International Journal of Scientific & Engineering Research Volume 2, Issue 6, June-2011 1

ISSN 2229-5518

Selecting of Slotted AFPM Motors with High

Torque Density for Electric Vehicles

S.Asghar Gholamian, M. Ardebili, K. Abbaszadeh and Seyed Akbar Gholamian

Abstract— Double-sided axial flux PM motors (AFPM) are the most promising and widely used types. There are two topologies for slotted double-sided AFPM motors. Selecting an AFPM motors with high torque density is an important parameter in applications. So, comparison of torque density between different topologies of double-sided AFPM motors seems to be necessary.

In this paper, the sizing equations of axial flux slotted one-stator-two-rotor (TORUS) and two-stator-one-rotor (AFIR) type PM motors is pre- sented and comparison of the TORUS and AFIR topologies in terms of torque density is illustrated. Field analysis of both Topologies of slot- ted motors is investigated using Finite Element method (FEM) software. Finally a high torque double-sided slotted AFPM motor is intro- duced in the paper.

Index Terms— axial flux PM motors (AFPM), torque density, electrical loading and Finite Element method (FEM).

1 INTRODUCTION

——————————  ——————————

n conventional machines, the air gap flux density has normally radial direction. In AFPMs, the air gap flux den- sity presents mainly axial direction. In general, AFPMs exhibit an axial length much smaller than the length of a
conventional motor of the same rating [1-3].
AFPM motors are particularly suitable for electrical vehicles and industrial equipment. The large diameter rotor with its high moment of inertia can be utilized as a flywheel. These machines are ideal for low speed applications, as for example, electromechanical trac- tion drives hoists. Traction electric motors for EVs should meet high power density, high torque at low speed for starting and climbing, high speed at low torque for cruising, high efficiency over wide speed and torque ranges [1,6].
Selecting of double-sided AFPM motors with high torque density is an important parameter, especially in electrical vehicle applications. So, comparison of torque density between different topologies of double- sided AFPM motors seems to be necessary [3].
The AFPM machine, also called the disc-type machine,
is an attractive alternative to the cylindrical RFPM ma- chine due to its pancake shape, high efficiency, com- pact Construction and high power density [1,3].

————————————————

 S. Asghar Gholamiann, Faculty of Electrical Engineering, Babol University of Technology, Babol, Iran, Email: gholamian@nit.ac.ir

 M. Ardebili, Electrical Engineering Department of K.N. Toosi University of Technology, Tehran, Iran, Email: ardebili@eetd.kntu.ac.ir

 K. abbaszadeh, Electrical Engineering Department of K.N. Toosi Universi- ty of Technology, Tehran, Iran, Email: abbaszadeh@eetd.kntu.ac.ir

 Seyed Akbar Gholamian, Department of Industrial Engineering, Payame

Noor University, Babol, Iran, ag1358@gmail.com

There are two topologies for slotted double-sided AFPM motors. These topologies are axial flux slotted one-stator-two-rotor (TORUS) and two-stator-one- rotor (AFIR) type PM motors. Two AFPM motors and their acronyms are selected TORUS-S (Axial flux slot- ted external rotor internal stator PM stator) and AFIR- S (Axial flux slotted internal rotor external stator PM motor) for detailed analysis. The stator cores of the machine is formed by tape wound core with a lap and short-pitched polyphase AC winding located in punched stator slots. The rotor structure is formed by the axially magnetized NdFeB magnets [4,5].
The topologies used in the study are illustrated in

Fig.1.

(a)
(b)

Fig.1. Axial flux slotted (a) one-stator-two-rotor

TORUS-S type (b) two-stator-one-rotor AFIR-S type

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Flux directions of both AFIR and TORUS slotted to- pologies at the average diameter in 2D are also shown in Fig. 2a and 2b.
rent,  is machine efficiency, m is number of phases of the machine and T is period of one cycle of the EMF[4,5,7].
The quantity Kp is termed the electrical power wave- form factor and defined as

T

K  1

e(t )  i(t ) dt

T

1 f (t ) . f

(t )dt

(2)

p 

0 pk

 I pk

 T e i

0

(a)
where

fe(t)=e(t)/ Epk and fi(t)=i(t)/ Ipk are the expressions for the normalized EMF and current waveforms. In order to

indicate the effect of the current waveform, a definition for current waveform factor, Ki, is also useful,

0.5

I  T 

2 

K  pk   1   i(t )  

(3)

i I  T  I

 dt 

rms

where

 0 

pk  

Irms is the rms value of the phase current. The peak val- ue of the phase air gap EMF for AFPM in (1) is given by:

E  K N

B . f .(1  2 ) D2
(4)
(b)

pk e

where

ph g p o

Fig.2. One pole pair of the (a) TORUS-S (b) AFIR-S

Increasing the air gap length, maximum torque density will change in AFPM motors. These changes are not the same in different topologies. Maximum torque density of TORUS-S is higher than AFIR-S in large air gap length.
In Section2, the generalized sizing approach for TO- RUS-S and AFIR-S types PM motors is briefly dis- cussed. Then, some results of comparisons of the TO-

Ke is the EMF factor which incorporates the winding

distribution factor Kw and the per unit portion of the total air gap area spanned by the salient poles of the machine (if any), Nph is the number of turn per phase, Bg is the flux density in the air gap, f is the converter frequency, p is the machine pole pairs,  is the diame- ter ratio for AFPM defined as Di /Do, Do is the diameter of the machine outer surface, Di is the diameter of the machine inner surface. The peak phase current in (1) is given by:
RUS-S and AFIR-S topologies in terms of torque densi-
ty are illustrated in Section3. In Section 4, Field anal- yses of both Topologies of slotted motors are investi-
1  

I pk  A  K i 2 .

where

Do

2m1 N ph
(5)
gated using Finite Element method (FEM) by MAX-
WELL10 software. In Section 5, effect of electrical load-
ing and current density are illustrated. The conclusions are given in Section6.

m1 is number of phases of each stator and A is the elec- trical loading.

Combining (1) through (5), the general purpose sizing equations take the following form for AFPM.

2. Sizing equations of AFPM Motors

m  f 2 1   3

Pout  Ke K p Ki A Bg  (1   )( ) D

(6)
In general, if stator leakage inductance and resistance

m1 2

p 2 o

are neglected, the output power for any electrical ma- chine can be expressed as
The machine torque density for the total volume can
be defined as

Pout

(7)

m T Tden   2

Pout  

T

 e(t ).i(t ) dt  mK p E pk I pk

0

(1)

m 4

where

Dtot

Ltot

where

e(t ) and Epk are phase air gap EMF and its peak value,

i(t) and Ipk are phase current and the peak phase cur-

m is the rotor angular speed, Dtot is the total machine outer diameter including the stack outer diameter and the protrusion of the end winding from the iron stack

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in the radial direction, Ltot is the total length of the ma- chine including the stack length and the protrusion of
the attainable flux density on the surface of the PM. The PM length LPM can be calculated as
the end winding from the iron stack in the axial direc- tion [4,5,7].

LPM

 r B g



 K f

Br  

 K d



B g 



K c g

(16)

1.1. Sizing Equations for the TORUS-S

The generalized sizing equation approach can easily be applied to axial flux permanent magnet TORUS type motor [5].
The outer surface diameter Do can be written as

1 / 3

where

 r is the recoil relative permeability of the magnet, Br

is the residual flux density of the PM material, Kd is the leakage flux factor, Kc is the Carter factor, Kf =Bgpk/Bg is the peak value corrected factor of air gap flux densi-



D   P

 m

K K K A B

 f (1  2 )(1   ) 

(8)
ty in radial direction of the AFPM motor. These factors

o  out



2m1 e p i g p 2 

can be obtained using FEM analysis [5].
The machine total outer diameter Dtot for the TORUS- S motor is given by

1.2. Sizing Equations for the AFIR-S

Dtot  Do  2Wcu

where
(9)
The concept of Double-sided Axial Flux two-
stator-one-rotor (AFIR) type PM motors was presented in [4].

Wcu is the protrusion of the end winding from the iron

stack in the radial direction. For the back-to-back
The outer surface diameter Do is obtained from (6).

1 / 3

wrapped winding, protrusions exist toward the axis of



D   2 P

 m

K K K A B

 f (1  2 )( 1   ) 

(17)
the machine as well as towards the outsides and can be

o  out



2 m1 e p i g p 2 

calculated as

 A D 

The machine total outer diameter Dtot for the AFIR
type machines is given as

Di 

D2   2

g 

Kcu J s

Dtot

 Do
 2Wcu
(18)

Wcu   

2

where
(10)
where

Wcu is the protrusion of the end winding from the iron

Dg is the average diameter of the machine, Js is the
stack in the radial direction and can be calculated as
current density and Kcu is the copper fill factor.
Note for the slotted topology machines the depth of

Wcu

 (0.46  0.62 ) Do

p

(19)

the stator slot for slotted motors is Lss=Wcu.

The axial length of the machine Le is

The axial length of the machine Le is given by

Le  Lr  2Ls  2 g

(20)

Le  Ls  2Lr  2 g

where
(11)
where

Ls is axial length of the stator, Lr is axial length of the

Ls is axial length of the stator, Lr is axial length of the rotor and g is the air gap length. The axial length of the

rotor and g is the air gap length. The axial length of a
stator Ls is
stator Ls is

Ls  Lcs  2Lss (12)

Ls  Lcs  dss

where
(21)
The axial length of the stator core Lcs can be written as

Lcs is the axial length of the stator core, and the depth

of the stator slot for slotted machines dss is

Lcs 

B g  p Do (1   )

4 p Bcs
(13)

D i 

d 

2  2 A D g i



 s K cu





J s 

(22)
where

Bcs is the flux density in the stator core and

p is the

ss 2

where
ratio of average air gap flux density to peak air gap flux density.The axial length of rotor Lr becomes

 s is the ratio of stator teeth portion to the stator pole.

The axial length of the stator core Lcs can be written as

Lr  Lcr  LPM

(14)

Lcs

B g  p Do (1   )


8 p B
(23)
Also, the axial length of the rotor core Lcr is cr

Lcr

Bu  Do (1   )

8 p Bcr
(15)
Since there is no rotor core in rotor PM topologies, the
axial length of rotor Lr is
where

Lr  LPM

(24)

Bcr is the flux density in the rotor disc core, and Bu is

The PM length LPM can be calculated as

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LPM 

2  r B g

 K



K c g





(24)

Br  

 d

B g 



3. Comparison of slotted TORUS and

AFIR

Comparison of two different Double-sided axial flux slotted PM motors in terms of torque density is ac- complished for 10KW output power, 4 poles and 60Hz drive. In this comparison, other constant parameters of motors are tabulated in table1.

Table1. Constant parameters of motors in comparison

In AFPM motors, the air gap flux density and diameter ratio are the two important design parameters which have significant effect on the motor characteristics. Therefore, in order to optimize the motor performance, the diameter ratio and the air gap flux density must be chosen carefully. Fig.3 shows the torque density varia- tion as a function of air gap flux density and the diam- eter ratio for the AFIR-S and TORUS-S motors.
(a)
(b)

Fig.3. Torque density vs. air gap flux density and diameter

ratio for A=30000 (A/m), g=1 (mm), Js=9000000 (A/m2) a) TORUS-S b) AFIR-S

As can be seen from Fig.3b, the maximum torque den- sity occurs at Bg=0.51 (T) and   0.27 gap length, the maximum torque density occurs in dif- ferent Bg and  .
Table2 shows maximum torque density with corre- sponding Bg and  .

Table2. Maximum torque density with corresponding Bg and 

Fig.4 shows the maximum torque density variation as a function of air gap length for the AFIR-S and TO- RUS-S motors for A=30000 (A/m), Js=9000000 (A/m2).
In special air gap length (this air gap length is called
GT) maximum torque density of AFIR-S and TORUS-S motors will be the same. Considering Fig.4, it can be concluded that in large air gap length, slotted TORUS motor has high power density.

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Fig.5. flux distribution over one pole pair for AFIR-S

Fig.4. Maximum torque density

AFIR-S and TORUS-S vs. air gap length

4. 2D Finite element method Analysis of field

In order to analyze the magnetic circuit and power density, 2D Finite Element Analysis was used for both TORUS-S and AFIR-S type motors [2]. The purpose of the FEM is to get the overall picture of the saturation levels in various parts of the machine, to compare the flux densities obtained from FEM and sizing analysis.

4.1. FEM of the AFIR-S Motor

The motor parameters and important design dimen- sions used for the AFIR-S model are shown in Table 3. Fig.5 shows the flux distribution over one pole pair using FEM.
Fig.6 shows the air gap Flux density over one pole at the average diameter (Dg) using FEM. This curve shows that the flux density on the edge of the Slots is about 13% lower than the flux density on the center of the PM because of the magnet leakage flux.

Table3. Parameters and dimensions of slotted AFIR-S mo- tor

Fig.6. Air gap flux density over one pole for AFIR-S

A flux density comparison between the FEM results and sizing analysis results on various parts of the slot- ted AFIR motor at no load is tabulated in Table4. The comparison table shows that the FEM results are con- sistent with the results obtained from the sizing analy- sis.

Table4. Flux density comparison of slotless AFIR-S motor

4.2. FEM of the TORUS-S Motor

The parameters and optimized TORUS-S motor di- mensions used in the design which are calculated us- ing sizing equations are shown in Table 5.

Table5. Parameters and dimensions of slotted TORUS-S

motor.

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Fig.7 shows the flux distribution over one pole pair using FEM. The air gap flux density at the average di- ameter (Dg) over one pole using FEM was obtained and is shown in Fig.8.

Fig.7. flux distribution over one pole pair for TORUS-S

Fig.8. Air gap flux density over one pole for TORUS-S

A comparison of the flux densities between the FEM results and sizing analysis results for different parts of the machine at no load is tabulated in Table 6.

Table6. Flux density comparison of slotless TORUS-S mo- tor

From the no load flux density plots, it is seen that the results are again consistent with the results obtained from the sizing analysis, the maximum flux density values on the rotor and stator came out almost the same. Also, the maximum and average air gap flux densities obtained from the FEM and sizing analysis agree well.

5. Effect of electrical loading and current density

The considerable point is that the value of GT will vary when the electrical loading 'A' changes.
Fig.9 shows the variation of the maximum torque den- sity as a function of air gap length in A=25000 (A/m) for the AFIR-S and TORUS-S motors.

Fig.10 shows the variation of the maximum torque density as a function of air gap length in A=35000 (A/m) for the AFIR-S and TORUS-S motors also. According to fig.10 it can be concluded that point GT is shifted to larger air gaps and this means that in smaller air gaps AFIR-S motor has higher maximum torque density. According to figure 5 it can be concluded that point GT is shifted to smaller air gaps and this means that in higher air gaps TORUS-S motor has higher maximum torque density. Other value of GT for vari- ous A is tabulated in table 7.

Fig.9. Maximum torque density AFIR-S and TORUS-S

vs. air gap length for A=25000 (A/m)

Fig.10. Maximum torque density AFIR-S and TORUS-S vs. air gap length for A=35000 (A/m)

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Table7. Other value of GT for Various A

6. CONCLUSION

Selecting an AFPM motors with higher torque density is an important parameter in applications. The main goal of this paper has been introduce to double-Sided Axial Flux Slotted PM Motors with maximum torque density. There are two topologies for slotted double- sided AFPM motors.
The maximum torque density is changed by different value of the air gap and electrical loading. TORUS-S topology has high torque density in low electrical load- ing. But, AFIR-S topology has high torque density in high electrical loading.
A flux density comparison between the various parts
of the slotted AFIR-S and TORUS-S motors obtained from the FEM and sizing analysis at no load agree well.

REFERENCES

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[2] S. Asghar Gholamian, M. Ardebili. K. Abbaszadeh,”Selecting and Construction of High Power Density Double-Sided Axial Flux Slotted Permanent Magnet Motors for Electric Vehicles”, IREE, Vol.

4. n. 3, pp. 477-484, 2009.

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[6] Caricchi, F.; Capponi, F.G.; Crescimbini, F.; Solero, L.; “Experimental study on reducing cogging torque and core power loss in axial-flux permanent-magnet machines with slotted winding”, Industry Applications Conference, 2002.

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