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.     

Force characteristics and gain determination for a slotless self-bearing motor

In this paper, we use the Maxwell stress tensor method to derive the analytical force and torque expressions for a large-scale slotless permanent-magnet (PM) self-bearing motor actuator that uses common coils to produce both the torque and radial forces, in order to include all the possible interactions among the PMs, currents, and stator/rotor back iron. We solve the radial and angular components of the two-dimensional instantaneous magnetic field distribution in the low-permeability region induced from the rotor PMs and stator windings separately, using the unwrapped geometry, and then superimpose them. Instead of being incorporated into the boundary conditions, the general winding current and PM magnetization distributions are expanded into the Fourier series in the separate source layers, with respect to one motor revolution and one PM pole pair, respectively. For each source, we first solve one homogenous Laplace's equation in the planar layer without source and one nonhomogenous Laplace's equation in the planar layer with source simultaneously in Cartesian coordinates for a centered rotor and then add the rotor eccentricity. We compare the analytical solutions for the individual magnetic field distributions, as well as the total force and torque production, to those from the finite-element analysis (FEA), and find excellent agreement between the two. We characterize the open loop current and negative stiffness gains of the SBM from the linearized force-current-displacement relationship, which forms the basis for the linear system modeling and controller design, and validate our results by comparison with the FEA results.     

Switched Reluctance Motor Design Using Neural-Network Method With Static Finite-Element Simulation

The paper describes a neural network method for optimal design of a switched reluctance motor (SRM). The approach maximizes average torque while minimizing torque ripple, considering mainly the stator and rotor geometry parameters. Before optimization takes place, an experimental validation of the SRM model, based on the finite-element method, is performed. The validation predicts average torque and torque ripple characteristics for several motor configurations while stator and rotor pole arcs are varied. The numerical results are highly nonlinear, and a function approximation of the data is therefore difficult to implement. We therefore interpolate the data by using a neural network based on a generalized radial basis function. The computed results allow us to search for optimum motor parameters. The optimum design was confirmed by numerical field solutions.     

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.     

Characterization and Reduction of Magnetic Noise Due to Saturation in Induction Machines

This paper derives the analytical characterization of Maxwell radial vibrations due to saturation effects in induction machines, and especially in traction motors. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the stator and rotor slot numbers, and stator natural frequencies, these forces can be responsible for high magnetic noise levels during starting and braking. A simple rule to avoid saturation magnetic noise is then proposed, and applied to an industrial motor. Simulation results show that the new proposed motor improves magnetic noise level up to 20 dB, whereas experiments give a 15 dB improvement.      

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.     

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     

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.      

一种用于非圆异形孔加工的电磁驱动机构及控制方法研究

研究了用于非圆异形孔加工的电磁驱动机构及控制方法。为了对镗杆施加径向随动作用力,研制了由电磁定子和电磁转子组成的回转式电磁驱动机构。当改变定子线圈中的控制电流时,可以改变电磁定子与电磁转子之间的电磁驱动力,进而带动镗刀做径向微位移。通过电磁驱动力在静态工作点附近的线性化,建立了电磁驱动力与控制电流之间的线性关系,分析了实现电磁驱动力同步控制的方法。对电磁驱动机构进行了动态模拟试验,试验结果表明,随着转子的转动,在转子与定子之间可以形成一个同步旋转的电磁驱动力,实现镗杆中心的径向可控微位移。因此采用本文提出的回转式电磁驱动机构加工非圆异形孔是可行的。     

电动车驱动用永磁同步电机力矩特性的研究

对影响内置式永磁同步电机转矩特性的三个关键设计参数——永磁体宽度、定子绕组匝数及转子铁心外形进行了研究。以具体样机为例,分析了定子绕组匝数、永磁体充磁方向长度和转子外形对转矩特性的影响。分析结果表明：永磁体宽度接近于整数倍定子齿距可降低负载脉动转矩;采用偏心分段圆弧法优化转子外形有利于提高电机的转矩特性。通过实验验证了理论分析的正确性。     

Analysis of magnetic field and levitation force characteristics for 3-DOF deflection type PM motors

The mechanism and characteristics of the electromagnetic radial force are important for motors with complicated structures. The three-dimensional analytical model of the air gap between the rotor and stator is established under rotor eccentricity conditions. Then, aiming at solving the unbalanced radial force problem with rotor static eccentricity, the air-gap flux density, radial electromagnetic force, and the comparisons of harmonic contents are calculated and presented based on FEA (Finite Element Analysis) and MATLAB simulation. Finally, the magnetic field model has been validated by experiments utilizing a prototype system. The results provide a theoretical guide for configuration design, optimization, and levitation control research on three degree of freedom deflection type motors.     

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.     

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.      

Bridge configured winding for polyphase self-bearing machines

The self-bearing or bearingless machine is an electromagnetic device that supports its own rotor by way of magnetic forces generated by windings on its stator. Various winding configurations have been used to accomplish the task of force production. This paper proposes a winding based on a bridge connection for polyphase self-bearing rotating electrical machines with advantages such as: 1) requiring only one power supply for torque production; 2) lateral forces are produced using auxiliary power supplies of relatively low current and voltage ratings; 3) relatively low power loss; and 4) preserving the flexibility for extensions to other polyphase machines. The bridge connection has been verified to exhibit the characteristics of a self-bearing motor via an electrically coupled finite-element analysis. A comparison of power loss with conventional winding schemes and general applications of such a proposed scheme are also presented.     

基于峰谷互补方法的开关磁阻电机转矩脉动抑制研究

开关磁阻电机的非线性电磁特性以及脉冲工作方式会产生明显的转矩脉动,针对这一问题,在分析开关磁阻电机转矩脉动产生原因和实际测量转矩脉动波形的基础上,提出了一种基于峰谷互补原理抑制开关磁阻电机转矩脉动的方法.该方法使用2套定转子参数相同的电机系统,使之产生相位互差180°电角度,幅值近似相同的转矩脉动波形,利用峰谷互补原理...     

Force transfer model and characteristics of hybrid transducer type ultrasonic motors

The characteristics of longitudinal-torsional hybrid transducer-type ultrasonic motors (HTUSM) are low speed and high torque. The discontinuous-surface-contact mode between the stator and the rotor is different from the many-point-contact mode of traveling wave motors, which is also an essential cause for high torque. Therefore, it is important to analyze its force transfer model between the rotor and the stator. In this paper, issues of using the method of equivalent circuit model are addressed. The relationships between the contact angle, preload, and physical parameters of frictional materials are given, according to the impulse conservation law axially. The equations describing output torque, amplitudes of longitudinal and torsional vibration, and parameters of the rotor are derived according to the principle that the work done by the load is equal to that by the driving force in one vibrating cycle. All factors that influence the mechanical characteristics are analyzed, and accuracy and suitability of the force transfer model are verified by comparison with the prototype motor. The formula for transfer efficiency on the stator/rotor interface is given, and the low-efficiency of this type motor is explained. The wide-working frequency range property of this type motor is shown with experimental results. Based on this study, the parameters of the rotor and preload are determined. The maximum torque of the prototype motor is up to 13.2 nm, and no-load speed of this type of motor is 12.5 rpm.     

永磁直流无刷电机定子振动动力学分析及实验研究

在集中驱动的电动汽车中,电机是电动汽车振动和车内外噪声的主要源头之一。因此,设计人员都期望于在设计阶段能对电机的振动噪声性能进行分析。本文基于电磁场分析理论对电动汽车驱动用永磁直流无刷电机径向力波进行了有限元仿真计算,进而对电机定子进行了动力学建模与仿真研究,实现了车用定子振动动力学特性分析。仿真结果与电机振动试验结果相符,验证了分析的正确性,为进一步实现低噪声驱动电机的优化设计打下了基础。     

Analytical Modeling of Axial Air Gap Solid Rotor Induction Machines Using a Quasi-Three-Dimensional Method

This paper presents an analytical model of axial air gap induction motors with solid rotors that includes the two-dimensional current distribution in the rotor. The model is quasi-three-dimensional and considers the circumferential as well as radial and angular dimensions. Also, one can consider the various arrangements of the stator windings i.e., single layer, double layer, and gramme for this type of motor. The method is valid for both constant current and constant voltage sources. Comparison of the simulation results of the produced torque with the experimental ones shows the high accuracy of the proposed method.     

Improved analytical model for predicting the magnetic fielddistribution in brushless permanent-magnet machines

A general analytical technique predicts the magnetic field distribution in brushless permanent magnet machines equipped with surface-mounted magnets. It accounts for the effects of both the magnets and the stator windings. The technique is based on two-dimensional models in polar coordinates and solves the governing Laplacian/quasi-Poissonian field equations in the airgap/magnet regions without any assumption regarding the relative recoil permeability of the magnets. The analysis works for both internal and external rotor motor topologies, and either radial or parallel magnetized magnets, as well as for overlapping and nonoverlapping stator windings. The paper validates results of the analytical models by finite-element analyses, for both slotless and slotted motors     

Analytical closed-form investigation of pwm inverter induction motor drive performance under dc bus voltage pulsation

The voltage unbalance conditions at the input rectifier stage of the AC?DC?AC rectifier-inverter fed induction motor drive is analysed. This unbalance can cause significant voltage harmonic of twice the line frequency 2f1 in the DC bus. This voltage ripple can have a degrading effect on the induction-machine performance characteristics. The authors present an analytical closed-form mathematical model and analysis of the impact of DC bus ripple voltage of the three-phase voltage source inverter with the space-vector PWM on the induction machine phase voltages, currents and torque pulsations. The analytical expressions for the voltage and current space vectors as a function of the DC bus voltage pulsation are derived. Using superposition, the separate parts of the motor currents can be determined. From the current space vectors, the torque behaviour is estimated, again as a function of DC link voltage pulsation. Next, it is shown that the DC link voltage ripple components may cause large torque pulsation. The proposed analytical method is based on the mixed p?z approach, enabling presentation of the results in lucid and closed form. To verify the effectiveness of the proposed analytical model, experimental results based on laboratory setup were obtained.