Design and Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis

Transcription

1 University of Tennessee, Knoxville Trace: Tennessee Research an Creative Exchange Masters Theses Grauate School Design an Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis SeongTaek Lee University of Tennessee - Knoxville Recommene Citation Lee, SeongTaek, "Design an Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis. " Master's Thesis, University of Tennessee, This Thesis is brought to you for free an open access by the Grauate School at Trace: Tennessee Research an Creative Exchange. It has been accepte for inclusion in Masters Theses by an authorize aministrator of Trace: Tennessee Research an Creative Exchange. For more information, please contact trace@utk.eu.

2 To the Grauate Council: I am submitting herewith a thesis written by SeongTaek Lee entitle "Design an Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis." I have examine the final electronic copy of this thesis for form an content an recommen that it be accepte in partial fulfillment of the reuirements for the egree of Master of Science, with a major in Electrical Engineering. We have rea this thesis an recommen its acceptance: Jack S. Lawler, John Chiasson (Original signatures are on file with official stuent recors.) Leon Tolbert, Major Professor Accepte for the Council: Dixie L. Thompson Vice Provost an Dean of the Grauate School

3 To the Grauate Council: I am submitting herewith a thesis written by SeongTaek Lee entitle Design an Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis. I have examine the final electronic copy of this thesis for form an content an recommen that it be accepte in partial fulfillment of the reuirements for the egree of Master of Science, with a major in Electrical Engineering. Leon Tolbert Major Professor We have rea this thesis an recommen its acceptance: Jack S. Lawler John Chiasson Accepte for the Council: Anne Mayhew Vice Chancellor an Dean of Grauate Stuies (Original signatures are on file with official stuent recors)

4 Design an Analysis of New Concept Interior Permanent Magnet Synchronous Motor by 3D Finite Element Analysis A Thesis Presente for the Master of Science Degree The University of Tennessee, Knoxville SeongTaek Lee August 2005

5 DEDICATION This thesis is eicate to my family; my wife Min-young an aughter Jennifer, an my mother, who always encourage me with their love. ii

6 ACKNOWLEDGMENTS I wish to thank all those who helpe me in completing my egree. I thank Dr. Tolbert for his continuous guiance throughout the process of writing my thesis. I thank all the professors who have contribute to my eucation at The University of Tennessee. They have emane excellence an mae me a better engineer. I especially thank Dr. Lawler an Dr. Chiasson for serving on my committee. I woul also like to thank the National Transportation Research Center at the Oak Rige National Laboratory to give me the chance to research there. In particular, I woul like to thank Dr. John Hsu who has supporte an encourage me while I was pursuing my egree. iii

7 ABSTRACT Throughout the years Hybri Electric Vehicles (HEV) reuire an electric motor which has high power ensity an wie constant power operating region as well as low manufacturing cost. For these purposes, a new concept permanent magnet motor is esigne an analyze with the basic theories about Interior Permanent Magnet Synchronous Motor (IPMSM). This new motor has DC excitation coils an flux paths, which can increase the output torue an be controlle for fiel weakening operating. The analysis has been conucte by three-imensional Finite Element Analysis. The results show the possibility of the new motor for HEV applications. The new motor has several avantages: low manufacturing cost, low inertia of the rotor, an the irect controllability of air-gap flux. iv

8 LIST OF CONTENTS 1. Introuction 1.1. Backgroun Comparison of Electric Motors Inuction Motor Permanent Magnet Synchronous Motor Switche Reluctance Motor Research Objective Thesis Organization Analysis of Interior Permanent Magnet Synchronous Motor (IPMSM) 2.1. Backgroun Torue Euation from Steay-State Phasor Diagram Torue Euation from Magnetic Fiel Energy Finite Element Analysis Maxwell 3D Summary FEA Simulation of the Concept of a New IPMSM 3.1. Introuction Moeling Numerical Analysis Simulation Results v

9 4. Design a New Concept Motor 4.1. Design Proceure Pre-evelope Motor Geometries an materials of pre-evelope motor Simulation results of pre-evelope motor Emboiment of the Concept Sie-poles an sie-magnets Excitation flux paths Excitation coil resistance Simulation Results of Final Moel Air-gap flux Output torue Summary an Discussion Conclusions an Future Works 5.1. Conclusions Future Works REFERENCES APPENDICES A. Flowchart of Maxwell 3D B. Park s transformation an Reference Coorinate systems VITA vi

10 LIST OF FIGURES 1.1 Reuire characteristics of traction motor in a vehicle running moe Spee-Torue curves for variable freuency control of IM Various rotor configurations with PM Phasor iagram for IPMSM Torue-angle characteristic of IPMSM A simple rotating machine Comparing B-H curve between linear an nonlinear material Simulation concept moel to increase air gap flux FEA simulation result of air-gap flux ensity of the concept moel Simulation moel with sie cores an woun coils Simplifie moel for excite flux path Simulation results of air-gap flux ensity for ifferent excitation conitions B vector on three cut-planes in the simulation moel A uarter moel of pre-evelope motor for FEA The location of PMs in the rotor B-H curves for non-linear materials Air-gap flux ensity istribution of pre-evelope motor Output torue versus current phase angle for pre-evelope motor vii

11 4.6 Configuration of sie-poles Configuration of sie-poles an sie-magnets Flux ensity vector istributions aroun sie-pole at centere N-position Magnitue of the flux ensity on the sie-pole an the clamping at centere N-position Axial flux path of the motor Flux ensity vector istributions on the axial cut plane at N-position Flux ensity vector istributions on the axial cut plane at S-position Simulation results of air-gap flux ensity for ifferent excitation values Flux ensity vector istributions at no phase current Magnitue of flux ensity at no phase current Flux ensity vector istributions at maximum torue position Magnitue of flux ensity at maximum torue position Overall magnitue of flux ensity at maximum torue position Comparison of output torue between pre-evelope an final moel Comparison of output torue uner various excitation current values Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc = 3000At) Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc = 0At) Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc = -1500At) B.1 A uarter IPMSM moel for references of the three-phase viii

12 CHAPTER 1 Introuction 1.1 Backgroun Throughout the years hybri electric vehicles (HEVs) have prove themselves worthy to replace a conventional vehicle with an internal combustion engine (ICE). Recently, the commercial HEVs evelope by Toyota an Hona have proven about 50% fuel saving in urban riving in comparison with an euivalent ICE vehicle [1]. This is great progress, but the fuel saving still cannot compensate for the extra cost of an HEV in initial purchase an maintenance. Thus, the price an reliability of the traction motor is one of the most critical issues in eveloping an HEV system. Various types of electric motors have been investigate for use in an HEV system in the fiels of output power, maximum spee, efficiency, manufacturing cost, an urability. Figure 1.1 shows the motor reuirements of an HEV in the ifferent vehicle running moes. The maximum motor torue is etermine by acceleration at low spee an hill climbing capability of a vehicle, the maximum motor RPM by the maximum spee of a vehicle, an the constant power by vehicle acceleration from the base spee to the maximum spee of a vehicle. The shae areas inicate the ranges freuently use for a vehicle; so, high efficiency is reuire. In a conventional ICE powere vehicle, the wie constant power is accomplishe by a multi-gear transmission. When a vehicle is operate with start-go riving pattern, such as the urban cycle in Figure 1.1, the average 1

13 POWER TORQUE Urban cycle Highway cycle Base spee SPEED Figure 1.1 Reuire characteristics of traction motor in a vehicle running moe operating efficiency of the traction system is very low [2]. Aitionally, the gearbox nees extra space in a vehicle an increases the total weight of the vehicle. Therefore, the necessity of multi-gear transmission system is unfavorable for vehicles. However, an electric motor powere vehicle can be operate efficiently in an urban area with a singlegear transmission to meet the reuirement of vehicle performance. Then, the structure of the traction system will be significantly simplifie. But the problem of an electric motor lies in the high-spee region, since increasing motor spee while holing constant power cannot be realize easily. Thus, recently the wier constant power region in the highspee range is the key point of the research about the traction motor for HEV. 2

14 1.2 Comparison of Electric Motors Until a ecae ago, DC motor systems were popularly use for riving an EV (Electric Vehicle) or an HEV, because they coul be use with irect current supplie from batteries without AC conversion. However, in reality DC motors cannot be attractive for EV or HEV systems anymore because of their low efficiency an freuent nee of maintenance. Therefore, thanks to the rapi evelopment of large scale integrate (LSI) circuits an powerful switching evices such as IGBT (insulate gate bipolar transistor), the Inuction Motor (IM), Permanent Magnet Synchronous Motor (PMSM) *, an Switche Reluctance Motor (SRM) have replace the traction system of EV or HEV Inuction Motor The avancement of power semiconuctors allows the IM to be use in the application where wiely varying spee or precision control of spee is reuire. The torue control of an IM is achieve through PWM control of the current. To hol the current control capability beyon base spee with constant power, the IM shoul be operate in the fiel weakening region. However, the presence of breakown torue of IM limits its extene constant power operation as shown Figure 1.2. Above a critical spee, ω c, the IM cannot sustain its constant power. Any attempt to operate the machine beyon this critical spee with maximum current will stall the IM. Typically, a properly esigne IM can achieve fiel weakening range of 3~5 times its base spee. This * Sometimes PMSM is also calle BDCM (Brushless DC Motor, BLDC). However, in general PMSM has sinusoial or uasi-sinusoial istribution of flux in the air-gap an BDCM has rectangular istribution. 3

15 Air-gap Torue T max Constant Torue Locus Constant Power Locus Increasing freuency 0 ω b ω c Motor Spee Figure 1.2 Spee-Torue curves for variable freuency control of IM approach, however, results in increase breakown torue, an thereby the motor size also is increase [2] Permanent Magnet Synchronous Motor Since a PMSM has the magnetic fiel excite by permanent magnets, it has many avantages compare with an IM. The high energy permanent magnet, such as rare earth or samarium cobalt, enables the PMSM to be significantly smaller than the IM in size an weight by increasing available fiel strength. Corresponingly, The PMSM has outstaning capability in torue or power ensity. The PMSM also has better efficiency 4

16 an power factor because of the absence of a rotor wining an the small size of the rotor [3]. Aitionally, since the PMSM is efficient at low spee, the HEV using a PMSM is attractive in the city moe in which the vehicle is reuire to freuently start an stop. However, the PMSM has a problem with operating in the constant power region. The presence of the permanent magnetic fiel limits its fiel weakening capability because the air-gap magnetic fiel can only be weakene through prouction of a stator fiel component that opposes the rotor fiel. Recently, there is research about an aitional fiel wining of PMSM * to control the fiel current for increasing fiel weakening region, an the maximum spee with the constant power is achieve up to 4 times of the base spee, such as conventional phase avance [2]. But the low inuctance value of PMSM still limits its constant power operation by increasing the phase current rating [4]. Thus, the spee ratio is still not enough to meet the vehicle reuirement, an the complex rotor structure increases the cost of the motor with the high price of permanent magnets. The high cost is a critical rawback of PMSM Switche Reluctance Motor Recently, an SRM has gaine consierable attention as a caniate of electric propulsion for EV an HEV. Its simple an rugge construction an simple stator wining can reuce the manufacturing cost of the SRM significantly. Above all things, the capability of extremely high spee operation make the SRM highly favorable for a * It is calle a PM hybri motor. 5

17 vehicle traction application. Because there is no fixe magnet flux, the maximum spee with constant power is not as restricte by controller voltage as it is in PMSM. However, the absence of excitation from a permanent magnet imposes the buren of excitation on the stator winings an the controller; thus the overall efficiency ecreases with the increasing copper loss [5]. In aition, the clear isavantages of the SRM are torue ripple an acoustic noise cause by its non-uniform air-gap structure [6]. Also, the torue ensity is much smaller than the PMSM [3]. 1.3 Research Objective The importance of high efficiency at low spee an high torue/power ensity make many manufacturing companies select a traction motor using permanent magnets. * Especially, interior permanent magnet synchronous motor (IPMSM) or permanent magnet assiste reluctance synchronous motor (PM-RSM) appeal to the makers with eveloping various control strategies. Actually, these two types of motors have almost the same operating principal in using both permanent magnet generate torue an reluctance torue. The ifference is that in PM-RSM the amount of magnet an the magnet flux linkage are small in comparison with the conventional IPMSM [7], but there is no clear bounary between two kins of motor. Thus, in this paper IPMSM inclues PM-RSM. * Mostly Neoymium-Iron-Boron (NFeB) Reluctance Synchronous Motor without permanent magnet shows similar behavior an characteristic with Switche Reluctance Motor as a traction application. 6

18 Many researchers have presente results that suggest the IPMSM or PM-RSM is a better solution for HEV than IM [1], an there is alreay a commercial HEV aopting this kin of motor *. However, the high price of high-energy permanent magnets an the complexity of the controller for fiel weakening are still major problems of IPMSM. Therefore, the main objective of this research is to esign a new concept motor, which is base on IPMSM for the application of HEV propulsion system with low price. To reuce the manufacturing cost of a high-performance PM machine, the motor must use less magnet material an be easily controllable in the constant power region. For this purpose, the new concept motor uses a DC excitation coil, which can increase flux in the air-gap an also control the flux for fiel weakening; because DC current is easy to control, an the conuctors (copper) are much cheaper than permanent magnet material. The excitation coils are woun aroun raial irection of the motor; thus, the flux by DC excitation current has the axial irection, which comes into the rotor an combines with the PM flux. As an excitation flux path, the frame is use. The frame is attache to the stator an makes axial air-gap with the rotor to make close flux path with the rotor which is rotating continuously. Three-imensional (3D) finite element analysis (FEA) is use for this research to get the optimal esign parameters of the motor. * Toyota Prius It is also calle finite element metho (FEM). 7

19 1.4 Thesis Organization This thesis is organize in the following manner: Chapter 2 organizes the euations of IPMSM for generating torue using steay-state phasor iagram an magnetic fiel energy, an a FEA computing proceure for torue is briefly explaine in the latter part of chapter 2. The base concept of the novel machine in this research is introuce in chapter 3. Chapter 4 escribes the esign objective an process with FEA an shows the results from FEA simulations. For conclusion, chapter 5 briefly summarizes the research in this thesis an aresses future works. 8

20 CHAPTER 2 Analysis of Interior Permanent Magnet Synchronous Motor (IPMSM) 2.1 Backgroun As it is mentione in chapter 1, the main characteristic of IPMSM is generating its output torue by both permanent magnet alignment an reluctance. IPMSM has the following useful properties when compare to traitional surface mounte PMSM [5]: Fiel weakening capability with high inuctance Uner-excite operation for most loa conitions High resistance from emagnetization High temperature capability There are several types of IPMSM, an each type has its own avantages an specific applications. Figure 2.1 shows some examples of IPMSM rotor configurations. If there are no magnets in each rotor configuration, the motor is to be a pure reluctance synchronous motor. Most IPMSM have some empty spaces, calle flux barriers, insie the rotor for increasing its reluctance torue. 9

21 Air (Flux Barrier) (a) (b) (c) () Permanent Magnet Figure 2.1 Various rotor configurations with PM 10

22 Much research has been conucte to etermine the PM portion in the flux barriers in the same rotor structure an conclue that more PM increases the torue an efficiency but ecreases the constant power region [7], [8]. Also, the ouble layer configuration in Figure 2.1 (b) has a higher torue an wier efficiency operating range than the single layer [9], but it cannot avoi the increase PM cost. The arrangement of Figure 2.1 (c) is known as a flux-concentrating esign because the magnet pole area at the air-gap prouces an air-gap flux ensity higher than that in the magnet [5]. In this chapter, the basic theory for generating torue of an IPMSM is analyze in etail. An then, the relationship between output torue an energy is escribe with analyses of Maxwell euations. Finally, basic FEA concepts for computing machine torue are presente. 2.2 Torue Euation from Steay-State Phasor Diagram The steay-state phasor iagram of IPMSM can be constructe in the same way like general PMSM. The open-circuit phase emf (electromotive force) is E f = je = jω Ψ (2.1) a where, ω is synchronous spee (rotor spee) an Ψ a is the flux linkage ue to the funamental component of -axis flux prouce by the permanent magnet. Although 11

23 there exists some -axis emf associate with the leakage flux [5] *, in most cases it is negligible. From the phasor iagram shown in Figure 2.2, V = X I + RI (2.2) V = E + X I + RI (2.3) The angles δ an γ are efine as shown in Figure 2.2; then, the voltage an current in the motor is efine by V I = V sinδ, V V cosδ (2.4) = = ± I sin γ, I I cosγ (2.5) = an (2.3), In a large capacity motor, the armature resistance, R, is negligible, an from (2.2) I I V E = (2.6) X V = (2.7) X E * actually, 1 with the resistance f = E + je = ω Ψ + jωψ I = RV 1 + X V E R 2 + X X, I R V E X = R 2 + X X V 12

24 V X I δ X I RI E γ I X I V X I I γ δ RI E (a) (b) Figure 2.2 Phasor iagram for IPMSM: (a) magnetizing armature current in the -axis. (b) emagnetizing armature current in the -axis. The complex power per phase per pole-pair into the motor is S = V I = ( V + jv )( I ji ) = V I * + V = P + jq I + j( V I V I ) (2.8) Substitute (2.4), (2.6) an (2.7) into (2.8); the real power is 13

25 14 ( ) ( ) ) sin(2 2 sin ) ( 2 δ δ t t X X V X X X E V X X V V X X X E V X V V X E V V I V I V P + = + = = + = (2.9) where, 2 2 t V V V + = Assume that there is no loss, then the total output torue for three phases with p pole-pairs is ( ) + = = ) sin(2 2 sin δ δ ω ω t t X X V X X X V E p P p T (2.10) In a pure reluctance synchronous motor, = 0 E ( ) ) sin( δ ω ω t X X V X X p P p T = = (2.11) The first term of (2.10) is the PM generate torue, an the secon term is the reluctance torue which is proportional to the ifference in stator inuctance, L -L. For a

26 general PMSM, L is almost the same as L, thus the reluctance torue term is cancele. In IPMSM, L is lower than L because the magnet flux flowing along the -axis has to cross through the magnet cavities in aition to the rotor air-gap, while the magnet flux of the -axis only crosses the air-gap [5]. Euation (2.10) shows that the perio of the reluctance torue is one half of that of the PM generate torue. Figure 2.3 illustrates that the IPMSM can achieve higher torue than a surface mounte PMSM which oes not have any reluctance torue component. However, the appearance of the reluctance torue oes not mean that IPMSM can have higher power ensity than surface mounte PMSM because the magnet flux linkage in IPMSM is not the same as that in the surface mounte PMSM with the same magnet volume. Euation (2.12) is another form of the torue euation (2.10), an (2.13) suggeste by Phil Mellor shows that the total torue of an IPMSM is increase with the saliency of the rotor [10]. T 3p = 2 [ Ψ I + ( L L ) I I ] a (2.12) T T base ξ 1 I S = cosδ sin(2δ ) (2.13) 2 I base where, T base = PM generate torue at I base L ξ = = saliency ratio L I s = Input current 15

27 PM torue Total torue Reluctance torue Figure 2.3 Torue-angle characteristic of IPMSM 16

28 The ξ term is calle the saliency factor an generally cannot be more than 3 [10]. Figure 2.3 also inicates the optimum commutation angle may have been avance from 90 (the optimum commutation angle for PMSM). 2.3 Torue Euation from Magnetic Fiel Energy For electric machinery, the torue acting on the rotor can be foun by ifferentiating the total system energy with respect to rotor position. Theoretically, this energy calculation can be simplifie if the inuctance L(θ) of the machine is known as a function of rotor angle θ. The energy store in the inuctor is well known as shown following euation [11]: 1 LI 2 W 2 m = (2.14) The relationship between flux linkage an inuctance makes it possible to obtain inuctance from the flux ensity or magnetic fiel. λ = NΦ = N B s = LI (2.15) s where N is the number of turns in the excitation coils circling the area s of the stator; an assuming that the flux (Φ) linke in the stator approximately euals that at the rotor poles. 17

29 To fin the torue on the rotor in Figure 2.4, the magnetic fiels must first be foun. The high permeability of the core confines the magnetic fiel prouce by the N- turn coil an guies the flux to the pole faces where the small air gaps between core an PM rotor to close on itself to make the loop. From Gauss law in Maxwell s euation, the flux ensity, B, must be continuous across the two air-gaps [11]. Euation (2.16) means that the flux ensity is the same everywhere in the loop. In other wors, B = 0 (2.16) B = core = B airgap B rotor (2.17) I, N turns θ Figure 2.4 A simple rotating machine 18

30 Since the magnetic fiel intensity *, H, is efine as (2.18) an the permeability, µ, of the core an rotor have very high permeability (for ieal case, µ is assume as infinity in soft magnetic materials [12]), the total magnetic fiel intensity concentrate on the two air-gaps is H B B = = (2.18) µ µ µ o r where, µ o = permeability of free space (= 4π 10-7 ) µ r = relative permeability thus, o H stator H g << = µ µ H g H = 2 H g (2.19) Therefore, using Ampere s law (2.20), the magnetic fiel intensity of the air-gap, H g, can be represente by input current, I, as l = J s = c H NI (2.20) s NI = H l + H l + 2H l 2H core core g rotor rotor g NI H g = (2.21) 2l g g l g * It is also calle just magnetic fiel 19

31 where l g is the length of the air-gap an the epth of air-gap, D, shoul be sufficiently larger than l g. Next relate euation (2.21) with the flux linkage, λ, λ = N Φ = N B s = NBg Ag = Nµ o H g s 2 µ o N IAg = (2.22) 2l g A g using (2.14) an (2.15), 2 λ µ o N Ag L = = (2.23) I 2l W g LI λ λ lg λ lg = = = = (2.24) 2 2 2L µ N A µ N RDθ m 2 o g o Faraay s law in Maxwell s Euations shows the flux linkage is constant with time when the coil is short circuite as follows: c 1 λ ε l = B s = = 0 (2.25) t N t s Euation (2.25) means that the flux linkage is time-constant. Uner constant flux linkage, the torue euation is given by [13]: W λ θ = m (, ) T (2.26) * θ * for constant current conition, 20

32 therefore, T 2 W λ lg = m = (2.27) 2 2 θ µ N RDθ o Using (2.22) to substitute for λ, T µ N I 4l 2 2 o = (2.28) g RD In this section we foun that the torue of electric machine can be obtaine from its magnetic fiel energy. In other wors, if we can compute the energy of an electric machine, we can also calculate the machine torue an wining inuctance. Base on this energy-torue relationship, we can calculate a machine torue using Finite Element Analysis (FEA). 2.4 Finite Element Analysis Maxwell 3D Obtaining the correct value of flux ensity an magnetic fiel remains an important issue for esigning an electric machine in verifying the magnetic flux loop an checking the saturation of flux ensity in each part of the machine. For this purpose, FEA is use extensively for the esign an performance preiction of all types of electric machines. It is a numerical techniue base on the etermination of the istribution of the 21

33 electric or magnetic fiels insie the machine structure, by means of the solution of Maxwell s euations. FEA coul answer the value of torue or force, wining inuctances, fiel istributions, back-emf waveforms, emagnetization withstan of magnets, etc [15]. To present electric or magnetic fiels over a large, irregularly shape region, each region of the moele machine is ivie into many hexaheral or tetraheral elements. * The collection of elements is referre to as the finite element mesh. In FEA computation, the value of a vector fiel at a location within an element is interpolate from its noal value of the fiel. For magnetic fiel calculation, Maxwell 3D solver ivies the H-fiel into a homogeneous an a particular solution. The solver stores a scalar potential at each noe for the homogeneous solution of magnetic fiel ensity, H, an stores the components of H that are tangential to the element eges [14]. Thus, to obtain a precise escription of the fiel, each element of the moel is small enough for the fiel to be aeuately interpolate from the noal values. However, there is a trae-off between the number of the elements an the amount of computing resources reuire for the computation. The accuracy of the solution also epens on how small each of the iniviual elements is. Thus, a user shoul choose an aeuate mesh size for fitting his computer capability. The computing proceure is as follows. First, the current ensity, J, is calculate by input current conition. Using Ohm s law (2.29), the J of all elements in the moel is obtaine an store. * Maxwell 3D uses tetraheral elements. 22

34 J = σ E = σ V (2.29) where, E is the electric fiel σ is the conuctivity of the material V is the electric potential Uner steay state conitions, the charge ensity, ρ, in any region of the moel oes not change with time [14]. That is J ρ = = 0 t (2.30) Substituting (2.29) into (2.30): ( V ) = 0 σ (2.31) The ifferential euation (2.31) is solve to get the J for all elements. After computing the current ensity, the FEA solver computes the magnetic fiel using Ampere s law an Maxwell s euation escribing the continuity of flux, H = J (2.32) B = 0 (2.33) Next, the energy is calculate. In a linear material, the energy, W, is the same as its coenergy, W c, as 23

35 W = v 1 ( B) Hv = B Hv 2 v (2.34) 1 ( H ) v = B Hv W Wc = B = 2 v v (2.35) However, in a nonlinear material, the coenergy is ifferent from its energy like shown in Figure 2.5. Energy an coenergy in the figure inicate the area above an below the B-H curve. If the motion of a material has occurre uner constant current conitions (steaystate), the mechanical work one can be represente by increasing its coenergy [13]. FEA solver is computing H uner constant input current conition, thus, it uses coenergy ifferentiation over a given angle instea of energy ifferentiation for torue calculation with nonlinear ata of the materials. B B Energy Energy Coenergy Coenergy H H (a) Linear material (b) Nonlinear material - µ is constant - µ is not constant - energy is eual to coenergy - energy is less than coenergy Figure 2.5 Comparing B-H curve between linear an nonlinear material 24

36 T Wc = (2.36) θ Computing inuctance of conuctors from the flux linkage is an aitional function of FEA, an these calculate inuctance values can be use for ynamic analysis of the esigne machine combine with its controller circuits. 2.5 Summary This chapter escribes the basic theories analyzing the generating torue in IPMSM for steay-state; using phasor iagrams. Euations (2.10) an (2.12) present that IPMSM has two torue components: permanent magnet torue an reluctance torue. By the existence of reluctance torue, the torue of IPMSM is not linearly proportional to the stator phase current amplitue. Therefore, FEA is an effective metho to preict the value of output torue of IPMSM. This chapter introuces how the energy of a machine can convert to its output torue; an then shows the basic theories about FEA for calculation of machine torue. 25

37 CHAPTER 3 FEA Simulation of the Concept of a New IPMSM 3.1 Introuction The basic iea is simple; use DC excitation current to control air-gap flux. Conventional electric machines are constructe from the following parts: a rotor assembly, laminate stator material, phase current-carrying conuctors, an a physical structure to support the entire machine. When a current-carrying conuctor is place in a magnetic fiel from the rotor, the conuctor experiences a mechanical force or torue. This force or torue is irectly proportional to the intensity of the magnetic fiel. Thus, generating a magnetic fiel from permanent magnets enables a machine to have high power ensity an efficiency. However, the fixe magnetic fiel limits its fiel weakening capability for wie constant power operation. If a controllable magnetic fiel can be ae to the fiel of a permanent magnet, we can vary the fiel intensity while still maintaining the avantages of PM machines. DC current is a goo source for this purpose, because it is easily increase an ecrease. Moreover, the flux generate by DC current is linearly proportional to the amount of the current flow until it reaches the saturation region of the flux-carrying material. FEA is a useful metho to check this iea. A simple moel is constructe for trial simulation, an the results are use for the actual esign. 26

38 3.2 Moeling Figure 3.1 shows the basic moel which nees to increase air gap flux. The permanent magnet use in this moel is a ferrite magnet of which the resiual flux ensity, B r, is 0.4 T an the relative permeability, µ r, is The steel is a kin of cast steel of which the µ r is about 900 in the linear region. The flux from the left sie of the PM travels through the left upper core, air gap, top core, air gap again, right upper core, an then returns to the right sie of PM. After FEA simulation, the calculate air-gap flux ensity of this simple moel is about 0.28 T (Figure 3.2). The object is to increase this air-gap flux ensity by DC excitation current. Top Core Air gap Left Upper Core Right Upper Core Lower Core Figure 3.1 Simulation concept moel to increase air gap flux 27

39 Figure 3.2 FEA simulation result of air-gap flux ensity of the concept moel To use excitation current, an aitional flux path is neee. For this purpose, two sie cores are attache to the original moel as shown in Figure 3.3. Each sie core is irectly contacte with half of the top core an makes another air-gap (sie air-gap) with an upper core on both sies. The reason to make the sie air-gap between sie core an upper core is that the upper cores are consiere as parts of rotor assembly for the rotating machine. Two coils are woun on each sie core to carry DC excitation current. The irection of the flux from excitation current is perpenicular to that from PM, an the two fluxes will be combine in the main air-gap between the upper core an the top core. Actually, there are several methos to attach a sie core, but the arrangement in 28

40 current irection Z Y X excitation flux path sie air-gap Figure 3.3 Simulation moel with sie cores an woun coils 29

41 Figure 3.3 is the best position from the results of FEA simulations about various configurations. 3.3 Numerical Analysis Assume that the excite flux from each sie core flows through just one half of the top core with the x-axis irection in Figure 3.3. Then, the new flux path for excitation current can be simplifie as Figure 3.4. The imensions of the simulation moel are inicate in Figure 3.4. The epth of each part is 40 mm for sie core, 50 mm for top core, an 45 mm for upper core. Suppose that the flux flows only at the center of each core an air-gap, then the path can be ivie with 7 parts: 1, 2 *, 3, 4, 5, g1, an g2. For each part of the path, the length an cross-sectional area are l 1 = 144 mm l 2 = 50 mm l 3 = 30 mm l 4 = 10 mm l 5 = 50 mm l g1 = l g2 = 2 mm * For this part, assume that the flux flows in only the top portion of the top core. 30

42 I l 1 l 2 Top core l l g1 2 Sie core l g2 l 5 l 4 Upper core Figure 3.4 Simplifie moel for excite flux path A 1 = = 800 mm 2 A 2 = = 1000 mm 2 A 3 = = 5000 mm 2 A 4 = = 4500 mm 2 A g1 = = 5000 mm 2 A g2 = = 900 mm 2 Since the reluctance of the magnetic path is efine as l R = (3.1) µ o µ r A 31

43 an the relative permeability of the core is 900, the total reluctance is π R 1 = = [At/Wb] R = [At/Wb] R = [At/Wb] R = [At/Wb] R = [At/Wb] R g = 3.18 [At/Wb] 1 10 R g 2 = [At/Wb] 5 R total = R [At/Wb] If the input current is 1000 At, then the flux an main air-gap flux ensity are Φ = R NI = [Wb] 4 Φ B g = = 0.09 [T] 6 A g with the PM. Therefore, we can expect that the main air-gap flux ensity reaches about 0.37 T 32

44 3.4 Simulation Results FEA simulations have been conucte uner four ifferent input current conitions: 1000 At, 500 At, 0 At, an -500 At. The negative value means that the current flows the reverse way an the irection of excite flux also changes. The calculate values of the main air-gap flux ensity are shown in Figure 3.5. The value at 1000 At is about 0.35 T an is a little lower than the expecte value, 0.37 T. The reason is that the aitional flux path, sie core, increases the total reluctance, an then ecreases the flux from the PM in the air-gap. The simulation result also shows that the flux ensity is about 0.26 T with sie core an no current, an this value is lower by about 0.02 T than the result without sie core. Consiering this situation, the main air-gap flux ensity increases about 0.09 T. This result totally agrees with the numerical analysis. Aitionally, Figure 3.5 shows that the main air-gap flux ensity coul be greatly reuce by changing the DC current irection. Comparing Figure 3.6 (a) an (b), the flux in the sie core changes its irection an the air-gap flux is reuce. The arrows in the air-gap hol their irection but the size of the arrows is shrunk. This chapter valiates the effectiveness of the esign concept for a new IPMSM. As a conseuence of the results of the simulations in this chapter, DC excitation current can be use for increasing an controlling air-gap flux of the electric machine. However, constructing an aeuate flux path for the excite flux is a ifficult task in the actual machine esign. An inaeuate flux path can increase the total reluctance of PM an the leakage flux of the machine. 33

45 Figure 3.5 Simulation results of air-gap flux ensity for ifferent excitation conitions 34

46 (a) Excitation current source is 1000 At (b) Excitation current source -500 At Positive air-gap B vector on each cut-plane Figure 3.6 B vector on three cut-planes in the simulation moel 35

47 CHAPTER 4 Design a New Concept Motor 4.1 Design Proceure As mentione in the previous chapter, the objective of this research is to esign an electric machine which has high torue ensity an has controllable air-gap flux irectly for the application of HEV systems. For this purpose, the esign proceure is as follows: 1) analysis of pre-evelope machine by FEA - without DC excitation parts - calculating output torue an air-gap flux ensity 2) analysis of raft-esign machine by FEA - attaching DC excitation parts - checking flux saturation an leakage parts 3) fixing esign parameters of the new machine by FEA - reforming flux saturation an leakage parts - comparing output torue an air-gap flux ensity with the results of the pre-evelope machine 36

48 4.2 Pre-evelope Motor Geometries an materials of pre-evelope motor Figure 4.1 shows a uarter part of a pre-evelope motor which has been esigne at National Transportation Research Center of Oak Rige National Laboratory. The imensions of the stator an rotor are given in Table 4.1. This IPMSM is a threephase an eight-pole (four-pole pair) machine which means that the number of stator slots per pole per phase is 2. The wining pattern is a single-layer wining with 9 turns an the wining span is full-pitch as shown in Figure 4.1. The permanent magnet material use in this motor is ferrite of which remanence flux ensity (B r ) is 0.4 T, coercive fiel (H c ) is A/m, an relative permeability (µ r ) is The location of the PM in the rotor is inicate in Figure 4.2. Laminate silicon steel is use for stator an rotor core to reuce hysteresis an ey current loss, an the shaft is mae of mil-steel. These two materials have a nonlinear magnetic characteristic, which is shown in Figure 4.3. Table 4.1 Specifications of stator an rotor parameters value parameters value Number of stator slots 48 Air-gap length in Outer stator iameter in Outer rotor iameter in Inner stator iameter in Inner rotor iameter in Stator tooth with in Rotor rib thickness 0.05 in Slot opening with in Rotor axial length 2.75 in Stator axial length 2.5 in PM thickness 0.25 in 37

49 -axis rotor b S b a a c c b -axis S N N N b a a S c c shaft PM stator Figure 4.1 A uarter moel of pre-evelope motor for FEA 38

50 rotor rib Figure 4.2 The location of PMs in the rotor 39

51 (a) Silicon steel (b) Mil steel Figure 4.3 B-H curves for non-linear materials 40

52 4.2.2 Simulation results of pre-evelope motor The no-loa simulation is implemente to check the istribution of the air-gap flux. Figure 4.4 is a flux ensity curve for no-loa conition along the line which places on the mile of the air-gap at the center of the rotor in an axial irection. In the figure, it is observe that the slot openings affect the flux ensity istribution an the flux wave is well balance between north (positive) an south (negative) poles. The average value of the magnitue of the flux ensity is T but the effective value coming through the stator teeth is about 0.3 T as shown in Figure 4.4. Figure 4.4 Air-gap flux ensity istribution of pre-evelope motor 41

53 Figure 4.5 shows the current phase angle versus output torue characteristic at which the maximum phase current is 200 A with a 3.75 phase angle step. It is obvious that the torue is compose of the magnet torue an the reluctance torue as shown in Figure 2.3. The maximum torue is Nm at of phase angle, which means that the reluctance torue is very large. If the reluctance torue is significantly larger than the magnet torue, the maximum torue will be place at 135. The pure magnet torue is Nm at 90. With high salient ratio (L/L >3), the output torue of IPMSM is compose of a larger portion of reluctance torue than magnet torue [16]. Figure 4.5 Output torue versus current phase angle for pre-evelope motor 42

54 4.3 Emboiment of the Concept Sie-poles an sie-magnets To make a flux path for the excitation current, sie-poles are use. These siepoles are attache to the rotor assembly as shown in Figure 4.6. In the figure, the right sie-pole is arrange to meet the north pole of the PM (N-position), an the left siepoles are place to face the south pole of the PM (S-position). Since the sie-poles are mae with mil steel an clampe by non-magnetic material (aluminum), the axialirection flux can come into or out from the rotor only through the sie-poles. A conseuence of FEA has reveale that much leakage flux flows into the rotor by clamping. To prevent this leakage flux, permanent magnets are use. These magnets are calle sie-magnets an place between sie-poles at S-position for right sie an at N-position for left sie of the rotor as shown in Figure 4.7. At S-position, they block the flux from flowing into the rotor through the sie-poles because the permanent magnets are magnetize to have the irection from left to right. Figure 4.8 an Figure 4.9 clearly shows that the leakage flux is significantly reuce an more flux comes into the rotor through the sie-poles. Corresponingly, the air-gap flux is also increase. The excitation flux path is inicate in Figure The flux generate by DC excitation current will flow through the frame, flux collector, sie air-gap, sie-pole, rotor core, air-gap, an stator. At N-position, the sie-poles will attract the axial flux, an then will sen the flux into the rotor. As a result, the air-gap flux will be increase. In contrast, left sie-poles will o the reverse role at S-position. The etails will be explaine in the latter part of this section. 43

55 Rotor assembly Metal bining Sie-pole Sie-pole Clamping (a) Sie-pole S N S S (b) left view of rotor assembly (Two sie- poles place at S-position) (c) right view of rotor assembly (One sie-pole places at N-position) Figure 4.6 Configuration of sie-poles 44

56 Sie-magnet (a) Sie-poles Sie-pole S S S Sie-magnet Sie-magnets (b) left view of rotor assembly (Two sie- poles place at S-position) (c) right view of rotor assembly (One sie-pole places at N-position) Figure 4.7 Configuration of sie-poles an sie-magnets 45

57 Sie-pole Rotor Leakage flux (a) with sie-pole only Sie-pole Sie-magnet S N (b) with sie-pole an sie-magnet Leakage flux Figure 4.8 Flux ensity vector istributions aroun sie-pole at centere N-position 46

58 (a) with sie-pole only (b) with sie-pole an sie-magnet Figure 4.9 Magnitue of the flux ensity on the sie-pole an the clamping at centere N-position 47

59 Frame Stator Excitation coils Sie-magnet S N N S Sie-pole Flux collector PM Shaft (a) N-position S S N Sie-pole N Sie-magnet (b) S-position PM flux Excitation flux with sie-pole Excitation flux without sie-pole penetrating flux Figure 4.10 Axial flux path of the motor 48

60 4.3.2 Excitation flux paths Figure 4.10 shows how the excitation flux flows insie the motor. Figure 4.10 (a) is the axial cut plane at the N-position, an (b) is the plane at the S-position. For N- position, the excitation flux from the right sie in the Figure 4.10 (a) combines with the main PM flux in the air-gap, whereas the excitation flux from left sie changes its way to the raial irection along the stator an combines at the flux collector. In the same way, the excitation flux makes its path for S-position as shown in Figure 4.10 (b). There shoul also be some penetrating flux which flows along the outer surface of the stator an shaft. Figure 4.11 an Figure 4.12 are the simulation results showing that the excitation flux flows along the same way as the concept in Figure On the left sie in Figure 4.11 an the right sie of Figure 4.12, the flux ensity vectors make an inepenent open path separate from the main close path. Therefore, the flux on the open path shoul go out an come in from the raial irection Excitation coil resistance If the excitation coils absorb much real power, the operating temperature will be significantly increase, an the efficiency of the motor will be also ecrease. Therefore, it is necessary to ensure the low resistance of the excitation coils. Resistance in general is given by the following expression R l c = ρ (4.1) A c 49

61 Figure 4.11 Flux ensity vector istributions on the axial cut plane at N-position Figure 4.12 Flux ensity vector istributions on the axial cut plane at S-position 50

62 where l c is the conuctor length, A c is the cross sectional area of the conuctor, an ρ is the conuctor resistivity. For most conuctors, incluing copper, resistivity is a function of temperature that can be linearly approximate as 2 ) ρ( T1 ) 1 [ + ( T )] ρ ( T = β T (4.2) 2 1 where ρ(t) is the resistivity at a temperature T an β is the temperature coefficient of resistivity. For anneale copper commonly use in motor winings, ρ(20 C) = Ωm, an β = C -1 [17]. Suppose that the excitation coil temperature increases up to 100 C, then the resistivity of the excitation coils is ρ(100 C) = ρ(20 C) 1 = = [ + β ( 100 C 20 C) ] 8 3 [ ( ) ] 8 [ Ωm] For the space of the excitation current, suppose that the axial height of each frame is increase 0.5 inches, then the aitional space, A space Ds, out Ds, in A space = 0.5 = 0.5 = [in 2 ] 2 2 where D s,out an D s,in are stator outer iameter an inner iameter respectively. With the coil packing factor 0.5, the total space allowe for the excitation coils is A 0.5A = [in 2 ] [mm 2 ] exc = space 51

63 The above result means that the excitation coils can be compose of 1mm 2 coils with 300 turns. The length of excitation coils can be calculate with the average value of the outer an inner stator iameters. ( D D ) 300 = ( ) l = π π [in] exc s, out s, in = [m] thus, the resistance value of the excitation coils is R exc ρ(100 C) l A = exc = 6 exc = [Ω] When the maximum excitation current is 10 A, the power loss from both sies of the excitation coils is 2 loss, exc = DC exc = 2 P 2 I R = [W] For a high power motor (over 50 kw), the power loss is less than 4 % of its output power. Consiering that the motor nees not to be always operating at the maximum output an the output power can be controlle by the excitation current, the power loss is not severe. 52

64 4.4 Simulation Results of Final Moel After conucting several simulations, the moel is moifie by eliminating the saturation part of the machine. Also, the inner iameters of sie-poles, sie-magnets, an flux-collector are ecrease to reuce the leakage flux in the axial irection Air-gap flux To check the relationship between the excitation current an air-gap flux, FEA simulations have been conucte uner several ifferent excitation current values: 3000 At, 2000 At, 1000 At, 0 At, an At. The simulation results are shown in Figure Uner positive excitation current, there is a little unbalance between positive an negative main curves. It may be ue to the leakage flux that penetrates the rotor an stator in the axial irection. Comparing Figure 4.4, the air-gap flux ensity significantly increases when the excitation current is 3000 At (from T to T in average value). Aitionally, Figure 4.13 shows that the air-gap flux ensity is reuce by ecreasing the excitation current value without changing its own shape. When the negative excitation current is less than At, the magnitue of the flux ensity is almost the same as when At, but it loses its own shape. Consiering that the funamental component of the air-gap flux is mainly relate with the motor performance, it is meaningless to compare between the values when less than At an others. 53

65 Figure 4.13 Simulation results of air-gap flux ensity for ifferent excitation values 54

66 With At of excitation current, the air-gap flux can be weakene by about 6.5% of the maximum value. In other wors, the maximum spee of the motor can be 15 times its base spee by just controlling its c excitation current, if the entire fiel crossing the phase conucts is epenent on this air-gap flux. Figure 4.14 is the flux ensity vector istributions in the stator an rotor at no phase current with excitation current of 3000 At, an Figure 4.15 is the magnitue of flux ensity in the same conition with Figure Figure 4.16 shows the flux ensity vectors in the stator an rotor at the maximum torue position ( ) uner the maximum phase current of 200 A an excitation current of 3000 At. The corresponing magnitue of flux ensity istribution is shown in Figure Both figures (Figure 4.16 an Figure 4.17) present that the flux lines are well balance an there is no saturation part in the stator an rotor except rotor ribs. (Stator an rotor is saturate at about 1.8 T as inicate in Figure 4.3.) Although the flux flowing through the rotor ribs is also a leakage flux which remains insie rotor without crossing the air-gap, the ribs are necessary for mechanical reason: to maintain laminate rotor core shape. In normal conition, the ribs cannot avoi to be saturate [18]. Figure 4.18 is the overall magnitue of the flux ensity with the maximum phase current of 200 A an excitation current of 3000 At. The circumferential area of sie-poles is saturate as shown in the figure. That means the excitation flux is concentrate at the sie-pole from the frame which is the main path of the excitation flux. 55

67 Figure 4.14 Flux ensity vector istributions at no phase current (I exc =3000At) Figure 4.15 Magnitue of flux ensity at no phase current (I exc =3000At) 56

68 Figure 4.16 Flux ensity vector istributions at maximum torue position (I ph,max = 200A, I exc =3000At) Figure 4.17 Magnitue of flux ensity at maximum torue position (I ph,max = 200A, I exc =3000At) 57

69 Figure 4.18 Overall magnitue of flux ensity at maximum torue position (I ph,max = 200A, I exc =3000At) 58

70 4.4.2 Output torue Figure 4.19 shows the current phase angle versus output torue characteristic at which the maximum phase current is 200 A an the excitation current is 3000 At. In the figure, the results are compare with those of the pre-evelope motor before attaching the excitation magnetic circuit. The maximum torue is increase from Nm to Nm (25.7 % increase). Since the excitation current increases the air-gap flux, the magnet torue is also increase; an then, the maximum torue position is shifte slightly from to Table 4.2 presents the output torue results along the various excitation current values; Figure 4.20 is the graph of Table 4.2. Figure 4.19 Comparison of output torue between pre-evelope an final moel 59

71 Table 4.2 Calculate output torue uner various excitation current values [Nm] Phase Angle 3000 At 2000 At 1000 At 0 At At Figure 4.20 Comparison of output torue uner various excitation current values 60

72 4.5 Summary an Discussion FEA simulations have been conucte for a newly esigne PM machine that attaches excitation coils an excitation flux path to the target moel which is escribe in Section 4.2. The results of the simulations clearly show the outstaning characteristic of the newly esigne motor as compare to that of the pre-evelope motor. The maximum torue increases Nm to Nm (25.7 % increase). The simulations have also confirme that the air-gap flux can be change by the excitation current value. Uner 3000 At, the average of the air-gap flux ensity is T, which is about 15.3 times of the value uner At ( T). The pure PM torue can be obtaine from Table 4.2 at 90 phase angle, Nm uner 3000 At an Nm uner At. Since the PM torue is irectly proportional to the air-gap flux *, the pure PM torue of At is too large consiering its air-gap flux ensity. When At, the calculate torue value is about 30.8 % of the value in case of 3000 At, but the air-gap flux is only 6.5 %. A comparison between the pre-evelope motor an the final moel with 0 At of excitation current reveals that there is a big ifference in the air-gap flux ensity ( T for the pre-evelope motor an T for 0 At) since the excitation flux paths can increase the total reluctance of the motor. Corresponingly, the calculate PM torue in both cases is clearly ifferent ( Nm for the pre-evelope motor an Nm for 0 At). However, the percentage of the pure PM torue is similar that of the air-gap flux ensity (77.4 % for torue an 73.8 % for flux ensity) because the air-gap flux an the * T=K T I, an K T Φ 61

73 flux linkage of the phase conuctors come from only PMs when the excitation current is 0 At. Therefore there must be other magnetic fiels which cross the phase conuctors without passing the air-gap. Table 4.3 inicates PM torue an air-gap flux ensity ratios of each excitation current to the excitation current of 0 At. When the excitation current is positive, the torue ratio is much less than the flux ensity ratio; an when negative, the torue ratio is greater than the flux ensity ratio. These results suggest that positive excitation current ecrease the flux linkage crossing the phase conuctors an negative excitation current increase that. Comparing Figure 4.21 (positive excitation current, I exc =3000At) with Figure 4.22 (no excitation current), the flux ensity in the stator teeth is not uniformly istribute along the axial irection. At N-position in Figure 4.21, the flux ensity is counterbalance in the mile of the left part of stator teeth, an at S-position, the right part. As a conseuence, the effective flux crossing the phase conuctor will be reuce. With negative excitation current, the flux ensity vectors change their irection in the air-gap (Figure 4.23, I exc = -1500At). That means the air-gap flux in the raial irection will be Table 4.3 Comparing PM torue an air-gap flux ensity in each excitation current Excitation PM torue Average air-gap flux ratio current [Nm] ensity[t] ratio 3000 At At At At At

74 (a) N-position (b) S-position Figure 4.21 Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc =3000At) 63

75 (a) N-position (b) S-position Figure 4.22 Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc =0At) 64

76 (a) N-position (b) S-position Figure 4.23 Flux ensity istributions on the axial cut-plane (I ph,max = 200A, I exc = -1500At) 65