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The purpose of this study is to calculate the normal force of a two degree of freedom direct drive induction motor considering coupling effects based on an analytical model. Compared with the traditional single degree of freedom motor, normal force characteristics of two-degree-of-freedom direct drive induction motor (2DOFDDIM) is affected by coupling effect when the machine is in a helical motion. To theoretically explain the influence mechanism of coupling effect, this paper conducts a quantitative analysis of the influence of coupling effect on normal force based on the established analytical model of normal force considering coupling effect.

Firstly, the normal forces generated by 2DOFDDIM in linear motion, rotary motion and helical motion are investigated and compared to prove the effect of the coupling effect on the normal force. During this study, several coupling factors are established to modify the calculation equations of the normal force. Then, based on the multilayer theoretical method and Maxwell stress method, a novel normal force calculation model of 2DOFDDIM is established taking the coupling effect into account, which can easily calculate the normal force of 2DOFDDIM under different motions conditions. Finally, the calculation results are verified by the results of 3D finite element model, which proves the correctness of the established calculating model.

The coupling effect produced by the helical motion of 2DOFDDIM affects the normal force.

In this paper, the analytical model of the normal force of 2DOFDDIM considering the coupling effect is established, which provides a fast calculation for the design of the motor.

To improve the power density and generation efficiency of the tubular permanent magnetic linear generators (TPMLGs) under realistic sea-stator condition, a TPMLG with 120° phase belt toroidal windings (120°-TPMLG) for wave energy conversion is proposed in this paper.

First, the structure of the 120°-TPMLG is introduced and its operation principle is analyzed. Second, the design process of the 120°-TPMLG is described. Meanwhile, the finite-element models of the 120°-TPMLG and the TPMLG with traditional fractional pitch windings (T-TPMLG) are established based on the similar overall dimensions. Then, the electromagnetic characteristics of the 120°-TPMLG are analyzed, such as air gap flux density, back electromotive force and load voltage. Finally, a comparative analysis of the magnetic flux density, flux linkage, load and no-load performance of the two generators are conducted.

The result shows that the 120°-TPMLG has higher power density and generation efficiency than the T-TPMLG.

This paper proposes a TPMLG with 120° phase belt toroidal windings (120°-TPMLG) to improve the power density and generation efficiency.

This study aims to unveil the generation mechanism of the thrust force in a tubular flux-switching permanent magnet (PM) linear (TFSPML) machine; the operation principle of the TFSPML machine is analyzed.

First, the air-gap flux density harmonic characteristics excited by PMs and armature windings are investigated and summarized based on a simple magnetomotive force (MMF)-permeance model. Then, the air-gap field modulation theory is applied in analyzing the air-gap flux density harmonics that contribute to the electromagnetic force. In addition, a simple method for separating the end force of the TFSPML machine is proposed, which is a significant foundation for the comprehensive analysis of this type of machine. As a result, the operation principle of the TFSPML machine is thoroughly revealed.

The analysis shows that the average electromagnetic force is mainly contributed by the air-gap dominant harmonics, and the thrust force ripple is mainly caused by the end force.

In this paper, the operation principle of the TFSPML machine is analyzed from the perspective of air-gap field modulation.