Improved Analytical Model of a Permanent-Magnet Brushless DC Motor

In this paper, we develop a comprehensive model of a permanent-magnet brushless DC (BLDC) motor. An analytical model for determining instantaneous air-gap field density is developed. This instantaneous field distribution can be further used to determine the cogging torque, induced back electromotive force, and iron losses in the motor. The advantage of analytical models is that they can be readily used for optimization of BLDC motor because they are fast.      

Demagnetization Assessment for Three-Phase Tubular Brushless Permanent-Magnet Machines

We describe an analytical technique for assessing the risk of partial demagnetization in tubular permanent-magnet (PM) machines. The technique establishes analytical expressions for the open-circuit and armature reaction fields in the cylindrical coordinate system and superposes the fields in the permanent-magnet regions to determine the extent to which the magnets may be partially irreversibly demagnetized. We have applied the technique to a quasi-Halbach magnetized tubular PM machine equipped with a modular stator winding, and have validated the predictions by finite-element analysis. We found that partial demagnetization may occur even under an open-circuit operating condition when the machine is operating at high temperature. We propose alternative Halbach magnetization distributions that improve the demagnetization withstand capability. The analytical technique provides a computationally efficient tool for identifying regions that are prone to partial demagnetization and for assessing the consequences. It enables the risk of demagnetization to be fully assessed at the design stage so as to achieve a robust machine, particularly when operating in harsh environments.      

Simplified Design Methodology for a Slotless Brushless DC Motor

The paper presents a simplified analytical method to design a small two-pole slotless brushless dc motor. Using only a few approximations, the motor analytical model is formulated to generate a system of equations. The system can be solved analytically, producing a motor design for given specifications. The method is used to design a motor with the specifications 150 W, 10 000 rpm, and 18 V     

Minimizing Thrust Fluctuation in Moving-Magnet Permanent-Magnet Brushless Linear DC Motors

We present the results of our research on the factors that cause thrust fluctuation in moving-magnet-type permanent-magnet brushless DC linear motors (PMBLDCLM). We combined Fourier transforms and finite-element models to obtain the power spectra of three components of the detent force. We developed a method of optimizing magnet width to minimize the detent force on the basis of harmonic analysis. To verify this method, we designed several motor models with different magnet widths and analyzed them by finite-element methods. The calculations and experimental results prove that thrust fluctuation of the motor can be effectively reduced with our method     

In-Depth Study of the Torque Constant for Permanent-Magnet Machines

The torque constant, together with the back-EMF constant, was originally used in permanent-magnet dc commutator (PMDC) motors to couple electric circuit equations with mechanical equations. It is still an open question how these two constants should be defined in brushless dc (BLDC) motors and permanent-magnet (PM) ac motors. We present an in-depth study of these two constants, and conclude that the definition based on the $dq$ axes is applicable for the dynamic motion control of not only PM ac motors, but also BLDC motors.      

Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines

Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.      

Analysis of Relationship Between Abnormal Current and Position Detection Error in Sensorless Controller for Interior Permanent-Magnet Brushless DC Motors

We have analyzed the characteristics of terminal voltages used to detect rotor position in interior permanent-magnet (IPM) brushless DC (BLDC) motors in sensorless control by employing a two-phase conduction method. We found that a detected zero crossing point (ZCP) of the open phase voltage advances the real rotor position due to additional voltage components caused by variation of inductance with rotor position. We conclude that the amount of position error is related to rotor saliency, load, and motor speed. We also present the relationship between abnormal currents and amount of position errors in the sensorless controller by using simulations that take into account additional voltages in our model of terminal voltages and motor neutral voltage as well as experiments with a position sensor. We verified the validity of our analysis on IPM motors having various motor parameters under sensorless control.      

无刷直流电动机自适应模糊变结构速度控制器的研究

设计了一种无刷直流电动机的新型高性能自适应模糊变结构速度控制器。该控制器具有如下优点：减小了变结构控制带来的抖振,在保证系统稳定性的同时加快了响应速度,解决了传统的变结构控制器设计需要事先测定扰动量范围的问题,在线调整模糊控制器输出的自适应算法简化了模糊控制器的设计。实验结果证明这是一种无刷直流电动机的高性能速度控制器。     

永磁无刷直流电动机换相脉动转矩及抑制方法

通过分析永磁无刷直流电动机的换相过程,得到了电动机绕组电流换相产生的脉动转矩表达式。为了验证理论分析的正确性,首先对电流换相产生的脉动转矩及相关特性进行了仿真,然后采用永磁旋转角加速度传感器对电动机轴上的脉动转矩进行了实际测量,验证了电机输出转矩中的脉动转矩分量的客观存在性及相关特性。针对脉动转矩,提出了一种基于峰谷互补的抑制方法,并建立了对应的实验平台开展了实验研究,理论分析和实验测量取得了一致的结果,从而证明了该抑制方法的正确性。     

Comparison of Demagnetization Models for Finite-Element Analysis of Permanent-Magnet Synchronous Machines

We have studied a few simple demagnetization models, which are quick and easy to implement in finite-element calculations, and compared them with measured recoil behavior of Nd-Fe-B magnet material, also using a hysteresis model for comparison. The models are used to estimate post-demagnetization performance of an overloaded surface magnet synchronous machine. Two of the simple models, the sloped linear model and the exponent function model, give the most accurate results without significantly increasing the computation time.     

A Quantitative Comparative Analysis of a Novel Flux-Modulated Permanent-Magnet Motor for Low-Speed Drive

A novel low-speed flux-modulated (FM) permanent-magnet (PM) motor that breaks the traditional design rule, which stipulates that the number of stator pole pairs and the number of rotor pole pairs must be the same, is proposed. The FM motor has a special physical structure with iron segments in the air gap to modulate the magnetic field. In the design, the free space between adjacent stationary iron segments also acts as ventilating ducts to help improving the heat dissipation and ventilation of the motor. Its cogging torque is very small. In this paper, a rule for comparing the power density of electric motors is proposed. The performance of the FM motor is compared with those of a magnetic-geared PM motor, a traditional PM motor, and a fractional-slot PM motor by using magnetic field finite-element analysis.     

Using Modular Poles for Shape Optimization of Flux Density Distribution in Permanent-Magnet Machines

A modular configuration for a type of permanent-magnet pole is proposed for use in permanent-magnet (PM) machines. The pole consists of three or more permanent-magnet pieces. The main objective of this configuration is to shape the air-gap flux density distribution produced by the pole. An optimization procedure based on an analytical model is then used to determine the optimal pole specifications. A finite-element method is finally carried out to evaluate the proposed configuration. Extensive investigations on a linear permanent-magnet motor demonstrate that the proposed configuration reduces flux density as well as back electromotive force harmonics. This pole configuration also results in more efficient use of PM materials.      

Properties of Cogging Torque, Starting Torque, and Electrical Circuits for the Single-Phase Brushless DC Motor

A single-phase brushless dc motor requires an asymmetric air gap to eliminate the dead point where the excitation net torque is zero. In this paper, we use the finite-element method (FEM) to analyze the properties of cogging torque, starting torque, and electrical circuits. Others have discussed the influences of various asymmetric air gaps on these properties. However, the optimum asymmetric air-gap condition is very difficult to find. Here, we describe an optimum asymmetric air-gap structure that not only produces an optimum starting torque but also reduces the cogging torque to a tolerable range. We compare simulation results with the measurement results to illustrate the accuracy of the FEM model.      

Selection of Materials for High-Speed Motor Rotors

We present strength and fatigue characteristics of materials suitable for high-speed motor rotors used in centrifugal compressors. We established that laser shock peening efficiently produces deep compressive stresses and significantly decreases the fatigue crack growth rate in titanium alloys. For titanium alloys of all types considered, the microstructure of the heat-affected zone after laser treatment significantly differs from the microstructure of the original alloy. Grain coarsening occurs both in unalloyed titanium and in near-alpha, alpha–beta, near-beta, and metastable alloys. For practical applications, titanium alloys require additional heat treatment. In particular, aging and mechanical treatment are used for increasing strength characteristics.     

Application of Schwarz-Christoffel Mapping to Permanent-Magnet Linear Motor Analysis

Several well-known analytical techniques exist for the force profile analysis of permanent-magnet linear synchronous motors. These techniques, however, make significant simplifications in order to obtain the magnetic field distribution in the air gap. From the field distribution, the force profile can be found. These widely used techniques provide a reasonable approximation for force profile analysis, but fail to give really accurate results in the sense of the exact shape of the force profile caused by effects that due to simplification are not fully included. To obtain the exact shape for the force profile in these cases, the computationally expensive finite-element method (FEM) is often applied. In this paper, an elegant semianalytical approach is presented to acquire the force profile. First, the magnetic field distribution in the air gap is determined by means of Schwarz-Christoffel (SC) mapping. The SC mapping allows a slotted structure of the machine to be mapped to a geometrically simpler domain for which analytic solutions are available. Subsequently, the field solution in the slotted structure can be determined by applying the mapping function to the field distribution in the simplified domain. From the resulting field distribution, the force profile is calculated by means of the Maxwell stress tensor. The results are compared with those from the commonly used equivalent magnetic circuit modeling and 2-D FEM software to demonstrate the accuracy which can be reached by application of the SC method.     

Electromagnetic Forces Acting on the Planar Armature of a Core-Type Synchronous Permanent-Magnet Planar Motor

The core-type synchronous permanent-magnet planar motor (SPMPM) discussed in this paper includes one or more planar armatures each of which contains two sets of three-phase windings named ${rm x}$-winding and ${rm y}$-winding. For each planar armature, a magnetic field energy equation is established first. This equation describes the mechanism of the coupling between the permanent-magnet array, the ${rm x}$-winding and the ${rm y}$ -winding in the core-type SPMPM. By using virtual work principle, ${rm x}$-direction thrust force, ${rm y}$ -direction thrust force and vertical force acting on the planar armature are modeling analytically. For eliminating the coupling in these force models, the excitation flux linkages and phase currents are all transformed into ${rm d}hbox{-}{rm q}$ synchronous reference frame. From the decoupling force equations, some characteristics of the vertical component of force on the planar armature are obtained. The electromagnetic force model is helpful for the design of the contactless planar bearing and the servo control system of the SPMPM.      

Inductance Calculations of Permanent-Magnet Synchronous Machines Including Flux Change and Self- and Cross-Saturations

Accurate inductance calculation of permanent-magnet synchronous machines is a relevant topic, since the inductances determine a large part of the electrical machine behavior. However, the inductance calculation, as well as the inductance measurement, is never a completely straightforward task when saturation occurs. In this paper, the total flux in the $d$ and $q$ axes are obtained from finite-element method or measurements and therefore include saturation and cross-couplings. The inductances are obtained from analytical post-processing based on an equivalent magnetic circuit. The originality of this method is that it accommodates the changes in the magnet flux and the inductances with the level of saturation. The resulting inductance values are the ones seen by the converter or the grid, as found by a more accurate approach.      

Analytical Calculation of No-Load Voltage Waveforms in Machines Based on Permanent-Magnet Volume Integration

We develop an analytical expression for predicting electromotive force (EMF) waveforms resulting from permanent magnets (PMs) in electrical machines. The expressions for the flux linkage are based on a volume integral over the magnet volume, rather than the usual surface integral over the coil. The proposed method consists of applying a virtual current in the coil of the machine and calculating the magnetic field generated inside the PM volume. The EMF waveform is obtained by taking the derivative of the flux linkage with respect to time. We present analytical expressions of the EMF for various PM shapes and Halbach magnetization patterns. We tested a total of four configurations of PMs, and the experimental waveforms confirmed the validity of the expressions obtained theoretically.     

Finite-Element Analysis of the Magnetic Field and Electromechanical Parameters Calculation for a Slotted Permanent-Magnet Tubular Linear Motor

We have calculated magnetic field distribution and integral parameters for the slotted, five-phase, permanent-magnet tubular linear motor (PMTLM). We used a finite element (FE) model for the field analysis. We carried out the field analysis for different values of the exciting current and for variable mover position. To obtain experimentally the field distribution and its integral parameters, we developed and tested a physical model of the motor. We compared the calculation results with the measured ones and found a good conformity.     

Analytical Solution for Rotor Eddy-Current Losses in a Slotless Permanent-Magnet Motor: The Case of Current Sheet Excitation

We present an analytical solution for the magnetic field, induced eddy currents, and the corresponding losses generated in the rotor of a slotless permanent-magnet (PM) motor. The field excitation is a current sheet placed at the stator interior surface. The solution is based on an analytical solution of the diffusion equation using double Fourier series and in the complex domain. The first and the second Fourier series correspond to the time and space harmonics, respectively. We have analyzed the effect of each time harmonic in detail, and verified the results with FEM software.