Design Bpm Techniques 2011

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 9, SEPTEMBER 2011

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A Review of the Design Issues and Techniques for Radial-Flux Brushless Surface and Internal Rare-Earth Permanent-Magnet Motors David G. Dorrell, Senior Member, IEEE, Min-Fu Hsieh, Member, IEEE, Mircea Popescu, Senior Member, IEEE, Lyndon Evans, David A. Staton, Member, IEEE, and Vic Grout, Senior Member, IEEE

Abstract—This paper reviews many design issues and analysis techniques for the brushless permanent-magnet machine. It reviews the basic requirements for the use of both ac and dc machines and issues concerning the selection of pole number, winding layout, rotor topology, drive strategy, field weakening, and cooling. These are key issues in the design of a motor. Leading-edge design techniques are illustrated. This paper is aimed as a tutor for motor designers who may be unfamiliar with this particular type of machine. Index Terms—Analysis, brushless permanent-magnet (PM) motors, design, internal PM (IPM), torque.

I. I NTRODUCTION

T

HERE ARE MANY excellent books on the design of brushless permanent-magnet (PM) motors. Examples of well-known and established texts are given in [1]–[5], while more recently, there have been tutorials at leading international conferences with accompanying Course Notes Texts [6]. These cover dc and ac motors and mostly cover the design of ferritemagnet machines although rare-earth machines are also covered. Materials are discussed in a variety of specialized texts; these include magnets [7], [8], steels [9], [10], and insulation systems [11]. Noise is also covered by several texts [12], [13]. This list is far from comprehensive, and there are many other monographs that cover specialist aspects of electric motor operation that are relevant to brushless PM motors. There is still relatively little on the thermal design of electrical machines in terms of texts although the number of technical papers is increasing; illustrations of this are [14] and [15], while

Manuscript received April 14, 2010; revised July 23, 2010; accepted October 1, 2010. Date of publication October 28, 2010; date of current version August 12, 2011. D. G. Dorrell is with the School of Mechanical, Electrical and Mechatronic Systems, University of Technology Sydney, Sydney, N.S.W. 2007, Australia (e-mail: [email protected]). M.-F. Hsieh is with the Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University (NCKU), Tainan 701, Taiwan (e-mail: [email protected]). M. Popescu, L. Evans, and D. A. Staton are with Motor Design Ltd., SY12 9DA Shropshire, U.K. (e-mail: [email protected]; [email protected]; [email protected]). V. Grout is with the Centre for Applied Internet Research, Glyndwr University, LL11 2AW Wrexham, U.K. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2010.2089940

[16]–[18] show coupled electromagnetic and thermal considerations in PM machines. In recent years, there have been many papers that cover various aspects of the electromagnetic design on rare-earth PM motors; for instance, [19]–[25] show recent papers on PM-motor design in a variety of situations. The aim of this paper is not to highlight particular design aspects of one form of brushless PM motor but rather to give an overview of many of the factors dictating option selection and design solutions. Therefore, in this paper, the key design points related to the design of brushless rare-earth PM machines are outlined and solutions are discussed. Techniques for analysis are outlined, and these should be useful to a machine designer who is unfamiliar with this particular type of machine. Section II will consider electromagnetic and structural issues, while Section III will discuss thermal considerations. Section IV will put forward analysis techniques. Design examples are included in the discussions. II. I NITIAL E LECTROMAGNETIC D ESIGN C HOICES In this section, some basic design choices are discussed. These are necessary at the outset of the design procedure. A. Radial or Axial Flux? Generally, most PM motors are of the radial-flux type. The reason for this is that fabrication is straightforward and established, using slotted stators with standard round radial laminations, and the electrical loading can be maximized because of the use of the slots. However, there are good examples of using axial-flux machines, and the design of these machines is discussed in [26]. In these machines, the windings tend to be air-gap windings (although they can have teeth [27]) which can limit the amount of copper that can be used and, hence, can limit the amount of loading possible. The windings tend to be specially formed and shaped, and often, Torus windings are used; Mendrela et al. [27] review different options for this type of machine. Axial-flux machines are often used as motors although they have many advantages (usually related to their low armature reactance) in the area of generation [28], particularly in wind generation [29]. However, axial-flux applications can still be considered as niche, and the focus of this paper will be on radial-flux laminated motors since these constitute the majority of brushless PM motors.

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TABLE I TYPICAL TRVs [1]

an engineering approach to sizing the rotor. The sheer stress allows a more fundamental stress-limiting calculation, as shown in the Appendix, based on the electric loading and the air-gap flux-density limits. As can be seen in Table I, there is a wide variation in TRV—a median for first-pass design of a larger, efficient, and well-designed rare-earth magnet machine would be about 40 kN · m/m3 , which is a sheer stress of 2 N/cm2 .

B. Ratings, Motor Classes, and TRV

C. AC or DC Control?

The rating of a machine is important and will dictate the size and design demands for a machine. The torque-per-unit-rotor volume (TRV) is a useful guide to how “good” a machine is. The TRV is related to the tangential stress by

Brushless PM motors generally fall into two classes: ac and dc. There are different requirements when designing them, and this is related to the back-EMF waveform and the rotor-position sensing. Consider a three-phase operation. For ac operation, the phase current will be sinusoidal, and there is a 180◦ conduction for each inverter leg using a pulsewidth-modulation strategy with a position encoder. For dc control, the current waveform is trapezoidal with 120◦ conduction with three Hall effect probes usually used to detect the switching positions. Hence, an ac machine requires sinusoidal back EMF generated by the PM rotor, while the dc machine requires a more trapezoidal backEMF waveform. Some machines have back-EMF waveforms that are intermediate and can be used with either ac or dc control. Generally, dc motors are suitable for power drives which can tolerate some torque ripple and do not require substantial field weakening at higher speeds, while ac motors are more suitable for servo drives where smooth operation and extended field weakening are required. DC control can offer a higher power density, and this is illustrated in the Appendix. The characteristics for DC and AC operations can be summarized. The following are the characteristics of dc operation: 1) full-pitched and concentrated windings for trapezoidal back EMF; 2) higher power density; 3) Hall effect probes to detect the correct current switching positions (low cost); 4) suitable for power drives. The following are the characteristics of ac operation: 1) distributed and fractional-slot windings for sinusoidal back EMF and smooth operation; 2) better control and extended field weakening; 3) shaft encoder to control current (high cost); 4) suitable for servo drives and drives requiring excellent field-weakening capabilities. There are several strategies to make the machines sensorless (no Hall probes or shaft encoder) although the norm in industrial applications is still to use position feedback. Generally, the current phasor from the three-phase-winding current set should be located on the rotor q-axis unless field weakening is used. This is used above the base speed when, essentially, the inverter voltage has reached its maximum where the current cannot be controlled and the maximum current cannot be achieved. The inverter switching is advanced, and this can be effective up to maybe 15–20 electrical degrees depending on the machine. This is shown in Fig. 1 for a small four-pole dc-controlled machine [shown later in Fig. 6(b)]. It can be seen that the torque range is extended from about 2500–3000 r/min.

TRV = 2σmean

(1)

where σmean is the sheer stress on the rotor (in newtons per square meter). The sheer stress will be discussed later. Common limits for the TRV in various machines are quoted in [1], and these are listed in Table I. However, it can be seen that, generally, the larger and better cooled the machine, the higher the TRV. In totally enclosed fan-cooled machines, typical windingcurrent-density levels are in the region of 5–6 A/mm2 . This limits the electric loading and, hence, stress, which results in a low-range TRV. Larger water- or oil-cooled machines can push this much higher. In electric vehicle (EV) and hybrid EV drive motors [30], the peak power rating is a transient rating at lower speeds, and the current density during a transient (or acceleration) period can be in excess of 20 A/mm2 for a period of several seconds or tens of seconds. Some basic motor types are listed in Table I although, at this stage, no distinction is made between ac- and dc-controlled brushless PM machines. These volumes can be used to calculate an approximate rotor size. However, initially, a diameter has to be selected based on the choice of pole number, magnet size, and rotor topology. The geometry may also be dictated by the space in which the motor has to fit. Starting with a two-pole motor geometry, the diameter-to-axial-length ratio will be close to unity and will increase with pole number (moving from a long cylindrical shape to a disk shape). This is a crude sizing approximation for radial-flux machines over a wide power range. The first key point to remember is that the stator yoke thickness is governed by the flux per pole (since it has to carry this); therefore, it decreases as the pole number increases. High-pole-number machines tend to have a much higher diameter compared with the axial length. In totally enclosed machines, the TRV tends to be in the range of 7–14 kN · m/m3 for small ferrite-magnet motors, 20 kN · m/m3 for bonded Nd–Fe–B magnets, and 14–42 kN · m/m3 for rare-earth magnets, and it is hard to increase beyond this without using a very specialized topology. If high-energy magnets are used, then high-efficiency machines can be designed, and also, it allows the motor to be more compact. When Nd–Fe–B magnets are utilized, it is reasonable to expect a peak electromagnetic efficiency of over 90% even on smaller machines. In terms of the sheer or tangential air-gap stress, (1) shows a direct relationship to the TRV, as proved in [1]. The TRV gives

DORRELL et al.: REVIEW OF DESIGN ISSUES AND TECHNIQUES FOR PERMANENT-MAGNET MOTORS

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Fig. 1. Field weakening (phase advance) for a small surface-magnet dc machine.

Fig. 2. Surface- and interior-PM four-pole rotors with red and blue magnets oppositely polarized. Gray areas denote the laminated core. Red and blue areas are oppositely magnetized magnets. (a) Nonsalient surface-magnet rotor. (b) Salient interior-magnet rotor.

Phase advance has the effect of weakening the main field by rotating the current phasor so that there is a component on the −d-axis. AC-controlled machines with internal-PM (IPM) rotors can have much higher field-weakening capability, and the machine used in [30] has 60◦ phase advance—this is studied later. IPM motors can have considerable reluctance torque as well as excitation torque. The machine in [30] is required to have a wide field-weakening capability because the base speed is 1500 r/min, whereas the maximum speed is 6000 r/min. D. Choice of Rotors There are many possible topologies for the rotor—too many to comprehensively list here. They lie in two basic topologies. One has surface magnets with little saliency, which are common in dc motors as already mentioned (although they are also often used in ac motors), while the second has embedded magnets and considerable saliency. Fig. 2 shows some examples of these. Many of these topologies can be simulated in the SPEED simulation package from the University of Glasgow, U.K., and Miller [31] lists many brushless PM-motor rotor arrangements. For a surface-magnet nonsalient rotor, Xd = Xq , as shown in Fig. 2(a). Embedded magnets are possible in the rotor, as shown in Fig. 2(b). These are used in ac machines, although they can be used in dc machines. They have q-axis saliency (i.e., Xq > Xd ). The advantage of this is that the peak torque is moved from the q-axis to an angle of about 100–120 electrical degrees away from the d-axis. This means that if there is a transient overload when the current is on the q-axis, there

Fig. 3. Phasor diagram and equivalent circuits for brushless permanent ac machines. (a) Phasor diagram for salient-pole PM motor—the q-axis is often taken as the vertical-axis reference (in surface-magnet rotors, Xe = Xq ). (b) Per-phase equivalent circuit for nonsalient PM motor. (c) d–q-axis equivalent circuits for salient-pole PM motor.

will be extra torque available to bring the motor back to the correct firing angle, preventing pole slipping. The saliency also offers additional reluctance torque, and this is illustrated by the example in Section IV-B. The phasor diagram for the two types of rotor is shown in Fig. 3(a) (assuming ac control). This is a general case in steady state; the difference in operation is that if there is no saliency, then Xd = Xq and the steady-state circuit in Fig. 3(b) can be utilized. If there is q-axis saliency, then the steady-state circuits have to be resolved into two (onto the d- and q-axes), as shown in Fig. 3(c); this represents an IPM machine. Under lowsaturation conditions, then Xd and Xq are independent and are functions of the d- and q-axis reluctances. However, when there is high saturation, there is cross-coupling between the d- and q-axis components so that Xd = f (Id , Iq ) and Xq = f (Id , Iq ). If an extended field-weakening range (from the base speed upward) is required, then the IPM rotor should be used. A surface-magnet motor simply cannot cope with this range because the field-weakening capability is limited. This occurs when the current phasor is advanced away from the q-axis so that there is a component on the −d-axis, as shown in Fig. 3(a). This has three effects: It can be seen that there is a negative Xd Id phasor on the q-axis. This weakens the motor flux which reduces the iron loss at high speed. Additionally, it reduces the voltage requirement from the inverter supply. The third effect is the introduction of reluctance torque in the machine. This is shown in Fig. 3(c), which breaks down the voltages onto the d- and q-axes. The power due to the excitation torque is 3EIq (where E is the back EMF induced into the rotor by the IPM

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Fig. 4. Pole-face slots for control of Xq in IPM rotor.

rotor), whereas the total output power, including the reluctance, is 3E Iq [where E is the total rotor EMF due to the magnets and q-axis saliency, as defined in Fig. 3(c)]. In Fig. 2(b), it can be seen that it is possible for q-axis flux to flow across the surface of a pole face which may lead to excessive Xq , in which case, holes or slots can be used in the pole face to control Xq (Fig. 4). The use of the pole-face slots will also control the cross-saturation, making the machine performance more predictable and stable. E. Pole-Number Selection It is important to select the correct pole number for the machine. DC machines tend to have lower pole numbers (2, 4, 6, etc.), while ac motors often have higher pole numbers (8, 12, 16, etc.), although this is not a firm guideline. Higher pole numbers enable fractional-slot windings. The pole number should be a function of the speed of the machine, and the following points should be addressed. 1) The flux in the machine should not alternate at a high frequency; otherwise, the iron losses will be excessive, although field weakening can be used at higher speed to limit the iron losses (see example later). 2) Flux frequency = Rotor rotational frequency × pole-pair number. 3) For normal laminated steels, do not go beyond 150– 200 Hz, although at lower fluxes, it is possible to operate successfully at maybe 400 Hz even for normal steels. 4) A two-pole PM motor can be difficult to fabricate, and also, the end windings are long (leading to increased losses) and the stator yoke is wide (leading to increased machine diameter). Popular pole numbers tend to be higher in fractional-slot ac machines to enable distributed windings. In smaller machines, a nine-slot eight-pole number is popular [32] although 9/6 arrangements are used and a 12/10 machine was reported in [33]. In [34], the base slot number of 18 was used with different rotors with 12 and 16 poles. In [35], an unusual rotor design using consequent IPM poles (alternate magnet and iron poles) with dovetail-shaped magnetic poles is discussed with pole numbers varying between 6 and 14. All the machines in [32]– [35] are ac drives. F. Noise, Vibration, Cogging Torque, and Torque Ripple This should not be ignored. Larger drives should be smoother in operation; otherwise, they will cause excessive noise. The

9/8 machine reported in [32] is popular for small machines but it creates high unbalanced magnetic pull (UMP—a net radial force on the rotor). This makes it more unsuitable for larger machines. The UMP is much less in a 9/6 machine. In [34], the effects of winding harmonics on the UMP were studied; Zhu et al. [36] followed a very similar method with more slot/pole combinations but without the detailed method. However, UMP is not the focus of this paper. More relevant is the production of cogging torque due to the rotor-magnet and stator-slot combination (which is an alignment torque) and torque ripple due to the interaction of the magnet air-gap flux waves with stator MMF spatial harmonics (which is an excitation torque). Cogging torque is an alignment torque between the stator teeth and rotor magnets and is most prominent in surfacemagnet motors with integral slots per pole or pole pair. It is a reluctance type of torque, and there are a variety of methods for calculating it using analytical methods [37] and finite-element analysis (FEA) (there are many studies of cogging using this method, e.g., [38]). There are also several ways to improve the cogging torque, such as skew (gradual in either stator or rotor or using skewed axial rotor segments [38]), bifilar teeth [38], pitching and staggered magnet spacing in a surface-magnet rotor [39], and slot opening adjustment, and in ac machines, fractional slotting is a standard way to reduce cogging. This means that there is a fractional number of slots per pole, e.g., the 9/8 configuration aforementioned is an example of this. Cogging torque in brushless dc machines was reviewed in [40]. Load torque ripple is a function of the interaction of the PM air-gap flux waves with the winding MMF. This is reviewed in [41] (which also discussed nodal vibration and noise). Torque ripple under load is often neglected in studies, with a preference for static or mean torque. This is because accurate calculation of torque, even by using FEA, can be difficult [42], [43]. Mean torque can be calculated using current–flux-linkage loops [44] (indeed, so can cogging torque [45]) although many still only do a load calculation at one position. Torque ripple tends to be implicit in a dc machine due to the fully pitched windings and the need to get a trapezoidal winding. For an ac machine, there is a greater emphasis in smooth operation so the winding layout is more sinusoidal and torque ripple is minimized. Skew will also help reduce the load torque ripple. Considering the equation for stress in (1), the torque (for an unskewed machine) will be T (t) = L

D 2

πD σ(y, t) dy 0

πD D br (y, t)Jst (y, t) dy =L 2

(2)

0

where y is the circumferential distance around the air gap (so that ky = θ and k = 2/D where D is the mean air-gap diameter) and L is the axial length. We can define the stator electric loading as a stator surface current density Js (in amperes per meter), while we can define the rotor radial flux density in the air gap as br . The product of these at any particular point will


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give the sheer stress. The air-gap flux density due to the PM rotors is br (y, t) = Brm cos (mp(ωr t − ky + φm )) (3) m

where m = 1, 3, 5, etc. A general phase angle is set by φm . The synchronous rotational velocity of the rotor is ωr , and this is matched to the supply frequency ωs (in radian per second) by the equation ωs = pωr where p is the pole-pair number of the machine. In many machines, it can be assumed that the winding is a balanced three-phase winding. However, in a fractionalslot machine, it should not be assumed so that the winding MMF is made with a fundamental one-pole-pair harmonic with second, third, fourth, fifth, sixth, seventh, etc., windings. The fundamental harmonic has to be taken as two for the general case, and harmonics are eliminated if they are zero. Hence, assuming the current phasors are in phase with the rotor flux Jsnw cos(ωs t − nw ky + φnw ) Js (y, t) = nw

=

Jsnw cos(pωr t − nw ky + φnw )

(4)

nw

where nw = ±1, ±2, ±3, etc., for the general case in a threephase winding. Using (2), the product of (3) and (4) shows that torque is a function of the product of the cosine terms when the phase angles are equal. For the main torque, nw = mp, where m = 1 and time variation is zero, i.e., a steady torque. Working through the mathematics, the general case for the torque vibration is m±1 ftorque

= (m ± 1)fsupply |nw =±mp

(5)

Fig. 5. Example of 18-slot 8-pole ac machine with one slot skew. (a) Distribution of one phase for three-phase sine winding. (b) Half cross-section for IPM machine. (c) Three-phase controlled sinusoidal current on rotor q-axis. (d) Three-phase back EMF. (e) Electromagnetic torque. TABLE II 18-SLOT 8-POLE IPM AC MOTOR EXAMPLE—OPERATING AND G EOMETRIC P ROPERTIES

where m = 1, 3, 5, etc. This does not necessarily mean that these torque vibrations exist. If there is no matching spatial winding harmonic and magnet flux wave, then there is no torque. There can be winding harmonics below the pole number, and these have no effect since there is no corresponding magnet flux wave. This tends to mean that dc machines have some torque vibration while ac machines tend to have winding harmonics and flux waves that, spatially, do not match so that there is less torque ripple. This is investigated in the next section. G. Winding Arrangement There are a variety of methods for winding a brushless PM motor depending on whether it is an ac or dc motor. The aim of an ac winding is to obtain a sinusoidal open-circuit back-EMF waveform. For a dc winding, it is to obtain a trapezoidal waveform. Therefore, is it appropriate to consider them separately. Slot fill is considered in Section II-J. 1) AC Windings: Distributed windings are often utilized in ac machines with coil pitches of one slot. An excellent examination of this arrangement was put forward in [46]. The correct winding for a machine is very much a function of the pole number and slot number and whether there are one or

two coil sides per slot (concentric, lap, or concentrated round one tooth), as discussed in [31]. Here, a simple example of an 18-slot 8-pole IPM machine is shown in Fig. 5. This is a fractional-slot machine. The winding is illustrated for one phase in Fig. 5(a), showing the distributed nature of the winding. The rotor arrangement is shown in Fig. 5(b). The machine was modeled using the SPEED software package PC-BDC [47] from the University of Glasgow, U.K., and the machine data are given in Table II; this gives the operating point data together with various geometrical and winding data. There is one statorslot skew in this machine which helps form the back EMF into a very sinusoidal wave, as shown in Fig. 5(d), so that the torque

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Fig. 7. Interaction of back EMF and current in dc machine, illustrating torqueproducing region in waveforms.

there are three slots per pole which is not accounted for in the waveforms. It is also necessary to consider the torque-producing region of the waveforms. This is shown in Fig. 7. If the back-EMF wave is too narrow, then there is torque ripple when the back EMF is multiplied by the current. In addition, the dc machine used Hall probes, and if they are only slightly out of position, then there will be considerable torque ripple. This was investigated in [39]. 3) Delta Connection: Delta connection is not recommended in a brushless PM machine. If there is any third time harmonic in the phase back EMF, then this will induce a circulating zeroorder current in the mesh, as shown in Fig. 8. This will cause excessive current and copper losses and potential burnout of the winding. Fig. 6. Comparison of idealized short-pitched and fully pitched windings in a 12-slot 4-pole dc machine. The windings are one phase of a balanced three-phase set in each case. (a) Short-pitched coils (two-third pitching). (b) Fully pitched concentrated coils. (c) Trapezoidal 120-electrical-degree three-phase current set. (d) Three-phase back EMF with short-pitched windings. (e) Electromagnetic torque with short-pitched winding. (f) Three-phase back EMF with fully pitched windings. (g) Electromagnetic torque with fully pitched winding.

is smooth, as shown in Fig. 5(e). The efficiency is only 85%, but at 6000 r/min with eight poles, the frequency in the iron is 400 Hz. This may require high-grade aerospace steel, although this was not used in this instance (Losil 800 was used), and therefore, the iron loss dominated the loss components. 2) DC Winding: DC machines require a different winding strategy with the aim of obtaining a trapezoidal back-EMF waveform. This will interact with the trapezoidal current (with 120◦ conduction period) to produce a smooth torque. This requires fully pitched concentrated windings. Fig. 6 shows the winding layout for one phase of a three-phase set for a 12-slot 4-pole machine. The first simulation uses a short-pitched distributed winding, while the second uses a fully pitched concentrated winding. The waveforms illustrate the torque production and the fact that there is inherent torque ripple with the shortpitched winding. This is very much an idealized waveform. The back EMF usually has some distortion to produce ripple, and this arrangement would have substantial cogging torque since

H. Magnet Selection and PC The type of magnet used will have a great effect on the motor performance and cost. The increased cost of high-energy magnets may be offset by the fact that less magnet material is required and the motor will be more compact. Typical remanent magnetism and recoil permeability values at 25 ◦ C for various magnets are listed Table III. Further details are put forward in [7] and [8]. The nonlinear characteristics of the specific magnets should be inspected. The magnets should not be used in the nonlinear area, as shown in Fig. 9, and sufficient design tolerance should be built in so that the magnets are not demagnetized even under overload. The operating point can be found by calculating the permeance coefficient (PC) and also the electric loading effects. For ferrite-magnet motors, a PC of at least eight is usually required, but for rare-earth magnets, this can be lower since the magnets are much stronger and linear. The PC can be improved by the use of a narrow air gap and shorter flux path lengths and wide teeth and stator yoke. Lower flux-density levels also improve the PC. The thermal performance of the magnet material also has to be considered, as shown in Fig. 10. While this paper is mostly concerned with rare-earth magnet machines, it is worth considering ferrite-magnet material for completeness. The


Fig. 8.

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Zero-order 3rd time harmonics in delta-connected brushless PM motor. (a) 3-phase current and 3rd time harmonics. (b) Circulating zero-order set. TABLE III TYPICAL MAGNET DATA

Fig. 9. Second quadrant operation for ferrite (grades 1 and 5) and Nd–Fe–B (Crumax 2830) magnets.

ability to withstand demagnetization for a magnet is dependent upon the magnet temperature and the magnet type. The typical values of temperature coefficient for the magnet intrinsic coercivity Hcj are as follows: 1) ferrite: +0.4%/◦ C; 2) Sm–Co: −0.2%/◦ C to −0.3%/◦ C; 3) Nd–Fe–B: −0.6%/◦ C to −0.11%/◦ C. Ferrite is worse at lower temperatures due to the negative temperature coefficient, whereas rare-earth magnets are worse at higher temperature. Ferrite magnets have a nonlinear region which can be easily moved into with overload and overtemperature operation. The following points summarize the discussion for ferrite magnets. 1) Ferrite magnets need a good magnetic circuit and a low reluctance; otherwise, their load line will not be steep enough and the operating point will be close to the nonlinear region. 2) The slope of the load line is equal to negative PC when the x-axis is scaled by μ0 . 3) PC = (magnet thickness×air-gap area)/(air-gap length× magnet area). The PC can be used to set the magnet thickness. 4) Air-gap area ≈ magnet area for surface magnet.

Fig. 10. Ferrite and rare-earth magnet thermal considerations. (a) Ferritemagnet example. (b) Rare-earth magnet example.

5) Therefore, the magnet thickness has to be considerably greater that the air-gap length. 6) Hence, a lot of magnet material is required. To summarize the discussion for rare-earth magnets: 1) The PC does not need to be as high when using rareearth magnets so that less material is required (which is necessary since it is more expensive), and again, the PC can be used to set the magnet thickness. 2) They have high energy, and handling can be difficult when magnetized. 3) Premagnetizing may be required.

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Most magnet steels will saturate between 1.5 and 1.7 T (where the knee points of the B/H curves are in Fig. 12). The sheer stress can be maximized in high-performance machines by increasing the flux using cobalt–iron alloys. These alloys can have a knee point above 2 T [64]; however, they tend to be very expensive and applicable to premium-cost applications. Manufacturing affects the iron loss. The properties of the steel are affected by punching and cutting. If a complicated lamination shape is used, the properties will be affected. Worn lamination punches will tend to lead to increased iron losses with lamination edges having burr, which causes shorting between laminations and increased eddy-current loss. For an IPM rotor, a very fine cut across the surface can remove a lot of the burr and improve iron loss. J. Insulation Systems, Slot Fill, and Mechanical Aspects of Rotor Structure Fig. 11. Illustration of demagnetization of rare-earth magnet with thermal overload. Red dots illustrate points after permanent demagnetization.

4) It is possible to demagnetize the magnets under thermal stressing, as shown in Fig. 11.

I. Steel Selection and Iron Loss The two basic properties of interest are the B/H curve and the iron loss in the steel. The B/H curve sets the flux levels possible in the machine and the degree of saturation, while the iron loss is important to the machine efficiency. The loss calculation is often done by using a modified version of the Steinmetz equation to obtain hysteresis and eddy-current loss [48]. This loss-calculation method is used in the SPEED modeling software used in this paper, and the equation utilized for the watts-per-cubic-meter iron loss in [31] and [47] is obtained from P = Ch f

a+bB Bpk pk

+ Ce1

dB dt

2 (6)

where there are various coefficients necessary for accurate calculation. The loss calculation is really an estimate and only good if the material loss data are accurate (often, they are not). Lookup iron-loss tables are often utilized rather than the implementation of a complicated equation set, and these are given in [9]. As an example of the effect of steel, consider the ac motor design in Section II-G1. The material used in this example was Losil 800/65, and the iron loss was calculated to be 623 W. The material can be replaced with Transil 35, which has a lower flux density for a given MMF, as shown in Fig. 12. However, it is a low-loss steel, as shown in the comparison in Fig. 12, so that the iron loss is now 122 W. Loss is often a function of the amount of silicon in the steel. Increasing the amount of silicon (up to a maximum of 3% [9]) can reduce the loss in the steel. Reference should be made to manufacturer’s data. The thickness of the lamination also makes a significant difference to the eddy-current loss. For instance, for Transil 330, at 1.5 T and 50 Hz, 0.35-mm laminations have a loss of 2.9 W/kg, while 0.5-mm laminations have 3.15 W/kg [1].

Insulation systems have been standardized and graded by their resistance to thermal aging and failure. Four insulation classes are in common use, as set by the National Electrical Manufacturers Association (NEMA), U.S., and these have been designated by the letters A, B, F, and H, as shown in Table IV. The temperature capabilities of these classes are separated from each other by 25 ◦ C increments. The temperature capability of each insulation class is defined as the maximum temperature at which the insulation can be operated to yield an average life of 20 000 h. A maximum temperature rise is also set. There have been new classifications introduced in 2009 (although not yet extensively adopted) which correspond to the traditional classifications; the new equivalent International Electrotechnical Commission classes are also quoted. In terms of low-voltage machines with random-wound coils, the system will consist of a slot liner into which the coil is inserted. The coil will be formed from enameled copper wire, and the coil will be automatically wound in situ, or automatically or manually inserted as a complete coil. There may be top wedges to lock the coil into the slot, and if there are two coil sides in the slot, then there may be a phase separator. The stator may be dipped in an epoxy-resin-type varnish with the aim of impregnating deep into the slot. This varnish has two functions. It will fill and set so that the winding is not loose in the slot, which will prevent vibration damage. It will also provide good thermal conduction from the coil to the core, which is necessary for effective cooling. Loose windings in slots are not a good manufacturing solution. If the stator is not dipped in resin, then it is often trickled as a hot solution down into the slots in order to secure the coils. Different insulation systems are described in [11]. If the wire is too thick for winding the coil, then wind with multiple strands and connect in parallel. These are often described as “strands in hand” and should not be confused with parallel windings, where complete coils are connected in parallel. The fill factor is the ratio of the copper in a slot to the slot area. A common mistake made is to assume a fill factor that cannot be realized. There is a slot liner, and there may be wedges which will occupy slot space. Also, the conductors are round and have an enamel insulation coating so that there will


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Fig. 12. Comparison of B/H and frequency/iron-loss curves for Losil 800/65 and Transil 35 steels (B = 1.7 T for loss data). TABLE IV INSULATION CLASSIFICATIONS [NEMA MG 1-2006] (AMBIENT BELOW 40 ◦ C)

4) What is the duty cycle? 5) How effectively can we cool the machine? The latter two points will affect the thermal rating of the machine, and this is addressed in the next section. III. C OOLING AND T HERMAL I SSUES

be space even when tightly packed. Therefore, high fill factors should be approached with caution. For instance, automotive alternators are low voltage (12 V) and often have very few turns of very thick wire. Manufacturers often work with a maximum slot fill of 30% or less. Many machines have environmental considerations that require the stator and/or rotor to have a protective can which can be conducting (for instance, from stainless steel [49]) or nonconducting. These cans can add eddy-current loss to the machine and lengthen the air-gap length so that the cans can be accommodated. However, they can add considerable mechanical stability to the rotor and help retain the magnets on the surface of the rotor. Both surface magnets and IPM motors have structural issues with retaining the magnets and pole faces (in IPM rotors). The mechanical stresses in an IPM rotor were described and discussed in [50], while the use of retaining sleeves in a high-speed surface-magnet rotors was highlighted in [51] and mechanical retention of magnets was further discussed in [52]. The mechanical integrity of a rotor may restrict the maximum speed of a machine and also the possible maximum rotor diameter. The losses in the machine can be split up into copper, iron, and mechanical losses. Some of these losses can be difficult to assess. For instance, there will be eddy-current losses in surface magnets due to slotting [53] and possibly proximity losses in conductors if they are air-gap windings or even thick conductors [54]. However, these are normally low; Yamazaki [55] gives a good account of the loss distribution in an IPM motor. K. Sizing-Issues Summary The sizing of a machine can be a complex matter. To summarize the issues, the following points should be considered. 1) Is there a restriction on length or diameter? 2) Is it in an environment that is sensitive or hazardous? 3) What are the application torque requirements?

There is a strong requirement for more energy-efficient motors. Improved thermal design can lead to a cooler machine with reduced losses. Copper loss is a function of winding resistance and, therefore, is a function of temperature. Rare-earth PM flux reduces with increased temperature. The size of a motor is ultimately dependent upon the thermal rating. The motor components that are limited by the temperature are wire or slot liner/impregnation, bearings (life), magnet (loss of flux and demagnetization limit), plastic cover (low melting point), encoder, and housing (safety limit). The temperature of the winding insulation has a large impact on the life of the machine. Many companies use curves such as that shown in [56] to estimate motor life, and these are related to the insulation classifications in Table IV. Magnets are usually isolated from the main heat sources so that they are protected from severe transient overloads. The windings are most susceptible to transient overloading. However, rare-earth magnets (Sm–Co and Nd–Fe–B) exhibit local eddy-current losses as heat sources, which are difficult to estimate or measure. Hence, there is a much longer time constant for magnets compared with windings although it is essential to know the magnet temperature for transient and demagnetization calculation. In this section, traditional thermal designs will be outlined, and then, modern techniques will be reviewed. A. Traditional Thermal-Sizing Methods Traditional thermal sizing uses a single parameter, which is a thermal resistance, as shown in Fig. 13(a), for the housing heattransfer coefficient. In addition, the winding current density and specific electric loading are considered. Traditional thermal modeling tends to be empirical with data obtained from the following: 1) simple rules of thumb, e.g., for a totally enclosed machine, a conductor current density of 5 A/mm2 and a heattransfer coefficient [Fig. 13(b)] of 12 W/m2 /◦ C;

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C. Cooling Types and Methods

Fig. 13. Traditional thermal modeling using single thermal resistance and single heat-transfer coefficient. (a) Thermal resistance from winding to ambient. (b) Heat-transfer coefficient. TABLE V TYPICAL CURRENT DENSITY AND HEAT-TRANSFER COEFFICIENTS

2) tests on existing motors; 3) competitor catalogue data for similar products. These methods can be inaccurate. A single parameter fails to describe the complex nature of motor cooling, and there is poor insight into which aspects of the thermal performance of a motor need to be focused upon. Table V lists typical values for the current density and heat-transfer coefficient.

B. Modern Thermal Design Techniques There are two options for modern thermal design. These are lumped-circuit analysis (network analysis) [14], [15], [18], [57]–[59] and numerical analysis using FEA and computational fluid dynamics [16]. While computational fluid dynamics gives more accurate solutions for particular examples, it can be time consuming to set up the model. In the design office, the lumpedcircuit analysis is more useful for faster and more interactive design procedures. It can be linked into electromagnetic design, as illustrated in [18] where the thermal package Motor-CAD from Motor Design Ltd., U.K., [60] is linked with the SPEED software [47]. In the examples put forward in this paper, these environments are used. A typical lumped circuit from MotorCAD is shown in Fig. 14; the literature has several examples of this type of circuit as developed by many researchers (e.g., [14]–[18], which are, by no means, comprehensive). When there is a high temperature gradient, more nodes are required so the slot is modeled as a multishell structure, as shown in Fig. 14(b). The accuracy of the circuit model in Fig. 14(a) very much depends on the accuracy of the lumped parameters; if one is substantially inaccurate, then it can affect the temperatures of the surrounding nodes. Therefore, the components have to account for the heat flow in terms of the conduction, convection, and radiation. Several aspects of the model are manufacturing dependent as well as material dependent. For instance, the thermal conductivity of the coil is a function of the impregnation of the resin.

Motor-CAD covers several thermal networks including a range of cooling types that represent the standard methods of motor cooling. 1) Natural convection (TENV): This is very common with many housing design types. 2) Forced convection (TEFC): There are many fin channel design types, and fans are commonly fitted to industrial drives. 3) Through ventilation: This utilizes rotor and stator cooling ducts. 4) Open end-shield cooling. 5) Water jackets: There are many design types (axial and circumferential ducts), and they can be for either stator or rotor. 6) Submersible cooling. 7) Wet rotor and wet stator cooling: This is common for pumping. 8) Spray cooling. 9) Direct conductor cooling using slot water jacket. 10) Conduction: Internal conduction and the effects of mounting. 11) Radiation: Both internal and external. Hence, there are many ways to implement effective motor cooling. IV. M OTOR D ESIGN T ECHNIQUES AND E XAMPLES Modern design techniques usually use detailed analytical algorithms and electromagnetic FEA methods to analyze a design. While the SPEED package already mentioned used analytical calculations, sometimes, detailed calculations require FEA, such as to obtain accurate cogging torque and load torque in IPM motors with phase advance. A finite-element bolt-on package can be used for this [61]. This arrangement is not unique; many finite-element packages now feature spreadsheet and initial calculation tools to enter data for an initial motor design. In this section, some additional motor-analysis techniques will be highlighted and design and analysis examples put will be forward. A. Current–Flux-Linkage Loops (I–Psi Diagrams) The mean torque can be obtained in a brushless PM machine in a similar way to the switched reluctance by forming a current-against-flux-linkage loop (I–Psi). This method was detailed in [44] and [45]. The area enclosed (W ) is equal to the work done during the rotation so that the torque is then the work done divided by the distance moved. For a machine with m pole pairs and n phases, the electromagnetic torque is m × W. (7) Te = n × 2π For a balanced machine, each phase will trace out the same loop with area W . By using the example with the short-pitched machine in Section II-G2, with both sine- and square-wave excitation, the loops are shown in Fig. 15. The mean torque for the dc control is 1.0 N · m, while for ac control, it is 0.87 N · m.


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Fig. 14. Thermal circuits and winding model of machine. (a) Lumped thermal model (part model) with heat sources, thermal resistances, and thermal capacitances—surface-magnet rotor. (b) Multilayer winding representation when there is a high temperature gradient. Traditional winding for random-wound coils and 54% slot fill.

Fig. 15. Comparison of I–Psi loops for dc and ac controls.

The peak current for both simulations was 15 A, and the same short-pitched winding in Fig. 6(a) was utilized. Interestingly, in the Appendix, the theoretical ac/dc control rating ratio was calculated to be 1.5. Here, by simply changing from sineto square-wave control, the torque increases by 1.15. If the winding is fully pitched for the dc control, then the torque is 1.07 so that the ratio is 1.23. However, the rms current with the dc control is higher. Using the same rms currents and fully pitched winding in the dc simulation gives a torque ratio of 1.07. These results were obtained in the SPEED PC-BDC and PC-FEA environments. B. Frozen Permeability Method This method is a very powerful tool for separating out the different torque components due to excitation and reluctance

Fig. 16. Prius PM-motor cross section in SPEED PC-BDC—this shows two magnets per pole and high saliency.

torques [62]. This technique is used in an FEA, and many packages allow this function. To summarize, using a magnetostatic model, a full nonlinear solution is carried out, and the total torque can be obtained from this solution. The saturated magnetic permeances are then locked. If the magnets are then “switched off” (by setting the remanent magnetism Br to zero) and the solution restarted with the locked permeances from the full solution, then the reluctance torque can be calculated. This reluctance torque includes the saturation effects from the full solution. An example is shown in Fig. 16, which is a SPEED simulation of the Toyota Prius machine in [30]. This machine operates at a high phase advance to allow for a very wide field-weakening range (from 1500 to 6000 r/min) and relies on substantial reluctance torque. This is an eight-pole machine. The peak current occurs at the base speed of 1500 r/min. This is a transient point, and the current density (over

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Fig. 17. One-pole machine from static FEA solution. Peak flux density in teeth is about 2.10 T. Load current is 190.9 A on the q-axis (1500 r/min).

20 A/mm2 at 190.9 A) and flux densities are high if the current is maintained on the q-axis, as shown in Fig. 17. The frozen permeability method was implemented at 1500 and 6000 r/min, and the results are shown in Figs. 18 and 19. It can be seen that the torque peaks between 30◦ and 50◦ phase advance. With 60◦ phase advance, it was found that the base speed current could be reduced to 141.1 A at 1500 r/min for a required maximum torque of about 300 N · m. Comparison of Fig. 18, where the current level is much higher, with Fig. 19 shows different curve shapes for both the excitation and reluctance torques. This illustrates the effect cross-saturation can have on the performance, as discussed earlier. C. Efficiency Plots Efficiency is becoming a more important factor in machine design and is indeed crucial in many designs. Computational design solutions are becoming increasingly rapid, and it is now possible to scan a range of operating points and produce a plot of the efficiencies over a 2-D array of torques and speeds. In [30], measured efficiency plots were used to illustrate the motor operation, and these can be obtained from simulations too. Fig. 20 shows the efficiency plot for the machine in the previous section using SPEED PC-BDC. For a brushless PM motor, there are several parameters that can be set. In this case, at each load point, the phase angle advance was set at 0◦ , 30◦ , and 60◦ , and the current varied until the correct torque was obtained. The highest efficiency was then selected as the operating point. The selected phase angle is shown in the top chart, while the efficiencies are shown as colored regions and contour lines in the bottom plot. D. Fractional-Slot Design-Size Rationalization Here, an example is put forward for the rationalization of a motor design by consideration of the thermal design [63].

The existing motor has 50 mm of active length (core length), a 130-mm-long housing with a traditional lamination, and overlapping windings. The new motor still has 50 mm of active length; however, the housing is now only 100 mm long. It produces 34% more torque for the same temperature rise. The machine uses segmented-lamination nonoverlapping windings (one-slot pitch concentrated coils). In order to optimize the new design, an iterative mix of electromagnetic and thermal analysis was performed. Extensive thermal modeling was carried out. The new design is shown in Fig. 21. Both arrangements had an 80-mm diameter; however, the traditional design had 18 slots and 6 poles [Fig. 21(b)] and overlapping windings, while the new design has concentrated windings and a 12-slot 8-pole layout [Fig. 21(c)]. This illustrates that the slot/pole combination is flexible for a particular application. The traditional winding only had a 54% slot fill but the new arrangement and the techniques that can be applied to manufacture it (precision bobbin wound) means that this was increased to 82% in the new design. Potting/impregnation material improvement was also possible. The new design has a k factor of 1 W/m/◦ C, whereas previous materials have a k factor of 0.2 W/m/◦ C. This gave a 6%–8% reduction in winding temperature (with respect to Celsius scale). A potted (encapsulated in resin) end-winding design showed a 15% reduced temperature compared with that of the previous nonpotted design. Vacuum impregnation can eliminate air pockets. The new design here shows 9% decrease in temperature in a perfectly impregnated motor compared with the one with 50% impregnation. All these design and manufacturing improvements lead to a much improved thermal performance for the new motor design. This means it can be more highly rated, and so, the size can be reduced by a reduction in the active axial length. V. C ONCLUSION This paper has described the design philosophy for dc and ac PM machines. It goes on to discuss many of the modern-day analysis techniques that can be used to assess the performance of a machine. Many of the techniques are illustrated with examples, and the need to consider the electromagnetic design, thermal analysis, and manufacturing techniques in conjunction is stressed. This paper will be very useful to an electrical machine designer who requires more detailed information about the steps necessary to analyze and improve a motor design of this ilk. A. Further Literature There are many sources of design method information from many researchers. In terms of further texts, [65] gives a treatise specific to PM motor design, while general ac machine design and operation are considered in [66] and [67], which can be very helpful in terms of winding theory and practice and other aspects of machine operation. The technology is rapidly developing due to new material design refinement. There are continuing developments of algorithms that are aimed at the automated and precise design of an electrical machine; [68] and [69] are illustrations of these, and a literature review would


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Fig. 18. Separation of torque at 1500 r/min with 190.9-A loading—variation of current phase with respect to q-axis.

Fig. 19. Separation of torque at 6000 r/min with 35.4-A loading—variation of current phase with respect to q-axis.

Fig. 21. Design renationalization using concentrated one-tooth windings and T-piece stator sections. (a) New design manufactured and T-piece stator. (b) Previous design. (c) New design.

[70] is a further example in addition to the text in [13] and technical publications [17] and [36]. B. Commercial Design Tools

Fig. 20. Efficiency plot for PC-BDC simulations using phase angles of 0◦ , 30◦ , and 60◦ .

highlight further examples. This paper has not considered noise and vibrations; however, these are important. There are several papers on this subject as applied to brushless PM motors, and

The work in this paper often uses various commercial software products as the working environments while discussing the fundamental design concepts. The products are not necessarily unique, and a designer should consider trying different products in order to assess their suitability and even developing their own design software using the large body of scientific algorithms and design and analysis techniques already published. In terms of alternatives, there are other notable examples

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peak of the flux density wave is limited by the steel saturation characteristics. The analysis here makes that assumption. Hence, under ac control, only the fundamental of the air-gap flux density wave should be considered, together with the main current density wave. This is for a distributed winding, and a three-phase winding is assumed. The mean stress is then σmean =

Bpk(fund) Jrms Bpk(fund) Jpk √ = 2 2

(A1)

where the stator current density can be estimated from a sinusoidal spatial variation on the stator surface [Fig. 22(a)] so that Jrms =

Fig. 22. Air-gap flux density and stator surface current density for ac and dc motors. (a) B and J for ac machine. (b) B and J for dc machine.

such as RMxprt from Ansoft (Ansys), U.S. This uses first-pass analytical calculations to feed into Maxwell FEA. Infolytica Corporation, Canada, has developed MotorSolve BLDC (and other packages) for template-based design which feeds into the MagNet FEA package. Cedrat Group, France, uses Flux and Motor Overlays to specify template geometries for motor simulation in Flux2D and 3-D, and indeed, SPEED can feed into this package. JSOL Corporation, Japan, has developed the JMAG FEA package, and this also has Motor Template (similar to Motor Overlays) and JMAG-Studio and JMAG designer can be accessed through CAD Link. This package also has a SPEED link. The FEA package Opera from Cobham, U.K., (formerly Vector Fields) has application-specific tools for frontend design of rotating machines. These examples illustrate a commonality between many packages; these tend to allow easy geometry, material, and control setup for faster motor design. Many packages now link to standard mechanical CAD packages so that geometries can be imported and initial design calculation can be done before resorting to more complex and slower FEA solutions. The aforementioned list is far from comprehensive but represents a global cross section of examples; many companies and specialists have developed their own in-house design tools, as already suggested as an option. The market is continually changing, hence the recommendation for trial of products. A PPENDIX The maximum mean sheer stresses can be estimated for brushless dc and ac machines in order to compare their torque densities. Consider Fig. 22. The dc machine has a trapezoidal waveform for the current density if the winding is fully pitched and 120◦ conduction exists, while the ac has low harmonic content and the current is sinusoidal. The idealized stress waveforms are shown for both control strategies, and approximate stress calculations can be derived to illustrate that the dc machine has a higher theoretical mean stress. AC Control—Flux Density Limited by Peak of Fundamental Sinusoidal Flux Wave: In an IPM motor, the flux density in the air gap can be shaped for smoother operation. This is particularly important in a servo system. Ideally, the air-gap flux wave would be sinusoidal for low torque ripple, and the

AC Nph Irms 3KW × . 2 D

(A2)

The mean air-gap diameter is D, the number of series phase AC winding turns is Nph , the fundamental winding factor is KW , and the winding current (assuming no parallel winding) is Irms . The 3/2 factor is valid for a three-phase sinusoidal current set. Assuming the winding factor is unity, then from (A1) and (A2) σmean =

6Bpk(fund) Nph Irms 3Bpk(fund) Nph Irms √ . = 0.55 πD 2 2D (A3)

AC Control—Fully Pitched Surface-Magnet Rotor: If we assume that the air-gap wave is trapezoidal (and a full square wave with 180-electrical-degree pitch), then the air-gap flux will be limited by the peak of the trapiziodal wave, as in Fig. 1(b); a Fourier analysis of a fully pitched trapezoidal wave gives a peak fundamental ratio where Bpk(fund) =

4 Bpk(trap) . π

(A4)

Hence σmean =

6Bpk(trap) Nph Irms 4 3Bpk(trap) Nph Irms √ . = 0.7 π πD 2 2D (A5)

DC Control: Assuming trapezoidal flux density and current density with a 120-electrical-degree pulsewidth σmean =

2 × Bpk(trap) Jpk . 3

(A6)

Again, assuming trapezoidal current density, this can be related to the phase current by DC × Jpk = KW

2Nph Ipk 6Nph Ipk DC = KW . × 2/3 × πD/2 πD

(A7)

For a trapezoidal current waveform with a width of 120 electrical degrees [Fig. 22(b)], the rms current is 2 Ipk . Irms = (A8) 3 Putting (A5) into (A7) gives 2 3 6Bpk(trap) Nph Irms × σmean = 3 2 πD 6Bpk(trap) Nph Irms . = 0.82 πD

(A9)


Comparison of Stresses: Comparing (A3)–(A9) shows that, for a given phase current (whether sinusoidal or trapezoidal), dc control gives higher stress density than ac control for a given peak flux density in the ratio 0.82/0.55 = 1.5. However, dc control tends to give more torque ripple and is more suitable for power drives. If a surface-magnet rotor is used, then (A4) can be compared with (A9), and this time, the theoretical stress limits are in the ratio 0.82/0.7 = 1.17, which is much closer. Relationship Between DC Link Voltage and Power Conversion: Assume that the machines operate with unity power factor. In a three-phase ac machine where the phase voltages and currents are sinusoidal and where there is 180◦ conduction in the inverter, the voltages and currents can be related to each other where Idc = Ipk and Vdc = 3Vpk /2. Therefore Vdc Idc = 3

Vpk Ipk = 3Vrms Irms . 2

[17]

[18] [19] [20] [21]

[22]

(A10)

For a dc machine, where the waveforms are trapezoidal and where there is 120◦ conduction in the inverter, Idc = Ipk and Vdc = 2Vpk . The rms-to-peak values are 2 2 Vrms = Vpk and Irms = Ipk (A11) 3 3

[23] [24]

[25]

so that the relationship between the dc link and ac rms values is Vdc Idc = 2Vpk Ipk = 3Vrms Irms .

(A12)

[26] [27]

Comparing (A10) and (A12) shows that the same relationship holds whether it is ac or dc. [28]

R EFERENCES [1] J. R. Hendershot and T. J. E. Miller, Design of Brushless PermanentMagnet Motors. Oxford, U.K.: Clarendon, 1994. [2] J. R. Ireland, Ceramic Permanent-Magnet Motors. New York: McGrawHill, 1968. [3] T. Kenjo and S. Nagamori, Permanent-Magnet and Brushless DC Motors. Oxford, U.K.: Clarendon, 1994. [4] J. F. Gieras and M. Wing, Permanent Magnet Motor Technology. New York: Marcel Dekker, 2002. [5] D. C. Hanselman, Brushless Permanent Magnet Motor Design. Lebanon, OH: Magna Physics, 2006. [6] N. Bianchi, M. D. Prè, L. Alberti, and E. Fornasiero, “Theory design of fractional-slot PM machines,” Tutorial Course Notes, IEEE IAS’2007 Annu., Meeting, Sep. 23, 2007, CLEUP editor (Padova, Italy); New Orleans: USA. [7] P. Campbell, Permanent Magnet Materials and Their Applications. Cambridge, U.K.: Cambridge Univ. Press, 1994. [8] L. R. Moskowitz, Permanent Magnet Design and Application Handbook. Melbourne, FL: Krieger, 1995. [9] P. Beckley, Electrical Steels for Rotating Machines. London, U.K.: IEE, 2002. [10] P. Beckley, Electrical Steels. Newport, U.K.: Eur. Elect. Steels, 2000. [11] G. C. Stone, E. A. Boulter, I. Culbert, and H. Dhirani, Electrical Insulation for Rotating Machines. Piscataway, NJ: IEEE Press, 2004. [12] S. J. Yang and A. J. Ellison, Machinery Noise Measurement. Oxford, U.K.: Clarendon, 1985. [13] P. L. Timár, Noise and Vibration of Electrical Machines. Amsterdam, The Netherlands: Elsevier, 1989. [14] M. A. Valenzuela and J. A. Tapia, “Heat transfer and thermal design of finned frames for TEFC variable-speed motors,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3500–3508, Oct. 2008. [15] J. Nerg, M. Rilla, and J. Pyrhonen, “Thermal analysis of radial-flux electrical machines with a high power density,” IEEE Trans. Ind. Electron., vol. 55, no. 10, pp. 3543–3554, Oct. 2008. [16] F. Marignetti, V. Delli Colli, and Y. Coia, “Design of axial flux PM synchronous machines through 3-D coupled electromagnetic thermal

[29]

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[33]

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[64] R. V. Major, “Development of high strength soft magnetic alloys for high speed electrical machines,” in Proc. IEE Colloq. New Magn. Mater.— Bonded Iron, Lamination Steels, Sintered Iron and Permanent Magnets (Digest No. 1998/259), London, U.K., May 28, 1998, pp. 8/1–8/4. [65] R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives. Boca Raton, FL: CRC, 2010. [66] J. Pyrhonen, T. Jokinen, and V. Hrabovcova, Design of Rotating Electrical Machines. Chichester, U.K.: Wiley, 2007. [67] T. A. Lipo, Introduction to AC Machine Design. Madison, WI: Univ. Wisconsin Press, 2004. [68] W. Ouyang, D. Zarko, and T. A. Lipo, “Permanent magnet machine design practice and optimization,” in Conf. Rec. 41st IEEE IAS Annu. Meeting, Tampa, FL, Oct. 8–12, 2006, pp. 1905–1911. [69] S. Huang, M. Aydin, and T. A. Lipo, “Torque quality assessment and sizing optimization for surface mounted permanent magnet machines,” in Conf. Rec. 36th IEEE IAS Annu. Meeting, Chicago, IL, Sep. 30–Oct. 4, 2001, pp. 1603–1610. [70] S. Huang, M. Aydin, and T. A. Lipo, “Electromagnetic vibration and noise assessment for surface mounted PM machines,” in Proc. IEEE Power Eng. Soc. Summer Meeting, Vancouver, BC, Canada, Jul. 15–19, 2001, pp. 1417–1426. David G. Dorrell (M’95–SM’08) is a native of St. Helens, U.K. He received the B.Eng. (Hons.) degree in Electrical and Electronic Engineering from The University of Leeds, Leeds U.K., in 1988, the M.Sc. degree in Power Electronics Engineering from The University of Bradford, Bradford, U.K., in 1989, and the Ph.D. degree from The University of Cambridge, Cambridge, U.K., in 1993. He has held lecturing positions with Robert Gordon University, Aberdeen, U.K., and the University of Reading, Berkshire, U.K. He was a Senior Lecturer with the University of Glasgow, Glasgow, U.K., for several years. In 2008, he took up a post with the University of Technology Sydney, Sydney, Australia, where he was promoted to Associate Professor in 2009. He is also an Adjunct Associate Professor with National Cheng Kung University, Tainan, Taiwan. His research interests cover the design and analysis of various electrical machines and also renewable-energy systems with over 150 technical publications to his name. Dr. Dorrell is a Chartered Engineer in the U.K. and a Fellow of the Institution of Engineering and Technology. Min-Fu Hsieh (M’02) was born in Tainan, Taiwan, in 1968. He received the B.Eng. degree in mechanical engineering from National Cheng Kung University (NCKU), Tainan, in 1991 and the M.Sc. and Ph.D. degrees in mechanical engineering from the University of Liverpool, Liverpool, U.K., in 1996 and 2000, respectively. From 2000 to 2003, he served as a Researcher with the Electric Motor Technology Research Center, NCKU. In 2003, he joined the Department of Systems and Naval Mechatronic Engineering, NCKU, as an Assistant Professor. In 2007, he was promoted to Associate Professor. His area of interests includes renewable-energy generation (wave, tidal current, and wind), electric propulsors, servo control, and electric machine design. Dr. Hsieh is a member of the IEEE Magnetics, Industrial Electronics, Oceanic Engineering, and Industrial Applications Societies.

Mircea Popescu (M’98–SM’04) received the D.Sc. in electrical engineering from Helsinki University of Technology, Helsinki, Finland, in 2004. He has more than 25 years of experience in electrical motor design and analysis. He worked for the Research Institute for Electrical Machines, Bucharest, Romania; Helsinki University of Technology; and SPEED Laboratory, University of Glasgow, Glasgow, U.K. In 2008, he joined Motor Design Ltd., Shropshire, U.K., as an Engineering Manager. He published over 100 papers in conferences and peer-reviewed journals. Dr. Popescu was the recipient of the first prize best paper awards from IEEE Industry Applications Society Electric Machines Committee in 2002, 2006, and 2008.


Lyndon Evans received the B.Sc. (Hons.) degree in computer networks from Glyndwr University, Wales, U.K., in 2008. He qualified as a Television and Video Service Engineer in 1988 and worked in this field for over 15 years before returning to study and receiving his B.Sc.(Hons.) degree. He is a Software Developer with Motor Design Ltd., Shropshire, U.K., in partnership with Glyndwr University, and is studying for a research degree. Mr. Evans is a member of The Institution of Engineering and Technology and an associate member of the British Computer Society.

David A. Staton (M’90) received the Ph.D. degree in computer-aided design of electrical machines from The University of Sheffield, Sheffield, U.K., in 1988. Since then, he has worked on motor design and particularly the development of motor design software at Thorn EMI; the SPEED Laboratory, University of Glasgow, Glasgow, U.K.; and Control Techniques, U.K. In 1999, he set up a new company, Motor Design Ltd., Shropshire, U.K., to develop a thermal analysis software for electrical machines. He published over 50 papers in conferences and peerreviewed journals.

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Vic Grout (M’01–SM’05) received the B.Sc. (Hons.) in Mathematics and Computing from The University of Exeter, Penryn, U.K., in 1984, and a Ph.D. in Communication Engineering from Plymouth Polytechnic, Devon, U.K., in 1988 He is a Professor of Network Algorithms and the Director of the Centre for Applied Internet Research, Glyndwr University, Wales, U.K. He has worked in senior positions in both academia and industry for over 20 years and has published and presented over 200 research papers and 4 books. He is an Electrical Engineer, Scientist, Mathematician, and IT Professional. Mr. Grout is a Chartered Engineer and a Fellow of the Institute of Mathematics and its Applications and British Computer Society and The Institution of Engineering and Technology.

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