Permanent Magnet Linear Synchronous Machine Research Articles

Design and analysis of PMLSM with SIN + 3rd shaping mover

PurposeThe purpose of this paper is to investigate the electromagnetic performances of the permanent magnet linear synchronous machines (PMLSM) with sine and third harmonic (SIN + 3rd) shaping mover in comparison with the PMLSM with sine (SIN) shaping mover and conventional shaping mover.Design/methodology/approachThe optimal amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping permanent magnet (PM) for maximizing the thrust force is analytically derived and confirmed by finite element method (FEM). Furthermore, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are optimized. It is found that the optimal amplitude of the injected third harmonic is one-sixth of the fundamental one, the optimal PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are 0, 0.85 and 0.5 mm, respectively. In addition, the electromagnetic performances are analyzed and quantitatively compared for the PMLSM with SIN + 3rd shaping mover, SIN shaping mover and conventional shaping mover.FindingsThe average thrust force and efficiency of the PMLSM with SIN + 3rd shaping mover are improved significantly, while the thrust ripple is not increased, comparing to those of the PMLSM with SIN shaping mover. Meanwhile, the thrust ripple is lower than that of the conventional shaping mover.Research limitations/implicationsThe purely sinusoidal currents are applied in this analysis and the influences of harmonics in the current on electromagnetic performances are not considered.Originality/valueThis paper presents a PMLSM with SIN + 3rd shaping mover to improve the thrust force and efficiency without increasing the thrust ripple, considering the effects of the amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping PM, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio.

Characteristic Analysis of the Influence of Auxiliary Teeth and Notching on the Reduction of the Detent Force of a Permanent Magnet Linear Synchronous Machine

This study considers the reduction of the force ripple of a permanent magnet linear synchronous machine (PMLSM). The PMLSM has a relatively large magnetic air gap. Therefore, a slotted type of stator structure is generally employed. Furthermore, the detent force, which is caused by the energy imbalances owing to the interaction between the teeth-slot structures and the permanent magnets, must be minimized for better start-up performance. Therefore, in this study, the addition of the auxiliary teeth and teeth notching are employed to reduce the detent force. In particular, the influence of the auxiliary teeth and notching on the detent force is analyzed, and an experiment is performed to verify the proposed design.

Analysis and Minimization of Detent End Force in Linear Permanent Magnet Synchronous Machines

In this paper, the end forces caused by the longitude end effects in linear permanent magnet synchronous machines (LPMSMs) are analyzed and minimized. First, the left/right-end forces are calculated based on an analytical model and the Maxwell stress tensor, in which the optimal integration surfaces are investigated. Then, based on the spectrum analysis of the left/right-end forces, two different methods are adopted to minimize the fundamental and high-order harmonics, respectively. The optimal length of the primary iron is obtained from the phase difference of the fundamental and a two-step iteration instead of the trial-and-error with the finite element method. Furthermore, step-skewed auxiliary irons are added to the primary end to eliminate the high-order harmonics. Third, to reduce the secondary end effect when the primary moves to the secondary end, a compensation method of adding mirror permanent magnet is proposed and good results are obtained. Finally, an LPMSM prototype is manufactured and experiments are conducted. The experimental results verify the theoretical study.

Design, analysis and fabrication of a linear permanent magnet synchronous machine

This paper deals with the design, analysis and fabrication of a 320 W, 5 m/s, 4-pole permanent-magnet-based linear synchronous machine (LPMSM). The design deals with conventional hand calculations followed by design fine-tuning and analysis using standard FEM packages. Fabrication of the machine has been also done at the works of a local small machine manufacturer after procurement of imported permanent magnets (PMs). The work presented here focuses on design and fabrication of LPMSM linor stampings with fixed dimensions and standard available PM tablets with a view to providing simple design guidelines. This prototype forms part of a variable speed linear motor drive that is being developed. The approach presented here might provide new ideas to those researchers who may not have the capability to bear cost of fabrication of lamination and PMs from scratch but would like to manufacture LPMSMs from available stampings and tablet PMs. Additionally, it may serve as a base document for the R&D personnel in this area.

No-Load Magnetic Field and Cogging Force Calculation in Linear Permanent-Magnet Synchronous Machines With Semiclosed Slots

This paper presents an improved analytical subdomain model for predicting the magnetic field in linear permanent magnet synchronous machines (LPMSMs) with semiclosed slots accounting for the finite length of primary iron core and secondary back-iron. The whole field domain is divided into eight subdomains and the magnetic field in each subdomain is solved by applying the variable separation method, adequate boundary conditions, and interface conditions. In this model, both the slot and end effects are considered. The thrust and normal forces are calculated by the Maxwell stress theory. The finite element analysis is carried out to validate the analytical model. Finally, an LPMSM prototype is manufactured and tested. The experimental results show that the developed analytical model has high accuracy for predicting the magnetic field and forces.

Fast Calculation of Detent Force in PM Linear Synchronous Machines With Considering Magnetic Saturation

The detent force of permanent magnet (PM) linear synchronous machines is the main source of thrust ripple. Its calculation becomes significant, especially under different load conditions. By using frozen permeability (FP) method, it can be obtained based on either the integral of Maxwell stress tensor or the virtual work principle. However, the calculated result from the former has nonzero average value, and the latter is complicated with general commercial finite element (FE) packages. For fast calculation and high precision, a hybrid FE-analytical method based on d-q axis flux linkage model is proposed, which only needs to calculate the thrust force and the flux linkage of two FE models. One is the nonlinear model with both PM and armature current excitations, and the other is the linear model with armature current only by using the FP method. The predicted result is compared with those of two existing approaches, which validates that the detent force can be calculated properly under different load conditions by the proposed method.

Armature Reaction Field and Inductance Calculations for a Permanent Magnet Linear Synchronous Machine Based on Subdomain Model

This paper proposes an analytical technique for calculating the armature reaction field and inductance of permanent magnet linear synchronous machines based on a subdomain analytical model. The analytical solutions based on the subdomain model in terms of a 2-D Cartesian coordinate system are obtained using continuous and Neumann boundary conditions. The analytical results of the magnetic field are validated extensively with finite element method (FEM). Based on these solutions, the inductance is also determined analytically. In addition, we improve the accuracy of the analysis by using a simplified method of calculating the end inductance. Finally, the predictions are compared with a 3-D FEM and measured data to confirm the validity of the analysis methods presented in this paper.

Detent Force Minimization of Permanent Magnet Linear Synchronous Machines Using Subdomain Analytical Method Considering Auxiliary Teeth Configuration

This paper presents electromagnetic modeling and analysis of the detent force in a permanent magnet linear synchronous machine (PMLSM) according to auxiliary teeth configuration. Analytical solutions for magnetic fields generated by PMs are derived based on the Maxwell equation in terms of a 2-D Cartesian coordinate system. The magnetic vector potential of each subdomain (PM, air-gap, slot, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. Based on the analytical solution, the magnetic force is derived by using the Maxwell stress tensor. All the analytical results were extensively validated using nonlinear finite-element analysis and experimental results. Using the proposed method, we investigated the influence of the machine parameters on the detent force. Therefore, the proposed method can be very useful in the initial design and optimization process of PMLSM for detent force analysis.

Adaptive Sliding Mode Control of PMLSM Drive

In this paper, we propose a study by software MATLAB/Simulink of the adaptive nonlinear controller of permanent magnet linear synchronous machine. The lumped uncertainties due for saturation magnetic and temperature and distribution load effects in performances of the system control. To resolve this problem the sliding mode controller is designed with estimator of load force by MRAS method the simulation results prove clearly the robustness of controlling law and estimator method.

Magnet pole shape design for reduction of thrust ripple of slotless permanent magnet linear synchronous motor with arc-shaped magnets considering end-effect based on analytical method

The shape of the magnet is essential to the performance of a slotless permanent magnet linear synchronous machine (PMLSM) because it is directly related to desirable machine performance. This paper presents a reduction in the thrust ripple of a PMLSM through the use of arc-shaped magnets based on electromagnetic field theory. The magnetic field solutions were obtained by considering end effect using a magnetic vector potential and two-dimensional Cartesian coordinate system. The analytical solution of each subdomain (PM, air-gap, coil, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. In particular, an analytical method was derived for the instantaneous thrust and thrust ripple reduction of a PMLSM with arc-shaped magnets. In order to demonstrate the validity of the analytical results, the back electromotive force results of a finite element analysis and experiment on the manufactured prototype model were compared. The optimal point for thrust ripple minimization is suggested.

Magnetic Field and Force Calculation in Linear Permanent-Magnet Synchronous Machines Accounting for Longitudinal End Effect

This paper presents an improved analytical method for predicting the magnetic field and forces in linear permanent-magnet synchronous machines (LPMSMs) accounting for both the primary end effect and secondary end effect. So far, the magnetic field calculation of LPMSM in most studies is conducted in Cartesian coordinate, whereas the end effect is neglected by applying periodic boundary. In this paper, to implement the analytical model, a polar presentation of the machine geometry is proposed and the subdomain method is applied to calculate the magnetic field. Then, according to the developed model, the tangential thrust and normal forces are calculated based on the Maxwell stress theory. Numerical results are subsequently obtained by finite-element method and employed to validate the analytical model. Finally, an LPMSM prototype is manufactured and experiments are conducted. The results show that the developed analytical model has high accuracy for predicting the magnetic field and forces.

No-Load Analysis of PMLSM With Halbach Array and PM Overhang Based on Three-Dimensional Analytical Method

This paper presented a 3-D analytical method, based on transfer relations for permanent-magnet (PM) linear synchronous machine (PMLSM). The PMLSMs in this paper have a double-sided mover structure with Halbach array PMs and a slotless stator core. In addition, in order to complement the leakage and fringing flux density, we use a PM overhang in the mover structure. The analysis of this method's phenomenon is the proposed 3-D analytical method in this paper. Furthermore, we present experimental verification using a prototype model.

Performance Analysis and Modeling of a Tubular Staggered-Tooth Transverse-Flux PM Linear Machine

This paper investigates the performance analysis and mathematical modeling of a staggered-tooth transverse-flux permanent magnet linear synchronous machine (STTF-PMLSM), which is characterized by simple structure and low flux leakage. Firstly, the structure advantages and operation principle of the STTF-PMLSM are introduced, and a simplified one phase model is established to investigate the performance of the machine in order to save the computation time. Then, the electromagnetic characteristics, including no-load flux linkage, electromotive force (EMF), inductance, detent force and thrust force, are simulated and analyzed in detail. After that, the theoretical analysis of the detent force, thrust force, and power factor are carried out. And the theoretical analysis results are validated with 3-D finite-element method (FEM). Finally, an improved mathematical model of the machine based on d-q rotating coordinate system is proposed, in which inductance harmonics and coupling between d- and q-axis inductance is considered. The results from the proposed mathematical model are in accordance with the results from 3-D FEM, which proves the validity and effectiveness of the proposed mathematical model. This provides a powerful foundation for the control of the machine.

Thermal modeling and analysis of double-sided water-cooled permanent magnet linear synchronous machines

Purpose – With the popularization of permanent magnet linear synchronous machines (PMLSMs) in recent years, the temperature rise has attracted increasingly attention since excessive heat generated in the windings could deteriorate the electromagnetic performance. In order to solve this problem, adopting water-cooled system is an effective method. The purpose of this paper is to investigate a 12-slot/11-pole (12S/11P) water-cooled double-sided PMLSM, which adopts the all teeth wound concentrated winding and shifted armature ends. Design/methodology/approach – Based on 2D finite element analysis (FEA), the thermal performances, such as temperature distribution, the optimization of water flow rate and the influence of demagnetization, are investigated under the condition of continuous duty. Then the maximum current density and average thrust force are calculated for PMLSMs with or without water-cooled system. Finally, the detailed comparison is made between single-sided PMLSM and double-sided PMLSM. Findings – With water-cooled system, the thermal performance of PMLSM can be improved, such as an efficient decrease of temperature rise, restriction of permanent magnet demagnetization and a dramatic increase of the maximum thrust force. It is found that the water flow rate has a significant impact on temperature rise, which can be optimized according to demands. Originality/value – Electromagnetic and thermal coupled analysis is proposed in this paper. It can approximately predict thermal performance and save the manual iteration time at the same time. This method also can provide as a reference of thermal analysis for other PMLSMs.

Analysis of thrust ripple harmonics on different electric loadings in PM linear synchronous machines with skewed PMs

Purpose – Permanent magnet linear synchronous machines (PMLSMs) have large thrust ripple due to the longitudinal end effect caused by the finite length of the armature compared with rotary machines. The purpose of this paper is to analyze the influence of electric loading on thrust ripple performances based on a 12 slots/14 poles (12S/14P) PMLSM. Furthermore, the method of skewed PMs to reduce thrust ripple is investigated based on multi slices 2D finite element (FE) models. Design/methodology/approach – The thrust ripple of PMLSM under open-circuit condition results from the slotting and the longitudinal end effects. Therefore, periodical model has been designed to clarify the effect of the longitudinal end effect. Under on-load condition, the thrust ripple increases and exhibits an effective component of thrust force. To analyze the thrust ripple under on-load condition, frozen permeability (FP) technique is employed. In addition, the method of skewed PMs is analyzed in this paper to obtain more smooth thrust force performance. The effectiveness of skewing accounting for skew angles, step skew numbers and slot/pole number combinations was highlighted. Findings – The longitudinal end effect dominates the thrust ripple of PMLSM in both cases, i.e., open-circuit and on-load conditions. Under on-load condition, the second harmonic component of thrust ripple related to flux linkage harmonics increases significantly. Moreover, the effectiveness of skewed PMs is largely reduced with the increase of magnetic saturation. At last, a proper skew angle and step skew number are obtained for the conventional PMLSM with fractional-slot winding. Originality/value – By 60 electrical degrees and two or three step skewed PMs, the thrust ripple can be decreased to a tolerable limite for conventional PMLSM. The thrust ripple harmonics contributed by longitudinal end effect and flux linkage harmonics are analyzed, respectively, which is beneficial to exploring other techniques such as adding end auxiliary teeth to obtain lower thrust force pulsation.

Position varying MEC-based investigation of the no-load operation of T-LPMSMs

Purpose – The purpose of this paper is to deal with the investigation of no-load operation of tubular linear permanent magnet synchronous machines (T-LPMSMs). It is aimed at the prediction of the phase flux linkages, the back-EMF and the cogging force using a position varying magnetic equivalent circuit (MEC). Design/methodology/approach – This study is based on the elaboration and the resolution of the position varying MEC, and the utilization of its results for the prediction of the phase flux linkages, the back-EMF and the cogging force, considering a general topology of T-LPMSMs. Then, a case study is treated with a position varying MEC-based investigation of its no-load features. These are validated by a 2-D finite element analysis (FEA). Findings – It has been found that the developed position varying MEC can be regarded as an accurate tool that requires a low CPU-time. Research limitations/implications – Beyond the FEA validation, this work should be extended to an experimental one. Moreover, the position varying MEC validity should be extended to load operation in order to enable the prediction of the force production capability. Practical implications – The developed position varying MEC could be suitably used for the pre-design of T-LPMSMs. These are currently given an increasing attention in many applications, such as wave energy conversion and free-piston engines. Originality/value – The paper proposes a position varying MEC for the prediction of the features of T-LPMSMs.

Analysis and Optimization of a Novel Tubular Staggered-Tooth Transverse-Flux PM Linear Machine

A novel tubular staggered-tooth transverse-flux permanent magnet linear synchronous machine is proposed. The machine is characterized by simple structure and low flux leakage. First, the structure and the operational principle are introduced. Second, the 3-D equivalent magnetic circuit model of the machine is built, and the analytical expression of the electromagnetic force is derived. Last, the force density and the force ripple are optimized with respect to three key dimensional ratios by the 3-D finite-element method. An optimized scheme with the high force density of $2.697 \times 10^{5}$ N/ $\text{m}^{3}$ and the low force ripple of 2.78% is achieved. In addition, the characteristics of the proposed machine are compared with other topologies of linear machines.

Research of Sliding Mode Control with Integral Compensator for Permanent Magnet Linear Synchronous Machine

In order to solve the high-frequency chattering and low anti-disturbance in conventional variable structure control (VSC) method with sliding mode, a compensator scheme of introducing integral structure before control object is proposed. Firstly, the position loop VSC state equations and equivalent control model are established based on the analyses of the mathematical model of permanent magnet linear synchronous machine (PMLSM). Then it presents a more accurate and comprehensive method to determine the control parameters and the equivalent model parameters. Computer simulation with the motor parameters of a flat type PMLSM verifies the feasibility and effectiveness of the compensator structure. Compared with the conventional VSC, the proposed structure can solve the vibration caused by external disturbance and load variations, and attenuate the chattering effectively. It is concluded through further analyses that the proposed structure can overcome the system oscillations generated by mover mass and permanent magnet flux linkage, and improve the robustness and control precision of the system.

Comparison of a High Thrust Force Density Segmental Stator Linear Switch Reluctance Machine for with Different Topologies

Linear switch reluctance machine (LSRM) has been an alternative to linear permanent magnet synchronous machine and linear induction machine. However, the nature of reluctance force production, together with the air gap which is always much larger than rotary SRM, result in low propulsion force density in LSRM. This is an inherent demerit of LSRM, limiting its applications where the machine size is strictly set. This paper presents a novel linear switch reluctance machine with segmental stator, which consists of series of ferrite-magnetic segments. The principle of the proposed LSRM featuring high force density has been introduced. A variety of topologies of the proposed machine have been presented including single stator, dual stator and non-stator yoke structure. This paper deals with the comparison of the proposed segmental stator linear switch reluctance machine and traditional teeth type linear reluctance machine in terms of the propulsion force, normal force and force ripple as well as the force density and active pay load ratio. Finite Element Method is implemented to obtain the correlated results. Some conclusions are drawn to verify the analysis above.

Fields and Inductances of the Sectioned Permanent-Magnet Synchronous Linear Machine Used in the EMALS

Some intriguing advantages of permanent-magnet linear synchronous machines (PMLSMs), such as simple structure, high thrust, high efficiency, ease of maintenance, and controller feedback, make it possible to take the place of steam catapults in the future. The conventional PMLSM is renowned for its simple structure and high efficiency, whereby the high reactive power resulted from great leakage inductances during the long stator. Thus, great concern is paid to the section structure of the PMLSM. A sectioned permanent-magnet linear synchronous machine (SPMLSM) used in the EMALS is introduced in this paper, whose stator core is continuous but the armature winding is divided into two sectioned parts. First, the electromagnetic fields of the SPMLSM are investigated analytically. Then, the fields are computed by the finite-element method (FEM) and measured experimentally. Not only are the self-inductances and mutual inductances in one section studied but also the mutual inductances between the two sections. These inductances are then calculated by the FEM and measured experimentally. Good correlation among the results was obtained by these three methods.