Three-Dimensional Temperature Field Calculation and ... - MDPI

energies Article

Three-Dimensional Temperature Field Calculation and Analysis of an Axial-Radial Flux-Type Permanent Magnet Synchronous Motor Dong Li 1,2, * 1 2 3

*

ID

, Yinghong Wen 1 , Weili Li 2 , Bo Feng 3 and Junci Cao 2

ID

School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China; [email protected] School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China; [email protected] (W.L.); [email protected] (J.C.) Harbin Power System Engineering & Research Institute Co. Ltd., Harbin 150046, China; [email protected] Correspondence: [email protected]; Tel.: +86-10-5168-5723

Received: 13 April 2018; Accepted: 7 May 2018; Published: 9 May 2018







Abstract: This article concentrates on the steady-state thermal characteristics of the Axial-Radial Flux-Type Permanent Magnet Synchronous Motor (ARFTPMSM). Firstly, the three-dimensional mathematical models for electromagnetic calculation and analyses are established, and the machine loss, including the stator loss, armature winding loss, rotor loss, and axial structure loss is calculated by using time-step Finite Element Method (FEM). Then, the loss distribution is assigned as the heat source for the thermal calculation. Secondly, the mathematical model for thermal calculation is also established. The assumptions and the boundary conditions are proposed to simplify the calculation and to improve convergence. Thirdly, the three-dimensional electromagnetic and thermal calculations of the machine, of which the armature winding and axial field winding are developed by using copper wires, are solved, from which the temperature distributions of the machine components are obtained. The experiments are carried out on the prototype with copper wires to validate the accuracy of the established models. Then, the temperature distributions of machine components under different Axial Magnetic Motive Force (AMMF) are investigated. Since the machine is finally developing by using HTS wires, the temperature distributions of machine developed by utilizing High Temperature Superconducting (HTS) wires, are also studied. The temperature distribution differences of the machine developed by using copper wires and HTS wires are drawn. All of these above will provide a helpful reference for the thermal calculation of the ARFTPMSM, as well as the design of the HTS coils and the cryogenic cooling system. Keywords: axial-radial flux-type permanent magnet synchronous motor; steady-state temperature field; axial magnetic motive force; time-step Finite Element Method

1. Introduction The High Temperature Superconducting (HTS) electric machines, of which the field windings or the armature windings are developed by utilizing the HTS wires, has advantages, such as higher power density, smaller volume, and less weight, etc. [1,2]. Therefore, it has been attracting worldwide attentions of the researchers. With the increase of the current-carrying capability and the critical properties, and the decrease of the construction cost, HTS wires or magnets are suitable to develop the high efficiency electric machines. Up to now, almost all types of HTS electric machines have been developed corresponding to the conventional machines [3–10]. However, we found that the researches on the HTS electric machines mainly focus on the electromagnetic calculations and the performance

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investigations [11–13]. With the rapid development of the HTS electric machines, operation safety and stability become more and more important. The critical current of HTS windings is significantly influenced by the surrounding magnetic flux density and ambient temperature. If the HTS windings are used as the armature or field windings for electrical machines, the ac loss will generate within the HTS windings due to the ac current transportation. If the ac loss could not transfer to the ambient in time, the temperature of HTS windings will arise, and then the resistance of the HTS windings will increase due to the temperature rise. If this situation continues, the HTS windings may overheat or even quench [14,15]. Thus, it is vital to study the temperature distributions of the HTS electric machines. Most of the literatures about the conventional electric machines are concentrated on the electromagnetic and thermal analyses [16–19], while for HTS electric machines, the literatures are mainly on the electromagnetic analysis or performance investigation [1,2,11,12], very few on thermal analysis. K. Sato et al. presented a nonlinear heat analysis technique, and by using the technique, he studied the temperature field of the 1000 MVA inner rotor superconducting generators [14]. P. J. Masson et al., utilize the thermal circuit method to establish the electro-thermal analysis model [7]. With the development of the computing technique, the Finite Element Method (FEM) could obtain more accurate results than the thermal circuit method [11]. Therefore, the FEM has been widely subjected to study the thermal field of the electric machines [11,12,17]. In the article, a new axial-radial flux-type permanent magnet synchronous motor is presented. Different from the conventional electric machines, the performance of Axial-Radial Flux-Type Permanent Magnet Synchronous Motor (ARFTPMSM) can be adjusted by changing Axial Magnetic Motive Force (AMMF). The three-dimensional steady-state temperature field distributions of ARFTPMSM under different AMMF are investigated by using time-stepping FEM. The comparisons of the temperature distributions between ARFTPMSM with copper wires and ARFTPMSM with HTS wires are conducted. Although the ARFTPMSM is developed with copper windings, the structure is actually designed for ARFTPMSM with HTS windings. When compared with the conventional HTS electric machines, the ARFTPMSM with HTS windings has the following characteristics: firstly, the axial field windings and the radial field windings are both fixed on the stator. During operation, they do not rotate, thereby, the cryogenic cooling system would be simpler and more reliable. Secondly, the radial air-gap magnetic flux density could adjust by changing AMMF, thus, we can change the performance of ARFTPMSM by adjusting the AMMF, which differs from the conventional electric machines. Thirdly, the rated frequency of the machine is only 20.83 Hz, thus the ac loss of the HTS windings is very small and can even be ignored, so it can reduce the power of the cryogenic cooling system [20,21]. The total loss of the machine would be less than the machines that were developed by using the copper wires. Lastly, the rotor core is developed by using solid iron; thereby, the motor could be started up by itself [22,23]. The solid rotor core can increase the rotor loss and decrease the efficiency of the machine, but it has more merits than the lamination rotor core: (1) the machine with the solid rotor core can start up by itself, thus the converter can be saved. Therefore, the entire system of machine with solid rotor core is simpler, more reliable, and has higher efficiency; (2) Since the converter is saved, the machine can feed on ac source directly; the machine can operate with a good performance because of less current harmonics; (3) Each pole is composed of two radial magnets and two circumferential magnets, thus most parts of the rotor core are cut down for putting the magnets, so the solid rotor core has a higher strength than the lamination rotor core. Based on the analysis, the solid rotor core is used for the development of the prototype. In order to investigate the influence of AMMF on the temperature distributions of the machine components, firstly the three-dimensional mathematical models for the electromagnetic field and temperature field calculations are established. When combined with the given boundary conditions, the electromagnetic model is solved by using the time-step FEM. The loss extracted from the electromagnetic calculations is then assigned as the heat sources for the thermal calculations. The three-dimensional steady-state temperature field calculation model is also established according

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the physical structure and the dimensions of the prototype, and then the temperature distributions of the machine components are studied separately. Then, the temperature field of ARFTPMSM to the physical structure and the dimensions of the prototype, and then the temperature distributions under rated load are calculated, the results are compared with the experimental data to validate the of the machine components are studied separately. Then, the temperature field of ARFTPMSM accuracy of the established models. Then, the temperature field of ARFTPMSM under different under rated load are calculated, the results are compared with the experimental data to validate AMMF are comparatively analyzed. Since the final goal is to develop ARFTPMSM with HTS wires, the accuracy of the established models. Then, the temperature field of ARFTPMSM under different the temperature distributions of ARFTPMSM with HTS wires are also analyzed. The comparisons of AMMF are comparatively analyzed. Since the final goal is to develop ARFTPMSM with HTS wires, the temperature distributions between the ARFTPMSM with copper wire and the ARFTPMSM with the temperature distributions of ARFTPMSM with HTS wires are also analyzed. The comparisons of HTS wires are conducted. The contents in the paper can provide helpful guidelines for thermal the temperature distributions between the ARFTPMSM with copper wire and the ARFTPMSM with design and temperature analyses of the axial-radial flux-type permanent magnet synchronous HTS wires are conducted. The contents in the paper can provide helpful guidelines for thermal design motor. and temperature analyses of the axial-radial flux-type permanent magnet synchronous motor. 2. Heat Determination for for Thermal Thermal Analysis Analysis 2. Heat Source Source Determination 2.1. Physical Structure of ARFTPMSM showsthethe basic physical structure of ARFTPMSM. Themagnetic radial magnetic flux is Figure 11shows basic physical structure of ARFTPMSM. The radial flux is provided provided by permanent magnets, the axial magnetic flux is by field the axial field windings. by permanent magnets, while the while axial magnetic flux is excited byexcited the axial windings. Both the Both the armature axial field windings are developed by utilizing the copper armature windingswindings and the and axialthe field windings are developed by utilizing the copper wires. wires. The machine is designed with 10 poles and 12 slots, thus, the armature windings can use the The machine is designed with 10 poles and 12 slots, thus, the armature windings can use the concentrate concentrate So,toit develop is suitable to develop machine with HTS windings. In order provide windings. So,windings. it is suitable machine with HTS windings. In order to provide more to radial flux, morerotor radial flux, each rotor poleradial is composed of two magnets magnets. and twoThus, circumferential each pole is composed of two magnets and two radial circumferential most parts magnets. Thus, parts core are cut out to put To strength, strengthen mechanical of the rotor coremost are cut outof tothe putrotor magnets. To strengthen themagnets. mechanical thethe rotor core are strength, the rotor iron, core while are fabricated solid iron, whileby thesilicon statorlamination core is constructed by silicon fabricated by solid the statorby core is constructed sheets to reduce the lamination core loss. sheets to reduce the core loss. 1 5

2 3

6 4

7 9

10

8

Figure 1. Physical structure of Axial-Radial Flux-Type Permanent Magnet Synchronous Motor Figure 1. Physical structure of Axial-Radial Flux-Type Permanent Magnet Synchronous Motor (ARFTPMSM). 1-Enclosure, 1-Enclosure, 2-Stator 2-Stator Core, Core, 3-Armature 3-Armature Windings, Windings, 4-Rotor 4-Rotor Core, Core, 5-Permanent 5-Permanent (ARFTPMSM). Magnets, 6-Outer Ferromagnetic Ring, 7-Inner Ferromagnetic Ring, 8-Axial Field Windings, Magnets, 6-Outer Ferromagnetic Ring, 7-Inner Ferromagnetic Ring, 8-Axial Field Windings, 9-Shaft, 9-Shaft, 10-End Cover. 10-End Cover.

To save construction cost and to investigate the operating principles and performances of To save construction cost and to investigate the operating principles and performances of ARFTPMSM, a prototype, of which the armature windings and axial field windings are developed ARFTPMSM, a prototype, of which the armature windings and axial field windings are developed by utilizing copper wires, has been developed. The basic structure of the prototype is as shown in by utilizing copper wires, has been developed. The basic structure of the prototype is as shown in Figure 2 and the design parameters are listed in Table 1. Figure 2 and the design parameters are listed in Table 1.

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Figure 2. 2. Basic Basic structure structure of of the the prototype. prototype. 1-Enclosure, 1-Enclosure, 2-Stator 2-Stator Core, Core, 3-Armature 3-Armature Windings, Windings, 4-Outer 4-Outer Figure FerromagneticRing, Ring,5-Inner 5-InnerFerromagnetic FerromagneticRing, Ring,6-Rotor 6-RotorCore, Core,7-Shaft. 7-Shaft. Ferromagnetic Table1.1. Design Design parameters parametersof ofthe theprototype. prototype. Table

Items Items Rated power/kW Rated power/kW Frequency/Hz Frequency/Hz Synchronous speed/(r/min) Synchronous speed/(r/min) Core length/mm Core length/mm Stator outer outer diameter/mm Stator diameter/mm Stator inner inner diameter/mm Stator diameter/mm Slots Slots Poles Polestype Cooling Cooling type

Value 3.5 3.5 20.83 20.83 250 250 50 50 230 230 140 140 12 12 10 10 Self-cooling Self-cooling Value

2.2. Mathematical Model for Electromagnetic Calculations 2.2. Mathematical Model for Electromagnetic Calculations Due to the special structure of ARFTPMSM, the axial magnetic circuit is coupled with the Due to the special structure of ARFTPMSM, the axial magnetic circuit is coupled with the radial magnetic circuit, and AMMF can change the radial flux density distributions of ARFTPMSM, radial magnetic circuit, and AMMF can change the radial flux density distributions of ARFTPMSM, thus, the loss calculations of ARFTPMSM is more complicated than the conventional machines. The loss thus, the loss calculations of ARFTPMSM is more complicated than the conventional machines. The of ARFTPMSM is composed of the armature winding loss, stator core loss, axial field windings loss, loss of ARFTPMSM is composed of the armature winding loss, stator core loss, axial field windings rotor core loss, and eddy current loss of permanent magnets and axial ferromagnetic rings. Because the loss, rotor core loss, and eddy current loss of permanent magnets and axial ferromagnetic rings. stator core loss, the rotor core loss and eddy current loss of permanent magnets are hard to determine Because the stator core loss, the rotor core loss and eddy current loss of permanent magnets are by using analytical method, thus, in the paper, we use the time-stepping FEM to calculate the loss of hard to determine by using analytical method, thus, in the paper, we use the time-stepping FEM to the machine. Due to the coupled magnetic circuits, 2d electromagnetic model could not satisfy the calculate the loss of the machine. Due to the coupled magnetic circuits, 2d electromagnetic model requirements for the loss calculation, therefore three-dimensional (3d) transient electromagnetic field could not satisfy the requirements for the loss calculation, therefore three-dimensional (3d) transient model is established to consider the influence of AMMF. To simplify the electromagnetic calculation electromagnetic field model is established to consider the influence of AMMF. To simplify the model and to save the calculation amount and time, the following assumptions are proposed [19,24]: electromagnetic calculation model and to save the calculation amount and time, the following assumptions are harmonics proposed [19,24]: 1. The current produced by the controller are ignored, so the machine is fed on ac source. 2. Because of the low frequency and the the displacement current 1. The current harmonics produced by multi-strand the controllerwindings, are ignored, so the machine is fedwithin on ac the armature windings is regardless. source. 3. According temperature the temperature the machinecurrent is very within small, 2. Because of to thethe low frequency measurements, and the multi-strand windings, rise the of displacement thus, the influences of the temperature on material conductivity and permeability are ignored. the armature windings is regardless. 4. Since the end cover and the measurements, enclosure are developed by using 3. According to the temperature the temperature rise high of themagnetic machine permeability is very small, materials, thus, the flux that is leaked into the air can be ignored. thus, the influences of the temperature on material conductivity and permeability are ignored.

4.

Since the end cover and the enclosure are developed by using high magnetic permeability materials, thus, the flux that is leaked into the air can be ignored.

The mathematical model described by using the magnetic vector potential A is established, as given in (1) [25].

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  ∂  1  ∂Ay ∂A   ∂  1  ∂A ∂A   5 of 21 dA     − x  −   x − z  = J x − σ dt ∂y   ∂z  μ  ∂z ∂x     ∂y  μ  ∂x   The mathematical model potential Ay using  1  ∂Az ∂by  1 magnetic ∂Ay ∂Axvector   ∂ the  dA A is established, as  ∂ described − − Ω :     −    = J y − σ given in (1) [25]. dt ∂z   ∂x  μ  ∂x ∂y   (1)   ∂z  μ  ∂y   h  i h i   A ∂A ∂A   ∂∂  11  ∂∂A dAdA  ∂ ∂ 1 1 ∂A ∂A  ∂yAx− ∂A y     J z J−xσ− σ dt − ∂yxz   − − ∂z  µ  ∂zzx −− ∂xz  = = µ  ∂y ∂x       h i h i    μ μ dt x z x y y z ∂ ∂ ∂ ∂ ∂ ∂   z ∂Ay    Ω : ∂ 1 ∂A ∂A x  ∂  1  ∂Ay − − − = J − σ dA y µ µ ∂z ∂y ∂z ∂x ∂x ∂y dt  (1)   h i h i S:A=0  ∂Ay   ∂A ∂A ∂A ∂ 1 ∂ 1 dA x z z   − − − = J − σ  z ∂x µ ∂z ∂x ∂y µ ∂y ∂z dt    where, A = [ Ax AyS A: zA]T=is0 the magnetic vector potential, Ω is the solution domain,

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T

J = [ J J J ] is the current density of the exciting source, the armature winding current and the where,x A y= [zA x Ay Az ] T is the magnetic vector potential, Ω is the solution domain, J = [ Jx Jy Jz ] T is S is the boundary of the solution domain, in and this the paper it isfield assigned to axial field current the current densityincluded, of the exciting source, the armature winding current axial current μ is the permeability, σ itisisthe the enclosure andboundary the end cover, electrical conductivity. included, S is the of the solution domain, in thisand paper assigned to the enclosure and the end cover, µtoisthe thevariation permeability, and σthe is the electrical conductivity. According principle, variation equation that is derived from (1) is given in (2). According to the variation principle, the variation equation that is derived from (1) is given in (2).



1

1

2

( f ( A) = t Ω rotA2 dv −t Ω J ⋅ Adv  f ( A) = 122 Ω µ1μ|rotA| dv − Ω J · Adv nn ×  × AA|ss==0 0

(2) (2)

Equation (2) (2) is is discretized discretized and and solved solved by by using using Galerkin Galerkin FEM. To To fit fit the the complicated complicated physical physical Equation structure of the machine, the tetrahedral elements are employed to mesh the solution domain. While structure of the machine, the tetrahedral elements are employed to mesh the solution domain. While the the mesh process finalized, are 142,204 tetrahedral elements the solution domain. To mesh process finalized, therethere are 142,204 tetrahedral elements withinwithin the solution domain. To obtain obtain the electromagnetic field distribution, should solve 217,669 The finalized mesh the electromagnetic field distribution, we shouldwe solve 217,669 matrix. Thematrix. finalized mesh elements of elements of partial machine are as shown in Figure 3. partial machine are as shown in Figure 3.

Figure Figure 3. 3. Partial Partial mesh mesh elements elements for for the the electromagnetic electromagnetic calculation. calculation.

calculations, the the material materialproperties propertiesofofthe thecomponents componentsare areset, set,asasshown shown Table During FEM calculations, inin Table 2. ◦ ◦ 2. The remanence of permanent magnets is about 1.21 T at 20 °C, temperature coefficient is The remanence of permanent magnets is about 1.21 T at 20 C, temperature coefficient is −0.095%/ C. −0.095%/°C. For soft magnetic materials, the core loss can be calculated by (3) [26,27]. For soft magnetic materials, the core loss can be calculated by (3) [26,27]. PFe = ph (t) + pc (t) + pe (t) (3) 2 1.5 2 PFe = = pk hh B( t )f ++pkcc((tB)f+) p+e (kte)( B f ) (3) 1.5 where: ph (t) is the static hysteresis loss, = kphcB(t)2 fis+the kc (classical Bf )2 + keddy e ( Bf )current loss, pe (t) is the additional loss. kh , kc , ke are the coefficients of the loss, respectively; B is the flux density, and f is the frequency. h(t) is the static hysteresis loss, pc(t) isthe thecore classical eddy at current loss, pe(t) is the where: The losspcoefficients can be calculated by using loss curves different frequency. Inadditional the paper, h,e kare c, keset areas the coefficients the loss, respectively; B W/kg, is the flux density, and f is the frequency. kloss. 0.0234 W/kg,of 4.9068 W/kg, and 3.4328 respectively. During calculations, h , kc ,kk Thestack loss factor coefficients can beaccording calculatedthe byreal using the core loss curves at different frequency. In the the is set to 0.94 prototype.

paper, kh, kc, ke are set as 0.0234 W/kg, 4.9068 W/kg, and 3.4328 W/kg, respectively. During calculations, the stack factor is set to 0.94 according the real prototype. Energies 2018, 11, 1208

Table 2. Material properties for electromagnetic field analysis.

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Items Material Relative Permeability Bulk Conductivity Stator core DW310-35 Refer to Figure 4 0 Table 2. Material properties for electromagnetic field analysis. Armature windings Copper wire 1 5.91 × 107 S/m Rotor core DT-4 Refer toPermeability Figure 4 1.03Conductivity × 107 S/m Items Material Relative Bulk Permanent Magnets N35EH 1.05 6.85 × 105 S/m Stator core DW310-35 Refer to Figure 4 0 7 Outer Ferromagnetic DT-4 wire Refer to Figure 4 1.03 Armature windingsRing Copper 1 5.91 × × 10 107 S/m S/m Inner Ferromagnetic Ring DT-4 Refer 1.03 Rotor core DT-4 RefertotoFigure Figure 44 1.03 × × 10 1077 S/m S/m Permanent Magnets N35EH 1.05 6.85 × × 10 1075 S/m S/m Axial Field Windings Copper bar 1 5.91 7 S/m Outer Ferromagnetic Ring DT-4 Refer to Figure 4 1.03 × 10 7 Shaft Steel 45 Refer to Figure 4 2.0 × 10 S/m Inner Ferromagnetic Ring DT-4 Refer to Figure 4 1.03 × 1077 S/m Enclosure Steel 45 Refer to Figure 4 2.0 × 10 S/m Axial Field Windings Copper bar 1 5.91 × 1077 S/m EndShaft Cover Steel Refer 2.0 Steel45 45 RefertotoFigure Figure 44 2.0 × × 10 107 S/m S/m Enclosure

Steel 45

Refer to Figure 4

2.0 × 107 S/m

The magnetizing characteristics ofSteel soft45 magnetic materials used4in the prototype End Cover Refer to Figure 2.0 × 107 are S/mas shown in Figure 4. From which, it can observe that the electrical iron DT-4 have the great magnetic permeability as DW310-35 silicon lamination sheets, while used the steel shows poor The magnetizing characteristics of soft magnetic materials in the45 prototype are asmagnetic shown in permeability by comparing it with DW310-35 and DT-4. However, it is used to fabricate the shaft, Figure 4. From which, it can observe that the electrical iron DT-4 have the great magnetic permeability end cover, and enclosure because of the low cost. All of the materials refers to Chinese standard of as DW310-35 silicon lamination sheets, while the steel 45 shows poor magnetic permeability by materials. comparing it with DW310-35 and DT-4. However, it is used to fabricate the shaft, end cover, As stated above, the rotor core is fabricated by using the solid electrical iron, the eddy current and enclosure because of the low cost. All of the materials refers to Chinese standard of materials. loss component of the solid rotor core is calculated in a transient FEM simulation by referring to the As stated above, the rotor core is fabricated by using the solid electrical iron, the eddy current corresponding material conductivity. The other loss components of the solid core are loss component of the solid rotor core is calculated in a transient FEM simulation by referring to the post-processed through the built-in Bertotti equation in the FEM software. The corresponding corresponding material conductivity. The other loss components of the solid core are post-processed coefficients refer to [28], where the kh and ke are 496.5 WsT−2m−3 and 0, other quantities refer to the through the built-in Bertotti equation in the FEM software. The corresponding coefficients refer to [28], material properties. Extracted from FEM simulation, the eddy current loss is about 14.8 W while the where the kh and ke are 496.5 WsT−2 m−3 and 0, other quantities refer to the material properties. hysteresis loss is only 0.024 W, thus the hysteresis loss is neglected during the rotor loss Extracted from FEM simulation, the eddy current loss is about 14.8 W while the hysteresis loss is only calculations. 0.024 W, thus the hysteresis loss is neglected during the rotor loss calculations. 2.4

DW310-35

DT-4

Steel 45

2.2

Flux density (T)

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

0

10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

Field intensity (H/m) Figure Figure4.4.Magnetizing Magnetizingcurves curvesof ofthe theferromagnetic ferromagneticmaterials. materials.

Based on the analysis above, the electromagnetic field is calculated and the mainly loss obtained from FEM simulations are as shown in Table 3. The winding loss includes the armature winding loss and the axial field winding loss. The rotor loss is composed of the rotor core loss and the eddy current loss of permanent magnets. The axial field loss is composed of two parts: dc resistance loss and eddy

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Based the analysis above, the electromagnetic field is calculated and the mainly loss obtained Energies 2018, on 11, 1208 7 of 21 from FEM simulations are as shown in Table 3. The winding loss includes the armature winding loss and the axial field winding loss. The rotor loss is composed of the rotor core loss and the eddy current loss loss.ofSince the axial field windings arefield fed on thus, ring loss is current permanent magnets. The axial lossdcissupply, composed ofthe twoferromagnetic parts: dc resistance loss mainly sourced from the end edge leakage flux. and eddy current loss. Since the axial field windings are fed on dc supply, thus, the ferromagnetic ring loss is mainly sourced from the end edge leakage flux. Table 3. Main Loss in the Prototype.

Table 3. Main Loss in the Prototype. Items Value

Items Stator core loss windings Stator core loss loss Ferromagnetic windings loss rings loss Rotor loss Ferromagnetic rings loss Rotor loss 3. Mathematical Model for Thermal Calculation

Value 1.96 W 17.4 1.96WW 0.76 17.4WW 14.8 W 0.76 W 14.8 W

3. Mathematical Model for Thermal Calculation 3.1. Assumptions and Boundary Conditions 3.1. Assumptions and Boundary Conditions The presented prototype is a fully enclosed self-cooling machine, thus, the temperature distributions are highly related to the loss distributions. Due to the special structure, the 3d The presented prototype is a fully enclosed self-cooling machine, thus, the temperature mathematical model is necessary for the thermal calculation. According to heat transfer theories distributions are highly related to the loss distributions. Due to the special structure, the 3d and the physical structure of the machine, 3d steady-state temperature field calculation model are set mathematical model is necessary for the thermal calculation. According to heat transfer theories and up as shown in Figure 5. All of the components are constructed corresponding to the real structure the physical structure of the machine, 3d steady-state temperature field calculation model are set up and the dimensions of the prototype. To save the computations and time, the following assumptions as shown in Figure 5. All of the components are constructed corresponding to the real structure and are proposed to simplify the calculations [29,30]. the dimensions of the prototype. To save the computations and time, the following assumptions are proposed simplify the calculations Sincetothe rotor core is developed[29,30]. by using solid iron, the eddy loss is distributed with a certain 1. 1.

2. 2. 3. 3. 4. 4.

thickness according the skin effect. So, when the loss real state of the losswith distributions, Since the rotor core istodeveloped by using solidconsidering iron, the eddy is distributed a certain the eddy current losstoof the the rotor is distributed a certain the thickness according skin core effect. So, when within considering thepenetration real state depth of theofloss rotor core. distributions, the eddy current loss of the rotor core is distributed within a certain penetration During loss calculations, the temperature effect on the material properties are ignored, depth of the rotor core. thus, the of the temperature on the effect heat transfer is regardless. During theinfluence loss calculations, the temperature on the material properties are ignored, thus, the influence of the temperature on the heat enclosed transfer isstructure, regardless. Due to the low rotating speed and totally the influence of the flowing air Due to the machine low rotating speed totally enclosed structure, the influence of the flowing air within on the heatand transfer is also ignored. within machine on the heat transfer is alsoisignored. Duringthe the assembly process, the machine vacuum-dipped to evacuate the air within the During assembly process, machine is vacuum-dipped to evacuatejoints. the air within the connectthe joints, so it regards thatthe there is no air-gap between the connection connect joints, so it regards that there is no air-gap between the connection joints.

1 2 3 4 5

S Figure Figure 5. 5. Three-dimensional Three-dimensional(3d) (3d)steady-state steady-statetemperature temperaturefield fieldcalculation calculationmodel. model. 1-Stator 1-Stator Core, Core, 2-Armature Windings, 3-Axial Field Windings, 4-Permanent Magnets, 5-Ferromagnetic Ring, 2-Armature Windings, 3-Axial Field Windings, 4-Permanent Magnets, 5-Ferromagnetic Ring, S-Boundary S-Boundary Thermal Calculations. for Thermal for Calculations.

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According to thermodynamics principles, 3d steady-state temperature field mathematical model and its boundary conditions are described in (4) [18,24]: According to thermodynamics principles, 3d steady-state temperature field mathematical model and its boundary conditions  ∂are ∂T  ∂in(4) [18,24]: ∂T  ∂  ∂T   described

(  y    z    x    ∂x  ∂x ∂y ∂y  ∂∂z  ∂T ∂z   Ω : ∂  λ x ∂T  + ∂ λy ∂T + ∂x ∂z λz ∂z = − q ( x, y, z ) T ∂x  ∂y  ∂y ∂∂T   SS ::−−λλ = α T − Tf f  ∂n = α T − T Ω:



λ

∂n

+

(

λ

+

λ

= − q x, y , z )

)

(4) (4)

where thethe temperature in the solution domain, λx , λλ thermal conductivity along x-axis, y, λthe z are the thermal conductivity along whereTTis is temperature in the solution domain, y ,x,λzλare y-axis, z-axis, respectively, q is the heat is theflux, normal of the boundary S, α is x-axis,and y-axis, and z-axis, respectively, q flux, is then heat n isvector the normal vector of surface the boundary the heat transfer coefficient, Tf iscoefficient, ambient temperature, S is the outer the enclosure surface S, α is the heat transfer Tf is ambientand temperature, andsurface S is theofouter surface ofand the end cover (as in Figure 5). enclosure andshown end cover (as shown in Figure 5). Similar Similarto tothe theelectromagnetic electromagneticcalculation, calculation, the the Equation Equation (3) (3) could could also alsodiscretize discretize and andsolve solveby by using usingFEM. FEM.Different Differentwith withthe theelectromagnetic electromagneticmodel, model,the thethermal thermalmodel modelisismeshed meshedaccording accordingto tothe the component component structure, structure, e.g., e.g., The Thestator statorand androtor rotorcores coresare aremeshed meshedwith withtriangular triangularor orquadrangular quadrangular prism prismelements, elements,while whilethe thearmature armaturewindings windingsand andthe theaxial axialfield fieldwindings windingsare aremeshed meshedby byusing usingthe the sweep sweepmethod methodwith withquadrangular quadrangularprism prismelements, elements,etc. etc.while whilethe themesh meshprocess processisisfinalized, finalized,there thereare are total total86,735 86,735elements elementswith with235,505 235,505nodes nodesfor forthe theentire entiremodels. models. 3.2. 3.2.Thermal ThermalConductivity ConductivityofofAir-Gap Air-Gap The thethe airair between the the static partsparts and the parts parts changes with Thethermal thermalconductivity conductivityofof between static andmovable the movable changes the rotating speed. To stress the influence of the rotating speed on the thermal conductivity, we consider with the rotating speed. To stress the influence of the rotating speed on the thermal conductivity, using the equivalent thermal conductivity the static airoftothe account effect of for rotating speed we consider using the equivalent thermalofconductivity static for air the to account the effect of on the thermal conductivity. In ARFTPMSM, the air-gap includes the normal air-gap between the rotating speed on the thermal conductivity. In ARFTPMSM, the air-gap includes the normal air-gap stator andthe rotor, as shown in Figure 6a, andinthe axial 6a, air-gap axial between field windings andfield the between stator and rotor, as shown Figure and between the axialthe air-gap the axial ferromagnetic rings, as shown in Figure 6b. The thermal conductivity of the normal air gap and axial windings and the ferromagnetic rings, as shown in Figure 6b. The thermal conductivity of the air gap should treated due be to the different structures. normal air gapbe and axial separately, air gap should treated separately, due to the different structures.

(a)

(b)

Figure 6. Schematic diagram of air-gap of the machine, (a) normal air-gap; and, (b) axial air-gap. Figure 6. Schematic diagram of air-gap of the machine, (a) normal air-gap; and, (b) axial air-gap.

3.2.1. Thermal Conductivity of Normal Air-Gap 3.2.1. Thermal Conductivity of Normal Air-Gap Figure 6a shows the schematic diagram of the normal air-gap. The rotation of the rotor drives Figure 6a shows the schematic diagram of the normal air-gap. The rotation of the rotor drives the air in the normal air-gap to spin. Thus, the thermal conductivity will influence by the flowing the air in the normal air-gap to spin. Thus, the thermal conductivity will influence by the flowing state of the air in the air gap. To simplify the calculation, the equivalent thermal conductivity λr is state of the air in the air gap. To simplify the calculation, the equivalent thermal conductivity λr is introduced to represent the heat exchange capacity of the rotating air in the normal air-gap. By this introduced to represent the heat exchange capacity of the rotating air in the normal air-gap. By this way, the rotating air could be equivalent to the static air. The equivalent thermal conductivity could way, the rotating air could be equivalent to the static air. The equivalent thermal conductivity could be be determined, as follows [24,30]: determined, as follows [24,30]: The Reynolds number R in the normal air-gap is calculated by (5). The Reynolds number Raain the normal air-gap is calculated by (5).

n n R a = πD60 2 gγ

Ra = π D2 g

(5) (5) 60γ Where D2 is the outer diameter of the rotor, m; g is the normal air-gap length, m; n is the motor speed, r/min; and, γ is the kinematic viscosity of air, m2/s.

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where D2 is the outer diameter of the rotor, m; g is the normal air-gap length, m; n is the motor speed, r/min; and, γ is the kinematic viscosity of air, m2 /s. The critical Reynolds number Rcr is given by (6). s Rcr = 41.2

Di1 g

(6)

where Di1 is the inner diameter of the stator, m. If Ra < Rcr , the air flowing in the air-gap is laminar, the heat dissipation of the air-gap is independent of the rotation of the rotor, the heat transfer form in air-gap is heat conduction, and the equivalent thermal conductivity λn equals to static air heat conductivity λair ; however, if Ra > Rcr , then the air flow in the air-gap is turbulent, and the equivalent thermal conductivity λn is determined by (7) [31,32]. (

λn = 0.069η −2.9048 R a 0.4614 ln(3.33361η ) D2 η= D

(7)

i1

3.2.2. Thermal Conductivity of Axial Air-Gap Figure 6b shows the schematic diagram of the axial air-gap. The rotation of the rotor also drives the air in the axial air-gap to spin. For the smooth end surface of the axial field windings and the ferromagnetic rings, theReynolds number of the axial air-gap is less than the critical Reynolds number. So, the equivalent thermal conductivity λa equals to the air heat conductivity λair . 3.3. Heat Transfer Coefficient of the Enclosure The heat transfer coefficient α of the enclosure could be determined, as follows [33]: s 3 θ  α = 14(1 + 0.5 ωi ) 25

√

(8)

where, ω i is wind velocity blowing to the surface of the enclosure; and, θ is the enclosure temperature. Due to the fully enclosed self-cooling structure and the low speed of the machine, the influence of the flowing air going through the outer surface of the machine on the heat transfer coefficient could be ignored. So, the heat transfer coefficient of the enclosure could be calculated by (9). s 3 θ  α = 14 25

(9)

In this paper, the machine is tested indoor with no wind, and the ambient temperature is 22 ◦ C. The heat transfer coefficient that was obtained from (9) is 31.8 W/(m2 K). 3.4. Thermal Conductivity of Armature Windings Before the thermal calculations, the thermal conductivity of the armature windings should be determined due to the anisotropic properties caused by the wire package. As shown in Figure 7a, the real armature windings is made up by using multi-strand copper wires, and each strand of the wire are insulated by using the wire package. To simplify the calculation model, we use the equivalent winding, as shown in Figure 4b, to replace the multi-strand copper wires. During the equivalent process, the equivalent winding has the same heat transfer capacity as the real multi-strand copper

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wires. Then, the equivalent thermal conductivity of the armature windings can be determined by the equations below [34]. S λ0 = S (10) Sin cu Energies 2018, 11, x FOR PEER REVIEW 10 of 21 λcu + λ in

where, λ’ ,λλ’,cuλ, cuand λinλare thethe equivalent thermal conductivity of theofequivalent winding, copper copper wire, where, , and in are equivalent thermal conductivity the equivalent winding, and the and wirethe package, respectively. S, Scu , andS,Sin the Sareas occupied by occupied the equivalent wire, wire package, respectively. Scuare , and in arethat the are areas that are by the winding, the copper wire, and the wire package, respectively. equivalent winding, the copper wire, and the wire package, respectively.

Figure Equivalent model the armature windings one slot, real model windings stator Figure 7. 7. Equivalent model ofof the armature windings inin one slot, (a)(a) real model ofof windings inin stator slot; and, equivalent model windings stator slot. slot; and, (b)(b) equivalent model of of windings in in stator slot.

Based on the analysis above, the material properties for thermal field analysis are summarized Based on the analysis above, the material properties for thermal field analysis are summarized in Table 4. From which, it can be obtained that the thermal conductivity of stator core is anisotropic. in Table 4. From which, it can be obtained that the thermal conductivity of stator core is anisotropic. When comparing the armature windings with the axial field windings, the thermal conductivity of When comparing the armature windings with the axial field windings, the thermal conductivity of armature windings is far lower than the axial field windings. armature windings is far lower than the axial field windings. Table 4. Material properties for thermal field analysis. Table 4. Material properties for thermal field analysis.

Items Items

Stator core Stator core

Armature windings

Armature windings Slot insulation Slot insulation Slot wedge Slot wedge Normal air-gap Normal air-gap Permanent magnets Permanent magnets Rotor core Rotor core Shaft Shaft Enclosure & end cover Enclosure & end cover Axial field windings Axial field windings Axial ferromagnetic rings air gap AxialAxial ferromagnetic rings

Axial air gap

Mass Density Mass Density

7600 kg/m3

7600 kg/m3

8900 kg/m3

8900 kg/m3 3 1020 kg/m 1020 kg/m3 3 3 900 kg/m 900 kg/m 3 1.2 kg/m3 1.2 kg/m 3 7600 kg/m 7600 kg/m3 3 7870 kg/m 7870 kg/m3 7850 kg/m3 3 7850 kg/m 7850 kg/m3 3 3 7850 kg/m 8900 kg/m 3 3 8900 kg/m 7870 kg/m 3 1.2 kg/m 7870 kg/m3

1.2 kg/m3

Specific Heat Capacity Specific Heat Capacity

470 J/(kg K)

470 J/(kg K)

504 J/(kg K)

504 J/(kg K) 1000J/(kg J/(kgK)K) 1000 800 J/(kg K) 800 J/(kg K) 1005J/(kg J/(kgK)K) 1005 502 502J/(kg J/(kgK)K) 460J 460JJ/(kg J/(kgK)K) 472 J/(kg K) 472 J/(kg K) 472 J/(kg K) 472J/(kg J/(kgK)K) 504 504J/(kg J/(kgK)K) 460 1005 460J/(kg J/(kgK) K)

1005 J/(kg K)

Thermal Conductivity 43 W/(m K) in x,y-axis 43 W/(m K) in 0.62 W/(m K)x,y-axis in z-axis 0.62 W/(m K) in z-axis 1.7 W/(m K) 1.7 W/(m K) 0.23 W/(m 0.23 W/(m K)K) 0.25 W/(m 0.25 W/(m K)K) 0.045 W/(m 0.045 W/(m K)K) 1212W/(m W/(mK)K) 4848W/(m W/(mK)K) 49.8 W/(m K) 49.8 W/(m K) 49.8 W/(m K) 49.8 W/(m 398 W/(m K)K) 398 W/(m 48 W/(m K) K) 0.045 48 W/(m W/(m K) K) 0.045 W/(m K)

Thermal Conductivity

4. Steady-State Temperature Field Calculation for Prototype 4.1. Verification for Mathematical Models Based on the established models and material properties, 3d temperature field mathematical model of the prototype operating at a rated torque of 8.6 N m and 0 Ampere-turn (At) AMMF is solved. Then, the temperature distributions of the machine can be obtained, as shown in Figure 8.

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4. Steady-State Temperature Field Calculation for Prototype 4.1. Verification for Mathematical Models Based on the established models and material properties, 3d temperature field mathematical model of the prototype operating at a rated torque of 8.6 N m and 0 Ampere-turn (At) AMMF is solved. Then, the temperature distributions of the machine can be obtained, as shown in Figure 8. Observed from Figure 8, the max temperature is about 52.54 ◦ C, located on the armature windings, while the min Energies 2018, 11, x FOR PEER REVIEW 11 of 21 temperature is 32.04 ◦ C, located on the enclosure. Whenn compared with the ambient temperature, the rated temperature is 29.54 K.rise is 29.54 K. temperature, the rated rise temperature

Figure temperaturedistributions distributionsofofmachine machine operating at rated torque of N 8.6mNand m 0and 0 At Figure 8. 3d temperature operating at rated torque of 8.6 At Axial Axial Magnetic Motive (AMMF) Magnetic Motive Force Force (AMMF) (◦ C). (°C).

To validate the accuracy of the established electromagnetic and the thermal field mathematical To validate the accuracy of the established electromagnetic and the thermal field mathematical models, the temperature experiments have carried out on the prototype under rated load and 0 At models, the temperature experiments have carried out on the prototype under rated load and 0 At AMMF. The temperature probes (Pt 1000) are fixed on the end of the armature windings and the AMMF. The temperature probes (Pt 1000) are fixed on the end of the armature windings and the outer outer surface of the enclosure. During the test process, we can record the resistance of the surface of the enclosure. During the test process, we can record the resistance of the temperature temperature probes by using the resistance measurement instrument. Then, we can obtain the probes by using the resistance measurement instrument. Then, we can obtain the temperature by temperature by referring to the given temperature-resistance tables. By this measurement method, referring to the given temperature-resistance tables. By this measurement method, the precision can the precision can keep within 0.1 °C. During temperature measurement, the resistance data is keep within 0.1 ◦ C. During temperature measurement, the resistance data is recorded every 5 min. recorded every 5 min. When the temperature between two measured points are within 0.1 °C, it can When the temperature between two measured points are within 0.1 ◦ C, it can regard that the machine regard that the machine reaches up to a thermal steady state. reaches up to a thermal steady state. Table 5 shows the comparison of the calculation results and measurements. From which, we Table 5 shows the comparison of the calculation results and measurements. From which, we could could get that the temperature difference between the calculation results and the measurements of get that the temperature difference between the calculation results and the measurements of the end the end radial armature windings is 1.05 °C While the temperature difference between the radial armature windings is 1.05 ◦ C While the temperature difference between the calculation and the calculation and the measurement results of ◦the enclosure is 0.96 °C, both of the errors are less than measurement results of the enclosure is 0.96 C, both of the errors are less than 5%, it could satisfy the 5%, it could satisfy the requirements in engineering. The differences between the calculation results requirements in engineering. The differences between the calculation results and measurements are so and measurements are so small, and it can prove that the electromagnetic and thermal calculation small, and it can prove that the electromagnetic and thermal calculation models for the machine is models for the machine is accurate enough for the electromagnetic field and thermal field analyses. accurate enough for the electromagnetic field and thermal field analyses. Table 5. Comparison of Calculation Results with Measurements under rated torque and 0 At AMMF. Table 5. Comparison of Calculation Results with Measurements under rated torque and 0 At AMMF.

Items Items

Calculation Results

Measurements

Error (%)

51.15

50.10

2.10%

Calculation Results

Measurements

51.15

50.10

End armature windings/°C End armature Enclosure/°C windings/◦ C Enclosure/◦ C

32.04

32.04

33.00

33.00

Error (%)

2.10%−2.91%

−2.91%

4.2. Temperature Field under Different AMMF The 3d temperature field mathematical models of the machine under 0 At, 600 At, and 900 At AMMF are calculated to investigate the influence of AMMF on the temperature distribution of the machine. During the calculations, the load torque is still kept at 8.6 N m. The calculation results are compared, as shown in Table 6. From which, one can obtain that the temperature of the end armature windings and the enclosure increases as AMMF increases. The enclosure temperature increases faster than the temperature of the end armature windings. The reason can be explained

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4.2. Temperature Field under Different AMMF The 3d temperature field mathematical models of the machine under 0 At, 600 At, and 900 At AMMF are calculated to investigate the influence of AMMF on the temperature distribution of the machine. During the calculations, the load torque is still kept at 8.6 N m. The calculation results are compared, as shown in Table 6. From which, one can obtain that the temperature of the end armature windings and the enclosure increases as AMMF increases. The enclosure temperature increases faster than the temperature of the end armature windings. The reason can be explained that, as AMMF increases, the axial field winding loss increases dramatically, the axial air gap can prevent the heat transfer from the axial field windings to stator and rotor cores because of the poor thermal conductivity of the axial air-gap. Therefore, the heat that is generated in the axial field windings can only transfer Energies 2018, 11, x FOR PEER 12 of 21 to armature windings byREVIEW through the ferromagnetic ring and end cover. In addition, the increase of AMMF can also made the harmonic components of the air gap flux density arise, which will density arise, which will also rotormade loss. the All temperature of these above made the temperature also can increase the rotor loss.can Allincrease of thesethe above increase significantly as increase significantly as AMMF increases. AMMF increases. Table6.6.Calculation CalculationTemperature Temperatureofofmachine machinecomponents componentsunder underDifferent DifferentAMMF. AMMF. Table

AMMF/AT AMMF/AT 0 0 600 600 900 900

End Armature Windings/°C End Armature Windings/◦ C 51.15 51.15 54.7 54.7 60.9 60.9

Enclosure/°C 32.0 32.0 36.8 36.8 52.8 52.8

Enclosure/◦ C

Because the temperature limitation of components is different, the temperature distribution of Because the temperature limitation of components is different, the temperature distribution of the the machine components should be studied separately. machine components should be studied separately. 4.2.1. Thermal Analysis for the Rotor Components 4.2.1. Thermal Analysis for the Rotor Components The remanence of the permanent magnets may demagnetize as the temperature increases. The The remanence of the permanent magnets may demagnetize as the temperature increases. rotor core is built by using solid iron, it has larger loss than the silicon lamination sheets. The The rotor core is built by using solid iron, it has larger loss than the silicon lamination sheets. permanent magnets are encompassed by the rotor core, therefore, the temperature distributions of The permanent magnets are encompassed by the rotor core, therefore, the temperature distributions of the rotor core are studied firstly. The obtained temperature distribution of the rotor core is as shown the rotor core are studied firstly. The obtained temperature distribution of the rotor core is as shown in Figure 9. The temperature of the middle parts of the rotor core is higher than the temperature of in Figure 9. The temperature of the middle parts of the rotor core is higher than the temperature of the normal air gap and the shaft. It indicates that the heat generated in the rotor core is transferred to the normal air gap and the shaft. It indicates that the heat generated in the rotor core is transferred to ambient by two ways: one is going from the air gap to stator core and another is going from the ambient by two ways: one is going from the air gap to stator core and another is going from the ambient ambient by through the shaft. When compared with the machine with 0 At AMMF, the max by through the shaft. When compared with the machine with 0 At AMMF, the max temperature of the temperature of the rotor core of the machine under 600 At and 900 At AMMF increases by about 4.09 rotor core of the machine under 600 At and 900 At AMMF increases by about 4.09 ◦ C and 12.42 ◦ C, °C and 12.42 °C, respectively. As AMMF increases, the temperature distributes more evenly, because respectively. As AMMF increases, the temperature distributes more evenly, because the heat transfer the heat transfer capacity of the shaft is very small. As the loss increases, the shaft can not transfer all capacity of the shaft is very small. As the loss increases, the shaft can not transfer all of the loss to the of the loss to the ambient through the shaft. ambient through the shaft.

(a)

(b)

(c)

Figure 9. Temperature distribution of the rotor core under different AMMF (°C); (a) 0 At AMMF; (b) Figure 9. Temperature distribution of the rotor core under different AMMF (◦ C); (a) 0 At AMMF; 600 At AMMF; and, (c) 900 At AMMF. (b) 600 At AMMF; and, (c) 900 At AMMF.

The temperature distributions of the permanent magnets are as shown in Figure 10. The max temperature located on the outer surface of the circumferential magnets while the min temperature is on the inner surface of the radial magnets. The temperature decrease along the radial direction, which also confirms that the shaft can transfer the heat to the ambient. The temperature differences between the max and the min temperature under 0 At, 600 At, and 900 At is 0.82 °C, 0.76 °C, and 0.69 °C, respectively. In addition, when we compare Figure 9 with Figure 10, the max temperature of the

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The temperature distributions of the permanent magnets are as shown in Figure 10. The max temperature located on the outer surface of the circumferential magnets while the min temperature is on the inner surface of the radial magnets. The temperature decrease along the radial direction, which also confirms that the shaft can transfer the heat to the ambient. The temperature differences between the max and the min temperature under 0 At, 600 At, and 900 At is 0.82 ◦ C, 0.76 ◦ C, and 0.69 ◦ C, respectively. In addition, when we compare Figure 9 with Figure 10, the max temperature of the permanent magnets equals to the temperature of the rotor core at all occasions. It is because the permanent magnet loss is far less than the rotor core loss. Therefore, the temperature distribution of Energies 2018, 11, x FOR REVIEW 13 of 21 permanent isPEER actually determined by the temperature field of the rotor core. Energies 2018,magnets 11, x FOR PEER REVIEW 13 of 21

(a)(a)

(b) (b)

(c)(c)

Figure 10. Temperature distributions of the permanent magnets under different AMMF (°C); (a) 0 At Figure10. 10.Temperature Temperaturedistributions distributionsofofthe thepermanent permanentmagnets magnetsunder underdifferent differentAMMF AMMF(◦(°C); (a)00At At Figure C); (a) AMMF; (b) 600 At AMMF; (c) 900 At AMMF. AMMF; AMMF;(b) (b)600 600At AtAMMF; AMMF;(c) (c)900 900At AtAMMF. AMMF.

4.2.2.Thermal ThermalAnalysis Analysisfor forthe theStator StatorComponents Components 4.2.2. 4.2.2. Thermal Analysis for the Stator Components Thebasic basicstructure structureofofthe thestator statorisisasasshown shown inFigure Figure11. 11.The Thestator stator iscomposed composedofofthe thestator stator The The basic structure of the stator is as shown ininFigure 11. The stator isiscomposed of the stator core and armature windings. The temperature distributions of the stator are as shown in Figure 12. coreand andarmature armaturewindings. windings. The Thetemperature temperature distributions distributions of of the the stator stator are are as as shown shown in in Figure Figure 12. 12. core Themax maxtemperature temperatureofofthe thestator statorlocated located onthe thearmature armaturewindings windingswhile whilethe the mintemperature temperature is The The max temperature of the stator located onon the armature windings while the minmin temperature is onis on the outer surface of the stator core. Because of the poor heat transfer capacity of the slotinsulation insulation on outer the outer surface of the stator core. Because poor heat transfercapacity capacityofofthe theslot slot the surface of the stator core. Because of of thethe poor heat transfer insulation and slot wedge, they construct a thermal barrier to prevent the heat transferring to the stator core. andslot slotwedge, wedge,they theyconstruct constructaathermal thermal barrier barrier to to prevent prevent the the heat heat transferring transferring to to the the stator stator core. core. and Thus,there there isobvious obvioustemperature temperaturedifference differencebetween betweenthe thearmature armaturewindings windingsand andthe thestator statorcore. core. Thus, Thus, there isisobvious temperature difference between the armature windings and the stator core. The max temperature of the stator core locates on the tooth top; therefore, the temperature The max maxtemperature temperature of ofthe thestator statorcore corelocates locateson onthe thetooth toothtop; top;therefore, therefore,the thetemperature temperature The variations on the stator core tooth top are also studied as shown in Figure 13. The position the variationson onthe thestator statorcore coretooth toothtop topare arealso alsostudied studiedasasshown shownininFigure Figure13. 13.The Theposition positionon onon the variations the statorcore coretooth toothtop top isasasshown shownininFigure Figure11. 11.From Fromwhich whichone onecan canobserve observethat thatthe thetemperature temperature stator stator core tooth top is is as shown in Figure 11. From which one can observe that the temperature from from position a to position b decreases firstly and then increases, from position b to position from position a to position b decreases firstly and then increases, from position b to position c,c,it it position a to position b decreases firstly and then increases, from position b to position c, it shows showsthe thesimilar similarvariation variationtrend trendwith with thatfrom fromposition positiona atotoposition positionb.b.it itisisdetermined determinedbybythe the shows the similar variation trend with that fromthat position a to position b. it is determined by the physical physical structure of the stator core tooth top. In addition, the temperature of the stator core tooth physical of structure of core the stator core In tooth top. Inthe addition, the temperature thetooth stator core tooth structure the stator tooth top. addition, temperature of the stator of core increases as increasesasasthe theAMMF AMMFasaswell. well. increases the AMMF as well.

End End Section Section Middle Middle Section Section

Figure 11. Schematic diagram of the stator components. Figure11. 11.Schematic Schematicdiagram diagramofofthe thestator statorcomponents. components. Figure

Middle Section

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Figure 11. Schematic diagram of the stator components.

Armature Windings

Stator Tooth

(a)

(b)

(c)

Figure 12. Temperature distributions of the stator (°C); (a) AMMF 0 AT; (b) AMMF 600 AT; and, (c) Figure 12. Temperature distributions of the stator (◦ C); (a) AMMF 0 AT; (b) AMMF 600 AT; AMMF 900 AT. and, (c) AMMF 900 AT.

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Temperature (℃)

54

14 of 21

900At 600At 0At

52 46 44 42

a

b

c

Position in the Stator Tooth (mm)

Figure 13. 13. Temperature Temperature variations of the stator core tooth top under different AMMF. Figure AMMF.

Figure Figure 14 14 shows shows temperature temperature distributions distributions of of the the armature armature windings windings under under different different AMMF. AMMF. From which, one can observe that the temperature on the end windings are higher than the middle From which, one can observe that the temperature on the end windings are higher than the middle part. While AMMF increases from 0 At to 600 At, the max and min temperature increases by 3.15 ◦°C part. While AMMF increases from 0 At to 600 At, the max and min temperature increases by 3.15 C and 3.12 °C, respectively. The average temperature increases about 6.9%. However, while AMMF ◦ and 3.12 C, respectively. The average temperature increases about 6.9%. However, while AMMF rises rises At to theand max and min temperature increases °C and 6.83 average °C The ◦ C 6.24 ◦ C The from from 600 At600 to 900 At,900 theAt, max min temperature increases by 6.24 by and 6.83 average temperature increases by about 15.2%. The variation trend is nonlinear. Thus, it should pay temperature increases by about 15.2%. The variation trend is nonlinear. Thus, it should pay more more attention the adjustment thefield axialcurrent. field current. attention to the to adjustment of the of axial

(a)

(b)

(c)

Figure 14. Temperature Temperature distributions distributions of of the the armature armature windings windings under under different different AMMF AMMF ((°C); At ◦ C); (a) Figure 14. (a) 00 At AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF. AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF.

4.2.3. Thermal Analysis for Axial Field Structure The axial field structure consists of the axial field windings, axial air-gap, and the ferromagnetic rings. Figure 15a,b show the cross-section of the tooth and slot of the outer ferromagnetic ring, respectively. The temperature distributions on the cross-section are as shown in Figure 16. As observed from Figure 16, it can be seen that the temperature of the field windings increases significantly as AMMF increases. It is because that the axial field winding loss increases quickly as AMMF. From the enlarge view of the temperature distribution of the axial field windings (as shown

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4.2.3. Thermal Analysis for Axial Field Structure The axial field structure consists of the axial field windings, axial air-gap, and the ferromagnetic rings. Figure 15a,b show the cross-section of the tooth and slot of the outer ferromagnetic ring, respectively. The temperature distributions on the cross-section are as shown in Figure 16. As observed from Figure 16, it can be seen that the temperature of the field windings increases significantly as AMMF increases. It is because that the axial field winding loss increases quickly as AMMF. From the enlarge view of the temperature distribution of the axial field windings (as shown in Figure 16a), it is clear that the heat conducts from the ferromagnetic rings to the axial windings through the axial air-gap. When compared with Figure 16a,b, it shows that the temperature of the axial field windings is lower than the ferromagnetic rings, thus the heat will transfer from the ferromagnetic rings to the axial field windings. However, viewed from Figure 16c, the temperature of the field windings are larger than thex FOR ferromagnetic rings, it would cause the heat transfer direction reverse by comparing Energies 2018, 11, PEER REVIEW 1515ofof2121 Energies 2018, 11, x FOR PEER REVIEW with Figure 16a,b.

(a)(a)

(b) (b)

Figure 15.15.Cross-section Cross-section forfor the axial field structure. 1-ferromagnetic rings, 2-axial air-gap, 3-axial Figure15. Cross-section the axial field structure. 1-ferromagnetic rings, 2-axial air-gap, 3-axial Figure for the axial field structure. 1-ferromagnetic rings, 2-axial air-gap, 3-axial field field winding, 4-electrical insulation; (a) left section of the axial field structure; and, (b) right section field winding, 4-electrical insulation; left section of the axial field structure; right of section winding, 4-electrical insulation; (a) left (a) section of the axial field structure; and, (b)and, right(b) section the of the axial field structure. of the axial field structure. axial field structure.

(a)(a)

(b) (b)

(c)(c)

Figure distributions ofof the axial field structure under different AMMF (°C); (a)(a) 0At Figure16. 16.Temperature Temperature distributions the axial field structure under different AMMF 0At Figure 16. Temperature distributions of the axial field structure under different AMMF (◦(°C); C); (a) 0At AMMF; (b)(b) 600 AtAt AMMF; and, (c)(c) 900 AtAt AMMF. AMMF; 600 AMMF; and, 900 AMMF. AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF.

5.5.Temperature TemperatureField Fieldfor forARFTPMSM ARFTPMSMwith withHTS HTSWindings Windings 5. Temperature Field for ARFTPMSM with HTS Windings Since the final goal isistotodevelop ananARFTPMSM with HTS thus Sincethe the final develop ARFTPMSM HTSwindings, windings, thuswe weshould should Since final goalgoal is to develop an ARFTPMSM with HTSwith windings, thus we should investigate investigate the temperature field firstly. So, it can provide us guides for the construction of the HTS investigate the temperature field firstly. So, it can provide us guides for the construction of the HTS the temperature field firstly. So, it can provide us guides for the construction of the HTS machine. machine. Once the axial field windings and armature windings are developed by using HTS wires, machine. Once the axial field windings and armature windings are developed by using HTS wires, Once the axial field windings and armature windings are developed by using HTS wires, the loss of the theloss lossofofthe thearmature armaturewindings windingsand andthe theaxial axialwindings windingsare arevery verysmall, small,sosothey theycould couldbebeignored. ignored. the armature windings and the axial windings are very small, so they could be ignored. The heat The heat transfer process may differ from the ARFTPMSM with copper wires. In order The heat transfer process may differ from the ARFTPMSM with copper wires. In ordertotocompare compare transfer process may differ from the ARFTPMSM with copper wires. In order to compare with the with withthe theprototype, prototype,we wecontinue continuetotouse usethe themodel modeland andthr thrmaterial materialproperties propertiesfor fororiginal originalprototype. prototype. prototype, we continue to use the model and thr material properties for original prototype. Therefore, Therefore, the difference between the HTS motor and the copper motor is only caused Therefore, the difference between the HTS motor and the copper motor is only causedbybythe the the difference between the HTS motor and the copper motor is only caused by the windings loss. windings windingsloss. loss. 5.1. Temperature Field for the Rotor Components 5.1. 5.1.Temperature TemperatureField Fieldforforthe theRotor RotorComponents Components Firstly, the temperature distribution of the rotor core is studied. When compared with Figure 17a–c, Firstly, the distribution ofofthe core isisstudied. When with Firstly, thetemperature temperature distribution therotor rotor studied. Whencompared compared withFigure Figure we could obtain that: (1) the max temperature located incore the rotor core, whereas the min temperature 17a–c, we could obtain that: (1) the max temperature located in the rotor core, whereas the min could obtain(2) that: thetemperature max temperature in the rotor core,600 whereas thethan min is17a–c, on thewe normal air-gap. The(1) max and thelocated min temperature under At is less temperature is on the normal air-gap. (2) The max temperature and the min temperature under 600 temperature is on the normal air-gap. (2) The max temperature and the min temperature under 600 that under 0 At and 900 At. What we observed could be explained as follows. While AMMF increases AtAtisisless than that under 0 At and 900 At. What we observed could be explained as follows. While less than that under 0 At and 900 At. What we observed could be explained as follows. While AMMF AMMFincreases increasesfrom from0 0AtAttoto600 600At, At,the theaxial axialflux fluxreinforces reinforcesthe thenormal normalair-gap air-gapflux. flux.Thus, Thus,it itneeds needs less armature current in order to produce the same torque. Thus, the small armature less armature current in order to produce the same torque. Thus, the small armaturecurrent currentwill will produce small rotor loss. Then, the corresponding temperature will also decrease. As the increase produce small rotor loss. Then, the corresponding temperature will also decrease. As the increaseofof the theAMMF AMMFcontinues, continues,the theaxial axialflux fluxwould wouldweaken weakenthe thenormal normalair-gap air-gapmagnetic magneticflux, flux,there thereneed need

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from 0 At to 600 At, the axial flux reinforces the normal air-gap flux. Thus, it needs less armature current in order to produce the same torque. Thus, the small armature current will produce small rotor loss. Then, the corresponding temperature will also decrease. As the increase of the AMMF continues, the axial flux would weaken the normal air-gap magnetic flux, there need larger armature current to produce the same torque. Thus, the corresponding temperature increases. In addition, since the loss of axial field winding and armature winding is very small, the entire temperature decreases, Energies 2018, 11, x FOR PEER REVIEW 16 of 21 Energies 2018, 11, x FOR 16 of 21 when comparing withPEER the REVIEW temperature distributions of the machine with copper wires.

(a) (a)

(b) (b)

(c) (c)

Figure 17. Temperature distribution of the rotor core (°C); (a) 0 At AMMF; (b) 600 At AMMF; and, (c) Figure 17. Temperature distribution of the rotor core◦ (°C); (a) 0 At AMMF; (b) 600 At AMMF; and, (c) 900 At17. AMMF. Figure Temperature distribution of the rotor core ( C); (a) 0 At AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF. 900 At AMMF.

The temperature distributions of the permanent magnets under different AMMF are as shown The 18. temperature distributions of thebetween permanent magnets under AMMF are as°C, shown in Figure The temperature differences the max and the different mindifferent temperature areas 0.51 0.34 The temperature distributions of the permanent magnets under AMMF are shown in in Figure 18. The temperature differences between the max and the min temperature are 0.51 °C, 0.34 °C, and 0.54 °C, respectively, which are still less than 1 °C The max temperature locates on the inner ◦ ◦ Figure 18. The temperature differences between the max and the min temperature are 0.51 C, 0.34 C, °C, and of 0.54 °C, respectively, which are still less thanespecially 1 °C The concentrates max temperature locates on the inner surface the circumferential and radial magnets, on the connection joint ◦ ◦ and 0.54 of C,the respectively, whichand are radial still less than 1 especially C The max temperature on the inner surface circumferential magnets, concentrates onlocates the connection joint with the rotor core, it is veryand different with the temperature distributions of the permanent magnets surface of the circumferential radial magnets, especially concentrates on the connection joint with with the rotor core, it is very different with the temperature distributions of the permanent magnets with copper It indicates core loss distributions is larger thanof the permanent magnet loss, and the rotor core,wires. it is very differentthat withthe therotor temperature the permanent magnets with with copper wires. It indicates that the rotor core loss is larger than the permanent magnet loss, and the heat of theItrotor core that transfers to thecore permanents. copper wires. indicates the rotor loss is larger than the permanent magnet loss, and the the heat of the rotor core transfers to the permanents. heat of the rotor core transfers to the permanents.

(a) (a)

(b) (b)

(c) (c)

Figure 18. Temperature distribution of the permanent magnets under different AMMF◦(°C); (a) 0 At Figure 18.18. Temperature distribution ofof the permanent magnets under different AMMF ( C); Figure distribution the permanent magnets under different AMMF (°C);(a)(a)0 At 0 At AMMF; (b)Temperature 600 At AMMF; and, (c) 900 At AMMF. AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF. AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF.

Figure 19 compares the rotor core temperature of the machine that was developed by using Figure compares the rotor temperature the machine that developed by using Figure 1919 compares rotor corecore temperature of theof machine that was developed by the using copper copper wires and HTSthe wires. From which, the following results could be was obtained: rotor core copper wires and HTS wires. From which, the following results could be obtained: the rotor core wires and HTS wires. From which, the following results could be obtained: the rotor core temperature temperature of the machine with copper wires increases with the increase of the AMMF; however, temperature of the machine with copper wires increases with increase of the AMMF; however, ofthe therotor machine with copper wires increases with the increase of the AMMF; however, the rotor core core temperature of the machine with HTS wires decreases firstly, and then increases as the rotor core temperature ofexplained the machine with HTSfirstly, wires decreases firstly,although and then as temperature of the machine with HTS wires and then increases as AMMF increases. AMMF increases. It could be thatdecreases for machine with copper wires, theincreases axial field AMMF increases. could be explained thatchange for machine copper wires, axial field Itflux could explained that for copper wires, although axial fieldlittle fluxthe can adjust canbe adjust theItnormal airmachine gap flux,with the of the with normal air the gap fluxalthough has influence on flux can adjust the normal air gap flux, the change of the normal air gap flux has little influence on the normal air gap flux, the change of the normal air gap flux has little influence on the rotor loss. the rotor loss. Since the loss of armature winding and the axial field winding is too large, the the rotor loss. Since the loss of armature winding and the axial field winding is too large, the Since the loss of armature winding and the axial field winding is too large, the temperature is still temperature is still determined by the armature winding and axial field winding. However, for the temperature still determined by the armature winding and axial winding. However, for the determined byisthe armature winding axial field winding. theismachine with HTS machine with HTS wires, the loss ofand armature winding andHowever, axial field fieldfor loss ignored, thus, the machine with HTS wires, the loss of armature winding and axial field loss is ignored, thus, the wires, the loss of armature winding and axial field loss is ignored, thus, the temperature distributions temperature distributions is manly determined by the stator core loss and rotor loss. From the temperature distributions manly by loss the stator core loss and rotor core loss. From the iselectromagnetic manly determined by the is stator coredetermined loss androtor rotor loss.is From the than electromagnetic calculations, calculations, we know that the far larger the stator loss. Thus, electromagnetic calculations, we know that the rotor loss is far larger than the stator core loss. Thus, the temperature distributions of the rotor are determined by the rotor loss. Thus, the little change of the rotor temperature the rotor are determined by theWhen rotor AMMF loss. Thus, the little change of the loss willdistributions reflect on theofrotor temperature distributions. increases from 0 At to the At, rotor will reflect on the rotor temperature When8.84% AMMF increases from 0 At to 600 theloss max and min temperature of rotor core distributions. decreases by about and 2.87%, respectively; 600 At, the max and min temperature of rotor core decreases by about 8.84% and 2.87%, respectively; however, while comparing temperature of rotor core of the machine with HTS wires under 900 At however, while comparing temperature rotor core of machine with HTSbywires under 900and At with that under 0 At, the max and min of temperature ofthe rotor core increases about 8.84%

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we know that the rotor loss is far larger than the stator core loss. Thus, the temperature distributions of the rotor are determined by the rotor loss. Thus, the little change of the rotor loss will reflect on the rotor temperature distributions. When AMMF increases from 0 At to 600 At, the max and min temperature of rotor core decreases by about 8.84% and 2.87%, respectively; however, while comparing temperature of rotor core of the machine with HTS wires under 900 At with that under 0 At, the max and min temperature of rotor core increases by about 8.84% and 8.05%, respectively. While under 600 At AMMF, the max rotor temperature of machine with copper wires is about 47.96% larger than Energies 2018, 11, x FOR PEER REVIEW 17 of 21 that of the machine with HTS wires. Energies 2018, 11, x FOR PEER 60 REVIEW

Temperature (℃)

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Max Temperature of Rotor-Copper Wires Min Temperature of Rotor-Copper Wires Max Temperature Wires Max TemperatureofofRotor-HTS Rotor-Copper Wires Min Temperature Wires Min TemperatureofofRotor-HTS Rotor-Copper Wires Max Temperature of Rotor-HTS Wires Min Temperature of Rotor-HTS Wires

45 50 40 35 30 25

45 40 35 30

600 900 AMMF (At) 600 900 AMMF (At) Figure 19. Comparisons Comparisonsofofthe therotor rotor core temperature of the machine developed by using Figure 19. core temperature of the machine developed by using coppercopper wires 19. Comparisons ofSuperconducting the rotor core temperature of the machine developed by using copper wires and Temperature High Temperature (HTS) andFigure High Superconducting (HTS) wires. wires. 25

0

300

0

300

wires and High Temperature Superconducting (HTS) wires.

5.2. Field for for the the Stator Stator 5.2. Temperature Temperature Field 5.2. Temperature Field for the Stator Figure describes the of the the machine machine with with HTS HTS wires. wires. From Figure 20 20 describes the stator stator temperature temperature of From which, which, we we can can Figure 20 temperature describes the stator temperature of stator the machine with HTS wires. From which, weofcan observe that the decreases from the core tooth top to the outer surface the observe that the temperature decreases from the stator core tooth top to the outer surface of the back observe that the temperature decreases from the stator core tooth top to the outer surface of the back of the stator core. The temperature of the armature windings also decreases along the radial of the stator core. The temperature of the armature windings also decreases along thealong radial direction. back of the stator core. The temperature of the armature windings also decreases the radial direction. It indicates that the heat transfer path goes from the rotor core to the enclosure by It indicates that heat transfer from the to the the normal direction. It the indicates that thepath heatgoes transfer pathrotor goescore from the enclosure rotor corebytothrough the enclosure by through the normal air-gap and the stator core. When compared with the machine operating at 0At air-gap andthe thenormal stator air-gap core. When compared with thecompared machine operating at 0At operating AMMF, the max through and the stator core. When with the machine at 0At AMMF, the max stator temperature of the machine under 600 At and 900 At decreases by about 2.93% stator temperature the temperature machine under 600machine At andunder 900 At600 decreases by At about 2.93% by and increases AMMF, the max of stator of the At and 900 decreases about 2.93% and increases 16.22%, respectively. 16.22%, respectively. and increases 16.22%, respectively.

(a) (a)

(b) (b)

(c) (c)

Figure 20. Stator temperature distributionofofthe themachine machinewith with HTS wires wires (°C); (a) 00 At (b) Figure 20. Stator Stator temperature distribution (a)AMMF; AtAMMF; AMMF; Figure 20. temperature distribution of the machine with HTSHTS wires (◦ C); (°C); (a) 0 At (b) 600(b) At 600 At AMMF; and, (c) 900 At AMMF. 600 At AMMF; (c)AMMF. 900 At AMMF. AMMF; and, (c)and, 900 At

Stator temperature machinethat thatwas wasdeveloped developed by by copper copper wires Stator temperature of of thethemachine wires and and HTS HTSwires wiresisis described, as shown Figure Forthe themachine machinewith withcopper copper wires, wires, the described, as shown in in Figure 21.21.For the differences differencesbetween betweenthe the max and min stator temperature under 0 At, 600 At, and 900 At are 9.57 °C, 9.57 °C, and 9.74 °C, max and min stator temperature under 0 At, 600 At, and 900 At are 9.57 °C, 9.57 °C, and 9.74 °C, respectively. The temperature gradient of the stator do not change as AMMF increases. However, respectively. The temperature gradient of the stator do not change as AMMF increases. However, for the machine with HTS wires, the differences between max and min stator temperature under 0 for the machine with HTS wires, the differences between max and min stator temperature under 0 At, 600 At, and 900 At are 0.35 °C, 1.04 °C, and 4 °C, respectively. The temperature gradient At, 600 At, and 900 At are 0.35 °C, 1.04 °C, and 4 °C, respectively. The temperature gradient increases with AMMF. increases with AMMF.

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Stator temperature of the machine that was developed by copper wires and HTS wires is described, as shown in Figure 21. For the machine with copper wires, the differences between the max and min stator temperature under 0 At, 600 At, and 900 At are 9.57 ◦ C, 9.57 ◦ C, and 9.74 ◦ C, respectively. The temperature gradient of the stator do not change as AMMF increases. However, for the machine with HTS wires, the differences between max and min stator temperature under 0 At, 600 At, and 900 At are 0.35 ◦ C, 1.04 ◦ C, and 4 ◦ C, respectively. The temperature gradient increases with AMMF. Energies 2018, 11, x FOR PEER REVIEW 18 of 21 Max Stator Temperature- Copper Wires Min Stator Temperature- Copper Wires Max Stator Temperature- HTS Wires Min Stator Temperature- HTS Wires

65

(℃) Temperature Temperature (℃)

60

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Max Stator Temperature- Copper Wires Min Stator Temperature- Copper Wires Max Stator Temperature- HTS Wires Min Stator Temperature- HTS Wires

4560 4055 3550 3045 2540 35

0

300

600

AMMF (At)

900

Figure 21. Comparisons of the stator temperature of the machine developed by copper wires and Figure 21. Comparisons of30the stator temperature of the machine developed by copper wires and HTS wires. HTS wires. 25

0 Field Structure 300 5.3. Temperature Field for the Axial

600

AMMF (At)

900

5.3. Temperature Field the Axial Field are Structure Since the for axial field windings excited by the dc source, if the axial field windings developed Figure 21.the Comparisons the statorloss temperature the machine developed byofcopper wires and by HTS wires, axial field of windings could beofnegligible. Thus, the loss the ferromagnetic

Sincerings the axial fieldheat windings bystructure. the dc source, the axial field windings by isHTS thewires. only source ofare theexcited axial field Figure 22ifshows the temperature field ofdeveloped the HTS wires, thefield axial field windings lossAMMF. could be negligible. thethat losstheofmax the temperature ferromagnetic rings axial structure under different From which, we Thus, can obtain 5.3. Temperature Field for theall Axial Fieldon Structure located the ferromagnetic however the min temperature is the onlyunder heatdifferent source AMMF of the are axial field structure. Figure 22rings, shows the temperature field isof the axial with the minthe temperature. The heat transfer path goes from the ferromagnetic rings to the axial field Since axial field windings are excited by the dc source, if the axial field windings developed field structure under different AMMF. From which, we can obtain that the max temperature under windings through axial air gap. by HTS wires, thethe axial field windings loss could be negligible. Thus, the loss of the ferromagnetic different AMMF are all located on the ferromagnetic rings, however the min temperature is with the Figure compares the axial temperature machine developed by copper rings is the23 only heat source of thefield axialstructure field structure. Figureof22the shows the temperature field of the min temperature. The heat path goes the ferromagnetic tothe the axial wires HTS wires.transfer For thedifferent machine with from copper wires, the between max andfield min windings axialand field structure under AMMF. From which, wedifferences can obtainrings that the max temperature temperature the axialare field structure 11.87 °C, 4.41 rings, °C, and 10.8 °C, respectively. Theis under AMMF all located on are the ferromagnetic however the min temperature through the axialdifferent air of gap. temperature gradient the The axialheat fieldtransfer structure can be adjusted AMMF. However, for with the min temperature. path goes from the by ferromagnetic rings to the axial field Figure 23 compares theof axial field structure temperature ofchanging the machine developed by copper the machine with HTS wires, windings through the axial airthe gap.differences of the max and min temperature of the axial field wires andwindings HTSFigure wires. For the machine withstructure copper wires, theofdifferences between the max and min are 23 8.98 °C, 6.63 °C, axial and 11.72 respectively. It indicates the influence of by thecopper axial compares the field °C, temperature the that machine developed ◦ C, 4.41 ◦ C, and 10.8 ◦ C, respectively. The temperature temperature of the axial field structure are 11.87 field winding loss on the temperature gradient is very small. wires and HTS wires. For the machine with copper wires, the differences between the max and min of thestructure axial fieldcan structure are 11.87 4.41 °C, and 10.8 °C, respectively. The machine gradient oftemperature the axial field be adjusted by°C, changing AMMF. However, for the temperature gradient of the axial field structure can be adjusted by changing AMMF. However, with HTS wires, the differences of the max and min temperature of the axial field windingsfor are 8.98 ◦ C, the machine with HTS wires, the differences of the max and min temperature of the axial field ◦ ◦ 6.63 C, andwindings 11.72 are C, respectively. It indicates that the influence of the axial field winding loss on the 8.98 °C, 6.63 °C, and 11.72 °C, respectively. It indicates that the influence of the axial temperature gradient very small. field windingis loss on the temperature gradient is very small.

(a)

(b)

(c)

Figure 22. Temperature distribution of the axial field structure under different AMMF (°C); (a) 0 At AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF.

(a)

(b)

(c)

Figure 22. Temperature distribution of the axial field structure under different AMMF (°C); (a) 0 At

Figure 22. Temperature distribution theAt axial field structure under different AMMF (◦ C); (a) 0 At AMMF; (b) 600 At AMMF; and, of (c) 900 AMMF. AMMF; (b) 600 At AMMF; and, (c) 900 At AMMF.

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Max Temp of Axial Field Structure - Copper Wires Min Temp of Axial Field Structure - Copper Wires Max Temp of Axial Field Structure - HTS Wires Min Temp of Axial Field Structure - HTS Wires

60 Temperature (℃)

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55 50 45 40 35 30 25 0

300

AMMF (At)

600

900

Figure 23. Comparisons of the axial field structure temperature of the machine developed by copper Figure 23. Comparisons of the axial field structure temperature of the machine developed by copper wires and HTS wires. wires and HTS wires.

6. Conclusions

6. Conclusions

In this article, a new axial-radial flux-type permanent magnet synchronous motor is presented;

In article, new axial-radial flux-type permanent magnet synchronous motor is presented; thethis normal air a gap flux can be adjusted by changing the axial magnetic motive force. Firstly, the the normal air gap flux can be adjusted by changing the axial magnetic motive force. Firstly, temperature distribution of machine components under different AMMF are investigated, and then while considering the HTS applications, the temperature distributions of the machine that and was then the temperature distribution of machine components under different AMMF are investigated, by using copper wires and HTS are also comparatively Based onthat the was whiledeveloped considering the HTS applications, thewires temperature distributionsanalyzed. of the machine analyses, the following conclusions can be obtained: developed by using copper wires and HTS wires are also comparatively analyzed. Based on the analyses, the following conclusions cancarried be obtained: 1. Validated by the experiments out on the prototype, the differences between the 1.

2.

3.

4.

calculations and the measurements of the end armature temperature and enclosure are 1.05 °C

Validated by the experiments carried out on the prototype, the differences between the and 0.96 °C, respectively. It indicates that the established models and the presented ◦ calculations and the measurements of the end armature temperature and enclosure are 1.05 C assumptions are reasonable for the thermal analysis of ARFTPMSM. ◦ and For 0.96machine C, respectively. It wires, indicates that the established models and the presented assumptions 2. with copper although AMMF can adjust the normal air gap flux density, but are reasonable for the thermal analysis of ARFTPMSM. it can also increase the harmonic components of the normal air gap flux density. Thus, the temperature ofcopper machinewires, components increases as can AMMF increases, e.g., the For machine with although AMMF adjust the normal airmax gaptemperature flux density,ofbut it the rotor corethe of harmonic the machine under 600 At andnormal 900 At air AMMF increases by about °C and can also increase components of the gap flux density. Thus, 4.09 the temperature 12.42 °C,components respectively,increases while when compared with thee.g., machine withtemperature 0 At AMMF. of While AMMF of machine as AMMF increases, the max the rotor core of rises from 0 At to 600 At, the average temperature of armature windings increases about 6.9%; ◦ ◦ the machine under 600 At and 900 At AMMF increases by about 4.09 C and 12.42 C, respectively, however, while AMMF rises from 600 At to 900 At, the average temperature increases about while when compared with the machine with 0 At AMMF. While AMMF rises from 0 At to 600 At, 15.2%. the average temperature of armature windings increases about 6.9%; however, while AMMF rises 3. While the machine is developed by HTS wires, the temperature distribution is quite difference fromwith 600 the At to 900 At,with the average temperature 15.2%.distribution of rotor, the machine copper wires. Viewingincreases from the about temperature While therotor machine is developed by HTS temperature distribution is quite difference max temperature of machine withwires, copperthe wires is about 47.96% larger than that of the with HTS thatwires. are under 600 Atfrom AMMF. withmachine the machine withwires copper Viewing the temperature distribution of rotor, the max 4. the machine with copper differences betweenlarger the max rotorFor temperature of machine with wires, copperthe wires is about 47.96% thanand that min of thestator machine temperature under 0 At, 600 At, and 900 At are 9.57 °C, 9.57 °C, and 9.74 °C, respectively. The with HTS wires that are under 600 At AMMF. temperature gradient do not change as AMMF increases. However, for a machine with HTS For the machine with copper wires, the differences between the max and min stator temperature wires, the differences between max and min stator temperature under 0 At, 600 At, and 900 At under 0 At, 600 At, and 900 At are 9.57 ◦ C, 9.57 ◦ C, and 9.74 ◦ C, respectively. The temperature are 0.35 °C, 1.04 °C, and 4 °C, respectively. The temperature gradient increases as AMMF. gradient do not change as AMMF increases. However, for a machine with HTS wires, the differences between max and min stator temperature under 0 At, 600 At, and 900 At are 0.35 ◦ C, 1.04 ◦ C, and 4 ◦ C, respectively. The temperature gradient increases as AMMF.

Author Contributions: D.L. has done the electromagnetic and thermal analyses and supervised the entire process for the paper, Y.W. provides the analysis method for the axial field magnetic motive force, W.L. provides the thermal calculation method. B.F. has done the electromagnetic and loss analyses. And J.C. has done the equivalent process of the material thermal conductivity. Funding: This research was funded by National Natural Science Foundation of China (51577007) and Fundamental Research Funds for the Central Universities (2015RC016).

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Conflicts of Interest: The authors declare no conflict of interest.

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