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This paper aims to propose a novel mathematical model of bearingless switched reluctance motor (BSRM). This model differs from conventional mathematical models in the calculation of torque and suspension forces. Conventional mathematical models neglect the coupling relationship between the α- and β-axes or ignore the magnetic saturation of the Si-Fe material. This study considers these issues simultaneously. Additionally, considering the air-gap edge effect, the fringing coefficient is used to establish a high-precision mathematical model.

An innovative mathematical model of BSRM based on the Maxwell stress method was established by selecting an appropriate integration path. The fringing coefficient of the air-gap was computed based on the finite element analysis results at the aligned position of the stator and rotor poles. Using the least squares fitting method, the piecewise fitted magnetization curve of the Si-Fe material was utilized to calculate flux density.

The appropriate integration path of the Maxwell stress method was selected, which considered the coupling relationship of the suspension forces in the α- and β-axes and was closer to the actual situation. The fringing coefficient of the air-gap improved the calculation accuracy of air-gap flux density. The magnetomotive force was consumed by the magnetic resistance of the stator and rotor poles considering the magnetic saturation.

A novel mathematical model of BSRM is proposed. Different from conventional mathematical models, the proposed model can effectively solve the coupling relationship of the suspension forces in the α- and β-axes. Additionally, this model is consistent with the actual situation of motor as it includes a reasonable calculation of the air-gap flux density, considering the air-gap edge effect and magnetic saturation.

This paper aims to establish a piecewise Maxwell stress analytical model of bearingless switched reluctance motor (BSRM) for the full rotor angular positions. The proposed model varies from the existing models, which are only applicable to the partial-overlapping positions of stator and rotor poles. By extending the applicable rotor angular positions, this model provides a basic analytical model for the multi-phase excitation control of BSRM.

The full rotor angular positions are classified into the partial-overlapping positions and the non-overlapping positions. At first, two different air gap subdividing methods are proposed, respectively, for the two-position ranges. Then, different integration paths are selected accordingly. Furthermore, two approximate methods are presented to calculate the average flux density of each air gap subdivision. Finally, considering the mutual coupling between the two perpendicular radial suspension forces, a piecewise Maxwell stress analytical model is derived for the full rotor angular positions of BSRM.

A piecewise Maxwell stress analytical model of BSRM is built for the full rotor angular positions, and applicable to the multi-phase excitation mode of BSRM. For the partial-overlapping positions and the non-overlapping positions, two sets of air gap subdividing methods, integration paths and approximate calculation methods of air gap flux densities are proposed, respectively. The accuracy and reliability of the proposed model are verified by the finite element method.

The piecewise Maxwell stress analytical model of BSRM for the full rotor angular positions is proposed for the first time. The novel air gap subdividing methods, integration paths, approximate calculation methods of air gap flux densities and the coupling between the two radial suspension forces are adopted to improve the modeling accuracy. As the applicable range of rotor angular position is extended, this model overcomes the limitation of the existing models only for single-phase excitation mode and contributes to the accurate control of BSRM multi-phase excitation mode.

The novel bearingless switched reluctance motor (BSRM) is proposed recently, which is different from the conventional BSRM in the stator structure and suspension winding arrangement. The reduced number of suspension windings makes the novel BSRM much simpler, so that the control circuit and algorithm are greatly simplified when compared to those of the conventional BSRM. This paper for the first time proposes the novel BSRM's analytic model, including the mathematical relationships among the winding currents, rotor angle, radial forces, and motor torque, to further achieve the suspending forces and torque control. The paper aims to discuss these issues.

The magnetic equivalent circuit method is employed to obtain the self-inductances and mutual-inductances of the motor torque windings (main windings) and suspension windings (control windings). The straight flux paths are combined with the elliptical fringing flux paths to calculate the air-gap permeances, and the stored magnetic energy. Then, the mathematical expressions of radial forces and torque are derived. A novel BSRM prototype is analyzed through using the proposed analytical model and the finite element model. The results of both methods are compared to verify the proposed mathematical model.

The proposed mathematical model of the novel BSRM considering unsaturated magnetic circuits is verified by finite-element analysis results.

The mathematical model represents the situation of magnetic circuit unsaturated and is not suitable for the magnetic circuit saturation. It cannot be used to control the motor which is working in the deep magnetic circuit saturation region.

Building mathematical model is a necessary step for the motor's suspension and rotating control. The built model provides the fundamental for the preliminary control algorithm and experimental study of this novel BSRM.

For the first time, the novel BSRM's mathematical model is proposed. It provides necessary fundamental for the motor's further analysis, design, and suspending and rotating controls.

This paper is concerned with the design and analysis of a bearingless motor.

The bearingless motor is obtained by a regular three-pole active magnetic bearing with an intentionally attached unbalanced mass on the rotor. It is the unbalanced mass that will generate the rotational torque for the motor function. Modeling and control of the unbalanced mass-type bearingless motor have been considered.

It is found through simulations that both functions of motor and magnetic bearing can indeed be achieved in this system.

This novel bearingless motor requires no additional windings and permanent magnets. Thus, it can greatly reduce the cost and design of the bearingless motor.

This paper seeks to propose a novel bearingless switched reluctance motor (BSRM).

The operating principle and structure characteristics of the proposed three‐phase 12/8‐pole BSRM is analyzed in detail. Finite element method‐based calculations are applied to a prototype and some important characteristics are obtained, including radial force, static torque, air‐gap magnetic flux density, and effect of control winding current on the torque, where magnetic saturation is taken into account by using a nonlinear B‐H curve.

On the basis of the simulated results, it can be concluded that the proposed BSRM presents an excellent performance in the suspending force and in the torque. The analyzed results show that the two control‐winding currents can effectively control the radial suspending forces and produce negligible effect on the motor torque, which is mainly produced by the main‐winding currents.

In this paper, a novel BSRM is proposed. Instead of the six sets of radial suspending control windings required by conventional three‐phases BSRM, the proposed structure requires only two sets of suspending control windings, regardless of the phase number, leading to a simpler power converter with less power switches, thus lowering the overall system cost.

An improved analytical method for calculating the natural frequencies of a switched reluctance motor (SRM) stator is proposed in this paper. The method is different from traditional analytical methods, which only consider the influence of mass of the stator poles and windings on the natural frequencies of the SRM stator. This paper aims to consider the influence of stiffness and mass of the stator poles and windings simultaneously and reasonably.

An innovated analytical method based on the electromechanical analogy method is presented. In the proposed analytical formulae for calculating the natural frequencies, the influence of the windings on natural frequencies is considered by using the springs to simulate the flexible connection between the stator core and windings, and the stator poles are treated as both additional mass and additional equivalent stiffness. Both three-dimensional (3D) finite-element analysis (FEA) and experimental modal analysis results validate the improved method.

The influence of the mass and stiffness of stator winding is considered by using the springs to simulate the flexible connection between the stator core and windings, and the stator poles are treated as both additional mass and additional equivalent stiffness. The traditional analytical method only considers the influence of mass. Therefore, the calculation results are comparatively lower than 3D FEA results and may lead to a large error. The 3D FEA and experimental modal analysis confirm that the proposed method has good precision for low-order natural frequency calculation of SRMs.

An improved analytical method for calculating the natural frequencies of an SRM stator is proposed. Unlike the traditional analytical method, the proposed method can consider the influence of stiffness and mass of the stator poles and windings. This method is valuable for designers to predict the natural frequencies accurately.

The purpose of this paper is to achieve the multi-objective optimization design of novel tubular switched reluctance motor (TSRM).

First, the structure and initial dimensions of TSRM are obtained based on design criteria and requirements. Second, the sensitivity analysis rules, process and results of TSRM are performed. Third, three optimization objectives are determined by the average electromagnetic force, smoothing coefficient and copper loss ratio. The analytic hierarchy process-entropy method-a technique for order preference by similarity to an ideal solution-grey relation analysis comprehensive evaluation algorithm is used to optimize TSRM. Finally, a prototype is manufactured, a hardware platform is built and static and dynamic experimental validations are carried out.

The sensitivity analysis reveals that parameters significantly impact the performance of TSRM. The results of multi-objective optimization show that the average electromagnetic force and smoothing coefficient after optimization are better than before, and the copper loss ratio reduces slightly. The experimental and simulated results of TSRM are consistent, which verifies the accuracy of TSRM.

In this paper, only three optimization objectives are selected in the multi-objective optimization process. To improve the performance of TSRM, the heating characteristics, such as iron loss, can be considered as the optimization objective for a more comprehensive analysis of TSRM performance.

A novel motor structure is designed, combining the advantages of the TSRM and the linear motor. The established sensitivity analysis rules are scientific and suitable for the effects of various parameters on motor performance. The proposed multi-objective optimization algorithm is a comprehensive evaluation algorithm. It considers subjective weight and objective weight and fully uses the original data and the relational degree between the optimization objectives.

To investigate transverse vibration of the eccentric rotor in a 12/8 poles switched reluctance motor (SRM), a transverse analytical vibration model is built by finite element method (FEM) under the interaction of radial magnetic resultant and vibration displacement. External forces, including radial magnetic resultant and centrifugal force, are also derived in detail, according to the variation of airgap and current and other intermediate parameters with rotation angle.

The transverse vibration response of the eccentric rotor including radial magnetic resultant and vibration displacement is solved by Newmark-β method, after inputting the currents of three phase windings under angle position control strategy. The basic characteristics of radial magnetic resultant and vibration displacement are reflected in time and frequency domain.

The magnetic resultant vector of the eccentric rotor presents multi-petals star geometric shape. The frequency distribution of magnetic resultant relates to rotation speed, current waveform and the least common multiple of the stator and rotor teeth. However, the frequency distribution of the vibration displacement also relates closely to the first-order critical whirl speed of the rotor. When the rotor is running at certain speeds, it will display superharmonic resonance and show abundant displacement locus.

By using this analytical model and solving process proposed in this paper, the nonlinear coupled vibration response of the eccentric rotor in SRM can be analyzed and discussed rapidly; only the stator’s winding currents obtained by experiment or electromagnetic simulation is needed as input.

The purpose of this paper is to propose an analytical model for the calculation of forces ripples in bearingless permanent magnet motor.

The model is based on a spectral modeling of the forces based on a spectral analysis of the air-gap flux density.

The proposed methodology allows the prediction of the ripples of the levitation according the design of the machine and the topology of the winding. It can be used in the design procedure of bearingless motor in order to avoid mechanical resonance of the rotor shaft.

This model cannot be used for high saturated machines.

The main originality of this paper consists in the evaluation of the field harmonics according to their sources and the contribution of the different harmonics to the force ripples. This can help the designer to focus on reducing or eliminating only the harmonics of flux density which create the force ripples.

The purpose of this paper is to propose a new three-phase switched reluctance motor (SRM), and achieve high-torque and low-cost. This new SRM's winding configuration uses the double-layer distributed windings, which is different from the conventional SRM's single tooth coils.

The operating principle of new SRM is analyzed, and the voltage equation and the generated torque are deduced. Finite element method (FEM) and finite element circuit coupled method are utilized to evaluate the new motor's operating performances. The two dimensional (2D) frequency response analysis model is employed in the FEM model. Based on the 2D frequency response analysis model, the magnetic field distribution, self-inductance, and mutual-inductance for the new SRM are analyzed in detail. A co-simulation model using FE analysis package and Matlab-Simulink is proposed to simulate the new SRM drive. The simulated and experimental results verify the new SRM.

For the new SRM with double-layer distributed windings, a co-simulation method is proposed to analyze its characteristics. The new SRM presents lower torque ripple coefficient and generates larger torque than the conventional SRM, with three-wire and standard full bridge power converter, rather than six-wire and asymmetric half-bridge converter for conventional SRM.

This paper proposes a new SRM with the double-layer distributed windings driven by a standard full bridge inverter. In order to calculate dynamic characteristics of the new SRM, a co-simulation method using FEM and Simulink is proposed to simulate the new SRM drive, where the power inverter and the current chopping control algorithm are implemented.