Research on Heat Transfer of Submersible Motor Stator based on Air Gap Flow Characteristics

Shibin Zhang; Huayang Ren; Yongcun Wang; Yu Miao; Yan Shang; Yunbing Feng

doi:10.26866/jees.2025.2.r.286

J. Electromagn. Eng. Sci > Volume 25(2); 2025 > Article

Zhang, Ren, Wang, Miao, Shang, and Feng: Research on Heat Transfer of Submersible Motor Stator based on Air Gap Flow Characteristics

Regular Paper

Journal of Electromagnetic Engineering and Science 2025;25(2):144-153.

Published online: March 31, 2025

DOI: https://doi.org/10.26866/jees.2025.2.r.286

Research on Heat Transfer of Submersible Motor Stator based on Air Gap Flow Characteristics

Shibin Zhang^1,^*

, Huayang Ren¹

, Yongcun Wang²

, Yu Miao²

, Yan Shang¹

, Yunbing Feng³

¹School of Mechanical Engineering Zhengzhou, North China University of Water Resources and Electric Power, Henan, China

²Henan Longyu Energy Co., Shangqiu, China

³Zhengzhou Coal Industry (Group) Co. Ltd., Zhengzhou, China

^*Corresponding Author: Shibin Zhang (e-mail: zhangshibin@ncwu.edu.cn)

Received March 22, 2024 Revised June 5, 2024 Accepted August 4, 2024

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

To address the heat dissipation problem of submersible motors, an improved strategy based on the characteristics of air gap fluid is proposed to avoid localized overheating of the motor to obtain better heat dissipation. Considering the heat exchange form of the submersible motor and the influence of multiple heat sources on the motor stator, a numerical calculation model of the temperature field inside the water-filled submersible motor is established. The temperature distribution of the stator of the submersible motor under different air gap inlet fluid flow rates is simulated based on the finite element analysis method. The simulation results show that the stator winding insulation realizes the necessary cooling. The reasonable axial flow rate of the motor air gap inlet fluid is 2 m/s. Finally, the validity of the method is verified by comparing the calculated results with the experimental data. The results of the study provide a theoretical basis for the determination of the reasonable flow rate of the air gap fluid and the optimization of the design of submersible motor drive pump wheel.

Keywords: Air Gap, Finite Element Simulation, Fluid Flow Characteristics, Submersible Motor

I. Introduction

To cope with mine accidents, submersible motors are widely used in rescue and dewatering operations because of their high safety and reliability. However, due to the complex and harsh operating conditions of submersible motors [1], the estimation of heat source losses tends to deviate from the actual values, which complicates the determination of the appropriate flow rate of the air gap fluid and makes it difficult to define a reasonable air gap fluid velocity [2, 3].

However, most of the studies have focused on the electromagnetic design of the motor [4, 5], ignoring the thermal analysis. In fact, the temperature field and the magnetic field of the motor are interrelated, the magnetic field affects the temperature rise of the motor, and the change of the motor temperature affects the distribution of the magnetic field, which in turn affects the motor losses and leads to the increase of the internal temperature of the motor [6]. The stator of a water-filled submersible motor is in direct contact with the windings, and the high operating temperature will directly affect the insulation life of the motor windings [7]. Therefore, in order to accurately predict the temperature distribution in the motor, it is necessary to combine the internal temperature rise with the flow characteristics for accurate and reliable analysis [8, 9].

The research of scholars has focused on air-cooled motors, DC motors, permanent magnet motors, and large hydro generators [10–13], examining their internal flow fields, temperature fields, and influencing factors. Furthermore, various cooling methods regarding motors have been investigated, including natural air cooling, direct liquid cooling, and the use of heat pipes [14]. Some scholars have conducted in-depth thermal analysis of conventional motors using numerical analysis [15, 16]. In [17, 18], the authors utilizes the equivalent thermal mesh method, which is widely used in the parametric design and optimization of various motors, to collect the heat sources of the mesh, locate them at different nodes, and then establish the network topology according to the heat transfer paths within the motor. The numerical calculation method mainly adopts the finite element analysis method [19–21], which has good versatility and can accurately analyze models with complex structures like submersible motors [22].

However, there are relatively few studies on the thermal analysis of high-power water-filled submersible motors, and the studies on the cooling structure, fluid flow characteristics, temperature distribution and testing of water-filled submersible motors are still relatively limited [23, 24]. In this study, a numerical model for calculating the temperature field inside a water-filled submersible motor is developed considering the internal fluid dynamics. By examining the heat transfer paths of the motor and formulating appropriate assumptions, we constructed an equivalent heat path diagram for the water-filled submersible motor. To validate the accuracy of our approach, we built an experimental platform to perform temperature rise tests on the submersible motor. The platform considered the effects of various heat sources on the motor stator. The calculated results were then compared and correlated with data from prototype tests to assess their consistency. The results provide a theoretical basis for the determination of reasonable flow rates for air gap fluids and the optimal design of submersible motor-driven pump wheels.

II. Methods

1. Prototype

Water-filled submersible motors are commonly paired with high-head submersible pumps to constitute submersible electric pumps. Owing to the particular requirements of their operational environment, spatial constraints limit their radial dimensions, necessitating a slender structural design. Submersible motors operate within wells for extended periods, and the complex surrounding environment influences the heat transfer characteristics of the motor due to the internal air gap fluid dynamics. It is crucial for these motors to manage heat dissipation efficiently when operating under high-temperature conditions. Typically, the motor’s inner cavity is filled with a cooling lubricant or water, which serves to lubricate and cool the various components within the motor.

This study focuses on a 3,200 kW water-filled submersible motor. Its fundamental parameters are listed in Table 1, and the three-dimensional assembly drawing is presented in Fig. 1.

Drawing upon the structural and operational features of the water-filled submersible motor, the submersible motor is designed in a cooling water channel for both internal and external circulation. The internal cooling water flows through the channel created based on the driving pump wheel, while it is integrated with the external water circulation structure of the suction cover, a common component in drainage engineering. This dual internal-external water circulation cooling structure expands the cooling surface area of the motor stator. During operation, the motor’s internal heat is directly conveyed to the motor casing through the circulating cooling water, facilitating the transfer of heat outside the motor and significantly enhancing the cooling performance of the submersible motor. The cooling channel for the submersible motor’s water circulation is depicted in Fig. 2.

The external water circulation cooling structure augments the heat dissipation capacity of the submersible motor and extends the versatility of the submersible electric pump’s applications. The external water cooling structure is illustrated in Fig. 3.

The internal and external water circulation structures is characterized as follows: when the submersible motor is running, the driving pump wheel rotates at the same speed with the rotor of the submersible motor, which drives the cooling water inside the submersible motor to circulate along the designed flow channel, forming a water circulation cooling system inside the submersible motor. The cooling water enters the submersible pump through the water channel between the suction cover and the submersible motor to take away the heat generated by the submersible motor.

To gain a deeper insight into the submersible motor’s internal structure, the stator and rotor are modeled in three dimensions. To simplify subsequent meshing and computations, the model construction disregards the effects of chamfers and irregularities on the stator and rotor on the unsmooth place. The three-dimensional solid model of the 3,200 kW water-filled submersible motor’s stator and rotor is shown in Fig. 4.

2. Analysis of Heat Transfer Paths inside the Motor

Water-filled submersible motors are designed to be filled with a sufficient quantity of water to act as a cooling medium during operation, especially when they are part of high-power submersible pump systems such as deep-well submersible electric pumps. In the course of operation, both the stator windings and the rotor are submerged in the cooling water. The heat generated by copper losses in the stator windings is partially conducted through the insulation to the stator core and then to the motor casing. This heat is subsequently dissipated by the flow of water external to the motor. Moreover, another portion of the heat generated by copper losses is removed by the internal cooling water and directly transferred to the motor shell, which is likewise dissipated by the external water flow.

During operation, the heat generated by copper losses in the rotor windings, as well as the frictional losses between the rotor and the water, is initially absorbed by the motor’s internal cooling water. Subsequently, a fraction of this heat is conveyed through the stator to the motor casing, while another portion is dissipated directly by the motor’s internal cooling water interacting with the motor shell. The mechanical losses, primarily caused by bearing friction, are conducted to the motor casing via the end cover and motor shaft, and are then removed by the external flow of water.

To conduct a more detailed analysis of the internal heat transfer mechanisms in a water-filled submersible motor, it is essential to construct an equivalent thermal circuit diagram for the motor. This involves analyzing the motor using the equivalent thermal circuit method and illustrating the heat transfer pathways with a diagram.

The following reasonable assumptions are made. P_Cu1 denotes the stator winding copper losses of the motor, where P_Cu11 refers to the stator slot winding losses, which are entirely transmitted through the stator core to the chassis. P_Cu12 represents the stator end winding losses, which are completely transferred through the circulating cooling water to the chassis. P_Cu2 signifies the rotor winding losses, with P_Cu21 denoting the portion of the rotor winding copper losses that produce heat conducted via the stator core to the chassis, and P_Cu22 indicating the portion of the rotor winding copper losses where the heat is conducted to the chassis through the cooling water. It is assumed that these each account for half of P_Cu2.

P_t1 is the stator core tooth iron loss, and P_j1 is the yoke iron loss of the motor stator core; both are conducted through the motor stator to the chassis or cooling water. P_s1 represents the stator stray losses, which are transmitted to the motor casing through the motor stator. P_s2 is the rotor stray losses, with P_s21 being the part of the rotor stray losses that is conducted to the motor casing through the motor stator, and P_s22 being the part of the rotor stray losses that is conducted to the motor casing through the cooling water. It is assumed that these each account for half of P_s2.

P_fw1 corresponds to the rotor and cooling water friction losses, while P_fw2 is associated with the losses generated by the motor’s thrust bearings and guide bearings.

R_CF is the thermal resistance from the stator winding to the core, R_f1 is the thermal resistance from the stator core teeth to the casing, and R_j1 is the thermal resistance from the stator core yoke to the casing. represents the thermal resistance between the stator and rotor to the cooling water in the air gap, R_c1 is the thermal resistance from the stator winding to the motor’s cooling water, and R_c2 is the thermal resistance from the motor rotor winding end’s coolant.

R₀ denotes the thermal resistance from the coolant inside the motor to the casing, while R₀’ signifies the thermal resistance from the coolant inside the motor to the end cap. R_c is the thermal resistance of the casing, and R_c’ is the thermal resistance of the motor end cap. R_k is the thermal resistance from the motor casing to the external mine water, and R_k’ is the thermal resistance from the motor end cap to the external mine water.

The equivalent thermal circuit of the water-filled submersible motor is illustrated in Fig. 5.

As the submersible motor without forced cooling system, the heat generated during operation can only be inside and outside the casing for heat exchange, and through the well fluid flowing through the casing will be exchanged to take away the heat, so the purpose of the analysis using the thermal mesh method is to calculate the convection coefficient of heat dissipation as well as the material heat transfer coefficient is fitted to the overall thermal conductivity differential equations, and then through the calculation of the submersible motor ministries to bring the heat loss, and ultimately solved for the each node temperature.

3. Numerical Calculation Model

Differential equations for internal thermal conductivity in deep-well water-filled submersible motors:

(1)

λx∂2T∂x2+λy∂2T∂y2+λ∂2T∂z2+qv=ρc∂T∂t,

where λ_x, λ_y, λ_z are thermal conductivity along the coordinate axes X, Y, Z direction; q_v is internal heat source of the submersible motor; ρ is density of water; and c is specific heat capacity of water.

3.1 Boundary conditions of heat conduction

Numerical calculation model of heat conduction in water-filled submersible motor:

(2)

{λx∂2T∂x2+λy∂2T∂y2+λ∂2T∂z2=-qv-λ∂T∂n|S2=g(x,y,z,t)λ∂T∂n|S3=-α(T-T1).

4. Calculation of Correlation Coefficients

4.1 Heat source

In general, water-filled submersible motor operation process where the internal heat source is generated encompasses stator iron consumption, winding copper consumption and mechanical losses. Simulation of the heat load loading mode, the heat generation rate as a heat load loaded on the motor stator, the heat generation rate that is the heat flow density, can be expressed as:

(3)

Q=Wq/V,

where W_q is sum of motor stator heat losses (W); and V is volume of motor stator (m³).

4.2 Thermal conductivity

Thermal conductivity refers to a physical property of materials, which is used to reflect the strength of the thermal conductivity of materials. The coefficient of thermal conductivity of a material is directly correlated with the type of material, physical properties, temperature and other factors, and should be determined by using experimental methods. The thermal conductivity of the materials used in the motor is listed in Table 2.

The surface heat transfer coefficient in the turbulent state of the air gap fluid in the submersible motor can be expressed as:

(4)

α=0.23 Re0.8Pr(cp)0.4ɛl/λ,

where α is surface heat transfer coefficient; λ is thermal conductivity coefficient; l is equivalent diameter of the fluid in the submersible motor; and C_p is constant pressure heat capacity.

5. Experimental Platform

A temperature rise test was conducted on the submersible motor. To meet the requirements of the submersible motor testing, a deep-well submersible motor integrated test platform was designed, the structure of which is depicted in Fig. 6. A critical aspect of this platform’s design involves the installation of a 10-MPa manually adjustable gate valve at the outlet of the submersible pump. This pump outlet is equipped with a pressure measurement port to monitor the outlet pressure of the submersible pump. The test is executed by modulating the gate valve’s aperture to regulate the pressure at the submersible pump’s outlet, thereby adjusting the submersible electric pump to various operating conditions. To simulate the operational state of the MkQ3200-1,000/810 submersible motor and electric pump at a drainage depth of 800 m, the gate valve is adjusted to set the submersible pump’s outlet pressure to 8 MPa, enabling the submersible electric pump to replicate the operating conditions of a mine with an 800m drainage depth. The structure for installing the submersible motor test is illustrated in Fig. 7. The comprehensive submersible pump test platform is presented in Fig. 8.

III. Result and Discussions

1. Loss in Motor

A motor is a device that converts electrical energy into mechanical energy. During this energy conversion process, losses are inevitable, and most of these losses are ultimately converted into heat within the motor, resulting in a temperature increase in all motor components. For the water-filled submersible motor analyzed in this study, its internal heat sources can be categorized according to the losses generated: basic stator core loss, winding loss, mechanical loss, and additional loss. The loss of the motor is measured in a no-load test and the calculated results for the 3,200 kW water-filled submersible motor’s core and mechanical losses are shown in Table 3.

2. Stator Steady-State Temperature Field Analysis

To analyze the impact of axial flow rate on the temperature rise of the motor stator, a 3,200 kW water-filled submersible motor was evaluated. The stator windings of the water-filled submersible motor investigated in this study are insulated with cross-linked polyethylene. It is noted that the maximum safe operating temperature for cross-linked polyethylene insulation material should not exceed 80°C.

The axial flow rate of the fluid at the motor air gap inlet was set at 1 m/s, 2 m/s, 3 m/s, and 4 m/s, respectively, with the motor’s ambient temperature maintained at 30°C. The temperature field of the water-filled submersible motor’s stator was simulated and analyzed following the aforementioned steps. This resulted in obtaining thermal contour maps illustrating the stator temperature distribution under varying air gap inlet fluid flow rates, as depicted in Figs. 9 –12.

From the data presented in Figs. 9 –12, it is observed that for the 3,200 kW water-filled submersible motor, as the fluid flow rate at the air gap inlet increases from 1 m/s to 4 m/s, the highest stator temperatures, located at the stator yoke near the motor’s air gap outlet, decrease successively. The peak temperature values are recorded as 82.236°C, 76.102°C, 72.295°C, and 69.486°C, respectively. Correspondingly, the highest cross-sectional average temperatures are 78.034°C, 71.143°C, 66.941°C, and 64.561°C. Conversely, the lowest stator temperatures are consistently found in the stator teeth at the motor air gap inlet, with the minimum temperatures being 60.445°C, 56.685°C, 54.501°C, and 53.207°C, and the average temperatures at the inlet section are 65.13°C, 61.22°C, 58.51°C, and 56.82°C, respectively.

The fluid flow rate at the water-filled submersible motor air gap inlet directly affects the stator’s cooling performance. By adjusting the flow rate, one can achieve the required cooling effects for the stator winding insulation. At an air gap inlet flow rate of 1 m/s, the average temperature at the bottom circumference of the stator teeth near the air gap outlet is 79.96°C, with a maximum temperature of 80.7°C, which may not fully ensure the safety of the motor winding insulation. At a flow rate of 2 m/s, the average temperature is 74.36°C and the maximum temperature is 75.23°C, with no location exceeding 80°C, thus ensuring the insulation safety of the motor winding. For a flow rate of 3 m/s, the average temperature is 71.44°C, and the maximum temperature recorded along the circumference is 72.23°C, also without exceeding 80°C, which secures the motor winding insulation safety. Finally, at a flow rate of 4 m/s, the average temperature at the bottom circumference of the stator teeth at the air gap outlet end is 68.64°C, with the highest temperature on the circumference being 69.25°C, which is well within the safety threshold for motor winding insulation.

3. Experimental Data Comparison

Temperature values at the stator air gap inlet and outlet of the MkQ3200-1,000/810 submersible motor, as well as the thrust bearing temperature values, were obtained through testing, as presented in Table 4. The comprehensive performance curve of the MkQ3200-1,000/810 submersible electric pump system was derived, as illustrated in Fig. 13. The test data provide a foundation for validating the simulation results, and the testing confirms the accuracy of the research methodology and the validity of the findings presented in this study.

For easy comparison, the simulation results can be represented as Table 5 and Fig. 14.

The test results indicate that the experimental conditions of the prototype are in close agreement with the simulation. When comparing the temperatures at the air gap inlet and outlet across various flow rates in the test data with those in the simulation data, the comparative results are summarized in Table 6.

The comparative analysis in Table 6 reveals that the relative error of the calculated value is 1.37%, which is within acceptable limits for actual operating conditions. The experimental outcomes demonstrate that the analysis approach is sound and confirm the precision of the method used to study the internal temperature distribution within the motor.

IV. Conclusion

In this paper, a submersible motor model is established, the three-dimensional model of the motor is simulated and analyzed by using the finite element method, and the temperature distribution of the inlet and outlet of the air gap fluid of the submersible motor is analyzed in detail by the method of temperature rise experiment. We can draw the following conclusions:

1) The lowest temperature of the motor stator is located in the stator tooth part at the air gap fluid inlet, and the highest temperature is located in the stator yoke part near the air gap fluid outlet of the motor. The temperature of the motor stator decreases with the increase of the axial flow rate of the air gap inlet fluid, but the decrease is gradually weakened.
2) With an air gap inlet flow rate of 2 m/s, the average temperature at the bottom circumference of the stator teeth near the air gap outlet is measured to be 74.36°C, with a maximum temperature of 75.23°C observed along the circumference. No locations exceed 80°C, which ensures the safety of the motor winding insulation. This method is readily implementable in engineering applications. For the 3,200 kW water-filled submersible motor examined in this study, to achieve the necessary cooling for the stator winding insulation, it is essential to maintain an axial water flow velocity of at least 2 m/s at the stator-rotor air gap inlet.
3) The findings of this study provide a theoretical foundation for determining the appropriate fluid flow rate in the air gap and for the optimal design of the pump wheel driven by the submersible motor.

Notes

This work was supported by the Joint Funds of the National Natural Science Foundation of China (Project No. U1904210-4).

Fig. 1

Submersible motor three-dimensional assembly diagram.

Fig. 2

Submersible motor internal water circulation cooling structure (1, motor case; 2, motor stator; 3, cooling water channel; 4, motor rotor; 5, pump wheel; 6, cooling tube; and 7, cooler).

Fig. 3

A diagram of the external water cooling structure of a water-filled submersible motor (1, submersible motor; 2, submersible pump; 3, pump-machine coupling part; 4, pump-machine coupling sleeve; 5, upper suction port; 6, lower suction port; 7, spit section; and 8, suction cover).

Fig. 4

A 3D solid model of stator and rotor of water-filled submersible motor.

Fig. 5

Equivalent thermal circuit diagram of water-filled submersible motor.

Fig. 6

Deep well submersible pump comprehensive test platform schematic (1, shaft; 2, water suction hood; 3, wet submersible motor; 4, temperature measuring element; 5, cable; 6, submersible pump; 7, check valve; 8, drainage pipe; 9, seat pipe; 10, support beam; 1, support beam; 12, 90° elbow; 13, manual adjustment gate valve; 14, manometer tube; 15, pressure gauge; 16, temperature measuring device; 17, manometer; 18, flow meter; 19, electric gate valve; 20, outlet pipe; and 21, return tank).

Fig. 7

Submarine motor test installation structure (1, ground lifting structure; 2, pulley; 3, supporting structure; 4, high-strength pipeline; 5, submersible electric pump, upper pump and lower machine installation; 6, suction cover; 7, perforated screen; and 8, ground winch).

Fig. 8

Submersible pump comprehensive test platform: (a) experimental platform physical picture, (b) experimental platform outlet.

Fig. 9

Stator temperature distribution cloud diagram when the air gap inlet fluid velocity is 1 m/s: (a) stator upper end temperature cloud diagram, (b) stator lower end temperature cloud diagram.

Fig. 10

Stator temperature distribution cloud diagram when the air gap inlet fluid velocity is 2 m/s: (a) stator upper end temperature cloud diagram, (b) stator lower end temperature cloud diagram.

Fig. 11

Stator temperature distribution cloud diagram when the air gap inlet fluid velocity is 3 m/s: (a) stator upper end temperature cloud diagram, (b) Stator lower end temperature cloud diagram.

Fig. 12

Stator temperature distribution cloud diagram when the air gap inlet fluid velocity is 4 m/s: (a) stator upper end temperature cloud diagram, (b) stator lower end temperature cloud diagram.

Fig. 13

MkQ3200-Comprehensive performance curve of 1,000/810 submersible pump system.

Fig. 14

Stator temperature at different air gap fluid flow rates.

Table 1

Basic parameters

Parameter	Value
Rated power (kW)	3,200
Rated voltage (kV)	10
Inner diameter of stator (mm)	423
Outer diameter of rotor (mm)	417
Supporting circulation pump wheel	Flow rate of 40 m³/hr, head range of 10 m
Air gap height (mm)	3
Design temperature rise	When the ambient temperature is 40°C, the temperature rise shall not exceed 40°C

Table 2

Thermal conductivity of common materials in submersible motors

Materials	λ(W/m·K)
Copper	380–385
Water	0.569–0.676
Brass	110–130
Gray cast iron	41.9–58.6
Aluminum	202–220
Stainless steel	25–30
Cold rolled silicon steel sheet along the layering direction	37.01
Cast aluminum	150.7
Cold rolled silicon steel sheet vertical layering direction	3.55
Alloy steel	33–40
Hot rolled silicon steel sheet along layering direction	35
Vertical layering direction of hot rolled silicon steel sheet	0.57–1.1

Table 3

Loss calculation value of 3,200 kW submersible motor

Test program	Calculated value
Stator resistance, 60°C (Ω)	0.225
No-load current (A)	97
Stator no-load copper consumption (kW)	2.117
No-load input power (kW)	131.477
Iron consumption (kW)	40.16
Mechanical loss (kW)	89.2
Full load copper consumption (kW)
Stator	27.2
Rotor	44.7
Stray dissipation (kW)	16

Table 4

MkQ3200-1,000/810 submersible motor test data

Delivery head (m)	Flow rate (m³/hr)	Temperature (°C )

		Inlet	Outlet	Thrust bearing
745	1,236.5	55.6	59.0	72.1
767	1,181.7	55.6	59.1	72.3
785	1,130.9	55.6	59.0	72.3
796	1,095.7	55.4	58.9	72.2
806	1,056.5	55.4	58.8	72.2
816	1,017.4	55.3	58.8	72.1
826	982.17	55.3	58.8	72.2
836	954.78	55.4	58.8	72.1
847	915.65	55.3	58.7	72.2
867	798.26	55.2	58.7	72.3

Table 5

Different air gap fluid inlet flow rates

Inlet velocity (m/s)	Temperature (°C )

	Max	Max cross-section average	Min	Min cross-section average
1	82.236	78.034	60.445	65.13
2	76.102	71.143	56.685	61.22
3	72.295	66.941	54.501	58.51
4	69.486	64.561	53.207	56.82

Table 6

Comparison of stator winding test values and simulation values

Parameter	Value
Simulation value (°C)	98.14
Experimental value (°C)	99.5
Absolute error (%)	1.36
Relative error (%)	1.37

References

1. C. Wang, W. Shi, Y. Li, and W. Cao, "Structural analysis of explosion proof mine pump base on the material of QT600-3," Journal of Computational and Theoretical Nanoscience, vol. 10, no. 12, pp. 2847–2852, 2013. https://doi.org/10.1166/jctn.2013.3289

2. B. Guan, C. Di, Z. Ke, and X. Bao, "A numerical model for single-point bearing faults analysis in submersible induction motors," IEEJ Transactions on Electrical and Electronic Engineering, vol. 17, no. 12, pp. 1811–1819, 2022. https://doi.org/10.1002/tee.23691

3. J. Li, C. Di, and X. Bao, "Efficiency improvement for submersible motors by optimizing the ratio of diameter to shaft length," IEEE Transactions on Magnetics, vol. 58, no. 2, article no. 8200806, 2022. https://doi.org/10.1109/TMAG.2021.3081800

4. Q. Wu, L. Wang, G. Yang, E. Tang, L. Li, and A. Al-Zahrani, "A novel design of permanent magnet linear synchronous motor with reduced end effect," Journal of Electromagnetic Engineering and Science, vol. 23, no. 2, pp. 171–179, 2023. https://doi.org/10.26866/jees.2023.2.r.157

5. Y. Wang, K. Fan, and Q. Pang, "Magnetic field analysis of hollow Halbach long stator permanent magnet synchronous linear motor for suspension permanent magnet maglev train," Journal of Electromagnetic Engineering and Science, vol. 23, no. 4, pp. 326–334, 2023. https://doi.org/10.26866/jees.2023.4.r.174

6. Y. Xu, M. Ai, and Y. Yang, "Research on heat transfer of submersible motor based on fluid network decoupling," International Journal of Heat and Mass Transfer, vol. 136, pp. 213–222, 2019. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.002

7. Y. Xu, M. Ai, and J. Zhang, "The influence of the inner circulation oil circuit of the submersible motor on the heat transfer of the submersible motor," Electric Machines and Control, vol. 23, no. 1, pp. 80–88, 2019. https://dx.doi.org/10.15938/j.emc.2019.01.010

8. J. R. Martins, D. da Cunha Ribeiro, F. D. A. R. Pereira, M. P. Ribeiro, and O. J. Romero, "Heat dissipation of the Electrical Submersible Pump (ESP) installed in a subsea skid," Oil & Gas Science and Technology–Revue d’IFP Energies Nouvelles, vol. 75, article no. 13, 2020. https://doi.org/10.2516/ogst/2020009

9. Z. Wan, B. Sun, X. Wang, W. Wen, and Y. Tang, "Improvement on the heat dissipation of permanent magnet synchronous motor using heat pipe," Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 234, no. 5, pp. 1249–1259, 2020. https://doi.org/10.1177/0954407019880444

10. Y. Gu, X. Wang, P. Gao, and X. Li, "Mechanical analysis with thermal effects for high-speed permanent-magnet synchronous machines," IEEE Transactions on Industry Applications, vol. 57, no. 5, pp. 4646–4656, 2021. https://doi.org/10.1109/TIA.2021.3087120

11. G. Du, W. Xu, J. Zhu, and N. Huang, "Rotor stress analysis for high-speed permanent magnet machines considering assembly gap and temperature gradient," IEEE Transactions on Energy Conversion, vol. 34, no. 4, pp. 2276–2285, 2019. https://doi.org/10.1109/TEC.2019.2939220

12. F. Zhao, Z. Yu, J. Cao, and L. Li, "Design and optimization of a high-speed permanent magnet synchronous machine for gas compressors," IEEE Transactions on Magnetics, vol. 58, no. 2, article no. 8100905, 2022. https://doi.org/10.1109/TMAG.2021.3078464

13. G. Liu, M. Liu, Y. Zhang, H. Wang, and C. Gerada, "Highspeed permanent magnet synchronous motor iron loss calculation method considering multiphysics factors," IEEE Transactions on Industrial Electronics, vol. 67, no. 7, pp. 5360–5368, 2020. https://doi.org/10.1109/TIE.2019.2934075

14. M. A. Mueller, J. Burchell, Y. C. Chong, O. Keysan, A. McDonald, M. Galbraith, and E. J. E. Subiabre, "Improving the thermal performance of rotary and linear air-cored permanent magnet machines for direct drive wind and wave energy applications," IEEE Transactions on Energy Conversion, vol. 34, no. 2, pp. 773–781, 2019. https://doi.org/10.1109/TEC.2018.2881340

15. H. Li and Y. Shen, "Thermal analysis of the permanent-magnet spherical motor," IEEE Transactions on Energy Conversion, vol. 30, no. 3, pp. 991–998, 2015. https://doi.org/10.1109/TEC.2015.2419636

16. S. Lucas, R. Marian, M. Lucas, T. Ogunwa, and J. Chahl, "Employing the Peltier effect to control motor operating temperatures," Energies, vol. 16, no. 5, article no. 2498, 2023. https://doi.org/10.3390/en16052498

17. S. Nategh, O. Wallmark, M. Leksell, and S. Zhao, "Thermal analysis of a PMaSRM using partial FEA and lumped parameter modeling," IEEE Transactions on Energy Conversion, vol. 27, no. 2, pp. 477–488, 2012. https://doi.org/10.1109/TEC.2012.2188295

18. S. Nategh, Z. Huang, A. Krings, O. Wallmark, and M. Leksell, "Thermal modeling of directly cooled electric machines using lumped parameter and limited CFD analysis," IEEE Transactions on Energy Conversion, vol. 28, no. 4, pp. 979–990, 2013. https://doi.org/10.1109/TEC.2013.2283089

19. Y. Xu, M. Ai, and Y. Yang, "Heat transfer characteristic research based on thermal network method in submersible motor," International Transactions on Electrical Energy Systems, vol. 28, no. 3, article no. e2507, 2018. https://doi.org/10.1002/etep.2507

20. F. Rezaee-Alam, AN. Marashi, and S. Roozbehani, "Modified magnetic equivalent circuit model for magnetic field analysis of one cage-rotor induction motor used in electric submersible pumps," IET Electric Power Applications, vol. 17, no. 6, pp. 802–812, 2023. https://doi.org/10.1049/elp2.12305

21. J. H. Chow, Z. W. Zhong, W. Lin, L. P. Khoo, and C. M. Kiew, "A finite-difference thermal model of a three-phase coreless linear motor as a heat source," Applied Thermal Engineering, vol. 87, pp. 605–614, 2015. https://doi.org/10.1016/j.applthermaleng.2015.05.064

22. X. Zheng, Y. Wang, M. Jiang, and S. Zhang, "Numerical simulation of interior turbulent flow regulation of wet submersible motor," Wireless Personal Communications, vol. 102, pp. 1443–1459, 2018. https://doi.org/10.1007/s11277-017-5204-1

23. Q. Zhang, Z. L. Li, X. W. Dong, Y. X. Liu, and R. Yu, "Comparative analysis of temperature field model and design of cooling system structure parameters of submersible motor," Journal of Thermal Science and Engineering Applications, vol. 13, no. 5, article no. 051002, 2021. https://doi.org/10.1115/1.4049754

24. N. Egidi, P. Maponi, L. Misici, and S. Rubino, "A three-dimensional model for the study of the cooling system of submersible electric pumps," Mathematics and Computers in Simulation, vol. 82, no. 12, pp. 2962–2970, 2012. https://doi.org/10.1016/j.matcom.2012.05.014

Biography

Shibin Zhang, https://orcid.org/0009-0000-4652-027X was born in 1985. He received a Ph.D. degree from China University of Mining and Technology (Beijing), Beijing, China, in 2018. He is currently a lecturer and postgraduate tutor at North China University of Water Resources and Electric Power, Zhengzhou, China. His current research interests include mechatronics engineering, mine emergency drainage engineering technology and equipment.

Biography

Huayang Ren, https://orcid.org/0009-0003-1495-5764 was born in Nanyang, Henan, China, in 2000. He received his bachelor of Engineering from North China University of Water Resources and Electric Power in 2018. He is currently pursuing a master’s degree at North China University of Water Resources and Electric Power. His research interests include the design of submersible motor and Submersible sewage pump.

Biography

Yongcun Wang, https://orcid.org/0009-0000-1380-054X was born in Yongcheng, Henan, China, in 1977. He received his Bachelor of Engineering from Henan Polytechnic University in 2013, majoring in electrical automation, he is now engaged in coal mine electromechanical transportation professional work.

Biography

Yu Miao, https://orcid.org/0009-0006-0104-1287 was born in Yongcheng, Henan, China, in 1977. He received his Bachelor of Engineering from China University of Mining and Technology in 2012, majoring in mechanical engineering and automation, he is now engaged in coal mine electromechanical transportation professional work.

Biography

Yan Shang, https://orcid.org/0009-0009-1760-6870 was born in 1990. She received a Bachelor of Engineering from North China University of Water Resources and Electric Power, Zhengzhou, China, in 2015. She is currently a teaching assistant at North China University of Water Resources and Electric Power, Zhengzhou, China. Her current research interests include mechanical engineering and automotive design.

Biography

Yunbing Feng, https://orcid.org/0009-0000-2348-4595 was born in Hebi, Henan, China, in 1987. She received her Bachelor’s degree from Pukyong National University in 2011, she is now engaged in the research of machinery used in coal mines.