Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole

We develop an analytical model for predicting the eddy-current loss in the rotor magnets of permanent-magnet brushless machines that have a fractional number of slots per pole, when either all the teeth or only alternate teeth are wound, and in which the unwound teeth may be narrower than the wound teeth. The model enables the magnetic field distribution in the air gap and magnet regions to be determined, by neglecting the eddy-current redistribution effect and assuming that the eddy currents are resistance limited. It can account for space-harmonic magnetomotive forces (MMFs) resulting from the winding distribution and time-harmonic MMFs due to nonsinusoidal phase currents, as well as for the effect of curvature and circumferential segmentation of the magnets. We have validated the model by finite-element analysis, and used it to investigate the eddy-current loss in the magnets of three surface-mounted magnet brushless motors that have similar slot and pole numbers, and employ identical rotors but different stators, when they are operated in brushless ac (BLAC) and dc (BLDC) modes. We show that the stator winding configuration, as well as the operational mode, significantly influence the resultant eddy-current loss.     

Effect of Magnetic Saturation on Static and Mixed Eccentricity Fault Diagnosis in Induction Motor

We have investigated the effect of magnetic saturation of core materials on the diagnosis of static and mixed-eccentricity faults in induction motors. We modeled the faults by using a modified winding function (MWF) and time-stepping finite-element (TSFE) methods to compute the stator currents of both healthy and faulty motors for processing. We then analyzed the stator signal spectra of the motors by the MWF and TSFE methods and estimated the amplitudes of sideband components attributable to the faults. The results obtained by TSFE agreed well with experimental measurements. However, there was considerable discrepancy between the MWF results and the experimental measurements. We investigated the reason for the discrepancy by analyzing the air gap magnetic field distribution in both healthy and faulty induction motors in order to determine their linear and actual magnetization characteristics. We found that, in a faulty motor, for fixed permeability, the analytic method yields a much larger magnetic flux amplitude than is actually the case. At the same time, the distribution of magnetic flux in the air gap is more asymmetric than the actual case. Here, we present our experimental results and those obtained with the MWF method, using the finite-element analysis package Opera2d 10.5, for two three-phase, four-pole, 60-Hz, 3-hp motors having 36 stator slots and 44 and 28 rotor slots, respectively.      

Conceptual Design of a Field Coil for 5 MW HTS Synchronous Machine

Compared with a conventional rotating machine, a superconducting rotating machine fabricated by High Temperature Superconducting (HTS) tape has superior performance and efficiency due to the HTS field coil for the rotor which can generate high magnetic flux intensity. The two primary factors for the design of the HTS rotational machine are how to construct the optimal magnetic field path through the air gap located between the rotor and the stator and how to enhance the linkage magnetic flux density between the armature coil in the stator and the field coil in the rotor. A 5 MW HTS motor for ship propulsion is planned for development in early 2011 by a Korean collaboration group of KERI and DOOSAN Heavy Industry. As a part of this R&D efforts, we designed and analyzed the field coil for a 5 MW HTS synchronous motor. In this paper, the computational results of the magnetic field distribution on the whole winding regions of the HTS field coil of the superconducting rotating machine will be also presented and discussed.     

Time-harmonic finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor

A finite-element model for calculation of eddy-current and circulating current losses in a multi-conductor stator winding of a cage induction motor is presented. In this model, the eddy current formulation of the series and parallel connected stator bars is solved together with the circuit and field equations using a two-dimensional time-harmonic approximation. The Newton-Raphson method is applied to solve the total system of nonlinear equations. The finite-element mesh is discretised finely enough in order to take the phenomena correctly into account. The eddy-current loss distribution of the stator bars and the quantitative results of eddy-current and circulating current losses have been studied with two different conductor arrangements inside the stator slots. The results show that the eddy-current loss in the stator winding is one of the most significant loss components. They also show that the radial position of the stator bars has a remarkable effect on the losses. The radial flux that passes through the stator bars can be guided to stator teeth by using magnetic slot wedge material to reduce the eddy-current loss.     

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.     

Time-stepping finite-element analysis of eddy currents in the form-wound stator winding of a cage induction motor supplied from a sinusoidal voltage source

The eddy-current effects of multi-conductor form-wound stator winding because of the fundamental and high-frequency magnetic flux in a cage induction motor are studied. The time dependence of the field and circuit variables and the motion of the rotor are modelled by the backward Euler time-stepping method. The motor was supplied from a sinusoidal voltage source. The series and parallel connected stator bars are strongly coupled with the circuit and field equations. The Newton-Raphson method is applied to solve the system of non-linear equations. The eddy-current loss distribution of the stator bars and the quantitative results of eddy-current losses are studied. The radial distance of the stator bars from the air gap has a remarkable effect on the losses and the hot spots. Methods to minimise the losses and to avoid the local hot spots are studied.     

Effects of pulse-width-modulated supply voltage on eddy currents in the form-wound stator winding of a cage induction motor

The eddy currents of a form-wound multi-conductor stator winding because of the non-sinusoidal supply voltage in a cage induction motor are studied. The time and space dependence of the field, circuit variables and the motion of the rotor are modelled with the time-discretised finite-element analysis. A pulsewidth- modulated voltage is used to supply the motor. The eddy-current loss distribution of the stator bars and the total eddy-current losses are studied. The radial distance of the stator bars from the air gap is re-emphasised as a design parameter because of its effect on the losses and the hot spots. The means for minimising the losses and avoiding the local hot spots are studied.     

基于霍尔效应的感应式瞬时旋转角速度传感器

设计了一种基于霍尔效应的感应式瞬时旋转角速度传感器,主要包括定子铁心及绕组、霍尔元件和永磁转子3大部分,且永磁转子的磁通在空间气隙中呈正弦规律分布。传感器工作时,永磁转子与被测旋转设备同轴连接,永磁转子的磁场与定子绕组匝链耦合,绕组中产生与瞬时旋转角速度呈对应关系的感应电动势。由于定子绕组与霍尔元件的控制端直接连接,则霍尔元件中存在电流,在永磁转子磁场的作用下,霍尔元件产生与瞬时旋转角速度成正比的直流霍尔电势。推导了传感器的输出特性,并对传感器进行了特性测定实验,结果表明其灵敏度系数约为203 mV/(rad·s^-1),线性误差约为0.5%。     

Analytical Prediction of Cogging Torque in Surface-Mounted Permanent-Magnet Motors

We present a new approach to computing cogging torque based on only one analytical field solution in surface-mounted permanent-magnet (PM) motors. We use conformal transformation to compute the magnetic field created by the permanent magnets in the air gap with a single slot. Then, we derive the cogging torque due to the single-slot effect at different rotor positions directly from the 2-D analytical field solution. The total cogging torque is synthesized from the contribution of each slot. We have applied our approach to predicting the cogging torque of two surface-mounted PM motors, one with 4 poles, 24 slots and the other with 42 poles, 36 slots. The predicted cogging torques for both applications agree well with those obtained from 2-D finite-element analysis.      

An Analytical Determination of Eddy-Current Losses in a Configuration With a Rotating Permanent Magnet

The paper presents a completely analytical method for determining the eddy currents in a cylindrical configuration. The configuration consists of a cylindrical permanent magnet rotating inside a conducting hollow cylinder (stator). The solution is obtained by solving a generalized form of the diffusion equation and applying the modified Bessel functions. The determination of the magnetic field in the air and in the stator, and the losses generated by the eddy currents, is completely analytical. The results are verified by finite-element software.     

Development of superconducting generator having highly stabilized superconducting field winding––70 MW class superconducting generator

The development of a practical superconducting generator has been carried out in Japan since 1988. The authors have developed a rotor with a highly stabilized superconducting field winding and a stator with an air gap winding composed of double transposed copper coils. A series of tests was completed at the end of 1997. The output of 78.8 MW was recorded, which was the highest value obtained to date worldwide. The development of the generator and the test results are described.     

Analytical calculation of the switched reluctance motor's unalignedinductance

This paper develops an analytical model for the unaligned inductance of the switched reluctance motor. The analytical model is useful as long as the machine's stator and rotor poles do not overlap and its iron does not saturate. Iron saturation is almost never experienced when the rotor is in the unaligned position for practical winding currents. This paper expands on results presented previously to include the contribution to the unaligned inductance of the flux in both the stator slot and the rotor slot. The approximations that are inherent to the analytical model are stated, and a detailed development of the model is provided. Finally, the paper compares predictions of the unaligned inductance computed by the analytical model to those obtained by finite-element analysis for three different machines with different pole counts and rotor diameters     

Extension of winding function theory for nonuniform air gap in electric machinery

This paper extends the winding function theory for nonuniform air gap in rotating electric machinery. It shows that the winding function differs from that used in the symmetrical case, although several papers employ the uniform air-gap winding function to study electric motor performance under fault conditions. The extended theory will be particularly helpful in the study of squirrel-cage induction motors with a nonuniform air gap such as that caused by eccentricity of the rotor and stator.     

气隙对电流比较仪磁屏蔽屏蔽效能影响的研究

电流比较仪的磁屏蔽是减小磁性误差,提高测量精度的重要组成部分,但实际中磁屏蔽往往存在气隙导致屏蔽效能下降,影响比较仪的测量精度。通过建立有限元模型,研究磁屏蔽上引线穿出气隙对屏蔽效能的影响,得到了屏蔽效能随气隙高度变化的规律。对于该模型,气隙高度小于10 mm时,屏蔽效能下降不大;当气隙高度大于10 mm后,屏蔽效能下降明显。最后,搭建实验平台验证气隙对屏蔽效能的影响,实验结果与有限元计算结果相吻合,小气隙对屏蔽效能的影响不大,当气隙超过一定高度后对屏蔽效能影响很大,实际设计中应予以避免。     

Three-Dimensional Magnetic Effects in Permanent-Magnet Magnet Synchronous Machines

This paper presents the results of an investigation of the three-dimensional (3-D) magnetic effects in permanent-magnet synchronous machines (PMSMs). Using 3-D finite-element analysis, effects of geometry and also a high-frequency excitation on the magnetic parameters of the machine have been studied. According to our findings, high-frequency phenomena come into effect at excitation frequencies of the order of a few kilohertz, which is not uncommon when the machine is operated at super high speeds. Our results show that normalized torque productivity is a function of stack length and an increase in stack length results in an increased torque density. It is also observed that an increase in excitation frequency decreases the self inductance of the stator windings while the phase difference between the flux linkage and magnetomotive force increases. This is a significant finding, especially the shift in the phase of the air gap flux, as it has a direct impact on the accuracy of the controller that drives the PMSM under field-oriented control. Another significant observation was the reduction in the induced voltage (back electromotive force) in a search coil located in the stator slots at high frequencies. Such observations mandate the use of 3-D analysis of machine geometry to optimize performance throughout the machine's speed range.     

Field weakening for radial force reduction in brushless permanent-magnet DC motors

In brushless permanent-magnet dc (BLDC) machines, the attraction between the rotor permanent magnets and the stator iron causes radial stator forces that excite the stator structural response and radiate unwanted acoustic noise. In this paper, we develop an analytical model that predicts rotor torque and radial force ripple as functions of the stator currents. The model shows that field weakening of sinusoidally commutated BLDC machines can reduce radial forces but requires higher currents to maintain the desired torque. We confirmed the analytical results numerically on a BLDC motor using ANSYS finite-element analysis and found a 30% reduction in force ripple at no load.     

Unified winding function approach for dynamic simulation of different kinds of eccentricity faults in cage induction machines

The multiple coupled circuit model of a three-phase cage induction machine and the uses of a modified winding function theory to calculate the time-dependent inductances of the motor with a general eccentricity fault, including static, dynamic and mixed eccentricities, in a unified manner are considered. By defining the inverse air gap function of the eccentric machine, determining its indefinite integral and assuming step variations for the turn functions at the centres of the slots, precise analytic equations are obtained for the inductances. Differentiating these analytic equations against the rotor angular position also gives precise analytic equations to calculate the derivatives of the inductances, which may be used to determine the electromagnetic torque. Consequently, dynamic simulations of an induction machine with any eccentricity type and degree as well as a healthy one is made possible in the frame of a single Simulink program. At the beginning of the simulation process, the eccentricity components' degree and position are introduced and the program is then executed accordingly. A simple technique was used to make an industrial induction motor temporarily eccentric, with varying degrees, and experiments were conducted on it. By defining and applying effective air gap length and effective eccentricity components' degrees, good agreements are achieved between the simulated and the experimental results, which implies that the whole unified simulation program is effective.     

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.      

Analysis of large synchronous machines with axial skew, part 2: inter-bar resistance, skew and losses

Assuming knowledge of the flux density distribution due to field and armature windings in the air gap of a large synchronous machine, it is possible to calculate the impact that inter-bar resistance and skew have on the amortisseur winding currents. A theoretical approach to predict amortisseur currents is developed and then the effect on open circuit voltage harmonics is investigated. Developing theory to predict the losses in the core of the machine, the impact of skew and inter-bar resistance on the predicted core loss is also investigated.     

The effects of the air gap between pancake windings on the central magnetic field in a high temperature superconducting magnet

In an HTS magnet consisting of pancake windings, an air gap between the pancake windings can be used to increase the central magnetic field because the air gap increases the critical current of pancake windings. The effects of an air gap on the central magnetic field of an HTS magnet are discussed in this paper according to the various number of turns and also to the number of pancake windings. Results of calculation show the air gap could increase the central magnetic field and the field uniformity simultaneously. The optimum air gap which maximized the central magnetic field was about 4 mm at eight pancake windings and 50 turns per pancake winding. The central magnetic field increased 6.2% from 0.225 T (no air gap) to 0.239 T (4 mm air gap) at that case.