Modeling switched-reluctance Machines by decomposition of double magnetic saliencies

This paper presents a novel analytical model for a switched-reluctance machine (SRM) based on decomposition of its inherent double joint magnetic saliencies due to rotor and stator salient poles and saturation of magnetic field at high stator currents. With this method, the magnetic characteristics of the motor, such as flux linkage and incremental inductance, are decomposed to vector functions of rotor position and phase current. Dynamic state and torque equations for the SRM are derived on the basis of this representation. The proposed model is appropriate for online identification and for sensorless position control algorithms. It is easy to implement and computationally efficient. Comparison of the predicted motor magnetic characteristics to machine data from finite-element analysis verifies the accuracy of the model.     

Research on Torque Calculation Method of Permanent-Magnet Spherical Motor Based on the Finite-Element Method

In this paper, the finite-element method (FEM) is used to calculate the spinning torque of the permanent-magnet (PM) spherical motor. Three-dimensional (3-D) FE model of the PM spherical motor is established. Spinning torque distribution on the spherical surface and its variation curve on the equator are obtained respectively. In order to avoid the complicated torque calculation process under 3-D magnetic field and thus reduce the computational burden, the torque calculation method based on the 2-D conversion model is proposed. This method equivalently simplifies the magnetic field of the spherical PMs and the shape of cylindrical stator windings to be simulation parameters of the 2-D conversion model. With these parameters, 2-D conversion model of the PM spherical motor is established. Spinning torque variation curves obtained by the 3-D model and the 2-D conversion model respectively are compared and the results agree extremely well. By comparing the maximum static torque (MST) obtained under different configuration parameters of the PM spherical motor, it is found that the errors are within the allowable range. Therefore, the reliability of the proposed torque calculation method in the paper is verified. Finally, based on the 2-D conversion model, variation curves of the MST with the length of the air gap, the ampere turns, the length of stator windings and the outer radius of stator windings are obtained, and they are validated by those based on the 3-D model. These results can provide the basis for the optimization of the PM spherical motor.      

Apparatus for experimental simulation of magnetic flux and power loss distribution in a turbogenerator stator core

An experimental model recently built to simulate magnetic flux and power loss distribution conditions in a large turbogenerator stator core is described. The model consists of a stack of laminated steel segments of around 0.5 cm depth. It is excited by a three-phase winding wound in the stator slots and arranged to allow easy replacement of stator segments. A plain disc stationary laminated steel "rotor" provides a low reluctance path across the machine. Results of various performance tests are presented and it is concluded that the pattern of flux distribution displayed by the model is of the correct general form. Typical results are included from measurements of local flux using small search coils and of loss using miniature thermocouples. The model should be valuable for studies of the effects of changes in various design parameters where its representation of local conditions is likely to be superior to currently available mathematical models.     

Principle of Operation and Feature Investigation of a New Topology of Hybrid Excitation Synchronous Machine

We present a new topology of hybrid excitation synchronous machine (HESM) and describe operational principles and features of the new configuration. Using the radial/axial distribution of the magnetic field, we develop an equivalent magnetic circuit model. We obtain magnetic flux, flux density, and induced voltage with various electrical magnetomotive forces by calculating the nonlinear magnetic circuit equation. We studied the Influence on the radial magnetic field of the axial magnetic field by 3-D finite-element method. The results are in good agreement with calculation by our magnetic circuit model. Our findings indicate that the air-gap flux density of a flux-concentrating HESM is high and the magnetic field in the air gap can be successfully regulated. Experimental results of 3 kVA prototype machine verify the feasibility of the structure and the correctness of our analysis.      

Calculation and Analysis of Stator End-Winding Leakage Inductance of an Induction Machine

This paper proposes an improved method for calculating the value of and for analyzing the frequency-dependence of the stator end-winding leakage inductance of an induction machine. The method was based on the stored magnetic energy, which was calculated by a 3-D time-harmonic finite element analysis. In this method, there were no rotary parts in the model of the simulated machine. The results of the analysis show that the stator end-winding is capable of influencing the end of the active region of the machine whereas the influence on the central part of the active region is small. In addition, the phenomenon that the stator end-winding leakage inductance, as well as the magnetic energy in the machine, relates to the frequency of the stator current is explored.      

Characterization of noise and vibration sources in interior permanent-magnet brushless DC motors

This work characterizes electromagnetic excitation forces in interior permanent-magnet (IPM) brushless direct current (BLDC) motors and investigates their effects on noise and vibration. First, the electromagnetic excitations are classified into three sources: 1) so-called cogging torque, for which we propose an efficient technique of computation that takes into account saturation effects as a function of rotor position; 2) ripples of mutual and reluctance torque, for which we develop an equation to characterize the combination of space harmonics of inductances and flux linkages related to permanent magnets and time harmonics of current; and 3) fluctuation of attractive forces in the radial direction between the stator and rotor, for which we analyze contributions of electric currents as well as permanent magnets by the finite-element method. Then, the paper reports on an experimental investigation of influences of structural dynamic characteristics such as natural frequencies and mode shapes, as well as electromagnetic excitation forces, on noise and vibration in an IPM motor used in washing machines.     

Design Consideration to Reduce Cogging Torque in Axial Flux Permanent-Magnet Machines

In designing new topologies for permanent-magnet machines based on rare earth magnets, it is necessary to diminish the undesired cogging torque. This paper presents a 3-D finite-element analysis to evaluate the effect of magnet shape and stator displacement on cogging torque reduction, for axial flux machines. It analyzes the final electromagnetic torque for the proposed configurations. Finally, it presents the resultant cogging torque waveform for a 5.0 kW prototype, based on our optimization techniques.     

Detailed study of the magnetic circuit in a longitudinal flux permanent-magnet synchronous linear generator

We present the results of a theoretical study of the magnetic circuit of a longitudinal flux permanent-magnet synchronous linear generator. In our study, we used a coupled field and circuit model solved by a time-stepping finite-element technique to analyze the machine. We investigated the effects of different permanent-magnet shapes and sizes, as well as different stator steel geometries. We noted a significant difference in performance for different magnet shapes. Our results also illustrate how small changes, on a millimeter scale, will affect the flux path, and thereby the overall performance of the machine, highlighting the importance of stator steel geometry.     

Four-quadrant instantaneous torque control of switched reluctance machine at low speed based on co-energy control

An instantaneous torque control scheme of switched reluctance machines for four-quadrant operation at low speed based on co-energy considerations is presented. The co-energy is estimated online with a co-energy estimator, which only requires easily obtainable parameters such as the machine terminal quantities and the machine characteristics at low current. By regulating the co-energy while tracking a one-dimensional co-energy profile, the torque contribution of each phase of the switched reluctance machine can be controlled and optimised. Thus, the requirement of pre-measured data is reduced when compared to current-profiling methods. The closed-loop control system is analysed and then designed based on internal model control. The excitation sequence and torque sharing function for four-quadrant operation to produce smooth torque output are also presented. The operation limits of the scheme are examined. Computer simulation and experimental results confirm that the proposed scheme can be exploited to reduce the high-frequency torque ripples significantly.     

Analytical Computation of the Full Load Magnetic Losses in the Soft Magnetic Composite Stator of High-Speed Slotless Permanent Magnet Machines

This paper presents an analytical model for predicting the stator full load magnetic losses in high-speed slotless permanent-magnet machines with surface-mounted magnets on the rotor and a stator core made of isotropic and conductive soft magnetic composite material (SMC). The losses are derived from the computation of the two-dimensional magnetic field distribution created by the rotor magnets, the currents in the stator windings and the eddy currents that circulate in the SMC stator core, according to the time and space harmonics. Both eddy currents and hysteresis losses are computed. The model is cross-validated by 2-D FE analysis in terms of magnetic field distribution and eddy currents losses. 3-D FE simulations are also carried out to quantify the end-effect on the stator no-load eddy current losses. The developed model is an efficient machine design tool, used here to quantify the variations of both the eddy currents and hysteresis losses under full load operation when the control angle is modified.      

Flux level selection in vector-controlled dual stator winding induction machines

The dual stator winding induction machine has two three-phase stator windings with dissimilar number of poles. This machine can be regarded from the point of view of control as two different induction machines coupled by a rotor. To improve the machine's performance, the total flux generation must be correctly distributed between the two windings. This study focuses on the flux distribution necessary to achieve a nearly maximum torque per stator ampere operation, which is indicated in applications requiring high dynamics. In addition, efficiency and voltage utilisation will be also considered.     

Development of a High-Speed Permanent-Magnet Brushless DC Motor for Driving Embroidery Machines

We describe the development of a permanent-magnet (PM) brushless DC motor for driving high-speed embroidery machines by employing advanced design and analysis techniques. In the design of the motor, magnetic field finite-element analyses accurately calculate the key motor parameters such as the air-gap flux, back electromotive force (EMF), and inductance. Using the numerical magnetic field solutions, a modified incremental energy method calculates the self and mutual inductances of the stator windings. A phasor diagram is derived to compute the motor's steady-state characteristics. To predict the dynamic performance and increase the prediction accuracy, a Simulink-based model simulates the motor performance with the real waveforms of applied phase voltage, back EMF, and current. The motor prototype tested with both a dynamometer and a high-speed embroidery machine validated the theoretical calculations.     

Design of a wound-field flux switching machine with dual-stator to reduce unbalanced shaft magnetic force

Abstract

This paper presents the design and experimental verification of an outer-rotor, wound-field flux switching machine for in-wheel traction applications. The 12-stator slot, 7-rotor pole topology was selected because it produces higher torque and fewer back-electromotive force voltage harmonics than the other topologies. The machine was designed on the basis of the physical dimension limitations for in-wheel traction in a lightweight electric scooter. Because this machine exhibits shaft radial magnetic force caused by the odd rotor poles, a novel dual-stator motor structure is proposed to reduce this force. The finite element analysis calculation results demonstrated that the shaft radial force can be reduced to nearly 0 with this design, whereas the generated torque reduced only by 3%. The effectiveness of the design was also verified through the experiments that compared the vibrations of the original and the dual-stator motors. The vibration of the dual-stator motor was substantially lower than that of the original motor.     

Three-dimensional analytic model of permanent magnet axial fluxmachine

A three-dimensional (3-D) magnetic field problem in an axial flux machine with a toroidal winding is considered. The precise solutions generated by the integral transform and Fourier methods in elementary subregions are joined using the iterative Schwartz algorithm. The comparison between two dimensional and 3-D models is performed and a correction factor taking into account the radial variation of the magnetic flux is given     

Influence of an aperture on the performance of a two-degree-of-freedom iron-cored spherical permanent-magnet actuator

This paper describes a computational and experimental study of a two-degree-of-freedom spherical permanent-magnet actuator equipped with an iron stator. In particular, it considers the effect of introducing an aperture in the stator core to facilitate access to the armature. The resultant magnetic field distribution in the region occupied by the stator windings, the net unbalanced radial force, and the resulting reluctance torque are determined by three-dimensional magnetostatic finite-element analysis. The predicted reluctance torque is validated experimentally, and its implications on actuator performance are described.     

Magnetically induced vibration in a permanent-magnet brushless DC motor with symmetric pole-slot configuration

The paper reports a numerical and experimental study of magnetically induced vibration associated with rotor/stator eccentricity and imperfect magnetization for 8-pole 6-slot symmetric brushless dc (BLDC) motors. Magnetic forces and cogging torque are calculated for various slot angles by using the finite-element method (FEM). The results show that there is an optimal slot angle for minimum cogging torque, but this slot angle is not optimal for reducing magnetic forces. In the idle acoustics test, the motors with reduced magnetic forces show clear reduction at the expected frequencies while the motors with minimum cogging torque show no change at the cogging torque frequency, which implies unbalanced magnetic forces have greater effect on actual vibration of the spindle motor than cogging torque. The results show that the proper direction in motor design is to reduce unbalanced magnetic forces when both cogging torque and unbalanced magnetic forces are not achievable simultaneously.     

Analysis of electromagnetic performance of flux-switching permanent-magnet Machines by nonlinear adaptive lumped parameter magnetic circuit model

A nonlinear adaptive lumped parameter magnetic circuit model is developed to predict the electromagnetic performance of a flux-switching permanent-magnet machine. It enables the air-gap field distribution, the back-electromotive force (back-EMF) waveform, the winding inductances, and the electromagnetic torque to be calculated. Results from the model are compared with finite-element predictions and validated experimentally. The influence of end effects is also investigated, and optimal design parameters, such as the rotor pole width, the stator tooth width, and the ratio of the inner to outer diameter of the stator, are discussed.     

Dynamic performance of a brushless DC tubular drive system

The authors describe the computer-aided analysis of the dynamic performance of a tubular linear machine system with permanent magnetic cogging forces. These forces include not only the conventional tooth cogging force apparent in both linear and rotary machines but also a force unique to permanent magnet linear machines that is due to the finite length of the stator. System equations which describe both the machine and the inverter supply are solved by a step-to-step numerical method to find the dynamic performance of the machine in an oscillator mode. The work is verified by experimental results obtained for a practical model     

Comparison of the Unbalanced Magnetic Pull Mitigation by the Parallel Paths in the Stator and Rotor Windings

An eccentric rotor creates an electromagnetic force between the rotor and stator of an electrical machine. This force tends to further increase the rotor eccentricity and may severely degrade the performance of the machine, causing acoustic noise, vibration, excessive wear of bearing, rotor and stator rubbing, and so forth. Parallel connections are known to be a simple yet effective remedy for the problems associated with rotor eccentricity. We have investigated two common types of electrical machines running with eccentric rotors. We examined operation over a wide whirling frequency range. We numerically evaluated and compared the effects of parallel connections in the stator and rotor windings on the eccentricity force. We found that the parallel stator windings can be more effective in mitigating the unbalanced magnetic pull than the rotor cage (or damper winding), which normally has many more parallel circuits.     

Optimizing the overlap between the stator teeth of a claw pole transverse-flux permanent-magnet Machine

The paper presents a three-dimensional finite-element analysis-based optimization of the overlap between adjacent stator teeth of a claw pole transverse flux permanent magnet machine (TFPM). Two major optimization criteria are considered: 1) the maximization of the output torque and 2) the minimization of the cogging torque. The paper shows that an overlap of almost 30% fulfills both optimization criteria.