Unbalanced Magnetic Force Research Articles

Dynamic characteristics analysis of high-speed motorized spindle system considering unbalanced magnetic pull and non-linear bearing restoring force

Abstract The high-speed motorized spindles play a pivotal role in modern machining, holding vast application potential and profound research significance. To analyze the dynamic characteristics of the high-speed motorized spindle system, an fourteen-degree-of-freedom dynamic model has been established using the lumped parameter method, and numerical methods have been employed for computation. Then, the bearing stiffness, the variation of the restoring force, and the unbalanced magnetic force are considered. Additionally, the parameters of the model were optimized using the genetic algorithm. Finally, the effects of spindle speed, initial eccentricity, and bearing parameters on the vibration behavior and stability of the motorized spindle were analyzed using bifurcation diagrams, time-frequency waveform, spectra, trajectories, and Poincaré. The study provides a valuable reference for the design and optimization of motorized spindle systems.

Effects of slot-pole combinations on vibration and performance in fractional slot permanent magnet synchronous machines

Abstract Unbalanced Magnetic Force (UMF) is a critical factor that significantly impacts vibration and overall performance in Permanent Magnet Synchronous Machines (PMSMs). This study investigates the influence of different fractional slot combinations on UMF behavior in PMSMs using finite element analysis (FEA). The focus is on the canceling and additive effects of UMFs generated by radial and circumferential stresses. Two PMSM configurations with slot and pole numbers differing by one—26 poles/27 slots and 28 poles/27 slots—are analyzed to evaluate the effect of varying pole configurations while keeping the slot count constant. The analysis employed the Maxwell stress tensor method to quantify the UMFs in these designs. The results underscore the critical role of the magnet configuration in determining UMF characteristics, providing essential insights for optimizing machine design to minimize vibration and enhance performance. These findings serve as a valuable reference for designing and operating high-performance fractional slot PMSMs, particularly for industrial and automotive applications.

Analysis of rotor vibration characteristics of surface mounted permanent magnet synchronous motor under air gap eccentricity fault

Taking a permanent magnet synchronous motor as the research object, the effect of air gap eccentricity fault on the vibration response characteristics of the motor rotor is analyzed through theoretical calculations, numerical simulation and finite element simulation. First, the change of air gap magnetic field under air gap eccentricity fault is analyzed, and then further calculated to obtain the unbalanced magnetic force under air gap fault by the expression of air gap magnetic field, at last, the rotor’s vibration response characteristics under the action of unbalanced electromagnetic force are obtained by the Newmark- β calculation method. Detailed analysis of the effects of eccentricity distance, eccentricity angle and motor pole-pair number on motor rotor vibration. Finally, the synchronous motor eccentricity fault model is built in ANSYS Maxwell electromagnetic simulation software, and the change characteristics of rotor unbalanced magnetic force after eccentricity fault are calculated and the results are consistent with the theoretical calculations.

Study of Unsymmetrical Magnetic Pulling Force and Magnetic Moment in 1000 MW Hydrogenerator Based on Finite Element Analysis

The large dimensions of the 1000 MW hydroelectric generator sets require high mounting accuracy. Small deviations can lead to asymmetry, which in turn triggers unbalanced magnetic pulls and moments. Therefore, symmetry is a central challenge in the installation and operation of giant hydroelectric generators. In this paper, the effects of radial eccentricity, axial offset, and rotor shaft deflection on the unbalanced magnetic pull and moment are investigated by transient finite element analysis of the asymmetric magnetic field. The results of the time-domain and frequency-domain analyses show that asymmetric operation generates unbalanced magnetic forces and moments. These forces and moments increase linearly with increasing offset or deflection rate. When the eccentricity meets the installation criteria, the unbalanced magnetic pull forces are small and within acceptable limits. This study helps to understand the relationship between asymmetry and unbalanced magnetic pulling forces in large hydroelectric generators, and provides a theoretical basis for standardizing installation deviation control.

Vertical vibration control to the in-wheel-motor electric vehicles with static eccentricity based on a reinforcement learning method

The in-wheel-motor electric vehicle (IWM-EV) is hailed as the epitome of driving ingenuity within the realm of electric vehicles. Nonetheless, the intricate nature of its components, compounded by the intricate interplay of multiple force fields, poses a significant detriment to ride comfort. In the present study, an IWM-EV driven by a permanent magnet synchronous motor was employed as a representative case study. Initially, the calculations were conducted to determine the unbalanced magnetic force (UMF) in the presence of static eccentricity of the stator. Subsequently, the characteristics of UMF across different ratios of static eccentricity as well as different velocities in the time domains were analyzed. Furthermore, the road-electromagnetic-mechanical model was developed to investigate the influence of UMF on the vertical vibration of IWM-EV under static eccentricity, comparing it against the scenario devoid of UMF. Finally, a reinforcement learning control approach was adopted to regulate the active suspension system, comparing its efficacy with that of passive suspension and semi-active suspension (specifically, skyhook control). Through extensive simulations, the results demonstrated that the reinforcement learning control strategy derived from the road-electromagnetic-mechanical model outperforms the other two control strategies, exhibiting commendable resilience and adaptability across diverse road surfaces and velocities. This study unveiled the potential of RL methods in enhancing riding comfort through active suspension control.

Comparative Study of High-speed Permanent Magnet Synchronous Motors with In-line Slot Conductors and Equidirectional Toroidal Windings

The high-speed permanent magnet synchronous motor (HSPMSM) plays an important role in a wide range of engineering fields due to its high power density, high efficiency, and light weight. In this paper, a HSPMSM equipped with in-line slot conductors(I-LSC) is proposed and compared with one equipped with equidirectional toroidal winding (ETW). Firstly, the differences between them are revealed, including topology, back-electromotive force (EMF), slot fill factor, copper loss, and torque. Secondly, two-dimensional finite element method (2D-FEM) tools are used to obtain more precise performance such as air-gap field, back-EMF, torque characteristics, efficiency maps, and the unbalanced magnetic force (UMF). Considering the end-windings of copper loss of ETW and the end ring copper loss of I-LSC, the losses and efficiency of two motors are simulated by three-dimensional finite element method (3D-FEM). Finally, the simulation results validate the feasibility of the newly proposed winding and indicate that in-line slot conductors have superiority in power density due to the high slot fill factor.

Calculating torque, back-EMF, inductance, and unbalanced magnetic force for a hybrid electrical vehicle by in-wheel drive application

To use a Hybrid Excitation Synchronous Machine (HESM) in a hybrid electrical vehicle (HEV), its performance indicators such as back-EMF, inductance and unbalanced magnetic force should be computed preferably by an analytical method. First, the back-EMF is calculated by considering alternate-teeth and all-teeth non-overlapping and overlapping windings. The effects of three types of magnetization patterns including the radial, parallel and Halbach magnetizations on the back-EMF waveform have also been investigated. Then, the self-inductance of the stator and rotor windings, the mutual inductance between the stator and rotor windings, and the mutual inductance between the stator phases are computed. Next, the components of the unbalanced magnetic force (UMF) in the direction of the x and y axes and its amplitude are computed. Moreover, the effects of the magnetization patterns on those magnetic pulls are investigated. To minimize the UMFs, symmetry must be implemented in the excitation sources; therefore, first the stator winding then the permanent magnet and rotor winding are modified in such a way that the UMFs are reduced. Increasing the temperature leads to a weakening of the magnet’s residual flux density, which strongly affects the performance characteristics of the electric machine such as Back-EMF and UMF. Finally, the ratio of the permanent magnet flux to the rotor flux is determined in such a way that the average torque is maximized. In this section, the effects of three magnetization patterns will be investigated.

The influence of ITSF on vibration of high voltage Line-Start permanent magnet synchronous motor

PurposeThe purpose of this paper is to present the influence of inter-turn short circuit faults (ITSF) on electromagnetic vibration in high-voltage line-starting permanent magnet synchronous motor (HVLSPMSMS).Design/methodology/approachIn this paper, the ampere–conductor wave model of HVLSPMSM after ITSF is established. Second, a mathematical model of the magnetic field after ITSF is established, and the influence law of the ITSF on the air-gap magnetic field is analyzed. Further, the mathematical expression of the electromagnetic force density is established based on the Maxwell tensor method. The impact of HVLSPMSM torque ripple frequency, radial electromagnetic force spatial–temporal distribution and rotor unbalanced magnetic tension force by ITSF is revealed. Finally, the electromagnetic–mechanical coupling model of HVLSPMSM is established, and the vibration spectra of the motor with different degrees of ITSF are solved by numerical calculation.FindingsIn this study, it is found that the 2np order flux density harmonics and (2 N + 1) p order electromagnetic forces are not generated when ITSF occurs in HVLSPMSM.Originality/valueBy analyzing the multi-harmonics of HVLSPMSM after ITSF, this paper provides a reliable method for troubleshooting from the perspective of vibration and torque fluctuation and rotor unbalanced electromagnetic force.

Comparative analysis of dual stator machines

Electromagnetic performance of three different types of double stator permanent magnet machine is analyzed and compared in this study. The analyzed machines in this study are Machine 1, Machine 2 and Machine 3. These machines are designated as: M 1, M 2 and M 3, respectively. The studies are implemented using two-dimensional and three-dimensional finite element analysis (2D-FEA and 3D-FEA) methods. The predicted performance indices are: total harmonic distortion of the voltage, torque ripple, cogging torque, winding inductances, output torque and unbalanced magnetic force (UMF). The studies show that the investigated machine types have negligible reluctance torque and thus, similar axes inductance values. Therefore, the machines’ bulk torque components are contributed mainly by the magnets while the armature excitation sources yield lesser torque components. Amongst the compared machines, M 3 type has an outstanding performance in almost all the performance metrics, compared to M 2 and M 1 types. Nevertheless, M 1 machine type has some good attributes, particularly, with respect to its high output torque per applied magnet volume, in addition to its widest operating speed range ability. Low-speed high-torque applications are most suitable for the investigated machines in practice.

Analysis of longitudinal-vertical coupling vibration of four hub motors driven electric vehicle under unsteady condition

The influence of hub motor unbalanced magnetic force (UMF) on the vibration of electric vehicle under steady state conditions has been known, but under unsteady conditions, the hub motor UMF will change with the vehicle operation condition, and there would exist complex coupling vibration for the hub motors driven electric vehicle. Here, the longitudinal-vertical coupling dynamics of the four hub motors driven electric vehicle under unsteady condition is studied. Integrating the motor electromagnetic excitation and electric vehicle dynamics, a longitudinal-vertical coupling dynamics model of the four hub motors driven electric vehicle is established. Based on the variable switching frequency field-oriented control model, analytical model of the UMFs acting on the motor stator and rotor parts under unsteady condition are developed. For model validation, a four hub motors driven electric vehicle has been tested, the accuracy of the longitudinal-vertical coupling dynamics model established in this paper was verified. Then, longitudinal-vertical coupling vibration characteristics of the four hub motors driven electric vehicle under road excitation and coupling excitation are analyzed. The results show that the longitudinal and vertical movement of the four hub motors driven electric vehicle is coupled by hub motor. In addition, under unsteady condition, the motor UMFs will cause vertical vibration of the electric vehicle body and hub motor stator, the vibration shows order characteristics including low order harmonic hfc and inverter switching frequency sideband harmonic k1 fs±k2 fc ( fc = pn/60, fs is inverter switching frequency, k1 and k2 are positive integers, p is the number of pole pairs and n is motor speed.). The motor electromagnetic torque will cause longitudinal vibration of the electric vehicle body, the vibration shows order characteristics including harmonics fs±3 fc and 2 fs. The main harmonic of vehicle body pitch angle acceleration is 2 fs.

Vibration analysis of a permanent magnet synchronous generator considering electromagnetic vibration sources under AC and DC load conditions

As the performance of permanent-magnet synchronous generators improves, research on device noise is also becoming important. This study analyzes the causes of electromagnetic noise, such as the back electromotive force, cogging torque, torque ripple, unbalanced magnetic force, and harmonics that occur during operation for each DC and AC load. In particular, it shows that the influence of the waterfall diagram changes depending on the harmonic order of the torque ripple. By combining 2D finite element analysis and 3D mechanical analysis, electromagnetic analysis can be used to analyze the noise-generating relationship. Based on the analysis results, the electromagnetic noise generation results depending on the load are presented. The electromagnetic performance and mechanical reliability of the designed model were verified by comparing the finite element method and experimental results.

Investigation of Five-Phase Flux-Switching Permanent Magnet Machines for EV and HEV Applications

As a member of stator permanent magnet (PM) brushless machines, flux-switching (FS) PM machine features outstanding advantages, e.g., robust rotor structure, easy temperature management, high torque density, etc. In this paper, the five-phase FSPM machines for electric vehicle (EV) and hybrid electric vehicle (HEV) applications are investigated. Firstly, the working principle of such machine is analyzed by air-gap field modulation theory. Then, the feasible slot/pole combination is discussed, considering flux leakage, back electro-magnetic force (EMF) quality and unbalanced magnetic force (UMF). Besides, in order to further choose the recommendable slot/pole combination, the torque performances are studied and compared by taking the 20-stators-slot FSPM machines as examples, such as rated torque, overload capability, flux weakening capability and fault tolerance capability. Further, in order to optimize the slot/pole combination which suffers from severe UMF, two different techniques for UMF reduction are proposed, including chamfering both in stator and rotor side. Finally, finite element analysis is employed to verify the analytical analyses. Meanwhile, a 20/18 prototyped machine is manufactured and tested. It is found that the experimental results verify the effectiveness of the analytical analyses.

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Analytical Cogging Torque and Unbalanced Magnetic Force Calculations in Slotted Surface-PM Machines Assuming Finite Iron Permeability

Unbalanced magnetic pull in angular eccentricity magnetic screw

AbstractThis paper investigates the unbalanced magnetic force (UMF) produced by angular eccentricity in a magnetic screw. The principle of eccentricity is briefly outlined and an analytical expression that can be used to predict UMF of a magnetic screw is established. A 3D magnetic screw model with helically magnetized permanent magnets (PM) has been built and simulated in ANSYS Maxwell with different angular eccentricities. Comparing the finite elements (FE) simulation and analytical calculation results, there is a certain difference in the UMF of the magnetic screw, which is also caused by the asymmetry of the magnetic screw structure. It has been shown that compared to the linear tubular PM motor with the same thrust force capability, the magnetic screw has a much small UMF, which greatly simplifies the mechanical design of the magnetic screw.

A New Technique for the Subdomain Method in Predicting Electromagnetic Performance of Surface-Mounted Permanent Magnet Motors With Shaped Magnets and a Quasi-Regular Polygon Rotor Core

Surface-mounted permanent magnet (SPM) motors with shaped magnets and a quasi-regular polygon rotor core (QPRC) are challenging to analyze in terms of accuracy and speed because of the special structure. This article proposes a new technique for the subdomain method which can accurately predict the electromagnetic performance of this kind of motor. The proposed new technique deals with the shaped magnet based on the method of magnet symmetrical segmentation, and it can solve the magnetic field generated by a pair of symmetrical segments together at each time. Especially, for the QPRC, the idea of variable rotor core radius is used in the new technique to analyze different segments. Furthermore, the new technique adopts a periodic boundary condition, which can quickly predict the electromagnetic performance of the motor, such as air-gap flux density, cogging torque, no-load back-EMF, winding inductance, electromagnetic torque and unbalanced magnetic force (UMF). This proposed new technique is applied to a 12-pole/3-phase SPM motor with shaped magnets and a QPRC, and its correctness is verified by finite-element analysis and experiment. The new technique can analyze the motor accurately, and its calculation speed is two orders of magnitude faster than that of the finite-element method.

Vibration and Noise Optimization of New Asymmetric Modular PMaSynRM

This study proposes an optimized structure to weaken the vibration and noise of a new asymmetric permanent magnet-assisted synchronous reluctance motor (PMaSynRM). The new asymmetric PMaSynRM has the advantages of a low torque ripple and high fault tolerance. However, the asymmetric structure generates an unbalanced magnetic force (UMF), which results in vibration and noise problems. In this study, the vibration and noise of the motor are analyzed and optimized. First, the radial pressure is analyzed, and an optimized structure is proposed. The electromagnetic performance of the motor before and after optimization is analyzed using the finite element method. Second, a three-dimensional model is established, and modal analysis is conducted considering the orthotropy of the stator and effective windings. Finally, the vibration and noise are simulated and analyzed, and the validity of the analysis results is verified experimentally. The analysis results indicate that the optimized motor realizes a reduction in the motor vibration and noise.

A review on analytical models of brushless permanent magnet machines

AbstractThis study provides an in‐depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite‐element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time‐consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent circuits (MEC) or solving Maxwell's equations can be faster and more flexible, but less accurate for complex machine structures. The paper focuses on the recent development of analytical models for brushless permanent‐magnet (PM) machines that have become increasingly popular in low and medium‐power applications. The literature review covers the recent developments in analytical models for PM machines with respect to various machine quantities such as magnetic flux density components, induced voltage, inductances, electromagnetic force/torque, efficiency, or unbalanced magnetic force (UMF). It outlines the advantages and disadvantages of different analytical models such as the zero‐dimensional (0‐D), one‐dimensional (1‐D), two‐dimensional (2‐D), and three‐dimensional (3‐D) analytical methods, as well as the Maxwell and basic mathematical analysis. Although the MEC models are faster than the numerical model, they are not as accurate for various structures of electrical machines including a great magnetic air gap. They also note that the analytical models based on the Maxwell equations are faster than the numerical ones and have the potential to obtain acceptable accuracy similar to the numerical models in electrical machines. Overall, this literature review provides valuable insights for researchers and engineers in selecting appropriate analytical models for PM machines. It highlights the trade‐offs between accuracy and computational efficiency when choosing between numerical and analytical models, and the flexibility of analytical models to address changes in machine geometries or input values. Additionally, this helps researchers save time in determining appropriate references regarding the analytical models of brushless PM machines.

Calculation and analysis of the unbalanced magnetic thrust for the linear motor drive motion system

AbstractThe unbalanced magnetic thrust caused by the mover eccentricity for the linear motor drive motion system is analytically represented. Firstly, the relative complex magnetic permeability function is introduced to represent the effects of the mechanical installation errors and vibrations on the mover eccentricity. Then, the distortion of the magnetic field caused by the mover eccentricity is represented based on the Maxwell equation. The spectrum characteristics of the unbalanced magnetic thrust force is analytically calculated taking into account the harmonics in the drive circuit. Finally, the validity of the theoretically analysis is verified by the experiments. The results show that the static eccentricity caused by the mechanical installation error will produce the unbalanced magnetic thrust, affecting the thrust characteristics of the linear motor. In particular, the dynamic mover eccentricity caused by the mechanical vibration will produce paired unbalanced magnetic thrust harmonics on both sides of the original thrust harmonics, deteriorating the dynamic precision and efficiency of the direct drive motion system.

Effect of Unbalanced Magnetic Pull of Generator Rotor on the Dynamic Characteristics of a Pump—Turbine Rotor System

In pumped storage units, the rotor-bearing electromagnetic system is under the joint influence of hydraulics, mechanics, and electromagnetics, and the mechanism of unit vibration problems is very complex to investigate. ANSYS software is used to establish a three-dimensional model of a pumped storage power plant’s rotor-bearing electromagnetic system, and the stiffness coefficient of the unbalanced magnetic traction forces is calculated using the Fourier series of the magnetic conductivity of the air gap. This shows that the nonequilibrium magnetic attraction increases non-linearly with increasing excitation current and eccentricity of the rotor. At each order, the critical velocity of the rotor system increases as the stiffness factor of the bearing increases, with the greatest increase in critical velocity at the third and fourth orders. In the first-order mode-oscillation pattern, the unbalanced magnetic attraction has an effect on the intrinsic frequency of the transverse oscillation, with a reduction in the amplitude of the intrinsic frequency by 34.65%. Axial and transverse modal vibrations manifest themselves as upward and downward motions and transverse oscillations in different portions of the rotor system, respectively, whereas torsional modal vibrations manifest as a radial broadening or reduction in the generator rotor, runner, and coupling portions of the rotor system. The results of the study provide a theoretical foundation and a computational method for the dynamic analysis and design of the rotor system of pumped storage power stations.

Investigation of Flux-Modulating Consequent Pole Motors

This article investigates the electromagnetic performance of a novel variable-flux permanent magnet (PM) motor, named the “flux-modulating consequent pole motor (FCM),” through finite element analysis (FEA) and experiments. The FCM is a combination of a flux-modulating (FM) motor and a consequent-pole PM motor, whose torque can be generated from both the FM and PM motors without causing unbalanced magnetic forces (UMFs). Two models with 16 and 20 poles are used to analyze the torque, efficiency, and power factor of the FCM. Moreover, efficiency maps of the FCM are compared with those of the conventional PM synchronous motors. It is revealed that the torque of the FCM depends on the values of winding factors of the FM and PM motors. Finally, experimental results on a 20-pole prototype machine are presented to validate the operating principle of the FCM and the FEA simulations.