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Compared to traditional single-axis motors, reluctance spherical motors (RSMs) can generate rotational torque in three spatial latitudes on a single motor, thus enabling three degrees-of-freedom (DOF) motion. Due to the complexity of their structure, the finite element method (FEM) is usually used to calculate the torque, but this method has the problem of consuming huge computational resources and long computation time. To address the problem that the FEM for calculating the torque of RSM consumes a lot of computation time, the torque model of RSM is developed by using the virtual work method considering the nonlinear cases of the magnetic circuit in this paper. Firstly, the inductance simulation of a single stator coil of a RSMs is carried out using finite element simulation software to obtain its inductance model. When the magnetic circuit is linear, the torque is obtained by partial differential calculation of the inductance surface. When the magnetic circuit is nonlinear, the distribution of flux linkage is first solved. Then, the electromagnetic torque is obtained by partial differential calculation of the magnetic co-energy. The calculated results are then projected to the global coordinate system to convert the two-DOF torque to the three-DOF torque. Finally, the experimental torque measurement platform is built, and the torque is measured and compared with the analytical calculation results. The results show that this method greatly reduces the amount of computing and simulation work with accurate modeling and provides a theoretical basis for the study of energization strategies and real-time control of the reluctance spherical motors. [ABSTRACT FROM AUTHOR]

A permanent magnet spherical motor (PMSpM) is a representative multiple degree-of-freedom electric apparatus. This paper proposes new analytical models for the PMSpM with stepped cylindrical permanent magnets (PMs). The research is not only to obtain the magnetic field and torque models of the PMSpM but also to yield a potential analytic tool for the spatial magnetic field and torque decomposition. The model decomposition aims to acquire a potential tool for the future research on PMSpM topology optimization and working mechanism. To achieve the two research targets above, the toroidal expansion method is used for magnetic field modeling, and the finite element method verification and experimental verification are conducted. Then, forces and torques are deduced from the Lorentz force law. In addition, a prototype PMSpM has been produced and the comparison studies of the air-gap flux density and torque among decomposed components are conducted using finite element analysis results and experimental results. It is concluded that the proposed analytical PMSpM models and the model decomposition method are proved. [ABSTRACT FROM AUTHOR]

A holographic spectrum method (HSM) of multi-phase and multi-layer winding magnetomotive force (MMF) for 12-slot/10-pole combination with fractional-slot concentrated-winding (FSCW) is proposed in this paper. Taking two kinds of traditional winding layout as example, amplitude and phase distribution of the vth harmonic are calculated. The holospectrum of the multi-phase and multi-layer winding are derived based on three-phase single-layer (TP-SL) and three-phase double-layer (TP-DL) holospectrum theory. Then the finite element method (FEM) is used to validate the resultant winding MMF calculated by the holospectrum method. Results show that two methods have a good consistency in changing tendency. Prototype manufacture and test of axial-flux PMSM with a double-three-phase four-layer (DTP-FL) winding have been completed. A load experiment with two groups of resistance is established to validate its output power of axial-flux permanent magnet synchronous machine (PMSM). The temperature distribution of axial-flux PMSM is evaluated with PT100 and infrared thermal imager. The experiments shows that the axial-flux PMSM runs at a relative temperature rise. [ABSTRACT FROM AUTHOR]

A novel three-degree-of-freedom (3-DOF) spherical motor based on the principle of minimum magnetic reluctance is proposed in this paper. This paper firstly introduces the structure of the reluctance spherical motor and explains the principle of 3-DOF motion of the motor in detail. Then, an analytical model for reversible torque-angle characteristics is established to accurately describe a complex nonlinear system of the spherical motor model by using piecewise function nonlinear fitting method. Finally, the simulation results of torque-angle characteristics based on the nonlinear model are compared with those of the 3D finite element method (FEM), which verifies the feasibility of the nonlinear modeling. [ABSTRACT FROM AUTHOR]