【summary】
To compare and analyze the feasibility of different thermal calculation methods in motor thermal design and engineering applications, this paper takes a self-fan-cooled permanent magnet motor as the research object, analyzing its fan operating flow rate, motor fluid field, and motor temperature rise. The rated operating airflow of the motor fan is calculated using both analytical and finite volume methods, and the velocity distribution of the overall fluid domain of the motor is obtained using the finite volume method. Based on fluid calculations, the motor temperature rise is predicted using both the equivalent thermal path method and the finite volume method. Comparison of calculated and measured values shows that both methods have a certain degree of reliability. The finite volume method is more suitable for motor design improvement and optimization, while the analytical method can be used for derivative motor design and preliminary scheme evaluation.
introduction
With economic and social development, low-carbon environmental protection and high-efficiency energy saving have become the focus of attention in all walks of life. Among them, rare earth permanent magnet motors have received widespread attention and application due to their simple structure, small size, light weight and high efficiency [1-2]. In the field of rail transit, in order to effectively protect the permanent magnets, permanent magnet motors generally adopt a fully enclosed structure, which leads to harsh heat dissipation conditions for the motor; in addition, the increase in motor power density increases the unit volume loss generated by the motor during operation, which will aggravate the temperature rise of various parts of the motor. Once the high temperature causes irreversible demagnetization of the permanent magnets, it will seriously affect the safe operation of the motor. As the core component of rail transit vehicles, the accurate calculation and prediction of the internal temperature field of the motor lays a solid foundation for ensuring the safe operation of the motor, saving design costs and shortening the research and development cycle. The main methods of motor thermal design include simplified formula method, equivalent thermal circuit method, thermal network method and numerical calculation method, etc., and these methods have their own advantages and disadvantages in terms of calculation accuracy and design cycle [3-6].
To investigate the feasibility and effectiveness of different calculation methods in motor thermal design and practical engineering applications, this paper takes a fully enclosed permanent magnet synchronous traction motor with built-in fan cooling as the research object and compares and analyzes the motor thermal design methods. This paper uses analytical and simulation calculation methods to calculate and compare the motor temperature rise. First, analytical calculations and three-dimensional fluid field simulation analysis are performed on the motor fan and its flow channel to obtain the air volume generated by the fan under rated operating conditions. Then, based on the fluid field calculation results, the motor temperature rise is calculated and analyzed using the thermal circuit method and the finite volume method [7-9]. Since the permanent magnet motor rotor basically does not generate heat, the analytical method based on the equivalent two-heat-source thermal circuit is simple to calculate and can quickly predict the stator winding temperature rise, allowing for a preliminary judgment on the rationality of the motor's electromagnetic scheme design. Simulation calculations based on the finite volume method can analyze and evaluate the fluid field and temperature field of the entire motor domain, which is more conducive to the improvement and optimization of the motor scheme.
1. Permanent Magnet Motor Structure
The permanent magnet motor described in this article adopts a fully enclosed structure, which mainly includes components such as stator, rotor, shaft, fan, front and rear end covers, stator pressure ring, and rotor pressure ring. Figure 1 shows its axial cross-section. The ventilation channel formed by the motor end cover, stator pressure ring, and ventilation holes on the outside of the stator lamination constitutes the external circulation air path, including the fan; the air path formed by the air gap and ventilation holes on the inside of the stator lamination constitutes the internal circulation air path, including the rotor rear pressure ring.
Figure 1 shows the axial structure of a permanent magnet motor. 1—Shaft; 2—Mesh plate; 3—Fan; 4—Rear end cover; 5—Stator winding; 6—Rotor rear pressure ring; 7—Stator pressure ring; 8—Stator core; 9—Rotor core; 10—Rotor front pressure ring; 11—Front end cover; 12—Bearing. This motor is required to rotate in both directions, therefore a centrifugal fan is used. The fan is mounted on the motor shaft, with its blades evenly distributed radially, as shown in Figure 2. When the motor is working, the fan rotates along with the motor. Air is drawn into the motor through the inlet, cooled by the ventilation ducts inside the motor, and then discharged into the outside atmosphere through the outlet. The cooling effect of the fan on the motor is greatly affected by the motor speed.
Figure 2 shows the fan structure. The main function of the internal circulation air path of the motor is to accelerate the heat transfer inside the motor by disturbing the gas inside the motor cavity. This not only allows the heat generated by the loss inside the motor to be quickly transferred to the external circulation air path, but also effectively balances the distribution gradient of the internal temperature field of the motor.
2 Fan Flow Calculation and Fluid Field Simulation 2.1 Fan Blade and Flow Calculation Based on Empirical Formulas The size of the fan blades can be determined according to the installation space of the motor and fan. The fan blade parameters and working flow rate are determined based on the outer diameter D1, inner diameter D2, axial length b of the blades, and rated speed nN of the motor. The formulas for calculating the cylindrical surface area S of the gas swept by the outer diameter of the impeller, the linear velocity v1 of the outer diameter of the impeller, the linear velocity v2 of the inner diameter of the impeller, the maximum air volume QM that the radial blade fan can generate, and the number of blades N are shown in equations (1) to (5): S=0.92π*D1*b (1) v1=nN*π*D1/60 (2) v2=nN*π*D2/60 (3) QM=0.42*Sv1 (4) N=8.5/(1-D2/D1) (5) According to the above formulas, the permanent magnet motor fan is calculated to have S=0.056m2, v1=22.765m/s, v2=10.501m/s, QM=0.538m3/s, and N=16. Therefore, the number of fan blades is set to 16; the fan operating flow is calculated as 40% of the maximum air volume, so the operating flow that the fan can generate is approximately 0.215 m3/s.
The amount of airflow through the fan when the motor fan is working is crucial for the accurate calculation of the motor temperature field. In order to obtain more accurate values of fan working airflow and wind speed in the stator ventilation hole of the motor, numerical simulation and calculation of its external circulation air path were performed based on FLUENT software [10].
2.2 Simulation Analysis of Fan Fluid Field The fluid solution domain model of this motor is shown in Figure 3. The cooling medium is air. Since the Mach number inside the motor is relatively small, it is treated as an incompressible fluid. To balance computational accuracy and model mesh quality, some machining fillets and chamfers are ignored, and the air inlet and outlet are defined as the air inlet and outlet in the structural sense of the motor, respectively.
Figure 3 shows the solution domain of the three-dimensional fluid field. The fluid domain model is relatively complex, so different mesh types are used for different parts, and the mesh size does not exceed 3 mm. When solving, an implicit steady-state solver based on pressure is selected. The Reynolds number of the fluid inside the motor is relatively large. In order to accurately simulate the swirling effect, the “RNGk-ε” model [11-12] is selected as the turbulence model and “SwirlDominatedFlow” is selected as the RNG option (RNGOptions). The near-wall surface meets the requirements of the standard wall function; the turbulence intensity at the inlet and outlet is moderate turbulence intensity (5%). The fan rotation is simulated using multiple rotating coordinate systems [13-14]. The fan area is set as a rotating fluid domain with the rotation speed the same as the rated speed of the motor. The relative rotation speed of the fan blades and the fan hub wall is set to 0, and other areas are static fluid domains. The air inlet and outlet are both set as pressure outlets with a value of one standard atmosphere (i.e., 101325 Pa). The pressure-velocity coupling was performed using the SIMPLE method, and all convection terms in the equations were discretized using a first-order precision scheme, with a solution accuracy set to 10⁻⁶. During the simulation, the airflow at the inlet and outlet was monitored until convergence. Figure 4 shows the traces of the external circulation fluid domain of the motor, and Figure 5 shows the velocity field distribution of the external circulation fluid.
Figure 4 Streamline diagram
Figure 5 shows the velocity field distribution. The fan rotation causes uneven airflow in the same ventilation hole within the end cover and pressure ring, resulting in inconsistent airflow in adjacent stator ventilation holes (Figure 5). This is related to the fan's rotation direction. The average airflow in the stator ventilation holes is 17 m/s. Calculations show that the motor's airflow is approximately 0.221 m³/s, which is basically consistent with the working airflow value calculated and verified using fan parameters. The average airflow velocity at the inlet is 2.6 m/s, and the average airflow velocity at the outlet is 12 m/s.
3 Motor Temperature Rise Calculation and Analysis 3.1 Temperature Rise Calculation Based on Equivalent Thermal Circuit Method There are many heat sources in the motor and they are not easy to calculate accurately. The heat transfer path is complex and the motor itself involves structural components of different materials. Therefore, when calculating the temperature rise of the motor, some appropriate assumptions are often made as needed to simplify the solution process. The establishment of the equivalent thermal circuit model of the motor is based on the following assumptions and dependencies: (1) The stator winding and stator core are isothermal heating bodies.
(2) The conductors in the stator slots are evenly arranged and the radial temperature difference is negligible; the insulating varnish of the copper wires is evenly distributed; the impregnation varnish of the windings is completely filled.
(3) The current in the winding is uniformly distributed on the cross section, and the skin effect caused by the leakage magnetic field in the coil is ignored.
(4) The rotor of the permanent magnet motor does not generate heat, and the calculation is performed using a two-heat-source thermal path including the copper loss of the stator winding and the iron loss of the stator.
The equivalent thermal circuit of the motor with two heat sources in steady state is shown in Figure 6. In the figure, PCu is the heat loss in the stator coil, PFe is the heat loss in the stator core, RCF is the insulation conduction thermal resistance between the winding and the stator core, RCu is the heat dissipation thermal resistance between the winding end and the air, RF1 is the heat dissipation thermal resistance of the stator core ventilation channel to the air, RF2 is the heat dissipation thermal resistance between the inner circle of the stator core and the air, RF3 is the heat dissipation thermal resistance between the outer circle of the stator core and the air, ΔTCu is the temperature rise of the stator winding, and ΔTFe is the temperature rise of the stator core.
Figure 6 shows the thermal circuit of the motor with two heat sources. The thermal resistance inside the motor is mainly divided into conductive thermal resistance Rt1 and heat dissipation thermal resistance Rt2. The specific calculation is shown in equations (6) and (7): Rt1=δ/(λ*A) (6) Rt2=1/(α*A) (7) Where: δ——length of the heat conductor in the direction of heat flow, m; λ——thermal conductivity of the heat conductor, W/m·K; A——thermal conduction area perpendicular to the heat flow, mm2; α——surface convection heat dissipation coefficient, W/m2·K.
Based on the motor structure and material properties, the thermal resistance values of each part are calculated using equations (6) and (7): RCF = 0.01118 K/W, RCu = 0.35371 K/W, RF1 = 0.04131 K/W, RF2 = 0.15674 K/W, RF3 = 0.32154 K/W. Ignoring the effects of mechanical losses and stray losses, the copper loss of the motor stator winding is 2125 W, and the iron loss of the stator is 968 W. Based on Figure 6 and the calculated thermal resistance values, the average temperature rise of the motor stator winding is 103.6 K, and the average temperature rise of the stator core is 62.3 K.
The simplified equivalent thermal circuit method is used to calculate the motor temperature rise. While simple and fast, it only yields the average temperature rise of the stator windings and cannot determine the overall temperature field distribution within the motor, especially the highest temperature point. To ensure the reliability of the motor's thermal design and its safe operation, a three-dimensional fluid-structure interaction temperature field simulation analysis is necessary.
3.2 Temperature field simulation based on finite volume method The simulation analysis of motor temperature field is based on the following basic assumptions: (1) The physical properties of the materials involved in the model do not change with temperature.
(2) When modeling the geometry, ignore the fan part and establish a simplified 1/8 model based on the motor structure. The end cover and the shaft are simplified. All contacting solid parts are in close contact.
(3) The stator coil is treated as a straight bar along the axial direction; the impregnation varnish is completely filled; the insulation in the stator slot is treated as an integrated unit, with the same thermal performance and isotropic.
(4) Motor radiation heat dissipation and surface natural heat dissipation are characterized by the motor surface convection heat dissipation coefficient.
(5) The rotor rotation is simulated using a multi-rotating coordinate system model.
(6) Ignore the unevenness of the air velocity in the stator ventilation holes of the external circulation air path.
Excluding the motor fan, the motor structure is circumferentially symmetrical. The operating flow rate of the motor was obtained through fluid domain simulation calculations of the external circulation path, including the fan. When establishing the temperature field solution domain, based on the actual motor structure and assumed conditions, a three-dimensional temperature field solution domain model of the motor was established using 1/8 of the motor's circumferential cross-section (Figure 7). The model mainly includes the stator core, stator windings and their insulation system, rotor core, rotor pressure rings, internal fan, bearings, end covers, and shaft.
Figure 7 shows the solution domain of the three-dimensional temperature field. The motor end cover, coil copper wire, insulation, slot wedges, permanent magnets, and shaft are made of isotropic materials with thermal conductivity set to 38 W/m·K, 387 W/m·K, 0.18 W/m·K, 0.22 W/m·K, 12 W/m·K, and 48 W/m·K, respectively. The stator and rotor cores are made of anisotropic silicon steel sheets with a thermal conductivity of 40 W/m·K radially and 1.6 W/m·K axially.
During the solution process, the ambient temperature was 29℃, and losses were evenly distributed across all components. Specifically, the winding copper loss was 2125W; the stator iron loss was 968W; stray losses were 480W, distributed 1:1 between the stator and rotor; and the bearing losses at both ends were 80W. A pressure-based implicit steady-state solver was selected. The "Standard k-ε" model was chosen as the turbulence model, with the near-wall surface conforming to the standard wall function requirements. The air inlet was set as a velocity inlet, based on the fluid field calculations and the average wind speed within the end cap ventilation holes, with a value of 12 m/s. The outlet was a pressure outlet, with a value of one standard atmosphere. The turbulence intensity at both the inlet and outlet was set to moderate 5%, and the hydraulic diameter was 0.026 m.
Figure 8 shows the calculation results for the temperature field. It can be seen that the stator winding temperature is the highest, occurring at the lower winding end of the motor's outlet end, at 138.7℃; the average temperature of the stator winding is 131.2℃, resulting in an average temperature rise of 102.2K. Due to the motor's fully enclosed structure, the effective stator section temperature is low, while the end temperature is high, with the outlet winding end temperature higher than the inlet winding end, resulting in a maximum temperature difference of approximately 8.5K between the two ends (Figures 8(b) and 8(c)). This is because the cooling air carries away heat while its own temperature rises during the process from the inlet to the outlet, thus the cooling effect at the inlet end is better than at the outlet end. According to the calculation results, after the motor temperature rise reaches a steady state, the average temperature at the motor inlet is 29.8℃, and the average temperature at the motor outlet is 43.1℃, resulting in a temperature difference of 13.3K between the inlet and outlet.
Figure 8 Temperature field calculation results 3.3 Comparison of calculated temperature rise with experimental results A temperature rise test was conducted on the motor prototype (ambient temperature was 29℃), and the air velocity at the motor inlet and outlet was measured to estimate the motor's operating air volume. During the test, the average temperature rise of the stator winding was obtained by the thermal resistance method, and the temperatures of the stator core and transmission end bearings were measured by the temperature sensor PT100.
Under rated operating conditions, the average wind speed at the motor inlet was measured to be 2.8 m/s, and the average wind speed at the outlet was measured to be 13.0 m/s. Based on the area of the motor inlet and outlet, the estimated operating airflow of the motor fan was 0.237 m³/s. The relative errors between the fan airflow calculated by the analytical method and the finite volume method and the measured values were 9.2% and 6.7%, respectively, both meeting the engineering requirements. However, the finite volume method had higher calculation accuracy, mainly because the analytical method, based on empirical formulas, has a certain degree of inaccuracy.
Table 1 shows the calculated and experimental temperature rise results. The simulation calculation values for the windings are based on the average temperature rise of the windings, while the simulation calculation values for the core and bearings are based on the average values at the measured locations. Compared to the thermal circuit method, the design values obtained through simulation calculation have smaller errors. The equivalent thermal circuit method replaces the complex heat transfer process within the motor with a smaller equivalent thermal resistance, and involves the selection of many parameters during the calculation, thus causing larger errors. Simulation calculation can obtain the temperature field distribution across the entire motor, but its calculation cycle is long. According to the data comparison, both thermal design methods can meet the practical engineering needs of motor design.
Table 1 Comparison of calculated values and prototype test values
4 Conclusion
This paper takes a self-fan-cooled permanent magnet motor as the research object and uses different methods to calculate the motor's flow field and temperature rise. When analyzing the motor fan's airflow, analytical methods and finite volume methods are used for calculation and simulation. Then, equivalent thermal circuit methods and finite volume methods are used to calculate and simulate the motor's temperature rise. Comparison with experimental data shows that both methods have a certain degree of reliability in analyzing motor airflow and average temperature rise. The finite volume method has higher calculation accuracy and can obtain the distribution of the motor's global velocity and temperature fields, especially the value and location of the highest temperature point, facilitating motor optimization and improvement. However, due to its long calculation cycle and high requirements for computer hardware resources, it will consume a lot of time and cost for derivative motor development and market-oriented motor projects. Using empirical formulas and the equivalent thermal circuit method for motor thermal design can only roughly obtain the average temperature rise of the motor windings, but the calculation can be completed in a very short time, with low computer resource requirements, and can be used for rapid evaluation of motor design schemes and prediction of temperature rise in derivative motors. The specific motor thermal design method used needs to be selected based on the specific nature of the project.
