Open access peer-reviewed chapter

A Comparative Thermal Study of Two Permanent Magnets Motors Structures with Interior and Exterior Rotor

By Naourez Ben Hadj, Jalila Kaouthar Kammoun, Mohamed Amine Fakhfakh, Mohamed Chaieb and Rafik Neji

Submitted: October 23rd 2010Reviewed: July 14th 2011Published: September 12th 2011

DOI: 10.5772/17905

Downloaded: 3426

1. Introduction

Considering the large variety of electric motors, such as asynchronous motors, synchronous motors with variable reluctances, permanent magnets motors with radial or axial flux, the committed firms try to find the best choice of the motor conceived for electric vehicle field.

The electric traction motor is specified by several qualities, such as the flexibility, reliability, cleanliness, facility of maintenance, silence etc. Moreover, it must satisfy several requirements, for example the possession of a high torque and an important efficiency (Zire et al., 2003; Gasc, 2004; Chan., 2004).

In this context, the surface mounted permanent magnets motor (SMPMM) is characterized by a high efficiency, very important torque, and power-to-weight, so it becomes very interesting for electric traction.

In the intension, to ensure the most suitable and judicious choice, we start by an analytical comparative study between two structures of SMPMM which are the permanent magnets synchronous motor with interior rotor (PMSMIR) and the permanent magnets synchronous motor with exterior rotor (PMSMER), then, we implement a methodology of design based on analytical modelling and the electromagnetism laws. Also, in order to understand the thermal behaviour of the motor, we implant a comparative thermal performance of the two structures illustrated with careful attention to the manufacturing techniques used to produce the machine, and the associated thermal resistances and capacitances, to obtain good steady state and transient thermal performance prediction.

2. Modelling of two SMPMM structures

2.1. Structural data

The structures of motors allowing the determination of the studied geometry are based on three relationships.

The ratio β is the relationship between the magnet angular width Lmand the pole-pitchLp. This relationship is used to adjust the magnet angular width according to the motor pole-pitch.

β=LmLpE1
Lp=πpE2

The ratio Rldlais the relationship between the angular width of a principal tooth and the magnet angular width. This ratio is responsible for the regulation of the principal tooth size which has a strong influence on the electromotive force form.

Rldla=AtoothLmE3

The Rdidratio is the relationship between the angular width of the principal tooth and the angular width of the inserted toothAtoothi. This relationship fixes the inserted tooth size.

Rdid=AtoothLmE4

2.2. Geometrical structures of PMSMIR and PMSMER

This part is devoted to an analytical sizing allowing calculation of geometrical sizes of the two SMPMM configurations which are the PMSMER and the PMSMIR.

Figure 1 represents the PMSMER and the PMSMIR with the number of pole pairs is p=4 and a number of principal teeth is 6, between two principal teeth, an inserted tooth is added to improve the wave form and to reduce the leakage flux (Ben Hadj, N. et al., 2007). The slots are right and open in order to facilitate the insertion of coils and to reduce the production cost (Magnussen, F. et al., 2005; Bianchi, N..et al., 2003; Libert, F. et al., 2004).

Figure 1.

Permanent magnets motors with exterior rotor and interior rotor

2.3. Analytical sizing of the two SMPMM structures

The analytical study of motor sizing is based on the schedules data conditions parameters (Table 1), the constant characterizing materials (Table 2), the expert data and configurations of the two motors.

DefinitionSymbolValue
Electric vehicle massM1000 kg
Angle of startingad
Time of startingtd4 s
Outside temperatureTout40°C
Maximum motor powerPmmax21,635 kW
Winding temperatureTw95°C
Base speed of the vehicleVb30 km/h
Maximum Speed of the vehicleVmax100 km/h
Slots load factorkr0,44
Current density in the slotsδ7 A/mm2

Table 1.

The schedules data conditions

DefinitionSymbolValue
Remanent magnetic induction of the magnetsBm1,175 T
Demagnetization InductionBc0,383 T
Magnetic induction in teethBtooth0,9 T
Magnets permeabilityμa1,05
Mechanical losses coefficientkm1%
Copper resistivity at 95°CRcu17,2 10-9 Ωm
The copper resistivity variation coefficientα0,004
Density of the electrical sheetsMvt7850 kg
Density of magnetsMva7400 kg
Density of copperMvc8950 kg
Sheets quality coefficientQ1,1

Table 2.

Specific constants of materials

Expert data

The expert data are practically represented by three sizes which are, the magnetic induction in the air gap Be, the magnetic induction in the stator yoke Bsy and the magnetic induction in the rotor yoke Bry. It should be noted that the zone of variation of these three parameters varies between 0,2 to 1,6T (Ben Hadj et al., 2007).

Structural data

For the two configurations, we adopted the same number of pole pairs P=4, with an air gap thickness equivalent to 2mm, with a relationship β equal to 0,667 and Rldla equal to 1,2.

Data identified by the finite elements method

Kfu is the leakage flux coefficient of the PMSMIR which is fixed to 0,95 whereas for the PMSMER, kfu is equal to 0,98. In this context, we define a ratio Rdid equal to 0,2.

2.4. Geometrical sizes

Geometrical parameters of the two structures motors are defined in figure 2. Where:

  1. The magnet height, hm

  2. The slots height hs and the tooth height htooth

  3. The rotor yoke height, hry

  4. The stator yoke height, hsy

  5. The air gap thickness, e

Figure 2.

PMSMER and PMSMIR parameters

In the stator of the PMSMIR, geometrical sizes are defined by:

The slot average width:Ws

Ws=Dm+e+htooth2AsE5

The principal tooth section:Stooth

Stooth=Dm+e2AtoothlmE6

Wherelm, Dmare the average motor length and the average motor diameter.

The inserted tooth section:Stoothi

Stoothi=Dm+e2AtoothilmE7

The slot section: Ss

Ss=12[2πNtoothAtoothAtoothi]Dm+e2lmE8

In the stator of the PMSMER, geometrical sizes are defined by:

The slot average width:Ws

Ws=Dmehtooth2AsE9

The principal tooth section:Stooth

Stooth=Dm+e2AtoothlmE10

The inserted tooth section:Stoothi

Stoothi=Dm+e2AtoothilmE11

The slot section: Ss

Ss=12[2πNtoothAtoothAtoothi]Dme2lmE12

The teeth height htoothof the PMSMIR and the PMSMER are expressed by equation Eq. 13 and Eq. 14 where Nsphis the number of turns per phase,Inis the rated current and Nteethin the number of teeth.

htooth=Nsph.InNteethδKrAs+(Dm+e2)2Dm+e2E13
htooth=Nsph.InNteethδKrAs+(Dme2)2Dme2E14

The stator yoke thickness hsyis obtained by the application of the flux conservation theorem, where Btoothis the magnetic induction in the tooth.

hsy=BtoothStooth2lmBsyE15

In the rotor of the two structures, geometrical sizes are defined by:

The expression of the magnet height hmis the same one in the two structures. It is obtained by the application of the Ampere theorem.

Where μais the air permeability and kfuis the flux leakage coefficient.

hm=μaBeeM(Ta)BekfuE16

Where the magnet induction M(Ta)at Ta°C is defined by:

M(Ta)=M[1+αm(Ta20)]E17

The rotor yoke thickness hryis defined:

hry=BeStooth2kfulmBryE18

2.5. Electrical sizing

The electromotive force in the two SMPMM structures is expressed by:

EMFi(t)=8πNsphlmDmBesin(πβ2)sin(π2βRldla)Ωmsin(pΩmt)E19

The motor electric constant : Ke

Ke=12πNsphlmDmBesin(πβ2)sin(π2βRldla)E20

The electromagnetic torque :Tem

Tem(t)=1Ωi=13EMFi(t)ii(t)E21

whereEMFi, iiand Ωmrepresent respectively the electromotive force, the current of the i phase and the angular speed of the motor.

The motor rated current In is the ratio between the electromagnetic torque and the motor electric constant.

In=TemKeE22

The phase résistance of the motor : Rph

Rph=Rco(Tw)NsphδLspIn/2E23

where Rco(Tw)is the copper receptivity at the temperature of winding Twand Lspis the spire average length (Ben Hadj et al., 2007).

3. Comparative thermal study between the two SMPMM

In this study, the comparison between the two SMPMM structures consists on the thermal analysis which is based upon lumped-circuit analysis. It represents the thermal problems by using the thermal networks, analogous to electrical circuits. The thermal circuit in the steady state consists of thermal resistances and heat sources connected between motor component nodes. For transient analysis, the heat/thermal capacitances are used additionally to take into account the change in internal energy of the body with time. The thermal resistances for conduction and convection can be obtained by:

Rconvection=lAk[K/W]E24
Rconduction=lAch[K/W]E25

Where lis the distance between the point masses and Ais the interface area, k is the heat conductivity, Acis the cooling cross section between the two regions and h is the convection coefficient calculated from proven empirical dimensionless analysis algorithms.

The heat capacitance is defined as follow:

C=Vρc[Ws/K]E26

Where V is the volume,ρis the density and c is the heat capacity of the material. The simplified stator for the thermal study of the two SMPMM structure are given by figures 3 and 4, also the thermal model for the two structures are implemented in MATLAB simulater where the different radius for the PMSMER dimensions are defined as follow:

Rcarter=R1=Rf+e2+hm+hry+ecarterE27
Rrotoryoke=R2=Rf+e2+hm+hryE28
Rmagnet=R3=Rf+e2+hmE29
R4=Rf+e2E30
Rslot=R5=Rfe2E31
Rinsolator=R6=R5hsE32
R7=R5hstinsolatorE33
R8=R7hsyE34

The thermal resistances are calculated along the radial direction. The Riradius are calculated from dimensions of motor, where Rfis the Bore raduis and tinsolatoris the thickness insulator.

The different radius for the PMSMIR dimensions are defined as follow:

R1=Rf+e2E35
R2=Rf+e2+htoothE36
R3=Rf+e2+htooth+tinsolatorE37
R4=Rf+e2+htooth+tisnolator+hsyE38
R5=Rf+e2+htooth+tinsolator+hsy+tcarterE39

Figure 3.

Simplified stator for the thermal study in the PMSMER

Figure 4.

Simplified stator for the thermal study in the PMSMIR

As described earlier, the thermal resistance values are automatically calculated from motor dimensions and material data.

Figure 5 shows the thermal model in transient behaviour of the PMSMIR.

Figure 5.

Thermal model of the PMSMIR in transient behaviour

In this model, the heat sources are respectively the copper losses and iron losses in the stator. The Tivariables are the temperatures in various points of the motor. The expressions of thermal resistances of the PMSMIR result from the resolution of the heat equation at the fields borders.

Rcoilrepresents the coil thermal resistance (K.W1).

Rcoil=14πlmλcoil[1-2R12R22-R12lnR2R1]E40

Rinsorepresents the isolator thermal resistance (K.W1).

Rinso=lnR3R22πλinsolmE41

Rinso-sy represents the contact thermal resistance between insolator and the stator yoke (K.W1).

Rinsosy=13002πR3lmE42

Rjcorepresents the thermal resistance of stator yoke (K.W1).

Rjco=lnR4R32πλironlmE43

Rfcorepresents the thermal resistance of conduction in the stator yoke (K.W1).

Rfco=14πlmλiron[1-2R32R42-R32lnR4R3]E44

Rsycarepresents the thermal resistance between stator yoke and the carter (K.W1).

Rsy-ca=115002πR4lmE45

Rcarepresent the thermal resistance of carter (K.W1).

Rca=lnR5R42πλcalmE46

Rextrepresents the convection thermal resistance between the carter and ambient air (K.W1).

Rext=lhSextE47

In the previous expression, Sextrepresents the outer surface of the motor and his the heat transfer coefficient between the carter and the ambient air. It can be between 20 and 40 K.W1m2for a motor with natural ventilation, and may exceed 80 K.W1m2for the motor forced air.

To calculate the outer surface of SMPMM, we considered only the outer surface of the cylinder with radius R5and height lm(Gasc, 2004; Chan., 2004).

Sext=2πR5lmE48

The expressions of heat capacities of the PMSMIR are given by the following equations:

Ccoilrepresents the heat capacity of coil (JK1).

Ccoil=ρcoVcoCthcoE49

Cinsorepresents the heat capacity of insolator (JK1).

Cinso=ρinsoVinsoCthinsoE50

Csyrepresents the heat capacity of stator yoke (JK1).

Csy=ρironVsyCthironE51

Ccarepresents the capacity of carter (JK1).

Cca=ρaluVcaCthaluE52

Figure 6 shows the thermal model in transient behaviour of the PMSMER.

Figure 6.

Thermal model of the PMSMER in transient behaviour

The expressions of the PMSMER thermal resistances obtained from the resolution of the heat equation at the fields borders.

Rsyrepresents the stator yoke thermal resistance (K.W1).

Rsy=14πlmλiron[12R82R72R82lnR7R8]E53

Rinsorepresents the insolator thermal resistance (K.W1).

Rinso=14πlmλinso[2R72R62R72lnR6R7]E54

Rcoilrepresents the coil thermal resistance (K.W1).

Rcoil=14πlλco[12R62R52R62lnR5R6]E55

Rmagrepresents the magnet thermal resistance (K.W1).

Rmag=lnR1R22πλmaglmE56

Rryrepresents the rotor yoke thermal resistance (K.W1).

Rry=lnR2R32πλironlmE57

Rcarepresents the thermal resistance of carter. (K.W1)

Rca=lnR1R22πλcalmE58

To calculate the outer surface of SMPMM, we considered only the cylinder outer surface with radius R1and the heightlm.

Sext=2πR1lmE59

The expressions of heat capacities of the PMSMER are given by the following equations:

Cmagrepresents the heat capacity of magnet (JK1).

Cmag=ρmagVmagCthmagE60

Cryrepresents the heat capacity of rotor yoke (JK1).

Cry=ρironVryCthironE61

Ccoilrepresents the heat capacity of coil (JK1).

Ccoil=ρcoVcoCthcoE62

Cinsorepresents the heat capacity of insolator (JK1).

Cinso=ρinsoVinsoCthinsoE63

Csyrepresents the heat capacity of stator yoke (JK1).

Csy=ρironVsyCthironE64

The below table presents the different thermal conductivities of materials (Jérémi, R., 2003)

MaterialConductivities
(Wm-1K-1)
Mass heat capacity (Jkg-1K-1)Density
(Kgm-3)
Copper (Coil)λco=5Cth-co= 398ρco = 8953
Insolatorλinso =0.25Cth-inso= 1250ρinso = 1200
(Iron)Stator Yokeλiron =25Cth-iron= 460ρiron = 7650
Magnetλmag =6.5Cth-mag= 420ρmag = 7400
aluminium (Carter)λca =180Cth-alu = 883ρalu = 2787

Table 3.

The thermal conductivities of materials

6. Results and simulations

Simulation results with Matlab software allowed us to obtain the curves of temperatures specific to different materials of the PMSMER and PMSMIR structures. The thermal results at steady and transient state is reached by figures 7, 8.

According to the results, we find that the steady state in the PMSMIR is reached after 4000s. However, the steady state in the PMSMER is achieved after 2000s.

By comparing the results in steady and transient state between the two configurations, we note that temperatures of different parts in PMSMIR are higher than temperatures in PMSMER (especially the coil temperature). That’s why, we choose the PMSMER configuration as the best solution in electric traction field.

Figure 7.

Various temperatures in different parts of the PMSMER in transient state.

Figure 8.

Various temperatures in different parts of the PMSMIR in transient state.

Moreover, we always look to get a permissible values of coil temperature, based on the proper choice of motors geometric parameters in order to ensure a good compromise between geometric dimensioning and thermal modeling motor.

7. Conclusion

In this paper, a thermal model of two SMPMM with interior rotor and exterior rotor was realised, the intension to compare the evolution of the temperatures of different parts of the two motor configurations and especially the modeling of temperature at the coil is made.

© 2011 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike-3.0 License, which permits use, distribution and reproduction for non-commercial purposes, provided the original is properly cited and derivative works building on this content are distributed under the same license.

How to cite and reference

Link to this chapter Copy to clipboard

Cite this chapter Copy to clipboard

Naourez Ben Hadj, Jalila Kaouthar Kammoun, Mohamed Amine Fakhfakh, Mohamed Chaieb and Rafik Neji (September 12th 2011). A Comparative Thermal Study of Two Permanent Magnets Motors Structures with Interior and Exterior Rotor, Electric Vehicles - Modelling and Simulations, Seref Soylu, IntechOpen, DOI: 10.5772/17905. Available from:

chapter statistics

3426total chapter downloads

1Crossref citations

More statistics for editors and authors

Login to your personal dashboard for more detailed statistics on your publications.

Access personal reporting

Related Content

This Book

Next chapter

Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled

By Saïd Drid

Related Book

First chapter

A Survey on Electric and Hybrid Electric Vehicle Technology

By Samuel E. de Lucena

We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities.

More About Us