Temperature rise characteristics of permanent magnet synchronous motor considering boiling heat transfer

The temperature rise characteristics of PMSM (permanent magnet synchronous motor) during operation were studied under the condition of BHT (boiling heat transfer) in cooling water. The subcooling boiling heat transfer model, RPI (Rensselaer polytechnic institute), was used to calculate and improve the computational accuracy of simulation results. The experiments have shown that, when the motor was tested and simulated after preheating, the temperature rise characteristics were similar to test data because the boiling heat transfer phenomenon of the motor was taken into account, with an error of 1.7%, which was more accurate than the error of 7.5% without boiling. Therefore, from the results obtained from the experiments, the phenomenon of boiling heat transfer in cooling system has a significant effect on the temperature rise characteristic of the motor, which should be regarded as an important factor. Due to the influence of two-phase flow boiling heat transfer, the temperature rise of the motor in the plain areas is 4–5 °C higher than that in the high altitude areas. Consequently, if the motor is operated in high altitude areas, its temperature rise characteristic has better effect compared with plain area. Additionally, when BHT in cooling water is considered, the temperature of the motor drops as the rate of flow increases. In the meantime, the temperature difference between the minimum flow rate and the maximum flow rate is about 1 °C, which means that the increase in rate of flow can enhance the boiling heat transfer effect.


Introduction
In order to reform and develop electric vehicles, various countries have issued a large number of policies to encourage the development of electric vehicles, which has led to rapid growth in the production of electric vehicles [1,2].It is well known that the temperature of motors rise with increase in altitude, which makes the temperature rise characteristics of the motor have a large influence in the high altitude areas, especially in highland areas, and the performance of the motor will also be reduced.Moreover, the variation of temperature has an effect on the performance of pure electric vehicle motors, Which will also affect the operation of electric vehicles in highland areas [3].When motors are operated at high temperatures, the PM will be demagnetized due to high temperature, and in serious cases, it will also cause insulation damage and affect the performance of the motor [4][5][6].Additionally, insulation damage and irreversible demagnetization of PM will cause its structural strength significantly reduced and a dramatic reduction in service life [7,8].In a highland environment, as the altitude rises, the atmospheric pressure drops and so does the saturation temperature of the cooling water.So the cooling system should have two forms of heat transfer, one for simple one-way fluid convection heat transfer, and the other for two-phase flow boiling heat transfer [9].Consequently, it will be of great importance to research the 123 variation of supercooled boiling point heat transfer characteristics of PMSM in electric vehicles under the special plateau environment, which can enhance the efficiency of PMSM in the plateau environment.
Gao et al. developed an efficient method to estimate the temperature of the PM in high power density PMSM by considering magnetic saturation.Compared with the conventional method, this method adds saturation coefficients for analysis, which greatly improves the accuracy of the proposed method, and the validity of the revised method is verified by using the magneto-thermal coupled finite element model [10].Wan et al. designed a new motor with heat tube for electric vehicles, aiming at reducing the end winding temperature, and simulated its temperature field by using FLUENT software, the innovative design shows that the heat pipe can transfer the heat from windings to the end cover, thus reducing the temperature of the motor and ensuring the operating efficiency [11].Fang et al. proposed a torque-free ripple signal injection method for estimating the temperature of windings of the stator from the stator resistance.The results of simulation experiments show that the method can accurately calculate and analyze the temperature of stator winding, and the method is simpler than traditional methods [12].Wang et al. calculated temperature rise curves and the distribution of temperature fields of each parts of hub motors under various cooling methods by establishing the three-dimensional finite element analysis models with natural cooling and inner-oil cooling for the inwheel motor [13].Based on the basic assumptions, Ding et al. analytically calculated several temperature fields by adopting the finite volume analysis based on given heat transfer and boundary conditions of the generator, and then analyzed the calculated result together with the measured data to verify the reasonableness of the numerical calculations.Thus, the experiment lays the foundation for the safe operation of the generator in the plateau area [14].Zhou et al. used a new double-layer water-cooling structure to form thermal insulation according to the temperature rise index and operating characteristics of ultra-high-precision planar motor.In addition, calculate the motor stator fluid-solid coupled heat transfer model to obtain the flow field of coolant and temperature distribution of stator under different water-cooling structures and different operating conditions with computer software [15].Zhang et al. proposed a new thermal analysis method for underwater induction machines called multi-physics field coupling analysis, based on the interaction between the radiator and the underwater motor and circulating impeller in terms of pressure and temperature losses, which revealed the temperature variation laws such as copper and oil wear losses.Additionally, verified the reasonableness and practicality of this method through experiments [16].Lim et al. invented a new type of oil injection cooling system for vehicle wheel motors by optimizing the design of the channel shape in the oil injection system to improve the efficiency of cooling oil transport, and obtained the advantages of this model by comparing it with the conventional thermal model [17].According to the Eulerian two-phase flow boiling model, Dong et al. established a new BHT model to analyze the heat transfer process of the internal combustion engine.In addition, the model is also used to couple heat transfer calculations for experimental projects.Finally, the reasonableness and practicality of the model were also verified by comparison with Robinson's rectangular channel tests [18].
In summary, current research on automotive PMSM has rarely considered its operation in highland areas, ignoring the temperature rise characteristics of motors when coolant boils due to the increase in altitude.The subcoolant boiling model is taken into account in the motor temperature rise simulation calculation, which can better approximate the experimental results.It provides a better theoretical method for the design and optimization of the motor when operating in the plateau area.In this paper, a vehicle PMSM was used as the research object and its power rating was 38 kW.Firstly, the theoretical analysis and numerical calculation of the test are carried out.Then, the temperature fields of the motor were simulated with the 3-D finite element simulation software CFX and RPI heat transfer model, so the two-phase flow model of BHT and the single-phase flow model without boiling were obtained.At the same time, the accuracy and rationality of the two-phase flow calculation of motors when considering BHT was proved through bench experiments when the wall temperature was high.Finally, according to the comprehensive analysis of test data, when the phenomenon of BHT exists, the temperature rise characteristics of this prototype are basically consistent with the test results, with an error of 1.7%.

Model determination of motor temperature field
Based on the basic analytical method of heat transfer, the transient temperature fields are studied, and the 3-D temperature fields of a motor are also simulated and numerically calculated by using the fluid-structure coupling thermal analysis method.Due to the complexity of the internal heat transfer process, it will be transformed into a 3-D transient heat conduction problem with internal heat sources, according to [19][20][21].The boundary conditions and the thermal differential equations are as follow where k x ,k y and k z are the thermal conductivity of different media in motors in different directions such as x,y and z; c is the constant pressure specific heat; ρ is the object density; T is the object temperature; t is the time; s1, s2, s3 are the boundary surfaces of the solid; T w is the temperature of the boundary surface; q v is the heat generation density of heat sources; q w is the thermal flow density at the boundary surfaces; n is the normal vector of the s2 boundary; h is heat transfer coefficient of surface flow at the boundary; T f is the convection heat coefficient around a water jacket; and k is the thermal conductivity of boundary conditions perpendicular to the boundary surface.

Euler model
In [22,23], according to the Eulerian two-phase flow model theory, the model requires that each phase must satisfy a group of energy equations, and the gas phase continuity equation can be expressed as where α q is the volume fraction;ρ q is the density;v q is the velocity vector;m pq and m qp are the mass transferred between the two phases; n is the sum of phases; and S q is the source phase.momentum equation is shown in Eq. ( 3) where R pq is the interphase interaction force; F td,q , F vm,q , F wl,q , F lift,q and F q are turbulent discrete force, virtual mass force, wall dissipation force, buoyancy force and the external volume force, respectively;τ q is Tensor of stress-strain; and g is the gravitational force.
Energy equation can be expressed as where h q is the enthalpy of phase q;∇q q is the thermal flux; and both h pq and h qp are latent heat.

BHT model of the wall surface
Based on the RPI boiling model, it is known that the total thermal flow over the wall is generally divided into three parts, which are heat transfer from the bubble, convective heat transfer between the liquid without bubble coverage and the wall and thermal conduction on the wall [24,25].i.e., where Q e is the heat flow due to the occurrence of phase change in the bubble growth cycle, unit is W/m 2 ;Q q is the extraction thermal flow resulting from the influx of the surrounding subcooled liquid into the wall after bubbles leave the surface of the wall, unit is W/m 2 ;Q c is the convective heat transfer thermal flow between the liquid and the wall not covered by bubbles; and unit is W/m 2 .The extracted heat flow can be calculated from Eq. ( 6) where A q is the percentage of the wall that participates in the extraction heat flow; f is the number of periodic changes in the nucleation of the bubble;λ lip is the thermal conductivity of liquid phase;c p, lip is the specific heat capacity of liquid;t wait is the time required from the detachment of the bubble to the creation of another bubble;ρ lip is the density of liquid phase; and T lip and T w are the liquid temperature and the wall temperature, respectively.Q c can be calculated from Eq. ( 7) when the interaction between bubbles is not considered where u lip is the rate of flow of the liquid phase close to the surface of the wall; and St is the Standon number.Q e can be calculated from Eq. ( 8), which is calculated as follows where ρ g is the density of gas phase; and H 1g is the latent heat of vaporization of the liquid.Among them δ 185 T w − T lip 1.805 (10) where n is the density of the nucleation point; k is the ratio of the area of the bubble to the area near the nucleation points where heat transfer is influenced when the bubble is detached; and d dep is the bubble detachment diameter.

Sub-model of bubble boiling
The detached diameter of the bubble can be expressed as where T sat is the saturated temperature of the liquid phase, and it is influenced by the pressure of cooling water, when the pressure of the cooling water is 0.7 atm and 1 atm, the temperature is 89.96 °C and 100 °C, respectively.The bubble detachment frequency is where g is the gravitational acceleration.
The waiting time of the air bubble can be expressed as 3 Establishment of finite element model and setting of boundary conditions

Basic parameters of the motor
The PMSM studied in this paper adopts water cooling for heat dissipation, and Table 1 shows the basic parameters required.

Calculation of motor heat loss
The main heat source of motors mainly comes from the eddy current, iron and copper current losses generated during its operation [26].It is the primary condition to correctly calculate the loss of each part of the motor for studying the temperature rise characteristics of the motor.The sum of the losses of the motor during the operation can be expressed as P P + P w + P t1 + P t2 + P c ( 14) where P is the sum of the losses of the motor; P is the sum of stray and mechanical losses;P w is the eddy current losses in PM; P t1 is the iron losses of the rotor; P t2 is the iron losses of the stator; and P c is the copper losses of the windings and stator.
The transient electromagnetic field of a PMSM is analyzed by using Maxwell to obtain the accurate loss values of each parts of this motor during operation.Table 2. shows the heat source distribution data for each motor component when the experimental prototype is running at rated torque.

Temperature field model
Before completing the 3D finite element simulation, the following assumptions need to be made in order to reasonably simplify the solution process [27].
1.The motor temperature will gradually rise during operation, and the heat generated during this process is evenly distributed in each components, which mainly comes from the PM, stator core, winding and rotor core.2. Ignore the effect of temperature change on the surface convective heat transfer coefficient and thermal conductivity of each motor component.
3. Ignore the friction losses of the wind and the bearing.4. The conductive media of all materials inside the motor are isotropic.
A temperature field solution model is established for each part of the motor, which includes the shaft, housing, rotor, cooling water, windings, stator and PM, so as to simplify analytical models and calculate values accurately, in addition, because the base part has a small effect on the heat dissipation of motors, it can be ignored.The temperature field solution model is shown in Fig. 1a, and b.It shows the spiral cooling water channel of the prototype.

Boundary conditions
Boundary conditions of convective heat transfer.
1.The inlet boundary of cooling water is the mass flow, and the test inlet flow is 8 L/min.2. The fluid-solid coupled surface is a no-slip boundary condition in the analysis.3. The coolant outlet is zero pressure outlet.4. The heat dissipation coefficient of each components of the motor is dealt with in reference [23].
Boundary conditions in plateau environments.
1.The saturation temperature of cooling water is 89.96 °C and the atmospheric pressure is 0.7 atm, when the simulated environment is taken as 3 km above sea level [14].2. The inlet fluid of the two-phase flow is water, where the volume fraction of water vapor is 0 and the volume fraction of water is 1 [20].3. The temperature of the liquid phase is used as the inlet temperature, where water vapor should be the discrete phase, which uses the heat transfer model with zero resistance, and the wall of the discrete phase is the free-slip wall condition; additionally, the liquid phase is continuous phase, which uses two-equation model of turbulent.

Temperature field solving
Figure 2 shows the temperature distribution of each motor component through single-phase flow calculation of the motor transient temperature field at 38 kW and 4000 rpm rated operating conditions, where the MT (maximum temperature) of the winding is 127.9 °C occurring at its end and this temperature is also the highest temperature of this motor; the MT of the PM is 102.2 °C; the MT of the stator is 102.4 °C; and the MT of the rotor is 108.5 °C.Obviously, the temperature in the middle of each parts of the motor is lower than the temperature at both ends.The specification of PM material is grade 42EH high performance NdFeB, so the temperature of the PM is within the maximum permissible temperature range of the material, and the temperature of the winding is also within the maximum allowable temperature range, that is, the motor winding will not be damaged and the PM will not be demagnetized.Dynamometer tests the power and transmitted power of the motor and the controller regulates the torque and speed of the system.In addition, to ensure the accuracy of temperature monitoring, thermocouples will be embedded in the end of the winding, and sufficient thermocouples will be placed on the core, end caps and other stator components to provide temperature change data.The data acquisition system records the transmitted speed, torque, load and temperature variations.The thermostatic tank is used to regulate inlet temperature of cooling water.
Figure 4 shows the overall flow diagram of the cooling system.The cooling water is concentrated in the tank and the throttle valve and flow valve control the speed and flow of the required cooling water.The circulating water pump delivers the cooling water to the controller.Therefore, the cooling water will first enter the controller to absorb heat and later enter the PMSM to absorb heat.The cooling water piping of the motor can be seen in Fig. 1.The temperature monitor monitors the temperature of the returning cooling water and heat exchanger absorbs heat from cooling water.Finally, the cooling water flows back to the tank to complete the cycle.
The experimental method is to run the motor at rated torque and rated speed, and measure the temperature rise of the windings during this process, and compare it with the  single-phase flow and two-phase flow models through the test, and the type and ranges of the experimental equipment are shown in Tables 3.
Figure 5 shows the simulation results for single-phase flow and two-phase flow under the preset operating conditions.The temperature extracted from the simulation and the temperature recorded by the thermocouple in the test are at the winding ends.
The temperature variation curve of the windings working for 4200 s under single cycle condition can be known from Fig. 6.During the experiment, the motor temperature rise is considered to be stable if the data collected by the temperature sensor at the same position does not change more than 1 °C within half an hour.Obviously from the graph, the temperature of the motor test remains basically stable at 2100s and the motor simulation temperature remains basically stable at 1500s.When the winding temperature rise tends to balance, the temperature of the two-phase flow simulation is maintained at 138.4 °C, the simulation temperature of the single-phase flow simulation is stable at 127.9 °C, and the test temperature is 136 °C.By combining experimental data with simulation results to analyze, it is found that the simulated two-phase flow analysis results are closer to the test data with an error of 1.7% and the error of the single-phase flow simulation results is 7.5%.It indicates that during the test and simulation after the motor is heats up, there is a phenomenon of BHT in cooling water channels.It is obvious that if the RPI boiling heat transfer model is applied to the two-phase flow boiling heat transfer of cooling water, the simulated heat transfer in the motor cooling water channel can be made closer to the actual situation and more accurate.
The cloud map of the volume fraction distribution of water vapor and water inside the motor water channel simulated by the RPI model is shown in Fig. 7.It is obvious that the Fig. 7 Cloud map of water vapor and water volume fraction distribution inside the channel boiling point of motors occurs mainly on the inner side of the water channel, while the water vapor is mainly distributed in the inner water channel, which is near the side of stator, the main reason is that the water channels of the PMSM are composed of the smooth inner surface of the shell and the water groove cut on the external surface of the stator, which makes it easier to form the location-vaporization core where bubbles are generated in water channels, and the inner side of the water channel is heated.The mainstream liquid is mainly distributed outside the water channel due to the inertial force and centrifugal force.

Effect of different external factors on BHT
The BHT is affected by many external factors in the phase change process, so it has a certain complexity, these factors include the flow velocity, pressure and inlet temperature of the coolant.Therefore, it is of great necessity to research the influence of the inlet temperature of the coolant, atmospheric pressure and flow velocity on the temperature rise of the motor.

Effect of inlet temperature on the temperature rise of the motor
Figure 8 shows the temperature rise of each important component of the motor under rated operating conditions calculated by two-phase flow boiling heat transfer at different atmospheric pressures of 0.7atm and 1atm and different cooling water inlet temperatures, as well as a inlet flow rate of cooling water of 2 m/s and a bubble diameter of 1 mm.In Fig. 8, as the coolant temperature rises, the MT of each important parts of the motor will also rise, so reducing the coolant temperature plays an important role in improving the heat transfer effect.When the coolant flows over the heating surface, the lower the inlet temperature of coolant, the higher the superheat temperature.From the BHT curve, it can be discovered that the increasing superheat makes the vaporization core also increase.The enhancement of bubble disturbance improves thermal flow and heat transfer coefficient.Consequently, the more heat absorbed by cooling water, the lower temperature of the motor.However, when the inlet water temperature increases, it will lead to an increase in the number of bubbles generated in a water channel, a weakening of the disturbance between the gas and liquid phases, and a decrease in the heat transfer intensity of cooling systems, resulting in a gradual increase in motor temperature.Furthermore, because of the increase in the number of bubbles, the flow velocity of the coolant is constant, making it difficult for the bubbles generated by boiling to be carried away by the mainstream liquid, causing many bubbles to adhere to the walls.In Formula (5), because of the reduction of extraction heat flow and convective heat transfer heat flux, the total thermal flux is also decreased, which leads to the increase of motor temperature.However, if the temperature of the coolant is too low, it will be prone to excessive cooling, so it is necessary to reasonably control the coolant temperature to make supercooled boiling in the water jacket and enhance heat transfer.

Effect of atmospheric pressure intensity on the motor temperature rise
The engineering of highly reinforced or heavy machinery is often done by increasing the pressure of the cooling system to inhibit the boiling of the coolant.However, as the pressure increases, the loss of pressure in cooling system also gradually increases, which makes the pump power consumption increase.Since the saturation temperature of coolant is affected by atmospheric pressure and varies with it, the influence of pressure on subcooled boiling heat transfer is greater than that on natural convection heat transfer.Figure 9 shows that the variation of the highest temperature of the windings and PM of the motor at different atmospheric pressures of 0.7 atm and 1 atm when the bubble diameter is 1 mm and the inlet flow rate of cooling water is 2 m/s.As shown in Fig. 7, when the rate of flow of the incoming water and the temperature remain constant, the motor temperature gradually falls as the atmospheric pressure drops, that is to say, when the motor runs in the high altitude areas, as the altitude rises, the atmospheric pressure gradually drops.Since the saturation temperature of coolant is affected by the atmospheric pressure, it decreases as the atmospheric pressure decreases.In addition, in a same heat source, if the coolant pressure is lower, the boiling degree will be stronger and the heat transfer effect will be better; in this case, as the motor temperature decreases, the BHT will increase.After the inlet temperature exceeds 90 °C, the motor temperature at 0.7 atm will rise sharply and when the inlet temperature exceeds 97 °C, the motor temperature rise at 0.7atm will be higher than this motor temperature rise at 1atm.The reason for this is that after the inlet temperature reaches 90 °C, the cooling water saturation temperature at 0.7 atm is 89.96 °C, which causes the temperature of the main body of the motor cooling water to be higher than the saturation temperature, the water channel is saturated boiling.In addition, the cooling water and the stator wall are overheated over 25 °C, the heat flux density exceeds the critical heat flux density and the wall surface appears transitional boiling.The bubbles converge and cover the wall resulting in vapor heat transfer in part of the area covered by the bubbles, reducing the heat transfer efficiency in cooling system, so the temperature of the motor at 0.7 atm is higher than the motor temperature Fig. 9 Temperature rise curve of windings and permanent magnets at different atmospheric pressures a temperature rise curve of windings; b temperature rise curves of permanent magnets at 1 atm.Obviously, in this case, the motor has better performance characteristics when operating in the high altitude areas.

Effect of inlet flow velocity on motor temperature rise
The temperature rise curves of windings and PM under different coolant flow rates when the bubble diameter is 1 mm and the atmosphere pressure is 0.7 atm are shown in Fig. 10. Figure 10 shows that as the rate of flow increases, the temperature of windings and PM also rises gradually.The temperature of PM and windings at a rate of flow of 6 L/min Fig. 10 Temperature rise curves of winding and permanent magnets at different flow rates a temperature rise curve of windings b temperature rise curve of permanent magnets is about 1 °C higher than that at 9 L/min.This is mostly because of the increase in the rate of flow, which causes the turbulence between the two phases within the water jacket to gradually increase as well, thus increasing the kinetic energy of the turbulence and improving the effect of convective heat transfer.When the superheating degree of the wall surface is not large, convective heat transfer accounts for a larger proportion of the total heat flow than BHT, so that an increase in rate of flow can enhance the heat transfer effect.When the rate of flow is 6 L/min, as the inlet temperature increases, the temperature of the motor also rises, which causes an increase in the degree of superheat, an increase in phase change heat and an increase in thermal flux and heat transfer coefficient.
Because the flow velocity is low at this time, a large number of bubbles generated near by the wall surface can gather and approach the mainstream area, the phenomenon of supercooling is obvious, the heat of phase change accounts for a large proportion of the wall heat transfer, and the wall heat transfer coefficient increases, Therefore, if the rate of flow is 6 L/min and the inlet temperature exceeds 85°C, the temperature growth rate of motors will decrease.

Conclusion
1.By combining the analysis of experimental data and simulation data, it is obvious that when the motor is tested and simulated after preheating, the temperature rise characteristics of this motor are closer to the experimental result under the condition of considering BHT.Thus, the error of only considering single-phase flow heat transfer is large and the temperature rise characteristics of the motor at high temperatures cannot be accurately studied.It is obvious that the effect of two-phase flow boiling heat transfer in the cooling system should be considered as an important influencing factor.2. As the atmospheric pressure drops, the motor temperature also gradually decreases, that is to say, the motor has better temperature rise characteristics when operating in high altitude areas than in plain areas because of the influence of phase change heat transfer of cooling water.3.Under the condition of considering BHT, the motor temperature in both plain or high altitude environments increases with the inlet temperature of cooling water and also with the inlet temperature of the coolant, and the motor windings and PM temperature drop as the flow rate increases due to the turbulent disturbance effect of the coolant.Therefore, in the case that the superheating degree of the wall surface is not large, increasing the rate of flow can strengthen the boiling heat transfer effect.
Since the model in this paper is mainly based on the discussion of conventional motor cooling systems, this does not satisfy us to extend the model to newer areas.Therefore, combining the model proposed in this paper with additive manufacturing will be the focus of our next research direction.

Fig. 1
Fig. 1 The model of the motor a temperature field model, b cooling water channel

Fig. 2 Figure 3
Fig. 2 Cloud diagram of temperature distribution of each parts of the motor a windings, b permanent magnet,c rotor, d stator

Fig. 5 Fig. 6
Fig. 5 Simulation results of single-phase flow and two-phase flow a single-phase flow, b two-phase flow

Fig. 8
Fig. 8 Temperature rise curves of motor under various inlet water temperatures a motor temperature rise curve at 0.7atm, b motor temperature rise curve at 1atm

Table 1
Technical data of the studied motor

Table 2
Distribution of heat sources when the motor is running at rated torque

Table 3
Type of experimental equipment