A two degrees of freedom (2-DOF) actuator capable of producing linear translation, rotary motion, or helical motion would be a desirable asset to the fields of machine tools, robotics, and various apparatuses. In this paper, a novel 2-DOF split-stator induction motor was proposed and electromagnetic structure parameters of the motor were designed and optimized. The feature of the direct-drive 2-DOF induction motor lies in its solid mover arrangement. In order to study the complex distribution of the eddy current field on the ferromagnetic cylinder mover and the motor's operating characteristics, the mathematical model of the proposed motor was established, and characteristics of the motor were analyzed by adopting the permeation depth method (PDM) and finite element method (FEM). The analytical and numerical results from motor simulation clearly show a correlation between the PDM and FEM models. This may be considered as a fair justification for the proposed machine and design tools.Index Terms-Finite element method (FEM), induction motor, permeation depth method (PDM), solid rotor, split stator, two degrees of freedom (2-DOF).

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Abstract-This paper presents a composite multilayer method (CMM) to evaluate the performance of a two-degree-of-freedom (2DoF) direct drive induction motor (2DoFDDIM) whose solid rotor is coated with a copper layer. It includes a rotary part and a linear part. Based on the traditional multilayer theory, a complete 2DoFDDIM CMM computer program importing propagation constants is built. Due to the complex magnetic field in a 2DoFDDIM, this paper mainly analyses it from the perspective of a single DOF motor. An equivalent circuit for the rotary part of the 2DoFDDIM is then derived applying CMM and the two-dimensional magnetic field distribution is obtained by solving Maxwell's equations in motor layers.

Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor (SIPMSM), it is important to accurately calculate the temperature field distribution of SIPMSM, and a magnetic-thermal coupling method is proposed. The magnetic-thermal coupling mechanism is analyzed. The thermal network model and finite element model are built by this method, respectively. The effects of power frequency on iron losses and temperature fields are analyzed by the magnetic-thermal coupling finite element model under the condition of rated load, and the relationship between the load and temperature field is researched under the condition of the synchronous speed. In addition, the equivalent thermal network model is used to verify the magnetic-thermal coupling method. Then the temperatures of various nodes are obtained. The results show that there are advantages in both computational efficiency and accuracy for the proposed coupling method, which can be applied to other permanent magnet motors with complex structures. Index Terms-Equivalent thermal network method, magnetic-thermal coupling method, power frequency, iron loss, surface-mounted and interior permanent magnet synchronous motor(SIPMSM), temperature field.

-The two-degree-of-freedom direct drive induction motor, which is capable of linear, rotary and helical motion, has a wide application in special industry such as industrial robot arms. It is inevitable that the linear motion and rotary motion generate coupling effect on each other on account of the high integration. The analysis of this effect has great significance in the research of two-degreeof-freedom motors, which is also crucial to realize precision control of them. The coupling factor considering the coupling effect is proposed and addressed by 3D finite element method. Then the corrected mathematical model is presented by importing the coupling factor. The results from it are verified by 3D finite element model and prototype test, which validates the corrected mathematical model.

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Due to the lack of mature design program for the tubular permanent magnet linear wave generator (TPMLWG) and poor sinusoidal characteristics of the air gap flux density for the traditional surface-mounted TPMLWG, a design method and a new secondary structure of TPMLWG are proposed. An equivalent mathematical model of TPMLWG is established to adopt the transformation relationship between the linear velocity of permanent magnet rotary generator and the operating speed of TPMLWG, to determine the structure parameters of the TPMLWG. The new secondary structure of the TPMLWG contains surface-mounted permanent magnets and the interior permanent magnets, which form a series-parallel hybrid magnetic circuit, and their reasonable structure parameters are designed to get the optimum pole-arc coefficient. The electromagnetic field and temperature field of TPMLWG are analyzed using finite element method. It can be included that the sinusoidal characteristics of air gap flux density of the new secondary structure TPMLWG are improved, the cogging force as well as mechanical vibration is reduced in the process of operation, and the stable temperature rise of generator meets the design requirements when adopting the new secondary structure of the TPMLWG.

This paper proposes a demagnetization fault detection, mode recognition, magnetic pole positioning, and degree evaluation method for permanent magnet synchronous motors. First, the analytical model of the single-coil no-load back electromotive force (EMF) of demagnetization fault for Permanent magnet synchronous motor (PMSM) arbitrary magnetic poles is established. In the analytical model, the single-coil no-load back EMF residual of the health state and the single magnetic pole sequential demagnetization fault are calculated and normalized. Model results are used as the fault sample database. Second, the energy interval database of the single-coil no-load back EMF residual with different numbers of magnetic pole demagnetization is established. Demagnetization fault detection and degree evaluation are performed by the real-time acquired amplitudes of the single-coil no-load back EMF residual. The number of demagnetization poles is determined by comparing the energy of the single-coil no-load back EMF residual with the energy interval database. Demagnetization mode recognition and magnetic pole positioning are realized by analyzing the correlation coefficients between normalized the single-coil no-load back EMF residual and the fault sample database. Finally, results of analysis of the finite element simulation validate the feasibility and effectiveness of the proposed method.