Modeling and thermal analysis of a canned permanent magnet machine with a novel network model

Abstract

Due to use of cans in the airgap, the eddy current induction occurs and generates can loss. The loss on cans is considerably high and leads to excessive temperature rise of a canned motor, a fast and accurate temperature is necessary. In this paper, a compensation element assisted thermal model is proposed and stressed, due to the inaccuracy of tradition thermal network model. First, the studied canned motor is described. Second, the thermal analysis principle is studied. Then, the novel thermal network model with compensation element is studied, with thermal resistance calculation. Finally, compare motor temperature that is measured by thermal network model and finite element (FE). FE is used as reference and complement.

Keywords

Thermal analysis lumped parameter thermal network compensation elements canned permanent magnet machine can loss

1. Introduction

The canned motor is applied in pharmaceutical, chemical and nuclear field, to transport poisonous and high pressure liquid [1,2]. The liquid is able to get into armature winding, the metallic cans can be effective to prevent liquid leakage. Due to use of cans in the airgap, eddy current is inevitably induced and generates can loss. Can loss is the highest loss of motor, and thus leads to higher temperature rise than ordinary motor, excessive temperature maybe cause motor structure damage. To have high reliability, temperature calculation and analysis is necessary for a canned motor [3,4].

The main temperature rise calculation methods include numerical analysis [5,6], the exact analytical calculation [7] and lumped-parameter thermal network [8–10]. The numerical analysis occupies a deal with computer calculation spaces, and needs a long time to calculate the FE model. This is a defect of the FE analysis, but the result is very accurate. The classic lumped parameter thermal model [11], derived from machine geometry, heat sources, material and cooling, this model is detailed by taking all major components and heat transfer mechanisms [12,13]. In [14], a simplified thermal model for variable-speed self-cooled induction motor is proposed, with the formula inference and calculation of the thermal resistance. In [15], for temperature rise of stator winding with complex knitted transposed structure, the thermal equivalent network method is proposed. In [16], the electromagnetic and thermal characteristics of a novel switched reluctance machine is studied.

The traditional thermal model assumes the heat flow is constant in one object, whereas in fact it alters linearly, which leads to higher calculation result than actual temperature. In the past, such assumption is eliminated by adjusted load or heat transfer coefficients. For the canned motor, due to high can loss and sensitive shielding material, it is worthwhile to find out thermally sensitive location of the can and thus beneficial to improve the reliability of motor.

In steady state condition, the equivalent thermal network can further be simplified, the capacitors are omitted, the thermal resistances and heat sources make up the model. Heat generators are taken the corresponding power losses in the components of motor.

In this paper, a compensation element assisted thermal model is proposed and stressed, the compensation element works as amendment for deviation caused by heat flow, with emphasizing the influence of slot effect and distributed winding, as well as formula inference and the establishment of thermal network model. The 3D FE is used to validate the novel thermal model.

2. The canned permanent magnet motor

Recently, permanent magnet synchronous motor (PMSM) is an attractive drive candidate [17–19], and some canned PMSM motors are also reported in pump industry [20,21]. In Fig. 1 a couple of motors, with identical geometry except one of them is canned, are shown. Figure 1a shows the canned motor with distributed winding, this winding topology shows characteristics that are as follows: (1) more sinusoidal airgap flux field; (2) lower harmonic electromagnetic force. Consequently, this topology is suitable for the canned motor. Compared with Fig. 1b, a couple of cans are used in the airgap, namely the stator can and rotor can. The stator can is fixed into the inner surface of the stator teeth to protect the armature windings, and the rotor can is fixed into the outer surface of the permanent magnets to protect magnets from corrosion, meanwhile to reduce hydraulic friction.

Fig. 1.

The PMSM prototypes, (a) canned, (b) ordinary.

Geometrical specifications are listed in Table 1. To accommodate PMs and cans, the airgap width with PMs enlarges to 7.9 mm. Because airgap width is artificially increased to install cans, the mutual induction can be neglected. Each can redial thickness is approximately 0.5 mm to resist centrifugal force, a higher value for large canned motors. The can shield material is Hastelloy C(H-C), a nickel-based nonmagnetic alloy with low electrical conductivity that restrains eddy current. The value is 800000 S/m at 20 °C and approximately 1.4 times higher at every 100 °C rise. Hence, the total airgap including cans is conductive but nonmagnetic.

Table 1

The canned motor parameter overview

Rated power (kW)	32	Motor type	PMSM
Rated speed (rpm)	3000	Airgap thickness incl. cans/PMs (mm)	7.9
Rated voltage (V)	380
Stator outer bore radius (mm)	134.62	Stator/rotor can thickness (mm)	0.5
Axial length (mm)	83.82	PM thickness (mm)	6
PM material	N36Z	Can material	H-C

3. The thermal analysis principle

In Fig. 2 the function of the compensation element is illustrated, and formula inference is discussed. Figure 2a shows the temperature distribution of the hollow cylinder. Assuming the heat dissipation conditions of the two end surfaces are the same, and the circumferential surface is thermally insulated. The temperature presents linear distribution. Figure 2b shows the traditional nodal thermal network model.

Fig. 2.

Introducing compensation elements, (a) temperature distribution, (b) traditional network model, (c) novel network model with compensation elements, (d) compared results.

Likewise, according to the heat transfer theory, the thermal resistance of the hollow cylinder can be roughly written as $\begin{eqnarray}\displaystyle R_{th\_1}=R_{th\_2}=\frac{1}{2}R_{th}=\frac{l/2}{k\cdot A} & & \displaystyle\end{eqnarray}$ (1) where l is the axial length, k is the heat transfer coefficient, A is heat transfer area.

For the case T ₁ ≠ T ₂, the heat flow of the thermal model can be calculated as $\begin{eqnarray}\displaystyle I_{1}=-\frac{T_{1}-T_{2}}{R_{th}}+\frac{P_{\mathit{Loss}}}{2};\quad I_{2}=\frac{T_{1}-T_{2}}{R_{th}}+\frac{P_{\mathit{Loss}}}{2}. & & \displaystyle\end{eqnarray}$ (2)

Consequently, as the electric circuit theory, the temperature at the node m can be calculated as $\begin{eqnarray}\displaystyle T_{m}=T_{2}+R_{th\_2}\cdot I_{2}=\frac{T_{1}+T_{2}}{2}+\frac{1}{4}p_{\mathit{Loss}}\cdot R_{th}. & & \displaystyle\end{eqnarray}$ (3)

The traditional thermal model with adjusted load has been validated to achieve the correct temperature at the midpoint of the regarded volume, it can be calculated as $\begin{eqnarray}\displaystyle T_{m}=T_{1}+R_{th\_1}\cdot I_{1}=\frac{T_{1}+T_{2}}{2}+\frac{1}{8}p_{\mathit{Loss}}\cdot R_{th}. & & \displaystyle\end{eqnarray}$ (4)

Through the analysis above, the novel thermal model with compensation element is shown in Fig. 2c. Compensation element t _comp is calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle t_{comp1}=\left(\frac{P_{\mathit{Loss}}}{4}\right)\cdot (R_{th\_1})\end{eqnarray}$ (5) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle t_{comp2}=\left(\frac{P_{\mathit{Loss}}}{4}\right)\cdot (R_{th\_2})\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle t_{comp1}\neq t_{comp2}.\end{eqnarray}$ (7)

Figure 2d shows the results of temperature estimated by three methods, the characteristics are as follows: (1) T _max is at the center of the object; (2) The temperature is calculated by traditional thermal model is relatively higher, this is due to assuming heat flow constant and the center inputting loss is too large; 3) The novel model calculation result is more accurate.

4. The thermal network model

4.1. Model overview

As shown in Fig. 3, the whole model consists of 11 parts, namely (1) frame (abbreviated as fr), (2) stator yoke (SY), (3) stator teeth (ST), (4) stator windings (wi), (5) end windings (EW), (6) stator can (OC), (7) airgap (AG), (8) rotor can (IC), (9) permanent magnet (PM), (10) rotor yoke (RY), (11) shaft (sh). Due that cooling condition leads to necessity of using compensation, the windings should be divided into wi and EW.

Fig. 3.

Motor axial model.

The nodal temperature T of each part is defined in Table 2. Note that abbreviated subscripts indicate component names. Consequently, according to Fig. 2, the resulting temperature is the maximum average temperature.

Table 2

Node temperature of each component

Frame	T _fr	Stator Yoke	T _SY	Stator Teeth	T _ST
Stator Winding	T _wi	End Winding	T _EW	Stator Can	T _OC
Rotor Can	T _IC	PMs	T _PM	Rotor Yoke	T _RY

4.2. The heat sources

In the lumped parameter thermal model, losses are seen as heat sources. The losses of each component are calculated by FE. In the FE model, all segments of motor are columnar and separated from each other. For the sensitive component of can, the conductivity is given and assumed to be constant. The loss is calculated by Poynting’s theorem. The loss of stator windings is calculated by 2d FE, the loss of windings is calculated by 3d FE, the loss of end windings is separated from 3d FE. In this paper, the working temperature of motor is constant in steady state operating point, i.e. the loss of motor is considered to be constant. Figure 4 shows the loss of stator can and stator windings.

Fig. 4.

Loss of each part, (a) stator can, (b) stator winding.

The losses of each node are demonstrated in Table 3. Because the frame does not produce losses, there is not heat inside. P _SY, P _ST and P _RY are iron loss, P _wi and P _EW are copper loss, P _OC, P _IC and P _PM are eddy current loss.

Table 3

The losses of each nodes

Component	Symbol	Value (W)
Stator Yoke	P _SY	62.19
Stator Teeth	P _ST	76.01
Stator Winding	P _wi	436.21
End Winding	P _EW	50.60
Stator Can	P _OC	3855
Rotor Can	P _IC	1.12
PMs	P _PM	3.26
Rotor Yoke	P _RY	0.5

Temperature difference between stator windings and end windings due to cooling condition, the windings should be divided into stator and end windings. Note that the loss of windings can be seen as constant. In rated load, ideal 3-phase sinusoidal AC excitation is applied. Due to the manufacturing constrains, the can is made up of the bulk metal instead of lamination. In the airgap flux field, eddy current is induced on stator can that is still in the airgap, the amplitude of eddy current is considerably large and thus leads to higher can loss, the loss on stator can is far greater than copper loss and iron loss. The loss of rotor can is considerably lower, due to the synchronous rotation of the rotor can that disables the cut by airgap flux field. However, the loss on rotor can still exists, due to the cogging effect that makes slightly relative motion between airgap field and the rotating can.

4.3. Calculation of thermal resistances

In the novel thermal network model, thermal resistance includes conduction resistance, convection resistance and contact resistance. The heat conduction is caused by the exchange of energy between adjacent objects or by the internal exchange of energy in an object due to a temperature gradient, such as between stator yoke and stator teeth. Heat convection occurs between solid and fluid, such as between frame and ambient. Contact is the inadequate contact between two objects.

Table 4 shows the definition of thermal resistance in the network. Pointing out a criterion, R _{th_1_2} = R _{th_2_1}. ‘th’ is short for ‘thermal’, the thermal resistance between objects is superimposed by that of the corresponding contact parts.

Table 4
Definition of thermal resistance in the network

Symbols Between Type

R _{th_ fr_amb} Frame and ambient Convection

R _{th_ fr_SY} Frame and Stator Yoke Contact

R _{th_SY_ST} Stator Yoke and Stator Teeth Conduction

R _{th_ST_OC} Stator Teeth and Stator Can Conduction

R _{th_OC_IC} Stator Can and Rotor Can Convection

R _{th_IC_PM} Rotor Can and PM Conduction

R _{th_PM_RY} PM and Rotor Yoke Conduction

R _{th_RY_sh} Rotor Yoke and shaft Contact

R _{th_wi_SY} Stator Winding and Stator Yoke Contact

R _{th_wi_ST} Stator Winding and Stator Teeth Contact

R _{th_wi_air} Stator Winding and Slot Air Convection

R _{th_wi_EW} Stator Winding and End Winding Conduction

R _{th_OC_air} Stator Can and Slot Air Convection

Symbols	Between	Type
R _{th_ fr_amb}	Frame and ambient	Convection
R _{th_ fr_SY}	Frame and Stator Yoke	Contact
R _{th_SY_ST}	Stator Yoke and Stator Teeth	Conduction
R _{th_ST_OC}	Stator Teeth and Stator Can	Conduction
R _{th_OC_IC}	Stator Can and Rotor Can	Convection
R _{th_IC_PM}	Rotor Can and PM	Conduction
R _{th_PM_RY}	PM and Rotor Yoke	Conduction
R _{th_RY_sh}	Rotor Yoke and shaft	Contact
R _{th_wi_SY}	Stator Winding and Stator Yoke	Contact
R _{th_wi_ST}	Stator Winding and Stator Teeth	Contact
R _{th_wi_air}	Stator Winding and Slot Air	Convection
R _{th_wi_EW}	Stator Winding and End Winding	Conduction
R _{th_OC_air}	Stator Can and Slot Air	Convection

4.3.1. Conduction

This section calculates R _{th_SY_ST}, R _{th_ST_OC}, R _{th_IC_PM}, R _{th_PM_RY} and R _{th_wi_EW}. The thermal conduction occurs in the couple of neighboring objects that are A and B. The basic hollow cylinder is shown in Fig. 5a, which can be effective to represent each component of the motor, Fig. 5b shows the simple two-node thermal network model, the calculation principle is as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_A\_B}=R_{th\_A\_2}+R_{th\_B\_1}\end{eqnarray}$ (8) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_A\_1}=\frac{ln(R_{A\_out}/R_{A\_avg})}{2{\pi}kL{\lambda}}\end{eqnarray}$ (9) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_B\_2}=\frac{ln(R_{B\_avg}/R_{B\_in})}{2{\pi}kL{\lambda}}\end{eqnarray}$ (10) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{A/B\_avg}=\frac{R_{A/B\_in}+R_{A/B\_out}}{2}\end{eqnarray}$ (11) where R _{A∕B_in} and R _{A∕B_out} are the inner and outer radius of the considered cylinder, R _{A∕B_avg} is the average radius, k is the conduction coefficients, and L is the cylinder length, 𝜆 is the lamination factor. All segments of motor can be divided into upper and lower parts, this is due to the T _max is assumed in the center of object in the thermal network model, R _{th_A_1} and R _{th_A_2} are respectively the upper and lower parts resistance.

Fig. 5.

Model of thermal calculation, (a) basic hollow cylinder, (b) simple two-node thermal network model.

In the motor model, the stator yoke, frame, stator can, rotor can, rotor yoke and shaft are treated as the concentric cylinder. R _{th_ fr}, R _{th_SY}, R _{th_OC}, R _{th_IC}, R _{th_RY} can be calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_fr\setminus SY\setminus OC\setminus IC\setminus RY\_1}=\frac{ln(R_{out}/R_{avg})}{2{\pi}kL{\lambda}}\end{eqnarray}$ (12) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_fr\setminus SY\setminus OC\setminus IC\setminus RY\_2}=\frac{ln(R_{avg}/R_{in})}{2{\pi}kL{\lambda}}.\end{eqnarray}$ (13)

Although the slot effect exists, the stator teeth can be still seen as cylinder, but a correction coefficient should be considered. The thermal resistance of stator teeth is calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_ST\_1}=\frac{ln(R_{out}/R_{avg})}{2{\pi}kL{\lambda}p_{ir}}\end{eqnarray}$ (14) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_ST\_2}=\frac{ln(R_{avg}/R_{in})}{2{\pi}kL{\lambda}p_{ir}}\end{eqnarray}$ (15) where p _ir is the correction factor, which is defined as the volume of the stator teeth compare to that of the stator teeth plus slot at a pole distance.

Likewise, due to the similar structure, calculation process of permanent magnet resistance is similar. Figure 7 shows the equivalent calculation process of permanent magnet. Due to manufacturing constrains, the air slots exist between permanent magnets. Consequently the coefficient p _PM should be considered, which is defined as the volume of the PMs compare to that of the PMs plus slot. The thermal resistance of permanent magnet can be calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_PM\_1}=\frac{ln(R_{out}/R_{avg})}{2{\pi}kL{\lambda}p_{PM}}\end{eqnarray}$ (16) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_PM\_2}=\frac{ln(R_{avg}/R_{in})}{2{\pi}kL{\lambda}p_{PM}}.\end{eqnarray}$ (17)

As to resistance calculation between stator teeth and can, due to slot effect that impedes the heat flow between two adjacent objects, the coefficient C _CR should be considered to amend the deviation that caused by the slot effect. Consequently, Fig. 6 shows the calculation principle by exemplifying pole pitch w _pp and slot width w _sw, coefficient C _{CR_ST↔SY} is defined as a ratio of connecting surface A _{ST_SY} to the inner surface of stator yoke A _INSY. Note that “ ↔” indicates unchangeable, i.e. C _{CR_ST↔SY} ≠ C _{CR_SY ↔ST}. $\begin{eqnarray}\displaystyle C_{CR\_ST\leftrightarrow SY}=\frac{A_{ST\_SY}}{A_{\mathit{INSY}}}=\frac{w_{pp}-w_{sw}}{w_{pp}}. & & \displaystyle\end{eqnarray}$ (18)

The thermal resistance between stator yoke and stator teeth can be calculated as $\begin{eqnarray}\displaystyle R_{th\_ST\_SY}=C_{CR\_ST\leftrightarrow SY}\cdot R_{th\_SY\_2}+R_{th\_ST\_1}. & & \displaystyle\end{eqnarray}$ (19)

Likewise, R _{th_ST_OC}, R _{th_PM_IC}, R _{th_PM_RY} are calculated, due to the similar structure.

Fig. 6.

Model of heat conduction, emphasizing slot effect.

Fig. 7.

Model of PM heat conduction, emphasizing slot effect.

4.3.2. Convection

Due to the existence of temperature difference between solid and fluid, the thermal convection occurs. Convection resistance involves conduction resistance, and this is due to the fluid is equivalent to appropriate solid. Heat convection between frame and ambient is typical, R _{th_ fr_amb} can be calculated as $\begin{eqnarray}\displaystyle R_{th\_fr\_amb}=\frac{1}{h_{cv\_fr\_amb}\cdot A_{fr\_amb}}+R_{th\_fr\_1} & & \displaystyle\end{eqnarray}$ (20) where h _{cv_ fr_amb} is convection coefficient, A _{fr_amb} means contact area. The first and second parts respectively demonstrate convection and conduction thermal resistance.

Figure 8 shows the convection ratio due to slot effect. Stator can is not only in contact with the stator teeth, but also with the slot air. Since the heat dissipation of the slot air is good, the heat flow between stator can and slot air should be considered. C _{CR_air↔OC} is introduced due to calculate heat flow into slot air. Pointing out C _{CR_air↔OC} + C _{CR_ST↔OC} = 1. The thermal resistance between slot air and stator can is calculated as $\begin{eqnarray}\displaystyle R_{th\_air\_OC}=\frac{1}{h_{cv\_air\_OC}\cdot A_{air\_OC}}+C_{CR\_air\leftrightarrow OC}\cdot R_{th\_OC\_1}. & & \displaystyle\end{eqnarray}$ (21)

Since rotor can is welded on the rotor end ring, and thus the entire components of rotor are sealed, which leads to poor heat cooling environment, so the air inside the rotor can be neglected. Convection in the winding is described in section E.

Fig. 8.

The convection ratio due to slot.

Due to the working environment, liquid cooling occurs between bath cans, which is the force heat dissipation condition. Likewise, the liquid is seen as concentric cylinder jacket, the thermal can be written as $\begin{eqnarray}\displaystyle R_{th\_Air}=\frac{ln(R_{out}/R_{in})}{2{\pi}Lk_{Liq}} & & \displaystyle\end{eqnarray}$ (22) where k _Liq is the equivalent coefficient of the liquid with turbulence. The thermal resistance between both cans is written as $\begin{eqnarray}\displaystyle R_{th\_OC\_IC}=R_{th\_Air}+R_{th\_OC\_2}+R_{th\_IC\_1}. & & \displaystyle\end{eqnarray}$ (23)

4.3.3. Contact

Following resistance R _{th_ fr_SY}, R _{th_RY_sh} is calculated. Note that contact thermal resistance includes conduction resistance. Contact resistance R _cv = 1∕(h _cv⋅A _cv), h _cv is contact quality coefficient, A _cv means the area of contact. The resistance between frame and stator yoke, rotor yoke and shaft can be written as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_fr\_SY}=\frac{1}{h_{ct\_fr\_SY}\cdot A_{fr\_SY}}+R_{th\_fr\_2}+R_{th\_SY\_1}\end{eqnarray}$ (24) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_RY\_sh}=\frac{1}{h_{ct\_RY\_sh}\cdot A_{RY\_sh}}+R_{th\_RY\_2}+R_{th\_sh\_1}.\end{eqnarray}$ (25)

Due to the complexity of the windings, the contact thermal resistance of the windings is described in detail in section E.

4.4. Compensation for each part

Table 5 shows the compensation for each part of the thermal network. Compensation, e.g. t _{comp_ST_SY}, t _{comp_ST_OC}, t _{comp_OC_IC}, t _{comp_IC_OC}, t _{comp_PM_IC}, t _{comp_PM_RY} can be calculated as $\begin{eqnarray}\displaystyle t_{comp\_A\_B}=\frac{P_{LOSS\_IC}}{4}\cdot R_{th\_A\_1\setminus 2}. & & \displaystyle\end{eqnarray}$ (26)

The direction of compensation is A to B, the thermal resistance depends on the part of the contact. Note that t _{comp_A_B} ≠ t _{comp_B_A}.

Table 5

Compensation for each part of the thermal network

Symbols	From	To	Symbols	From	To
t _{comp_ fr_SY}	Frame	Stator Yoke	t _{comp_SY_ fr}	Stator Yoke	Frame
t _{comp_SY_ST}	Stator Yoke	Stator Teeth	t _{comp_ST_SY}	Stator Teeth	Stator Yoke
t _{comp_ST_OC}	Stator Teeth	Stator Can	t _{comp_OC_ST}	Stator Can	Stator Teeth
t _{comp_OC_IC}	Stator Can	Rotor Can	t _{comp_IC_OC}	Rotor Can	Stator Can
t _{comp_IC_PM}	Rotor Can	PM	t _{comp_PM_IC}	PM	Rotor Can
t _{comp_PM_RY}	PM	Rotor Yoke	t _{comp_SY_PM}	Rotor Yoke	PM
t _{comp_ST_wi}	Stator Teeth	Winding	t _{comp_wi_ST}	Winding	Stator Teeth
t _{comp_SY_wi}	Stator Yoke	Winding	t _{comp_wi_SY}	Winding	Stator Yoke
t _{comp_wi_EW}	Winding	End winding	t _{comp_EWwi}	End winding	Winding

Due to the tooth and slot effect, some compensation elements are slightly different from the formula (26). Compensation between rotor can and PMs is written as $\begin{eqnarray}\displaystyle t_{comp\_IC\_PM}=\frac{P_{LOSS\_IC}}{4}\cdot C_{CR\_PM\leftrightarrow IC}R_{th\_IC\_2} & & \displaystyle\end{eqnarray}$ (27) where C _{CR_PM↔IC} is the contact coefficient. Likewise, t _{comp_SY_ST}, t _{comp_OC_ST}, t _{comp_RY_PM} can be written as the formula (27). Because the frame is not a heat source, t _{comp_ fr_SY} is equal to null. The compensation of windings demonstrates in section E in detail.

4.5. Model of a coil

As shown in Fig. 9, the pear-shaped slot and windings are equivalent to relevant rectangle, meanwhile the insulation of the wire is equivalent to a rectangular ring, the equivalent area is determined by the slot filling factor. The insulation of the windings should be taken into account when considering the thermal conductivity of the windings. The equivalent slot width and height are calculated as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle w_{wi}=(b_{1}+b_{2})/2\end{eqnarray}$ (28) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle h_{wi}=h_{1}+h_{2}.\end{eqnarray}$ (29)

The model of winding and thermal resistance is shown in Fig. 10. The heat transfer of the stator winding is divided into X, Y and Z axis. The thermal resistance between the stator winding and the stator yoke R _{th_wi_SY} is related to Y axis. The thermal resistance between the stator winding and stator teeth R _{th_wi_ST} is related to X axis. The thermal resistance between the stator winding and end winding R _{th_wi_air} is related to Z axis. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_wi\_SY}=R_{th\_ct\_wi\_SY}+R_{th(Y)\_wi}+C_{CR\_wi\leftrightarrow SY}R_{th\_SY\_2}\end{eqnarray}$ (30) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_wi\_ST}=R_{th\_ct\_wi\_ST}+R_{th(X)\_wi}+C_{CR\_wi\leftrightarrow ST}R_{th\_ST\_1}\end{eqnarray}$ (31) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_wi\_air}=\frac{1}{h_{cv\_wi\_air}\cdot A_{(X)\_wi\_air}}+R_{th(X)\_wi}\end{eqnarray}$ (32) where R _{th_wi_air} is convection resistance, A _{(X)_wi_air} is the convection area between winding and the slot air in the XZ plane. R _{th_wi_ST} and R _{th_wi_SY} are contact thermal resistance, R _{th_ct} = l∕(k⋅A), it is related to the contact coefficient and area, R _{th (Y)_wi} is the conduction thermal resistance. R _{th_ct_wi_SY} and R _{th_ct_wi_ST} can be written as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_ct\_wi\_SY}=\frac{1}{N_{s}}\cdot \frac{h_{wi}}{h_{ct\_wi\_SY}\cdot A_{(Y)wi\_SY}}\end{eqnarray}$ (33) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle R_{th\_ct\_wi\_ST}=\frac{1}{2N_{s}}\cdot \frac{w_{wi}}{h_{ct\_wi\_ST}\cdot A_{(X)wi\_ST}}\end{eqnarray}$ (34) where N _s is the number of slot, h _{ct_wi_ST} is the contact coefficient, A _{wi_ST∖SY} is the contact area.

Fig. 9.

Geometry of a coil and heat flow in a stator slot.

Fig. 10.

Model of winding and thermal resistance of each parts.

The sketch of external connections section is shown in Fig. 11. Due to the different cooling condition, R _{th_wi_EW} works as the connection of end windings and stator windings, which can be written as $\begin{eqnarray}\displaystyle \hspace{-15.60004pt}R_{th\_wi\_EW}=\frac{1}{2N_{s}}\cdot \frac{1}{2}(R_{th(Z)\_wi}+R_{th\_EW})=\left(\frac{L/2}{h_{c_{wi}}w_{wi}h_{wi}}+\frac{L_{EW}/2}{h_{c_{wi}}w_{wi}h_{wi}}\right)=\frac{L+L_{EW}}{8N_{S}\cdot h_{c_{wi}}w_{wi}h_{wi}} & & \displaystyle\end{eqnarray}$ (35) where 2N _s means the number of contacts between the stator winding and end winding in a slot.

Fig. 11.

Sketch of the external connections section.

Due to cooling environment, the heat dissipated by convection is less, the most heat is dissipated by stator teeth, yoke and end windings. Consequently, P _{LOSS_wy}, P _{LOSS_wt}, P _{LOSS_we} are respectively as heat flow from winding to stator yoke, stator teeth and end winding. Pointing out that P _{LOSS_wy} + P _{LOSS_wt}+P _{LOSS_we} = P _{LOSS_wi}. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle P_{LOSS\_wy}=a\cdot (P_{LOSS\_wi}-Q-P_{LOSS\_we})\end{eqnarray}$ (36) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle P_{LOSS\_wt}=(1-a)\cdot (P_{LOSS_{wi}}-Q-P_{LOSS\_we})\end{eqnarray}$ (37) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle a=\frac{0.5{\tau}^{2}}{{\tau}\cdot h_{wi}}=\frac{{\tau}}{2h_{wi}}\end{eqnarray}$ (38) where a refers to the proportion of heat flows into the yoke. Q is the amount of heat removed by slot air.

Compensation between stator winding and stator teeth t _{comp_wi_ST}, stator winding and stator yoke t _{comp_wi_SY}, stator winding and slot air t _{comp_wi_air}, stator winding and end winding t _{comp_wi_EW} can be calculated as $\begin{eqnarray}\displaystyle t_{comp\_wi\_ST}=\frac{P_{LOSS\_wt}}{4}\cdot \frac{1}{2}R_{th\_wi\_ST}. & & \displaystyle\end{eqnarray}$ (39)

As the heat flow of stator teeth only has radial direction, the heat of teeth does not flow into windings, i.e. t _{comp_ST_wi} = 0.

4.6. The machine end part

Figure 12 shows the model of the machine end part. Due to analytical complexity of heat dissipation, the end of motor is a complex system. Assumed heat flow from rotor end face and from end windings is seen connected with stator frame, to simplify the model end part. Consequently, a wye end topology is proposed in Fig. 12a, Fig. 12b shows the triangle model that is used to simplify the wye connect.

Fig. 12.

The model of machine end part.

5. Application and discussion

The heat transfer coefficient of each part is shown in Table 6, which is constant with load. The windings material is copper, which are simplified as a rectangle. Due to the insulation of coil, the heat coefficient of windings becomes one tenth of copper heat coefficient.

Table 6
Heat transfer coefficient of each component

Component Value Component Value

Frame 45 Stator Yoke 54

Stator teeth 54 Copper 400

Winding 40 Can 16.3

PM 8.95 Rotor yoke 54

Air 0.03 Moving liquid 0.5

Component	Value	Component	Value
Frame	45	Stator Yoke	54
Stator teeth	54	Copper	400
Winding	40	Can	16.3
PM	8.95	Rotor yoke	54
Air	0.03	Moving liquid	0.5

The thermal resistance values are shown in Table 7. R _{th_wi_SY} is high, due to the narrow contact area between equivalent windings and stator teeth. R _{th_OC_air} and R _{th_wi_air} are the highest, due to the poor cooling of the slot air. R _{th_RY_sh} is high, which indicates that heat rarely dissipates through the shaft.

Table 7

Thermal resistance values

Symbol	Value	Symbol	Value
R _{th_ fr_SY}	0.0033	R _{th_OC_IC}	0.1426
R _{th_SY_ST}	0.0219	R _{th_wi_SY}	2.4261
R _{th_ST_OC}	0.0208	R _{th_wi_ST}	0.0062
R _{th_IC_PM}	0.0098	R _{th_RY_sh}	2.2321
R _{th_PM_RY}	0.0136	R _{th_ fr_amb}	0.0017
R _{th_wi_EW}	0.0023	R _{th_OC_air}	4.1332
R _{th_wi_air}	6.5192

The compensation value is demonstrated in Table 8. Due that the frame has no heat source and the stator teeth heat flow is only radial, t _{comp_ fr_SY} and t _{comp_ST_wi} are null. The value of t _{comp_wi_ST} is high, due to the greater thermal resistance between of the stator winding and yoke. Obviously, compensation from A to B is not equal to that from B to A.

Table 8

Compensation values

Symbol	Value	Symbol	Value
t _{comp_ fr_SY}	0	t _{comp_SY_ fr}	0.0433
t _{comp_SY_ST}	0.02	t _{comp_ST_SY}	0.3911
t _{comp_ST_OC}	0.3911	t _{comp_OC_ST}	0.2126
t _{comp_OC_IC}	0.3483	t _{comp_IC_OC}	0.0001
t _{comp_IC_PM}	0.00009	t _{comp_PM_IC}	0.0077
t _{comp_PM_RY}	0.0080	t _{comp_RY_PM}	0.00047
t _{comp_wi_SY}	10.8980	t _{comp_SY_wi}	0.045
t _{comp_wi_ST}	0.3090	t _{comp_ST_wi}	0
t _{comp_wi_EW}	0.1243	t _{comp_EW_wi}	1.3808

The novel lumped-parameter thermal network model is shown in Fig. 13. The compensation element in the diagram is the voltage source, which is determined by the compensation formula. The heat source is the loss, expressed as a current source. Each node represents the temperature of each part. The values of loss come from Table 6, thermal resistance values from Table 7, while compensation from Table 8.

Fig. 13.

The improved network model with compensation (3d).

In this section, 3D FE is used to verify the novel lumped-parameter thermal network model, and make up for shortcoming that the thermal network cannot show the temperature distribution of each part. In FE, the loss is the heat source of each part, including iron loss, copper loss, can loss, eddy current loss of PMs.

The boundary conditions that applied in the FE are consistent with those in the thermal network, frame cooling h _{cv_ fr_amb} = 12k (Wm⁻² K⁻¹), nature slot convection h _{cv_wi_air} = h _{cv_oc_air} = 15.5 (Wm⁻² K⁻¹), h _{cv_PM_air} = 0.5 (Wm⁻² K⁻¹), and static coolant in airgap k _{eff_Liq} = 0.5 (Wm⁻² K⁻¹). In FE, the simplified model of the can motor is used, and the end is not considered. Therefore, the copper loss in the linear segment should be pre-calculated when the temperature field is calculated.

Figure 14 shows the temperature distribution of each part. As to stator yoke and teeth, Fig. 14a demonstrates the temperature distribution, temperature gradient presents decrease from inside to outside. The temperature of stator teeth is higher than that of stator yoke, depended on the cooling environment. As to stator can, Fig. 14b shows the temperature distribution with alternation, the intensified temperature areas occur in connection between can and slot air, consequently the weakened temperature areas occur in connection between can and teeth. Likewise, Fig. 14c shows the temperature distribution of stator winding, with gradient distribution. As to rotor can and PMs, Fig. 14d–e demonstrates the temperature distribution, with consistent distribution, the intensified temperature areas occur in the rotor slot. As to rotor yoke, Fig. 14f shows the temperature distribution, the higher temperature areas occur in connection between yoke and PMs and the lower temperature areas occur in end surface, due to the heat dissipation environment.

Fig. 14.

The temperature distribution of each part, (a) stator yoke and teeth, (b) stator can, (c) stator winding, (d) rotor can, (e) PM, (f) rotor yoke.

The distribution of heat flow is shown in Fig. 15. Figure 15a demonstrates the overall heat flow distribution, the characteristics are as follows: (1) As to overview, the direction of heat flow heat flow is from shaft to frame, due to heat dissipation environment; (2) For the heat flow, the intensified heat flow area occurs in stator can, due to the considerably higher stator can loss. Figure 15b shows the heat flow distribution of windings in detail, with the established coordinate axis that is consistent with that established in part E, the characteristics are as follows: (1) The intensified area of heat flow occurs between the stator yoke and winding; (2) Heat flow between winding and teeth is less. The FE winding model analysis validates the correction of the previous winding model.

Fig. 15.

Distribution of heat flow, (a) the overall distribution of heat flow, (b) the heat flow of winding in detail.

Temperature value of each component is calculated respectively by the conventional and improved network under different conditions in Tables 9–11. FE is used as reference. For the value is average based on all discretized elements. The accuracy of the improved network solution is better than that of the traditional one. For a higher power application, this model is more accurate. This is due to the inner heat flow alters more severe, and the function of compensation is more prominent.

Table 9

Temperature value of each component under natural cooling

	Methods
T (°C)	Conventional network	Improved network	FE (3D)
T _fr	29.43	29.43	30.13
T _SY	43.70	43.66	43.68
T _ST	112	115.5	115.63
T _OC	188.8	188.5	188.57
T _wi	114.2	113.4	113.42
T _IC	171.82	172.48	172.57
T _PM	170.61	170.6	170.58
T _RY	169.15	168.9	168.5
T _EW	114.2	112.2

Table 10

Temperature value of each component under the forced air cooling

	Methods
T (°C)	Conventional network	Improved network	FE (3D)
T _fr	28.23	28.23	29.43
T _SY	40.70	40.66	40.68
T _ST	93.39	92.99	92.69
T _OC	161	160.8	159.92
T _wi	94.1	93.99	93.76
T _IC	146.6	146.7	146.68
T _PM	145.7	145.6	145.63
T _RY	144.1	144.2	144.23
T _EW	94.1	92.19

Table 11

Temperature value of each component under the liquid water cooling

	Methods
T (°C)	Conventional network	Improved network	FE (3D)
T _fr	29.38	29.38	30.27
T _SY	42.86	42.86	42.98
T _ST	113.4	112.9	112.83
T _OC	111.35	111.2	111.24
T _wi	111.5	114.7	113.49
T _IC	93.25	93.1	93.15
T _PM	92.7	92.54	92.59
T _RY	91.89	91.73	91.68
T _EW	111.5	113.5

6. Conclusions

In this paper, a novel lumped parameter thermal network model with compensation element is proposed and stressed, which can be fast and accurate calculated temperature of a canned motor. A Canned permanent magnet motor, stator can and rotor can are fixed into the airgap that generates can losses. Due to higher can loss, excessive temperature rise occurs, it is worthwhile to calculate temperature of these motors. Compared traditional and novel thermal network model, FE is used as reference, the accuracy of the novel thermal network is higher. As a supplement of the thermal network model, the FE shows the temperature distribution of each part of the motor.

The novel thermal network can be applied to other devices, and for higher power devices, the solution accuracy is higher. For higher power motors, the heat flow changes more severe, and the compensation element can be efficient to amend the deviation caused by heat flow. The novel thermal model is also very flexible. For transient thermal analysis, the proposed model is also suitable, as long as heat capacitors are added to model.

Footnotes

Acknowledgements

This work is supported by the National Natural Science Foundation of Jiangsu Province under grant BK20190634, and China Postdoctoral Research Foundation under grant 2018M632417.

References

Robinson

R.C.

and Howe

, The calculation of can losses in canned motors, Trans. The American Institute of Electrical Engineers 76(4) (1957), 312–315, doi:10.1109/EE+1957.6643104.

Ergene

L.T.

, One-slot ac steady-state model of a canned solid rotor induction motor, IEEE Trans. Magn. 40(4) (2004), 1892–1896, doi:10.1109/TMAG.2004.831002.

Fan

and Wang

, A combined 2-D analytical and lumped-parameter thermal model for high power density permanent magnet machines with concentrated windings, in: 2018 IEEE Energy Convers., Portland, USA, 2018, pp. 6514–6520. doi:10.1109/ECCE.2018.8558201.

Huai

Melnik

R.V.N.

and Thogersen

P.B.

, Computational analysis of temperature rise phenomena in electric induction motors, J. Appl. Thermal Eng. 23(7) (2003), 779–795, doi:10.1016/s1359-4311(03)00013-9.

Arbab

Wang

Lin

Hearron

and Fahimi

, Thermal modeling and analysis of a double-stator switched reluctance motor, IEEE Trans. Energy Convers. 30(3) (2015), 1209–1217, doi:10.1109/TEC.2015.2424400.

Zhang

Ruan

Huang

Yang

Zhu

and Yang

, Calculation of temperature rise in air-cooled induction motors through 3-D coupled electromagnetic fluid-dynamical and thermal finite-element analysis, IEEE Trans. Magn. 48(2) (2012), 1047–1050, doi:10.1109/TMAG.2011.2174433.

Kuiyuan

Guan

and Jian

, Study on improving the allowed penetration level of distributed generations by utilizing the distribution network reconfiguration under considering network loss, in: 2018 China Int. Conf. Electr. Distr (CICED), Tianjin, 2018, pp. 2345–2349. doi:10.1109/CICED.2018.8592337.

Zhang

and Lu

, Thermal analysis of a flux-switching permanent-magnet double-rotor machine with a 3-D thermal network model, IEEE Trans. Applied Superconduct. 29(2) (2019), 1–5, Art no. 0600905, doi:10.1109/TASC.2019.2892307.

Laudensack

and Gerling

, Improved lumped parameter thermal model and sensitivity analysis for SR drives, in: The XIX Int. Conf. Electr. Mac. - ICEM 2010, Rome, 2010, pp. 1–6. doi:10.1109/ICELMACH.2010.5607746.

10.

Dajaku

and Gerling

, Novel lumped parameter thermal model for electrical systems, in: Proc. 2005 EPE Power Electronics and Applications Conf., pp. 1–10. doi:10.1109/EPE.2005.219225.

11.

Zhao

Gosselin

Fafard

and Ziegler

D.P.

, Heat transfer in upper part of electrolytic cells: Thermal circuit and sensitivity analysis, J. Appl. Thermal Eng. 14(1) (2013), 212–225, doi:10.1016/j.applthermaleng.2013.02.002.

12.

Ferrandi

Iorizzo

Mameli

Zinna

and Marengo

, Lumped parameter model of sintered heat pipe: Transient numerical analysis and validation, J. Appl. Thermal Eng. 50(1) (2013), 1280–1290, doi:10.1016/j.applthermaleng.2012.07.022.

13.

Uneyama

and Akiyama

, The proposal of can loss estimation method of canned motor, in: Int. Conf. Electrical Machines & Systems, ICEMS, Seoul, S. Korea, 2007, pp. 882–885.

14.

Boglietti

Cavagnino

Lazzari

and Pastorelli

, A simplified thermal model for variable-speed self-cooled industrial induction motor, IEEE Trans. Ind. Applicat. 39(4) (2003), 945–952, doi:10.1109/TIA.2003.814555.

15.

Wang

and Liang

, Thermal equivalent network method for calculating stator temperature of a shielding induction motor, Int. J. Therm. Sci. 147 (2020), doi:10.1016/j.ijthermalsci.2019.106149.

16.

Wang

X.S.

and Cheng

Y.H.

, Electromagnetic and thermal coupled analysis of can effect of a novel canned SRM as a hydraulic pump drive, International Journal of Applied Electromagnetics & Mechanics 54(1) (2017), 131–140, doi:10.3233/JAE-160126.

17.

Demir

and Aydin

, A novel dual three-phase permanent magnet synchronous motor with asymmetric stator winding, IEEE Trans. Magn. 52(7) (2016), 1–5, Art no. 8105005, doi:10.1109/TMAG.2016.2524027.

18.

Onsal

Demir

and Aydin

, A new nine-phase permanent magnet synchronous motor with consequent pole rotor for high-power traction applications, IEEE Trans. Magn. 53(11) (2017), 1–6, Art no. 8700606, doi:10.1109/TMAG.2017.2709788.

19.

Choi

J.H.

Kim

J.H.

Kim

D.H.

and Baek

Y.S.

, Design and parametric analysis of axial flux PM motors with minimized cogging torque, IEEE Trans. Magn. 45(6) (2009), 2855–2858, doi:10.1109/TMAG.2009.2018696.

20.

Wang

and Cheng

, Electromagnetic calculation and characteristic analysis of can effect of a canned permanent magnet motor, IEEE Trans. Magn. 52( 12) (2016), 1–6, Art no. 8108706.

21.

Peralta-Sanchez

Smith

A.C.

and Rodriguez-Rivas

J.J.

, Steady-state analysis of a canned line-start PM motor, IEEE Trans. Magn. 47(10) (2011), 4080–4083, doi:10.1109/TMAG.2011.2157906.

Modeling and thermal analysis of a canned permanent magnet machine with a novel network model

Abstract

Keywords

1. Introduction

2. The canned permanent magnet motor

4.1. Model overview

Table 6 Heat transfer coefficient of each component Component Value Component Value Frame 45 Stator Yoke 54 Stator teeth 54 Copper 400 Winding 40 Can 16.3 PM 8.95 Rotor yoke 54 Air 0.03 Moving liquid 0.5

Footnotes

Acknowledgements

References

Table 6
Heat transfer coefficient of each component

Component Value Component Value

Frame 45 Stator Yoke 54

Stator teeth 54 Copper 400

Winding 40 Can 16.3

PM 8.95 Rotor yoke 54

Air 0.03 Moving liquid 0.5