Cogging Effect Research Articles

Position Servo Control of Electromotive Valve Driven by Centralized Winding LATM Using a Kalman Filter Based Load Observer

The exhaust gas recirculation (EGR) valve plays an important role in improving engine fuel economy and reducing emissions. In order to improve the positioning accuracy and robustness of the EGR valve under uncertain dynamics and external disturbances, this paper proposes a positioning servo system design for an electromotive (EM) EGR valve based on the Kalman filter. Taking a novel valve driven by a central winding limited angle torque motor (LATM) as the object, we have fully considered the influence of the motor rotor position and load current, as well as the magnetic field saturation and cogging effect, improved the existing LTAM model, and derived accurate torque expression. The parameter uncertainty of the above internal model and the external stochastic disturbance were unified as “total disturbance”, and a Kalman filter-based observer was designed for disturbance estimations and real-time feed-forward compensation. Furthermore, using non-contact magnetic angle measurements to obtain accurate valve position information, a position control model with real-time response and high accuracy was established. Numerous simulated and experimental data show that in the presence of ± 25% plant model parameter fluctuations and random shock-type disturbances, the servo system scheme proposed in this paper achieves a maximum position deviation of 0.3 mm, a repeatability of positioning accuracy after disturbances of 0.01 mm, and a disturbance recovery time of not more than 250 ms. In addition, the above performance is insensitive to the duration of the disturbance, which demonstrates the strong robustness, high accuracy, and excellent dynamic response capability of the proposed design.

Primary component segmental design to suppress the normal force ripple for the permanent magnet linear synchronous motor

AbstractThere is not only thrust but also normal force between the primary and secondary components for the single‐side flat plate permanent magnet linear synchronous motor (PMLSM). The normal force will fluctuate periodically, which will cause friction perturbation and finally affect the positioning accuracy of linear feed system. For the single‐side flat plate PMLSM, the variation law of normal force ripple under the coupling effect of multiple effects is studied, and the method of primary component segmental design to suppress it is proposed. Firstly, the influence of the cogging effect, the end effect and the armature reaction on the normal force ripple is analysed. Meanwhile the mathematical model of normal force ripple is established. Secondly, the PMLSM with segmental primary component is introduced and its suppression mechanism to the normal force ripple is expounded. On this basis, a scheme combining the non‐integer pole slot matching with the primary component segmental design is proposed to further suppress the normal force ripple. Finally, an 18‐slot 96/5‐pole prototype is taken as an example to carry out the finite element simulation and experimental test, of which the results verify the research theory in this paper.

Research on Torque Ripple and Influencing Factors of Hydro-Generator

Background: The safe and stable operation of large-capacity hydro-generators is of great significance to the power grid. However, due to the armature reaction and the stator slots of the hydroelectric generator, the torque ripple of the generator is usually large. Long time running under the condition of large torque ripple will cause damage to the generator components and even threaten the safety of the power grid. Objective: To study the factors affecting the torque ripple of the hydro-generator and reduce the torque ripple. Methods: A 24 MW bulb tubular hydro generator is taken as an example, a two-dimensional transient electromagnetic field model was established, and the correctness of the model was verified by experiments. The causes of armature reaction and cogging effect on motor torque are analyzed. The effects of these two factors on torque ripple are studied respectively. The torque ripple under different working conditions is calculated, and the main factors causing and increasing torque ripple during normal operation of hydro generator are determined. Results: The torque ripple increases approximately linearly with the increase of the 7th and 11th harmonic contents, while it increases nonlinearly with the increase of the 5th harmonic contents. When the excitation current increases from 720 A to 960 A, the torque ripple is increased by 11.4kN•m. In addition, when the excitation current increases from 720A to 840A (Rated excitation current of the generator is 840A), the torque ripple increases greatly, the torque ripple increases by 6.6kN•m. When the excitation current exceeds the rated excitation current, due to the influence of magnetic saturation, the increasing extent of torque ripple gradually decreases. When the excitation current increases from 840A to 960A, the torque ripple increases only by 4.8kN•m. Conclusion: Due to the armature reaction, the harmonic magnetic potential will be generated in the generator, which will affect its torque ripple. The torque ripple of the generator will increase obviously with the increase of harmonic content. When the generator is in no-load operation, the slot effect is the main cause of the torque ripple. In the actual operation of the generator, it usually needs to adjust the excitation current to make the generator meet the requirements of various working conditions.

Magnetic Field Analysis for the Permanent Magnet Spherical Motor With SMC Core

This paper presents a permanent magnet spherical motor (PMSM) with soft magnetic composite (SMC) core. The analytical model of the no-load air-gap magnetic field of the PMSM with SMC core is obtained based on the Laplace equation with the boundary conditions. When the SMC core is added to the stator teeth, a cogging effect occurs, which makes the three-dimensional magnetic circuit of the entire spherical surface uneven. When the spherical motor completes multi-degree-of-freedom motion, the air-gap magnetic field is severely distorted. In order to solve the above problems, this paper proposes for the first time the method of adding spherical shaped pole shoes to the stator teeth, which perfectly solves the problem of magnetic field distortion in this paper. The air-gap magnetic field distribution is improved by optimizing the structure of the stator tooth pole shoes. Finally, the static torque measurement platform was built to test the rotation energized output torque. The research results of this paper lay a theoretical foundation for the structural optimization design of the PMSM with SMC core.

Optimization of Cogging Torque Based on the Improved Bat Algorithm

Permanent magnet motors have the advantages of high output torque, high efficiency, and low noise, but the cogging effect is obvious. The 24-slot 4-pole surface-mounted permanent magnet synchronous motor is taken as an example to reduce the cogging torque of permanent magnet synchronous motors. Firstly, the generation mechanism of cogging torque is analysed based on the energy method, and the pole arc coefficient, air gap length, magnetic pole eccentricity, permanent magnet thickness, and slot opening width are determined as optimisation parameters. Then, a cogging torque optimisation method is further proposed based on the Taguchi method and the response surface method, and the bat algorithm with the Lévy flight feature is applied to obtain the optimal solution for the response surface model. Finally, finite element software is used to simulate the optimal motor model. The experimental results show that the efficiency of the motor solved by optimal parameters is increased by 1.6%, the cogging torque is reduced by 82.16%, and the torque ripple is reduced by 8.2%. The optimisation of cogging torque in this paper avoids fluctuations in torque, reduces motor vibration and noise, and improves the control characteristics of the permanent magnet motors drive system, operational reliability, and low-speed performance in the motor speed control system and high accuracy positioning in the position control system.

Pole shape design of ring winding axial flux permanent magnet used in a direct‐drive electric boat for cost‐efficient cogging torque alleviation

AbstractThe recently introduced Ring Winding Axial Flux Permanent magnet Motor (RW‐AFPM) is inspired by the yokeless structure of Yokeless and Segmented Armature (YASA) AFPMs and the partitioned‐phases configuration of transverse flux motors. Its potential application for rim‐driven electric ships propulsion has been examined in the previous studies and, here, it will be studied for ultra‐light direct‐drive electric boats. Owing to their specific structural features, the relatively large cogging torque of RW‐AFPMs seems to be a significant challenge for such applications. On the other hand, as investigated in previous studies, cogging torque reduction methods, such as conventional skewing, seem unsuitable for this type of machine. Thus, this paper will address the cogging torque issue via a comprehensive pole shape analysis. The results will be useful for all kinds of partitioned‐phases topologies that have high specific torque capability but suffer from large cogging effects. All analyses are performed via 3D‐FE models, the accuracy of which is pre‐verified through experiments.

Analysis on the Air-Gap Magnetic Flux Density and Propulsion of the TFLSM Considering Cogging Effect

A novel transverse flux linear synchronous motor (TFLSM) is proposed, which can realize propulsion, levitation, and guidance functions in maglev train. Considering the cogging effect, a novel analytical method for calculating the air-gap magnetic flux density of the TFLSM is proposed. First, the overall configuration and operation principle of the TFLSM are discussed. Second, the model of the analytical method is proposed, and the magnetic permeability coefficients of the primary and secondary of the TFLSM are established and calculated; then, the air-gap magnetic flux density of the primary and the secondary is obtained. Besides, the propulsion force is calculated considering the cogging effect. Finally, the finite-element method (FEM) and experimental model of the motor are established, and by comparing the propulsion force of the analytical results with the FEM and measurement results, the correctness and effectiveness of the analytical calculation method are verified, which provides a basis for further establishing the real-time motion control model of TFLSM.

Analysis and Research on No-Load Air Gap Magnetic Field and System Multiobjective Optimization of Interior PM Motor

In this article, considering the influence of iron core saturation and complex boundary conditions, a novel no-load magnetic field analytical method and system multiobjective optimization model for interior permanent magnet synchronous motor (IPMSM) are proposed. First, an analytical method based on magnetic potential permeance method is proposed. The complex cogging effect and equivalent air gap permeability function are fully considered in this method. Furthermore, on the basis of Taguchi optimization design based on Fuzzy theory, an improved optimization model considering multivariable interaction is proposed. Among them, in order to comprehensively consider the performance of electromagnetic, vibration, and temperature rise, five optimization objectives including torque, pulsation, cogging torque, loss, and flux density are optimized. The sensitivity of design variables and the interaction between variables are not ignored. Finally, a 6-pole 36-slot IPMSM is manufactured for prototype experiments. A large number of prototype experiments, finite element, and computational fluid dynamics simulation analysis including no-load magnetic field, back electromotive force, temperature rise, electromagnetic torque, and so on are carried out. The accuracy and rationality of the proposed no-load magnetic field analysis method and global optimization model are well-verified.

An Improved PLL-Based Speed Estimation Method for Induction Motors through Harmonic Separation

The real-time speed estimation of induction motors (IMs) is important for the motors’ state monitoring and control. The utilization of rotor slot harmonics (RSHs) due to the inherent cogging effect is regarded as a promising way to realize the speed estimation of IMs. The key to the RSH-based speed estimation method is how to accurately and quickly identify the frequency of an RSH signal. However, as the RSH signal always consists of two side-frequency components that are adjacent to each other, it is actually improper to directly use the conventional phase-locked loop (PLL) method designed for single-frequency tracking. Furthermore, the form of the two side components in the frequency domain also leads to a significant amplitude fluctuation in the time-domain waveform of RSHs, thus resulting in the obvious frequency tracking errors of the conventional PLL method. In this paper, we proposed an improved PLL through harmonic separation to further improve the performance of the RSH-based speed estimation method of multiphase IMs, so that the dynamic tracking errors of PLL due to the reasons mentioned above can be significantly reduced. Simulations and experiments in a wide speed range were also performed, with their results presented as verifications of the proposed method.

Research on Simulation Method for Wear for Dynamic Seal in Axial Flux Hub Motor

A simulation method for the wear of a dynamic seal in an axial flux hub motor is proposed in this work. A quasi-3D magnetic model without deflection between the axes of a stator and a rotor is built. An analytical model for unbalanced magnetic force considering the cogging effect and axial deflection is presented based on the quasi-3D magnetic model. Boundary conditions of the dynamic seal are obtained through solving the FE model of a hub motor. Both the structural and thermal FE model of a dynamic seal are built and the thermal–structural coupling method is given. A dynamic wear simulation method is displayed based on the mesh reconstruction method proposed previously. It is proved through the contrast with the experimental results that the presented method is feasible.

Research on Environmental Magnetic Field of Two-Pole Permanent Magnet Motor Considering Cogging

The peripheral magnetic field of the motor may cause magnetic field interference to the surrounding sensors, which would reduce the accuracy of sensors and affect the safety and concealment of vessel. This article explored the environmental magnetic field distribution law of a permanent magnet (PM) motor with two-pole parallel magnetization. A no-cogging magnetic field model was obtained by solving Maxwell equations, and the relationship between the air gap flux density and the environment flux density was built considering the motor cogging effect. In addition, a mathematical model of connections between the back electromotive force (EMF) and the environmental flux density was built, and the correctness of the model was verified by COMSOL. It is concluded that the circumferential and radial components of the environmental magnetic field are distributed sinusoidally, and the magnetic flux density modulus remains constant on the equidistant circumferential line, but attenuates squarely with the distance from the motor. It provides ideas for magnetic field analysis in the peripheral environment of other types of motors, sensors, and other anti-motor electromagnetic interference, magnetic field compensation for geomagnetic measurement, and motor fault diagnosis.

Analytical modelling of No‐load magnetic field for equivalent poles of a new type of double‐stator PM poles spherical motor

A double-stator swing rotating permanent magnet spherical motor (SR-PMSM) is designed, which can realize rotation, swing and spiral motion, and is used in the multi-degree-of-freedom motion fields of industrial robot joints, torque gyroscopes, panoramic photography tables and so on. The inner surface of the rotor of the motor is attached with cylindrical PM poles, and the outer surface is attached with trapezoidal PM poles. Cylindrical and trapezoidal PM poles are simple to manufacture, but the magnetic field model of a spherical motor with two kinds of PM poles is complex. Therefore, a magnetic field modelling method combining the geometric equivalence principle and analytical method is proposed. Using the method of shape approximation, according to the principle of equivalence, the key parameters of cylindrical PM poles and trapezoidal PM poles are replaced by the parameters of approximate dihedral PM poles in a spherical coordinate. Select the most suitable dihedral PM poles, establish the analytical model of the magnetic field in the spherical coordinate system and verify the analytical results by FEM method. A SR-PMSM motor with 6/4 pole (swing) and 12/10 pole (rotation) structure was assembled, and the experimental device was set up. The experimental results show that the experimental curve, analytical curve and FEM curve are in good agreement, which proves the accuracy of the equivalent model and is suitable for the magnetic field model of cylindrical and trapezoidal PM poles of the spherical motor. The research results of magnetic field lay a foundation for further analysis of the stator–rotor composite magnetic field considering cogging effect and edge effect, and analysis of load characteristics of the motor.

Analytical calculation of magnetic field of double‐stator permanent magnet spherical motor considering cogging effect and edge effect

A new type of double-stator permanent magnet spherical motor (DSSRPMSM) is proposed. Compared with most existing spherical motors, this motor uses a large number of stator iron cores, which can generate larger magnetic flux density and significantly improve torque capacity. The proposed DSSRPMSM can continuously rotate, swing and spiral, and can be used in the multi-degree-of-freedom motion fields of industrial robot joints, moment gyroscopes, panoramic photography tables and so on. Because the motor has the dual characteristics of rotary motor and arc linear motor, the comprehensive effects of stator slotting and stator iron core breaking should be considered. Cylindrical and trapezoidal PM poles are equivalent to dihedral PM poles, and stator coils are equivalent to PM pole models. Analytical models of PM pole magnetic field and stator magnetic field in a spherical coordinate system are established, and the air gap magnetic flux density under unequal magnetic potential boundary conditions is calculated by conformal transformation. The analytical calculation method proposed is consistent with the results of finite element method (FEM) simulation, and the experimental test further verifies the effectiveness and accuracy of this method.

Optimization Design of Unequal Amplitude Modulated Poles for the Bearingless PMSM

The structural parameters of an equal amplitude modulated magnetic pole is limited by the length of the air-gap. When the modulation ratio or carrier ratio is small, the spacing of permanent magnets is too large, which will lead to a worse cogging effect, and then the torque optimization effect is not satisfying. In order to improve the operation stability of a bearingless permanent magnet synchronous motor (bearingless PMSM), an unequal amplitude modulated magnetic pole structure is proposed according to the principle of magnetic pole modulation. The Taguchi method is used to optimize the structural parameters of the unequal amplitude modulated magnetic pole with the goal of reducing the torque and suspension force fluctuation. Three kinds of magnetic pole structures, named the whole magnetic pole, the equal amplitude modulated magnetic pole and the unequal amplitude modulated magnetic pole are compared and verified. The results show that the proposed structure of the unequal amplitude modulated magnetic pole can effectively further decrease the torque and suspension force fluctuations under the premise of the output capacity of the motor being unchanged, which improves the performance of the bearingless PMSM.

Reduction of cogging torque and electromagnetic vibration based on different combination of pole arc coefficient for interior permanent magnet synchronous machine

Cogging torque and electromagnetic vibration are two important factors for evaluating permanent magnet synchronous machine (PMSM) and are key issues that must be considered and resolved in the design and manufacture of high-performance PMSM for electric vehicles. A fast and accurate magnetic field calculation model for interior permanent magnet synchronous machine (IPMSM) is proposed in this article. Based on the traditional magnetic potential permeance method, the stator cogging effect and complex boundary conditions of the IPMSM can be fully considered in this model, so as to realize the rapid calculation of equivalent magnetomotive force (MMF), air gap permeance, and other key electromagnetic properties. In this article, a 6-pole 36-slot IPMSM is taken as an example to establish its equivalent solution model, thereby the cogging torque is accurately calculated. And the validity of this model is verified by a variety of different magnetic pole structures, pole slot combinations machines, and prototype experiments. In addition, the improvement measure of the machine with different combination of pole arc coefficient is also studied based on this model. Cogging torque and electromagnetic vibration can be effectively weakened. Combined with the finite element model and multi-physics coupling model, the electromagnetic characteristics and vibration performance of this machine are comprehensively compared and analyzed. The analysis results have well verified its effectiveness. It can be extended to other structures or types of PMSM and has very important practical value and research significance.

Research on rotor unbalance magnetic pull compensation method based on modular winding d‐axis current injection

Due to the dual air-gap topology of the direct-drive permanent magnet motor with inner enhance force (IEF-DDPMM), the radial EM exciting force generated in the inner and outer air gaps when the rotor is eccentric will act on the same rotor, and the unbalanced magnetic pull (UMP) on the rotor will reduce the fatigue life of the rotor structure and bring many problems such as vibration and noise. Therefore, the rotor UMP compensation method of IEF-DDPMM based on modular winding d-axis current injection is proposed to suppress the harm caused by eccentricity. The expression of electromagnetic (EM) exciting force considering the cogging effect and current time harmonic without rotor eccentricity faults is derived by the analytical method. Also, the EM exciting force newly introduced due to the rotor eccentricity is analysed. The effects of different eccentricity types on torque characteristics, the fatigue life of the rotor structure and stator vibration of IEF-DDPMM are compared and analysed by the FEM. Finally, the IEF-DDPMM rotor eccentricity models are optimised based on the method. The performance of the motor before and after rotor UMP compensation is evaluated by FEM. The results show that the proposed method is correct and effective.

Vibration Analysis of Hub Motor Based on ANSYS

The hub motor is designed with multidirectional excitation and Halbach Array, which includes inner rotor, left and right stator, outer stator, encoder and rotary transformer. The rotor consists of an axial disk and a top ring. The rotor’s permanent magnets are affixed to the left and right sides of the disk and to the outside of the top ring. The permanent magnets on the rotor adopt a Halbach Array. The three stators have not the iron core and they are arranged outside the rotor to form a three-way closed loop. The motor has high power density, high torque density, low heating, strong adaptability and no cogging effect. It is suitable for electric car control. On this basis, the dynamic equation of the hub motor is established, the vibration mode of the rotor system is analysed, when the inner rotor’s speed is 18000rpm. By use of the solid model, the hub-rotor’s accurate dynamics solution can be obtained. In the future, the effect of vertical coupling vibration will be investigated for its ride comfort and safety.

Analytical Calculation of Open‐Circuit Magnetic Field in Linear Phase‐Shifting Transformer Based on Exact Subdomain Model

Linear phase‐shifting transformers (LPSTs) are a new type of transformer that can be used in multi‐rectifier and multi‐inverter systems. However, calculating a precise magnetic field distribution in LPSTs, which is the key premise for obtaining accurate transformer parameters and performance evaluations, remains a challenging task. The present work addresses this issue applying the exact subdomain method (ESM) to establish an analytical model of the magnetic field distribution in an LPST with an arbitrary number of slots in two‐dimensional Cartesian coordinates using the magnetic vector potential as the solution variable. The Poisson equations are established in the slot subdomain of the primary side, and the Laplace equations are established in the slot subdomain of the secondary side and in the air gap subdomain. The harmonic coefficients are obtained using the Fourier series method in conjunction with the boundary conditions, and the distribution of the open‐circuit magnetic flux density is then solved in each subdomain. The model effectively accounts for the cogging effect on the magnetic field distribution. The inductance of the primary side and the induced potential of the secondary side are obtained using the magnetic flux linkage method. The accuracy of the proposed analytical model is verified by comparison of the results obtained with those obtained by the finite element method (FEM). © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A new method of phase-shifting and displacement of unit motor to suppress the thrust fluctuation of linear motor

Permanent magnet linear motors can cause thrust fluctuation due to cogging and end effects, which will affect the operation stability of the linear motor. In order to solve this problem, a new method of eliminating alveolar force by using phase-shifting and displacement is proposed in this paper. Taking the cylindrical permanent magnet linear motor as an example, the traditional cylindrical permanent magnet linear motor is divided into two unit-motors, and established finite element analysis model of cylindrical permanent magnet linear motor. It is different from other traditional methods, the thrust fluctuation was reduced by both phase-shifting and displacement simultaneously in this paper, and through simulation analysis, it is determined that the thrust fluctuation suppression effect was the best when the cogging distance was shifted by half. Furthermore, a comparative simulation was made on whether the magnetic insulating material was used. The simulation results show that: The method proposed in this paper can effectively suppress the thrust fluctuation of the cylindrical permanent magnet linear motor. And it can be applied to other similar motor designs. Compared with the traditional method of suppressing thrust fluctuation, the mechanical structure and the technological process of suppressing thrust fluctuation used in this method are simpler.

Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.