Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> In this paper, a general design procedure for the flux-switching permanent magnet (FSPM) machine with different topologies is proposed. Firstly, a 3-phase 12-stator-tooth/10-rotor-pole topology is introduced and its operation principle is described. Then, the basic design method, including determination of the stator, rotor and magnet dimensions, is proposed under the constraints of some dimensions and electrical parameters. The winding turns are obtained by iteratively solving the base-speed and current equations simultaneously. The influence of current density and slot packing factor on the flux-weakening capability is investigated in the design stage to satisfy the torque and wide-speed operation requirement. Further, the output power equation, consequently, the sizing equation is derived for determining the initial dimensions of a FSPM machine, in which the traditional D2 sil a is replaced by D2 sola. Hence, the power density of different topologies can be compared directly by the equation. It reveals that the 3-phase 12/10-pole topology can offer higher power and power density than those of the 2-phase 8/6-pole machine by ~11% in theory under the same conditions. The experiments on the prototype motor verify the performance predictions <s> BIB001 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> This paper compares the performance and material costs of two candidate tubular permanent magnet topologies, viz., quasi-Halbach magnetized moving magnet and flux switching (moving-iron) machines for applications in active vehicle suspension. Both machines are optimally designed for the same operating conditions and under the same volumetric and thermal constraints. It is shown that while the flux switching machine has a robust mover structure, it has relatively low force capability and suffers from higher manufacturing cost, and a heavier moving armature which impacts on the performance of active suspension. <s> BIB002 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> This paper describes a tubular, three-phase, flux-switching permanent magnet (PM) brushless machine that combines salient features from switched reluctance (SR) and conventional PM brushless machines. Feasible slot-pole number combinations, which are also applicable to rotary flux-switching machines, are derived. This paper also examines an alternative stator winding configuration, which is unique to the tubular machine topology. It is shown that this yields ~10%-15% higher thrust force capability as compared to a flux-switching machine equipped with a conventional winding. <s> BIB003 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> The iron loss in flux-switching permanent magnet (FSPM) machine is investigated by the finite element method in this paper. Since the permanent magnets in a FSPM machine are on the stator, rather than on the rotor as in the conventional PM machines, the iron loss exists not only in the stator but also in the rotor, while its calculation becomes more difficult due to complex flux density waveforms. A more accurate model for the iron loss calculation is proposed for the FSPM machine, with due consideration of the influence of operation conditions, including constant torque and flux-weakening. Finite element predicted open-circuit flux waveforms and iron loss are validated experimentally. <s> BIB004 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB005 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> We propose a new topology for a permanent-magnet flux-switching (PMFS) linear machine. We describe its unique structure and compare it with the conventional PMFS linear machine. Finite-element analysis (FEA) shows that the proposed machine not only inherits advantages from the conventional PMFS machines, but also possesses many new merits such as more efficient usage of magnets, high fault tolerance, and easy assembly. These positive features make the proposed machine suitable for many applications. We prototyped both the conventional and proposed machines for verification and found good agreement between FEA and the experimental results. <s> BIB006 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB007 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> This paper overviews the recent development and new topologies of flux-switching (FS) machines, with particularly emphasis on the permanent magnet (PM) type. Specific design issues, including winding configurations, combinations of stator and rotor pole numbers, rotor pole width, split ratio, etc., are investigated, while the torque capability of selected FSPM machines is also compared. <s> BIB008 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> A novel three-phase double sided flux switching linear motor topology with a stator-to-mover teeth ratio of 19/24 is presented. Finite element analysis of the electromagnetical performance of the initial design is conducted and shows that the topology suffers from an unbalanced EMF in terms of amplitude and phase shift between the three phases. On the other hand a low detent force is observed. By adding end-teeth to the structure, a balanced EMF is obtained, but the detent force also increases. A geometrical optimization is conducted on the end-tooth shape and stator tooth width to reduce the detent force while maintaining a balanced sinusoidal EMF. For the optimization a faster hybrid modeling tool is used. The hybrid model is based on the magnetic equivalent circuit method that employs the boundary element method to accurately determine the air gap permeances of the magnetic equivalent circuit. <s> BIB009 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> This paper overviews various switched flux permanent magnet machines and their design and performance features, with particular emphasis on machine topologies with reduced magnet usage or without using magnet, as well as with variable flux capability. In addition, this paper also describes their relationships with doubly-salient permanent magnet machines and flux reversal permanent magnet machines. <s> BIB010 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB011 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> Detent force in permanent-magnet (PM) linear machines is caused by both end effect and slot effect. Segregation of the detent force into its end-effect and slot-effect components is helpful to better analysis and design. For conventional PM linear machines, the end-effect component of detent force can be easily calculated in a related slotless linear machine model, where the slot effect is eliminated. However, the slotless model is not applicable to permanent-magnet flux-switching (PMFS) linear machines, where the magnets and core teeth are set together on either a same stator or a same mover. This is because the PMFS machines cannot work at all without the teeth or slots. Therefore, a new method for segregating the detent force in the PMFS linear machines is proposed in this paper. Since a linear machine can be considered as a part of a particular rotary machine with large radius, and furthermore, cogging torque in the PM rotary machine is caused by the slot effect only, thereby the slot-effect component of the detent force in the PMFS linear machine can be calculated from the cogging torque in a related rotary machine, while the residual of the detent force is the end-effect component. Both finite element analysis (FEA) and experimental results show that the proposed method works well for the PMFS linear machines. <s> BIB012 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB013 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB014 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> The flux-switching permanent magnet (FSPM) machine is widely investigated due to the advantages such as ease of the PM heat management, simple and robust structure of the rotor, high power density and torque density, sinusoidal back electromotive force (EMF) and fault-tolerance capability. The purpose of this paper is to propose a C-core linear FSPM machine for ropeless elevator, in which two positive additional teeth are employed at the each end of the primary side to reduce the asymmetry caused by the end effect. Firstly, the structure of the proposed machine is presented. Then the performances of the proposed machine are analyzed and compared with the counterpart without additional teeth based on the finite element analysis (FEA). The results verify the feasibility of the positive additional teeth. <s> BIB015 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> This paper investigates the influence of some leading design parameters on the force performance of a new complementary and modular linear flux-switching permanent-magnet (LFSPM) motor. The originality of the proposed structure is that each phase consists of two “E”-shaped modules, whose positions are mutually 180 ° electrical degrees apart. Also, there is a flux barrier between the two modules. First, the structure and influence of some leading design parameters on the force performance of the complementary and modular LFSPM motor are analyzed. Then, a conventional LFSPM motor obtained directly from a rotary FSPM motor is optimized and compared with the complementary and modular LFSPM motor based on finite-element method. The results reveal that the proposed motor has sinusoidal and symmetrical three-phase back electromotive force waveforms and smaller cogging force and force ripple than the existing motors. Moreover, a prototype of the proposed motor is built to validate the study. <s> BIB016 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB017 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB018 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB019 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB020 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> Two permanent magnet linear machines, i.e. partitioned stator flux reversal permanent magnet (PS-FRPM) and conventional switched flux permanent magnet (SFPM) linear machines, are compared, in terms of electromagnetic performance and demagnetization withstand capability. It is found that compared to the conventional SFPM linear machine, the PS-FRPM linear machine shows lower cogging force, higher thrust force capability, better PM utilization, and lower thrust force ripple. Moreover, it possesses better demagnetization withstand capability. <s> BIB021 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB022 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <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> BIB023 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> To incorporate the merits of simple and robust movers of induction linear motors and higher power factor and high efficiency of permanent magnet linear motors, a new long primary double-sided linear flux-switching permanent magnet (DSLFSPM) motor is proposed, investigated, and quantitatively compared with linear induction motors (LIM) for the electromagnetic launch system. First, the topology, operation principle, and electromagnetic performance of the DSLFSPM motor have been investigated. Then, in order to analyze the LIMs comprehensively, three LIMs have been designed based on the same overall dimensions and other key parameters. Finally, the electromagnetic performance of DSLFSPM motor and LIMs have been compared and summarized. The results show that the DSLFSPM motor has some merits such as higher efficiency, higher power factor, more robust mover, larger thrust force, and smaller force ripple than LIM motors. In order to validate the simulation results, a small-scale prototype of DSLFSPM motor has been built and measured. <s> BIB024 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> A new double-sided linear flux-switching permanent magnet (DSLFSPM) motor with a yokeless mover is proposed in this paper. First, the topology and structure of the proposed motor are presented, and the pole pitch ratio and segment number are shown to strongly affect performance. Second, the electromagnetic performance of DSLFSPM motors with a secondary yoke and without a secondary yoke are compared and described. Third, according to analytical models, air-gap flux-density levels and corresponding harmonics are investigated, and force production mechanisms of the proposed motor are presented. The analytical results match to the FEA results. Finally, experiments on a prototype are carried out to validate the simulation results. Back EMF, cogging force, and inductance values of the prototypes are measured and experimental results for the drive systems are presented. <s> BIB025 </s> Linear Machines for Long Stroke Applications—A Review <s> C. SWITCHED-FLUX MACHINES <s> Linear induction motors (LIMs) have been extensively adopted in urban railway transportation given their nonadhesion thrust and simple stator structure. However, these LIMs undergo unfavorable power factor and efficiency considering their copper and eddy losses. Recently, linear flux-switching permanent-magnet motors (LFSPMs) have attracted the attention of researchers due to their high power density, simple structure, easy heat dissipation, high efficiency, and high power factor. However, so far, no quantitative comparison exists between LFSPMs and LIMs of the size 1:1 to prove the feasibility of LFSPMs to be used in railway transit systems. Therefore, a comparative analysis between the two motors is conducted in this paper. First, this paper investigates the LIMs for railway transit using the finite element method (FEM). Second, the LFSPMs for railway transit is designed and optimized. Third, the electromagnetic performance of the two motors is compared and analyzed through the FEM. Finally, a small-sized prototype of the LFSPMs is constructed to validate the FEM results. It is concluded that LFSPMs offer a favorable thrust force, have high efficiency, and high power factor but have large normal force and force ripple. Therefore, applying LFSPM requires a reliable supporting device and a shock absorber. <s> BIB026
The other machines in the flux-switching family are the switched-flux machines. In fact, they are the machines that can produce the highest thrust density in the flux-switching family BIB015 . The primary of conventional LSFPMs consists of U-shaped silicon-steel modules joined by PMs of alternate magnetisation, so that each magnet is sandwiched between two modules and a concentrated winding. Figure 15 shows a conventional 12/10 primary/secondary pole machine. The LSFPMs produce highly sinusoidal back-EMF waveforms, and thus, they are most suited for a BLAC operation BIB018 , BIB019 , BIB020 , BIB025 . The reluctance force in this case is generally negligible too, thus, the sinusoidal phase currents are generally supplied in phase with the back-EMFs for an optimum operation BIB018 , BIB019 , BIB020 , BIB025 . In this case, the magnetisation direction of PMs is perpendicular to the flux generated by the primary coils. This provides LSFPMs a great immunity against demagnetisation in case of faults in the primary winding BIB014 , BIB002 , BIB012 , BIB023 . The immunity of PMs against permanent demagnetisation enhances the capability of LSFPMs work in the flux-weakening area BIB001 , BIB008 , BIB010 . A good overload ability is also mentioned in BIB014 ,  , BIB012 for the same reason. One of the main drawbacks of LSFPMs is the reduced space of the primary side. The designers have to deal with limited magnetic loading and slot areas BIB008 , BIB010 , BIB011 , BIB021 . Moreover, due to the modular structure, the primary of LSFPMs tends to be mechanically weak BIB005 , and their detent and thrust ripple performance is quite sensitive to manufacturing tolerances BIB005 . In fact, both the no load and on load ripples of LSFPMs are generally quite high BIB018 , BIB026 , BIB003 , BIB016 ,  . Another drawback of LSFPMs is the amount of PM material that they require per unit of thrust BIB002 , BIB006 , BIB008 , BIB010 . Due to the primary structure, the uppermost area of the magnets suffers from a severe flux leakage problem as it can be seen in Fig. 16 . There is yet another drawback for LSFPMs when compared to conventional LPMSMs. As the secondary does not have any magnets, the flux is bipolar in this side too. This means that iron loss is also present in this side, thus lowering the efficiency of LSFPMs BIB004 , BIB017 . However, the iron losses can be used as a safety feature. In BIB017 , Zhang et al. propose a LSFPM with a non-laminated secondary for a low-speed elevator. With their solution, the authors limit the falling speed to 1.35 m/s without any other safety devices. The usage of LSFPMs for elevators is also analysed in BIB015 , BIB022 , BIB020 . LSFPMs have also been applied for rail transit BIB026 , BIB023 , BIB013 and electromagnetic launch systems BIB024 , BIB025 . One of the most researched fields for LSFPMs is their thrust ripple. Skewing the secondary was classified as ineffective in BIB003 . In BIB007 Wang et al. propose to use two additional teeth in each end of the primary to reduce the end effect component of the detent force, and to apply the skew to lower the amplitude of the remaining harmonics afterwards. Additional PMs are placed in the ends of the machine in BIB009 . The aim of this solution is to balance the back EMF waveforms of the three phases of the machine, so that the electromagnetic thrust ripple is lowered. This solution is also tested in BIB015 . In this case, the on-load thrust ripple is 16.6 % lower after balancing the EMFs. Nonetheless, the addition of end PMs enlarges the detent force to 1.96 times the initial value. To reduce the detent force when employing additional PMs, a combination of those with additional assistant teeth can be employed BIB020 . Complementary solutions have also been employed in LSFPMs. Cao et al. BIB013 use a modular and complementary structure to reduce the ripple of the machine. Due to the complementary structure, the amplitude of the even harmonics of the back-EMFs is reduced to an almost negligible value. This reduces the ripple of the electromagnetic thrust. Moreover, due to the displacement between different modules, the detent force is also lower than the one from the original machine. A combination between end PMs and a complementary magnetic circuit is proposed in BIB018 . The authors compare a LSFPM with a sandwiched LSFPM, and results show that even if the thrust ripple is reduced in both cases, the sandwiched LSFPM shows the lower thrust ripple. Fault-tolerant capability is also obtained in by employing a modular structure BIB006 , BIB016 , BIB013 . In such modular structures each module only contains one coil, so the phase unbalance can be neglected, as all the individual modules are affected by the end effect in a similar order of magnitude. A parameter sensitivity analysis is performed in BIB016 for modular and complementary machines. By removing the PM from half of the primary teeth, E-Core LSFPMs improve the fault-tolerant capability of conventional LSFPMs without sacrificing average thrust production BIB011 . In order to improve the thrust density of LSFPMs, C-Core LSFPMs are proposed in BIB011 . Compared to the conventional 12/10 LSFPM, the 6/13 C-Core machine can achieve a 18.4 % higher average thrust force while the amount of PM material is 40.1 % lower. However, the detent force is increased from 10.39 % to 13.32 %. Besides, the power factor is generally low for C-Core LSFPMs BIB010 . A yokeless C-Core LSFPM is presented in BIB014 . The particularity of this design is that it adopts a series magnetic circuit, and doing so, Gandhi et al. improve both the thrust density and the power factor of a conventional LSFPM, 56 % and from 0.168 to 0.6 respectively. The proposed machine also reduces the average normal force value to zero. A similar structure is proposed in BIB025 and BIB024 , by adopting a double mover structure with a series magnetic circuit. However, the proposed machine has a long primary configuration, so the performance is very poor from both efficiency and power-factor viewpoints. The partitioned-stator configuration has also been proposed for LSFPMs, and an improvement of 32.2 % on the average thrust force has been reported BIB019 .