Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> This paper deals with the performance variation of permanent magnet linear synchronous motor (PMLSM) with skewed magnet according to various design parameters. The detent force, thrust and normal force characteristics are analyzed according to the variation of air-gap length, thickness of PM, overhang length of PM, width of PM and length of skew. And, the optimal length of skew that the detent force is minimized is determined. For the analysis, a 3-D equivalent magnetic circuit network (EMCN) method is used. To verify the analysis results, the results are compared with the measured ones. <s> BIB001 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Detent force produced in permanent magnet linear machines generally causes an undesired vibration and noise. This paper analyzes detent force and thrust in permanent magnet linear synchronous motor by using various detent force minimization techniques. A two-dimensional finite-element analysis is used to predict detent force and thrust due to structural factors and nonlinearity. Moreover, moving node techniques for the drawing models is used to reduce modeling time and efforts. <s> BIB002 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> In this paper a multiobjective design optimization of an air-core linear permanent magnet synchronous motor is presented. Thrust, thrust ripple and consumed magnet volume are chosen as objectives for design optimization. A 2D finite element analysis is carried out to evaluate the optimization results. <s> BIB003 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Although air-core linear permanent-magnet (PM) synchronous motors are widely used in precision applications because of their advantages such as fast dynamics, lack of detent force, and negligible iron loss, they basically suffer from low developed thrust, thrust ripple, and excessive use of permanent-magnet materials, all of which lead to undesirable performance and high production cost. In this paper, we analyze performance characteristics of an air-core linear PM synchronous motor by varying motor design parameters in a layer model and a d-q model of the machine. We propose a multiobjective design optimization to improve thrust, thrust ripple, and consumed magnet volume independently and simultaneously by defining a flexible objective function. A genetic algorithm is employed to search for optimal designs. The results confirm that desirable thrust mean and substantial reduction in magnet volume and thrust ripple can be achieved. We draw several design conclusions from the motor analysis and design optimization. Finally, we carry out a time-stepping finite-element analysis to evaluate the effectiveness of the machine models and the optimization method. <s> BIB004 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> The permanent magnet (PM) flux-switching linear motor, which is developed from the PM flux-switching rotary machine, possesses similar advantages such as high power density and simple structure. Furthermore, the PM flux-switching linear motor has a potential for mass production at low cost, since the expensive coils and magnets are both set on the short mover. However, the detent force which is induced by both slot-effect and end-effect deteriorates the motor performance. Some methods to reduce detent force which are effective in PM linear synchronous motors do not work in PM flux-switching linear motors, due to their special structure. This paper describes a new method to reduce the detent force by fixing assistant teeth on the mover ends. Finite element analysis shows some interesting results which will be detailed in this paper. <s> BIB005 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> The influence of manufacturing tolerances on the cogging torque waveforms, as well as the back-EMF waveforms, in 3- and 5-phase flux-switching permanent magnet (FSPM) machines having different numbers of stator/rotor poles is investigated by finite element analyses and experiments. The cause of excessive cogging torque in the prototype FSPM machines has been identified. It is due to modular stator structure which makes it mechanically weak, leading to the intrusion of C-core into the airgap and an uneven inner stator bore. The analyses presented in the paper should be useful to the design and analysis of modular PM machines in general. <s> BIB006 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> To make the ropeless elevator system become practical, one of the most important requirements is the high force density. The slotted iron core type permanent magnet linear synchronous motor (PMLSM) seems to be the best choice except the large detent force. Therefore, in this paper we will investigate the characteristics of detent force, normal force, and thrust of PMLSM under different motor topology structures. Finally, the long stator double-sided slotted iron core type PMLSM with fractional slot winding is selected for the best performance. <s> BIB007 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Linear flat switched flux permanent magnet (SFPM) brushless machines have significant potential for many applications including transportation, automobile and aerospace. Novel E-core and C-core linear SFPM machines are proposed and optimized by individual parameter optimization, when the copper loss and volume is fixed, in this paper by finite element (FE) analysis. Then, the results of the individual parameter optimizations are examined by a global optimization with genetic algorithm. Furthermore, the magnet thickness of all the machines and the middle teeth of the E-core machines are analyzed individually. Finally, the electromagnetic performance of the novel machines are analyzed and compared with the conventional machine. It shows that both E-core and C-core machines require significantly smaller magnet volume since only about half the number of permanent magnets is required. Furthermore, the C-core machines have the largest back-EMF and force density due to the largest slot area, and the E-core machines are suitable for fault-tolerant operations while the 6/11 mover/stator pole E-core SFPM machine has the smallest cogging force. <s> BIB008 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> In this paper, a complementary and modular linear flux-switching permanent magnet (MLFSPM) motor is investigated, in which both the magnets and armature windings are placed in the short mover, while the long stator consists of iron core only. The proposed MLFSPM motor incorporates the high power density of a linear permanent magnet synchronous motor and the simple structure of a linear induction motor. It is especially suitable for long stator applications such as urban rail transit. The objective of this paper is to build the mathematical model for the purpose of control of this motor. The simulation results by means of finite-element analysis (FEA) verified the theoretical analysis and the effectiveness of this model. Both the analytical model and the FEA results are validated by experiments based on a prototype motor. <s> BIB009 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Permanent magnet linear synchronous motor (PMLSM) for rope-less hoist system, which has the advantages of simple structure, small volume, high force, unlimited hoisting height and speed, is a research focus and difficulties in the vertical hoist field. In this paper, according to the key technical problems of PMLSM for rope-less hoist system, a design scheme of direct driving high-speed elevator is proposed, and then a small-sized home elevator prototype drove by PMLSM is built. Experimental results show the safe and stable operation performance of the experimental device, with good prospects for the development and application of PMLSM rope-less hoist system. <s> BIB010 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> This paper analyzes the thrust characteristics of the investigated permanent magnet linear synchronous motor (PMLSM) and discusses their differences with those of rotary motors. It shows that the main components of the thrust ripple are second, fourth, and sixth harmonics, which is produced by end-effect, not the 12th harmonic caused by cogging. The ripple suppression abilities of magnet step-skew method are analyzed through skew factors of thrust harmonics and effective electromagnetic thrust. The optimal step number and skew angle for PMLSM are studied with comparison to those of rotary motor. A 2-D FEM algorithm for the asymmetric PMLSM model analysis is investigated, with which the aforesaid skew step number selection and optimal skew angle are validated. <s> BIB011 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> The conventional linear flux-switching permanent-magnet (FSPM) motors directly split from a rotary FSPM motor suffer from drawbacks such as unbalanced magnetic circuit of end coil, bigger cogging force, and force ripple. In this paper, to reduce cogging force and thrust force ripple, some complementary and modular linear FSPM (LFSPM) (MLFSPM) motors with mover/stator pole pitch ratio τm/τs of about one, namely, τm/τs = 10/12, 11/12, 12/12, 13/12, 14/12, 15/12, will be investigated using finite-element method (FEM) and experimental method at first. Then, another new LFSPM motor with τm/τs = 3 is analyzed. Based on τm/τs = 3, some new MLFSPM motors are designed, investigated, and compared using FEM. To fully investigate these motors, the optimal MLFSPM motor with τm/τs = 3 is quantitatively compared with the two optimal motors with τm/τs ≈ 1 . Finally, the general design principle for this series of MLFSPM motors with different τm/τs values is concluded. <s> BIB012 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Linear permanent magnet machines have been increasingly used in several applications that require high reliability and good dynamic characteristics. In this paper, a novel double-sided design of a 3φ permanent magnet flux-switching linear synchronous machine (FSLSM) with a yokeless translator is proposed. It is found that the proposed design can achieve more than 50% higher thrust than a conventional FSLSM and excellent linearity even under high excitation currents. Optimization of the proposed machine is performed using individual parameter optimization and is compared with results from global optimization using genetic algorithm (GA). Force analysis of the proposed design is performed to establish the mechanical integrity of the design. The proposed FSLSM is most suitable for long-stroke applications and intermittent oscillatory type applications. <s> BIB013 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> This paper presents the optimal structure design and magnetic force analysis of a ropeless elevator model that employs permanent magnet linear synchronous motors (PMLSMs) with the structure of a double-sided long-stator. To obtain the optimal structure, the combination of response surface methodology and 2-D finite element analysis, which can solve the problem effectively without consuming much time, is utilized to estimate the design parameters of PMLSM. The numerical calculations and the experimental results are reported to validate the applicability of this double-sided long-stator type PMLSM for a ropeless elevator system. <s> BIB014 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> A novel partitioned stator flux reversal permanent magnet (PS-FRPM) linear machine with segmented iron mover is introduced. The operation principle of the PS-FRPM linear machine is described, and the optimisation of the machine leading design parameters for maximum thrust force using genetic algorithm has been carried out. Moreover, in order to investigate the longitudinal end effect on the machine performance a periodic model has been employed to compare with the real model. It is found that the end effect has a significant impact on the machine performance, particularly in terms of unbalanced magnetic circuit and cogging force. Additionally, the influence of the mover iron pole numbers on the electromagnetic performance of PS-FRPM linear machines has been examined, i.e. 6/4, 6/5, 6/7, 6/8, 6/10 and 6/11 stator/mover pole combinations are designed and compared. It is concluded that the machine with a mover pole pitch which is closer to the stator slot pitch exhibits the best performance among the others. <s> BIB015 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> In this paper, a new concept for the application of linear flux-switching permanent magnet (LFSPM) machine to ropeless elevator is proposed. The single-sided LFSPM machine with complementary and modular structure is investigated as a candidate. Moreover, the secondary stator is made of mild steel. The normal upward and downward characteristics of the linear machine are analyzed by the three-dimensional finite-element method. The falling speed of the linear machine in the case of electrical outage is also presented. <s> BIB016 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> 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. <s> BIB017 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> During past three decades, marine energy has become an attractive topic in renewable energy. Among various types of marine energy, present study focuses on wave energy because of its advantages such as high availability, high predictability, high stability, and high power density. Nowadays, most wave energy converters (WECs) installed have complex mechanical interfaces in their power-takeoff (PTO) system which results in complicated system structure and more maintenance requirements. These problems are solved in direct-drive wave energy converters (DD-WECs) by using linear generators, which simplify PTO system. The present review discusses different designs and technologies of linear generators employed in DD-WECs. After a brief explanation about WECs based on linear generators, all proposed topologies of linear permanent magnet generators are discussed and compared based on specifications such as flux path, core type, installation and magnetization of permanent magnets, etc. Finally, the best types of linear generators, in term of being economical and operational, are identified. <s> BIB018 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> C-core linear flux-switching permanent magnet (PM) machines (LFSPMs) are attracting more and more attention due to their advantages of simplicity and robustness of the secondary side, high power density and high torque density, in which both PMs and armature windings are housed in the primary side. The primary salient tooth wound with a concentrated winding consists of C-shaped iron core segments between which PMs are sandwiched and the magnetization directions of these PMs are adjacent and alternant in the horizontal direction. On the other hand, the secondary side is composed of a simple iron core with salient teeth so that it is very suitable for long stroke applications. However, the detent force of the C-core LFSPM machine is relatively high and the magnetic circuit is unbalanced due to the end effect. Thus, a new multiple additional tooth which consists of an active and a traditional passive additional tooth, is employed at each end side of the primary in this paper, so that the asymmetry due to end effect can be depressed and the detent force can be reduced by adjusting the passive additional tooth position. By using the finite element method, the characteristics and performances of the proposed machine are analyzed and verified. <s> BIB019 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Linear flux-switching permanent magnetic (LFSPM) machines are good choices for long stroke applications. These machines deliver high thrust force density in addition to the machine structure where permanent magnetics (PMs) and windings are all on the short mover. For LFSPM machines, their performance is always affected by big thrust force ripple. In this paper, for two C-core LFSPM machines of high thrust force capability, including a 6/13 C-core LFSPM (6/13LFSPM-C) machine and a sandwiched C-core LFSPM (SLFSPM-C) machine, and a thrust force ripple reduction method is proposed. The proposed method is developed by reducing the slot effect component of the cogging force based on staggered stator tooth, and suppressing the thrust force ripple caused by unbalanced three phase back-electromagnetic forces (EMFs) based on two end PMs. Based on finite element analysis (FEA) results, both C-core LFSPM machines can achieve small thrust force ripples as well as high sinusoidal back-EMFs, and at the same time, maintain high thrust force capability with the proposed method. It was also found that, the improved SLFSPM-C machine exhibited the same thrust force capability as the improved 6/13LFSPM-C machine, but with a much smaller thrust force ripple. <s> BIB020 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> Phase-shift or pole-shift method can reduce the detent force of the double-sided permanent magnet linear synchronous motor (DS-PMLSM) dramatically. However, this method causes a decrease in thrust and an increase in normal force simultaneously. To overcome this drawback, a novel slot-shift structure whose slots on the two sides of the primary component are staggered by an optimal distance is proposed in this paper. The models of the detent force including the end force and cogging force is established theoretically, and then verified by finite element analysis. The windings in the upper primary and the lower primary are arranged differently to improve the average thrust. The thrust characteristics of the DS-PMLSM under different shifted distances are analyzed and compared in detail. Furthermore, the primary component employing two kinds of core laminations is proposed to reduce both the dc component and ripple of the normal force. Finally, a DS-PMLSM prototype is tested, and the experimental results are compared with the analytical results to verify the effectiveness of the theoretical and simulation research. <s> BIB021 </s> Linear Machines for Long Stroke Applications—A Review <s> B. THRUST FORCE RIPPLE <s> The longitudinal end effect of the double-sided permanent magnet linear synchronous motor (DS-PMLSM) causes a large end force. To overcome this drawback, this paper proposes a novel DS-PMLSM structure, in which the upper or lower primary component is shifted by a certain distance. First, the end-force model of the DS-PMLSM is established, based on which, the influences of the staggered structure on the fundamental and higher order end-force components are analyzed. Following this, the DS-PMLSMs with different slot–pole combinations are divided into four categories, and the design principles of possible winding arrangements are discussed. Furthermore, the staggered structures are applied to four slot–pole combinations, namely 21-, 15-, 20-, and 16-pole/18-slot. The back electromotive forces, detent forces, thrusts, and normal forces of the four combinations are analyzed and compared through the finite-element method. The electromagnetic and output characteristics of the novel DS-PMLSM are also compared with the traditional DS-PMLSM prototype to verify the effect of the proposed structure on suppressing the end force. <s> BIB022
There are two main sources of thrust force ripple in LPMSMs, i.e. detent force and phase unbalance. The detent force also consists of two components: end effect force and traditional cogging force. VOLUME 8, 2020 If the main requirement of the installation is the removal of force ripples, air-cored machines are a great solution, as they are not affected by any means by the detent force BIB003 , BIB004 , BIB007 . However, the thrust density of these machines is quite low BIB003 , BIB004 , BIB007 , BIB014 , BIB018 , and either armature windings or secondary magnets need to be mounted in the long rail. Thus, core-less designs result in high-bulk and highcost machines. Even so, these machines can be interesting candidates for ultra-high precision applications. The usage of assistant teeth is a common solution for dealing with the end-effect force BIB005 , BIB008 , BIB019 . However, this solution implies an increased active length the machine, so if that dimension is strictly limited, other solutions must be found. Complementary configurations are another effective solution. As the complementary modules are displaced 180 • , all the odd harmonics of the detent force are in counter-phase, and thus, they compensate each other BIB012 , BIB016 ,  , BIB009 . Moreover, this solution also suppresses even order harmonics of the back-EMF. So it is also an effective solution to reduce the electromagnetic thrust ripple. Modular solutions are another option BIB009 if an adequate module-displacement is selected, both the detent force and phase voltage unbalance can be almost completely compensated. Segment-shifting BIB017 , BIB021 , BIB022 has also been proven to be effective in the reduction of the end-effect force. Moreover, if the windings are rearranged, the reduction of the EMF can be compensated BIB021 , BIB022 . Finally, by attaching additional magnets at the ends of the machine, the unbalance of the back-EMF can be completely compensated BIB020 . Nevertheless, this configuration might generate a higher detent force, so other solutions must be also combined if a good overall performance is to be achieved BIB019 . Conventional methods for dealing with the cogging force of LMs are equally effective in LMs. Fractional-slot designs are a good solution to reduce the cogging force BIB010 . PM-arc adjustment, semi-closed slots and asymmetric PM arrangements BIB002 are also another option to reduce the cogging effect. The skew is another effective way to deal with the cogging force BIB001 , BIB011 ,  . In the detent force optimisation, a periodic model can be used in FEM first BIB015 . In this way, there is no end effect, and the effectiveness of the selected cogging suppression solution can be evaluated. Then the real machine can be simulated, including the end force mitigation technique. The difference between the no-load forces of the real machine and the periodic machine is the end effect force. In the case of the modular, segmented, or partitionedprimary configurations, it may be very difficult to obtain the same results from the simulations in experimental machines, due to the manufacturing tolerances. It was stated in BIB013 that some thermally conductive epoxies such as Epoxies 50-3185 NC can be used to hold the pieces in place. However, if some pieces are slightly displaced, additional thrust ripple components might appear in the experimental machines BIB006 , which are very hard to predict.