analysis of heat distribution in a 8/6 switched reluctance

Analysis of heat distribution in a 8/6Switched reluctance machine

E.Annie Elisabeth JebaseeliSchool of Electrical and Electronics Engineering,

Sathyabama Institute of science and Technologyy,

Chennai-600119,Tamilnadu,India.

[email protected]

January 28, 2018

Abstract

In an electrical machine, the heat generated by the lossesis transferred to the atmosphere through the structure of themotor. The increase in temperature can lead to overheatingand reliability issues of electric motor resulting in deratingof motor. Hence designers of high performance motors are inneed of accurate thermal models to determine the specifiedrate of heat transfer. This enhances the removal of heat en-ergy so that overheating can be avoided and minimizes thedifference in temperature between the interior of the motorand environment. In this paper, various physical mecha-nisms of heat flow and the governing laws of heat transferare discussed. Also a finite element model of 8/6 SRM isdeveloped to analyze its performance in steady state andtransient conditions. Finally the simulated results are com-pared with the experimental results to prove the suitabilityof FEM in analyzing the thermal performance of SRM.

Key Words: Electrical Engineering, Finite elementanalysis, rotating machines, temperature control and ther-mal analysis.

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International Journal of Pure and Applied MathematicsVolume 118 No. 17 2018, 561-578ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

561

1 Basic concepts of heat transfer in

system

According to the first law of thermodynamics, [1,2] the energy bal-ance in any system may be expressed as the net change in the totalenergy of the system during a process is equal to the difference be-tween the total energy entering and total energy leaving the systemduring that process. Hence the equation for power balance can bewritten as in (1).

(Total energy entering the system Ein)-( Total energy leav-ing the system Eout) =(Change in the total energy of the system∆Esystem ) ——— (1)

Thus for any system undergoing any process, the energy balancecan be expressed as in (2).

EinEout = ∆Esystem —– (2)

Energy is a property whose value does not change unless thestate of the system changes. Therefore, if the process is understeady state condition, the change in energy of a system is zero. Inthis case, the energy balance reduces as in (3).

Ein = Eout ——– (3)

In heat transfer analysis, the energy is generally expressed interms of heat or thermal energy. Hence the energy balance undertransient condition can be expressed as in (4).

Qin −QOut + Egen = ∆Ethermalsystem —– (4)

where Qin is the total amount of heat transferred into the sys-tem, QOut is the total amount of heat transferred out of the system,Egen represents the amount of heat generated and ∆Ethermalsystem

is the change in thermal energy of the system. The sum of net heattransfer and heat generation causes change in thermal energy ofthe system. Let us consider a small volume of a solid element asshown in Fig.1.The dimensions are dx, dy, dz along the X, Y, and

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International Journal of Pure and Applied Mathematics Special Issue

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Z coordinates.

Figure1.Elemental volume in Cartesian coordinates

Initially conduction of heat is considered in the x direction. Letthe flow of energy flowing into the system in the X direction beqx/x.where qx is the flow of heat in the x direction in J/s or watts.The flow of energy flowing out of the system in the X direction beqx/(x + dx) Using Taylors series expansion, the expression can bemodified as in eqn.5

qx/(x+ dx) = qx/x+ (∂qx)/∂xdx —– (5)

where (∂qx)/∂x dx represents the rate at which heat changes.Thereforenetflow of energy in x direction is given as in eqn.6.

qx/x− qx/(x+ dx)—– (6)

=qx/x− (qx/x+ (∂qx)/(∂x)dx)

= - (∂qx)/(∂x)dx

The negative sign indicates that heat flows towards a directionof reduced temperature. Also the rate of heat generated is given ineqn.7.

Egen = q ∗ volume —– (7)

Egen = q ∗ dxdydz

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where q is the energy dx dydz per unit volume. If U is theinternal energy per unit mass then as in eqn.8

U = Cp(T − Tref ) — (8)

where Cp is the specific heat at constant pressure. Then therate of energy accumulated in a system can be written as in (9,10).

Ethermalsystem = (du/dt) ∗mass —- (9)

where du/dt=Cp —-(10)

which indicates the rate at which the integral energy changes.E(thermalsystem) = ρcp ∗ (dT/dt) ∗ dxdydz — (11) In a three di-mensional system, the heat flux is given as in (12).

qx = −K(dydz)∂T/∂x ( 12)

where K is the thermal conductivity of the material, dydz repre-sents the area through which heat is transferred, T/x is the temper-ature gradient. Therefore the net flow of energy in the x directionis as in (13).

(∂qx)/∂xdx = −∂/∂x(−K ∗ (dydz)∂T/∂x)dx —(13)

= ∂/∂x(K∂T/x)dxdydz

Similarly the net flow of energy in the y and z directions canbe calculated as∂/∂y(K∂T/∂y)dxdydz and ∂/∂z(K∂T/∂z)dxdydz.Now the heat flow equation in a three dimensional system can bewritten as in (14)

ρCp ∗ (dT/dt) ∗ dxdydz = ∂/(∂x)(K∂T/∂x)dxdydz+ ∂/∂y(K∂T/∂y)dxdydz + /z(K∂T/∂z)dxdydz+ =q ∗ dxdydzρcp ∗ (dT/dt) = ∂/(∂x)(K∂T/∂x) + ∂/∂y(K∂T/∂y) +∂/∂z(K∂T/∂z) + q —- (14)

In this work, only two dimensional analysis is considered ne-glecting the parameters in the Z direction since heat is distributed

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uniformly thorough out the body of the machine. Under steadystate condition dT/dt is zero. Hence the above equation reduces to(15).

∂/(∂x)(K∂T/∂x)+∂/∂y(K∂T/∂y)+∂/∂z(K∂T/∂z)+q′ = 0—– (15)

2 Modes of heat transfer

Heat transfer is defined as the transmission of energy from one re-gion to another. It occurs as a result of temperature differenceoccurring within a body or between its body and the surroundingmedium. This takes place by three different modes namely conduc-tion, convection and radiation. Only conduction and convectionmodes are considered here.

2.1 Heat Transfer by Conduction

In the conduction process, heat flows from more energetic particlesto less energetic ones because of the interactions between them.The conduction process is quantified by Fouriers law. Consideringa thermally isotropic medium, Fouriers law of heat conduction fortwo dimensional heat flow is given in (16).

Qconduction = −KA/L —-(16)

where K is the thermal conductivity of the material in W/mK,A represents the cross sectional area of heat transfer path in m2andL is the axial length in m. The minus sign in the above equationrepresents that heat is transferred in the direction of decreasingtemperature.

2.2 Heat Transfer by Convection

Liquid and gas particles when located near a heated body becomelighter and begin to rise. In turn they transfer the heat to the ad-jacent cooler particles. Thus natural convection takes place due to

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the changes in fluid density. This phenomenon occurs on the exter-nal housing of the machine. In modern machines, heat is removedby blasting air on the heated surfaces. In SRM, forced convection ispreferred due to the rotation of the rotor. This phenomenon takesplace on the external housing of the machine and in the air gap.In convection the convective heat flux q in W/m2 is governed byNewton’s Law as given by (17).

q = h(T1 − T2) —- (17)

where (T1 − T2) is the difference in temperature between thesurface to be cooled and the cooling medium. The convection heattransfer coefficient or film coefficient h in W/m2−◦C depends onvarious factors like whether convection is natural or forced, whetherflow is laminar or turbulent, the type of coolant and the geometryof the body.

2.3 Heat Transfer by Radiation

In a system, heat transfer can occur in the form of thermal radia-tion also. Here the radiation heat flux is given by Stefan-Boltzmannlaw as in (18).

Q = FσA(T 41 − T 4

2 ) —– (18)

where F is a factor which depends on geometry and surfaceproperties, σ is Stefan-Boltzmann constant, A is the surface areaand T1 and T2 are the surface temperatures. Since the radiationheat flux is proportional to the fourth power of the absolute tem-perature this makes the problem to be a non linear one. Hence thismode of heat transfer is not considered in this analysis.

3 Thermal modellng of SRM

An electrical machine is a complex engineering system [3,4]. It con-sists of various types of materials with diverse thermal propertiesand heat sources. In the field of Electric vehicle, the switched re-luctance machine finds suitability due to its simple structure, high

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starting torque with high efficiency[5]. Hence to design such energysaving electrical machines, thermal analysis has to be carried outon SRM apart from the conventional field analysis[6,7]. In recentdays, tools like mathematical modeling and computational analysis[8] play a vital role in the thermal monitoring of electrical machine.This section discusses the development of a thermal model for SRMusing FEM[9].

FEM is a prevailing technique to deal with the thermal behaviorof any system in engineering[10]. To carry this out, modeling andmeshing of the solid structure is the foremost step. This methodallows the designer to specify all structural and material character-istics which are obtained by measurements[11] on SRM. The specificgeometric dimensions used for modelling are measured on the 2hpSRM which is used for experimental validation.

Fig. 2. Geometrical model of 8/6 SRM

With the specified dimensions and properties of the 8/6 SRM,a finite element model is developed using FEM software ANSYS10 as shown in fig.2.. Using this model, the thermal distributionunder steady state and transient conditions are analysed in variousparts of the machine [12,13]. To validate the thermal model of SRM,simulated results are compared with the experimental results undersame conditions.

4 Losses in SRM

In the thermal analysis, the electromagnetic losses constitute theheat source [14,15]. It includes core loss and copper loss in the

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windings. Since experimental determination of power losses is ex-pensive, it can be determined either analytically or numericallyunder various loaded conditions [16] in order to use them as inputparameters for thermal analysis.

In SRM, core loss occurs in the stator and the rotor[17]. Thestator and rotor core are [18] laminated to reduce the eddy currentloss. The magnitude of the hysteresis loss is determined by the fre-quency of flux reversal and its path [19]. The loss coefficients Pnin watts/Kg can be evaluated from the loss characteristics of thematerial with respect to the frequency or its value is obtained fromthe specification sheet of the motor given by the manufacturer. Ifthe weights of the various iron segments Wn in Kg of the machineis known, then the total core loss is given by (19) .

Total Core loss =∑PnWn —— (19)

For any electrical machine, the copper loss can be estimatedfrom I2Rs [20] where Rs is the effective resistance of the windingper phase and I is the RMS value of the current. If m is the num-ber of stator phases, then the total copper loss for non overlappingcurrent in the stator is given by (20).

Copper loss in the stator windings = mi2Rs —— (20)

A finite element heat run is simulated with losses as the mainheat source. Then a 2-Dimensional steady state and transient anal-ysis are carried out to predict the temperature in SRM.

5 Steady state thermal analysis of SRM

In SRM, heat is transferred to various parts by conduction or con-vection. The heat generated in the body makes the liquid and gasparticles around it to become lighter and raise which in turn makesthe cooler particles to get heated and rise[21].

Considering a two dimensional steady state heat conduction[22,23],the heat diffusion equation is modified as in (21) since heat rate en-tering a region plus heat rate generated equals the heat rate comingout of the system.

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∂/(∂x)(K∂T/∂x) + /y(K∂T/∂y) + q′ = 0 —— (21)

Also, heat transfer from the body and the axial shaft at twoends is considered to be by the conduction process. Natural Con-vection is considered on stator external surface. Internal surfacesare subjected to have forced convection due to the rotation of therotor.

Figure 3. Steady state temperature distribution at 25 % load

Figure 4. Steady state temperature distribution at 50% load

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Figure 5. Steady state temperature distribution at 75% load

Figure 6. Steady state temperature distribution at full load

The ambient temperature is recorded as 33◦C when the real timemeasurement is carried out. At the same ambient temperature, asteady state analysis is carried out at various loaded condition .Byanalysing the temperature distribution presented in fig.3 to 6, it isclearly observed that at steady state the temperature rises due tocopper loss and the convective coefficients. Thus at full load thehighest temperature is found to occur in the stator winding. Henceit is considered as a point of reference for justification of the model.

6 Transient thermal analysis of SRM

Using ANSYS workbench software, a 2-D transient thermal analysisis carried out on a 8/6 SRM. In transient thermal analysis, temper-ature varies with respect to time [24,25]. Here the fluid parameters

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such as the heat transfer coefficient of convection represent the in-put. The other boundary conditions such as the losses generatedare also applied. Considering the cylindrical coordinate (r,Z), con-ductive heat transfer with various boundary conditions in a hollowcylinder is obtained from the Fourier law as given in (22).

1

r

∂

∂r(kr(

∂T

∂r)) +

1

r2(∂

∂θ)(k

∂T

∂θ) + (

∂

∂Z)(k

∂T

∂ Z) + ζ = ρc∂T

∂t– (22)

where ζ is the heat source which represents the estimated losses.Initially, the machine is considered to have atmospheric tempera-ture and then the temperature increases due to heat generated inthe machine [26]. Using this analysis, the time taken to reach steadystate temperature can be found out.

Figure 7. Initial nodal temperature distribution at full load

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Figure 8. Final nodal temperature distribution at full load

From the results shown in fig.7 and 8, it is observed that asthe load on the motor increases, the temperature of the windingincreases due to the increase in the losses. This generated heat istransferred by conduction and convection to the external surface.In transient thermal analysis, the distribution of heat within themachine components is analysed accurately with respect to timeand it is found that the winding area has the hot spot temperature.

7 Experimental verification of the ther-

mal model

The thermal model is developed taking into account the losses andthermal phenomena involved in it. The effectiveness of the de-veloped model is proved by comparing the simulation results withexperimental results. Thermal testing involves inserting ResistanceTemperature Detectors(RTD) into the selected parts of the machinenamely stator phase windings. The SRM is coupled to a self excitedDC machine. A resistive load acts as a load on the generator. Thereference speed of the machine is set by the potentiometer. Thenthe machine is operated under loaded condition until the tempera-ture reaches their steady state value. The experimental setup usedhere for the model validation is shown in fig.9. A 2 hp four phase8/6 SRM is tested in the laboratory to observe the temperature risein stator windings till it reaches the steady state condition.

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Figure 9. Experimental setup for the thermal testing of SRM

8 Comparison of simulated and exper-

imental results

From the analysis of the model, the temperature rise in the windingarea is recorded and compared with the experimental results asgiven in Table 2.

TABLE 2. COMPARISON OF SIMULATED ANDEXPERIMENTAL RESULTS

The results are compared based on the absolute percentage er-ror.. The good agreement of the temperature distribution betweenthe simulated and the measured results validated the proposed tech-nology. Hence this model can be applied to predict the temperatureof any electrical machine but it has its own limitations.

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9 CONCLUSION

In electrical machine, a high temperature is considered to be oneof the sources of increased stress occurring on it. Hence to in-crease the overall effectiveness of the motor design, this thermalfactor is calculated using finite element method. Using the finiteelement model, thermal analysis is carried out under steady stateand transient conditions using ANSYS 10. In real time environ-ment, temperature of the winding is measured using RTD. Thenthe simulated results are compared with the experimental resultsto prove its suitability. The estimated absolute percentage error isfound to be less than 5%. Hence the effectiveness of the thermalmodel of SRM based on FEA is proved.

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analysis of heat distribution in a 8/6 switched reluctance

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