A Novel Thermal Analysis Method Based on a Multi-Physics Two-Way Coupled Method and Its Application to Submersible Permanent Magnet Synchronous Motors

Abstract

As a submersible permanent magnet synchronous motor (SPMSM) must function in downhole high temperature crude oil for long periods of time, the accurate prediction of its temperature rise is crucial to improve the stability of the motor. However, the analysis of its temperature field involves multiple physical fields, such as the electric field, the magnetic field, the fluid field and so on, and it is difficult to calculate accurately. Motor loss is usually loaded as a fixed value when calculating the temperature field, while in reality, the loss always changes with temperature. Therefore, the calculation of temperature is inaccurate using this one-way coupled method. In this paper, the relationship between loss and temperature is investigated and an electromagnetic-thermal fluid multi-physics two-way coupled analysis method suitable for SPMSM is proposed. The loss can be loaded as a variable by this new two-way coupled method, which significantly improves the temperature calculation accuracy. In order to prove the feasibility of the two-way coupled method, experiments based of a prototype of high torque and low speed SPMSM and cavity pump are conducted with the fiber Bragg grating (FBG) sensor measuring SPMSM temperature. Finally, the multi-physics two-way coupled method proposed in this paper is proven to be rational and feasible in the analysis of the SPMSM temperature rise.

1. Introduction

1.1. Background

With the growth of oil production and permanent magnet technology, submersible permanent magnet synchronous motor (SPMSM) technology has been developed rapidly. As a new technology, the progressing cavity pump (PCP) directly driven by the high torque and low speed SPMSM, which can be better applied to heavy oil wells, horizontal wells, and high-sand content wells, is gradually applied to oil field production [1,2]. Compared with the traditional three-phase asynchronous submersible motor, the SPMSM has a distinct advantage in terms of efficiency and power factor [3,4]; however, it has not been widely used. On one hand, it produces a lot of heat per unit volume because of the high power density, and on the other hand, this heat dissipates with difficulty due to the high temperature of downhole. Moreover, the performance of the permanent magnet is greatly affected by heat, as they are severely demagnetized at high downhole temperatures. The power factor and efficiency after demagnetization may be much lower than that of ordinary asynchronous motor, and overcurrent damage of the motor is easily caused by demagnetization as well. Therefore, it is necessary to carry out research on SPMSM temperature rise.

1.2. Literature Review

Considering the working conditions and construction of SPMSM, multi-physics research is usually conducted regarding temperature rise analysis. Today, there is much literature about PMSM temperature rise, although the one-way coupled method of temperature field and electromagnetic field is most commonly studied. In this method, the loss is calculated by the electromagnetic field and is used as the fixed thermal load in temperature field calculation [5,6,7]. However, the loss is usually a variable in practice, because the loss is largely decided by wire resistance, and the resistance varies with the temperature [5]. In other words, the electromagnetic field, temperature field and fluid field of the motor system are closely coupled. So, in order to calculate the temperature rise of SPMSM accurately, the two-way coupled method of multi-physics need to be studied [6,7]. K. Preis carried out a coupling study of the electromagnetic field and the temperature field by using the calculated value of the electromagnetic field as the heat source [8,9]. D. Joo and J. Cho et al. took the PMSM for vehicles as their research object, set electromagnetic loss density as the heat source of temperature field and obtained the temperature distribution using the finite element method [10]. Jiang took the surface-mounted high-speed PMSM as the object and carried out the electromagnetic loss calculation and the electromagnetic–temperature field coupling analysis by employing iterative computing method [11]. Moreover, there are few relevant studies about the thermal analysis method of the low-speed motor, as researchers usually focus on studying high-speed motors. A. Tikadar and N. Kumar et al. developed a two-way coupling algorithm for the high speed motors of electric vehicles, which involves the electromagnetic field and the temperature field, regardless of fluid field state [12].

At present, thermocoupling based on the phenomenon of thermoelectric conversion is generally adopted to measure the temperature of downhole SPMSM by measuring the electromotive force [13,14]. Employing the FBG sensor for measuring temperature is an emerging temperature measurement technology developed in the 1970s [15]. The change of temperature causes the Bragg wavelength of the fiber grating to change, and the FBG sensor is able to obtain the measured temperature by demodulating the wavelength change value [16,17]. There are many advantages of the FBG sensor compared with the traditional sensors. The optical wave transmitted in the optical fiber is not interfered by other electromagnetic waves; it can be easily received by various optical detectors and can conveniently match with modern electronic devices and computers; as optical fiber is uncharged, small in size, light in weight and easy to bend, the loss during the transmission process is very low. In summary, it is especially suitable for harsh environments, such as those that are flammable, explosive, severely restricted and contain strong electromagnetic interference [18,19]. The rich results of the application of FBG temperature sensing technology have been achieved by certain developed countries and many FBG sensor systems have been put into practice to replace traditional temperature sensors [20,21,22,23]. However, there are almost no cases of FBG sensors being applied to measure the temperature of downhole SPMSM [24]. In this paper, a metal probe type FBG sensor is adopted to measure the SPMSM temperature.

1.3. Contributions of This Study

In this paper, an electromagnetic-thermal fluid multi-physics two-way coupled temperature analysis method for SPMSM is investigated, based on the traditional one-way coupled method. In order to verify the feasibility of this method, temperature calculations by different methods are conducted, respectively. Firstly, a one-way coupled analysis calculation was carried out and then multi-physics two-way coupled analysis calculation was performed. Then, a SPMSM test device and cavity pump prototype was built and temperature measuring experiments were conducted by using a FBG sensor. The results of the multi-physics two-way coupled method are closer to the experiment results than those of one-way coupled method. Therefore, the two-way coupled method proposed in this paper has a higher accuracy than the conventional one-way coupled method and can replace the one-way coupled method in the analysis of SPMSM temperature rise. Furthermore, it can provide a more reliable reference for SPMSM design.

2. Heat Transfer Theory

2.1. Thermal Conduction Differential and Boundary Conditions

In this study, a SPMSM that works in downhole high temperature crude oil is taken as the object. The heat, which results in the temperature rise of the SPMSM, mainly comes from winding, core, magnet, bearing and so on. There are two major forms of heat transfer: one is heat exchange with the external crude oil, which happens at the motor end with the help of the lubrication oil circulation inside the motor, and the other is the heat transfer to the housing through the stator and exchanges with the external crude oil. So the electromagnetic field, temperature field and fluid field interact with each other and the temperature rise is the result of the coupling calculation of the three fields.

The heat conduction differential equation established with the Cartesian coordinate system is introduced to develop the calculation process of the temperature field [25].

$$\left\{\begin{array}{l}{{\displaystyle \lambda }}_x\frac{{{\displaystyle \partial }}^2{{\displaystyle T}}_{}}{{{\displaystyle \partial x}}^2}+{{\displaystyle \lambda }}_y\frac{{{\displaystyle \partial }}^2{{\displaystyle T}}_{}}{{{\displaystyle \partial y}}^2}+{{\displaystyle q}}_{}={{\displaystyle c\rho \frac{\partial T}{\partial \tau }}}_{}\\ {{\displaystyle \left.{{\displaystyle -\lambda \frac{\partial T}{\partial n}}}_{}\right|}}_{{}^{{}_{S_1}}}={{\displaystyle 0}}_{}\\ {{\displaystyle \left.{{\displaystyle -\lambda \frac{\partial T}{\partial n}}}_{}\right|}}_{S_2}={{\displaystyle \alpha \left({{\displaystyle T}}_1-{{\displaystyle T}}_e\right)}}_{}\end{array}\right.$$

(1)

In Equation (1), λ_x is the heat conductivity of each part of the motor in the x-axis direction; λ_y is the heat conductivity of each part of the motor in the y-axis direction; T is the motor internal temperature; q is the heat source (W/mm³); ρ is the density of each part (kg/mm³); c is the specific heat capacity; and λ is the normal heat conductivity of the boundaries S₁ and S₂. S₁ is the second boundary condition of the motor; S₂ is the third boundary condition of motor; α is the heat transfer coefficient of S₂; T₁ is the temperature of S₁; and T_e is the temperature of the parts around S₂.

2.2. Governing Principle of Fluid Flow

The law of conservation of mass, the law of conservation of momentum and the law of conservation of energy should be followed in order to analyze the fluid flow and heat transfer effects of an SPMSM. The fluid both inside and outside the SPMSM is incompressible during the calculation. The laws of conservation of physics and governing equations are given as follows.

The continuity equation of incompressible fluid in SPMSM can be expressed as Equation (2) [26].

$$\frac{\partial u}{{\partial }_x}+\frac{\partial v}{{\partial }_y}+\frac{\partial w}{{\partial }_z}=0$$

(2)

In Equation (2), $u$, $v$ and $w$ are the components of velocity vector $\overrightarrow{u}$ in x, y and z directions, respectively.

The Navier–Stokes equation for SPMSM incompressible viscous liquid is given in Equation (3) [26].

$$p\frac{\partial (\rho \mu )}{\partial t}=-\nabla p+\mu \Delta v+pF$$

(3)

In Equation (3), ρ denotes density; t denotes time; p denotes the pressure on microelements; F denotes the force on microelements; μ denotes dynamic viscosity coefficient; and v denotes kinematic viscosity coefficient.

The energy conservation equation in SPMSM is expressed as Equation (4) [26].

$$\frac{\partial (pt)}{\partial t}+\mathrm{div}(\rho vT)=\mathrm{div}(\frac{\lambda }{c}\mathrm{grad}T)+S_T$$

(4)

In Equation (4), T denotes temperature; S_T denotes the viscous dissipation term; c denotes specific heat capacity; and λ denotes thermal conductivity.

An additional turbulent transport equation is required, while the fluid in SPMSM is in a turbulent state. On the basis of fluid mechanics, the standard $k-\epsilon$ model can be adopted to explain the fluid, which is incompressible and in a stable state. The general control equation can be expressed as Equation (5) [26].

$$\frac{\partial (\rho \phi )}{\partial t}+\mathrm{div}(\rho \nu \phi )=\mathrm{div}(\Gamma \mathrm{grad}\phi )+S$$

(5)

In Equation (5), ν and φ denote general variables; Γ denotes diffusion coefficient; S denotes source term; ρ and enotes fluid.

2.3. Sensing Principle of FBG

The Bragg wavelength of an FBG is given by Equation (6) [27].

$${\lambda }_B=2n_{eff}\Lambda$$

(6)

In Equation (6), ${\lambda }_B$ is the Bragg wavelength, $n_{eff}$ is the effective refractive index and $\Lambda$ is the Bragg grating period of FBG. Considering the influence of thermal expansion and elongation of FBG material on $n_{eff}$ and $\Lambda$, Equation (6) can be written as Equation (7) [28]:

$$\Delta {\lambda }_B={\lambda }_0\left[\left(1-P_{\epsilon }\right)\epsilon +(\alpha +\varsigma )\Delta T\right]$$

(7)

In Equation (7), ${\lambda }_0$ is the initial value of the Bragg wavelength, $P_{\epsilon }$ is the coefficient of the effective photo-elastic, $\epsilon$ is the strain of the gratings, $\alpha$ is the coefficient of the fiber material thermal expansion, $\varsigma$ is the coefficient of the thermo-optic and $\Delta T$ is the change in temperature.

If there is no stress on gratings, the strain can be ignored [29] and Equation (7) can be replaced by Equation (8).

$${\lambda }_B={\lambda }_0\left[1+\left(\alpha +\varsigma \right)\Delta T\right]$$

(8)

3. Electromagnetic-Thermal Fluid Multi-Physics Two-Way Coupled Analysis Method

By studying the relationship of temperature field, fluid field and temperature field, the method of electromagnetic-thermal fluid multi-physics two-way coupled analysis method is put forward in this paper.

3.1. Relationship between Magnetic Field and Temperature Field

The loss as heat source and the temperature field influence each other. In general, the temperature field calculation results are affected by loss: the larger the loss is, the higher the motor temperature will be. On the other hand, a change in temperature changes the material characteristics, which in turn changes the magnetic field and ultimately leads to a change in loss.

Considering that the motor studied in this paper is low in speed, the winding skin effect and magnet eddy current loss can be ignored. At the same time, as the core loss accounts for a small proportion of total loss, the effect of alternating magnetic field and rotating magnetic field on it is not considered. Therefore, the winding loss, which has the greatest impact on motor temperature, is deeply analyzed in this study. As we all know, the winding loss directly affects the motor temperature. Conversely, the temperature affects the winding loss by impacting winding wire resistance. So the correlation between the temperature and the winding loss can be expressed as a two-way coupling between the temperature field and magnetic field. The process is shown in Figure 1.

3.2. Relationship between Fluid Field and Temperature Field

When the SPMSM works, it is usually filled with lubricating oil inside and is immersed in the downhole flowing crude oil. As shown in Figure 2, lubricating oil is mainly found in the gap and the shaft internal channel, and the crude oil is in the flow channel between housing and wellbore. The flow rate affects the motor temperature, while temperature plays a part in changing the viscosity of the fluid. As the viscosity only affects the mechanical loss, which accounts for a small proportion of whole loss, the effect of temperature on fluid is not considered in this paper.

3.3. Multi-Physics Two-Way Coupled Calculation Process

The winding loss at different temperatures is calculated by Maxwell, and the function fitting is conducted using the least square method. Based on Fluent, the winding loss function is compiled into a UDF by C++, which can be loaded as heat source in Fluent. With the help of the UDF, the winding loss can be loaded as a variable. The lubricating oil inside and crude oil outside are analyzed to determine the heat transfer coefficient and flow rate. With all the conditions, including UDF, loss, velocity, etc., loaded, iteration is performed to finish the electromagnetic-thermal fluid multi-physics two-way coupled calculation and obtain the temperature distribution of the SPMSM. The process is shown in Figure 3.

4. Thermal Modelling and Calculation

4.1. SPMSM Configuration

The prototype is a high torque and low speed SPMSM with a rated power of 8.5 kW, rated speed of 180 r/min and maximum output torque of 450 Nm.

Table 1. Parameters of the SPMSM.

Parameters	Value
Rated power (kW)	8.5
Rated speed (r/min)	180
Frequency (Hz)	15
Rated voltage(V)	380
Pole/slot	10/12
Stator inner diameter (mm)	62
Stator outer diameter (mm)	102
Gap length (mm)	0.8

shows the specific parameters.

4.2. Loss Analysis and Calculation

The ambient temperature of SPMSM can be up to 100 °C. Winding insulation damage and demagnetization caused by overheating are the main causes of SPMSM failures from practical experience. The accurate calculation of various losses is of great significance to predicting SPMSM temperature rise.

4.2.1. Core Loss

Although the core loss accounts for a low proportion of total loss, as one of the heat sources of the motor, the core loss cannot be ignored in the temperature field analysis. Because the frequency of SPMSM is low, the effect of frequency on core loss can be ignored. Therefore, the traditional Bertotti formula, which divides the loss into hysteresis loss and eddy current loss, is used to calculate the core loss in this paper, and the calculation formula is as follows:

$${{\displaystyle P}}_{{}_{Fe}}={{\displaystyle P}}_{{}_e}{{\displaystyle +P}}_{{}_h}{{\displaystyle +P}}_{{}_{ex}}={{\displaystyle C}}_{{}_e}{f}^2{B}_m^2+{{\displaystyle C}}_{{}_h}f{B}_m^n{{\displaystyle +C}}_{{}_{ex}}{f}^{1.5}{B}_m^{1.5}$$

(9)

In Formula (9), P_e denotes eddy current loss; P_h denotes hysteresis loss; P_ex denotes additional loss; f denotes an alternate frequency of magnetic field in the motor; C_e denotes an eddy current loss coefficient; C_h denotes a hysteresis loss coefficient; C_ex denotes an additional loss coefficient; and B_m denotes magnetic density amplitude.

For the motor studied in this paper, f is 15 Hz and B_m can be approximately taken as 1.5 T. The values of C_e, C_h and C_ex can be referred to [30].

4.2.2. Winding Loss

Winding loss, known as winding copper loss, is the loss generated by the resistance of winding coils through which the current flows. In accordance with Joule’s Law, resistance and current together determine winding loss. In terms of the structure of SPMSM, winding loss only occurs in the stator and not in the rotor. Obviously, it is winding loss, which is the largest among all losses, that has the greatest impact on motor temperature [31]. In terms of the SPMSM especially, which has low frequency and small copper wire diameter, the skin effect and proximity circulation effect can be ignored [32,33].

On the basis of the Joule’s law, the winding loss calculation formula can be expressed as below:

$$P_{Cu}=n{I}^{2}R$$

(10)

In Formula (10), I denotes effective current value, n denotes the number of phases and R denotes winding resistance.

$$R=\rho N\frac{l_{cp}}{S}$$

(11)

In Formula (11), ρ denotes resistivity, N denotes the number of conductors, l_cp denotes turn length and S denotes cross-sectional area of conductor.

I can be obtained from rated power and voltage; n is 3 and N is 48 for this motor.

Resistivity is a physical quantity that is used to denote the resistance characteristics of a conductor. It is not affected by factors such as the length and cross sectional area of the conductor, but the material properties and temperature of the conductor itself have a greater influence on it. Experiments have proved that the resistivity increases with temperature. Consequently, the winding loss increases with temperature.

Winding loss at different temperature was calculated by Maxwell, and then the correlation of temperature and winding loss was studied.

Figure 4 demonstrates that the winding loss increases with the temperature rise, and the relationship between them is approximately linear, namely 1882.28 W at 80 °C and 1979.24 W at 100 °C. The correlation between winding loss and temperature is fitted by the least square method as shown below.

$$P_{cu}=4.99125T+1480.369$$

(12)

In Formula (12), P_cu denotes winding loss and T denotes temperature.

4.2.3. Mechanical Loss

Mechanical loss mainly involves friction loss. In line with previous experience, in this paper, 1.2% of the rated power was taken as mechanical loss for subsequent temperature calculation [34].

4.3. One- and Two-Way Coupled Calculation

The 3D finite element analysis model, including both inner fluid and outer fluid for a single motor, was built by NX, and the hexahedral mesh was generated by ICEM, as shown in Figure 5.

Table 2. Thermal conductivity of key parts.

Part	Material	Conductivity (W/m·°C)
Winding	Copper	397
Housing	45#	46.47
Stator core	DW470	35
Stator insulation	Polyimide film	35
Oil	45# transformer oil	0.12
Magnet	N35EH	9
Shaft	40Cr	30.98

indicates the thermal conductivity of key parts.

Table 3. Losses value and loading positions for one-way coupled calculation.

Loss Type	Value (W)	Position of Loading
Core loss	119.6	Stator
Winding loss	1854.7	Winding
Mechanical loss	127.5	Oil

demonstrates the losses value and loading positions for one-way coupled calculation.

Based on the one-way coupled calculation, two-way coupled calculation was performed. The thermal conductivity, flow rate and ambient temperature are the same as that of the one-way coupled calculation; however, the loss and heat generation rate are different.

Table 4. Losses value and loading positions for two-way coupled calculation.

Loss Type	Value (W)	Position of Loading
Core loss	119.6	Stator
Winding loss	$4.99125T+1480.369$	Winding
Mechanical loss	127.5	Oil

demonstrates the loss of two-way coupled calculation in which the winding loss is as shown in Formula (12).

The macro which defines energy properties was called DEFINE_SOURCE. The UDF of the winding loss heat generation was compiled by C++ and was loaded as one of the boundary conditions by COMPILED in Fluent. With the help of the UDF, the iterative calculation was carried out and the two-way coupled calculation was achieved. The temperature distribution was obtained after calculation convergence.

5. Results and Discussion

5.1. Results Comparison between One and Two-Way Coupled Method

The heat generation rate, which was calculated by loss value, was loaded into the corresponding parts. The temperature was set to 60 °C [35], the crude oil flow rate was set to 0.01 m/s [36] and the thermal conductivity was set according to Table 2. Then, both one-way and two-way coupled iterative calculations were performed until convergence, and SPMSM temperature distributions were obtained, as shown in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10.

Figure 6a and Figure 7a demonstrate that the maximum temperature is 80 °C through the one-way coupled method, but it is 105 °C when using the two-way coupled method, as shown in Figure 6b and Figure 7b. For the both coupled methods, the maximum temperature occurs in winding part; the second highest temperature is found in the stator core, rotor core and then the housing; and the external crude oil is the part with the lowest temperature (see Figure 6 and Figure 7). This agrees with the results of other studies [12,37].Thus, it can be summarized that winding loss plays the largest role in motor temperature rise and the heat generated in winding transmits from winding to the fluid outside in a radial direction.

Figure 8 shows the temperature distribution of housing using the both methods. In Figure 8a and

Table 5. Temperature of different parts obtained by different methods.

Part	One-Way Coupled		Two-Way Coupled
	Lowest (°C)	Maximum (°C)	Lowest (°C)	Maximum (°C)
Global	60	80	60	105
Housing	65.8	67.1	73.5	76.2
Winding	78	80.4	103.2	106
Stator core	65.9	68.1	73.8	78.5

, the maximum temperature of the housing is 67.1 °C and the lowest is 65.8 °C; thus, the average temperature is about 66.5 °C. In Figure 8b and Table 5, the maximum temperature is 76.2 °C and the lowest is 73.5 °C; thus, the average temperature is 74.9 °C and the difference between the maximum temperature and lowest temperature is 2.7 °C. The inner surface of the housing has a higher temperature than that of the outer surface in the radial direction, and the inlet end has a higher temperature than that of outlet end in the axial direction. The reason for this is that the axial flow of external crude oil helps to remove the heat from the interior of motor. These result are similar to those of other studies [38].

Figure 9 shows the temperature distribution of winding using both methods. In Figure 9a and Table 5, the maximum temperature of the winding is 80.4 °C and the lowest is 78 °C, and the average temperature is 79.2 °C. In Figure 9b and Table 5, the maximum temperature is 106 °C and the lowest is 103.2 °C, and the average temperature is 104.2 °C. Figure 10 shows the temperature distribution of the stator core using both methods. The maximum temperature is 68.1 °C and the lowest is 65.9 °C, as shown in Figure 10a, and the average temperature is 67 °C. The maximum temperature is 78.5 °C and the lowest is 73.8 °C, as shown in Figure 10b, and the average temperature is 76.15 °C.

In

Table 6. Average temperature obtained by different methods.

Method	Global (°C)	Housing (°C)	Winding (°C)	Stator Core (°C)
One-way coupled	80.0	66.5	79.2	67
Two-way coupled	105.0	74.9	104.2	76.15
Difference	+25	+8.4	+25	+9.15

, the global temperature obtained from two-way coupled method is 25 °C higher than that of the one-way coupled method. Additionally, it is 8.4 °C higher for the average housing temperature, 25 °C higher for the average winding temperature and 9.15 °C higher for the average stator core temperature.

All the simulations of the two methods are conducted under rated conditions of the SPMSM. However, the calculation results of temperature using the two-way coupled method is higher than that of the one-way coupled method, because the winding loss for two-way coupled method is variable, which is different from the constant value of the one-way coupled method, and the change of winding loss with temperature is considered by loading it as a variable for the two-way coupled method. This result is not only in accordance with the previous theoretical analysis but also agrees with other related studies [38,39].

5.2. Experimental Verification

On the basis of SPMSM and the progressing cavity pump prototype, an experiment device with an FBG sensor was established to verify the rationality of the multi-physics two-way coupled calculation method. In addition to the SPMSM and cavity pump, a downhole oil production simulation pipeline system, an optical sensing interrogator, a computer and an FBG sensor were also included in this experiment device. The detailed information of this experiment device is shown in Figure 11 and Figure 12 and

Table 7. The key data of main instruments.

Instrument	Key Data
Optical Sensing Interrogator	Model: Micron Optics si155 Sampling frequency: 5 kHz Number of channels: 4 Wavelength accuracy: 2 pm/3 pm Wavelength range: 1520 nm~1600 nm
FBG sensor	Centre wavelength: 1549.23 nm Operating temperature: −40 °C~120 °C Temperature sensitivity: ~10 pm/°C

.

As shown in Figure 13, the FBG sensor was placed into the wellbore and pasted on the surface of the motor casing in the radial direction. Considering the uneven temperature distribution of the housing surface, the sensor was attached to the middle of the single motor in the axial direction. In order to simulate the pressure and temperature environment of 1500 m underground, hydraulic oil was used to simulate the underground crude oil, the liquid pressure was adjusted through the downhole oil production simulation pipeline system and the temperature was adjusted through a heating system. The signal collected from the sensor was transmitted to the optical sensing interrogator through the signal cable.

The speed was adjusted to 180 rpm by frequency transformer and experiments were carried out in the simulated environment of 1500 m underground. The experimental results are shown in Figure 14, which demonstrates that after running for about 3000 min (50 h), the temperature of the housing tends to be stable at about 81.2 °C.

In order to compare the experiment results with that of the simulation, all the data are organized in

Table 8. Temperature of housing by different methods.

Different Methods	Average Temperature of Housing
One-way coupled	66.5 °C
Two-way coupled	74.9 °C
FBG sensor	81.2 °C

.

In Table 8, the temperature measured by the FBG sensor is the highest, followed by that of the two-way coupled method, and the temperature of the one-way coupled method is the lowest. The average temperature calculated by the two-way coupled method is 74.9 °C, which is 6.3 °C (7.8%) lower than that of the FBG sensor. Similarly, the temperature is 66.5 °C for the one-way coupled method and is 14.7 °C (18.1%) lower than that of FBG sensor. Therefore, the results of the two-way coupled method are closer to the FBG sensor than those of the one-way coupled method, and the accuracy is improved by 8.4 °C (10.3%). In addition, the reason that the temperature of the FBG sensor is higher than the two-way coupled method is that the magnet eddy current loss is ignored and the alternating and rotating magnetic fields are not considered in the core loss calculation.

In conclusion, the two-way coupled method has a higher accuracy in thermal analysis than the original one-way coupled method, and the results can provide an effective reference for SPMSM design.

6. Conclusions and Future Work

In this paper, the interaction between temperature and loss was studied and the user defined function (UDF) was used to describe this relationship. On this basis, the electromagnetic-thermal fluid multi-physics two-way coupled temperature rise analysis method suitable for SPMSM was proposed. The temperature of the SPMSM under the same working conditions were calculated using the one-way coupled method and the two-way coupled method in this paper. In addition, based on the prototype of the SPMSM and the cavity pump, an experiment device with an FBG sensor measuring the temperature was built, and experiments simulating an environment 1500 m underground were conducted. The results obtained using the two coupling simulation methods were compared with the results measured by the FBG sensor.

The results of the multi-physics two-way coupled method are closer to the experiment results than those of the one-way coupled method. In other words, the multi-physics two-way coupled method proposed in this paper has a higher accuracy in the SPMSM temperature analysis than the conventional one-way coupled method. Thus, it can be adopted for predicting SPMSM temperature and can provide reasonable reference for motor design. In this study, the research object was the SPMSM, which usually has low speed and high torque. Core loss is much smaller than winding loss; thus, the relationship of between core loss and temperature was ignored. In the future, however, despite the winding loss variable loading, the relationship between core loss and temperature should also be considered and utilized as a variable in simulation setting processes in order to improve the accuracy of the two-way coupled method.