Radial Force Density Research Articles

Fast Calculation of Electromagnetic Vibration of Surface-Mounted PMSM Considering Teeth Saturation and Tangential Electromagnetic Force

In view of the shortcomings of the existing calculation methods of electromagnetic forces, this paper proposes an analytical method (AM) combining the magnetomotive force (MMF)-permeance method and the improved subdomain method. The amplitude of each force density component considering stator teeth saturation and current harmonics is calculated, and the specific order and frequency components in the radial and tangential electromagnetic force densities are analyzed and sorted out. In modal analysis, the stator core and the casing are regarded as cylindrical shells with axial ribs, the natural frequencies of the stator are obtained based on the energy method, and the accuracy is well verified by the modal test. Finally, the frequency response functions of low-order modes of the stator only related to the stator structure parameters are determined, and the vibration accelerations under different working conditions are obtained based on the linear superposition principle by only updating the electromagnetic forces. Compared with the multi-physical coupling finite element analysis, the total calculation time of the proposed AM is reduced by more than 92%, which facilitates the fast prediction and effective reduction of electromagnetic vibrations in the motor design stage.

The modified force density method for form-finding of cable net structure

Form-finding is crucial for the design of typical cable net structures. Based on the original basic force density method, a modified force density method utilizing the concept of relation matrix is proposed in this paper. The modified method realizes the establishment of a clear correspondence between members and nodes of cable net structures. On the basis of the relation matrix, the find function is introduced, and the calculation formula of the modified branch-node matrix is derived. Meanwhile, the corresponding analysis steps and calculation process are given. The modified method is verified by the analysis of representative structural forms. The results show that for the saddle-shaped orthogonal cable net structure, the outcomes obtained from the modified force density method highly agree with the theoretical values, providing preliminary verification of the method's effectiveness. For single-layer spoke cable net structures, the relative error between the results calculated by the modified force density method and the numerical solution is approximately 5 %. The results of both methods are relatively consistent, and the relative error varies in relation to the ratio of inner ring cable force density to radial cable force density. For circular single-layer crossed cable net structure without inner ring, the results of the modified force density method are very close to the numerical solution. The maximum relative error between the two is 6.95 %, and the accuracy is higher than that of the nonlinear finite element method. The outcome of this research demonstrates the accuracy of the modified force density method and its effective application in the form-finding of actual cable net structures.

Estimation of Stator Vibration in DFIM Under Various Types of Rotor Excitation

Variable speed power generation using Doubly Fed Induction Machine requires an adjustable frequency supply at the rotor terminals which can be achieved using power converters. Ideally, a variable frequency sinusoidal voltage should be applied, but it is not possible without the help of power converters. For a typical 250 MW DFIM with a speed variation of -10.73% to +8.33%, excitation power of 25 MW at 3.3kV and 11600 Amps is required. With this much high rotor current at low fundamental rotor frequency (3.75 Hz) electromagnetic forces in the air gap contain harmonic force components. Also, any time harmonic of radial force density in the rotor will be induced in the stator as a distinct time harmonic, modified by the influence of space harmonics in DFIM with regular three phase integral slot winding on both stator and rotor and vice versa. So, if the frequency and order of electromagnetic force components conflicts with mode shape and natural frequencies of the machine stator strong magnification in vibration will occur or more severely develops mechanical resonance. The stator vibration of electrical machine is generated by the electromagnetic forces acting on the surface of the stator tooths. This paper analyzes stator vibration for 250 MW DFIM in multiphysics simulation with its rotor winding excited through pure sinusoidal excitation at fundamental rotor frequency of 3.75 Hz and with two-Level voltage source converter at 3.75 Hz fundamental rotor frequency. Hardware results with supported multiphysics simulation on a laboratory prototype of 2.2 kW rating DFIM.

유도전동기의 슬롯 조합에 따른 진동/소음 특성 분석

The objective of this study is to examine the vibration and noise characteristics of a four-pole induction motor regarding the number of rotor slots. There are thirty six stator slots in the reference model, and its results are theoretically verified in case of a twenty-four-slot stator. Radial force density is obtained from two magnetic flux densities in the radial and tangential direction, and vibration performance is comparatively evaluated in terms of a rotor slot number by dividing radial force density into its temporal and spatial components through Fast Fourier Transform (FFT). Noise as the definition of sound pressure level is estimated in the units of decibels, and the noise of each motor is correlated with its vibration acceleration regarding temporal and/or spatial harmonic orders. In conclusion, the combination of stator and rotor slot numbers is critical since the 2nd orders lead to the deterioration of vibration and/or noise. As a result, the existence of the 2nd orders has to be carefully checked in advance by using several equations before the determination of physical dimensions in an induction motor in detail. In this paper, those equations have been given, and the comparison of vibration and noise in terms of a slot combination has been detailed in the step-by-step manner.

Vibration analysis of a permanent magnet synchronous motor by a pole/slot combination

A sixteen-pole eighteen-slot (16p/18s) permanent magnet synchronous motor (PMSM) developed in Korea Electrotechnology Research Institute (KERI) for a vertical articulated robot is chosen as a reference model, and other two pole/slot combinations (20p/18s, 20p/24s) are together compared in terms of electrical and mechanical performance. Radial force density varying in time and space is decomposed through Fast Fourier Transform (FFT), and vibration is calculated from the harmonics of radial force. The vibration of 20p/24s is best due to its mode of 4 among the three pole/slot combinations. Additionally, the variation of radial force density with respect to torque is compared between 16p/18s and 20p/18s. Despite the same number of slots in both motors, the slope of 20p/18s is greater than that of 16p/18s in radial force density due to the different number of poles. As a result, the vibration of 20p/18s is worse than that of 16p/18s.

Nonlinear Force and Vibration Analysis of an Interior Permanent Magnet Synchronous Generator With Eccentricity Detection

In this article, an in-depth study on eccentricities and their resultant vibration characteristics of an interior permanent magnet synchronous generator (IPMSG) for portable power generation is proposed. Also, this article introduces the eccentricity detection through vibration tests, since the vibration patterns caused by eccentricities are unique. Three basic eccentricity cases are investigated, namely the static, dynamic, and elliptical. Air-gap radial flux density and radial force density profiles are theoretically analyzed through mathematical modeling. With the help of finite-element analysis, the unique force profiles are verified for IPMSG of different cases, and the tooth force chopping process is studied. With modal analysis and testing, the harmonic vibration responses are predicted. An IPMSG prototype is fabricated and an overall eccentricity evaluation is reported through vibration tests.

Air-Gap Permeance and Reluctance Network Models for Analyzing Vibrational Exciting Force of In-Wheel PMSM

There is recognized interest in in-wheel motors for vehicle traction. Studies have gradually focused the design of in-wheel motors on electro-mechanical vibration, subject to the demand of driving comfort. It is crucial to model, analyze, and minimize the air-gap exciting force, the dominant source of vibration. In order to qualitatively and quantitatively study the air-gap vibrational exciting force and evaluate its characteristic for an in-wheel outer-runner permanent magnet synchronous machine (PMSM), this research proposes an air-gap permeance model (APM) and a unique adaptive reluctance network model (ARNM). In the process of motor design, APM is a quick means of determining dominant radial force density (RFD) harmonics and minimizing specific components that may produce considerable vibration. Morphing surface-mounted magnets and nonuniform air-gap length are guided by design optimization which complicates the analysis. Yet, proposed ARNM can account for this geometry variation and handle deformed gap geometry by using modified equation-based local permeance and residual flux. The speed and accuracy of proposed model are verified through the comparison of flux density and force mapping data between the calculation by proposed analytical model and the simulation by finite element tools. A 3-kW prototype is fabricated and tested to explore the effectiveness of ARNM-based performance prediction.

Research on Electromagnetic and Structural Characteristics of Canned Electric‐Actuated Valve Permanent Magnet Synchronous Motor under Eccentricity

The high‐temperature canned electric‐actuated valve permanent magnet synchronous motor (CEAV‐PMSM) directly drives the valve load, which is prone to eccentricity operation, causing greater system vibration and shortening the valve operating life. In order to analyze the electromagnetic and structural characteristics of CEAV‐PMSM under different eccentricity faults, this paper uses analytical methods to derive the magnetic field distribution of the motor under normal and eccentricity conditions. Then, the Maxwell Stress Tensor method is used to derive the expression of the radial electromagnetic force under normal and eccentricity conditions, and the order of space–time harmonics that have a greater impact on CEAV‐PMSM are summarized. After that, the electromagnetic performance comparison of the three pole‐slot combinations under different eccentricity conditions, and the harmonic orders during eccentricity is analyzed by Fourier transform to obtain the optimal pole‐slot combination, which verified the correctness of the analytical calculations. In addition, the influence of different eccentricity conditions on the radial force density and unbalanced magnetic pull are studied. On this basis, the vibration response of the motor under eccentricity is analyzed, and the influence of the canned sleeve on the vibration performance of the motor is discussed. Finally, the modal analysis of CEAV‐PMSM is carried out to prevent the occurrence of resonance under eccentricity, which provides some references for reducing the vibration and noise of the canned electric‐actuated valve. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Vibration Performance of an Induction Motor with Respect to a Slot Number

In this paper, two four-pole induction motors having 36 and 24 stator slots are analyzed in terms of vibration performance with respect to the number of rotor slots. Radial and tangential flux densities in air gap are obtained by finite element analysis, and by using the flux densities, radial force density is calculated and separated into its temporal and spatial harmonic orders through Fast Fourier Transform (FFT). The variation of radial force density regarding a slot combination is investigated, and vibration acceleration is estimated by radial force density from FFT. The relation of vibration acceleration with a rotor slot number is scrutinized in terms of temporal and/or spatial harmonic orders. Main and diagonal orders among harmonics are defined, and it is found that vibration performance deteriorates in a rotor slot number creating the 2SUPnd/SUP diagonal orders. In this paper, it is claimed that the existence of the 2SUPnd/SUP diagonal orders is determined by several simple equations, and a slot combination is easily evaluated in terms of vibration performance by the equations obtained from this research.

Vibration Enhancement or Weakening Effect Caused by Permanent Magnet Synchronous Motor Radial and Tangential Force Formed by Tooth Harmonics

This paper investigates the vibration enhancement or weakening effect caused by permanent magnet synchronous motor radial and tangential force formed by tooth harmonics. First, the analytical expressions of an air gap magnetic field are deduced based on a permanent magnet synchronous motor model. Then, the Maxwell stress tensor method is employed to calculate the radial and tangential force density produced by permanent magnet magnetomotive force harmonics and tooth harmonics. Moreover, the spatial phase difference between the minimum non-zero spatial order radial and tangential force waves under loading operation are also obtained. It is followed by stator vibration deformation induced by radial and tangential force waves, and the vibration enhancement or weakening effect is discussed. This study shows that the tangential force wave has a significant influence on the vibration performance similar to the radial force wave. At specific frequencies, superposition of the radial and tangential force waves can intensify the vibration while weakening each other to reduce the vibration at other specific frequencies. Numerical simulation and a vibration measurement experiment of the prototype motor were carried out to confirm the proposed theory, which can guide motor designers in selecting an appropriate pole and slot combination to apply the weakening effect between radial and tangential force waves and improve PMSM vibration performance.

Radial Force Density Calculation of Switched Reluctance Machines Using Reluctance Mesh-Based Magnetic Equivalent Circuit

Acoustic noise and vibration is one of the shortcomings of a switched reluctance machine (SRM). Harmonics of the radial force waveform in the airgap excite the stator structure at different vibration modes with specific frequencies. The radial force density in the airgap should be calculated before analyzing and mitigating acoustic noise and vibration. This paper proposes a reluctance mesh-based magnetic equivalent circuit (MEC) model to calculate the airgap radial force density. Reluctance mesh-based MEC models are developed for 3-phase 6/4, 6/16, 12/8 and 4-phase 8/6, 8/10, and 16/12 SRMs. A technique for the dynamic modeling of SRMs is proposed using the reluctance mesh-based MEC method. Dynamic currents are calculated using the proposed technique and, then, the radial and tangential flux density in the airgap are calculated. The radial force density in the airgap is calculated by applying the Maxwell Stress Tensor method. Fourier series is used to calculate the harmonics of the radial force density. The results obtained from the MEC model are verified using finite element method (FEM) models. The implemented MEC-based dynamic modeling method is validated using experimental results.

Analysis and optimization of vibration and noise of high-speed magnetic suspension motor

In this paper, in order to reduce the influence of vibration and noise generated by the motor in rock cotton centrifuges on the quality of the output fiber and the damage to the operator’s hearing, it is meaningful to analyze and optimize the vibration and noise. A high-speed magnetic suspension motor is proposed for the rock cotton centrifuge in the paper. First, the motor model is established in Maxwell, the radial force density wave distributed in the air gap is calculated by the field solver, the main harmonic source is analyzed according to its FFT decomposition graph, and then the optimization scheme of short-range double-layer winding is determined. Second, the optimization scheme is analyzed in modal mode and harmonious response, and the vibration response spectrum of the motor stator is obtained. Finally, the electromagnetic noise characteristics of the motor are obtained through ANSYS acoustics simulation. The results show that the optimized motor noise has a reasonable level under the premise of ensuring electromagnetic performance.

New Three-Pole Combined Radial–Axial Magnetic Bearing for Industrial Bearingless Motor Systems

This article investigates combined radial–axial magneticbearing (CRAMB) technology as an enabling component for shafted bearingless motor systems. The unique requirements of high-speed bearingless motors designed for significant power levels are used to guide a literature review on CRAMB designs. Fundamental bearing topology aspects are identified and compared. Based on the outcome of this review, a new CRAMB topology is proposed and developed to meet the needs of a bearingless motor. Key features of the proposed design include a three-pole radial force stage (driven by a three-phase motor drive) and utilization of an optimal bias flux that improves radial force density by approximately 15% (improved rotor dynamics). A full design procedure for the new bearing topology is developed and it is shown that compared to a conventional four-pole side-by-side CRAMB, this topology decreases the bearing shaft length and requires two fewer power electronic switches (6 instead of 8). The new bearing is validated via finite-element analysis and experimental test results.

Vibration Reduction by Segmented Continuous Variable Width Pole for Rotating Armature Permanent-Magnet Motors

In the present study, to reduce the electromagnetic vibration of rotating armature permanent-magnet motor, a method is proposed by exploiting the magnetic pole with segmented continuous variable pole width. The distribution of flux density and radial force density in air gap is determined by the analytical method. In addition, the analytical solutions of radial exciting force and bending moment on the magnetic pole are yielded. After conducting the analysis, the principle of magnetic pole width adjustment to reduce radial exciting force and bending moment is formulated. With the three-dimensional finite element method, the magnetic field, Maxwell stress, cogging torque, vibration deformation, and acceleration of the motor are determined. To verify the effectiveness of the proposed method, a comparison is drawn between the proposed scheme and the other three conventional schemes. Finally, the experimentally achieved results regarding the four types of motors are compared to verify the proposed method.

Analytical Calculation of Temporal and Circumferential Orders of Radial Force Density Harmonics in External-Rotor and Internal-Rotor Switched Reluctance Machines

This paper presents an analytical method to calculate the temporal and circumferential orders of the radial force density harmonics in switched reluctance machines (SRMs) without running the electromagnetic finite element analysis (FEA). The characteristics of the radial force density harmonics in several SRM topologies are investigated, including the 6/4, 24/16, and 6/14 internal-rotor (IR) SRMs, and 12/16 and 18/24 external-rotor (ER) SRM. The study shows that the temporal and circumferential orders of the radial force density harmonics depend on the pole configuration, the rotational directions of the rotor, the phase excitation sequence, and the rotor or stator radial force density waveform. The acoustic noise of a four-phase 8/6 internal-rotor SRM and a three-phase 12/16 external-rotor SRM was experimentally measured to validate the calculation of the temporal and circumferential orders of the radial force density harmonics. The proposed analytical method helps locate the possible radial force density harmonics of a given SRM configuration. In order to determine the dominant radial force harmonics, the proposed method should be complemented by analyzing the natural frequencies of the motor structure and the forcing frequencies of the radial force harmonics.

Performance Evaluation of Permanent Magnet Synchronous Machines according to Rotor Types for Machine Tool Application

This paper deals with comparative investigation on permanent magnet synchronous machines (PMSMs) with identical stator structure based on electromagnetic field analysis. By considering their rotor types with rare-earth magnets, the influence of space vector pulse width modulation inverter on machine performance is investigated based on the predicted phase current. As analysis models, a surface-mounted PMSM (SPMSM) with parallel magnetization, a SPMSM with Halbach magnetization, and an interior PMSM (IPMSM) are employed for their comparison. For their effective investigation, machines are designed to have identical equivalent circuit parameters, such as resistance and induced voltage in no-load condition. Based on the dynamic modeling of the SVPWM inverter, the phase current is predicted, and their output characteristic, power losses and radial force density are comparatively investigated by electromagnetic field analysis. In addition, with a manufactured machine, the validity of this paper is demonstrated as well.

A Novel Axial Split Phase Bearingless Flywheel Machine With Hybrid-Inner-Stator Permanent Magnet-Based Structure

This article proposes a topology of special axial split phase (ASP) bearingless switched reluctance (BSR) machine for flywheel applications named ASP-bearingless flywheel (ASP-BF) machine, which adopts hybrid-inner-stator permanent magnet (PM) structure and exhibits complete decoupling of torque and radial suspension force, four degrees-of-freedom (DOF) actively controlled suspension, high torque and radial force density. The topologies of conventional radial split phase (RSP)-BSR machines and the proposed ASP-BF machine are comparatively investigated. It is found that problems of conventional RSP-BSR machines, i.e., the radial suspension force generation dead zone and strong coupling of radial suspension force and torque, can be solved in ASP-BF machines and the suspension DOF can be doubled. Electromagnetic performances, including magnetic field distribution, inductance, torque, radial force are comprehensively investigated. Further, the concept of degree-of-coupling (DOC) is introduced, and the DOCs of the proposed machine and conventional machines are quantitatively analyzed and compared. It shows that the DOC of ASP-BF machine in two cases are 3.41% and 4.05%, less than a quarter of the conventional 8/10 pole machine (22% and 16%) and less than half of the 12/14 pole machine (8.57% and 11.3%). Finally, a 3 kW/100 Wh prototype is built and the experiments proved the validity.

Vibration Reduction Characteristics of Permanent Magnet DC Motors With Sawtooth Edge Poles

It is known that the slot frequency vibration is the one of the main components in electromagnetic vibration spectrum of permanent magnet DC motors (PMDCM). After finding that the vibration reduction scheme of the piecewise varying pole width (PVPW) is only effective for the odd order harmonic of slot frequency vibrations by analytical method, the PM pole with sawtooth edge is put forward to reduce all harmonic components of slot frequency vibrations of PMDCM. In this article, after the air gap flux density and radial force density are analyzed, the two vibration sources, radial force and bending moment, are derived for the motor with sawtooth edge poles (SEP). Then the optimized pole shape is obtained to reduce all harmonic components of both the radial force and bending moment at the same time. Three dimensional finite element method of electromagnetic field and structure are used to calculate the magnetic flux density, radial force and vibration for the motors of PVPW and SEP. Three permanent magnet motors with fixed pole width (FPW), PVPW and SEP are manufactured and tested. The comparison and verification show that SEP is better than the other two schemes in general.

Research on weakening measure of radial electromagnetic force waves in permanent magnet synchronous motors by inserting auxiliary slots

The accurate calculation and analysis of electromagnetic force waves are especially crucial for comprehensively predicting and weakening the electromagnetic vibration of electrical machines. In this study, a fast and accurate calculation method of radial electromagnetic force density of surface-mounted permanent magnet synchronous motor (PMSM) is presented, the radial electromagnetic force density including amplitude, frequency and order is obtained and the accuracy is verified. Comprehensively considering that the effects of the auxiliary slots on cogging torque and torque ripple, the weakening measure of radial electromagnetic force waves by inserting auxiliary slots is research, and the optimal determinations of the number and the structural parameters of auxiliary slots in PMSMs with different slot–pole combinations are summarised, and six PMSMs with 6-pole/36-slot (6p36s), 4p36s, 6p9s, 8p9s, 8p12s and 10p12s are analysed to verify the universality of the conclusions.

Study on Electromagnetic Vibration Analysis Process for PM Motors

Conventional electromagnetic vibration analysis methods mainly focus on the spatial harmonic components of the radial force density. Because they do not consider time harmonics, they cannot consider the frequency component of electromagnetic vibrations. Therefore, they are not suitable for optimally designing motors by considering electromagnetic vibrations. In this paper, we propose a process to analyze electromagnetic vibrations considering time harmonics as well as spatial harmonics. For the calculation of the magnitude of electromagnetic vibrations with respect to the frequency, the natural frequency of the circumferential mode was calculated by simplifying the shape of the stator core. The natural frequency increases as the order of the stator circumferential mode increases. Using the vibration equation, it was confirmed that electromagnetic vibrations decrease as the natural frequency increases. For analyzing the correlation between the vibration source and the electromagnetic vibrations, the radial force was separated into time and spatial harmonics, and the contribution of each harmonic component to the vibration was calculated. The results revealed the harmonic components that have the most significant influence on the vibrations. Then, using the proposed process, the vibration performance, as well as the electromagnetic performance, can be used as an objective function to design motors. To verify the validity of the proposed process, the vibrations of conventional and proposed motors were analyzed. Finally, a prototype was manufactured, and its vibrations were tested using the proposed process.