Force formulation of tubular linear machines with dual Halbach array

This paper proposes a dual Halbach array to improve the thrust force of tubular linear machines. The force output of a single phase permanent magnet tubular linear motor (PMTLM) is obtained analytically. It is validated with finite element method (FEM). Based on the analytical force model, penalty method and scanning method are employed to conduct parameter optimization to maximize the force output for a given machine volume. One set of optimal parameters are determined, and used in the design of a research prototype.