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

Written By

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

Submitted: October 23rd, 2010 Published: September 12th, 2011

DOI: 10.5772/17905

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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.


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.


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.


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, 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.

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

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


The principal tooth section:Stooth


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

The inserted tooth section:Stoothi


The slot section: Ss


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

The slot average width:Ws


The principal tooth section:Stooth


The inserted tooth section:Stoothi


The slot section: Ss


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,In is the rated current and Nteethin the number of teeth.


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


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

The expression of the magnet height hm is 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.


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


The rotor yoke thickness hryis defined:


2.5. Electrical sizing

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


The motor electric constant : Ke


The electromagnetic torque :Tem


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.


The phase résistance of the motor : Rph


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:


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:


Where V is the volume,ρ is 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:


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

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


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).


Rinsorepresents the isolator thermal resistance (K.W1).


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


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


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


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


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


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


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).


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

Ccoilrepresents the heat capacity of coil (JK1).


Cinsorepresents the heat capacity of insolator (JK1).


Csyrepresents the heat capacity of stator yoke (JK1).


Ccarepresents the capacity of carter (JK1).


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).


Rinsorepresents the insolator thermal resistance (K.W1).


Rcoilrepresents the coil thermal resistance (K.W1).


Rmagrepresents the magnet thermal resistance (K.W1).


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


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


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


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

Cmagrepresents the heat capacity of magnet (JK1).


Cryrepresents the heat capacity of rotor yoke (JK1).


Ccoilrepresents the heat capacity of coil (JK1).


Cinsorepresents the heat capacity of insolator (JK1).


Csyrepresents the heat capacity of stator yoke (JK1).


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

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


  1. 1. ChanC. C.2004The Sate of the Art of Electric Vehicles, Journal of Asian Electric Vehicles, 22579600
  2. 2. JunakJ. .OmbachG. .StatonD.2008Permanent Magnet DC Motor Brush Transient Thermal Analysis, 978-1-4244-1736-0/08/$25.00 ©2008 IEEE.
  3. 3. DorrellDavid. G. .StatonMalcolm. A. .Mc GilpI.2006Thermal Approach to High Performance Specification, IEEE.
  4. 4. MagnussenF. .LendenmannH.2005Parasitic Effects in PM Machines with Concentrated Windings, IAS 40th Annual Meeting Hong Kong, 210451049
  5. 5. BenHadj. N. .TounsiS. .NejiR.SellamiF.2007Real coded Genetic algorithm for permanent magnet motor mass minimization for electric vehicle application, 3rd International Symposium on Computational Intelligence and Intelligent Informatics, Agadir-Morocco, March 28-30, 2007, 153158
  6. 6. ChinY. K.NordlundE.StatonE. A.2003Thermal analysis- Lumped circuit model and finite element analysis. Sixth International Power Engineering Conference (IPEC), 952957
  7. 7. StatonD. A.2001Thermal analysis of electric motors and generators, Tutorial course at IEEE IAS Annual Meeting,, Chicago, USA.
  8. 8. HolmanJ. P.1992Heat TransferSeventh Edition, McGraw-Hill Publication.
  9. 9. TounsiS.2006Modélisation et optimisation de la motorisation et de l’autonomie d’un véhicule électrique. Thèse de Doctorat, ENI Sfax
  10. 10. JérémiR.2003Conception de systèmes hétérogènes en Génie Électrique par optimisation évolutionnaire multicritère, thèsede doctorat, Institut National Polytechnique de Toulouse.
  11. 11. GascL.2004Conception d’un actionneur à aimants permanents à faibles ondulations de couple pour assistance de direction automobile Approches par la structure et par la commande, Thèse de doctorat, Institut national Polytechnique de Toulouse.

Written By

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

Submitted: October 23rd, 2010 Published: September 12th, 2011