End Effect Force Research Articles

Analysis of Detent Force in Flat‐Type Permanent Magnet Linear Synchronous Motor and Multi‐Objective Optimization Based on Parameter Classification

In order to reduce the thrust ripple caused by the detent force and improve the thrust capacity of the permanent magnet linear synchronous motor (PMLSM), a flat‐type PMLSM is taken as the study object to globally optimize the motor parameters. Firstly, an analytical model for PMLSM is established. The end effect force based on the virtual displacement principle and the cogging force using the equivalent air gap length are considered when analyzing the model. The detent force is found that closely related to the relative position of the primary and secondary, the end air gap volume and the equivalent air gap length. Then, a motor structure optimization method based on parameter classification is proposed in this paper. By sensitivity analysis, the parameters are divided into two types. For parameters with high sensitivity, the response surface methodology (RSM) is used to establish the second‐order regression equation between parameters and response, and then these parameters are optimized by the multi‐population genetic algorithm (MPGA) to improve thrust capacity and reduce thrust ripple. The optimal values of parameters with low sensitivity are obtained by the parametric search. Finally, the optimized motor is used to predict its thrust performance by the finite element method (FEM). The prediction results show that the optimized motor not only performs better but also improves the design efficiency through parameter classification. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Analysis of End-Effect Force and Weakening Method for Permanent Magnet Toroidal Motor

In the research of torque ripple of permanent magnet toroidal motor (PMTM), the planet gears are affected by the end-effect force during its rotation due to the special structure of the central worm stator. The existence of the end-effect force will cause vibration and noise, which will lead to poor operation accuracy of the planet gears. In view of the above problems, the formation mechanism of the torque ripple is analyzed. We point out that the sudden change in the magnetic induction intensity at the end of the central worm stator is the main source of the end-effect force. The Schwarz-Christoffel transformation method is used to analyze the magnetic field distribution at the end of the stator. The mathematical model of the end-effect force of PMTM is derived by applying Maxwell stress tensor method. The influence of the structural parameters on the end-effect force of PMTM is analyzed by finite-element simulation. The results show that the output fluctuation of PMTM can be effectively reduced by choosing the optimal wrap angle of the central worm stator by calculating. In addition, choosing the appropriate polar arc coefficient of the planet gears can further reduce the influence of the end-effect force. These research results can provide important reference for the structural optimization of PMTM.

Detent-Force Minimization of Double-Sided Interior Permanent-Magnet Flat Linear Brushless Motor

New detent-force minimization methodologies for a 6/4 double-sided interior permanent-magnet flat linear brushless motor configured with alternate teeth windings are presented in this paper. Based on the superposition principle, the end-effect and cogging forces are separately minimized using two different techniques. The end-effect force is reduced by a new 2-D optimization using the step-shaped end frames in the slotless stators. The cogging force is minimized through a destructive interference using the slot-phase shift between the upper and lower stators. Each technique is verified experimentally, and the optimal design parameters are formulated using Fourier series. The total detent-force reduction of 94% is achieved as compared with the base model. The steady-state force after applying these new detent-force-free techniques is demonstrated with actual measurements, and also compared with the finite-element analysis result and analytic solution.

A Model for Analyzing a Five-Phase Fractional-Slot Permanent Magnet Tubular Linear Motor with Modified Winding Function Approach

This paper presents a model for analyzing a five-phase fractional-slot permanent magnet tubular linear motor (FSPMTLM) with the modified winding function approach (MWFA). MWFA is a fast modeling method and it gives deep insight into the calculations of the following parameters: air-gap magnetic field, inductances, flux linkages, and detent force, which are essential in modeling the motor. First, using a magnetic circuit model, the air-gap magnetic density is computed from stator magnetomotive force (MMF), flux barrier, and mover geometry. Second, the inductances, flux linkages, and detent force are analytically calculated using modified winding function and the air-gap magnetic density. Finally, a model has been established with the five-phase Park transformation and simulated. The calculations of detent force reveal that the end-effect force is the main component of the detent force. This is also proven by finite element analysis on the motor. The accuracy of the model is validated by comparing with the results obtained using semianalytical method (SAM) and measurements to analyze the motor’s transient characteristics. In addition, the proposed method requires less computation time.

Phase Current Magnitude Variation Method to Reduce End-Effect Force of PM Linear Synchronous Motor

Numerous methods are available for reducing the end-effect force of linear machines. Majority of these methods focus on redesigning the poles or slots. However, these methods require additional manufacturing cost and decrease the power density. The current paper introduces another approach to reduce the end-effect force. The new approach is a method of tuning the input phase current magnitudes individually. According to the proposed method, reduction of the end-effect force could be achieved without redesigning the poles/slots or attaching auxiliary poles/slots. The proposed method is especially applicable when the target motor is very expensive or will be used for a special mission, such as hauling army vehicles equipped with three single-phase inverters. The validity of the suggested method was exemplified by the finite element method with three-phase permanent-magnet linear synchronous motor.

Single neuron network PI control of high reliability linear induction motor for Maglev

The paper deals with a new model of linear induction motor (LIM) to improve the reliability of the system. Based on the normal equation circuit of LIM considering the dynamic end effect, an equivalent circuit model with compensation of large end effect is constructed when the end effect force at synchronism is of braking character. The equivalent circuit model is used for secondary-flux oriented control of LIM. Single neuron network PI unit for LIM servo-drive is also discussed. The effectiveness of mathematical model for drive control is verified by simulations.

Prediction of thrust forces in tubular induction machines

Standstill forces on tubular induction machines are calculated by two methods: a simple one-dimensional technique and a two-dimensional axisymmetric finite element analysis. The end effect force produced by the finite length of the machine is calculated. The work is confirmed by tests taken on a practical machine. >

Force prediction in permanent magnet flat linear motors (abstract)

The advent of neodymium iron boron rare-earth permanent magnet material has afforded the opportunity to construct linear machines of high force to weight ratio. The paper describes the design and construction of an axial flux machine and rotating drum test rig. The machine occupies an arc of 45° on a drum 1.22 m in diameter. The excitation is provided by blocks of NdFeB material which are skewed in order to minimize the force variations due to slotting. The stator carries a three-phase short-chorded double-layer winding of four poles. The machine is supplied by a PWM inverter the fundamental component of which is phase locked to the rotor position so that a ‘‘dc brushless’’ drive system is produced. Electromagnetic forces including ripple forces are measured at supply frequencies up to 100 Hz. They are compared with finite-element analysis which calculates the force variation over the time period. The paper then considers some of the causes of ripple torque. In particular, the force production due solely to the permanent magnet excitation is considered. This has two important components each acting along the line of motion of the machine, one is due to slotting and the other is due to the finite length of the primary. In the practical machine the excitation poles are skewed to minimize the slotting force and the effectiveness of this is confirmed by both results from the experiments and the finite-element analysis. The end effect force is shown to have a space period of twice that of the excitation. The amplitude of this force and its period are again confirmed by practical results.

IN-PHASE COMPENSATION FOR A HIGH SPEED LINEAR INDUCTION MOTOR

Abstract The performance of a high speed linear induction motor is considerably degraded due to end-effects. This is particularly so as regards the force produced. In this paper, a new method called “In-phase compensation” method has been described to eliminate the end-effect force. Unlike the conventional methods, this method does not require phase angle control but only magnitude control of compensating current even for varying slips. A comparison of developed forces by this method of compensation has been made with an equivalent uncompensated LIM.