Integrated Design of a High Speed Magnetic Levitated Brushless Direct Current Motor System

energies

Article Integrated Design of a High Speed Magnetic Levitated Brushless Direct Current Motor System

Gang Liu 1,2 and Xu Liu 1,2,* ID

1 School of Instrumentation Science and Optoelectronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China; [email protected] 2 Beijing Engineering Research Center of High-Speed Magnetically Suspended Motor Technology and Application, Beijing University of Aeronautics and Astronautics, Beijing 100191, China * Correspondence: [email protected] or [email protected]; Tel.: +86-010-8233-9106

Received: 4 April 2018; Accepted: 10 May 2018; Published: 12 May 2018

Abstract: High speed magnetic levitated brushless direct current motor system mainly consists of a motor, a rotor and two magnetic bearings. New ideas demonstrate advances in the design of integration interface and selection of the dynamic design parameters. In this paper, integrated design procedure is interpreted, considering the structural, electromagnetic and thermal aspects with their contradiction and integration. The motor design is set as the initial design entrance to determine its stator diameters with other key parameters as dynamic design parameters. Then, magnetic bearing design is set as the interface for rotor, with magnetic bearings’ diameters and lengths determined. So, all the dynamic parameters will be specified considering rotor dynamics and the corresponding strength/thermal analysis. Finally, several validations including finite element method and experiment, have been carried out. Prototype of this maglev motor system has been designed and manufactured, with sufficient experiment processes validated. It rotates over 55,332 rpm under load with drag system, corresponding to above design results.

Keywords: design methodology; integrated design; brushless machines; FEM; magnetic bearing

1. Introduction With advances in active magnetic bearing (AMB) [1,2], electronic converters, new material, and control strategy, limitation of speed for rotating machines got a greatly improvment [3,4]. High speed maglev electric motors are widely and increasingly applied in various industrial applications [5–9]. The advantages gained by such high-speed motors with AMBs are that of being able to increase efficiency and reliability by removing bearing lubrication and suppressing rotor vibration, resulting in decrease of sizes [7]. No mechanical wearing parts or lubricants are utilized in magnetic levitated motor (MLM) thus further lessening life cycle costs [8]. Such MLMs have been applied in several different types such as turbo-machinery, centrifugal compressors, turbo-molecular pumps, turbo refrigerant compressors, turbo-expanders, and engine waste-heat recovery [9]. The performance of high speed MLM is much more improved by advanced design guidelines, better reliability of materials, and precisely manufacturing [2]. Further, volume constrains [2], need for heat dissipating [10], and stability control constrains of AMB-rotor [11] are main issues for design of MLMs. High-speed induction machine (IM) have some challenges in design procedure [2,10]. Brushless direct current motor (BLDCM) offer many advantages such as high-power density, high efﬁciency and low temperature rise etc. [12]. Therefore, design approaches for high-speed BLDCM are proposed [11], including multidisciplinary impact on its performance. There are more technical problems for MLMs than some other high speed machines [13], because the motor part and MBs of MLM all needed analyze

Energies 2018, 11, 1236; doi:10.3390/en11051236 www.mdpi.com/journal/energies EnergiesEnergies 20182018,, 1111,, 1236x FOR PEER REVIEW 22 ofof 2524

MLM all needed analyze and design [14]. Above all, design methods mentioned in above literatures andcan determine design [14]. initial Above design all, design parameters methods for mentioned high speed in motors above literatures[14–17]. can determine initial design parametersHigh-speed for high rotor speed of MLM motors is [suspended14–17]. by AMBs in five degree-of-freedom (DOF) directions, whichHigh-speed is driven by rotor a high of MLM-speed is IM suspended or BLDCM. by AMBs A high in-speed ﬁve degree-of-freedom MLM for ultra-centrifuge (DOF) directions, has been whichstudied is [18]. driven Various by a high-speed topologies IM of high or BLDCM.-speed motors A high-speed are applied MLM for for some ultra-centrifuge industrial or has science been studiedapplications [18]. [19] Various with different topologies control of high-speed technologies motors and design are applied methods. for someIn addition, industrial MLM or for science turbo applicationsmolecular vacuum [19] with pump different with fault control-tolerant technologies magnetic andbearings design has methods. been manufactured In addition, and MLM applied for turbo[20]. C molecularonfiguration vacuum of MLM pump for withturbo fault-tolerant refrigerant compressor magnetic bearings has been has researched been manufactured [21]. An active and appliedRMB is [20 developed]. Conﬁguration for high of-speed MLM forturbo turbo-machinery refrigerant motors compressor [22]. However, has been researched few literatures [21]. Ansystematically active RMB and is developed sequentially for high-speed introduce the turbo-machinery integration design motors guidelines [22]. However, for maglev few literatures BLDCM, systematicallyespecially for comprehensive and sequentially consideration introduce theof BLDCM integration and magnetic design guidelines bearings. for maglev BLDCM, especiallyAccounting for comprehensive for above consideratio considerationns, of this BLDCM paper and proposes magnetic integrated bearings. design procedures and tests Accountingof the maglev for BLDCM above considerations,system, which consists this paper of a proposeshigh-speed integrated rotor and design three stators procedures for radial and testsmagnetic of the bearing maglev (RMB) BLDCM [23 system,,24], combined which consists radial of-axial a high-speed magnetic rotor bearing and (CRAMB)three stators [25] for, radialand a magneticbrushless bearing DC motor (RMB) respectively [23,24], combined (Figure radial-axial 1).Here, magnetic ideas about bearing integration (CRAMB) design [25], and interface a brushless and DCdynamic motor design respectively parameters (Figure are1).Here, put forward. ideas about Mechanical, integration electromagnetic design interface and and thermal dynamic aspects design are parametersall synthesized are putfor forward.their contradiction Mechanical, and electromagnetic integration. The and motor thermal design aspects is set are as all the synthesized initial design for theirentrance, contradiction to determine and integration.the outer and The inner motor diameters design isofset stator as the with initial other design key parameters entrance, to as determine dynamic thedesign outer parameters. and inner diametersThen, MBs of design stator is with set otheras the keyinterface parameters for rotor, as dynamic with MBs’ design diameters parameters. and lengths Then, MBsdetermined. design isConst set asrains the interfaceabout rotor for rotor,diameters with MBs’among diameters MBs and and motor lengths are determined.established. ConstrainsWith rotor aboutdynamic, rotor strength diameters analysis among and MBs thermal and motor design are implemented, established. left With dynamic rotor dynamic, parameters strength are set. analysis Finite andelement thermal method design (FEM) implemented, is used for left validating dynamic parametersdesign model. are set. A prototype Finite element of maglev method BLDCM (FEM) is is usedmanufactured, for validating with design 1.21 kW/kg model. power A prototype density, of rotating maglev to BLDCM 33 kW, is 55 manufactured,,332 rpm under with load 1.21 with kW/kg drag powersystem. density, The contradictions rotating to 33 among kW, 55,332 various rpm requirements under load with and drag coupling system. effects Thecontradictions among multiphysics among variousare also requirements reflected. Finally, and coupling design results effects amongobtained multiphysics by above design are also methods reflected. are Finally, validated design by results drag obtainedtest and MBs’ by above stiffness design test methods [23–25] areto finish validated close byd loop drag of test the and whole MBs’ integration stiffness test design [23–25 procedure.] to finish closedIntegrated loop design of the wholemethod integration needs to be design reflected. procedure. Integrated design method needs to be reflected.

Motor RMB

CRAMB

TDB Rotor

Figure 1. The structure of the 30 kW MLBLDCM.MLBLDCM.

2. Determination of Structure and Design Process 2. Determination of Structure and Design Process The innovation of this work mainly focuses on comprehensive consideration of BLDCM and The innovation of this work mainly focuses on comprehensive consideration of BLDCM and magnetic bearings. The whole frame structure is determined based on mature experience. The design magnetic bearings. The whole frame structure is determined based on mature experience. The design procedure is initialized from electromagnetic torque of motor and suspending force of magnetic procedure is initialized from electromagnetic torque of motor and suspending force of magnetic bearings. The dynamic parameters are transferred among different design aspects to integrate

Energies 2018, 11, 1236 3 of 25 Energies 2018, 11, x FOR PEER REVIEW 3 of 24 bearings.engineering The requirements dynamic parameters of BLDCM and are transferredmagnetic bearings. among The different design design parameters aspects areto determined integrate engineeringafter strength requirements and thermal of analysis. BLDCM and magnetic bearings. The design parameters are determined after strength and thermal analysis. 2.1. The Establishment of the Whole Frame Structure 2.1. The Establishment of the Whole Frame Structure Schematic section view of the maglev BLDCM system is shown in Figure 1, in which the structureSchematic of it is section mature view and ofapplied the maglev in industrial BLDCM compressor system is shown and blower in Figure [26].1 ,The in which permanent the structure magnet ofbiased it is mature hybrid and magnetic applied bearings in industrial are chosen compressor for reducing and blower power [26 ]. loss The [21] permanent. The CRAMB magnet not biased only hybridlevitates magnetic rotor inbearings radial direction are chosen with for RMB, reducing but also power stabilizes loss [21 ].it Thein axial CRAMB direction. not only It is levitates proposed rotor for inlessening radial direction axial size with to improve RMB, but rotor also dynamic stabilizes performance it in axial direction. [26]. Thus, It isthe proposed volume is for shrunk. lessening Besides axial, sizethe to touch improve-down rotor bearing dynamic (TDB) performance protects rotor [26]. Thus, from the sudden volume falling. is shrunk. Sizes Besides, of MBs the and touch-down motor are bearingdesigned (TDB) coordinate protectsly rotorand fromintegrate suddendly, falling. to satisfy Sizes the of limits MBs and and motor requirements are designed of whol coordinatelye system andincluding integratedly, rotor’s tosize, satisfy volume the limitsand multi and- requirementsdomain performance. of whole For system electromagnetic including rotor’s performance size, volume and anddynamic multi-domain performance, performance. the rotor For diameters electromagnetic for MBs performanceand motor are and integrated dynamic performance,to design sequentially the rotor diametersvia dynamic for variables. MBs and motor are integrated to design sequentially via dynamic variables. AccountingAccounting for for resonance resonance suppression suppression control control of rotor of rotor vibration, vibration, cylindrical cylindrical solid shape solid is shape chosen is forchosen permanent for permanent magnet magnet (PM) instead (PM) ofinstead the block of the structure. block structure.

2.2.2.2. DesignDesign MethodologyMethodology forfor MaglevMaglev BLDCMBLDCM SystemSystem FirstFirst of of all, all, design design objectives objectives are are selected, selected, such such as as rotation rotation speed, speed, power power density density and and other other engineeringengineering design design objectives objectives also also including including the MB’s the maglevMB’s maglevforce. Then, force. design Then, limits design are determined, limits are suchdetermined, as limited such strength as limited of sleeve, strength temperature of sleeve, rise temperature capacity, magnetic rise capacity, suspend magnetic force of suspend MB, ﬂux force density of inMB, laminations flux density of in MB laminations and BLDCM, of MB and and natural BLDCM, frequency and natural of rotor. frequency All of limits of rotor. have All contradictions. of limits have Forcontradictions. example, demand For example, for high-power demand for leads high to-power increases leads of to winding increases coil of winding numbers coil and numbers permanent and magnetpermanent volume, magnet however, volume, demand however, for high demand power for density high power make decreasesdensity make of them decrease as Figures of2 them shows. as SoFigure they 2are shows. to be solvedSo they via are sequential to be solved design via interfaces, sequential by design means interfaces, of dynamic by variables means of(marked dynamic as yellowvariables color (marked in Figure as yellow3), which color are in mainly Figure innovative 3), which integrationare mainly innovative strategy. integration strategy.

Electromagnetic load

High power Thermal load Geometry size

Number of coil turns

High speed Rotor strength

Rotor modal

Temperature rise High power density Geometry size

Figure 2. Contradiction and integration in design procedure of maglev BLDCM. Figure 2. Contradiction and integration in design procedure of maglev BLDCM.

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Design requirement: electrical and mechanical loadings

Integration Design Variables and Objectives

Power density BLDCM Maximum speed Dynamic variables MB Suspending Force outer-diameters of rotor and PM thickness of PM Slot notch width Design Constraints Rotor Temperature rise dynamics Rotor stress Thermal Rotor natural frequency

Obtain design results Yes No Satisfy Yes Satisfy No constraints？ design objective？

Figure 3. Integrated design procedure for maglev BLDCM system. Figure 3. Integrated design procedure for maglev BLDCM system.

The integrated design strategy and the whole design process are express of the integration The integrated design strategy and the whole design process are express of the integration design design idea, as Figure 3 shows. The entire design is divided into four main design modules (marked idea, as Figure3 shows. The entire design is divided into four main design modules (marked as as red in Figure 3): brushless DC motor electromagnetic design, magnetic bearing electromagnetic red in Figure3): brushless DC motor electromagnetic design, magnetic bearing electromagnetic design, rotor dynamics design and thermal design. In order to ensure the output performance such design, rotor dynamics design and thermal design. In order to ensure the output performance such as as electromagnetic power and bearing capacity of the whole system, BLDCM and MB design module electromagnetic power and bearing capacity of the whole system, BLDCM and MB design module are are selected as the initial module to determine the size range of dynamic variables (marked as yellow selected as the initial module to determine the size range of dynamic variables (marked as yellow in in Figure 3), which are passed to other design modules. So the initial design of the motor and Figure3), which are passed to other design modules. So the initial design of the motor and magnetic magnetic bearing is carried out first, the analysis model and related methods are used for the initial bearing is carried out ﬁrst, the analysis model and related methods are used for the initial design of design of the motor [11,27], and MBs [24,28]: the motor [11,27], and MBs [24,28]: EM 24 TBLDAmax√ 2  ef si c 10 / 4 (1) EM 2 −4 Tmax = 2πBδ Le f Dsi Ac × 10 /4 (1)  fb k i i k s x   fk= k i AN+ 22k ixcos / x   bib0i s 0 0 (2)  22 22 3 ki = µ0 AN i0cosαb/x (2) ksb0 AN i 0cos / 0 x 0  2 2 3  ks = −µ0 AN i0cosαb/x0 Formula (1) is used for initial design of motor, where Dsi is determined based on demand for Formula (1) is used for initial design of motor, where D is determined based on demand for electromagnetic torque and power. The outer diameter and si stator length are all set by tradition electromagnetic torque and power. The outer diameter and stator length are all set by tradition experience and electromagnetic torque requirement. Formula (2) is used for initial design of MB. It experience and electromagnetic torque requirement. Formula (2) is used for initial design of MB. focuses on maglev force which is affected by stator sizes, as detailed in Section 3.2. Maglev force is It focuses on maglev force which is affected by stator sizes, as detailed in Section 3.2. Maglev force is determined by ki and ks, which are verified in Section 4.2. determined by k and k , which are veriﬁed in Section 4.2. Next, in orderi tos keep consistency of outer-diameters for rotor’s different part, the Next, in order to keep consistency of outer-diameters for rotor’s different part, the corresponding corresponding outer rotor diameter for MB and motor is set as the dynamic variable. The thickness outer rotor diameter for MB and motor is set as the dynamic variable. The thickness of the permanent of the permanent magnet, which affects the output performance, and the thickness of sleeve that magnet, which affects the output performance, and the thickness of sleeve that affects the mechanical affects the mechanical properties of the rotor are also set as dynamic variables. The slot size of the properties of the rotor are also set as dynamic variables. The slot size of the motor stator is also motor stator is also set as dynamic variable since it affects magnetic circuit of motor and the eddy current loss of rotor. After these dynamic variables are transmitted to the rotor design module and

Energies 2018, 11, 1236 5 of 25 set as dynamic variable since it affects magnetic circuit of motor and the eddy current loss of rotor. After these dynamic variables are transmitted to the rotor design module and thermal analysis module, theirEnergies ranges 2018 are, 11 determined, x FOR PEER REVIEW comprehensively via the combination of curves about performance5 of 24 parameters varied the rotor core diameter. These performance parameters are explained and verified thermal analysis module, their ranges are determined comprehensively via the combination of curves by FEMabout in Sectionperformance 3.3 including parameters the varied rotor the stress, rotor modal, core diameter. total loss, These and perf bearingormance capacity. parameters Performance are curvesexplained in thermal and designverified moduleby FEM in [29 Section] in Section 3.3 including 3.4 reflect the rotor relationships stress, modal, about total harmonicloss, and bearing distortion rate, outputcapacity. torque, Performance temperature curves in rise thermal and powerdesign densitymodule [29] varying in Section by air-gap 3.4 reflect length. relationships Above about processes of selectingharmonic design distortion points rate, via output dynamic torque, variables, temperature according rise and to power the curves density of varying various by performance air-gap parameters,length. Above are also processes the key of innovationselecting design of thispoints paper. via dynamic Finally, variables, dynamic according variables to the are curves determined of by meansvarious of performance the rotor dynamics parameters, design are also and the thermal key innovation design of modules.this paper. AsFinally, a result, dynamic the variables design flow of theare entire determined Maglev by motor means is of completed the rotor dynamics and entered design into and prototypethermal design manufacturing, modules. As a assemblyresult, the and design flow of the entire Maglev motor is completed and entered into prototype manufacturing, experimental testing, as described in Section4. assembly and experimental testing, as described in Section 4. Specific design variables are shown in Figure4. They are all critical dimensions such as inner Specific design variables are shown in Figure 4. They are all critical dimensions such as inner diameterdiameter of motor of motor stator stator and and pole pole lengthlength of of MB’s MB’s stator, stator, which which affect affect performance. performance. Stator sizes Stator are sizes are determineddetermined by by InitialInitial design. Rotor Rotor sizes sizes and and slot slot notch notch width width areare set set as asdynamic dynamic variables variables as as mentionedmentioned above. above.

Bs0 Hs0 Hs1 Bs1

Hs2

Bs2 X1

X4 X2

X5 (a)

l8 d8 d9

l9 d10 d11

d12

(b) l1 l2l3l4 l5 l4

l6 d 2 l7 d 3 d1

1 2 3 4 5 6 7 d d d d d d d

(c)

FigureFigure 4. Design 4. Design variables variables of theof the maglev maglev BLDCM BLDCM system:system: ( (aa)) Design Design variables variables of BLDCM; of BLDCM; (b) Design (b) Design variablesvariables of RMB; of RMB; (c) Design (c) Design variables variables of of CRAMB. CRAMB.

Energies 2018, 11, 1236 6 of 25

3. Design Process for Magnetic Levitated BLDCM

3.1. Electromagnetic Design of the High Speed BLDCM For this BLDCM, the PM is magnetized in parallel with two poles for high energy density and well sine wave of air-gap ﬂux density [19]. The BLDCM is designed for rated power 30 kW with highest speed 60,000 rpm. For coordinating electromagnetic and mechanical performance, the outer diameter and thickness of PM, and the outer diameter of rotor are set as dynamic variables, namely, key sizes left to determine in Sections 3.3 and 3.4. After initial design via Formula (1) for BLDCM [11], diameters and length of motor stator are set. Three dynamic variables left as Table1 shows and they are to be solved with MB design and mechanical design in the following Parts.

Table 1. Initial design parameters consisting of key sizes for BLDCM.

Motor Parameters Variables Design Value

Outer diameter of stator (mm) x1 178 Inner diameter of stator (mm) x2 67.6 Stator length (mm) x3 60 Outer diameter of rotor (mm) x4 (Dynamic variable) Outer diameter of PM (mm) x5 (Dynamic variable) Thickness of PM (mm) x6 (Dynamic variable)

With losses calculated by (4) and (5), the initial design parameters are defined as Table1 shows. They are set as design interface for MBs design, rotor design, and thermal design, to coordinate various requirements interactively. Back-EMF (electro-motive-force) of BLDCM Vemf, related to flux density and angular speed, is calculated by [30]: I I Vem f = Ns Edl = Ns (ω × B)dl (3) c c B is the flux density analyzed by electromagnetic equations of BLDCM. The maximum value of B is calculated as 0.35 T. The result of back-EMF coefficients are 0.0677 Vs/rad, which would be validated via deceleration EMF test in Section 4.1. The general solutions for back-EMF and the flux density distribution in air-gap are introduced in [31] in detail. Then, electromagnetic field equation is modeled. In addition the eddy current expression, including varieties of harmonic components penetrating into the whole surface of the rotor, can be deduced from equivalent current sheet [31]. Thus, based on the Poynting vector theory, the corresponding average electromagnetic power loss in rotor is given by [27]:

1 I h . . ∗i 1 Z αn2 . . H pr = Re E × H ds = ∑ Re Jz Hα LaRdθ (4) 2 s 2σr n αn1 r=rn

Because of obvious inﬂuence on eddy current loss (ECL) exerted by outer diameter of rotor and slot notch width, these two variables are set as dynamic variables. They are to be solved by means of mechanical and thermal analysis in following parts, jointly. Besides, core loss in stator can be calculated via [32]:

∞ ∞ 1.5 1.5 = + + = α + α + 2 2 2 + 2 + Ke 1 R T dBr(t) + dBθ (t) P Ph Pc Pe Kh f ∑ k Bkmax Bkmin Kc f ∑ k Bkmax Bkmin 3 T 0 dt dt dt (5) k=0 k=0 (2π) 2

The stator is divided into several subdomains, such as yoke and tooth, to get ﬂux discs, as Figure5 shows. Then Bkmax and Bkmin are obtained via Elliptic Fourier operator on each elliptic loci of ﬂux discs shown in Figure5 by algorithm. Energies 2018, 11, 1236 7 of 25

Energies 2018, 11, x FOR PEER REVIEW 7 of 24

)

( T tooth root 1 (

By 1 Stator yoke By

0 0 -1 0 1 -1 0 1 Bx (T) Bx (T)

-1

)

T (

1 1

)

( By

0 0 -1 0 1 -1 0 1 Bx (T) Bx (T)

tooth body -1 -1 tooth tip

Figure 5. Flux disc in standard parts of stator. Figure 5. Flux disc in standard parts of stator. Since size of yoke like outer diameter has been determined in initial design via Formula (1), the Since size of yoke like outer diameter has been determined in initial design via Formula (1), slot sizes are determined here via core loss by (5). Kh, Kc, Ke, varying by frequency of excitation current theand slotthickness sizes areof lamination, determined are here got via by core BP fitting loss by method (5). Kh, asK cTable, Ke, varying 2 shows. by frequency of excitation current and thickness of lamination, are got by BP fitting method as Table2 shows. Table 2. Core loss average coefficients. Table 2. Core loss average coefficients. Core Loss Average Coefficients Material (Craftwork) High FrequencyCore (3 Loss–5 kHz) Average Low Coefficients Frequency (0.2–1 kHz) Kh Kc Ke Kh Kc Ke Material (Craftwork) High Frequency (3–5 kHz) Low Frequency (0.2–1 kHz) 20WTG 0.2 mm (stamping, annealing) 464.9 0.12 0.92 216.7 0.47 0.79 20WTG 0.35 mm (stamping, annealing)Kh 405.4K c 0.27 0.19Ke 163.9 Kh 0.64 Kc 0.29 Ke 20WTG 0.2 mm (stamping, annealing) 464.9 0.12 0.92 216.7 0.47 0.79 20WTG 0.35 mm (stamping, annealing) 405.4 0.27 0.19 163.9 0.64 0.29 In Table 2, the steel lamination made of 20WTG with 0.2 mm thickness is adopted, whose α = 1.62 in low frequency. By means of the Formula (4) and (5), and core loss coefficients in Table 2, the ECL Inand Table core2 ,loss the steelcan be lamination calculated, made which of 20WTGis used for with estimat 0.2 mme efficiency thickness and is adopted, thermal whose heat source.α = 1.62 in lowBased frequency. on above By calculation, means of the as FormulaTable 3 shows, (4) and the (5), ECL and is core 289 lossW, and coefficients the core inloss Table is 1872, theW when ECL andthe machine core loss operates can be calculated, at 48,000 rpm. which The is loss used values for estimate are set as efficiency the design and interfaces thermal heatfor thermal source. design, becauseBased losses on aboveare heat calculation, source for as thermal Table3 calculationshows, the ECLand simulation. is 289 W, and Temperature the core loss rise is 187of motor W when got theby thermal machine analysis operates completes at 48,000 rpm.the design The loss loop values to improve are set as the the integration design interfaces design forprocedure thermal (which design, becausehas been losses shown are in heatFigure source 2). for thermal calculation and simulation. Temperature rise of motor got by thermal analysis completes the design loop to improve the integration design procedure (which has been shown in Figure2). Table 3. ECL and core loss of motor.

Loss 48,000 rpm (No-Load) 60,000 rpm (No-Load) 48,000 rpm (Under-Load) 60,000 rpm (Under-Load) Table 3. ECL and core loss of motor. ECL (W) 27 38 289 389 Core loss (W) 15 26 187 317 Loss 48,000 rpm (No-Load) 60,000 rpm (No-Load) 48,000 rpm (Under-Load) 60,000 rpm (Under-Load) ECL (W) 27 38 289 389 InCore Table loss (W) 4, x9 is left 15as dynamic variable, 26 for it affects ECL 187 obviously, so which 317 is to be solved after thermal analysis.

In Table4, x9 is left as dynamic variable, for it affects ECL obviously, so which is to be solved after Table 4. Design parameters of slot for BLDCM. thermal analysis. Slot Parameters Variables Design Value Slot notch height Hs0 (mm) x6 0.5 Slot shoulder height Hs1 (mm) x7 0.6 Slot body height Hs2 (mm) x8 24 Slot notch width Bs0 (mm) x9 (Dynamic variable) Slot upper width Bs1 (mm) x10 5.6 Slot bottom width Bs2 (mm) x11 11.34

Energies 2018, 11, 1236 8 of 25

Table 4. Design parameters of slot for BLDCM.

Slot Parameters Variables Design Value

Slot notch height Hs0 (mm) x6 0.5 Slot shoulder height Hs1 (mm) x7 0.6 Slot body height Hs2 (mm) x8 24 Slot notch width Bs0 (mm) x9 (Dynamic variable) Slot upper width Bs1 (mm) x10 5.6 Energies 2018, 11, x FOR SlotPEER bottom REVIEW width Bs2 (mm) x11 11.34 8 of 24

3.2.3.2. Electromagnetic Design of the MBs The actively controlled RMB and CRAMB are proposed for reducing power consumption, decreasing weight, increasing power density, and making dynamic performance of the rotor more robust reliabilityreliability andand activeactive controllability.controllability. The RMB with electromagnetic biasbias is adopted. For control performance, the RMB stator consists of soft magnetic laminations with eight poles and coils spaced equally, of which two of them are comprised for one positivepositive or negativenegative direction polepole in series.series. The RMB’s magnetic fluxflux path and configurationconfiguration are shown in Figure6 6[ [2323–25].]. The design model is established,established, as Formula (2) shows shows,, based on that magnetic fluxflux model,model, withwith designdesign parametersparameters shownshown asas TableTable5 .5.

N S

S N

N S

S N

Figure 6. Section view showing conﬁgurationconfiguration sketch and ﬂuxflux paths ofof RMB.RMB.

Table 5.5. DesignDesign parametersparameters forfor RMB.RMB. Parameters Description Design Value Parameters Description Design Value d9 inner radius of the stator yoke (mm) 129 dd129 Innerinner radiusradius of of the the stator RMB yoke rotor (mm) (mm) 12938 d12 Inner radius of the RMB rotor (mm) 38 d10 Outer radius of the pole shoe (mm) 86 d10 Outer radius of the pole shoe (mm) 86 d11 Inner radius of the pole shoe (mm) X4 + δb d11 Inner radius of the pole shoe (mm) X4 + δb dd88 OuterOuter radius ofof the the RMB RMB stator stator (mm) (mm) 140.5140.5 l8l8 WidthWidth of thethe toothtooth of of stator stator core core (mm) (mm) 7.57.5 l Width of the pole shoe (mm) 9 l99 Width of the pole shoe (mm) 9 l10 Thickness of the stator (mm) 23 l10 Thickness of the stator (mm) 23 B0 Bias flux density in air gap (T) 0.65 BB01 ControlBias flux flux density density in air gapgap (T) (T) 0.520.65 B1 Control flux density in air gap (T) 0.52 The simplified expression of radial force of RMB is obtained after its nonlinear terms over second The simplified expression of radial force of RMB is obtained after its nonlinear terms over second order are neglected. Besides, this principle has also been applied for deduction of magnetic force of order are neglected. Besides, this principle has also been applied for deduction of magnetic force of CRAMB in the followings. As a result, the total magnetic radial levitated force can be got by Formula (2), which is deduced from (6). Calculation values of current stiffness and position stiffness at rotor center position are 180 N/A and 587.1 N/mm respectively. They are to be validated by stiffness experiment in Section 4.2 to form a complete closed design loop for whole design procedure. A CRAMB is proposed in this paper for its small thrust disk and axial size, and low wind friction power consumption. Figure 7 illustrates the configuration and flux paths in CRAMB. It consists of RMB and thrust MB (TMB) units. Radial coils and axial coils generate control flux (indicated as blue dotted line), while the PM provides bias flux (indicated as green line). The similar structure of this CRAMB has been presented and analyzed in [21]. Its RMB unit is also designed by (2). Design parameters of CRAMB are shown in Table 6.

Energies 2018, 11, 1236 9 of 25

CRAMB in the followings. As a result, the total magnetic radial levitated force can be got by Formula (2), which is deduced from (6). Calculation values of current stiffness and position stiffness at rotor center position are 180 N/A and 587.1 N/mm respectively. They are to be validated by stiffness experiment in Section 4.2 to form a complete closed design loop for whole design procedure. A CRAMB is proposed in this paper for its small thrust disk and axial size, and low wind friction power consumption. Figure7 illustrates the configuration and flux paths in CRAMB. It consists of RMB and thrust MB (TMB) units. Radial coils and axial coils generate control flux (indicated as blue dotted line), while the PM provides bias flux (indicated as green line). The similar structure of this CRAMB has been presented and analyzed in [21]. Its RMB unit is also designed by (2). Design parameters of EnergiesCRAMB 2018 are, 11, shown x FOR PEER in Table REVIEW6. 9 of 24

Radial coil Magnetic ring S N PM Axial air gap Radial air gap y

z x

Bias flux Radial control flux Axial control flux Axial coil

Figure 7. Configuration of the CRAMB with its flux paths. Figure 7. Conﬁguration of the CRAMB with its ﬂux paths.

Table 6. Parameters and design variables of the CRAMB. Table 6. Parameters and design variables of the CRAMB. Parameters Description Values Parametersd1 Outer diameter Description of stator (mm) Values116 d2 d1 Inner diameterOuter of diameter magnetic of conducting stator (mm) ring (mm) 116106 d3 d2 Inner diameterInner diameter of magnetic of conducting yoke (mm) ring (mm) 106104 d3 Inner diameter of yoke (mm) 104 d4 Inner diameter of stator (mm) x4 + δb d4 Inner diameter of stator (mm) x4 + δb d5 Outer diameter of axial window (mm) 112 d5 Outer diameter of axial window (mm) 112 d6 d6 OuterOuter diameter diameter of thrust diskdisk (mm) (mm) 7575 d7 d7 InnerInner diameter diameter of of axial windowwindow (mm) (mm) 6565 l The axial length of radial stator (mm) 16.5 l1 1 The axial length of radial stator (mm) 16.5 l2 Length of magnetic guide ring (mm) 5 l2 Length of magnetic guide ring (mm) 5 l3 The PM length in its magnetized direction (mm) 8 l3 l4 TheThe PM axial length length in of its side magnetized plate of axial direction stator (mm) (mm) 3.88 l4 l5 The axialThe length axial length of side of plate axial windowof axial (mm)stator (mm) 13.23.8 l Axial length of inner side gap of axial stator (mm) 2.1 l5 6 The axial length of axial window (mm) 13.2 l7 The width of radial magnetic pole (mm) 32 l6 Axial length of inner side gap of axial stator (mm) 2.1 l7 The width of radial magnetic pole (mm) 32 Magnetic forces of CRAMB in radial and axial direction are all deduced base on the following formulaMagnetic [23–25 forces]: of CRAMB in radial and axial direction are all deduced base on the following dw 1 1 B B2 A 1 φ2 formula [23–25]: f = = BHA = B A = = (6) dδ 2 2 µ 2µ 2µ A dw1 1 B B22 A 1  Obtained by relationshipsf that the  bearing BHA  force B A varied  by  coil currents and rotor displacement(6) dA2 2  2  2  for RMB and TMB units of the CRAMB respectively via FEM, the predicted current stiffness and displacementObtained by stiffness relationships of the RMBthat the unit bearing at rotor force center varied position by coil are currents 137.3 and N/A rotor and displacement−692 N/mm forrespectively. RMB and TheTMB predicted units of currentthe CRAMB stiffness respectively and displacement via FEM, stiffness the predicted of the TMB current unit atstiffness rotor center and displacementposition are 261.5 stiffness N/A of and the− RMB1086 N/mm, unit at respectively,rotor center validatedposition are by experiment.137.3 N/A and For − rotor692 N/mm weight respectively. The predicted current stiffness and displacement stiffness of the TMB unit at rotor center position are 261.5 N/A and −1086 N/mm, respectively, validated by experiment. For rotor weight less than 8 kg, aforementioned current stiffness value promises that the rotor can be levitated fast and stably.

3.3. Design of High Speed Rotor Considering Its Dynamics Since high speed rotor is crucial part of high speed machine, the stress or strength limitation is influenced by materials and craftwork of the assembly of rotor enormously and inherently. And rotor mode limitation should be considered here. For active vibration control of rotor, the first order bending mode frequency of this high speed rotor should exist far from the operating frequency (60,000 rpm) for stable rotation. The configuration of this maglev high speed rotor is shown in Figure 8 in this work, and the material of every part in it is listed in Table 7. A pre-compressive stress is applied on the permanent

Energies 2018, 11, 1236 10 of 25 less than 8 kg, aforementioned current stiffness value promises that the rotor can be levitated fast and stably.

3.3. Design of High Speed Rotor Considering Its Dynamics Since high speed rotor is crucial part of high speed machine, the stress or strength limitation is influenced by materials and craftwork of the assembly of rotor enormously and inherently. And rotor mode limitation should be considered here. For active vibration control of rotor, the first order bending mode frequency of this high speed rotor should exist far from the operating frequency (60,000 rpm) for stable rotation. The configuration of this maglev high speed rotor is shown in Figure8 in this work, and the Energiesmaterial 2018 of, 11 every, x FOR part PEER in REVIEW it is listed in Table7. A pre-compressive stress is applied on the permanent10 of 24 magnet, by using an interference fit with sleeve to reduce the tensile stress against high speed magnet, by using an interference fit with sleeve to reduce the tensile stress against high speed centrifugal force. Total equivalent stress must be restricted below the yielding point of rotor assembly centrifugal force. Total equivalent stress must be restricted below the yielding point of rotor assembly material throughout the whole speed range. The value of interference fit is 0.18 mm, which is adopted material throughout the whole speed range. The value of interference fit is 0.18 mm, which is adopted between the cylindrical rotor parts and the sleeve. between the cylindrical rotor parts and the sleeve. Table 7. Material and stress of rotor parts. Table 7. Material and stress of rotor parts.

MotorMotor Part Part Screw-RingScrew-Ring ShaftShaft ProtectProtect Sleeve Sleeve ShaftShaft Stud Stud PMPM Rotor Rotor Core materialmaterial 40CrNiMo40CrNiMo 1Cr18Ni9Ti1Cr18Ni9Ti GH4169GH4169 40CrNiMo40CrNiMo Sm2Co17 20WTG1500 20WTG1500 MaximumMaximum stress stress (Mpa) 270270 0.560.56 663663 259259 21.821.8 217

Screw-ring Cylindrical permanent magnet Thrust disk

Shaft RMB rotor core Sleeve Shaft stud RMB rotor core

Figure 8. Configuration of maglev high speed rotor for maglev BLDCM. Figure 8. Conﬁguration of maglev high speed rotor for maglev BLDCM.

After the rotor is scattered into many finite units, the rotor mode can be calculated based on vibrationAfter equation: the rotor is scattered into many ﬁnite units, the rotor mode can be calculated based on vibration equation: 2 k2 m  j c X  0 krr− ω rr m rr + jω rr rcr X = 0(7 (7))

SSolutionolution existence existence condition ofof ωωrr is that thethe determinantdeterminant ofof displacementdisplacement impedance impedance matrix matrix as asZ Zis is 0, 0, that that is: is:

2 |Z| = kr − ω2r mr + jωrcr = 0 (8) Z kr  r m r  j r c r  0 (8) 2 While the mr, cr and kr are all positive definite matrixes, eigenvalues of it λi can be solved, of While the mr, cr and kr are all positive definite matrixes, eigenvalues of it λi2 can be solved, of which λi is mode. First order bending mode is calculated by transfer matrix method to determine which λi is mode. First order bending mode is calculated by transfer matrix method to determine initial rotor with stress analysis together. FEM results of first-order bending mode is used to validate initial rotor with stress analysis together. FEM results of first-order bending mode is used to validate the effectiveness of above analytical model. The CAD model of rotor assembly is imported into the effectiveness of above analytical model. The CAD model of rotor assembly is imported into ANSYS simulation interface for rotor modal, then mesh and solution of FEM model are completed. ANSYS simulation interface for rotor modal, then mesh and solution of FEM model are completed. Its first-order bending mode is 1596 Hz calculated by FEM, while the tested result is 1590.7 Hz by an Its first-order bending mode is 1596 Hz calculated by FEM, while the tested result is 1590.7 Hz by an excitation method (flexible free suspension of rotor), where error is less than 1%. Besides, the deviation excitation method (flexible free suspension of rotor), where error is less than 1%. Besides, the between the inertial spindle and rotating spindle is very small because of the better off-line and on-line deviation between the inertial spindle and rotating spindle is very small because of the better off-line dynamic balance operation, so the eccentricity led by rotor unbalance can be neglected, which has and on-line dynamic balance operation, so the eccentricity led by rotor unbalance can be neglected, been validated by experiment. which has been validated by experiment. The equivalent Mise stress of rotor is calculated based on Von-Mises yield criterion. The crucial The equivalent Mise stress of rotor is calculated based on Von-Mises yield criterion. The crucial stress evaluation generates at the interface between sleeve and PM. So, the stress analysis of PM is stress evaluation generates at the interface between sleeve and PM. So, the stress analysis of PM is shown as the followings: shown as the followings: Based on above deduction, the analytical expression for stress of permanent magnets under practical conditions can be obtained, with impact of assembly, centrifugal and temperature increase are all considered.

s r t rmr   rm r   rm r   rm s r t rmi r r m (9) mr    m r    m r    m

h Thus, the total equivalent Von-Mises stress of sleeve  vm is:

1 2 2 2 h           (10) vm2  rm m rm m which should satisfy the constraint:

Energies 2018, 11, 1236 11 of 25

Based on above deduction, the analytical expression for stress of permanent magnets under practical conditions can be obtained, with impact of assembly, centrifugal and temperature increase are all considered. s r t σrm(r) = σrm(r) + σrm(r) + σrm s r t rmi ≤ r ≤ rm (9) σθm(r) = σθm(r) + σθm(r) + σθm h Thus, the total equivalent Von-Mises stress of sleeve σvm is: r 1 h i σh = (σ − σ )2 + (σ )2 + (σ )2 (10) vm 2 rm θm rm θm which should satisfy the constraint: σh σh < max (11) vm n where n = 1.3. All stress components, including the static assembly stress and the dynamic stress, are shown as:  2 2 s rm ps rmi  σrm(r) = − 2 2 1 − 2 rmi ≤ r ≤ rm  rm −rmi r  2 2  s rm ps rmi  σ (r) = − 2 2 1 + 2 rmi ≤ r ≤ rm θm rm −rmi r 2 2 (12) r 3−2νm 2 2 2 rmi rm 2  σrm(r) = ρmω rm + rmi − 2 − r  8(1−νm) r  2 2  r 3−2νm 2 2 2 rmi rm 1+2νm 2  σ (r) = ρmω rm + r + − r θm 8(1−νm) mi r2 3−2νm where r is radius of PM or sleeve. ps is assembly pressure caused by interface fit. ρm is the density of PM, 7.4 × 103 kg/m3, or sleeve, 8.2 × 103 kg/m3. In assembling process, the sleeve is heated to 500 ◦C and lately cooled while the shaft stud, the RMB rotor core, and the shaft are placed at the assembly final position. The temperature during the assembly process is controlled under the one leading to demagnetization of PM, with mechanical performance also been considered. Here the thermal stress, caused by temperature increase, can be calculated as: " # " #−1" # σt 1 − vm α rm = Em Em m ∆T (13) σt − vm 1 α θm Em Em m In (13), motor’s temperature rise under load is obtained by thermal calculation in Part. D via thermal FEM to get maximum temperature rise. Here, the temperature rise ∆T is selected as the maximum value among the assembling temperature, the under-load temperature and demagnetization temperature. Thus, with Formula (16), the design interface between mechanics and thermal is t t constructed based on thermal stress σrm and σθm. To obtain integrated optimal design results, synthesis of different performance of rotor among several design aspects is necessary, as Figure9 shows this selection of design point of rotor diameter. As can be seen in it, the ratio of stress to natural frequency, just as σs/ fN, however, the Per-Unit 0 0 value of it, σs/ fN· fN/σs , is used to eliminate the effect of dimension here, as the left black vertical 0 0 axis shows, corresponding to two black curves in Figure9, where fN/σs is the initial value when the rotor diameter is 53 mm, thus, the Per-unit value of the ratio of rotor loss to bearing force is 0 0 represented by the right red axis, also corresponding to red curves in Figure9, namely Pr/FB·FB/Pr . Thus, these two Per-Unit values are all designed to minimize, so out-diameter of rotor is selected as 56 mm with representative air gap length 3 mm and 4 mm under comprehensive consideration. Besides, the variation tendency of them, and each respective design objective and aspect, all influence the selection point. So, dynamic variables of rotor are further determined. After above optimal selection, the air gap is 3 mm, where rotor loss is 1970 W at 60,000 rpm, radial bearing force can reach 270 N 0 0 with normal amplifier. Besides, from Figure9, the design sensitivity of Pr/FB·FB/Pr to the diameter 0 0 of rotor has little variation approximately, while, the sensitivity of σs/ fN· fN/σs begins to increase obviously when the out-diameter of rotor starts to increase from 57 mm, which is the inflection point Energies 2018, 11, 1236 12 of 25 for sensitivity. In the light of robust design, the out-diameter of rotor may affect the performance more obviously from 56 mm. Energies 2018, 11, x FOR PEER REVIEW diameter air gap-3mm 12 of 24 Energies 2018, 11, x FOR PEER REVIEW diameterdiameter airair gap-3mmgap-4mm 12 of 24 diameter air gap-4mm

1.6 2.5 1.6 2.5 air gap length=3mm 1.4 air gap length=3mm 1.4 2.0 2.0 1.2 air gap length=4mm 1.2 air gap length=4mm 1.5 1.0 1.5 1.0

1.0 0.8 1.0

Per-Unit value of rotor loss/bearing force loss/bearing rotor of value Per-Unit

Per-Unit value of stress/natrual frequency stress/natrual of value Per-Unit 0.8

Per-Unit value of rotor loss/bearing force loss/bearing rotor of value Per-Unit Per-Unit value of stress/natrual frequency stress/natrual of value Per-Unit 53 54 55 56 57 58 59 53 54 rotor55 core56 diameter57 (mm)58 59 rotor core diameter (mm) Figure 9. Selection about mechanical dynamic and rotor loss, and MBs etc. FigureFigure 9. SelectionSelection about about mechanical mechanical dynamic and rotor loss, and MBs etc etc.. With final design, the contact pressure in an interference fit is analyzed by means of the With final design, the contact pressure in an interference fit is analyzed by means of the numericalWith simulations ﬁnal design, using the FEM contact (using pressure Ansys in14.0 an to interference establish load ﬁt and is analyzedboundary bycondition). means ofThus, the numerical simulations using FEM (using Ansys 14.0 to establish load and boundary condition). Thus, numericalthe equivalent simulations effective using stress FEM contours (using of Ansys the sleeve 14.0 to are establish shown load in Figure and boundary 10b. The condition). maximum the equivalent effective stress contours of the sleeve are shown in Figure 10b. The maximum Thus,equivalent the equivalent stress of sleeve effective is 663 stress MPa, contours with safety of the factor sleeve being are 2. shown Based inonFigure the same 10b. FEM The process, maximum the equivalent stress of sleeve is 663 MPa, with safety factor being 2. Based on the same FEM process, the equivalentmaximum equivalent stress of sleeve stress is of 663 the MPa, permanent with safety magnet factor is being21.8 MPa 2. Based with onsafety the samefactor FEM 3.67. process, the maximum equivalent stress of the permanent magnet is 21.8 MPa with safety factor 3.67. maximumFigure equivalent 10c shows stress the of equivalent the permanent effective magnet stress is 21.8 distribution MPa with of safety the factor RMB 3.67. rotor core. The Figure 10c shows the equivalent effective stress distribution of the RMB rotor core. The maximumFigure equivalent 10c shows stress the equivalent of it is 217 effective MPa. The stress yield distribution stress in rotor of the core RMB of rotorthe RMB core. is The 380 maximumMPa. The maximum equivalent stress of it is 217 MPa. The yield stress in rotor core of the RMB is 380 MPa. The equivalentsafety factor stress is 1.75. of it is 217 MPa. The yield stress in rotor core of the RMB is 380 MPa. The safety safetyfactor isfactor 1.75. is 1.75.

(a) SUB = 1 (a) SUBTIME = =1 100 TIMESEQV = 100 (AVG) DMX = .106× 10−3 SEQV (AVG9) SMN = .490× 10−3 DMX = .106× 10 9 SMNSMX == ..490663×× 10109 SMX = .663× 109

.490× 109 .528× 109 .567× 109 .605× 109 .644× 109 .509× 109 .547× 109 .586× 109 .624× 109 .663× 109 .490× 109 .528× 109 .567× 109 .605× 109 .644× 109 .509× 109 .547× 109 ( b ) .586× 109 .624× 109 .663× 109 (b)

Figure 10. Cont.

Energies 2018, 11, 1236 13 of 25 Energies 2018, 11, x FOR PEER REVIEW 13 of 24

2.1722 × 108 Max 1.9451 × 108 1.7180 × 108 1.4909 × 108 1.2638 × 108 1.0367 × 108 8.0963 × 107 5.8253 × 107 3.5443 × 107 1.2833 × 107 Min

(c)

Figure 10.10. The rotor’s first ﬁrst-order-order bending mode, the equivalent effective stress contour for SleeveSleeve and rotor core lamination of the RMB: (a) AnalysisAnalysis results of bending vibration mode for rotor assembly by FEM; (b) Analysis results of stress for sleeve by FEM; (c) Analysis results of stress for rotor core lamination of the RMB byby FEM.FEM.

3.4.3.4. Thermal Design Considering Electromagnetic Aspect The crucial requirements and limitations for high power density and high speed motor could come down to the temperaturetemperature sustainability and thermal reliability. High current density in coils and volume limitations of BLDCM could lead to high temperature rise, thus, also lead to thermal design selection as for high speed motor. Besides,Besides, the cooling ability decidesdecides the thermal property of BLDCM, which is influencedinfluenced by air gap lengths of motor and MBs, with the air cooling and water jackets improving it, which are all set as design design feedback feedback interface interface for for structural structural design. design. T Temperatureemperature rise of each part in motormotor systemsystem should be belowbelow thethe allowableallowable temperaturetemperature rise with permittedpermitted allowance reserved. FEM process of three dimensional steady thermal field field and fluidfluid fieldfield of this BLDCM deserves fundamentals of heat transfer, namely, withwith regardregard toto analyzation of steady thermalthermal field,field, steady heat conduction equation does not contain the time term, term, meanwhile, meanwhile, including including heat source source and medium, medium, which can be expressed asas thethe shownshown below:below:

→K  T→ n   q ∇· K ·∇T n = −q (1(14)4) The boundary condition in adiabatic surface is Tn   0 , while in radiating surface is The boundary condition in adiabatic surface is ∂T/∂n = 0, while in radiating surface is      k T n T Tf  . −k·∂T/∂n = α T − Tf . After heatheat transfertransfer coefficients coefficients being being determined, determined, with with every every heat heat source source and and heat heat generation generation rate hasrate beenhas been obtained obtained (as Table (as Table8 shows) 8 shows) and assigned and assigned to corresponding to corresponding area, temperature area, temperature rise can rise be gotcan bybe (18)got viaby (18) FEM. via Here, FEM. thermal Here, analysis thermal takes analysis the form takes of the validation form of by validation FEM for the by final FEM determination for the final ofdetermination dynamic variables of dynamic as the variables final interface. as the final interface.

Table 8. Heat generation rate of BLDCM and AMBs.AMBs. Motor Motor Protect MB MB Motor Part Motor Motor Protect PM MB MB Motor Part Stator Winding Sleeve PM (Rotor End) (Anoth-er End) Stator Winding Sleeve (Rotor End) (Anoth-er End) Power loss (W) 317 450 546 41 132.5 124.8 Power loss (W) 317 450 546 41 132.5 124.8 Heat generation rate Heat generation rate 5.16 0.56 3.41 0.35 6.75 8.36 3 5.16 0.56 3.41 0.35 6.75 8.36 (mW/(mm(mW/(mm3)) ))

Energies 2018, 11, 1236 14 of 25 Energies 2018, 11, x FOR PEER REVIEW 14 of 24

With similar ideas ideas to to Figure Figure 9, synthesis synthesis of of electromagnetic, electromagnetic, thermal thermal,, and and power power performance performance is implementedis implemented as Figure as Figure 11 shows11 shows for forselection selection of design of design point point of air of gap air gaplength. length. In the In same the sameway, way,Per- UnitPer-Unit values values of the of ratio the of ratio total of harmonic total harmonic distortion distortion (THD) to (THD) output to torque output and torque the ratio and of the maximum ratio of temaximummperature temperature to density of to power density have of power the same have corresponding the same corresponding relationships relationships with vertical with axes vertical as the onesaxes asof theFigure ones 9.of M Figureinimum9. of Minimum Per-unit ofvalues Per-unit are valuesoptimal are for optimal design, for considering design, considering with rotor withdynamic rotors requirements,dynamics requirements, 3 mm air 3gap mm length air gap is lengthselected, is selected,approximate approximate to inflection to inflection point, w point,ith different with different ratios ofratios length of lengthof rotor of to rotor diameter to diameter (as L/D (as in L/DFigure in Figure11, 0.131 11 is, 0.131 the optimal is the optimal value) are value) considered. are considered. While ◦ WhileTHD = THD 9.6%, = 9.6%, TmaxTmax = 139 = °C 139. BesidesC. Besides,, from from Figure Figure 11 ,11 sensitivity, sensitivity about about air air-gap-gap length length begins begins to increase immediatelyimmediately whenwhen air-gapair-gap valuevalue is is 3 3 mm. mm. It It affects affects performance performance remarkably remarkably when when its its value value is ismore more than than 3mm. 3 mm. It alsoIt also can can be be seen seen from from the the sensitivity sensitivity that that the the air-gap air-gap length length is a keyis a key parameter parameter that thatit should it should be set be as set the as dynamic the dynamic variable variable to coordinate to coordinate every designevery design model model and determine and determine the overall the performanceoverall performance of the high of the speed high BLDCM. speed BLDCM. Accounting for for boundary boundary conditions, conditions, with with assignment assignment of ofthose those heat heat source source values values in Table in Table 8, the8, thermalthe thermal solution solution can be can obta beined obtained by FEM, by however, FEM, however, in which in whichheat transfer heat transfer coefficients coefficients (HTC) are (HTC) key valuesare key for values it. D forefinition it. Definition of HTC ofin HTC air gap in airand gap jackets and jacketsare described are described in [29] in by [29 computation] by computation fluid dynamicsfluid dynamics (CFD) (CFD) method, method, with others with others are defined are defined by material by material properties, properties, empirical empirical form formulas,ulas, and ◦ values.and values. The highest The highest temperature temperature is 139 is°C 139 locatedC located in the inpositive the positive center centerin cylindrical in cylindrical PM as Figure PM as 1Figure2 (in lower 12 (in right lower corner) right corner) shows. shows. The temperature The temperature of sleeve of sleeve and andPM can PM canbe substituted be substituted into into (22) (22) to validateto validate their their thermal thermal stress stress to tomake make thermal thermal-mechanical-mechanical coupling. coupling. Besides, Besides, the the highest highest temperature temperature ◦ of PMPM isis beyondbeyond its its demagnetization demagnetization point. point. While While at ofat theof statorthe stator is beyond is beyond 90 C 90 (in °C upper (in upper right corner right cornerin Figure in 12Figure), which 12), canwhich promise can promise the insulation the insulation of the winding of the winding below the below safety the value. safety Thus, value. the Thus, final thevalues final of the values dynamic of the optimal dynamic variables optimal are variables determined are after determined the thermal after analysis the thermal and selection analysis process, and selectionbased on process Figure 11, based as Table on 9Figure shows. 1 L.D-1-0.1311 as Table 9 shows. L.D-1-0.145 3.0 2.0

2.5 1.8 L/D=0.145 1.6 2.0

L/D=0.131 1.4 1.5

1.2

Per-Unit value of THD/Tout of value Per-Unit 1.0

1.0 power of Tmax/density of value Per-Unit

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 air-gap length (mm)

Figure 11. SelectionSelection about about electromagnetic electromagnetic and thermal performance etc.

Energies 2018, 11, 1236 15 of 25 Energies 2018, 11, x FOR PEER REVIEW 15 of 24

Energies 2018, 11, x FOR PEER REVIEW 15 of 24

Figure 12. The predicted temperature rise and measured temperature rise of the high speed BLDCM Figure 12. The predicted temperature rise and measured temperature rise of the high speed BLDCM with temperature distribution in stator, PM, and sleeve. with temperature distribution in stator, PM, and sleeve. Table 9. Final values of dynamic optimal variables. Figure 12. The predicted temperature rise and measured temperature rise of the high speed BLDCM Table 9. Final values of dynamic optimal variables. with temperature distributionKey Parameters in stator, PM , and sleeve.Variables Design Values Outer diameter of rotor (mm) x4 56 KeyTable Parameters 9. Final values of dynamic Variables optimal variables. Design Values Outer diameter of PM (mm) x5 46 Outer diameter of rotor (mm) x 56 ThicknessKey Parameters of PM (mm) Variablesx46 Design23 Values Outer diameter of PM (mm) x5 46 OuterSlot notch diameter width of Bs0rotor (mm) (mm) xx94 1.8656 Thickness of PM (mm) x6 23 Outer diameter of PM (mm) x5 46 Slot notch width Bs0 (mm) x9 1.86 3.5. Thermo-Structural VerificationThickness of PM (mm) x6 23 Slot notch width Bs0 (mm) x9 1.86 3.5. Thermo-StructuralThermo-structural Verification coupling analysis is implemented by Ansys software. Accounting for the characteristics of material and the computation effectiveness, the sequential coupling method for Thermo-structuralT3.5hermo. Thermo-structural-Structural analysis coupling Verification is adopted. analysis Theis implemented temperature fieldby Ansys is solved software. first. The Accounting temperature for the characteristicsdistributionThermo of of-structural material rotor is shown and coupling theas Figure computation analysis 13a is and implemented the effectiveness, maximum by temperature Ansys the sequential software. value Accounting coupling of rotor is method139 for the°C for Thermo-structuralascharacteristics Section 3.4 mentioned. of analysis material Then, is and adopted. the the temperature computation The temperature data effectiveness, of element field thenodes is sequential solvedare transferred first. coupling into The method the temperature stress for distributionanalysisThermo of-modestructural rotor as isboundary shown analysis ascondition. is Figure adopted. 13Whena andThe the the temperature constraints maximum and field temperature velocity is solved condition valuefirst. is The of assigned rotor temperature is to 139 the◦ C as Sectionmdistributionodel 3.4 mentioned.in stress of rotoranalysis Then,is shown mode, the as temperaturethe Figure stress 13a distribution and data the ofmaximum of element rotor istemperature nodes solved are as transferredFigurevalue of13b rotor shows. into is 139 the The °C stress maximum stress of rotor under maximum temperature achieves 817 MPa, with safety factor being analysisas Section mode 3.4 as mentioned. boundary Then, condition. the temperature When the data constraints of element and nodes velocity are transferred condition into is the assigned stress to 1.4.analysis So, the mode rotor as still boundary maintains condition. qualified When degree the of constraints safety even and its velocitymaximum condition temperature is assigned rises to to 139 the the model in stress analysis mode, the stress distribution of rotor is solved as Figure 13b shows. °Cm odelunder in rated stress load analysis with steadymode, state.the stress distribution of rotor is solved as Figure 13b shows. The The maximum stress of rotor under maximum temperature achieves 817 MPa, with safety factor being maximum stress of rotor under maximum temperature achieves 817 MPa, with safety factor being 1.4. So,1.4. the So, rotorthe rotor still still maintains maintains qualified qualified degree degree of of safety safety even even its maximum its maximum temperature temperature rises to 139 rises to ◦ 139 C°C under underrated rated load with with steady steady state. state.

(a)

Figure 13. Cont.

Energies 2018, 11, x FOR PEER REVIEW 16 of 24 Energies 2018, 11, 1236 16 of 25 Energies 2018, 11, x FOR PEER REVIEW 16 of 24

((b)

FigureFigure 13. Thermal13. Thermal and and and stress stress distribution distribution of of rotor rotor obtained by by thermos thermos-structuralthermos-structural-structural coupling coupling finite finiteﬁnite elemenelementelement analysis: t analysis: ( a) thermal( a) thermal distribution distribution of of rotor; rotor; ( b)) stress stress distribution distribution of ofrotor rotor.rotor. .

4. Experimental 4. Experimental Validation Validation Based Based on on Prototypes Prototypes 4.1. The High-Speed BLDCM Prototype and No-Load Test 4.14.1.. The High High-Speed-Speed BLDCM Prototype and No No-Load-Load Test Figure 14 shows the high speed BLDCM system with a high speed rotor and stators for BLDCM, Figure 14 shows the high speed BLDCM BLDCM system system with with a a high high speed speed rotor rotor and and stators stators for for BLDCM, BLDCM, RMB and CRAMB. Total mass of the assembly is 41 kg. In addition, no-load experiment is operated RMB to and validate CRAMB. the design TotalTotal of massmass the system, ofof the the assembly includingassembly isthe is 41 41rated kg. kg. Inpower, In addition, addition, the maximum no-load no-load speed, experiment experiment and the is stability operatedis operated to tovalidate validatecharacteristics the the design design of of th of thee MBsthe system, system,-rotor system, including including etc. the the rated rated power, power, the themaximum maximum speed,speed, andand the stability characteristicsFigure of 15 th the showse MBs MBs-rotor the-rotor control system, circuit etc. sketch and practicality about inverter, control board, and Figuresignal processing 1515 showsshows the board.the control control To satisfy circuit circuit with sketch sketch the and high and practicality speed practicality characteristics about about inverter, ofinverter, BLDCM, control control the board, controlled board and signal, and signalprocessingrectifier processing board. is selected. board.To satisfy So To when with satisfy the the motorwith high the isspeed driven high characteristics tospeed the synchronous characteristics of BLDCM, status of the BLDCM,based controlled on sensor the controlled rectifier-less is rectifierselected.control is So selected. strategy, when the theSo motor motor when iscould the driven motorbe accelerated to the is drivensynchronous by increasing to the status synchronous DC- basedbus voltage on status sensor-less via controlled based control on rectifie sensor strategy,r. -less controlthe motorWith strategy, DC could-DC the converter be acceleratedmotor being could got by be rid increasingaccelerated of, the advance DC-bus by increasing communication voltage DC via-bus strategy controlled voltage is adopted, via rectifier. controlled because With rectifie the DC-DC r. deep filter for high speed and high frequency would cause obvious signal delay. The motor adopts Withconverter DC-DC being converter got rid being of, the got advance rid of, the communication advance communication strategy isadopted, strategy is because adopted, the because deep filter the sensor-less position estimated strategy to obtain rotor angle position. Based on this control system, deepfor high filter speed for high and highspeed frequency and high wouldfrequency cause would obvious cause signal obvious delay. signal The motordelay. adoptsThe motor sensor-less adopts the acceleration and deceleration test for BLDCM is carried out. sensorposition-less estimated position strategy estimated to obtain strategy rotor toangle obtain position. rotor an Basedgle position. on this controlBased system,on this control the acceleration system, theand acceleration deceleration and test deceleration for BLDCM test is carried for BLDCM out. is carried out.

Stator of RMB

stator of BLDCM

High-speed rotor High-speed maglev BLDCM Stator of CRAMB stator of Figure 14. Key parts and assemblies for maglev BLDCM. BLDCM

High-speed rotor High-speed maglev BLDCM Stator of CRAMB

Figure 14. Key parts and assemblies for maglev BLDCM. Figure 14. Key parts and assemblies for maglev BLDCM.

Energies 2018, 11, 1236 17 of 25 Energies 2018, 11, x FOR PEER REVIEW 17 of 24 Energies 2018, 11, x FOR PEER REVIEW 17 of 24

Figure 15. Control circuit sketch and related practicality. Figure 15. Control circuit sketch and related practicality. Figure 15. Control circuit sketch and related practicality. Three-phase back-EMF waveforms are shown in Figure 16, where computation results (by FEM) are comparedThThree-phaseree-phase with back back-EMF measurement-EMF waveforms waveforms (by deceleration are are shown shown intest in Figure Figure after 1no166,-, whereload where acceleration) computation computation when results results the (by (byBLDCM FEM) FEM) areworksare compared compared at 60,000 with with rpm. measurement measurement Measured results (by (by deceleration deceleration of back-EMF test test is after after obtained no no-load-load by acceleration) acceleration)deceleration whentest, when agree the the BLDCM BLDCMing well worksworkswith the at at one60 60,000,000 got rpm. by FEM M Measuredeasured results ,results resultswith error of of back back-EMF between-EMF themis is obtained obtained 4.2%. by by deceleration deceleration test, test, agree agreeinging well well withwith Thethe the one onekey got gotparameters by by FEM resultsof results, BLDCM, with is error shown between in Table them 10. 4.2%. TheThe key key parameters parameters of of BLDCM BLDCM is is shown in Table 1010.. 300 measurement 300 measurementmeasurement 200 measurementmeasurement 200 measurementcomputation 100 computationcomputation 100 computationcomputation 0 computation Phase A 0 Back-EMF (V) Phase A -100 Phase C

Back-EMF (V) -100 Phase B Phase C -200 Phase B -200 -300 -300 0 40 80 120 160 200 240 280 320 360 0 40 80Mechanical120 160 angle200 (Degree)240 280 320 360 Mechanical angle (Degree) Figure 16. Back-EMF waveform of the BLDCM when it decelerates from 60,000 rpm (measurement FiguredataFigure from 16. 16. threeBackBack-EMF- phases:EMF waveform waveform 291.9 V max,of of the the computational BLDCM BLDCM when when prediction: it it decelerates decelerates 294.2 from from V max). 60,000 60,000 rpm rpm (meas (measurementurement datadata from from three three phases: phases: 291.9 291.9 V V max, max, computational computational prediction: prediction: 294.2 294.2 V V max). max). Table 10. Key parameters of BLDCM. Table 10. Key parameters of BLDCM. DesignTable 10. ParameterKey parameters (Unit) of BLDCM.Value OuterDesign diameter Parameter of stator (Unit (mm)) Value150 Design Parameter (Unit) Value OuterInner diameter of stator (mm) 15062 InnerOuter Statordiameter length of of stator stator (mm) (mm) (mm) 6260 150 InnerStator diameter length of stator (mm) (mm) 60 62 StatorRated length speed (mm) (rpm) 48,000 60 HighestRated speed speed speed (rpm) (rpm) (rpm) 4860 48,000,,000000 HighestRated speedpower speed (rpm) (kW)(rpm) 60 60,000,30000 SleeveRated thickness power power (kW) (kW) (mm) 306 30 Sleeve thicknessthickness (mm) (mm) 6 6 RatedRated voltage voltage (V) (V) 380 380 RatedPMPM radius radius voltage (mm) (mm) (V) 38022.5 22.5 RatedRatedPM radius current current (mm) (A) (A) 22.560 60 turnsturns×parallel× parallelRated currentconductorsconductors (A) per per slot slot 12 1260 ×× 88 turns×parallel conductors per slot 12 × 8 4.2. Experiment of Suspending Performance of AMBs 4.2. Experiment of Suspending Performance of AMBs The linearized models for MBs is set to define its controller parameters at equilibrium position [7]. Thus,The linearized the current models-force andfor MBsdisplacement is set to define-force stiffnessits controller become parameters important at forequilibrium it determining position the [7]. Thus, the current-force and displacement-force stiffness become important for it determining the

Energies 2018, 11, 1236 18 of 25

4.2. Experiment of Suspending Performance of AMBs The linearized models for MBs is set to deﬁne its controller parameters at equilibrium position [7]. Thus, the current-force and displacement-force stiffness become important for it determining the suspending capability, active resonance suppression control ability, and other dynamic performances. According to the linearized model of the AMB [23,24]:

Energies 2018, 11, x FOR PEER REVIEW 18 of 24 fb = kii + ksx (15) suspending capability, active resonance suppression control ability, and other dynamic whereperformances.fb is the bearing According force, tok thes is linearized the displacement model of the stiffness, AMB [23ki,24is]: the current stiffness, x is the rotor displacement, i is the control current. When the rotor is suspended in the original position, the exterior f k i k x (15) force can be exerted on the rotor by the pull meter,b i and s the control currents of AMBs is adjusted to keepwhere the rotor fb is suspendedthe bearing aroundforce, ks theis the original displacement position. stiffness, The forces ki is the can current be recorded stiffness, by xthe is the thrust rotor meter, and thedisplacement, control currents i is the can control be tested current. by When oscilloscope. the rotor The is suspended test platform in the and original related position, practicality the is shownexterior in Figure force 17 can. The be exerted displacement on the rotor can be by recorded the pull meter, by oscilloscope, and the control with currents the current of AMBs recorded is by upperadjusted monitor to askeep Figure the rotor 17 shows. suspended Series around forces the with original corresponding position. The controlforces can currents be recorded can be by obtained the thrust meter, and the control currents can be tested by oscilloscope. The test platform and related as shown in Figures 18a and 19a. In addition, control currents data here recorded are those subtracted practicality is shown in Figure 17. The displacement can be recorded by oscilloscope, with the current by the ones used to overcome gravity of the rotor. recorded by upper monitor as Figure 17 shows. Series forces with corresponding control currents can Thebe obtained displacement-force as shown in Figure stiffnesss 18a is and calculated 19a. In addition, by [25]: control currents data here recorded are those subtracted by the ones used to overcome gravity of the rotor. i The displacement-force stiffness is calculatedk = −by [25]:k (16) s x i i kk (16) where i/x is the slope of displacement-current curve.six It can be seen from Figures 18b and 19b, when no force exerted on the rotor at equilibrium position, the control currents are not equal to zero caused of a where i/x is the slope of displacement-current curve. It can be seen from Figures 18b and 19b, when little bias between the magnetic center and the gravity center of the rotor, which does not inﬂuence the no force exerted on the rotor at equilibrium position, the control currents are not equal to zero caused current-forceof a little and bias displacement-force between the magnetic stiffness. center andBased the on gravity the data center tested of the in radial rotor, andwhich axial does directions, not the linearinfluence ﬁtting the current curves-force can beand obtained displacement with-force corresponding stiffness. Based slopes. on the Thus data thetested displacement-force in radial and stiffnessaxial can directions, be obtained the vialinear the fitting slope curvesvalues canand becorresponding obtained with current-force corresponding stiffness slopes. values Thus obtained the by formerdisplacement process-force are substitutedstiffness can inbe (16). obtained via the slope values and corresponding current-force Thus,stiffness based values on obtained above testby former method, process test are results substituted of RMB in and(16). CRAMB are recorded in Figures 18 and 19 respectively.Thus, based on In above Figure test 18 method,, current test stiffness results of measurement RMB and CRAMB value are of recorded the RMB in Figure is 173.1s 18 N/A, withand error 19 3.9%, respectively. while, theIn Figure displacement 18, current stiffness stiffness 546.5 measurement N/mm, with value error of the about RMB 7.4%.is 173.1 As N/A, for Figurewith 19, error 3.9%, while, the displacement stiffness 546.5 N/mm, with error about 7.4%. As for Figure 19, current stiffness of the CRAMB’s RMB unit is 132.4 N/A, with error 3.7%, and the displacement stiffness current stiffness of the CRAMB’s RMB unit is 132.4 N/A, with error 3.7%, and the displacement 674.6stiffness N/mm, 674.6 with N/mm, error about with error 2.6%, about while 2.6% its TMB, while unit’s its TMB current unit’s stiffness current 243.8stiffness N/A, 243.8 with N/A, error with about 7.2%,error with about its displacement 7.2%, with its stiffnessdisplacement 998.4 stiffness N/mm, 998.4 with N/mm, error with about error 8.7%. about 8.7%.

Figure 17. Experimental platform and description for MB’s Stiffness test. Figure 17. Experimental platform and description for MB’s Stiffness test.

Energies 2018, 11, 1236 19 of 25 Energies 2018, 11, x FOR PEER REVIEW 19 of 24 Energies 2018, 11, x FOR PEER REVIEW 19 of 24 0.16 40 Measured data 0.16 Measured data 0.12 Measured data 40 MeasuredLinear fitting data curve Linear fitting curve 30 0.12 Linear fitting curve 30 Linear fitting curve 0.08 20 0.08 20 0.04 10 0.04 10 0.00 0

Control current (A)

Bearing force (N) force Bearing 0.00 0 -0.04

Control current (A)

-10(N) force Bearing -0.04 -10 -0.08 -20 -0.08 -20  -30 -0.12  -30 -0.12 -40 -0.16 -40 -0.16 -0.2 -0.1 0.0 0.1 0.2 -0.06 -0.04 -0.02 0.00 0.02 0.04 -0.2 -0.1Control 0.0current (A)0.1 0.2 -0.06 -0.04 Dispacement-0.02 0.00 (mm) 0.02 0.04 Control current (A) Dispacement (mm) (a ) (b ) (a) (b) FigureFigure 18. 18.Measured Measured bearing bearing force force data data versus versus current current and anddisplacement displacement and measured and measured control control current Figure 18. Measured bearing force data versus current and displacement and measured control versuscurrent displacement versus displacement for RMB for RMB getting for stiffness: getting stiffness: (a) bearing (a) force bearing versus force control versus current; control ( bcurrent;) Measured current(b) Measured versus control displacement current for versus RMB displacement for getting stiffness:. (a) bearing force versus control current; control current versus displacement. (b) Measured control current versus displacement. 70 0.06 Measured data for TMB unit 70 Measured data for TMB unit 60 MeasuredMeasured datadata forfor TMBRMB unitunit 0.06 Measured Measured data data for for TMB RMB unit unit 60 MeasuredLinear fitting data curve for RMB for RMB unit unit 0.04 MeasuredLinear fitting data curve for RMB for TMB unit unit 50 LinearLinear fittingfitting curvecurve forfor RMBTMB unit 0.04 LinearLinear fittingfitting curvecurve forfor TMBRMB unitunit 50 0.02 40 Linear fitting curve for TMB unit Linear fitting curve for RMB unit 0.02 40 TMB unit TMB unit 30 TMB unit 0.00 30 Control current (A) 0.00 TMB unit 20 Control current (A) -0.02 20 10 -0.02 Bearing force (N) RMB unit 10 -0.04

Bearing force (N) 0 RMB unit -0.04 RMB unit 0 -10 -0.06 RMB unit -10 -0.06 -20 -0.08  -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 -0.010 -0.005 0.000 0.005 0.010 -20 -0.08 Displacement (mm) -0.10 -0.05 0.00Control0.05 current0.10 (A) 0.15 0.20 0.25 -0.010 -0.005 0.000 0.005 0.010 Control current (A) Displacement (mm) (a ) (b ) (a) (b) Figure 19. Measured bearing force data versus current and displacement and measured control Figure 19. Measured bearing force data versus current and displacement and measured control Figurecurrent 19.versusMeasured displacement bearing for forceCRAMB data for versus getting current stiffness: and (a) displacementbearing force versus and measured control current; control current versus displacement for CRAMB for getting stiffness: (a) bearing force versus control current; current(b) Measured versus contro displacementl current forversus CRAMB displacement for getting. stiffness: (a) bearing force versus control current; (b) Measured control current versus displacement. (b) Measured control current versus displacement. 4.3. Under-Load Experiment Based on Drag System 4.3. Under-Load Experiment Based on Drag System 4.3. Under-LoadThe under Experiment-load experiment Based on site Drag based System on Drag system is shown as Figure 20, in which two BLDCMsThe underin this- loadproject experiment are set as sitemotor based and ongenerator Drag system respectively, is shown connected as Figure by 2flexible0, in which coupling. two The under-load experiment site based on Drag system is shown as Figure 20, in which two BLDCMsThe inverter in thisdriv projecting the are motor set ,as drag motorging and the generatorgenerator ,respectively, to put the output connected power by into flexible the load coupling. bank. BLDCMs in this project are set as motor and generator respectively, connected by ﬂexible coupling. The inverterload bank driv is ingconnected the motor by, powerdragging lines the to generator generator., to Two put theBLDCMs output are power suspended into the by load MBs bank. via The inverter driving the motor, dragging the generator, to put the output power into the load bank. Themagnetic load bankbearing is connected controller. by The power input lines power to generator.and output Two power BLDCMs are recorded are suspended by power by analyzer.MBs via The load bank is connected by power lines to generator. Two BLDCMs are suspended by MBs via magneticThe values bearing of phase controller. current and The voltage input power are recorded and output by oscilloscope. power are Thus,recorded the powerby power relationships analyzer. magnetic bearing controller. The input power and output power are recorded by power analyzer. Theamong values motor, of phase generator current, and and load voltage bank are are recorded established. by oscilloscope. Thus, performances Thus, the power of maglev relationships BLDCM The values of phase current and voltage are recorded by oscilloscope. Thus, the power relationships amongsystem including motor, generator MB-rotor, and system’s load stability, bank are motor’s established. sustainability Thus, performances and thermal ofreliability maglev can BLDCM all be among motor, generator, and load bank are established. Thus, performances of maglev BLDCM systvalidatedem including under loadMB- rotor condition. system’s In stability,practical motor’s operation, sustainability the initial and drive thermal voltage reliability of inverter can areall setbe system including MB-rotor system’s stability, motor’s sustainability and thermal reliability can all validatedunder 10 V under during load three condition.-stages start In -uppractical process operation, with PW M the modulation initial drive method voltage, after of it inverter is accelerated areset be validated under load condition. In practical operation, the initial drive voltage of inverter areset underover 8500 10 V rpm, during the three drive-stage modes start is converted-up process to PAMwith PW style,M modulationfor reducing method harmonic, after content it is accelerated to ensure under 10 V during three-stages start-up process with PWM modulation method, after it is accelerated overtemperature 8500 rpm, rise the and drive radial mode unbalanced is converted magnetic to PAM pull style, are under for reducing their limitations. harmonic The content drag tosystem ensure is overtemperatureloaded 8500 as cur rpm, riserent the and increasing drive radial mode unbalanced gradually, is converted stepmagnetic by to step. PAM pull Besides, style,are under for maximum reducing their limitations. current harmonic is Theunder content drag 67 systemA to during ensure is temperatureloadedthe load as experiment. cur riserent and increasing radial unbalanced gradually, step magnetic by step. pull Besides, are under maximum their limitations. current is under The drag 67 A system during is the load experiment.

Energies 2018, 11, 1236 20 of 25 loaded as current increasing gradually, step by step. Besides, maximum current is under 67 A during theEnergies load 2018 experiment., 11, x FOR PEER REVIEW 20 of 24

Figure 20. The site of under-load experiment based on Drag system. Figure 20. The site of under-load experiment based on Drag system.

To suppress resonance vibration at the high speed working condition, we add two closed loop To suppress resonance vibration at the high speed working condition, we add two closed loop in in traditional control loop to suppress the same frequency current with its corresponding bearing traditional control loop to suppress the same frequency current with its corresponding bearing force. force. During the whole load process, the input and output power of this drag system are displayed During the whole load process, the input and output power of this drag system are displayed and recorded by power analyzers for motor and generator respectively. Current and voltage data and recorded by power analyzers for motor and generator respectively. Current and voltage data are are recorded by oscilloscopes. This drag system is loading to 33 kW with 55,332 rpm angular speed. recorded by oscilloscopes. This drag system is loading to 33 kW with 55,332 rpm angular speed. The The peak-peak value of the 3-phase control current is 190 A. The mass of the BLDCM is 41 kg, and the peak-peak value of the 3-phase control current is 190 A. The mass of the BLDCM is 41 kg, and the power density is 1.21 kW/kg. All data results during acceleration under load have been recorded and power density is 1.21 kW/kg. All data results during acceleration under load have been recorded and arranged as the following diagram (Table 11). arranged as the following diagram (Table 11).

Table 11. Test data of drag system under load condition. Table 11. Test data of drag system under load condition.

Speed InputInput Power Power of ofPhasePhase Voltage Voltage PhasePhase Current Current PhasePhase Voltage Voltage of of Phase Current of OutputOutput Power Power of of Speed (rpm) (rpm) the Motorthe Motor (kW) (kW)of Motorof Motor (V) (V) of ofMotor Motor (A) (A) GeneratorGenerator (V) (V) Generator (A) GeneratorGenerator (kW) (kW) 20,00020,000 3.58 3.5871.85 71.85 14.26 14.26 70.2 70.2 12.16 0.8490.849 30,00030,000 7.91 7.91106.1 106.1 20.34 20.34 100.26 100.26 17.31 1.7341.734 40,00040,000 16.54 16.54142.1 142.1 28.36 28.36 130.65 130.65 24.74 11.92611.926 48,00048,000 24.73 24.73171.26 171.26 40.62 40.62 153.19 153.19 36.62 19.99619.996 50,00050,000 26.07 26.07159.85 159.85 52 52128 128 48 24.9124.91 52,50052,500 29.8 29.8179.8 179.8 62 62155.6 155.6 54 27.5427.54 55,00055,000 33.2 33.2196.8 196.8 69 69180.3 180.3 61 31.5531.55

Based on drag speed-upspeed-up testing data showingshowing in Table 1111,, varieties of loss can be separated based on drag drag system. system. V Viaia energy relationships among motor, generator,generator, and load box, box, combined combined withwith speed-upspeed-up and deceleration test,test, whenwhen the motor runs at 55,33255,332 rpm, varieties of power losses can be obtained,obtained, as TableTable 1212 shows.shows.

Table 12. Varieties ofof powerpower losseslosses viavia experimentalexperimental separation.separation.

Loss StyleStyle WindingWinding Loss Loss StatorStator Core Core Loss Loss EddyEddy Current Current Loss Loss WindageWindage Loss Loss TotalTotal Loss Loss Power loss (W) 93 278 410 865 1646 Power loss (W) 93 278 410 865 1646

The temperature measured by those thermocouple PT100, embedded as Figure 21 shows. The highestThe temperature temperature rise measured in motor byis iron those core, thermocouple the next is the PT100, inner embeddedsurface face as to Figurethe rotor 21 surface.shows. TheFor t highesto verify temperaturethe calculated rise temperature in motor rise is iron in maglev core, the BLDCM next is system, the inner 13 thermocouples surface face to are the placed rotor in the stator parts of the high-speed BLDCM, as shown in Figure 21. The temperature test environment is shown in Figure 22a, which are based on the drag load experiment. The thermocouple is connected to temperature patrol instrument, which upload test values to the upper monitor in real time. The measured temperature rise is shown in Figure 22b. The maximum temperature of HSPMSM exists in coils with F-level insulation, and stators, reaching 131 °C and 128 °C respectively. After

Energies 2018, 11, 1236 21 of 25 surface. For to verify the calculated temperature rise in maglev BLDCM system, 13 thermocouples are placed in the stator parts of the high-speed BLDCM, as shown in Figure 21. The temperature test environment is shown in Figure 22a, which are based on the drag load experiment. The thermocouple is connected to temperature patrol instrument, which upload test values to the upper monitor in realEnergies time. 2018, The 11, x measuredFOR PEER REVIEW temperature rise is shown in Figure 22b. The maximum temperature21 of of24 ◦ ◦ EnergiesHSPMSM 2018, exists 11, x FOR in coilsPEER withREVIEW F-level insulation, and stators, reaching 131 C and 128 C respectively.21 of 24 Afteradding adding water watercooling, cooling, the temperature the temperature can decrease can decrease more than more 19 than °C 19at least.◦C at Except least. Except rotor, in rotor, stator in ◦ addingstatorparts of parts water the ofBLDCM, cooling, the BLDCM, thethe keytemperature the temperature key temperature can isdecrease located is located more in tooth inthan tooth front 19 front°C (air at (airgap)least. gap),, theExcept thevalue valuerotor, is 114 isin 114 stator°C , asC, partsasshown shown of in the inposition BLDCM, position PTC PTCthe 5 key and 5 and temperature 6 6(Figure (Figure 2 1).21 is). locatedBecause Because in we wetooth can can’t ’tfront place place (air the the gap) temperature temperature, the value sensor is 114 on °C , the as shownrotor surface,surface in position, soso thisthis PTC approximateapproximate 5 and 6 (Figure substitution substitution 21). Because method method we has has can been been’t adopted,place adopted, the whichtemperature which has has been been sensor validated validated on the by rotornon-contactby non surface-contact measurement, so measurement this approximate via via indirectly indirect substitution infraredly infrared method thermal thermal has probe. been probe. adopted, which has been validated by non-contact measurement via indirectly infrared thermal probe. 13 12 11 4 6 8 10 9 7 5 3 2 1 13 12 11 4 6 8 10 9 7 5 3 2 1

Figure 21. Probe position of thermal resistors in MLBLDCM system. Figure 21. Probe position of thermal resistors in MLBLDCM system. Figure 21. Probe position of thermal resistors in MLBLDCM system. The error between the predicted maximum temperature and the measured one in stator parts is 9.3%.The The error minimum between temperature the predicted rise maximum curves are temperature the stator coils and of thethe measuredRMB and theone CRAMBin stator (PTCparts 12is 9.3%.and 13 The The in minimumFigure minimum 21). temperature temperatureFigure 22b riseshows rise curves curves the temperatureare are the the stator stator rise coils coils curve of ofthe theof RMB this RMB andmaglev and the the CRAMBBLDCM CRAMB (PTCsystem. (PTC 12 and12The and 13maximum 13in inFigure Figure temperature 21). 21 Figure). Figure rise22b 22 is bshows under shows the the the temperature safety temperature condition. rise rise curve curve of of this this maglev maglev BLDCM BLDCM system. system. The maximum temperature rise is under the safety condition.

130

130120 8 7 6 5 8 7 120110 6 5

4 11 ) 110100

4 11

℃

) ( 100

℃ ( 9080

8070

Temperature Temperature 60

13 Temperature Temperature 6050 10 9 3 1 2 12

10 3 1 2 12 13 5040 9

40 0 30 60 90 120 150 180 210 240 Time (min) 0 30 60 90 120 150 180 210 240 (a) Time(b) (min) (a) (b) Figure 22. Temperature rise experiment and testing curves the MLBLDCM system: (a) test bench for temperature rise experiment; (b) temperature rise curves. Figure 22 22.. Temperature rise experiment and testing curves the MLBLDCM system: ( a)) test bench for for temperaturetemperature rise experiment; (b) temperature rise curves.curves. 5. Conclusions 5. Conclusions 5. ConclusionsIn this paper, integration design procedure is put forward. The idea of dynamic variables based on designIn this interface paper, integration is proposed design for coordinat procedureing is contradictions put forward. The among idea muof dynamiclti-domain variables requirements based In this paper, integration design procedure is put forward. The idea of dynamic variables based onand design integrating interface different is proposed design for coordinat aspects, wingith contradictions an effective among integrated multi design-domain tool requirements based on on design interface is proposed for coordinating contradictions among multi-domain requirements andperformance integrating ratio different curves put design forward. aspects, The research with an is mainly effective on integratedthe following design aspects: tool based on performance ratio curves put forward. The research is mainly on the following aspects: a. BLDCM and MBs are designed initially based on respective design model which is validated by a. BLDCMFEM, generating and MBs design are designed interface initially and dynamic based on variables. respective design model which is validated by b. FEM,Design generating interfaces design between interface electromagnetic and dynamic design variables. of BLDCM and electromagnetic designs of b. DesignMB are interfacesintegrated between by rotor electromagneticdiameters for each design different of BLDCM rotor P artand. electromagnetic designs of c. MBThe arepaper integrated proposes by a rotor tool fordiameters integrating for each those different dynamic rotor parameters Part. to obtain the design point, c. Thethis toolpaper is basedproposes on performancea tool for integrating ratio curves those illustrated dynamic in parameters Sections 3.3 to and obtain 3.4. theDesign design interfaces point, thisamong tool electromagnetic is based on performance performance, ratio curvesthermal illustrated requirements in Section, ands me3.3 chanicaland 3.4. Designperformance interfaces are amongintegrated electromagnetic by means of variousperformance, ratios thermalamong different requirements performance, and me index,chanical such performance as rotor stress, are integrated by means of various ratios among different performance index, such as rotor stress,

Energies 2018, 11, 1236 22 of 25 and integrating different design aspects, with an effective integrated design tool based on performance ratio curves put forward. The research is mainly on the following aspects: a. BLDCM and MBs are designed initially based on respective design model which is validated by FEM, generating design interface and dynamic variables. b. Design interfaces between electromagnetic design of BLDCM and electromagnetic designs of MB are integrated by rotor diameters for each different rotor Part. c. The paper proposes a tool for integrating those dynamic parameters to obtain the design point, this tool is based on performance ratio curves illustrated in Sections 3.3 and 3.4. Design interfaces among electromagnetic performance, thermal requirements, and mechanical performance are integrated by means of various ratios among different performance index, such as rotor stress, total loss etc. Thus, the design point could be selected based on those ratio curves considering multi-physics effect and multi-domain performances comprehensively. They are all illustrated and shown in Figures9 and 11. d. Dynamic variables as integrated design tools are utilized to coordinate contradictions among multi-domain demands for motor. After initial design of motor and MB, the left dynamic variables are determined by mechanical and thermal analysis sequentially via design interfaces. e. The experiment, including drag test for BLDCM and stiffness test for MB, have been implemented to validate the effectiveness of the design results. And it makes the design procedure become a closed design loop. As measurement data of back-EMF coefﬁcient 0.0678 Vs/rad, and RMB’s stiffness 173.1 N/A, have little error 0.1% and 3.9% respectively, corresponding to the calculation results obtained by analytical design model.

The method presented in this paper is practical and convenient for modeling and designing of maglev BLDCM system based on design parameter selection procedure and integration tool proposed in this paper. It also can be applied to analogous motor systems.

Author Contributions: Each of the authors contributed to the preparation of this research paper. Xu Liu proposed the integrated design idea and model, calculated the key parameters, finished main simulations, and wrote the paper. He also contributed to the experimental work. Gang Liu contributed to revision and proofreading of the manuscript substantially. Acknowledgments: This research is supported by the Fundamental Research Funds for the Central universities. National nature science foundation of China: 61573032, 61421063, 61403015, 61773038 and the National Basic Research Program of China 2014CB744202. Besides, this work was also in part supported by the Beijing Science and Technology Program under Grant Z171100002217008, and in part by National Natural Science Foundation (NNSF) of China under Grant 61721091. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

EM Tmax maximum value of electromagnetic torque Bδ fundamental component of air-gap ﬂux density Dsi inner diameter of motor Lef effective electromagnetic length of motor stator Pout rated power of the BLDCM ω angular rotation speed Tm torque of the motor f rotational frequency Bg peak value of air-gap ﬂux density Ac current loading J stator current density Ns turns number per coil Energies 2018, 11, 1236 23 of 25

B flux density cutting across each coil σr conductivity of rotor parts for motor Jz eddy current density induced in axial direction Hα tangential component of magnetic field La effective electromagnetic length of rotor in motor part Ra outer diameter of rotor in motor part α1n, α2n angles spanned by the n-th region. Ph, Pce, Pcs hysteresis loss, eddy current loss (ECL), and stray loss respectively Bkmax, Bkmin major axis and minor axis of elliptic magnetic Kh, Kc, Ke coefficients of Ph, Pce, Pcs respectively α fitting coefficient of hysteresis loss αb half of the angle between two neighboring pole A effective cross area of each pole of RMB stator i0 bias current of RMB in coil i control current of RMB x rotor displacement ϕ magnetic flux though the pole of MB’s stator ωr frequency of rotor system mr mass matrix of rotor system cr damping matrix of rotor system kr stiffness matrix of rotor system fb radial force of RMB ki current stiffness of RMB ks displacement stiffness of RMB σrm total radial equivalent stress σθm total tangential equivalent stress t σr m radial component of thermal stress t σθ m tangential component of thermal stress t σm ax 1146 MPa, allowable limit of material GH4169 σs maximum value of total equivalent stress in rotor fN natural frequency of rotor system Pr total rotor loss FB maximum value of radial Force of magnetic bearing T temperature variable of motor in thermal equation K (kx, ky, kz) thermal conductivity, W/(m·K) q volume density summary of each heat source existing in solution domain, W/m3 α surface coefficient of heat transfer, W/(m2·K) Tf temperature of fluid around heat surface, K µ0 permeability of vacuum δb air-gap length of MB

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