Development of a Low-Cost Modular Structure Fault Tolerant Field Excited Flux Switching Linear Machine for Urban Rail Transit

This paper proposes double sided complementary modular field excited flux switching linear machine (FEFSLM). FEFSLM offers the low cost, variable flux capability for a wide speed range, a compact and robust stator which is suitable for the long stroke application. Compared to other linear machines, complementary modular design has more sinusoidal and symmetrical flux linkage and lower detent force. Initially, the topology and machine working principle is thoroughly discussed. To maximize the thrust force of the machine and optimize the geometric parameters, built-in genetic algorithm (GA) of JMAG ver. 20 is utilized. Furthermore, the modular design incorporates the concept of fault-tolerant capabilities to provide the required decoupling between phases. 2D finite element analysis (FEA) is used to analyze the machine performance. Comparatively the optimized design exhibits higher thrust force, lower thrust force ripples and higher efficiency than the initial design.


I. INTRODUCTION
Linear machines have been a popular alternative for urban rail transit systems due to its unique benefit of non-adhesive thrust force. The most notable example is the development and implementation of linear drive machines, which eliminate mechanical friction and produce thrust directly using electromagnetic force, showing great reliability for high speed and efficiency [1], [2]. Linear Induction Machine (LIM) is a conventional linear machine with a simple and robust stator configuration. As a result, LIM has been widely used as a driving motor for railway transit systems such as Guangzhou Metro Line 4 and China's Capital Airport Express Line [3], [4]. For long stroke application, the LIM has the advantages of low cost because there are no windings or magnets on the stator and only the aluminum sheet constitutes the stator, i.e., the rails. However, one of the obvious disadvantages of LIM is that its efficiency and power factor are not satisfactory due to the eddy effect. Presently, linear machines exist of several The associate editor coordinating the review of this manuscript and approving it for publication was Paolo Giangrande . types in which the most prominent is permanent magnet synchronous linear machine (PMSLM), which has high acceleration and thrust force density. Although, PMSLMs dispersed armature winding (AW) and permanent magnet throughout the primary and secondary components. So, a significant amount of PM or copper is required for long stroke applications [5], [6]. To overcome the problem of the PMSLM, primary permanent magnet linear machines (PPMLM) are investigated in [7]- [9]. In this scenario, the PM flux switching linear machine (PMFSLM) and the PM flux-reversal linear machine (PMFRLM) are regarded breakthroughs in the field of machines and have attracted the attention of many researchers [10]. In PMFSLM both AW and PM are placed in the primary component of these two types of machines, meanwhile the secondary component is constructed entirely of iron [11]. In design of PMFSLM, the excitation part which is primary component act as mover whereas the static secondary part made of iron only is termed as stator due to which preferred for long stoke applications. Since, PM and AW are housed at short mover, this drastically lowered the overall machine cost. However, PPMLM cannot provide a controllable airgap field, requiring the use of PM, which are expensive and vulnerable to demagnetization. Furthermore, the switched reluctance machines (SRM) have been investigated for the urban rail transit systems in recent years [10], [12], [13], which comprise of a short primary mover with yokeless iron and armature windings. The advantages of SRM include its simple construction, excellent robustness, and high reliability. SRM has a higher thrust density than LIM, particularly at high speeds and high efficiency and flexible operation for a wide constant power scale. SRM have the disadvantages of high acoustic noise, high thrust force ripples and high vibration [14]. The SRM's application prospects for railway transportation are not promising [15]. Therefore, field excited linear machines take the advantages of low cost and high reliability. A new field excited FRLM based on the magnetic gearing effect has been studied in [16], which not only has the advantages of reduced cost and flux changing capability, but also has better force capability when compared to the conventional. FRLM suffers from the more cogging force and unbalance sinusoidal back electromotive force (EMF). The field excited FSLM is presented in [17], [18] to overcome the aforementioned problems. The proposed machines have the advantages of low cost, reduced mover weight and improve the load capacity. However, based on the literature these types of machines have problem of high-end windings, because these machines adopt the overlapped armature and field windings which have high copper losses and reduce the efficiency of the machines. A new double-sided field excited FSLM with non-overlapped winding has been investigated in [19], [20]. This machine has the merits of low copper losses, high efficiency, larger thrust force, smaller normal force, and better heat dissipation.
Other than machine thrust force, some applications prefers high reliability and fault tolerant capability [21]. The fault-tolerant capabilities of existing machines have been significantly improved by adding alternate poles, introducing modular type design structure, and additional redundant windings in design [22]- [27]. By reducing coupling between phases, a low mutual inductance design may be used to enhance fault-tolerant performance [28], [29]. Meanwhile, to reduce the machines short-circuit current, a design with a high self-inductance can be used [30]. Furthermore, winding configuration in multiphase machines play vital role to enhance fault tolerant capability which make flexibility in control methods. To account, the properties of high fault tolerant performance, low cost and reduced thrust force ripples, this paper presents a double sided complementary modular field excited flux switching linear machine (FEFSLM) with three phase non-overlapped winding.
The rest of this paper is organized as follows, section II presents machine topology and operating principles. Section III investigates the design parameters of the FEFSLM. Detailed electromagnetic analysis based on finite element analysis (FEA) of FEFSLM is examined in section IV. Section V investigates the fault tolerant capability of the proposed machine. Finally, section VI presents the outcome of the study.

II. MACHINE TOPOLOGY AND OPERATING PRINCIPLE A. MACHINE TOPOLOGY
Proposed double sided complementary modular FEFSLM topology is shown in Figure. 1. It can be clearly seen that this design does not use any magnets in order to satisfy the requirements of low cost and high reliability. The primary consists of non-overlapped concentrated three phase armature windings and non-overlapped field windings, while the secondary is comprised of salient poles, resulting in a compact and robust construction. The armature windings should be in the same direction, but the field windings should be alternated. Back-to-back E-shaped cores can be seen in each module, whose positions are mutually λ 1 apart, and two consecutive modules combine only one phase.
And the displacement between the two adjacent phases can be found by the relation as where i and j are the two positive integers, with values of 2 and 5 respectively and τ s is the stator pole pitch. For phase A, coils set A1, A2, A3 and A4 are combined to results more sinusoidal and symmetrical EMF waveforms.
The mover slot in each back-to-back ''E'' shaped module is divided into two parts. The non-overlapped armature windings are accommodated in the slot towards the mover yoke, and the non-overlapped field windings are adjusted in the slot towards the airgap. Both windings are wound from the mid tooth of the back-to-back ''E'' shaped module. Between the two modules there is a flux barrier which reduce the mutual inductance and thrust force ripples of the machine. It's worth noting that employing a modular mover design can assist to reduce the amount of detent force. The exploded 3-D view of the proposed machine is shown in Figure. 2.

B. OPERATING PRINCIPLES
The operating principles are based on the no load flux flow generated from a 2D finite element analysis (FEA) using the VOLUME 9, 2021 JMAG software (version 20). The flux distribution of the proposed machine follows the two parallel magnetic circuit. The influence of a double-sided field excited coil is addressed, and the flux linkage within a single-phase armature coil is investigated. Figure. 3(a) displays initial location of the machine at θ = 0 • , the flux at that position is maximum positive because the ''E'' module of coil A1 is aligned with the stator poles. At mover position θ = 90 • , the flux of ''E'' module of coil A1 and ''E'' module of coil A2 are in the opposite direction, as a result, the net flux flow is zero as shown in Figure. 3(b). In Figure. 3(c), when the mover moves at position θ = 180 • , ''E'' module of coil A2 face the stator poles, which gives the maximum negative flux value. In Figure.

Objective function
Split ratio can be defined as [28] where h s , δ and h m denotes the stator height, length of airgap and mover heights respectively. The important geometric parameter in the machine is the mover tooth width which defines the section area of the magnetic flux. Another significant parameter is the mover yoke height, which has a greater impact on the magnetic circuit's loop flux while moving in various directions. In the case of the stator, the width and height of the stator tooth are optimized like mover.
The flowchart of the global optimization process utilizing GA is shown in Figure. 5. The optimization of the important geometric parameters is done with JMAG's built-in global optimization utilizing the GA method. In the optimization setting, the maximum generation is 20, the population size is 22, number of children is 23 and the stopping criteria is 12. After calculating seven hundred and twenty-two cases with GA, which took almost 192 hours, file size is 26.2 GB and the PC on which optimizing is running is hp core i5, 2.5 GHz, 8GB RAM.
The relationship between the thrust force ripples ratio and thrust force of the double sided FEFSLM with mover yoke, mover pole width, stator pole width and stator yoke are shown in Figure. 6(a-d) respectively. Furthermore, the optimized design exhibits higher thrust force than the initial design. Also, the optimized design shows smaller split ratio than the initial one. The globally optimized parameters of the proposed design are illustrated in table 4.

IV. COMPARATIVE ELECTROMAGNETIC PERFORMANCE
The electromagnetic performances of the initial and optimized FEFSLM including no load flux linkage, back EMF, detent force, airgap flux density and thrust force are investigated.

A. OPEN CIRCUIT FLUX LINKAGE
The open circuit flux linkage of the initial and optimized FEFSLM are shown in Figure.   there is no influence on end effect due to the complementary modular design. Although, the fundamental amplitude of the optimized design is greater than the initial design. From Figure. 8(b) the third order harmonics have a greater proportion, but have negligible amplitude as compared to the fundamental. However, Figure. 8(b) shows that the higher  order odd harmonics amplitude of the optimized design is smaller than the initial ones.

B. OPEN CIRCUIT BACK EMF
The open circuit back EMF of the initial and optimized are shown in Figure. 9(a). At the rated velocity of 1.5 m/s both designs offer the sinusoidal and balance three phase back EMF. Furthermore, the optimized design has greater fundamental amplitude as compared to the initial design as shown in Figure.    optimized design is shown in Figure. 10(b) and can be observed that both designs have quite similar flux density. The flux generated by the field windings mostly passes via the primary yoke, primary teeth, air gap, secondary teeth, and secondary yoke in a sequential order. Despite this, only a small amount of leakage flux passes through the mover slot, which is indicated in red.

D. DETENT FORCE AND THRUST FORCE
As can be seen from Figure. 11(a) that the optimized design exhibit relatively smaller detent force as compared to the initial design. The period of the detent force can be   (4) where N p and N s are the pole numbers and slot numbers respectively, while N c is the number of periods in one electrical cycle. Comparison with other linear machines, the end effect in the complementary modular design is negligible, due to which the detent force in these machines is lower than the other linear machines. However, Figure. 11(b) shows the thrust force waveforms of the initial and optimized designs, and optimized design has 31.91% greater thrust force than the initial.

E. THRUST FORCE RIPPLE RATIO
The thrust force ripple ratio is defined by where T .F max , T .F min , T .F avg are the maximum, minimum and average thrust force values respectively. The variation in the average thrust force of the optimized double sided FEFSLM is shown in Figure. 12(a), while the thrust force ripple ratio is depicted in Figure. 12(b). It can be concluded from Figure. 12 that the thrust force ripple ratio is lowest at the place where the average thrust force value is largest. The optimized design has a ripple ratio of just 7%, whereas the initial design has a ripple ratio of 13%.

F. CHARACTERISTICS OF THRUST FORCE AND POWER VS VELOCITY
The characteristics of thrust force and power against the velocity for the optimized design is shown in Figure. 13. The maximum output power at the rated velocity is 1326 watt and above rated velocity the power graph is decreasing. Furthermore, at rated velocity the thrust force region is constant, after that the thrust force is dropped to 163.7N at velocity of 3.64 m/sec. Performance comparison of the optimized and initial design are shown in table 5.

V. MATHEMATICAL MODEL OF THE MACHINE A. MATHEMATICAL MODELLING FOR THREE PHASE SYSTEM
The three-phase flux linkage of the double sided FEFSLM is defined by where 0 is the DC component and m is the fundamental peak amplitude and θ e denotes the electrical degree of the mover position. The self-inductances and mutual inductances   By adding flux gaps between adjacent back-to-back ''E'' shaped modules, which produces a change in the magnetic flux path and the independence between two phases is enhanced. In the mover frame the self-inductances of various phases and mutual inductance of different phases is shown in Figure. 14 and 15 respectively. Due to the physical separation between different phases, it can be observed from the Figure. 14 that the self-inductance is comparatively much more than the mutual inductance. In addition, higher self-inductance reduces short circuit currents in short circuit conditions while lower mutual inductance between different  phases reduce the interference between the healthy and defective phases.

B. DQ MODELLING IN THE STATOR FRAME
The back EMF and flux linkage waveforms are sinusoidal when the mover of the machine travels over one pole pitch of the stator. As a result, the machine d-and q-axis may be specified as illustrated in Figure. 16, in which the d-axis is that position at which the field flux linkage is at positive maximum, while q-axis is the position where the field flux linkage reaches to zero. The distance between d-and q-axis is 1/4 τ s .
The dq inductances can be computed through classical park transformation and can be expressed by The field flux linkage in the form of matrix is expressed as  From (10), where d-axis field flux linkage is equal to the fundamental negative peak value of the field flux linkage and q-axis field flux linkage is equal to zero.
The d-q axis inductance can be calculated by the following formula.
By substituting (7) (8) (9) in (11) we can derive it as Inductance profile of the proposed FEFSLM along the dqaxis is illustrated in Figure. 17. The resulting generated flux at the adjacent phase winding are 90 degrees apart leading to the least flux interaction between adjacent phase and no mutual flux interaction between end-to-end coils. Therefore, mutual inductance along the dq-axis is usually zero. However, due to  variable reluctance flux path in the salient stator and mover teeth, the d and q-axis flux interacts. As a result, mutual inductance along d and q-axis (L dq ) is not zero, indicating that the waveform amplitude is small and equals L dq and the waveform is shown in Figure. 18.

C. SHORT CIRCUIT CURRENT
In order to ensure the fault tolerant capability in the proposed machine, the two phases are short circuited through a switch. The current amplitude in the two phases is now higher than the pre-fault condition when the fault occurs at 0.072s (the end of the third electrical period). Figure 19 indicates that the healthy phase has no interdependency with the other two phases during faults, and so the healthy phase has a normal current amplitude before and after faults. As a result, the field excited linear flux switching machine exhibits fault tolerant capability through inductance calculations and short circuit current validation.

VI. CONCLUSION
In this paper a double sided complementary modular FEFSLM has been presented. The machine topology and working principle have been explained in detail. To improve the thrust force and optimize the geometric parameters some global optimization has been implemented on the design. Higher self-inductance and lower mutual inductances were identified in the optimized design, showing that the machine is more fault tolerant. The optimized design had a higher thrust force and reduced thrust force ripples, according to the electromagnetic study. Furthermore, the future work plan is to fabricate the optimized design in order to compare the simulated and experimental results.

APPENDIX
Different types of linear flux switching machines are investigated for urban transit at different scale i.e., as low and high based on mover length, velocity, air-gap length and stack length. At different system specification, the aforesaid parameters widely vary. Therefore, a detailed study on low and high scale design are added in table 6 to highlight variation of the key parameters with the system specification. Based on the design specification, the proposed model is designed at low scale, which can be rescale to large dimension based on the system specification. It is noteworthy that initially models are designed at low scale to save computational time as well as experimental prototype expense.