lumped-parameter thermal analysis and experimental validation … · lumped-parameter thermal...

J Electr Eng Technol.2018; 13(6): 2276-2283 http://doi.org/10.5370/JEET.2018.13.6.2276

2276 Copyright ⓒ The Korean Institute of Electrical Engineers

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Lumped-Parameter Thermal Analysis and Experimental Validation of Interior IPMSM for Electric Vehicle

Qixu Chen† and Zhongyue Zou*

Abstract – A 50kW-4000rpm interior permanent magnet synchronous machine (IPMSM) applied to the high-performance electric vehicle (EV) is introduced in this paper. The main work of this paper is that a 2-D T-type lumped-parameter thermal network (LPTN) model is presented for IPMSM temperature rise calculation. Thermal conductance matrix equation is generated based on calculated thermal resistance and loss. Thus the temperature of each node is obtained by solving thermal conductance matrix. Then a 3-D liquid-solid coupling model is built to compare with the 2-D T-type LPTN model. Finally, an experimental platform is established to verify the above-mentioned methods, which obtains the measured efficiency map and current wave at rated load case and overload case. Thermocouple PTC100 is used to measure the temperature of the stator winding and iron core, and the FLUKE infrared-thermal-imager is applied to measure the surface temperature of IPMSM and controller. Test results show that the 2-D T-type LPTN model have a high accuracy to predict each part temperature.

Keywords: Interior Permanent Magnet Synchronous Machine (IPMSM), Lumped-Parameter Thermal Network (LPTN), Thermal resistance, Thermal conductance.

1. Introduction Thermal analysis of interior permanent magnet synchro-

nous machine (IPMSM) is very important at load and overload, especially in the field of electric vehicle (EV) and hybrid electric vehicle (HEV), which requires higher power density and torque density. Therefore, accurate temperature rise calculation becoming increasingly more and more important. [1]

There are three basic analysis methods: 1) the lumped-parameter thermal model, 2) the finite element method (FEM) and 3) computed fluid dynamics (CFD). Mellor et al [2] studied an induction motor using the lumped parameter thermal model to calculate the average temperatures at different parts of the motor. A lumped-parameter thermal network model for radial flux IPMSM [3-5] and axial flux IPMSM [6-7] is used to calculate the average temperatures for different parts of IPMSM. Fluid flowing characteristics including gap air and coolant [8-9] are studied. Coupled electromagnetic and thermal analysis of IPMSM is carried out in the paper [10-14] and a test platform was established by temperature sensor and infrared thermal imager. P.W. Han, et al [14] used analytical lumped-circuit method and compared with the experiment results for a 29kW high speed induction motor at 12,000rpm. C.B. Park [15] conducted thermal analysis of the 110kW IIPMSM using

the 3-D thermal equivalent network with thermal equivalent circuit of the water cooling jacket. M. Polikarpova, et al [16] proposed hybrid cooling arrange-ment and adopted computational fluid dynamics and finite-element analysis for a 100kW AFPM electrical machine. An infrared camera was used to determine temperatures distribution outside the ISG. FEM simulations can be accurate to compute temperature distributions of motor parts, but convection heat transfer coefficients generally use empirical formula, which lead to the uncertainty of results.

An IPMSM is introduced in the paper. Forced liquid (50%water+50% glycol) cooling in shell jacket is adopted. A T-type lumped-parameter thermal network model of IPMSM for thermal design and analysis is presented. This method divided into two stages combines both analytical and CFD simulations. In the first stage, fluid can be modeled using CFD tools, and in this way, heat transfer coefficients can be accurately computed between solid surface and fluid surface, which are necessary for FEM and LPTN model. In the second stage, heat transfer coefficients obtained by CFD simulations can be used to amend the empirical formula. In this way, a simplified model considering its symmetry and period is introduced in this paper. Finally, a temperature rise test platform under the rated load and overload condition is established to verify the above-mentioned lumped-parameter thermal network result and CFD simulation result. Furthermore, a measured efficiency map is obtained at operation region. The temperature measurements of IPMSM are carried out using thermocouple PTC100 and FLUKE infrared-thermal camera device.

† Corresponding Author: Dept. of Electrical Engineering, Xi’an Jiaotong University, China. ([email protected])

** Dept. of Mechanical Engineering, Xi’an Jiaotong University, China. ([email protected])

Received: June 3, 2017; Accepted: May 31, 2018

ISSN(Print) 1975-0102 ISSN(Online) 2093-7423

Qixu Chen and Zhongyue Zou

http://www.jeet.or.kr │ 2277

2. Lumped Parameter Thermal Network A lumped-parameter thermal network model applied to

IPMSM is presented. Each cylindrical component can be described by lumped-parameter thermal network composed of radial resistance, axial resistance and heat source. The definition of thermal resistances in lumped-parameter thermal network is related to thermal conductivity of material and its dimensional information. In this paper, heat transfer mechanisms of IPMSM, which are generally classified as thermal conduction and thermal convection, are discussed in detail. A. B. Nachouane, et al [17] proposed a traditional lumped-parameter thermal network to estimate the temperature distribution for a 6kW integrated starter generator (ISG).

2.1 Model and parameter of IPMSM

The principle of volume equivalence is adopted in this

paper, in other words, the heat generation rate of heat source components needs to keep unchanged. Flow chart of nodal temperature rise calculation using LPTN method is given in Fig. 1.

Main parameters of IPMSM is shown as in Table 1.

Table 1. IPMSM dimensions and parameters

Parameter Symbol Value Rated power [kW]/speed [rpm] PN/n 50/4000

Stator outer [mm] Do 208 inner diameter [mm] Di 150

Stator iron length [mm] Lef 160 Number of parallel branches a 2

Number of turns per coil Ns 10 Length of air gap [mm] δ 1.5

PM thickness [mm] hpm 6 Number of stator slots/pole pairs Q /p 36/3

Winding connection type ― Y Coolant flow velocity [L/min] V 8

Start

Satisfy temperature rise

condition?

Save results

End

Compute loss

Compute coefficients of heat conductance and heat transfer

Compute node temperature rise

Compute nodethermal resistance

Generate thermal conductance matrix

Establish thermal equilibrium equationEstablish T-type

thermal network model

No

Yes

Modify

Fig. 1 Flow chart of nodal temperature rise calculation

Heat source components including stator iron, stator winding, rotor shoe, rotor yoke and PM in Fig. 2, can be equivalent to general cylindrical component model according volume equivalence in Fig. 3.

2.2 Thermal resistance definition

A general cylindrical component and its lumped-

parameter thermal network that is derived from the solution of the heat conduction equations are shown in Fig. 4. The

Table 2. Thermal resistance of cylindrical component

R Radial direction Axial direction

R1 ( )2

2 1 22 2

1 2

2 ln1 14 r

r r rk l r rp

é ù-ê ú

-ê úë û 2 2

1 22 ( )a

lk r rp -

R2 ( )2

1 1 22 2

1 2

2 ln1 14 r

r r rk l r rp

é ù-ê ú

-ê úë û ( )2 2

1 22 a

lk r rp -

R3 ( )

( )

2 21 2 1 22 2

1 2 2 21 2

2 21 2

4 ln

8 rr

r r r rr r

r rk l rp

- - +-

-

( )2 21 26 a

lk r rp

--

Fig. 2. IPMSM geometry model (half model)

Fig. 3. Equivalent model of heat source (half model)

Fig. 4. (a) Cylindrical component (b) Radial and axial

thermal network


2278 │ J Electr Eng Technol.2018; 13(6): 2276-2283

corresponding thermal resistance definition is given in Table 1 [5-7], where kr and ka are the thermal conductivity in the radial and axial directions respectively; l is the axial length and r2 and r1 are the outer and inner radius of the cylindrical component; T3 and T4 are the unknown temperatures on the inner and outer surfaces, and T1 and T2 are the unknown temperatures at two end face; Tm represents the average temperature of the component; P and C represent the corresponding internal loss and thermal capacitance. Thermal capacitance in steady state analysis is here under no consideration.

Table 3 gives some typical values for the thermal conductivities of solid materials applied to IPMSM [6].

2.3 Heat conduction and thermal convection

Heat conduction and thermal convection of the fluid

including liquid coolant and air are considered in calculating IPMSM temperature rise.

General formula of heat conduction Gmat is shown as

matmat

mat

AG

Ll

= (1)

where Gmat is heat conduction, λ is thermal conductivity, Amat is cross-sectional area, Lmat is path length along the heat conduction direction.

The equivalent thermal conductance Gmat1,2 with or without assembly clearance is considered as follows.

1,2

1 2

1,21 2

11 1 1

11 1

matmat air mat

matmat mat

GG G G

GG G

ì =ï + +ïíï =ï +î

(2)

where Gmat1 and Gmat2 are thermal conductance of different material, Gair is thermal conductance of air.

Most of heat generated by IPMSM parts could be taken away by circulating liquid coolant in shell jacket. Shell jacket includes S-type channel filling with liquid coolant. Pressure loss and wall heat transfer coefficient distribution of shell jacket is obtained by FLUENT in Fig. 5(a), and its equivalent water circuit is shown in Fig. 5(b).

The total loss is the sum of the losses of all parts as shown in

(a)

(b)

Fig. 5. Water channel (a) Pressure loss and wall transfer coefficient (b) Equivalent water circuit model

losses Cu Fe pm ro air be exP P P P P P P P

Q C T= + + + + + += × ×D

(3)

22

v QA

= (4)

where Plosses is total loss of IPMSM, PCu is copper loss, PFe is stator iron loss, Ppm is eddy current loss of PM, Pro is eddy current loss of rotor, Pair is friction loss of air, Pbe is bearing loss, Pex is extra loss, V2 is the velocity of the liquid coolant, Q is the flow of liquid coolant, A2 is the cross-sectional area of water channel.

As can be seen from Fig. 5, the total pressure loss p of liquid coolant through shell jacket can be expressed by

6

12

+n ii

p p p=

= D × Då (5)

( )( )

( )( )

2 2

2 2

3 3 3

3 3

22 2 2 21

1 1 1 1 2 22 2

3.52 23 3 2 3

22 2 2 23 3

4 4 5 5 32 2

3.52 26 6 3 2

1 1 1 11 ;2 2 2 21 0.131 0.16321 1 1 11 ; 12 4 2 21 0.131 0.1632

A Lp v v p v vA D

p v D D v

A Ap v v p v v

A A

p v D D v

mz r r z r r

z r r

z r r z r r

z r r

ì æ öïD = = - D = =ç ÷ï è øïD = = + ×ïïí

æ ö æ öD = = - D = = -ç ÷ ç ÷

è ø è ø

D = = + ×î

ïïïïï

(6)

where Δp1, Δp4, and Δp5 are pressure loss corresponding to the changing cross section, Δp2 is the pressure loss along the water channel, Δp3 and Δp6 are pressure loss due to its connection with the elbow, n is number of water channel.

Thermal conductance between inner wall of shell jacket and liquid coolant is shown by

Table 3. IPMSM thermal parameters

Thermal conductivity Symbol Value Silicon steel [W/(K.m)](x,y,z) λSi (4.5,45,45)

Copper [W/(K.m)] λCu 386 Aluminum alloy [W/(K.m)] λAl 201

Winding insulation [W/(K.m)] λInsu 0.26 PM [W/(K.m)] λpm 8

Steel 42CrMo [W/(K.m)] λSt 45



0.141/31/3 1/3 2

0.8 0.4

1.86Re Pr Re<2200

0.023Re Pr Re>2200

ewa

wa wa

wa

d vNu L u

ì æ öæ öï ç ÷ç ÷= í è ø è øïî

(7)

2 22Re( )

ewa

wa wa

d abv va bu u

= =+

(8)

Nu wawa

e

hDl

= (9)

wa wa waG h A= × (10)

where λwa is the thermal conductivity of liquid coolant, Nuwa is the Nusselt number of liquid coolant, Rewa is the Rayleigh number of liquid coolant., Pr is the Prandtl number, de is the equivalent diameter, a is the width of water channel, b is height of water channel, υwa is kinematic viscosity coefficient of liquid coolant, hwa is convective heat transfer coefficient of liquid coolant, L is the path length of water channel.

Thermal conductance Gair1 between rotor end surface and gap air is shown by (11)-(15). The heat transfer coefficient hair1 of air can be obtained by classical Nusselt number.

1airNuh ld×

= (11)

The Nusselt number Nu of air is calculated for three

different Taylor number Ta as shown in

0.367 4

0.241 4 7

2 for Ta<17000.128Ta for 1700<Ta<10.409 for 1e <Ta<1e

Nu eTa

ìï= íïî

(12)

where Taylor number Ta and Reynolds number Re are shown as

2ReTard×

= (13)

Re v du×

= (14)

where υ is kinematic viscosity of the air (m2/s) and v is linear speed of the rotor (m/s); Thermal conductance Gair1 at air gap is obtained by 1 1 1 oair air air airG h A h D Lp= = (15)

Heat transfer coefficient hair2 and thermal conductance

Gair2 between the rotating shaft and internal air can be written as

2 15.5 (0.39 1)airh v= × + (16) 2 2 2air air airG h A= × (17)

Heat transfer coefficient hair3 and thermal conductance

Gair3 at the location of end winding surface can be written as illustrated by

3 14.2 (1 )airh k v= × + (18) 3 3 3air air airG h A= × (19)

where k is the coefficient of the air blowing rate, Aair3 is surface area of end winding (unit:m2).

The thermal conductance Gair4 and external surface heat transfer coefficient hair4 between shell and ambient air can be evaluated as

( )1/3

4 14 1 0.5 25shell

airT

h v æ ö= + ç ÷è ø

(20)

4 4 4air air airG h A= × (21)

where v is wind speed (that is linear speed of shell surface. unit: m/s); Tshell is external surface temperature of shell (unit: K).Aair4 is surface area of shell (unit:m2).

2.4 Thermal conductance and T–type thermal network

For steady-state thermal analysis, the temperature rise T

of each node of lumped-parameter thermal network is calculated as shown in equation (22)-(24), where the dimension of thermal conductance matrix Gnxn is n=34.

G T W× = (22)

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1 1

2 2

1,1 1,2 1,i 1,2,1 2,2 2, 2,

,1 , 2 , ,

,1 , 2 , ,

i i

n n

G G G G n T WT WG G G i G n

T WG i G i G i i G i n

T WG n G n G n i G n n

é ù- ×× × - - é ù é ùê ú ê ú ê ú- ×× × - -ê ú ê ú ê úê ú ê ú ê ú× =ê ú ê ú ê ú- - ××× × × × -ê ú ê ú ê úê ú×× × ê ú ê úê ú ë û ë û- - ××× - ×× ×ë û

MM

M MM M O M M M

M MM M M O M

(23)

( ) ( ) ( )

( ) ( ) ( )1,

, ( , ) ,1 , 2

, 1 , 1 ,

n

j j iG i i G i j G i G i

G i i G i i G i n= ¹

= = + + ×××

+ - + + + ××× +

å (24)

Gauss elimination method, Gauss-Seidel iterative method,

Jacobi-Cholesky elimination method, or Conjugate gradient method can be adopted to solve thermal conductance matrix.

Because of the axial symmetry, only half temperature node distribution drawing of the IPMSM is built in Fig. 6 (a), and the corresponding equivalent T–type LPTN model in Fig. 6(b) in this paper is used for node temperature calculation. The power losses defined in Table IV are injected into the specified thermal nodes of the parts. In the thermal model, the geometry of the IPMSM is divided into the following 18 parts:

1), 2) internal air, 3) outer shell, 4) inner shell, 6) stator yoke, 8), 12) end-winding, 10) slotting winding, 14) stator



teeth, 15) gap air, 18) rotor shoe, 21) magnet, 24) rotor yoke, 27), 31) bearing, 29) shaft, 33), 34) end cap.

Main heat generated by losses is taken away by circulated coolant in shell, therefore, shell is divided into outer shell (3# node) and inner shell (4# node) considering heat convection. Due to the flux density difference between stator tooth (14# node) and stator yoke (6# node), losses of stator tooth and stator yoke are considered separately. Similarly, rotor iron loss fall into rotor shoe (18# node) loss and rotor yoke (24# node) loss.

In order to accurately calculate copper loss, winding is divided into slotting winding (10# node), and two end windings (8# node, 12# node). Bearing (27# node, 31# node) is also considered as a cylindrical component. Non-heat source parts, for example, end cap (33# node, 34# node), shaft (29# node) and shell (3# node, 4# node) are regarded as single node. Friction losses generated by wind are taken into account such as 1# node and 2# node [7].

Table 4 gives loss values for the heat generation applied to IPMSM.

2.5 3-D CFD Verification

B. Zhang, et al [18] adopted computational fluid

Table 4. Loss value of IPMSM parts

Parameter Symbol Value Stator tooth loss [W] PFet 271

Slot winding copper loss [W] PCu1 952 End winding copper loss [W] PCu2 284

Stator yoke loss [W] PFej 428 PM eddy loss [W] Ppm 38

Rotor iron loss [W] Pro 45 Air friction loss [W] Pair 10

Bearing loss [W] Pbe 4 Extra loss [W] Pex 15

Losses values at 50kW power and speed of 4000rpm

Fig. 7. Liquid-solid coupling model

(a)

(b)

Fig. 6 Interior IPMSM (a) schematic drawing; (b) lumped-parameter thermal resistance network



74.171.168.165.162.059.056.052.949.946.943.940.837.834.831.728.7

Fig. 8. Temperature distribution of IPMSM (°C)

thermocouple Stator

Stator winding

Stator iron

Rotor iron Rotor

Magnet

Fig. 9. Rotor and stator of IPMSM

Motor controller

Load motor

Constant temperature cooling tank

Power analyzer PMSM

Electric parameter sensor box

Load motor controller

Current clamp

Oscilloscope

Fig. 10. Dynamometer platform

Cooling-water machine

DC power supply

Upper computer console

System monitor interface

Fig. 11. Power supply and upper computer console

3. Prototype Manufacture and Test In order to verify the LPTN model and liquid-solid

coupling model, the prototype of IPMSM is manufactured, whose rotor and stator are shown in Fig. 9. A load test platform is established, which mainly include power supply, load motor controller, load motor, electric parameter sensor box, power analyzer, upper computer, IPMSM, controller, constant-temperature cooling tank and cooling-water machine as shown in Fig. 10-Fig. 11.

Measured phase current wave using three AC current clamps at rated load case is obtained in Fig.12, whose peak value reaches 232A.

Measured IPMSM efficiency map in the constant torque

Fig. 12. Phase current wave at rated load

Fig. 13. Efficiency map

Fig. 14. Infrared thermal image of IPMSM at T=119N.m,

n=4000rpm, Ia=151A



and the constant power operating regions is obtained as shown in Fig. 13.

The temperature measurement of IPMSM is carried out using thermocouple PTC100 and a FLUKE infrared-thermal camera device. Thermocouple temperature sensors PTC100 are located into each phase slot windings for measuring winding and iron core temperature. The outer surface temperature including IPMSM and its controller is

measured by using a FLUKE infrared-thermal camera device in Fig. 14-Fig. 15.

IPMSM phase current at overload case is obtained in Fig. 16, whose peak value reaches 382A. Infrared-thermal image of IPMSM and its controller at overload case are given in Fig. 17-Fig. 18. Power cable temperature of IPMSM and its controller reach 83.9˚C and 60.9˚C respectively.

Comparison among LPTN me thod, CFD method, and experiment results is shown in Table 5, which maintains consistency between experimental results and simulations.

4. Conclusion Heat transfer coefficients of fluid can be accurately

computed using CFD simulation in this paper, which can be used to amend the empirical formula. Therefore, a simplified model considering model symmetry and periodicity is built to reduce the computation time obviously. Assembly clearance between shell and stator iron core is also taken into account. By comparing LPTN result with 3-D liquid-solid coupling CFD result, LPTN method can accurately predict the temperature distribution. Meanwhile, temperature rise test platform including prototype manufacture is built to validate the above two methods using FLUKE infrared-thermal-imager and

Fig. 15. Infrared thermal image of motor controller at

T=119N.m, n=4000rpm, Ia=151A

Fig. 16. Phase current wave at overload case

Fig. 17. Infrared thermal image of IPMSM at T=295N.m,

n=2000rpm, Ia =351A

Fig. 18. Infrared thermal image of motor controller at

T=295N.m, n=2000rpm, Ia =351A

Table 5. Calculated and measured temperature at rated load

Parameter Method A Method B Method C Slot winding 74 76 75 Stator iron 60 62 64 Rotor iron 66 68 69

PM 66 67 70 Bearing 42 38 41

Shell 26 29 25 End cap 31 33 30

Shaft extension 34 36 32 A: Lumped-parameter thermal network; B: fluid-solid coupling CFD; C: Measured (50kW, 4000rpm, 151A) [°C]



thermocouple PTC100. The method will be important for practical engineering application.

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Qixu Chen He received bachelor’s degree in mechatronic engineering from North University of China, Taiyuan, China, in 2007, and master’s degree in mechatronic engineering from Xi Dian University, Xi’an, China, in 2010. He is currently working toward a doctor's degree in electric

engineering from Xi'an Jiaotong University, Xi’an, Shaanxi, China, His research interests include IPMSM design and drive of the electric vehicle.

Zhongyue Zou He received the B.S. degree from Shandong University of Technology and the M.S. degree from Shandong University of Science and Technology. He is currently working toward the Ph.D. degree in mechanical engineering from Xi’an Jiaotong University, Xi’an, China. His research

interests include energy management and energy manage-ment.

lumped-parameter thermal analysis and experimental validation … · lumped-parameter thermal...

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