0 Introduction
Permanent magnet motors have natural advantages when applied to cranes. Their strong overload capacity and high torque density are more suitable for the basic requirements of crane lifting mechanisms. However, compared with the traditional asynchronous motor plus reducer structure, the permanent magnet motor used for direct-drive cranes will inevitably increase in size. Considering the installation size of the permanent magnet motor on the crane, the motor size needs to be reduced as much as possible. This will increase the electrical density of the stator winding, causing the motor temperature to rise, which will reduce the performance of the motor. In severe cases, it will cause irreversible demagnetization of the permanent magnet, damage the motor, and cause factory shutdown. Therefore, it is crucial to study the selection of its thermal load [1].
Generally speaking, there are three main methods for analyzing motor temperature rise: formula method, equivalent thermal circuit method, and numerical analysis method. Formula method is based on Newton's law of cooling to calculate the average temperature rise of each part of the motor, but due to its low calculation accuracy, it cannot meet the requirements of motor thermal analysis. Equivalent thermal circuit method is based on the similarity between thermal circuit and circuit, and the series and parallel connection law in the circuit is also applicable to thermal circuit. It is intuitive and simple, with a small workload, but the disadvantage is that it cannot calculate the highest temperature rise point. Numerical analysis method is a method of solving numerical calculations using computers, which has high accuracy and can predict the actual temperature distribution of the motor. The optimal thermal load of the motor can be selected by optimizing the motor parameters, thereby improving the torque density. The numerical analysis method for the fluid-structure interaction heat transfer problem in the motor adopts the finite volume method (FVM) for more accurate calculation [2].
This paper simplifies a direct-drive permanent magnet motor model for a crane, calculates the equivalent heat dissipation coefficients of the air gap and casing, analyzes the axial and circumferential water cooling, establishes a 1/4 simulation model, performs fluid-structure interaction heat transfer simulation, calculates the temperature rise of key parts, and compares the simulation results with experimental data to verify the correctness of the simulation method.
1. Fluid-structure interaction heat transfer principle
The heat dissipation problem of water-cooled permanent magnet motors is a convective heat transfer problem between the coolant and the water channels in the motor casing. It cannot be given a thermal boundary in advance as a known condition, but can only be regarded as a calculation result. This dynamic heat exchange problem is called a coupled heat transfer problem.
The direct-drive permanent magnet motor for cranes dissipates heat through conduction and convection. According to the law of conservation of energy, at the fluid-structure interaction interface, the heat absorbed by the fluid equals the heat transferred from the solid component. The Fourier equations for heat conduction and convection heat transfer of the motor's solid component can be expressed as follows:
In the formula: kcond is the thermal conductivity of the solid, hconv is the local convective heat transfer coefficient, and Tf and Tw are the fluid temperature and the temperature at the wall, respectively.
2. Establishment of a Coupled Heat Transfer Model for Permanent Magnet Motor
2.1 Selection of Waterway Type
The water channels of water-cooled permanent magnet motors are mostly axial water channels and circumferential (spiral) water channels [3], as shown in Figure 1. By comparing and analyzing the temperature distribution, water velocity distribution and convective heat transfer coefficient distribution under the two different water channel forms, the spiral water channel form is more suitable.
(a) Axial waterway (b) Spiral waterway Figure 1 Comparison of the two waterway types
2.2 Computational Model and Basic Assumptions Computational Model
Including both solid and fluid components, the motor model must be simplified here due to limitations in computer resources [4, 5]. Basic assumptions: 1) Stator coils are heated uniformly; 2) Stator core is heated uniformly; 3) Rotor core losses are ignored; 4) Water is considered as an incompressible fluid; 5) Since the wire insulation, layer insulation, and slot insulation are all very thin, they do not need to be treated separately and are treated as a whole. The stator slot treatment is shown in Figure 2; 6) The spiral water channel is simplified to a circular water channel, and the motor can be equivalent to a symmetrical model. The 1/4 model is shown in Figure 3 using SolidWorks.
Figure 2 Equivalent diagram of conductor in the slot
Figure 3. Calculation model of three-dimensional temperature field
2.3 Treatment of thermal conductivity of each part
1) Due to the rotation of the rotor and the roughness of the rotor core surface, the heat conduction capacity of the air gap is stronger when the rotor is rotating than when it is stationary. Introducing the air gap thermal conductivity λδ, that is, using a new thermal conductivity to make the rotor equivalent to a stationary state, the heat transferred by the fluid in the air gap is equal in the two states per unit time.
Assuming the stator and rotor surfaces are smooth, calculate the Reynolds number at the air gap.
In the formula: nφ1 is the airflow velocity, i.e., the linear velocity of the rotor rotation, and nφ1 = D2n / 60; n is the motor speed; δ is the air gap length.
d = (Di1 - D2)/2; Di1 and D2 are the stator inner diameter and rotor outer diameter, respectively; ν is the kinematic viscosity of the fluid. The critical Reynolds number for air flowing in the air gap.
When Re < Reair, the gas flow is considered laminar, and the thermal conductivity is the same as that of air; when Re > Reair, the gas flow is considered turbulent, and the equivalent thermal conductivity is...
The calculation results are: Re = 262.06, Reair = 587.19, so the effective thermal conductivity at the air gap is the same as the thermal conductivity of air.
2) The heat dissipation coefficient of the casing surface is related to the external wind speed. In a windless indoor environment, the heat dissipation coefficient of the casing surface is given as 8 W/(m2·K) based on experience. The thermal conductivity of the other parts of the motor is shown in Table 1.
2.4 Heat source distribution
Because the direct-drive permanent magnet motor for cranes operates at a relatively slow speed and low frequency, the mechanical losses during motor rotation and the eddy current losses in the rotor core are negligible. The main heat-generating components are the copper losses generated by the windings and the iron losses generated by the stator. However, since the permanent magnets have very high temperature requirements and are very small in size, this heat generation cannot be ignored. The heat generation of each part of the motor is shown in Table 2.
2.5 Boundary Conditions
To obtain the temperature distribution in the heat-conducting medium, the heat flow differential equation must be solved, and its boundary conditions must be given: boundary conditions for thermal calculation (first-type boundary conditions).
In the formula: Tc is the given temperature on the object boundary S1, and f(x, y, z, t) is the temperature function. Heat flux boundary condition (second type of boundary condition)
In the formula: q0 is the heat flux density on the object boundary S2; g(x, y, z, t) is the heat flux density function; λ is the thermal conductivity perpendicular to the object surface [6, 7]. The Reynolds number Re of the fluid in this paper is greater than 2300, indicating turbulence. The relationship between its turbulent kinetic energy and the fluid velocity is as follows:
In the formula: u is the flow velocity, d is the hydraulic diameter, v is the kinematic viscosity, and Re is the Reynolds number.
3. Temperature Field Calculation and Analysis
3.1 Waterway configuration and temperature simulation
As mentioned earlier, with the same water channel area, the same surface heat source was added to the casing of the two water channel structures respectively, and the simulation analysis of the two water channels was performed using Fluent. The results are shown in Figure 4.
Figure 4 Calculation results of axial waterway
As shown in Figure 5, the axial water channel achieves the required heat dissipation effect, but the large temperature gradient in the circumferential direction causes uneven temperature distribution in the three-phase windings. Furthermore, the low flow velocity at water bends creates "dead water zones," leading to localized overheating. In contrast, the spiral water channel exhibits a smaller circumferential temperature gradient, resulting in a more uniform temperature distribution across the three-phase windings. It also provides stable water flow velocity and excellent heat dissipation. Therefore, based on the comparison, the spiral water channel design was ultimately chosen.
Figure 5 Calculation results of circumferential waterway
3.2 Overall Simulation of Permanent Magnet Motor
The permanent magnet motor described in this paper uses Class F insulation and N38SH magnets. Considering margins, it is assessed as Class B insulation. The winding and magnet temperatures must not exceed 130℃. Fluent was used to simulate the 1/4 scale model of the motor, with an ambient temperature of 40℃ and a water immersion temperature of 60℃. Specific cooling parameters are shown in Table 3. The simulation results are shown in Figure 6. Figure 6a shows the overall temperature rise of the motor simulation model. Based on the cloud map distribution, the calculation results converge, and no discontinuities are observed. Figure 6b shows the winding temperature distribution. The highest winding temperature is 99.42℃ at the end. This is because the end winding is in direct contact with the air in the cavity, and air has poor thermal conductivity, resulting in a slightly higher end temperature than the middle. The lowest temperature is 89.10℃ in the middle of the upper winding. This is because the upper winding is closer to the water channel, making it easier to carry away heat. The overall winding temperature difference is not significant because copper has a high thermal conductivity, resulting in a relatively uniform temperature distribution. Figure 6c shows the temperature distribution of the permanent magnet, indicating that the temperature in the middle is slightly higher than at both ends. This is because, in addition to heat dissipation through the water-cooled casing, some heat is also dissipated through the air inside the cavity at both ends. The difference between the highest and lowest temperatures is only 1.03℃, and both are far from reaching the temperature limit.
Figure 6 Temperature rise cloud map of various parts of the motor
3.3 Comparison of Simulation and Experimental Data
The average temperature rise of key components of the motor is compared with the experimentally measured data, as shown in the table below. The data shows that due to the deviation between the experimental and simulated ambient temperatures, there are some errors between the simulated temperature values and the experimentally measured temperatures, but overall the differences are not significant. This verifies the correctness of the simulation results.
4. Conclusion
This paper calculates the temperature field of a crane direct-drive permanent magnet motor using Fluent. For the water-cooled heat dissipation method, the motor structure is simplified, and the equivalent thermal conductivity of the air gap and casing is calculated. By comparing and analyzing the characteristics of axial and circumferential water cooling, the circumferential water channel is selected, and a 1/4 scale simulation model is established. By loading the heat source and water channel parameters, the highest temperature of the motor is calculated to be 99.42℃ using the finite volume method, located at the end of the winding. The highest temperature of the permanent magnet is 77.22℃, which does not reach the temperature rise limit. Furthermore, the temperature variation range of the winding and permanent magnet in the axial direction is relatively small. Comparison with experimentally measured data shows small calculation errors: 9.5% for the casing, 5.4% for the winding, 7.4% for the permanent magnet, and 10.3% for the stator core. The comparison results verify the feasibility of this method.
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