Torque Characteristic Analysis of a Transverse Flux Motor Using a Combined-Type Stator Core

applied sciences Article Torque Characteristic Analysis of a Transverse Flux Motor Using a Combined-Type Stator Core Xiaobao Yang, Baoquan Kou *, Jun Luo, Yiheng Zhou and Feng Xing Department of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China; hit08yxb@163.com (X.Y.); luojunlj@163.com (J.L.); sethvoler@163.com (Y.Z.); xing66feng@sina.com (F.X.) * Correspondence: koubq@hit.edu.cn; Tel.: +86-451-8641-4151 Academic Editor: Wen-Hsiang Hsieh Received: 4 October 2016; Accepted: 4 November 2016; Published: 8 November 2016 Abstract: An external rotor transverse flux motor using a combined-type stator core is proposed for a direct drive application in this paper. The stator core is combined by two kinds of components that can both be manufactured conveniently by generic laminated silicon steel used in traditional motors. The motor benefits from the predominance of low manufacturing cost and low iron loss by using a silicon-steel sheet. Firstly, the basic structure and operation principles of the proposed motor are introduced. Secondly, the expressions of the electromagnetic torque and the cogging torque are deduced by theoretical analysis. Thirdly, the basic characteristics such as permanent magnet flux linkage, no-load back electromotive force, cogging torque and electromagnetic torque are analyzed by a three-dimensional finite element method (3D FEM). Then, the influence of structure parameters on the torque density is investigated, which provides a useful foundation for optimum design of the novel motor. Finally, the torque density of the proposed motor is calculated and discussed, and the result shows that the proposed motor in this paper can provide considerable torque density by using few permanent magnets. Keywords: transverse flux; torque density; three-dimensional finite element method; external rotor 1. Introduction A traditional motor drive system is combined with an electromagnetic component (e.g., DC motor, induction motor, permanent magnet synchronous motor, and switched reluctance motor) and mechanical component (e.g., gear box, transmission). Some drawbacks are added into the system by using mechanical components, such as friction loss, maintenance cost and noise. Therefore, the direct drive motor system is proposed to avoid problems. In a direct motor drive system, the motor is coupled with load directly, and the direct drive motors are usually needed to own the features of low working speed and high output torque in most direct-drive applications (e.g., electrical vehicle, wave energy conversion, ship propulsion, railway traction, and wind power generation). A series of motor technologies has been investigated for direct-drive applications, such as the multi-pole permanent magnet synchronous motor (PMSM) [1], the brushless DC motor (BLDC) [2], the permanent magnet vernier motor (PMVM) [3 5] and the transverse flux motor (TFM) [6 9]. Among those motor technologies, the transverse flux motor has a unique transverse main flux path that is perpendicular to the rotate direction. In contrast to the radial flux technologies, the feature of the transverse flux path makes the electrical load and the magnetic load be decoupled from each other, which improves the torque density and the feasibility for multi-pole design. Nevertheless, the structure of TFM is usually complex as the 3D flux path, and the use of a silicon steel sheet is laminated. The soft magnetic composite (SMC) is a reasonable material for TFM [10]; however, the mechanical strength and magnetic characteristic of SMC is lower than a silicon steel sheet. Appl. Sci. 2016, 6, 342; doi:10.3390/app6110342 www.mdpi.com/journal/applsci

Appl. Sci. 2016, 6, 342 2 of 16 Appl. Sci. 2016, 6, 342 2 of 16 Various Various transverse transverse flux flux motor motor structures structures have have been been proposed proposed and and researched researched by by the the scholars scholars around around the the world world [11 14]. [11 14]. They They can can be be classified into synchronous type and reluctance type [15]: [15]:(1) (1) if ifthe permanent magnets are fixed on the rotor side (including mounted on the rotor core surface or or buried into the rotor core), the the motor can can be be classified as as a transverse a transverse flux flux permanent permanent magnet magnet synchronous synchronous motor motor (TFPM) (TFPM) [16,17]; [16,17]; (2) (2) if there if there is no is no permanent permanent magnet magnet on on the the rotor rotor side, side, the the motor motor can can be classified be classified aas transverse a transverse flux reluctance flux reluctance motor motor (TFRM) (TFRM) [18]. The [18]. TFPM The can TFPM obtain can larger obtain torque larger density torque than density the TFRM; than the meanwhile, TFRM; meanwhile, the manufacturing the manufacturing cost of TFRM cost isof lower TFRM andis reliability lower and ofreliability TFRM is higher. of TFRM Thus, is higher. the cost Thus, andthe cost characteristics and the characteristics of motors should of motors bothshould be considered. both be considered. In In this this paper, paper, a transverse-flux a transverse flux motor motor using using a combined-type a combined type stator stator core core (CS-TFM) (CS TFM) is proposed. is proposed. The The CS-TFM CS TFM is is a a kind kind of of external rotor motor. The rotor is iscomprised of of a arotor rotor teeth teeth core core and and non non-magnetic sleeve. sleeve. The The stator stator is comprised comprised of a ofcore, a core, permanent permanent magnet magnet and and armature armature winding. winding. Both Both the the rotor rotor core core and andthe thestator statorcore corecan canbe fabricated by a silicon steel steel sheet, sheet, which which can can improve improve the the mechanical mechanical strength strength and and simplify simplify the the processing processing technique. technique. Both Both permanent permanent magnet magnet and and armature armature winding winding are are fixed fixed on on the the stator stator side, side, and and the the rotor rotor structure structure is simple is simple and and reliable. reliable. The The torque torque density density of of CS-TFM CS TFM is improved is improved more more than than TFRM TFRM by by using using a permanent a permanent magnet, magnet, and and the the cost cost is lower is lower than than TFPM TFPM as as the the PM PM volume volume of CS-TFM of CS TFM is smaller. is smaller. In In Section Section 2, the 2, the detailed detailed motor motor structure structure and and working working principles principles are are introduced. introduced. In In Section Section 3, 3, the the theoretical theoretical expressions expressions of of electromagnetic electromagnetic torque torque and and cogging cogging torque torque are are deduced. deduced. In In Section Section 4, 4, the the basic basic characteristics characteristics such such as as permanent permanent magnet magnet flux flux linkage, linkage, no-load no load back back electromotive electromotive force force (no-load (no load BMF), BMF), cogging cogging torque, torque, and and load load torque torque are are analyzed by by 3D FEM in detail. In InSection Section5, 5, the theinfluence influenceof of structure structure parameters parameters on on the the torque torque density density is analyzed. is analyzed. In Section In Section 6, the torque 6, the torque densities densities of different of different direct drive direct-drive motor technologies motor technologies are calculated are calculated and compared, and compared, and a summary and a summary is included is included Section in Section 7. 7. 2. 2. Structure and and Working Principles of of TFM TFM 2.1. 2.1. Basic Basic Structure The The basic basic single-phase single phase unit unit structure is is shown in in Figure 1a. The stator core is iscomprised of of two two radial radial magnetic rings rings and and several several axial axial magnetic magnetic bridges. bridges. Both the Bothradial the radial flux ring fluxand ring the and axial the flux axial bridge fluxcan bridge be manufactured can be manufactured by silicon steel by silicon-steel sheets, and sheets, the direction and the of lamination direction of is shown lamination Figure is shown 1a; the inarmature Figure 1a; winding the armature is ring shaped, winding isand ring-shaped, it is fixed in and the itcoil is fixed window the of coil stator window core; the of stator PMs are core; radial the magnetized PMs are radial and magnetized fixed on the and outer fixed surface on theof outer the radial surface flux of ring, the radial each flux two ring, adjacent eachpms twoon adjacent the same PMs radial on the flux same ring radial have flux opposite ring have magnetization opposite magnetization direction, and direction, each two and axially eachcorresponding two axially corresponding PMs on two PMs different on two radial different flux rings radialalso flux have rings opposite also havemagnetization opposite magnetization direction; direction; the rotor is thecomprised rotor comprised of rotor of teeth rotorcores teeth cores and a and non magnetic a non-magnetic sleeve. sleeve. Three phase Three-phase motor motor structure can be beassembled by arranging three single-phase single phase units along the the axial axial direction with with 120 120 electrical angle angle difference between between each each other, other, as shown as shown in Figure in Figure 1b. 1b. Figure 1. Cont.

Appl. Sci. 2016, 6, 342 3 of 16 Appl. Sci. 2016, 6, 342 3 of 16 Figure Figure 1. 1. Basic Basic structure structure of of combined-type combined type combined-type combined type stator stator core core transverse transverse flux motor flux motor (CS-TFM): (CS TFM): single-phase; single phase; and and three-phase. three phase. 2.2. Working Principle 2.2. Working Principle The permanent magnet flux path of CS-TFM at two special rotor positions are shown in Figure 2a,b. The PM flux linkage reaches the positive maximum value at position a, and then reaches the negative maximum value at position c. When the leakage flux is neglected, the main flux from the PM goes radially through the air gap into a rotor teeth core, passing then axially along the rotor teeth core, again radially inward passing the air gap and the axially corresponding PM, passing then radially along the radial magnetic ring and axially along the axial magnetic bridge, again radially along the other radial magnetic ring, and finally returning to the PM, completing a flux loop. It can be seen that the flux path of proposed CS-TFM is transversal to the rotate vector of the rotor, and CS-TFM is a kind of transverse flux technology. As the variation of the magnetic circuit reluctance is due to the teeth-slot structure of rotor when the rotor rotates, the PM flux linkage in the armature winding is a variable about rotor teeth core position (e.g., the flux linkage direction reverses from position a to position c), and the variable flux linkage can induce a back electromotive force (BMF) in the armature winding, as shown in Figure 2c. When alternating sinusoidal current is applied in the winding, the BMF interacts with the current to generate electromagnetic torque. 2.3. Structure Advantages Based on the foregoing introduction of CS-TFM, the following advantages can be listed: 1. Using silicon-steel sheet. The special combined-type stator core of proposed CS-TFM makes it possible to use silicon-steel sheets for 3D flux path. Thus, the magnetic performance and mechanical strength of CS-TFM can be improved more than the TFM using soft magnetic materials (SMC). 2. High reliability. Both permanent magnet and armature winding are fixed on the stator side, and the rotor only be comprised of tooth cores (c) and a non-magnetic sleeve. This structure feature improves the reliability of motor. Figure 2. The permanent magnet flux path and induction principle of no load BMF for CS TFM: permanent magnet flux path at position a positive maximum flux linkage; permanent magnet flux path at position c negative maximum flux linkage; and (c) principle of no load BMF generation. The permanent magnet flux path of CS TFM at two special rotor positions are shown in Figure 2a,b. The PM flux linkage reaches the positive maximum value at position a, and then reaches the negative maximum value at position c. When the leakage flux is neglected, the main flux from the PM goes radially through the air gap into a rotor teeth core, passing then axially along the rotor teeth

Figure 1. Basic structure of combined type combined type stator core transverse flux motor (CS TFM): single phase; and three phase. Appl. Sci. 2016, 6, 342 4 of 16 2.2. Working Principle (c) Figure 2. The permanent magnet flux path and induction principle of no load BMF for CS TFM: Figure 2. The permanent magnet flux path and induction principle of no-load BMF for CS-TFM: permanent magnet flux path at position a positive maximum flux linkage; permanent magnet permanent magnet flux path at position a positive maximum flux linkage; permanent magnet flux path at position c negative maximum flux linkage; and (c) principle of no load BMF generation. flux path at position c negative maximum flux linkage; and (c) principle of no-load BMF generation. The permanent magnet flux path of CS TFM at two special rotor positions are shown in Figure 3. 2a,b. Theoretical The PM Analysis flux linkage of Torque reaches Characteristic the positive maximum of TFM value at position a, and then reaches the negative In order maximum to simplify value the magnetic at position field c. When analysis the of leakage motor, flux some is acceptable neglected, the assumptions main flux are from adopted the here: PM (1) goes the radially permeance through ofthe core air isgap infinity, into a and rotor the teeth magnetic core, passing potential then difference axially along inthe core rotor is ignored; teeth (2) the permeance of permanent magnet is equal to that of air; (3) the eddy and hysteresis effects are ignored; and (4) the saturation effect of the core is ignored. 3.1. Electromagnetic Torque The torque of CS-TFM can be seen as the interaction between the rotor core and the air-gap magnetic field, which is the sum of the permanent magnet field and the armature current magnetic field. It can also be explained in the magnetic field modulation method as shown in Figure 3: the distribution of magnetic field excited by armature current magnetomotive force (MMF) is modulated by the rotor teeth, and the MMF of permanent magnet can be replaced by the magnetizing imaginary current I m at the boundaries of the permanent magnet. Then, the torque of TFM is generated by the interaction of a modulated armature magnetic field and imaginary current. Thus, the electromagnetic torque can be calculated conveniently by the classical electromagnetic equation of BIL. From Figure 3, the air-gap flux density of armature MMF is a periodic function about position, the period is two times that of permanent magnet pole-pitch τ m When the center-line of rotor teeth is aligned to the center-line of permanent magnet (as the position shown in Figure 2a), the position is signed as origin, and the expression of air-gap flux density can be written as Fourier series: ( ) nπx B = B 0 + B n sin, (1) τ m

where hm is the thickness of permanent magnet, δ is the air gap length, μ0 is the permeability of Appl. Sci. 2016, 6, 342 5 of 16 B 0 = 1 τ m ( 0.5lrt B n = 1 ( 0.5lrt B τ teeth sin m 0 0 ( nπx τm B teeth dx + τ m ) dx + ) B slot dx, (2) 0.5l rt ( ) ) nπx B slot sin dx, (3) 0.5l rt where B 0 is the constant component, B n is the harmonic component, B teeth is the flux density in the teeth area, B slot is the flux density in the slot area, τ m is the permanent magnet pole-pitch, l rt is the circumferential rotor teeth length, and x is the distance between position and origin. Appl. Sci. 2016, 6, 342 5 of 16 τm τ m Figure Figure 3. 3. Magnetic field field distribution by the armature magnetomotiveforce force (MMF) and and imaginary current current distribution equivalent to to the the permanent magnet MMF. From Figure 3, the air gap flux density of armature MMF is a periodic function about position, the The period air-gap is two flux times density that of is permanent the product magnet of air-gap pole pitch permeance τm When and the armature center line winding of rotor MMF teeth [19]; is however, aligned to the the permeance center line calculation of permanent ismagnet generally (as the difficult position in shown transverse in Figure flux 2a), motors the position as the is flux distributions signed as origin, are three-dimensional. and the expression To avoid of air gap thatflux complexity, density can the be space written distribution as Fourier ofseries: the permeance can be obtained by using quasi-flux tubes with boundaries determined by straight line and semicircular segments Appl. Sci. 2016, drawn 6, 342 to approximately maximize π 0 sin nx B the B permeance B of each path [20], as shown in Figure 6 of 164. n (1) m, 1 0.5l rt m 0 0 teeth 0.5l slot rt m B B dx B dx, (2) 1 0.5lrt nπx m nπx Bn B 0 teethsin dx B 0.5 slotsin dx lrt m (3) m m, where B0 is the constant component, Bn is the harmonic component, Bteeth is the flux density in the teeth area, Bslot is the flux density in the slot area, τm is the permanent magnet pole pitch, lrt is the circumferential Figure Figure 4. 4. Equivalent Equivalent rotor teeth quasi-flux quasi flux length, tubes tubes and with x with is the boundaries distance determined determined between position by bystraight and line origin. line and andsemicircular segments segments The air gap for for permeance permeance flux density calculation. is the product of air gap permeance and armature winding MMF [19]; however, the permeance calculation is generally difficult in transverse flux motors as the flux distributions Then, Then, the the flux are flux density three dimensional. in in teeth area To and avoid slot area that can complexity, be expressed the as: as: space distribution of the permeance can be obtained by using quasi flux tubes μ with boundaries determined by straight line and semicircular segments drawn to approximately Bteeth maximize the permeance of each path [20], as B h (4) teeth = µ 0Ni a shown in Figure 4. h m + δ, (4) B slot h m μ0ni a π x/2, (5) i 2sin I t, (6) a

Appl. Sci. 2016, 6, 342 6 of 16 B slot = µ 0 Ni a h m + δ + πx/2, (5) i a = 2Isin (ωt + ϕ), (6) where h m is the thickness of permanent magnet, δ is the air-gap length, µ 0 is the permeability of vacuum, N is the armature winding turns, i a is the instantaneous armature current, I is the Root-Mean-Square (RMS) of armature current, ω = 2πf is the electrical angular velocity and ϕ is the initial phase angle of armature current. When the high order harmonic component of Equation (1) is neglected, the air-gap flux density can be simplified as: ( ) nπx B = B 0 + B 1 sin, (7) τ m B max = B 0 + B 1 = µ 0Ni a h m + δ, (8) B min = B 0 B 1, (9) k = B 1 B max, (10) where B max is the maximum value of air-gap flux density, B min is the minimum value of air-gap flux density, and k is the modulated factor of armature MMF field. The imaginary current of permanent magnet [21] can be expressed as: I m = B r µ 0 h m, (11) where B r is the residual magnetism of permanent magnet. Then, the electromagnetic force of each pair permanent magnet and the torque of single phase TFM can be written as: F = p (B al 2I m l m B ar 2I m l m ) = 2 2µ 0 jki m l m NI h m + δ [cosϕ cos (2θ + ϕ)], (12) B al = B 0 + B 1 sinθ, (13) B ar = B 0 + B 1 sin (θ + π), (14) θ = ωt = πx τ m, (15) where B al is the air-gap flux density at the position of left boundary of permanent magnet, B ar is the air-gap flux density at the position of right boundary of permanent magnet, p is the pole-pair number of TFM, θ is the relative angle when the rotor rotates. Then, the electromagnetic torque of single phase TFM can be written as: T = FD a 2 = 0.5T max [cosϕ cos (2θ + ϕ)], (16) T max = 2 2µ 0 pkd a I m l m NI, (17) h m + δ where T max is the maximum of the single-phase torque, and D a is the diameter of air-gap.

Appl. Sci. 2016, 6, 342 7 of 16 When the initial phase of armature current ϕ is zero, the amplitude of the single-phase torque reaches the maximum value according to Equation (16), and the electromagnetic torque of each phase can be respectively written as: and the total electromagnetic torque is: T A = 0.5T max [1 cos2θ] T B = 0.5T max [1 cos (2θ + 2π/3)] T C = 0.5T max [1 cos (2θ + 4π/3)], (18) T = T A + T B + T C = 1.5T max. (19) From Equation (19), the total electromagnetic torque is a constant if the cogging torque and high order harmonics of air-gap flux density are neglected. However, the cogging torque and harmonics of air-gap flux density actually exist in the motor, which will lead to the generation of torque ripple. 3.2. Cogging Torque The cogging torque is a result of the interaction between core teeth and permanent magnet in permanent magnet motors. Similar to the traditional permanent magnet synchronous motor (PMSM), the proposed CS-TFM contains a teeth-slot structure. The difference between them is that the teeth-slot structure of CS-TFM is on the rotor side instead of the one on the stator side in the PMSM. Therefore, the cogging torque of CS-TFM is caused by the interaction between the permanent magnet and rotor teeth. The fundamental frequency of the cogging torque is the least common multiple of the rotor teeth number and the stator pole number [17]; in the CS-TFM, the teeth number is p and the pole number is 2p. Thus, the fundamental frequency of cogging torque is 2p and the period is τ m. The cogging torque of each single-phase can be expressed as: T coga = T 1 sin (2θ + θ 1 ) + T 2 sin2 (2θ + θ 2 ) + T 3 sin3 (2θ + θ 3 ) +... T cogb = T 1 sin (2θ + θ 1 + 2π/3) + T 2 sin2 (2θ + θ 2 + 2π/3) + T 3 sin3 (2θ + θ 3 + 2π/3) +... T cogc = T 1 sin (2θ + θ 1 + 4π/3) + T 2 sin2 (2θ + θ 2 + 4π/3) + T 3 sin3 (2θ + θ 3 + 4π/3) +... where T i and θ i are the amplitude and initial phase angle of the ith order harmonic, respectively. Then, the total cogging torque of three-phase TFM is:, (20) T cog = T coga + T cogb + T cogc = 3T 3 sin3 (2ωt + θ 3 ) + 3T 6 sin6 (2ωt + θ 3 ) +... (21) Compared to Equations (20) and (21), the harmonic component besides the 3ith order is counteracted, and the amplitude of the three-phase cogging torque is reduced significantly. 4. Three-Dimensional Finite Element Analysis of TFM Different from traditional motors, which have 2-D flux paths, the magnetic field is complex and 3D distributional in TFMs, and the 3D FEM is necessary to analyze the electromagnetic characteristic accurately. Although 3D FEM can get accurate results, the calculation time is long when the model is large. As there is no magnetic field coupling between each phase of the TFMs, the single-phase model is built in FEM analysis to reduce the computation time, and the total result can be fitted by three single-phase results with 120 electrical angle difference. The main design parameters of TFM are shown in Table 1. The mesh results of model and flux density distribution under load conditions is shown in Figure 5.

3D distributional in TFMs, and the 3D FEM is necessary to analyze the electromagnetic characteristic accurately. Although 3D FEM can get accurate results, the calculation time is long when the model is large. As there is no magnetic field coupling between each phase of the TFMs, the single phase model is built in FEM analysis to reduce the computation time, and the total result can be fitted by three single phase results with 120 electrical angle difference. Appl. Sci. 2016, The 6, main 342 design parameters of TFM are shown in Table 1. The mesh results of model and flux 8 of 16 density distribution under load conditions is shown in Figure 5. Table Table 1. The 1. The main main design design parameters of stator core coretransverse flux flux motor motor (CS TFM). (CS-TFM). Parameter Parameter Data Data Parameter Parameter Data Data Rotor out Diameter Dout 248 mm Air gap Diameter Da 226 mm Rotor out Diameter D out 248 mm Air-gap Diameter D a 226 mm Stator Stator inner inner Diameter Diameter Din D in 140 140 mm mm Height of of Axial Axial bridge bridge hb h b 10 10mm Air-gap Air gap length length δ δ 11 mm mm PM 1 thickness h m hm 22mm Axial Axial length length of single-phase of single phase l a la 45 45 mm mm Pole-pitch Pole pitch τ m τm 11.83 mm Axial length of PM l m 11 mm rotor teeth length l rt 11.83 mm Axial length of PM lm 11 mm rotor teeth length lrt 11.83 mm Armature winding turns N 150 Pole pair number p 30 Armature Rated speed winding n turns N 100 r/min 150 Pole Rated pair current number I p 12.73 30 A Rated speed n 100 1 permanent r/min magnet. Rated current I 12.73 A 1, permanent magnet Figure 5. The three dimensional finite element model of single phase CS TFM: mesh result; and Figure 5. The three-dimensional finite element model of single-phase CS-TFM: mesh result; and magnetic field distribution under rated current. magnetic field distribution under rated current. Appl. Sci. 2016, 6, 342 9 of 16 4.1. Air Gap Flux Density 4.1. Air-Gap Flux Density magnetic An arc field is drawn is excited under by two the permanent pairs of poles magnet; in the the air gap, red line and refers the radial to the flux density on under the arc load is shown An condition arcin is when Figure drawn the 6a: under magnetic the two black field pairs line is refers of excited poles to by in the both the flux a air-gap, permanent density and under magnet theno load radial and flux armature condition density current; when on the arc is shown blue inline Figure refers 6a: to the the black flux density line refers under toload the flux condition density when under the permanent no-load condition magnet part when is replaced the magnetic field by is excited air and by the the magnetic permanent field magnet; is exited the only red by line an armature refers to current; the fluxthe density pink under line refers loadto condition the difference between the black line and the red line, and it is almost coincident with the blue line. This when the magnetic field is excited by both a permanent magnet and armature current; the blue line verifies that the total magnetic field under load condition is comprised of the permanent magnet field refers to the flux density under load condition when the permanent magnet part is replaced by air and and the armature current field. the magnetic The harmonic field is exited analysis only is by done an to armature calculate current; the amplitude the pink of line each refers component to the by difference Fast Fourier between the black Transform line and (FFT), the and red line, the results and itof is harmonic almost coincident analysis regarding with the blue the current line. This modulated verifiesfield that the are total magnetic shown field in Figure under 6b: load the amplitude conditionof isfundamental comprised harmonic of the permanent is 0.197 T, magnet and the constant field and component the armature current is 0.346 field. T. Figure 6. The radial flux density of air gap: waveform; and harmonic components. Figure 6. The radial flux density of air-gap: waveform; and harmonic components. 4.2. Permanent Magnet Flux Linkage The permanent magnet flux linkage waveform in armature winding is shown in Figure 7a, and the harmonic analysis result is shown in Figure 7b. It can be seen that the waveform of permanent magnet flux linkage is close to sinusoidal, the amplitude of PM flux linkage is 0.19 Wb, and the total harmonic distortion (THD) is 0.41%.

Appl. Sci. 2016, 6, 342 9 of 16 The harmonic analysis is done to calculate the amplitude of each component by Fast Fourier Transform (FFT), and the results of harmonic analysis regarding the current modulated field are shown in Figure 6b: Figure the amplitude 6. The radial offlux fundamental density of air gap: harmonic waveform; is 0.197 T, and and the harmonic constant components. is 0.346 T. 4.2. 4.2. Permanent Magnet Flux Linkage The The permanent magnet flux linkage waveform in armature winding is ishown in in Figure 7a, 7a, and and the the harmonic analysis result is is shown in Figure 7b. It can be seen that the thewaveform of of permanent magnet flux flux linkage is is close to sinusoidal, the amplitude of PM flux linkage is is 0.19 0.19 Wb, Wb, and and the the total total harmonic distortion (THD) is is 0.41%. Figure 7. The permanent magnet flux linkage of CS TFM: waveform; and Harmonic Figure 7. The permanent magnet flux linkage of CS-TFM: waveform; and Harmonic components. components. Appl. Sci. 2016, 6, 342 10 of 16 4.3. No-Load BMF 4.3. No Load BMF The The no load no-load BMF BMF waveform is is shown shown in in Figure 8a, 8a, and and the the harmonic harmonic analysis analysis result is is shown shown in in Figure 8b. The The amplitude amplitude of of no load no-load BMF under revolving revolving speed speed 100 100 r/min r/min is is50.80 50.80V, the the amplitude amplitude of of fundamental fundamental component component is is 56.55 56.55 V, V, and and the the largest largest components components are are the the 3rd 3rd and and 5th 5th harmonics. harmonics. The The THD THD is is 12.39%. 12.39%. Figure Figure 8. 8. The The no-load no load back back electromotive electromotive force of force CS-TFM: of CS TFM: waveform; waveform; and harmonic and components. harmonic components. 4.4. Cogging Torque 4.4. Cogging Torque The single-phase cogging torque and total cogging torque waveforms are shown in Figure 9a, and the harmonic The single phase analysis results cogging of torque them are and shown total cogging in Figure torque 9b. waveforms are shown in Figure 9a, and the harmonic analysis results of them are shown in Figure 9b. From the result, the amplitude of the single phase cogging torque and the total cogging torque are, respectively, 24.43 N m and 7.63 N m. The main components of single phase cogging torque are the 2nd harmonic, 4th harmonic and 6th harmonic, and the main component of the total cogging torque is the 6th harmonic, which is consistent with the forgoing analysis about them.

Figure 8. The no load back electromotive force of CS TFM: waveform; and harmonic components. 4.4. Cogging Torque Appl. Sci. 2016, 6, 342 10 of 16 The single phase cogging torque and total cogging torque waveforms are shown in Figure 9a, and the harmonic analysis results of them are shown in Figure 9b. From the result, the amplitude of of the the single-phase single phase cogging torque and and the the total total cogging cogging torque torque are, are, respectively, 24.43 24.43 N mn and m and 7.63 7.63 N m. N The m. The main main components of single-phase of single phase cogging cogging torque torque are are the the 2nd 2nd harmonic, harmonic, 4th harmonic 4th harmonic and 6th and harmonic, 6th harmonic, and the and main the component main component of the total of the cogging total torque cogging is torque the 6this harmonic, the 6th harmonic, which is consistent which consistent with the forgoing with the analysis forgoing about analysis them. about them. Figure Figure 9. 9. The The cogging cogging torque torque of of CS TFM: CS-TFM: waveform; waveform; and and harmonic harmonic components. components. 4.5. Torque 4.5. Torque The result of single phase torque is comprised of the cogging torque and electromagnetic torque The result of single-phase torque is comprised of the cogging torque and electromagnetic torque in the FEM analysis. The electromagnetic torque can be separated out by subtracting the cogging in the FEM analysis. The electromagnetic torque can be separated out by subtracting the cogging torque from the total single phase torque, as shown in Figure 10a. torque from the total single-phase torque, as shown in Figure 10a. The electromagnetic torque of single phase is nearly pulsating waveform as result of Appl. Sci. The 2016, electromagnetic 6, 342 torque of single-phase is a nearly pulsating waveform as a result 11 of of 16 Equation (16). The total torque waveform of three phase waveforms is shown in Figure 10b, the Equation (16). The total torque waveform of three-phase waveforms is shown in Figure 10b, the average average value isvalue 145.63 is 145.63 N.m, which N.m, which is approximately is approximately 1.5 times 1.5 times of of the the maximum value of single-phase single phase electromagnetic torque, and the torque ripple is 4.14%. Figure Figure 10. 10. The The torque torque of of CS TFM: CS-TFM: single phase single-phase torque; torque; and and total total torque. torque. 5. Influence of Structure Parameters on Torque Density 5. Influence of Structure Parameters on Torque Density As high torque density is the most attractive advantage of transverse flux motor, the torque As high torque density is the most attractive advantage of transverse flux motor, the torque density of CS TFM should be calculated, and the influence of structure parameters on torque density density of CS-TFM should be calculated, and the influence of structure parameters on torque density should be analyzed in order to find useful optimized method for future design process. should be analyzed in order to find a useful optimized method for future design process. The total volume of motor can be expressed as: 3π 2 V Sla Doutla 4. Then, the torque density of CS TFM can be deduced as: (22)

Appl. Sci. 2016, 6, 342 11 of 16 The total volume of motor can be expressed as: Then, the torque density of CS-TFM can be deduced as: V = S l a = 3π 4 D2 outl a. (22) ρ = T V = 4 2µ 0 pkd a I m l m NI πd 2 out l a (h m + δ). (23) The relationship between pole-pitch and air-gap diameter can be written as: Then, the torque density of CS-TFM can be expressed as: τ m = πd a 2p. (24) ρ = 2 2µ 0 kd 2 a I m l m NI D 2 out l aτ m (h m + δ). (25) From Equation (25), the main influencing factors of torque density are the pole-pitch τ m, the thickness of permanent magnet h m, the air-gap length δ and the field modulated factor k. When the out diameter D out, the air-gap diameter D a and the axial length of motor l a are kept as constant, the volume of motor V is a constant. Thus, the torque density corresponds with average torque, and the influence of structure parameters on average torque is analyzed by 3D FEM. 5.1. Pole-Pitch From Equation (25), if the pole-pitch is selected as the unique variable, the torque density of motor will be improved when the pole-pitch is decreased. However, the leakage flux between adjacent permanent magnets will also be increased with the decrease of pole-pitch, which brings a negative Appl. influence Sci. 2016, on6, the 342 torque density. Thus, there is a reasonable range of pole-pitch. 12 of 16 The pole-pitch τ m is analyzed as the unique variable by 3D FEM, and the results are shown in Figure The pole pitch 11. Fromτm Figure is analyzed 11: (1) as the the average unique torque variable is improved by 3D FEM, significantly and the results withare theshown decrease in Figure of pole-pitch 11. From when Figure pole-pitch 11: (1) the is larger average than torque 7.3 mm; is improved (2) the average significantly torque with is nearly the decrease kept constant of polepitch when when pole-pitch pole pitch is in is the larger range than of 5.8 7.3 mm; mm; (2) the (3) average the average torque torque is nearly is reduced kept constant with the when decrease polepitch of pole-pitch is in the range when of pole-pitch 5.8 7.3 mm; is smaller (3) the average than 5.8torque mm; and is reduced (4) the with torque the ripple decrease is reduced of pole pitch with when the decrease pole pitch of pole-pitch. is smaller than The 5.8 pole-pitch mm; and should (4) the betorque chosenripple in theis range reduced of 5.8 7.3 with the mm decrease from the of pole pitch. FEM results. The pole pitch should be chosen in the range of 5.8 7.3 mm from the FEM results. pole pitch τm Figure 11. The influence of pole-pitch τ m on on average torqueand torque ripple. 5.2. Thickness of Permanent Magnet From Equation (8), the maximum value of a modulated field excited by an armature current will be improved when the thickness of permanent magnet is decreased, which brings a positive influence on the torque density. From Equation (11), the amplitude of imaginary current of a permanent

Figure 11. The influence of pole pitch τm on average torque and torque ripple. 5.2. Thickness of Permanent Magnet From Equation (8), the maximum value of a modulated field excited by an armature current will be Appl. improved Sci. 2016, 6, when 342 the thickness of permanent magnet is decreased, which brings a positive influence 12 of 16 on the torque density. From Equation (11), the amplitude of imaginary current of a permanent magnet will be reduced when the thickness of the permanent magnet is decreased, which brings a 5.2. Thickness of Permanent Magnet negative influence on the torque density. When both positive and negative influences are considered, there From is a reasonable Equation (8), range theof maximum the thickness valueof of permanent a modulated magnet. field excited by an armature current will be improved The thickness when of thepermanent thickness of magnet permanent hm is magnet analyzed is decreased, the unique which variable bringsby a 3D positive FEM, influence and the results on the torque are shown density. in Figure From Equation 12. From (11), Figure the12: amplitude (1) the average of imaginary torque current reaches ofthe a permanent maximum magnet value when will bethe reduced thickness whenis the 1.5 thickness mm; and of(2) the the permanent torque ripple magnet reaches is decreased, the minimum which brings value awhen negative the thickness influence is on1.25 the mm. torque density. When both positive and negative influences are considered, there is a reasonable In addition, rangethe of the overload thickness capability of permanent of the motor magnet. is influenced by the thickness. If the permanent magnet Theis thickness thin, the ofcore permanent will become magnetmore h m is saturated analyzed as when the unique the motor variable works by 3D under FEM, overload and the conditions, results are shown as the equivalent in Figure 12. air gap Fromlength Figureis 12: small. (1) the Moreover, averagethe torque permanent reachesmagnet the maximum is more liable value to when be irreversibly the thickness demagnetized, is 1.5 mm; and which (2) theis torque dangerous ripplefor reaches the motor. the minimum Thus, a value larger when thickness the thickness should be is 1.25 chosen mm. when the overload capability is considered. Figure 12. The influence of permanent magnet thickness hm on average torque and torque ripple. Figure 12. The influence of permanent magnet thickness h m on average torque and torque ripple. In addition, the overload capability of the motor is influenced by the thickness. If the permanent magnet is thin, the core will become more saturated when the motor works under overload conditions, as the equivalent air-gap length is small. Moreover, the permanent magnet is more liable to be irreversibly demagnetized, which is dangerous for the motor. Thus, a larger thickness should be chosen when the overload capability is considered. 5.3. Air-Gap Length From Equation (25), the torque density will be improved when the air-gap length is decreased. The air-gap length is analyzed as the unique variable by 3D FEM, and the results are shown in Figure 13. From Figure 13, when the air-gap length is decreased from 1.4 mm to 0.4 mm, the average torque is improved significantly. However, the torque ripple is increased at the same time. The average torque under 0.4 mm gap is approximately 1.56 times the one under 1 mm. In addition, the air-gap length is always limited to the mechanical structure and manufacturing technique, and it should be chosen reasonably under the overall considerations of both working characteristics and machining technique.

The air gap length is analyzed as the unique variable by 3D FEM, and the results are shown in Figure 13. From Figure 13, when the air gap length is decreased from 1.4 mm to 0.4 mm, the average torque 13. From Figure 13, when the air gap length is decreased from 1.4 mm to 0.4 mm, the average torque is improved significantly. However, the torque ripple is increased at the same time. The average is improved significantly. However, the torque ripple is increased at the same time. The average torque under 0.4 mm gap is approximately 1.56 times the one under mm. torque under 0.4 mm gap is approximately 1.56 times the one under 1 mm. In addition, the air gap length is always limited to the mechanical structure and manufacturing In addition, the air gap length is always limited to the mechanical structure and manufacturing technique, and it should be chosen reasonably under the overall considerations of both working technique, and it should be chosen reasonably under the overall considerations of both working characteristics and machining technique. characteristics and machining technique. Appl. Sci. 2016, 6, 342 13 of 16 13. The of on Figure 13. 13. The Theinfluence of ofair gap air-gaplength δ on onaverage torque and torque ripple. 5.4. Rotor 5.4. Circumferential Rotor Teeth Length Another influencing factor of the torque density is the rotor teeth length, which Another influencing factor of the torque density is the circumferential rotor teeth length, which influences the modulated field of the field. In order to analyze the influences the modulated field distribution of the armature current field. In order to analyze the rotor rotor teeth ratio is introduced here: circumferential rotor teeth length more conveniently, a rotor teeth ratio is is introduced here: rt k (26) rt = l rt krt. (26) τ (26) m. krt is as the by 3D and the are The rotor teeth ratio krt k rt is isanalyzed as asthe unique variable by 3D FEM, and the results are shown in torque is is when when the the rotor rotor teeth teeth ratio ratio is is in Figure 14. From Figure 14, the maximum average torque is generated when the rotor teeth ratio in is in the the range range of of 0.6 0.7, 0.6 0.7, and and the the minimum minimum torque torque ripple ripple is 0.9% is 0.9% when when the the ratio ratio is 0.6. is 0.6. in the range of 0.6 0.7, and the minimum torque ripple is 0.9% when the ratio is 0.6. In the of the is is by the In addition, the overload capability of the motor is influenced by the circumferential rotor teeth If rotor teeth teeth length is is small, small, the the core core will will become become more more saturated saturated when when length. If the circumferential rotor teeth length is small, the core will become more saturated when the the motor motor works works under under overload overload conditions. conditions. Thus, Thus, a larger larger rotor rotor teeth teeth ratio ratio should should be chosen be chosen when when the motor works under overload conditions. Thus, a larger rotor teeth ratio should be chosen when the the overload overload capability capability is considered. is considered. the overload capability is considered. Figure 14. The influence of rotor teeth ratio k rt on average torque and torque ripple. 6. Discussion Based on the analysis results in Section 5, an optimized CS-TFM is designed and analyzed by 3D FEM, and the comparison between initial model and optimized model is listed in Table 2. It should be mentioned that the parameters of the optimized model in this section are preliminary optimization results based on the forgoing 3D FEM analysis. A more accurate optimization result can be obtained by

Appl. Sci. 2016, 6, 342 14 of 16 using some optimization methods in the motor design process for example, numerical optimization algorithms or approximate models [22,23]. According to the 3D FEM data, when the volume and ampere-turn are kept the same as that of the initial model, the electromagnetic performance of optimized CS-TFM is improved: the amplitude of no-load BMF is increased by 32.84%, the THD of no-load BMF is decreased by 38.09%, the cogging torque is decreased by 56.49%, and the average torque is increased by 29.48%. Meanwhile, the torque ripple is increased from 4.14% to 4.84%. Table 2. Initial and optimized parameters of the CS-TFM. Parameter Initial Optimized Rotor out Diameter D out 248 mm 248 mm Air-gap Diameter D a 226 mm 226 mm Stator inner Diameter D in 140 mm 140 mm Height of Axial bridge h b 10 mm 10 mm Axial length of single-phase l a 45 mm 45 mm Air-gap length δ 1 mm 1 mm rotor teeth ratio k rt 1 0.7 PM thickness h m 2 mm 2 mm Axial length of PM l m 11 mm 11 mm Pole-pitch τ m 11.83 mm 7.07 mm Pole pair number p 30 50 Armature winding turns N 150 90 Rated current I 12.73 A 21.22 A Rated current density J 4.5 A/mm 2 4.5 A/mm 2 Rated speed n 100 r/min 100 r/min Amplitude of fundamental no-load BMF 56.55 V 75.12 V THD of no-load BMF 12.39% 7.67% Amplitude of cogging torque 7.63 N.m 3.32 N.m Average torque 145.63 N.m 188.56 N.m Torque ripple 4.14% 4.84% The torque densities are calculated and compared among various types of direct-drive motors, as shown in Table 3. The torque density per volume of proposed CS-TFM is higher than BLDC in [2], TFRM in [13], and lower than ISDW-PMV in [5] and TFPM in [16]. The torque density per permanent magnet volume of CS-TFM is the largest among those motors. What should be noticed is that the results of torque density are not calculated under similar conditions (air-gap length, rated speed and current density are different from each other). Thus, it is difficult to evaluate the proposed motor simply. Table 3. Comparison of torque density. Parameter CS-TFM BLDC [2] ISDW-PMV [5] TFRM [13] TFPM [16] Air-gap length (mm) 1 1 0.5 0.25 1 Volume of motor (mm 3 ) 6.5 10 6 4.3 10 5 9.2 10 5 3.3 10 6 8.8 10 6 Volume of PM (mm 3 ) 9.4 10 4-8.0 10 4-7.7 10 5 Rated speed n (r/min) 100 250 600-66 Current density J (A/mm 2 ) 4.5 5.8 6.6 5.6 9.96 Average torque (N m) 188.6 10.1 61.7 30.0 360.0 Torque density per volume (kn m/m 3 ) 28.9 23.5 67.1 9.2 40.8 Torque density per PM volume (kn m/m 3 ) 2006.4-771.3-467.5

Appl. Sci. 2016, 6, 342 15 of 16 7. Conclusions An external rotor transverse flux motor is proposed for direct-drive application in this paper. The combined stator core structure makes it possible to use silicon steel sheets in this transverse flux technology, and it improves the mechanical strength and simplifies the manufacturing process of the proposed motor. Both permanent magnet and armature winding of the proposed CS-TFM are fixed on the stator side, and the rotor is only comprised of a core and sleeve. This structure feature improves the reliability of the motor. The theoretical expression of electromagnetic torque is deduced by a field modulated method. Then, the electromagnetic performance of CS-TFM is investigated by 3D FEM, and the results verify the correctness of theoretical analysis. The influences of pole-pitch, PM thickness, air-gap length and rotor teeth length on torque density are analyzed, and the results show that: the pole-pitch, PM thickness and rotor teeth ratio of CS-TFM can be chosen around an optical range of 5.8 7.3 mm, 1.5 2 mm, 0.6 0.7, respectively. The torque density can be improved significantly by decreasing the air-gap length. The performance of a preliminarily optimized CS-TFM is analyzed and compared with the initial one, and the no-load BMF and average torque are increased by 32.84% and 29.48%, respectively. At last, the torque density per volume and per PM volume are calculated, and the results show that the proposed CS-TFM can provide considerable torque density by using few PMs. Acknowledgments: This work was supported by The National Natural Science Foundation of China (51177023) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20132302110009). Author Contributions: The work was carried out with collaboration between all authors. Xiaobao Yang analyzed and wrote the paper. Baoquan Kou supervised the whole work. Jun Luo, Yiheng Zhou and Feng Xing offered useful suggestions for the preparation and writing of the manuscript. Conflicts of Interest: The authors declare no conflict of interest. References 1. Chung, S.U.; Kim, J.M.; Koo, D.H.; Woo, B.C.; Hong, D.K.; Lee, J.Y. Fractional slot concentrated winding permanent magnet synchronous machine with consequent pole rotor for low speed direct drive. IEEE Trans. Magn. 2012, 48, 2965 2968. [CrossRef] 2. Wrobel, R.; Mellor, P.H. Design considerations of a direct drive brushless machine with concentrated windings. IEEE Trans. Energy Convers. 2008, 23, 1 8. [CrossRef] 3. Kim, B.; Lipo, T.A. Operation and design principles of a PM vernier motor. IEEE Trans. Ind. Appl. 2014, 50, 3656 3663. [CrossRef] 4. Takano, M.; Shimomura, S. Study of variable reluctance vernier motor for hybrid electric vehicle. In Proceedings of the ECCE ECCE Asia Downunder (ECCE Asia), Melbourne, Australia, 3 6 June 2013. 5. Xu, L.; Liu, G.; Zhao, W.; Ji, J.; Zhou, H.; Zhao, W.; Jiang, T. Quantitative comparison of integral and fractional slot permanent magnet vernier motors. IEEE Trans. Energy Convers. 2015, 30, 1483 1495. [CrossRef] 6. Weh, H.; Hoffmann, H.; Landrath, J. New permanent magnet excited synchronous machine with high efficiency at low speeds. Proc. Int. Conf. Electr. Mach. 1988, 3, 35 40. 7. Zou, J.; Wang, Q.; Xu, Y. Influence of the permanent magnet magnetization length on the performance of a tubular transverse flux permanent magnet linear machine used for electromagnetic launch. IEEE Trans. Plasm. Sci. 2011, 39, 241 246. [CrossRef] 8. Polinder, H.; Mecrow, B.C.; Jack, A.G.; Dickinson, P.G.; Mueller, M.A. Conventional and TFPM linear generators for direct-drive wave energy conversion. IEEE Trans. Energy Convers. 2005, 20, 260 267. [CrossRef] 9. Hsu, Y.S.; Tsai, M.C. Development of a novel transverse flux wheel motor. IEEE Trans. Magn. 2011, 47, 3677 3680. [CrossRef] 10. Guo, Y.; Zhu, J.G.; Watterson, P.A.; Wu, W. Development of a PM transverse flux motor with soft magnetic composite core. IEEE Trans. Energy Convers. 2006, 21, 426 434. [CrossRef] 11. Oh, J.H.; Lee, J.H.; Kang, S.I.; Shin, K.S.; Kwon, B.I. Analysis of a novel transverse flux type permanent magnet reluctance generator. IEEE Trans. Magn. 2014, 50, 809 812. [CrossRef]

Appl. Sci. 2016, 6, 342 16 of 16 12. Baserrah, S.; Orlik, B. Comparison study of permanent magnet transverse flux motors (PMTFMs) for in-wheel applications. In Proceedings of the 2009 International Conference on Power Electronics and Drive Systems (PEDS), Taipei, Taiwan, 2 5 November 2009. 13. Amreiz, H.M. A comparison between transverse flux and conventional switched reluctance machines. In Proceedings of the 2010 XIX International Conference on Electrical Machines (ICEM), Rome, Italy, 6 8 September 2010. 14. Kruse, R.; Pfaff, G.; Pfeiffer, C. Transverse flux reluctance motor for direct servodrive applications. In Proceedings of the 1998 IEEE Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting, St. Louis, MI, USA, 12 15 October 1998. 15. Yang, G.; Cheng, D.; Zhang, H.; Kou, B. Bidirectional cross-linking transverse flux permanent magnet synchronous motor. IEEE Trans. Magn. 2013, 49, 1242 1248. [CrossRef] 16. Seibold, P.; Schuller, F.; Beez, M.; Parspour, N. Design and measurement of a laminated permanent magnet excited transverse flux machine for electrical vehicles. In Proceedings of the 2014 4th International Electric Drives Production Conference (EDPC), Nuremberg, Germany, 30 September 1 October 2014. 17. Zou, J.; Zhao, M.; Wang, Q.; Zou, J.; Wu, G. Development and analysis of tubular transverse flux machine with permanent-magnet excitation. IEEE Trans. Ind. Electron. 2012, 59, 2198 2207. [CrossRef] 18. Doering, J.; Steinborn, G.; Hofmann, W. Torque, Power, Losses, and Heat Calculation of a Transverse Flux Reluctance Machine with Soft Magnetic Composite Materials and Disk-Shaped Rotor. IEEE Trans. Ind. Appl. 2014, 51, 1494 1504. [CrossRef] 19. Kim, B.; Lipo, T.A. Analysis of a PM vernier motor with spoke structure. IEEE Trans. Ind. Appl. 2016, 52, 217 225. [CrossRef] 20. Matsui, N.; Nakamura, M.; Kosaka, T. Instantaneous torque analysis of hybrid stepping motor. IEEE Trans. Ind. Appl. 1996, 32, 1176 1182. [CrossRef] 21. Iwabuchi, N.; Kawahara, A.; Kume, T.; Kabashima, T.; Nagasaka, N. A novel high-torque reluctance motor with rare-earth magnet. IEEE Trans. Ind. Appl. 1994, 30, 609 614. [CrossRef] 22. Lei, G.; Wang, T.; Guo, Y.; Zhu, J.; Wang, S. System-level design optimization methods for electrical drive systems: Deterministic approach. IEEE Trans. Ind. Electron. 2014, 61, 6591 6602. [CrossRef] 23. Lei, G.; Wang, T.; Zhu, J.; Guo, Y.; Wang, S. System-Level Design Optimization Method for Electrical Drive Systems Robust Approach. IEEE Trans. Ind. Electron. 2015, 62, 4702 4713. [CrossRef] 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).