Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper describes the analysis, design, and experimental characterization of three-phase tubular modular permanent-magnet machines equipped with quasi-Halbach magnetized magnets. It identifies feasible slot/pole number combinations and discusses their relative merits. It establishes an analytical expression for the open-circuit magnetic field distribution, formulated in the cylindrical coordinate system. The expression has been verified by finite-element analysis. The analytical solution allows the prediction of the thrust force and electromotive force in closed forms, and provides an effective tool for design optimization, as will be described in Part II of the paper. <s> BIB001 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper proposes design and analysis of a new linear motor called flux reversal linear synchronous motor (FRLSM), which is cost effective for long stroke applications. Passive rotor configuration of a typical flux reversal machine (FRM) can be utilized for a linear machine with less permanent magnet (PM). Three different design choices are investigated and compared both in thrust and normal force. The investigation shows extremely low force ripple and good thrust linearity through skewing and three-phase sinusoidal control. Reduced PM configuration generates about 21% higher thrust even with half amount of PM. <s> BIB002 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Abstract This article presents a new comprehensive design procedure for longitudinal flux flat linear switched reluctance motors. The design process comprises all the steps from detailing the specifications to sizing the prototype to validating the design, and it can be applied to three types of flux flat linear switched reluctance motors: single sided, double sided, and modified double sided. The design is based on an analytical formulation of the average translation force determined using a simplified non-linear energy conversion loop. Special emphasis is devoted to the calculation of the number of turns per phase. A two-dimensional finite-element analysis, corrected to take into account end effects, and a lumped parameter thermal analysis were used to refine and/or validate the design. Finally, a linear switched reluctance motor prototype was built following the proposed design and was verified by experimental measurements. <s> BIB003 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <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> BIB004 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> The linear permanent magnet (PM) vernier machine is very suitable for direct-drive applications. This paper proposes a linear consequent pole stator PM vernier (LCPSPMV) machine, which can offer high thrust force due to the use of magnetic gear effect. The key of the proposed machine is the introduction of consequent pole. Thus the volume of the PM can be reduced, and the initial cost can be reduced consequently. Based on the finite element analysis, the static characteristics of the proposed machine including the PM flux linkage, no-load EMF, detent force and thrust force are accurately analyzed. Compared with the existing linear stator PM vernier (LSPMV) machine, the proposed machine can offer higher no-load EMF, lower detent force and enhanced power density in the conditions of the same rated speed, winding turns, electric loading. Hence, the validity of the proposed machine is verified. <s> BIB005 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> An air-bus system is proposed as one alternative to urban mass transportation. The propulsive force of this system is generated by a linear motor. Several single- or double-sided linear motor topologies could be employed, but a double-sided linear induction motor (LIM) is preferred due to its simple passive track and high value of force density. Several research works were carried out to develop analytical models for the analysis of LIM performance. In this paper, a quasi-1-D analytical method is proposed to analyze motor performance, and the longitudinal and transversal edge effects are considered as well. Accuracy of the proposed method is evaluated by comparing the analytical results with the experimental data, which shows acceptable conformity. Then, the motor design for the desired application is presented and its performance is evaluated by both finite-element method and analytical modeling. Derivations of major equations are given as well. <s> BIB006 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <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> BIB007 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Analytic modeling techniques of a double-sided interior permanent-magnet flat linear brushless motor (IPM-FLBM) with slot-phase shift and alternate teeth windings are proposed in this paper. Since the buried-type IPM-FLBM with the slot-phase shift and alternate teeth windings is fairly new compared with conventional linear motors, little research has been previously done in modeling and analysis. The analytic models presented in this paper provide the effective and reliable methods for this new type of linear motor. For this purpose, a simplified magnetic equivalent circuit and superposed winding function are investigated. A variable winding function is newly developed in order to evaluate the inductances of the salient motor with the alternate teeth windings. All analytic models are verified with 3-D finite-element analyses (FEAs) step by step. The steady-state thrust force is modeled using a classical closed-form solution for linear brushless ac motors. The static end-effect and cogging forces for the ripple force evaluation are investigated using FEA. The validities for performance parameters are demonstrated experimentally. <s> BIB008 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <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> BIB009 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> A novel primary consequent-pole tubular transverse-flux flux-reversal linear machine (TTFFRLM) is proposed in this paper. The permanent magnets (PMs) of the machine are located on the inner surface of the short teeth of the primary iron cores for reducing the amount of PM in long stroke drive systems, and the primary is easily manufactured. The structure and principle of this machine are analyzed in detail. Based on the unit machine, a no-load equivalent magnetic circuit model is established by using the magnetic circuit method. Then, the equations of the no-load back electromotive force (back-EMF) and the electromagnetic thrust force are deduced. The simulation models of the unit machine are established by equivalent 2D finite element method (FEM) for saving computation time, and the static characteristics, including the flux field, the no-load back-EMF, and the electromagnetic thrust force, are analyzed. Detailed simulation and experimental results of a three-phase 4-poles 12-slots machine are given. The results verify the correctness and effectiveness of topology, model, and analysis method of the proposed TTFFRLM. Compared with the conventional TTFFRLM, the proposed prototype has the advantages of a lower cost and smaller electromagnetic thrust force ripple. <s> BIB010 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Wave energy conversion can be simplified by using direct drive linear generators which may improve reliability. Numerous topologies of direct drive linear generators have been proposed in the last few decades such as the linear vernier hybrid permanent magnet (LVHPM) machine. However, the cost of this kind of machine is driven by the quantity of permanent magnet (PM) material. This paper proposes a linear vernier hybrid permanent magnet machine with consequent pole and concentrated windings for wave energy converters, which requires less magnet material for comparable performance. The key of the proposed design is the modular stator where the unbalanced magnetic circuit caused by consequent pole can be eliminated. Based on finite element analyses (FEA) the present machine is capable of higher thrust force, higher back EMF and lower cogging force as well as force ripple compared to that of a baseline LVHPM machine. <s> BIB011 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper investigates methods of magnet mass reduction in linear flux switching permanent magnet (LFSPM) machines by introducing tapered consequent poles. Based on the finite element analysis (FEA) three different models are designed, investigated and compared. The obtained results indicate that by adopting the proposed tapered ferromagnetic poles a considerable saving of material cost and weight is obtained without sacrificing the machine performance. <s> BIB012 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> In this paper, a new modular linear flux-switching permanent magnet machine is presented. The operation principle is illustrated in detail. The electromagnetic performance analysis of the machine is carried out by the finite-element method. To investigate the influence of the mover pole pitch to stator pole pitch ratio on the new modular machine, the proposed machines with three different ratios are designed and optimized for the specific ropeless elevator application. The optimization methodology is based on sequential surrogate model. The electromagnetic characteristics of the three modular machines with different mover and stator pole pitches are compared. <s> BIB013 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> A novel partitioned primary linear switched flux permanent magnet (PLSFPM) machine is presented, which adopts an odd number of primary poles. For the design objective of minimum thrust ripple, the optimized novel PLSFPM machine with 9 primary/10 secondary (9/10) pole combination is obtained. To this optimized PLSFPM machine, the electromagnetic performance is analyzed in detail and compared with that of the original one. The merits of this 9/10 pole combination are also proved by comparative study with other three available pole combinations. Moreover, comparison between the proposed PLSFPM machine and a conventional linear switched flux permanent magnet machine has been performed, which shows that the proposed machine can achieve better performances under both open-circuit and load conditions. The corresponding prototype is manufactured and the influences of possible machining errors during manufacture on thrust force performance are discussed. Finally, the experiment is carried out, which verifies the predicted results. The research shows that the proposed PLSFPM machine with 9/10 pole combination has high thrust force and low thrust ripple. <s> BIB014 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Partitioned stator flux reversal permanent magnet (PS-FRPM) linear machine is a type of permanent magnet linear machine with dual active stators and one passive mover. Pervious work was shown that such a machine possesses the advantage of having big slot area leading to reduced phase resistance and consequently improved electric loading capability. In order to verify the finite element (FE) results, a prototype of PS-FRPM linear machine is built and tested. A comparison between the test and FE results is presented in this paper, together with the investigation on the influence of axial length differences. <s> BIB015 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper proposes a new modular-stator tubular permanent-magnet (PM) Vernier motor. The proposed motor offers a good fault-tolerant capability and an improved force performance, suitable for the electromagnetic active vehicle suspension. The proposed motor artfully integrates PM Vernier motors and tubular motors together, offering a zero-net radial force between the armature and mover, and the robust mover structure and high thrust force. Meanwhile, the modular complementary stator structure is designed to decouple the adjacent phase windings, hence offering the desired fault-tolerant capability. Moreover, the PMs with two magnetized directions are adopted, namely radially and axially. One is used to produce the main flux, while another can reduce fringing leakage flux, hence increasing the thrust force. The electromagnetic performances are analyzed by using the finite-element method, verifying the effectiveness of the theoretical analysis. <s> BIB016 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> A novel interior permanent magnet linear vernier machine (IPM-LVM) is proposed and analyzed in this paper. Compared to the existing surface-mounted permanent magnet linear vernier machine (SPM-LVM) and the SPM-LVM with Halbach arrays, the proposed machine can offer higher flux density in both the air-gap and armature iron core, which lead to a higher back electric motive force (back EMF) and higher thrust density under the same mover volume and heat capacity. Besides, it is proven that the proposed IPM-LVM also has a lower demagnetization risk compared to the SPM-LVM. Furthermore, in order to reduce the thrust ripple of the proposed machine, the three-sectional structure is adopted in this paper, which makes the proposed IPM-LVM exhibit high thrust density and low thrust ripple at the same time. <s> BIB017 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper proposes a new flux concentrated version of a consequent pole linear Vernier hybrid permanent magnet machine. The Vernier hybrid machine stator has alternatively magnetised adjacent magnets directly in contact with each other. A salient rotor then switches the direction of flux past the stator coils. Alternate magnets can be removed to make the consequent pole version, where inset rectangular magnets are magnetized in a common direction and separated by soft magnetic poles. In a flux concentrated consequent pole configuration, each magnet pole comprises of two magnets forming a V -shape. This topology hence possesses a combination of consequent poles, flux concentration and flux switching machine topologies. Magnetic flux concentration increases the airgap flux density, which potentially leads to an improvement of the force density and operating power factor. This paper compares the inset and V -shape consequent pole topologies using finite element analysis simulations. Both machines have the same dimensions, magnet volume, rated speed and current density. The simulation results imply that the V-shape machine offers higher electromagnetic performance. To confirm this, two linear prototypes are currently under construction, where the key parts that already produced are presented in this paper. <s> BIB018 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper discusses the development of linear vernier hybrid machines for use in wave energy converters. A number of topology options are explored to reduce magnet usage and improve performance for use as a linear generator. Consequent pole, V-shape, and Halbach arrays are designed for a target 25 kW specification. A discussion of overall cost of energy produced is used to justify using efficiency and power factor to asses fixed magnet mass topology variants. A power factor improvement from 0.38 to 0.72 is presented. Physical integration of the electrical machine into wave energy converters is considered including flooded experimental results of thermal behavior and polymer bearing wear. <s> BIB019 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Linear flux-switching permanent-magnet (LFSPM) machines exhibit significant potential in many applications. A double-sided sandwiched LFSPM (DSSLFSPM) machine with high thrust force capability is investigated in this study. After being optimised for optimal thrust force using Maxwell 2D, this machine is found to deliver higher thrust force when compared with an optimised conventional 12/14 LFSPM machine. However, low thrust force ripple is also required in many applications. Thus, in order to reduce the thrust force ripple, the DSSLFSPM machine is improved by a staggered stator teeth structure and an end permanent-magnets method, then, two improved machines are obtained. The improved machines can reduce the thrust ripple to a very low level without thrust force density decrease. Further, the stator yoke thickness of the improved machines is optimised to reach optimal thrust force density. Finally, the performance of the DSSLFSPM-ST machines is analysed including the normal force, the efficiency and the power factor. It shows that the improved DSSLFSPM machines exhibit relatively low normal force and high thrust force density as well as low thrust ripples, indicating that they are suitable for long-stroke applications. <s> BIB020 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This study overviews recent development of a new class of magnetically geared machine topologies, i.e. partitioned stator (PS) machines. They are developed from magnetic gears and magnetically geared machines, as well as stator permanent magnet (PM) machines (switched flux, flux reversal, and doubly saliency PM), wound field, or hybrid PM and field winding machines. Based on the operating principle, i.e. magnetic gearing effect/air-gap field modulation and flux switching by the salient rotor iron poles, various PS machine topologies are developed. All have features of two stators, two air-gaps, and one segmented ferromagnetic rotor identical to a magnetic gear's modulating rotor. Their inherent relationships are revealed, while their electromagnetic performance is compared. Both PM and wound field PS machines are discussed, together with hybrid excited PS-PM machines and Vernier machines. It shows that all of these PS machines share the same torque production principle and the differences are mainly in PM configurations and relative positions of two stators. All PS machines have higher torque density per copper loss compared with their counterparts of single-stator machines. PS switched flux PM machines can produce the highest torque density per copper loss. <s> BIB021 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> This paper presents a linear variable reluctance permanent magnet (LVRPM) machine where the armature winding and inset Halbach array permanent magnets (PMs) are mounted on E-core stators. The Halbach array consists of a vertically magnetised PM pole and a salient ferromagnetic iron pole (split tooth) sandwiched between two horizontal PMs. The translator consists solely of laminations with salient iron poles. As a variable reluctance machine, it exhibits inherent magnetic gearing and a higher force and power density than the conventional synchronous PM machines. Finite element analysis (FEA) has been used to investigate the effect of machine parameters. The logical development of the LVRPM from the more conventional Vernier Hybrid machine is presented, including a near 50% reduction in magnetic flux leakage and a higher flux per unit magnet mass. <s> BIB022 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Permanent magnet vernier machines (PMVMs) gained a lot of interest over the past couple of decades. This is mainly due to their high torque density enabled by the magnetic gearing effect. This study will provide a thorough review of recent advances in PMVMs. This review will cover the principle of operation and nature of magnetic gearing in PMVMs, and a better understanding of novel PMVM topologies using different winding configuration as well as different modulation poles and rotor structures. Detailed discussions on the choice of gear ratio, slot-pole combinations, design optimisation and role of advanced materials in PMVMs will be presented. This will provide an update on the current state-of-the art as well as future areas of research. Furthermore, the power factor issue, fault tolerance as well as cost reduction will be discussed highlighting the gap between the current state-of-the art and what is needed in practical applications. <s> BIB023 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> In low-speed applications, variable-reluctance permanent magnet machines are often proposed due to their efficient use of magnet material and high torque density. This becomes even more important in large linear applications, where the translator is longer than the stator. Often, however, very low power factors are experienced by this class of machines. This paper proposes a V-shaped flux concentrated version of a consequent pole linear Vernier hybrid permanent magnet machine and compares it to a surface-mounted magnet variant. Using finite-element analysis validated by two laboratory prototypes, it is shown that the flux-concentrated version increases the airgap flux density, which potentially leads to an improvement in the force density and efficiency or can be used to increase the operating power factor. <s> BIB024 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <s> Traditionally, straggering the primaries of the double-sided permanent magnet linear synchronous motor (DS-PMLSM) is beneficial in helping to reduce the detent force caused by the longitudinal end effect, but leading to a reduction of the average thrust. To overcome this disadvantage, this paper provides a novel DS-PMLSM, which adopts the structure of staggering two primaries and rearranging windings. First, the characteristics of the voltage and detent force are analyzed theoretically and verified by finite element (FEM) simulations. The inductance, thrust, and normal forces are then compared with the traditional DS-PMLSM. Furthermore, the geometrical parameters are optimized to improve the thrust. Finally, one DS-PMLSM prototype is tested. The detent force and back electromotive force tested results verify the effectiveness of the topology proposed in this research. <s> BIB025 </s> Linear Machines for Long Stroke Applications—A Review <s> A. THRUST FORCE DENSITY <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> BIB026
To start with, the thrust force density is one of the most important characteristics of LMs. In general, gears and pulleys are removed for linear motor driven systems. Consequently, requirements many times involve low speed and high thrust capabilities. Thus, in order to reduce the bulk and material cost of LMs, the thrust density must be maximised. Consequent-pole machines ( Fig. 14 (b) ) are capable of improving the thrust density of LPMSMs BIB002 , BIB010 , BIB005 , BIB011 , BIB012 . This is achieved because, due to their structure the flux leakage is reduced BIB005 , BIB011 , BIB012 , BIB022 . Halbach arrays can improve the usage of PMs by concentrating the flux density in one side of the arrays BIB016 , BIB022 , BIB023 ,  . Moreover, as the flux generated by the magnets is almost completely shielded to a single side, very small yokes or even non-magnetic materials can be used with such configuration BIB001 . Thanks to the flux-focusing effect IPM configurations can enlarge the flux density in the airgap, which results in an increased thrust density BIB017 , BIB018 , BIB019 , BIB024 , BIB023 . Double-sided machines generally exhibit a higher thrust capability than the single-sided counterparts BIB006 , BIB003 , BIB008 , BIB009 , BIB025 , BIB026 , BIB020 , BIB007 . In such machines, the yokeless structure can enhance the thrust density of the conventional configuration BIB004 , BIB013 ,  . By removing the primary or secondary yoke, the height of the machines, and thus the cost in long rail applications, can be significantly reduced. Partitioned-stator configurations ( Fig. 14 (a) ) have been demonstrated to enhance the thrust density of LMs BIB014 , BIB007 - BIB015 , BIB021 . In primary PM LMs only LSFPMs and LFRPMs partitioned-stator machines have been found in the literature. Both doubly-salient and vernier machines could also benefit of this structure. More so, by combining some of the previous solutions, the enhancement of the thrust density can be improved even more, e. g. a halbach-array partitioned-stator LFRPM machine could improve the thrust density of the machine in BIB007 , by reducing the size of the second primary yoke.