Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents the comparison of four linear switched reluctance machines (LSRMs) as possible candidates for application in vertical elevators. Linear induction and linear synchronous machines have been presented and experimentally tested in vertical elevators. In this paper, four longitudinal LSRM configurations are presented and designed to operate as propulsion actuators in a vertical elevator prototype. Two of the four configurations have been presented earlier in horizontal propulsion experiments, and a third one has been proposed for application in vertical elevators. All four LSRMs are designed for similar static force profiles to allow for their comparison. The designed LSRM configurations are compared by using finite-element analysis and dynamic control simulations. The stator, translator, and copper winding weight and dimensions, footprint area, active material weight, normal forces and payload capabilities for all four configurations are contrasted. The configuration with the highest payload capability is chosen for implementation in an experimental prototype. The prototype vertical elevator is 1.27 m tall with a 1-ft-tall elevator vehicle with no counterweights and uses two LSRM setups on each side. The experimental correlation of propulsion force and inductance is presented to validate the theoretical design method used in this research. <s> BIB001 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> In this paper a magnetic circuit analysis has been developed to obtain flux linkage/current characteristics in aligned and unaligned positions for a Linear Switched Reluctance Motor. The model is based on lumped parameters and it takes into account the leakage pole flux and the end effects. The lumped parameter magnetic analysis proposed can be a useful tool for designing Linear Switched Reluctance Machines. The procedure has been verified using two dimensional finite element analysis and experimental measurements. <s> BIB002 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents a detailed sensitivity analysis of the effect of several geometrical parameters on the performance of a double-sided linear switched reluctance motor (LSRM). The analysis was conducted in two dimensions using finite-element method and takes into account only one part of the LSRM. This paper first investigates the powerful influence of stator- and translator-pole widths on force profiles. It then shows how these performance parameters are influenced by stator-pole length, translator-pole length, stack length, yoke length, and air gap. Experimental results confirm that the 2-D finite-element sensitivity analysis proposed in this paper may prove to be a useful tool for optimizing the geometry of a double-sided LSRM. <s> BIB003 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Low power density is an obstacle of linear switched reluctance machines (LSRMs) to be competitive candidates for the wave energy conversion, which is increasingly a potential source of renewable energy. Meanwhile, the strong coupling and nonlinearity of LSRMs and drives make it very difficult to derive a comprehensive mathematical model for the behavior of the system. This paper presents a new excitation winding configuration to improve the power density and proposes a new method to model the LSRM and drive based on the matrix and tensor approach. The accuracy of the model has been evaluated by comparison to the simulation result from the finite element analysis tool. <s> BIB004 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Force ripple is the main disadvantage of conventional linear switched reluctance actuators/motors (LSRAs/LSRMs). Based on finite element analysis (FEA), a new method to minimize force ripple is proposed for multimodular LSRAs/LSRMs in this paper. First, the force distribution of an LSRA/LSRM module is computed by using FEA. Then, the scheme of the spatial distribution of modules is developed. Finally, the modular spatial displacement is optimized to minimize force ripple. The computed results based on the FEA demonstrate the proposed method. The proposed method does not require any change in both module design and motor control. Thus, it is simple, cost-low, feasible, and effective. <s> BIB005 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> An improved force distribution function (FDF) of linear switched reluctance motors (LSRMs) based on nonlinear inductance modeling for force ripple minimization and smooth speed operation is proposed. Nonlinear inductance profile is divided into three segments with a K factor that depicts current effect on inductance of the LSRM. Speed controller based on the proposed FDF and the nonlinear inductance model is constructed. Both simulation and experimental results verify the proposed FDF with the nonlinear inductance modeling effectively reduce force ripples with uniform speed response. <s> BIB006 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Linear switched reluctance machine (LSRM) offer advantages to be used in harsh conditions and low cost applications, but subject to low force density because of the nature of force production which resemble the well-known rotary SRM. A new kind of LSRM with different structure and magnetic circuit topology is presented in this paper. The presented machine incorporates a simple concentric winding and concrete ferrite-magnetic segmentations instead of the teeth type stator. Compared to teeth type linear reluctance machine, it features unique magnetic circuit and higher thrust force density. This paper analyze the principle and evaluate the performance of the presented machine. The results show that the presented linear reluctance machine gains a favorable superiority over the teeth type linear reluctance machine in terms of high force density, high reliability and low cost. The presented machine with different structural configurations are given and their performance are evaluated and discussed. <s> BIB007 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents the numerical modeling of a classical switched reluctance motor (SRM) and a mutually coupled SRM (MCSRM); both have three phases with 12 slots and 8 poles. The multiphysics models have been developed, which can take into account the electromagnetic characteristics, mechanical vibration, and acoustic noise of the foregoing machines. A 2-D electromagnetic model has been used to calculate the magnetic force which is the main source of vibration of the entire motor system. The vibration of the motor is calculated by a mode superposition method, while the acoustic noise is predicted by a 3-D finite-element acoustic model. In order to validate the numerical models, experiments have been carried out. A good agreement between measured and numerical results has been observed, and it is found that the vibration and the noise levels of MCSRM are considerably lower than those of classical SRM. <s> BIB008 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> A mutually coupled switched reluctance machine (MCSRM) comparable with interior permanent magnet synchronous machines (IPMSM) and conventional switched reluctance machines (CSRM) have been designed for hybrid electric vehicle (HEV) applications. The MCSRM can utilize the standard six switch inverter. The designed MCSRM is capable of wide speed range operation and has power and torque densities comparable to IPMSM and CSRM. <s> BIB009 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents a new yokeless Linear Switch Reluctance Machine (LSRM) for Urban Rail Transit System (URTS) which primary and secondary sides both feature modular structure. The primary side consists of independent cores of different width with the bigger core wound by a simple concentric winding while the smaller core remains unwound. The secondary, i.e. the stator of the LSRM includes series of faro-magnetic segments which are magnetically and mechanically isolated with each other. The modular characteristics of the presented LSRM gains a superiority over the conventional teeth type LSRM in terms of high thrust density and low cost as long stroke linear driver. FEM model is established and employed to analyze and evaluate the machine performance which gives a fair comparison with the teeth type LSRM in terms of force density and force ripple. <s> BIB010 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper investigates the influence of mutual fluxes (inductances) on the resultant torque in three-phase conventional switched-reluctance machine (CSRM) and mutually coupled SRM (MCSRM) using the frozen permeability (FP) method. Under saturation conditions, the FP method allows accurately separating the torques due to self-flux and mutual flux, hence quantifying their contributions to torque generation. Then, appropriate current waveforms (unipolar or bipolar, square wave or sinewave) can be established to maximize the output torques. It is well known that the mutual torque of CSRM can be negligible. However, this paper has shown that when sinewave current is employed and under full or overload conditions, the torque will be significantly reduced due to non-negligible negative mutual torques. Different from CSRM, the self-torque and the mutual torque of MCSRM can be added if current waveform is properly chosen, e.g., sinewave currents. This can significantly boost the resultant torque. The predictions have been validated by experiments. <s> BIB011 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> The requirements of high efficiency and environment-friendly behavior for wave energy conversions (WECs) have promoted improving investigations of linear electric machines. As an alternative to these existing linear machines, a mutually coupled linear switched reluctance machine (MCLSRM) for direct-drive WECs is proposed in this paper. An extensive comparative study is carried out between the proposed machine and other two comparative machines. By analyzing the operation principles of the three machines, the flux linkage and electromagnetic force formulas are theoretically derived based on equivalent magnetic circuit models, and discussed with the aid of finite-element analysis. Due to high utilization of the electrical and magnetic circuits, it is possible to find an MCLSRM design with comparable force capability to a traditional linear permanent-magnet (LPM) machine with the same electrical loading and the similar overall volume. Furthermore, two prototypes of different machines of the proposed machine and its LPM counterpart are manufactured for experimental validation. From the comparison results, the proposed MCLSRM has a good performance to extract more power from the prime mover above the rated velocity and is highly economic. The LPM counterpart has higher efficiency due to its lower fundamental flux density. <s> BIB012 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents a comparative analysis of conventional switched reluctance machines (SRMs) and mutually coupled switched reluctance machines (MCSRMs) in terms of inductance profiles, torque profiles, the average torque, and the maximum torque. Four 3-phase, 12/8 SRMs including the conventional SRM, the short-pitched MCSRM, the fractionally-pitched MCSRM, and the fully-pitched MCSRM are evaluated. Compared to the conventional SRM, the MCSRMs can be driven by the three-phase standard voltage source converter and work in bipolar, two-phase excitation mode. In the bipolar, two-phase excitation mode, the fully-pitched MCSRM has the highest maximum and average torque production compared to the short-pitched MCSRM and the fractionally-pitched MCSRM. <s> BIB013 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Linear switched reluctance motors (LSRMs) have been an attractive solution for linear driving systems. This paper presents the design and performance comparison of dual side mover and segmental stator LSRM. A conventional teeth-type LSRM, which has identical dimensions, is designed and compared. A design process is developed based on the linear inductance model, and then a standard power equation of this kind of machine is derived, giving a guideline for the design process of the presented LSRM. Using the designed process obtained, a prototype machine is designed and manufactured. Finally, the experimental results from the prototype validate the design procedures and analysis. <s> BIB014 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Linear switched-reluctance motor (LSRM) is investigated and proved to be an alternative for direct linear driving systems, especially for long-distance transportation applications, such as vertical elevator driving motor. This paper presents the design, sensitivity analysis, and optimization of a toroidally wound mover LSRM with segmental stator. The presented LSRM has much higher copper utilization ratio and flux carrying capability than the conventional LSRM for vertical linear propulsion application. The features of motor performance influenced by various geometrical parameters are described using magnetic circuit and finite element analysis to give the guidelines for selecting the reasonable range of those parameters of this kind of machine. Furthermore, an optimization procedure is performed to obtain the optimal machine dimensions considering active payload ratio and force ripples. Finally, the experimental results from the prototype validate the design procedures and analysis above. <s> BIB015 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Thermal analysis is an important issue in machine design which allows to have a knowledge of the machine temperature rise. This paper presents the thermal analysis, modeling, and experiments of a linear-switched reluctance machine (LSRM) with toroidally wound mover and segmental structure. First, a 3-D heat flow model with the homogenized region for the presented LSRM is established using the thermal equivalent circuit. The equivalent thermal resistance of the model is developed together with the nodes forming of the thermal resistance network. The thermal identification to each component such as windings and core steel is performed. Then both the numerical 2-D and 3-D heat flow model for the presented LSRM are established by finite-element analysis which can give the detailed temperature distribution of the entire machine. At last, the actual experiment on a prototype is carried out, validating the accuracy, and feasibility of the thermal equivalent model above. <s> BIB016 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Linear switched reluctance motors (LSRMs) provide an alternative to linear induction motor and linear permanent magnet motor in both vertical and horizontal propulsion applications. This paper attempts to develop a unitized design method of a segmental secondary LSRM, which is characterized by a modular magnetic circuit structure and the independent operation of multimover units. The developed design method is directly performed in linear domain without transforming it to a rotary SRM, which complies with the essential natures of the segmental secondary LSRM, showing that it is capable of delivering more power at the same dimensions compared to the conventional tooth type LSRM. Further, the sensitivity analysis of the critical geometric parameters is performed, and the guidelines for selection of the best dimension parameters are given. Finally, the three-phase and four-phase LSRMs are designed and prototyped, respectively with a 1-m long stator. The experimental results validate the design procedures and analysis above. <s> BIB017 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> Switched reluctance motor (SRM) is gaining more interest in the last decades due to its simple and robust structure. SRMs are classified into conventional SRMs (CSRMs) and mutually coupled SRMs (MCSRMs). CSRMs are based on single-phase excitation and torque is generated by the variation of self-inductance with rotor position. MCSRMs are based on multi-phase excitation and torque is produced by the rate of change of both self- and mutual inductances. MCSRM has the advantages of using the standard voltage source inverter at balanced current operation, when the sum of the phase currents is zero, while CSRM requires an asymmetrical converter. This paper presents the state-of-the-art review of MCSRMs, including operating concept, winding, and pole configurations, control methods by using different current waveforms, performance comparison of MCSRM configurations, modeling methods, and future work for improving MCSRM performance. <s> BIB018 </s> Linear Machines for Long Stroke Applications—A Review <s> III. LINEAR SWITCHED RELUCTANCE MACHINES <s> This paper presents a novel modular-stator linear switched reluctance motor (MSLSRM) for elevator applications. The topology and its operating principle is illustrated and the magnetic equivalent circuit is derived for the aligned position. To attain the electromagnetic features of the motor, two dimensional and three dimensional finite element methods are employed. The static inductance and force profiles are obtained and the flux density distributions are given. Also, the dynamic operation of the introduced motor is performed. To demonstrate the positive sides of the suggested motor, a fair comparative study is done. To this end, two linear motors are considered and the static performance and dynamic waveforms of the three motors are compared. It is illustrated that the new motor has higher mean force and lower force ripple in comparison with the considered SRMs. <s> BIB019
Feature-wise, linear switched reluctance machines (LSRMs) are very similar to LIMs. Their main advantages are their low material and manufacturing cost BIB010 - BIB011 , simple structure BIB015 , BIB016 , BIB018 , and their inherent ruggedness BIB017 , BIB016 - BIB018 . They consist of a toothed structure on both primary and secondary sides, and do not require permanent magnets or windings in the secondary as it can be seen in Fig. 6 . The low number of elements makes these machines very easy to manufacture BIB012 ,  , and their wide constant power operating range BIB010 , BIB013 , has made them an interesting candidate for their application in elevators BIB001 , BIB015 , BIB019 or rail transit applications BIB010 . These machines generally rely on the variation of selfinductance to generate thrust force, and exhibit very low mutual-inductance values. This makes them highly reliable and fault tolerant BIB002 , BIB003 , BIB015 , BIB014 . They are also capable of achieving higher thrust densities than LIMs BIB010 , BIB014 , while lowering thermal management requirements on their secondary side BIB005 , BIB006 . Even so, their thrust capability is still lower than the one from LPMSMs BIB007 , BIB019 ,  . Thrust ripple, and high noise and vibration levels are common issues when these machines are used BIB013 , BIB019 , BIB018 . A common approach for reducing issues with the generated thrust ripple is the usage of the so called force distribution functions, which reduce the output force ripple by controlling the waveforms of the input currents BIB006 . However, apart from the reduction of the thrust force ripple, this control solution also reduces the average thrust produced by LSRMs, so the designer has to decide between higher ripple or lowered thrust density values. In the last years, two new topologies of LSRMs are showing promising performance improvements. These are the segmented secondary LSRMs BIB007 , BIB010 , BIB015 , BIB014 , BIB017 and the mutually coupled LSRMs BIB008 , BIB009 , BIB011 , BIB013 , BIB012 . By adopting a segmented structure, LSRMs have been found to improve the thrust density, while lowering the machine cost BIB015 , BIB017 , thanks to the suppression of the yoke in the secondary side. These machines can be configured with a secondary pole width to secondary pitch ratio of almost 1, much higher than the 0.5 limit for the conventional tooth type LSRMs. This means that the segmented configurations can carry more flux, and thus increase power density when compared with tooth type LSRMs BIB015 . A complete guide for designing segmental secondary LSRMs is given in BIB017 . Mutually coupled LSRMs have not received that much attention yet. Some papers have been published BIB004 , BIB012 analysing these configuration in the linear form, but most of the current research refers to rotary switched reluctance machines BIB008 , BIB009 , BIB011 , BIB013 . It is found that due to the double phase excitation capability of mutually coupled switched reluctance machines, their efficiency and power density values are higher than the ones from conventional machines. Kabir and Husain BIB009 conclude that the performance of this type of machines is comparable to that of the Toyota Prius interior PM machine in terms of torque density, efficiency and operating range. Lower noise and vibration levels are reported for these machines in BIB008 , due to much lower radial forces than in classical switched reluctance motors. In the linear form, a mutually coupled LSRM has been compared to a LPMSM in BIB012 , and the results show that for machines of the same dimensions, the mutually coupled LSRM can produce 1.6 % higher electrical power at rated velocity, while reducing the cost of the machine by 62 %. In spite of all of these advantages, mutually coupled switched reluctance machines are not as fault tolerant as the conventional counterparts, because they use the mutual flux to generate thrust. Moreover, a distributed winding is required for this type of machines, and thus, the end windings are bulkier, and may result problematic when tight space requirements are set BIB009 .