thorough
sensitivity analysis and design consideration of a linear stage for high
acceleration and low vibration applications is discussed.
