Maxwell's Tensor Method Research Articles

Accurate mathematical model of bearingless flywheel motor based on Maxwell tensor method

It is particularly important to build a correct mathematical model to precisely control single winding bearingless flywheel motor. Thus, a new modelling method based on the Maxwell tensor method is present. Different from the virtual displacement theory, there is no need of the detailed derivation and complex theoretical computation and possesses advantages of universality, accuracy, and directness. Before the mathematical model is established, the fringing magnetic path is improved from straight and circular lines to elliptical line. A correction function is taken to obtain an accurate mathematical model based on finite element analysis (FEA). The FEA results show that the model based on the Maxwell tensor method is feasible and has high precision.

Effect of Slot Opening on the Cogging Torque of Fractional-Slot Concentrated Winding Permanent Magnet Brushless DC Motor

Cogging torque will affect the performance of a permanent magnet Brushless DC Motor (BLDCM), thus the reduction of cogging torque is key for BLDCM optimization. In this paper, the phase shifting of cogging torque for a fractional-slot concentrated winding BLDCM is analyzed using the Maxwell tensor method. Moreover, a 9-slot 10-pole concentrated winding BLDCM driven by ideal square waveform is studied with the finite element method (FEM). An effective method to reduce the cogging torque is obtained by adjusting the slot opening. In addition, the influences of different slot openings on back electromotive force (back-EMF), air gap flux density and flux linkage are investigated and experimentally validated using the prototype BLDCM.

SUSPENSION FORCE MODELING AND ELECTROMAGNETIC CHARACTERISTICS ANALYSIS OF AN INTERIOR BEARINGLESS PERMANENT MAGNET SYNCHRONOUS MOTOR

Interior bearingless permanent magnet synchronous motors (IBPMSMs) are a new type of machines having two sets of windings in the stator, offering no lubrication and no mechanical friction, high efficiency, robust rotor construction, hybrid torque production nature and flux-weakening capability. In this paper, the suspension force modeling and the static electromagnetic characteristics of an IBPMSM are studied. The suspension force model of the IBPMSM is established and investigated based on the Maxwell tensor method. And then the static electromagnetic characteristics, including permanent magnet (PM) flux linkage, EMF, inductances, electromagnetic torque and suspension force, are discussed with the finite element analysis (FEA) method. The electromagnetic characteristics of the IBPMSM are very helpful for the design and optimization of the motor. The effectiveness of the proposed suspension force mathematical model is verified by comparing the theoretical results with FEA-based predictions. The work in this paper lays an important foundation for the optimization design and control strategies of the IBPMSM.

Radial force dynamic current compensation method of single winding bearingless flywheel motor

The position of rotor and stator in switched reluctance motor is exchanged to obtain the single winding bearingless flywheel motor (SWBFM), which is more useful for flywheel energy storage with outer rotor. Compared with the switched reluctance motor, bearingless flywheel motor has obvious advantages in cost savings and consumption reducing. The radial force and torque are produced by single windings and the outer rotor could directly drive the flywheel with less mechanical transmission. In this study, a mathematical model of SWBFM is established based on Maxwell tensor method, in addition, the correction factor is present to obtain an accurate mathematical model based on finite element. In energy storage keeping state, the flywheel energy storage system could run on rated speed without the power input. Considering the relationship between the angle and the radial force coefficient, and the difference of radial force coefficient with each tooth pole, radial force dynamic current compensation methods of without β direction constraint and β direction constraint are present to ensure the SWBFM stable suspension under the condition of winding open-circuit fault. The results show that the proposed compensation methods are feasible and have high precision.

Precision Modeling Method Specifically for AC Magnetic Bearings

Compared with dc magnetic bearings, an ac magnetic bearing has obvious advantages in cost savings and reducing power consumption. For more precise control of the ac magnetic bearing, it is particularly important to build a correct mathematical model of radial suspension forces. Due to the working principle of the ac magnetic bearing, it has similarities to the suspension subsystem of a bearingless motor, thus the modeling method for radial suspension forces of the bearingless motor could be referenced for modeling the radial suspension forces of the ac magnetic bearing. This paper presents a new modeling method based on the Maxwell tensor method for radial suspension forces of the ac magnetic bearing. Compared with existing methods, the invention method designed specially for the ac magnetic bearing overcomes inaccuracy and possesses advantages of directness and universality. Taking the ac hybrid magnetic bearing (ac HMB), for example, this paper presents the mathematical modeling process of radial suspension forces with the proposed method. The comparison result between the models established by the equivalent magnetic circuit method (the most classical modeling method for magnetic bearings currently) and by the proposed method shows the high uniformity in their forms of expression (the only difference is the coefficient between them). Being different from the traditional modeling method, we do not need the detailed derivation and complex theoretical computation based on the particular magnetic circuit analysis for this particular case but simply modify several key expressions representing magnetic circuit features in the modeling process with this method. Therefore, the proposed method invented especially for the ac magnetic bearing has the greater advantage of directness and universality than previous modeling method. To illustrate the precision of the proposed modeling approach, the verification experiment is designed and the encouraging experimental results show that the model based on the Maxwell tensor method is more close to the test results comparing with equivalent magnetic circuit method. Thus, the proposed modeling method makes the modeling results on radial suspension forces of the ac magnetic bearing more accurate, universal, and direct.

A novel modeling method for radial suspension forces of AC magnetic bearings

AC magnetic bearings have potential application prospects in high speed situations and low-speed lustration conditions with the advantages of no friction, no wear, no oil lubrication, seals, and low cost, low loss, long life and so on. For overcoming the shortcomings of modeling on radial suspension forces for AC magnetic bearing, such as imprecise model, and lack of directness and generality, a new radial suspension forces modeling method of AC magnetic bearing based on Maxwell tensor method is proposed in this paper, which makes modeling process accurate, direct and universal. The mathematical model of suspension forces for two degrees of freedom of AC hybrid magnetic bearing (HMB) is established with this proposed method, whose expression of suspension forces is proven to in accordance with the expression established by equivalent magnetic circuit method, (the only difference is the coefficient between them), so the correctness of the model and the feasibility of the method are verified by the results. Finally, the control block diagram of experimental system according to this model of two degrees of freedom AC HMB is presented and some related experiment is designed. The correctness of the suspension forces mathematical models of two degrees of freedom of AC HMB is verified by the experiment and the experimental results show that the proposed modeling method is more accurate than the equivalent magnetic circuit method.

A Novel Mathematic Model of Bearingless Switched Reluctance Motors

Radial weight and rotary torque load often demand large winding current in a bearingless switched reluctance motor (BSRM). This will tend to cause magnetic saturation. But traditional mathematic model can not fit for this saturated working state, which has formatted a sever limitation. With a BSRM model in Maxwell, its magnetic saturation characteristics were analyzed, and a critical criterion was computed. Then a novel mathematic model was established with Maxwell tensor method and confirmed by Finite element computing results. It could fit for both unsaturated and saturated working state, and also satisfy reversibility condition. These were both very useful for nonlinear decoupling with state feedback method and wide application in industry process. This proposed modeling and analyzing method could also provide useful references for motor’s optimization design and control algorithm research.

Magnetic force and torque calculations from complementary or self-dual approaches. A coenergy-based methodology toward full accuracy control

This paper deals with duality based approaches of field computations. It presents two methods that allow to obtain upper bounds for the error on the forces or torques. The first one is based on a double evaluation of the global coenergy for two values of the position. The second one resembles the popular Maxwell's tensor method and requires the field computation only once, but respecting an additional rule. For both methods, the force or torque are considered in respect of their average value on an interval of displacement, taken as configuration parameter.

A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness

The paper will present two general methods for the deduction of global information from the final result of the finite element computation of an electromagnetic device. The first one, called the local jacobian derivative, may be used for evaluation of the derivative of any integral quantity versus the parameter of motion of a rigid body. Typically, this method when applied to electromagnetic systems, can be used for the computation of magnetic force or torque by virtual-work principle. Compared with the popular Maxwell's tensor method, this procedure is easier to implement in a finite element package especially for 3D problems. The second method which is based on a stationary property of the field solution, allows the evaluation of a second order derivative of any integral quantity. For instance, computation of the stiffness of a magnetic system (derivative of a force or a torque) may be achieved as the second order derivative of the magnetic energy. It may be pointed out that this method requires the field computation once for a linear problem as well as for a non-linear one.