Radial Force Harmonics Research Articles

Investigation of the impact of rotor shaping on the torque and radial force harmonics of a V‐shape interior permanent magnet synchronous machine

AbstractThis paper introduces a technique aimed at improving the performance of an interior permanent magnet synchronous machine (IPMSM) by reducing torque ripple and radial force harmonics. Unlike conventional IPMSMs, the proposed method employs a variable airgap length that is defined by a mathematical function. Two distinct rotor shapes are investigated to determine the most efficient design. Finite Element Analysis is employed to assess both the electromagnetic and mechanical attributes of the proposed motors. It compares the results for three operating points of the shaped motor with those of a conventional one. The investigation delves into the influence of rotor geometry on key output parameters, including Back Electromotive Force (back‐EMF) harmonics, average torque, cogging torque, torque ripple, efficiency, power factor, and radial force harmonics. The findings indicate that optimising rotor shape can significantly enhance IPMSM performance by reducing torque ripples and radial force harmonics, while simultaneously increasing average torque and efficiency at different operating points.

Vibration and Acoustic Noise Reduction in Switched Reluctance Motor by Selective Radial Force Harmonics Reduction

This article presents a novel method for vibration and acoustic noise reduction in a three-phase 6/10 switched reluctance motor (SRM). The test machine has major vibration and acoustic noise at the 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{nd}}$</tex-math></inline-formula> , 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , 5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , 7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , and 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> harmonics. Accordingly, a novel method called “selective radial force harmonics reduction” is proposed. The proposed method selectively reduces the specific radial force harmonics at the stator teeth. By reducing the specific radial force harmonics such as 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{nd}}$</tex-math></inline-formula> , 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , 5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , 7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , and 8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{th}}$</tex-math></inline-formula> , the corresponding vibration and acoustic noise can be reduced significantly in the test machine. In this study, a current calculation for the proposed method is introduced. In addition, finite element analysis and experiments are conducted to verify the effectiveness of the proposed method. Compared with a conventional square current, the experimental results show that the overall sound pressure level is reduced by 7.1 dBA using the proposed method at the rated speed and torque. The dynamic conditions of the test machine using the proposed method are also presented. As a result, the proposed method is effective in reducing vibration and acoustic noise in the three-phase 6/10 SRM.

Influence of Pole and Slot Combination on Torque Characteristics and Radial Force of Fractional Slot Permanent Magnet Machines

The fractional slot concentrated winding structure effectively solves the difficulty of low‐speed and high‐torque permanent magnet (PM) machines with a large number of poles and slots, but it also brings a wealth of magnetomotive force (MMF) harmonic. The winding function method is used to compare and analyze the stator MMF distribution and harmonic content of the fractional slot PM machines with different pole and slot combinations, and the cogging torque waveform and torque ripple are calculated by the finite element method. The influence of pole and slot combination on radial force and vibration modes of fractional slot PM machines is studied. The main vibration mode can be determined from the lowest order of radial force harmonics. The results show that in a fractional slot PM motor, the radial force is the main cause of noise and vibration, rather than the cogging torque and torque ripple. The dominant radial force is mainly produced by the interaction of rotor field harmonics and armature reaction field harmonics, and the vibration and noise will significantly increase with the decrease of the dominant vibration mode order, which largely depends on the pole and slot combination. This paper provides a certain reference for the selection of pole and slot combination in the electromagnetic design process of low speed high torque fractional slot PM motors. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Electromagnetic Force and Vibration Study of Dual-Stator Consequent-Pole Hybrid Excitation Motor for Electric Vehicles

This paper investigates the electromagnetic force and vibration characteristics of a dual-stator consequent-pole hybrid excitation (DSCPHE) motor for electric vehicles. Firstly, the topology and operation principle of the DSCPHE motor are introduced. Subsequently, the temporal and spatial harmonic characteristics of airgap flux and electromagnetic force are derived and analyzed theoretically. The influences of circumferential-segmented winding, consequent-pole rotor, and excitation modes on radial force harmonics are investigated by finite element analysis (FEA). The vibration behaviors of the DSCPHE motor are investigated by the multi-physics FEA model based on mode superposition method. The radial force harmonics that dominate the motor vibration are analyzed. Finally, the DSCPHE motor prototype is built and tested. The motor vibration behaviors are experimentally measured and compared with an interior permanent-magnet synchronous motor (IPMSM) to validate the theoretical results. This work will contribute to the vibration suppression and optimization of the DSCPHE motor.

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.

Influence of the load angle on magnetic radial forces and torque ripple of a low power permanent magnet synchronous machine

This paper shows the influence of the shift phase angle ψ between phase currents and back-electromotive forces on magnetic radial forces and torque ripple for a specific low power permanent magnet synchronous machine. This influence is firstly demonstrated through analytical development considering only the first harmonic values. Then, magnetic pressure harmonics versus space and frequency as well as torque ripple are evaluated on the studied motor for different angles using finite element approach. The aim is to establish a good compromise between consumed current, torque and radial force harmonics at the origin of the electromagnetic noise. Experimental measurements with a sensorless field-oriented control are detailed.

Effect of Phase Shift Angle on Radial Force and Vibration Behavior in Dual Three-Phase PMSM

This article investigates the effect of phase shift angle on radial force and vibration behavior in the dual three-phase permanent magnet (PM) synchronous motor (DTP-PMSM). First, the elimination principles of stator magneto-motive force and radial force harmonics with different phase shift angles are derived. Afterward, a 48-slot/22-pole DTP-PMSM with appropriate windings configurations are analyzed from the perspectives of the electromagnetic performance and vibration behavior in detail. It is found that the 7.5° and 30° configurations have great significance for reducing the amplitude of radial force harmonics. The 7.5° configuration has the lowest second-order radial force amplitude, while the 30° configuration has the smallest amplitude of fourth-, sixth-, and eighth-order radial forces. According to the results calculated by the multiphysics vibration prediction model, the 30° configuration has lower vibration acceleration in the entire frequency band. Finally, the prototypes of the 48-slot/22-pole DTP-PMSMs with 30° and 60° phase shift angle are fabricated. The tests are conducted to validate the theoretical analysis.

Unequal Teeth Design to Reduce Electromagnetic Vibration in Fractional-Slot Concentrated-Windings Permanent-Magnet Machine

This paper presents a new stator topology of fractional-slot concentrated-windings permanent-magnet (FSCWPM) machine in order to reduce the electromagnetic vibration. First of all, the space orders and corresponding frequencies of the lowest order radial force of FSCW-PM machines is studied. A 12-slot/10-pole FSCW-PM machine is used as an example, and its lowest order radial force harmonics are calculated by analytical method and finite element method, respectively. Then, in order to minimize the amplitude of the vibration acceleration, a new stator structure of 12-slot/10-pole machine is designed, by which the amplitude of the lowest order radial force is greatly reduced. Afterwards, the modal and vibration experiments are performed. The result shows that the 2SUPnd/SUP order radial force with 2f0 frequency contributes most to overall vibration. Finally, vibration simulation models of both machines are established, the results show that the machine with unequal teeth design effectively reduce the electromagnetic vibration.

Influence of Converter Topology and Carrier Frequency on Airgap Field Harmonics, Magnetic Forces, and Vibrations in Converter-Fed Hydropower Generator

This paper investigates the effects of converter-fed operation on magnetic forces and vibration in a hydrogenerator. The variable-speed hydrogenerator (in a pumped–storage power plant) is a large synchronous machine with fractional-slot windings. In this paper, the generator is connected to either a resistive load or voltage source converter. Loading cases include two-level converter and three-level neutral-point-clamped converter, and the carrier frequency is equal to 450 and 1050 Hz. Using electromagnetic finite element analysis, airgap flux density harmonics are analyzed in different loading cases. In addition, electromagnetic torque and variations in the rotor field current are also studied. Using Maxwell stress tensor, radial force density distribution in the airgap is investigated and the effect of converter-fed operation on different radial force harmonics is studied. Moreover, structural analysis and electromagnetic vibration synthesis are presented to investigate the effect of converter harmonics on the stator vibration.

Vibroacoustic Analysis of Radial and Tangential Air-Gap Magnetic Forces in Permanent Magnet Synchronous Machines

This paper analyzes Maxwell tensor tangential and radial magnetic forces in permanent magnet synchronous machines in the no-load case. Using matrix notation in the complex domain, a simple expression of the Fourier harmonics of both radial and tangential forces is derived, including all space and time harmonics. These expressions prove that both the frequency content of cogging torque and zeroth-order radial forces are linked to the least common multiple between the stator slot number and the rotor poles number, and that the optimal pole arc to pole pitch ratio to reduce cogging torque is also optimal for the reduction of average radial magnetic forces. It is also shown that both the smallest non-zero spatial order of tangential and radial force harmonics are given by the greatest common divider of the number of slots and the number of poles. These results can be used during the design stage when choosing the pole and slot numbers combination. These analytical results are then compared with calculations using MANATEE vibroacoustic and electromagnetic simulation software. Finally, some variable speed acoustic noise simulations are carried out on three different designs to analyze the efficiency of different vibroacoustic design rules on the slot and pole numbers combination. An attempt to formulate a new vibroacoustic design rule choice is detailed. It is concluded that no simple analytical design rule can be used to evaluate noise and vibrations induced by magnetic forces, and that numerical simulation is necessary.

Influence of Radial Force Harmonics With Low Mode Number on Electromagnetic Vibration of PMSM

Permanent magnet synchronous machines (PMSM) have been widely used in a variety of applications. A strong electromagnetic force exists between the rotor magnets and the stator core in a PMSM. The force directly causes mechanical deformation and vibration of the stator. In small PM motors, mechanical vibration comes mainly from the electromagnetic force of the stator. This paper gives the general expression of the frequency and corresponding mode number of radial force harmonics for a PMSM with a three-phase symmetrical double-layer winding. The paper shows that the lowest mode number of radial force harmonics is the greatest common divisor of pole number and slot number. The force harmonics with a low mode number can induce a high mechanical vibration, especially for PMSMs with a fractional slot combination. This is simulated using a weak-coupling electromagnetic-mechanical finite element model. To illustrate the influence of radial force harmonics with a low mode number on vibration, a method to eliminate the lowest mode number force harmonics for the fractional slot combination motor is proposed. A test rig for the 12-slot 8-pole prototype motor is set up. The experimental and simulated results confirm that force harmonics with low mode number have a major impact on vibration.

Analysis of Radial Force on a Permanent Magnet Synchronous Motor Caused by Dimensional Variation

Main reasons for causing vibration in a permanent magnet synchronous motor (PMSM) are torque ripple and radial force harmonics, and hence, both of them are undesirable in high-precision machine tools and accurate motion-control actuators. Recent research on radial force is the prediction of major vibration frequencies and modes in terms of motor design such as different winding types and a fractional slot number per pole in the stator. Also, proper phase current has been investigated for minimizing radial force harmonics. During the previous studies, all the motors are assumed to be ideally built up in terms of mechanical dimensions, but it is impossible due to dimensional variation within or outside tolerance in production. Therefore, in this paper, the effect of several key factors on radial force is examined and compared regarding manufacturing imperfection.

A Field Reconstruction Method for Optimal Excitation of Permanent Magnet Synchronous Machines

Vibration caused by torque ripple and radial force harmonics is a concern in many applications of permanent magnet synchronous machines (PMSMs). Alternative methods of machine design and/or stator excitation to minimize torque ripple have received considerable attention in recent years. Comparatively, methods to minimize radial force harmonics have received less attention. In this paper, a field reconstruction (FR) method is derived that provides a designer with the capability to rapidly determine the radial and tangential components of force under arbitrary stator excitation. Using the field reconstruction method, stator current waveforms that minimize the ripple of both torque and radial force are derived subject to the constraint of maintaining a satisfactory level of torque density.