Synchronous reluctance motor magnetothermal coupling rapid calculation method based on dynamic thermal network

Abstract

The invention discloses a synchronous reluctance motor magnetothermal coupling rapid calculation method based on a dynamic thermal network, and belongs to the technical field of motors. Comprising the following steps: calculating motor loss by adopting a finite element electromagnetic field model, and calculating a convective heat transfer coefficient by adopting a finite element fluid field model; constructing a three-dimensional thermal network comprising conduction, contact, convection thermal resistance, thermal capacity and a heat source, and solving to obtain an average temperature and a boundary temperature of component nodes; constructing a sub-domain temperature field calculation model of the heat source component, and calculating temperature distribution in combination with boundary conditions; introducing average temperature compensation thermal resistance and carrying out dynamic correction; carrying out magnetothermal coupling iteration, and updating the loss and the temperature until the precision is met; and introducing maximum temperature compensation thermal resistance into the thermal network, and solving to obtain an average temperature and a maximum temperature transient temperature rise curve of each component. Based on the technical means of combining electromagnetic field and fluid field finite element simulation with thermal network and subdomain temperature field calculation, efficient calculation of magnetothermal coupling of the synchronous reluctance motor is achieved.

Description

Technical Field

[0001] This invention relates to the field of motor technology, and specifically to a rapid calculation method for magnetothermal coupling of a synchronous reluctance motor based on a dynamic thermal network. Background Technology

[0002] Synchronous reluctance motors have become key equipment in industrial drives and other fields due to their simple structure, low cost, and high efficiency. To achieve higher power density and dynamic response, high-performance synchronous reluctance motors generally employ high electromagnetic load and high-speed designs. However, the compact structural design limits heat dissipation space, leading to a sharp increase in internal loss density and a particularly prominent temperature rise problem, directly restricting their performance limits and operational reliability.

[0003] Against this backdrop, the importance of magnetothermal coupling analysis in the refined design of high-performance synchronous reluctance motors is self-evident. On the one hand, electromagnetic field calculation is the source of temperature field analysis: the magnitude and distribution of losses in various motor components directly depend on accurate electromagnetic field calculations. On the other hand, the temperature field has a significant feedback effect on electromagnetic losses: changes in operating temperature significantly alter winding resistance, thereby affecting copper losses. This bidirectional coupling relationship means that electromagnetic design detached from the influence of temperature is inaccurate. Therefore, achieving accurate and efficient magnetothermal coupling iterative analysis is a core element and key technological bottleneck for optimizing motor design, evaluating its extreme operating capabilities, and ensuring its long-term reliability.

[0004] Currently, the technical approach to achieving magnetothermal coupling analysis of synchronous reluctance motors mainly relies on two types of methods: (1) Magnetothermal coupling based on numerical analysis: This method uses the finite element method to calculate the electromagnetic field to obtain the loss, and then uses computational fluid dynamics to analyze the fluid field and temperature field. Its advantage is that it has high accuracy and can reflect the temperature distribution in detail. However, its biggest drawback is that the computational efficiency is extremely low. A single complete fluid temperature field analysis takes up to several hours, while magnetothermal coupling requires multiple iterations, which makes the entire analysis process potentially take several days, completely failing to meet the needs of rapid iterative optimization of multiple schemes in the early stages of design.

[0005] (2) Magnetothermal Coupling Based on Thermal Network Method: This method establishes a thermal network model through thermoelectric analogy, with a calculation speed in the order of seconds, which meets the requirements of coupling iteration in terms of speed. However, its core problem lies in insufficient calculation accuracy. Classical thermal networks are based on one-dimensional heat transfer assumptions and static thermal resistance, which makes it difficult to accurately reflect the real temperature gradient inside complex components, resulting in deviations in the average temperature estimation, and it is impossible to directly obtain the local hot spot temperature, which is crucial to the insulation life. If the accuracy is improved by increasing the number of nodes, its advantage of speed will be lost.

[0006] It is evident that high-precision numerical analysis methods are too slow for effective magnetothermal coupling iteration; while the fast classical thermal network method suffers from insufficient accuracy, significantly reducing the reliability of the coupling analysis results. This contradiction severely restricts the improvement of design efficiency and reliability of high-power-density synchronous reluctance motors. How to achieve rapid and accurate calculation of the transient and steady-state temperature fields of synchronous reluctance motors while ensuring engineering-acceptable computational efficiency is a pressing technical problem to be solved in this field. Summary of the Invention

[0007] To address the shortcomings and improvement needs of existing technologies, this invention provides a rapid calculation method for magnetothermal coupling of a synchronous reluctance motor based on a dynamic thermal network. The aim is to establish a three-dimensional dynamic thermal network of the synchronous reluctance motor by combining finite element simulation with techniques such as thermal network and subdomain temperature field calculation, thereby achieving rapid and high-precision temperature field calculation and further realizing magnetothermal coupling calculation.

[0008] To achieve the above objectives, according to one aspect of the present invention, a fast calculation method for magnetothermal coupling of a synchronous reluctance motor based on a dynamic thermal network is provided, the method comprising: S1. Initialize the temperature of each component of the motor, import the initial temperature into the finite element electromagnetic field model to calculate the motor loss, and import the loss into the fluid-structure interaction finite element model to determine the convective heat transfer coefficient of the fluid-structure interaction surface in the motor. S2. Based on the actual structural characteristics of the synchronous reluctance motor, perform geometric equivalent processing and thermal node division, calculate the three-dimensional conductive thermal resistance of the stator, rotor, winding, shaft, bearing, end cover and housing, the contact thermal resistance between different components, the convective thermal resistance of the fluid-structure interaction surface and the heat capacity of each component, connect the thermal nodes of each component and establish a complete three-dimensional thermal network. S3. Introduce the heat loss as a heat source into the three-dimensional thermal network, and solve the steady-state equation of the thermal nodes to obtain the average temperature and boundary temperature of each component; S4. Establish a three-dimensional subdomain temperature field model of the heat source components, which include the stator, rotor, windings, and bearings. The equivalent thermal nodes of the heat source components are called heat source nodes. Substitute the convective heat transfer coefficient obtained in S1 and the boundary temperature obtained in S3 as boundary conditions into the three-dimensional subdomain temperature field model to solve for the three-dimensional temperature distribution of the heat source components. S5. Calculate the error between the average temperature of S3 and the average value of the three-dimensional temperature distribution of S4. When the error does not meet the accuracy requirements, introduce the average temperature compensation thermal resistance into the heat source node in the three-dimensional thermal network of S2, and repeat steps S3-S5 to dynamically correct the average temperature compensation thermal resistance until the accuracy meets the requirements. S6. Calculate the error between the average temperature obtained in S5 and the calculated temperature of the heat source. If the error does not meet the accuracy requirements, correct the calculated temperature of the heat source and recalculate the loss. Repeat steps S3-S6 until the error accuracy meets the requirements. S7. Using the three-dimensional temperature distribution calculated in S4, determine the maximum temperature of the heat source component, and introduce the maximum temperature compensation thermal resistance based on the three-dimensional thermal network in S2 to obtain the maximum temperature thermal network; solve the transient equations of the thermal nodes to obtain the maximum temperature transient temperature rise curves and average temperature transient temperature rise curves of each component after magnetothermal coupling.

[0009] Preferably, in step S2, the slot winding and the end winding are equivalent to a homogenized solid with anisotropic thermal conductivity, and the formula for calculating the anisotropic thermal conductivity is:

[0010] in, , These represent the thermal conductivity of the insulating material and the copper wire, respectively. Indicates the fill factor of the bare copper slot. , , These represent the radial thermal conductivity, circumferential thermal conductivity, and axial thermal conductivity of the homogenized solid, respectively.

[0011] Beneficial effects: For complex components with multi-material windings, this method simplifies the thermal modeling process of the most complex structures in motors by equating them with homogeneous entities possessing anisotropic thermal conductivity. This approach avoids the enormous computational overhead of thermal modeling each conductor and insulating medium, and overcomes the significant errors caused by the simple isotropic assumption. It greatly reduces computational load while maintaining computational accuracy, laying a crucial technical foundation for the subsequent establishment of thermal networks.

[0012] Preferably, in step S2, the rotor side of the synchronous reluctance motor has multiple complex magnetic barriers. Based on the characteristics of rotor iron loss distribution, it is assumed that the rotor loss is distributed in the outer iron core and the inner iron core of the rotor, and the rotor magnetic permeability has no heat source of loss, thereby reasonably simplifying the rotor thermal path.

[0013] Beneficial Effects: For rotor structures with complex multi-layered magnetic barriers and magnetic permeability, this method creatively distinguishes the main heat source regions and the approximately lossless magnetic permeability sections by analyzing the rotor iron loss distribution, and accordingly simplifies the rotor thermal path. This approach effectively controls the complexity and scale of the rotor thermal network model, laying a key technical foundation for subsequent rapid solutions.

[0014] Preferably, in step S2, the equivalent homogenized solid in the slot and the stator teeth are equivalent to a tile structure; the housing, stator yoke, end winding homogenized solid, outer rotor core, inner rotor core, bearing and end cover are equivalent to a hollow cylindrical structure; and the shaft is equivalent to a solid cylindrical structure.

[0015] Furthermore, the formula for calculating the thermal resistance of the tile structure is as follows:

[0016] in , , These represent the axial, radial, and circumferential thermal conductivity, respectively. , These represent the outer diameter and the inner diameter, respectively. Indicates axial length. Indicates the circumferential angle of the tile structure. , , These represent the axial, radial, and circumferential thermal resistances, respectively. , , These represent the one-dimensional thermal conduction compensation thermal resistance of the axial, radial, and circumferential heat source nodes, respectively.

[0017] Furthermore, for hollow cylindrical components without a heat source, including housings and end caps, one-dimensional thermal conduction compensation thermal resistance can be ignored.

[0018] Furthermore, the formula for calculating the thermal resistance of a solid cylindrical structure is as follows:

[0019] in R Indicates the radius of a solid cylinder; Beneficial effects: To address the problem that it is difficult to simultaneously meet the requirements of computational accuracy and low-order node discretization level in existing motor thermal network analysis, this paper equates each component of the motor to regular geometric structures such as tiles and cylinders. By introducing one-dimensional heat conduction to compensate for thermal resistance derived from the one-dimensional Fourier heat transfer law, the calculation accuracy of the average temperature of the components is significantly improved while ensuring the discretization level of the low-order nodes of the model. This lays a key technical foundation for rapid and accurate thermal analysis and magnetothermal coupling calculation.

[0020] Preferably, in step S3, based on the idea of ​​thermoelectric analogy, the nodal voltage method is used to solve for the average temperature of each component node in the thermal network. The thermal network equation is as follows:

[0021] in, Represents the thermal conductivity matrix. Represents the node temperature rise matrix. This represents the node heat source matrix.

[0022] Beneficial effects: To address the complex problem of solving multi-node thermal networks, this invention employs a node voltage method based on thermoelectric analogy to construct a unified thermal network equation, transforming the solution of complex temperature fields into efficient matrix operations. This provides support for the rapid and stable solution of thermal network node temperatures and is key to achieving second-level temperature field calculations.

[0023] Preferably, in step S4, the subdomain temperature field is solved using a finite difference algorithm. Specifically, the steady-state heat conduction equation for the subdomain temperature field in cylindrical coordinates is:

[0024] in, r Represents radial coordinates, T Represents the three-dimensional temperature distribution. Indicates the heat source; The subdomain heat conduction equation is discretized as follows:

[0025] The temperature field distribution of the three-dimensional subdomain can be quickly solved by substituting the convection heat transfer boundary and the temperature boundary, where i, j, and k represent the node indices in the radial, circumferential, and axial directions, respectively.

[0026] Beneficial Effects: Addressing the problem that existing thermal networks neglect multidimensional heat flow and cannot calculate maximum temperature, this invention utilizes the boundary temperature and convective heat transfer coefficient obtained from thermal network calculations as boundary conditions to calculate the subdomain temperature field distribution of regular geometric components. The implemented finite difference discrete calculation scheme uses central difference to transform the three-dimensional partial differential equations into a large system of linear algebraic equations, providing a reliable approach for efficient and stable numerical solutions. Furthermore, the structure of the discrete equations clearly distinguishes between internal nodes and boundary nodes, allowing various complex engineering boundary conditions, such as convection and given temperatures, to be directly and accurately substituted into the equation system in a discretized manner. This approach greatly enhances adaptability to different cooling methods and operating conditions, giving the calculation method of this invention broad engineering practical value.

[0027] Preferably, in step S5, the formula for calculating the average temperature compensation thermal resistance correction is expressed as follows:

[0028] in, , These represent the average component temperatures obtained by the subdomain method and the thermal network method, respectively. This indicates component wear and tear.

[0029] Furthermore, in step S6, the formula table for calculating the maximum temperature-compensated thermal resistance is as follows:

[0030] in, This represents the maximum temperature of the component obtained by the subdomain method.

[0031] Beneficial effects: To address the problem that static thermal resistance in classical thermal networks does not change with operating condition losses, leading to significant temperature calculation errors, this invention proposes a method combining the subdomain method and the three-dimensional thermal network method to dynamically correct the average temperature compensation thermal resistance, thereby improving the accuracy of average temperature calculation. Furthermore, an additional maximum temperature compensation thermal resistance is introduced to quickly calculate the maximum temperature within the framework of the thermal network, significantly improving the efficiency and accuracy of magnetothermal coupling calculations. Moreover, the compensation thermal resistance will adaptively adjust with changes in operating conditions.

[0032] Preferably, in step S6, the state-space method is used to solve the transient equations of the hot nodes. Specifically, the temperature of the node with heat capacity is referred to as the state variable. thermal capacity matrix Node temperatures that do not have heat capacity are called non-state variables. This divides the nodal admittance matrix into blocks:

[0033] Furthermore, the equation of state for the thermal capacity node temperature and the non-thermal capacity node temperature is expressed as:

[0034] Furthermore, the transient solution equation for the state variable, namely the temperature at the heat capacity node, is derived:

[0035] Beneficial effects: Addressing the computational divergence and low efficiency issues inherent in traditional transient thermal network solutions due to time-domain integration of all nodes, the state-space method distinguishes and decouples nodes with and without heat capacity, focusing the transient problem on actual thermal inertial nodes, thus significantly reducing the order of the solution model. The derived state-space equations are well-formed and can be directly solved using an efficient and stable ordinary differential numerical integrator, greatly enhancing the numerical stability and reliability of the algorithm in long-term, multi-condition transient thermal simulations.

[0036] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) The present invention provides a fast calculation method for magnetothermal coupling of synchronous reluctance motor based on dynamic thermal network, which realizes the unity of speed and high accuracy in magnetothermal coupling calculation of synchronous reluctance motor, and effectively solves the contradiction between the long calculation time of traditional numerical analysis method and the insufficient accuracy of lumped parameter thermal network method.

[0037] (2) This invention addresses the complex internal structure of motors by treating the slot windings and end windings as homogeneous entities with anisotropic thermal conductivity. This not only simplifies the thermal modeling process of multi-material components and avoids the tedious process of modeling each conductor individually, but also accurately captures the radial, circumferential, and axial heat transfer characteristics through the anisotropic thermal conductivity formula, significantly reducing the model complexity while ensuring engineering-acceptable accuracy, thus laying the foundation for rapid iterative optimization.

[0038] (3) The present invention introduces a dynamic thermal resistance correction mechanism. By iteratively adjusting the thermal resistance through average temperature compensation, it adaptively responds to temperature changes under different operating conditions. It uses the calculation results of the subdomain temperature field to dynamically update the compensation thermal resistance value, which overcomes the error accumulation problem of static thermal resistance under variable loss conditions. This self-learning correction not only improves the accuracy of temperature calculation, but also enhances the robustness of the method to cooling methods and operating parameters, making the magnetothermal coupling process more flexible and reliable.

[0039] (4) The present invention innovatively introduces the maximum temperature compensation thermal resistance, which realizes the rapid and accurate prediction of the hot spot temperature of the synchronous reluctance motor, thereby significantly improving the engineering practicality and reliability of magnetothermal coupling calculation.

[0040] (5) At the solution algorithm level, this invention comprehensively utilizes numerical techniques such as nodal voltage method, finite difference method and state space method to optimize the steady-state and transient solution efficiency of thermal network and realizes second-level temperature field calculation. Compared with the several hours of time taken by the finite element method, the calculation speed is significantly improved. This provides a practical tool for transient simulation and real-time monitoring and promotes the engineering application of motor thermal analysis technology as a whole. Attached Figure Description

[0041] Figure 1 This is a flowchart of the fast calculation method for magnetothermal coupling of synchronous reluctance motor based on dynamic thermal network provided by the present invention.

[0042] Figure 2 This is a schematic diagram of the structure of a shaft-end fan self-cooled synchronous reluctance motor in an embodiment provided by the present invention, wherein 1-casing, 2-stator, 3-winding, 4-rotor, 5-bearing, 6-shaft, 7-shaft-end fan, 8-rectifier cover, and 9-end cover.

[0043] Figure 3 This is a simplified schematic diagram of the winding as a uniform solid in the embodiment provided by the present invention.

[0044] Figure 4 This is a topological schematic diagram of the dynamic thermal network of the slot winding component with average temperature compensation thermal resistance in an embodiment provided by the present invention.

[0045] Figure 5This is a schematic diagram of the complete three-dimensional dynamic thermal network of the synchronous reluctance motor in the embodiment provided by the present invention.

[0046] Figure 6 This is a schematic diagram of the maximum thermal network topology of the slot winding component with maximum temperature compensation thermal resistance in the embodiment provided by the present invention.

[0047] Figure 7 This is a comparison between the average and maximum transient temperature rise curves of the slot windings calculated under rated operating conditions in the embodiments provided by the present invention and the prediction results of commercial software.

[0048] Figure 8 This is a comparison between the steady-state average temperature and maximum temperature obtained from thermal network calculations under rated operating conditions in the embodiments provided by the present invention and the prediction results of commercial software. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] This invention provides a method for calculating the magnetothermal coupling of a synchronous reluctance motor based on a dynamic thermal network. The calculation flowchart is shown below. Figure 1 As shown. The synchronous reluctance motor is a shaft-end air-cooled synchronous reluctance motor, and the motor structure in the embodiment is as follows. Figure 2 As shown, the method includes: Step S1: Initialize the temperature definition of each component of the motor, import the initial temperature into the finite element electromagnetic field model to calculate the motor loss, and import the loss into the fluid-structure interaction finite element model to determine the convective heat transfer coefficient of the fluid-structure interaction surface in the motor.

[0051] In step S1, the motor losses include stator and rotor iron losses, winding copper losses, wind friction losses, and bearing losses; the fluid-structure interaction surfaces include the contact surface between the housing and the external air of the motor, the contact surface between the air gap and the stator and rotor, the contact surface between the internal air of the motor and the stator and rotor core, the end windings, the end cover, and the bearing.

[0052] Step S2: Based on the actual structural characteristics of the synchronous reluctance motor, perform geometric equivalent processing and thermal node division, calculate the three-dimensional conductive thermal resistance of the stator, rotor, winding, shaft, bearing, end cover and housing, the contact thermal resistance between different components, the convective thermal resistance of the fluid-structure interaction surface and the heat capacity of each component, connect the thermal nodes of each component and establish a complete three-dimensional thermal network.

[0053] In step S2, the slot winding and end winding are equivalent to homogenized solids with anisotropic thermal conductivity, such as... Figure 3 As shown, the formula for calculating its anisotropic thermal conductivity is:

[0054] in, , These represent the thermal conductivity of the insulating material and the copper wire, respectively. Indicates the fill factor of the bare copper slot. , , These represent the radial thermal conductivity, circumferential thermal conductivity, and axial thermal conductivity of the homogenized solid, respectively.

[0055] In step S2, the rotor side of the synchronous reluctance motor has multiple complex magnetic barriers. Based on the characteristics of rotor iron loss distribution, it can be assumed that the rotor loss is distributed between the outer and inner iron cores of the rotor, and the rotor magnetic permeability has no heat source for loss. Therefore, the rotor thermal path is reasonably simplified. The simplified rotor thermal path is as follows: Figure 4 As shown, the formula for calculating thermal resistance is:

[0056] in, Indicates the length of the heat transfer path. Indicates thermal conductivity in the direction of heat transfer. This represents the heat transfer cross-sectional area in the direction of heat transfer.

[0057] In step S2, the equivalent homogenized solid in the slot and the stator teeth are equivalent to tile structures; the housing, stator yoke, end winding homogenized solid, outer rotor core, inner rotor core, bearings and end cover are equivalent to hollow cylindrical structures; and the shaft is equivalent to a solid cylindrical structure.

[0058] The thermal network topology of the equivalent homogenized entity within the trench is as follows: Figure 4 As shown, the formula for calculating the thermal resistance of the tile structure component is:

[0059] in , , These represent the axial, radial, and circumferential thermal conductivity, respectively. , These represent the outer diameter and the inner diameter, respectively. Indicates axial length. Indicates the circumferential angle of the tile structure. , , These represent the axial, radial, and circumferential thermal resistances, respectively. , , These represent the one-dimensional thermal conduction compensation thermal resistance of the axial, radial, and circumferential heat source nodes, respectively.

[0060] For hollow cylindrical structural components, circumferential heat transfer can be neglected due to symmetry. The formula for calculating the thermal resistance of hollow cylindrical structural components is as follows:

[0061] For hollow cylindrical components without a heat source, including housings and end caps, one-dimensional thermal conduction can be ignored to compensate for thermal resistance.

[0062] The formula for calculating the thermal resistance of a solid cylindrical structure is:

[0063] in R Indicates the radius of a solid cylinder; Contact thermal resistance includes the contact between the housing and the stator core, the rotor and the shaft, the shaft and the bearing, the bearing and the end cover, and the end cover and the housing. The formula for calculating contact thermal resistance is:

[0064] in, The contact gap length, For the thermal conductivity of the contact gap, This refers to the contact area.

[0065] The formulas for calculating the heat capacity of each component of the motor are as follows:

[0066] in, For the specific heat capacity of motor components, For the mass density of motor components, This refers to the volume of the motor components.

[0067] Connect the thermal nodes of each component to establish a complete three-dimensional thermal network, such as... Figure 5 As shown.

[0068] Step S3: Introduce the heat loss as a heat source into the three-dimensional thermal network, and solve the steady-state equation of the thermal nodes to obtain the average temperature and boundary temperature of each component.

[0069] In step S3, based on the idea of ​​thermoelectric analogy, the nodal voltage method is used to solve for the average temperature of each component node in the thermal network. The thermal network equation is as follows:

[0070] in, Represents the thermal conductivity matrix. Represents the node temperature rise matrix. This represents the node heat source matrix.

[0071] The thermal conductivity matrix is ​​expressed as follows:

[0072] in, This represents the thermal conductance between node i and node j, where n is the number of nodes in the thermal network.

[0073] Step S4: Establish a three-dimensional subdomain temperature field model of the heat source components, which include the stator, rotor, windings, and bearings. The equivalent thermal nodes of the heat source components are called heat source nodes. Substitute the convective heat transfer coefficient obtained in S1 and the boundary temperature obtained in S3 as boundary conditions into the three-dimensional subdomain temperature field model, and use the finite difference algorithm to solve for the three-dimensional temperature distribution and average temperature of the heat source components.

[0074] In step S4, the subdomain temperature field is solved using the finite difference algorithm. Specifically, the steady-state heat conduction equation for the subdomain temperature field in cylindrical coordinates is:

[0075] in, r Represents radial coordinates, T Represents the three-dimensional temperature distribution. Indicates the heat source; The subdomain heat conduction equation is discretized as follows:

[0076] Where i, j, and k represent the node indices in the radial, circumferential, and axial directions, respectively.

[0077] For the temperature boundary, the boundary conditions are:

[0078] For a convective heat transfer boundary, the boundary equation is expressed as:

[0079] in, Indicates the thermal conductivity of air. This represents the heat transfer coefficient between fluid-structure interaction surfaces. Indicates air temperature.

[0080] The discrete equations for the convective heat transfer boundary can be obtained using the central difference algorithm:

[0081] The three-dimensional temperature field distribution of the subdomain can be obtained by substituting the discretized boundary conditions into the discretized equation of the subdomain.

[0082] Step S5: Calculate the error between the average temperature of S3 and the average value of the three-dimensional temperature distribution of S4. When the error does not meet the accuracy requirements, introduce the average temperature compensation thermal resistance into the heat source node in the three-dimensional thermal network of S2, and repeat steps S3-S5 to dynamically correct the average temperature compensation thermal resistance until the accuracy meets the requirements.

[0083] In step S5, the average temperature error expressions obtained by the two algorithms are as follows:

[0084] The formula for calculating the average temperature-compensated thermal resistance correction is expressed as follows:

[0085] in, , These represent the average component temperatures obtained by the subdomain method and the thermal network method, respectively. This indicates component wear and tear.

[0086] Step S6: Calculate the error between the average temperature obtained from the dynamic heat network in S5 and the calculated temperature of the heat source. If the error does not meet the accuracy requirements, correct the calculated temperature of the heat source and recalculate the loss. Repeat steps S3-S6 until the error accuracy meets the requirements.

[0087] In step S6, for synchronous reluctance motors, temperature has a significant impact on winding copper losses; therefore, only the change in copper losses is considered during the magnetothermal coupling iteration process. The formula for calculating winding copper losses considering temperature effects is:

[0088] in, Indicates the number of phases of the motor. Indicates phase current, Indicates the initial temperature The phase resistance below, This represents the temperature coefficient of resistance of the winding conductor. This represents the winding temperature obtained through magnetothermal coupling iteration.

[0089] Step S7: Use the three-dimensional temperature distribution calculated in S4 to determine the maximum temperature of the heat source component, and introduce the maximum temperature compensation thermal resistance based on the three-dimensional thermal network in S2 to obtain the maximum temperature thermal network; solve the transient equation of the thermal node to obtain the maximum temperature transient temperature rise curve and the average temperature transient temperature rise curve of each component after magnetothermal coupling.

[0090] In step S7, the formula for calculating the maximum temperature-compensated thermal resistance is expressed as follows:

[0091] in, This represents the maximum temperature of the component obtained by the subdomain method.

[0092] The heat network after introducing maximum temperature compensation thermal resistance is as follows: Figure 6 As shown.

[0093] The state-space method is used to solve the transient equations of hot nodes. Specifically, the temperature of the node with heat capacity is called the state variable. thermal capacity matrix Node temperatures that do not have heat capacity are called non-state variables. This allows the nodal admittance matrix to be divided into blocks, represented as:

[0094] The equation of state for the heat capacity node temperature and the non-heat capacity node temperature is expressed as:

[0095] The transient solution equation for the state variable, namely the temperature at the heat capacity node, is derived as follows:

[0096] The transient temperature rise curve of the node can be obtained by solving the transient equation for the temperature of the heat capacity node.

[0097] Figure 7 This is a comparison between the average and maximum transient temperature rise curves of the slot windings calculated under rated operating conditions in the embodiments provided by the present invention and the prediction results of commercial software. Figure 8 This figure compares the steady-state average temperature and maximum temperature calculated by the thermal network under rated operating conditions in the embodiments provided by the present invention with the prediction results of commercial software. As can be seen from the figure, the transient temperature rise curve obtained by the dynamic thermal network has a high degree of agreement with the temperature rise curve obtained by the commercial software, the steady-state temperature calculation error is within 3%, and the temperature prediction accuracy is high.

[0098] Table 1 below compares the calculation time for a single temperature field using the dynamic thermal network model and the finite element method. As can be seen from Table 1, the calculation speed of the dynamic thermal network method is significantly faster than that of the finite element method.

[0099] Table 1

[0100] In summary, the fast calculation method for magnetothermal coupling of synchronous reluctance motors based on dynamic thermal networks proposed in this invention significantly improves the calculation speed of magnetothermal coupling iteration while ensuring calculation accuracy. It will be readily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fast calculation method for magnetothermal coupling of a synchronous reluctance motor based on a dynamic thermal network, characterized in that, The method includes: S1. Initialize the temperature of each component of the motor, import the initial temperature into the finite element electromagnetic field model to calculate the motor loss, and import the loss into the fluid-structure interaction finite element model to determine the convective heat transfer coefficient of the fluid-structure interaction surface in the motor. S2. Based on the actual structural characteristics of the synchronous reluctance motor, perform geometric equivalent processing and thermal node division, calculate the three-dimensional conductive thermal resistance of the stator, rotor, winding, shaft, bearing, end cover and housing, the contact thermal resistance between different components, the convective thermal resistance of the fluid-structure interaction surface and the heat capacity of each component, connect the thermal nodes of each component and establish a complete three-dimensional thermal network. S3. Introduce the heat loss as a heat source into the three-dimensional thermal network, and solve the steady-state equation of the thermal nodes to obtain the average temperature and boundary temperature of each component; S4. Establish a three-dimensional subdomain temperature field model of the heat source components, which include the stator, rotor, windings and bearings. The equivalent thermal nodes of the heat source components are called heat source nodes. Substitute the convective heat transfer coefficient obtained in S1 and the boundary temperature obtained in S3 as boundary conditions into the three-dimensional subdomain temperature field model to solve for the three-dimensional temperature distribution of the heat source components. S5. Calculate the error between the average temperature of S3 and the average value of the three-dimensional temperature distribution of S4. When the error does not meet the accuracy requirements, introduce the average temperature compensation thermal resistance into the heat source node in the three-dimensional thermal network of S2, and repeat steps S3-S5 to dynamically correct the average temperature compensation thermal resistance until the accuracy meets the requirements. S6. Calculate the error between the average temperature obtained in S5 and the calculated temperature of the heat source. If the error does not meet the accuracy requirements, correct the calculated temperature of the heat source and recalculate the loss. Repeat steps S3-S6 until the error accuracy meets the requirements. S7. Using the three-dimensional temperature distribution calculated in S4, determine the maximum temperature of the heat source component, and introduce the maximum temperature compensation thermal resistance based on the three-dimensional thermal network in S2 to obtain the maximum temperature thermal network; solve the transient equations of the thermal nodes to obtain the maximum temperature transient temperature rise curves and average temperature transient temperature rise curves of each component after magnetothermal coupling.

2. The method as described in claim 1, characterized in that, In step S2, the method for establishing a complete three-dimensional heat network is as follows: (1) Perform geometric equivalence and thermal node division of components. The slot winding and end winding are equivalent to homogenized solids with anisotropic thermal conductivity. The formula for calculating their anisotropic thermal conductivity is as follows: in, , These represent the thermal conductivity of the insulating material and the copper wire, respectively. Indicates the fill factor of the bare copper slot. , , These represent the radial thermal conductivity, circumferential thermal conductivity, and axial thermal conductivity of the homogenized solid, respectively. The equivalent homogenized solid in the slot and the stator teeth are equivalent to tile-shaped structures; the housing, stator yoke, end winding homogenized solid, outer rotor core, inner rotor core, bearings and end cover are equivalent to hollow cylindrical structures; the shaft is equivalent to a solid cylindrical structure. (2) Calculate the conductive thermal resistance, contact thermal resistance, convective thermal resistance, and heat capacity. The formula for calculating the thermal resistance of the tile structure is as follows: in , , These represent the axial, radial, and circumferential thermal conductivity, respectively. , These represent the outer diameter and the inner diameter, respectively. Indicates axial length. Indicates the circumferential angle of the tile structure. , , These represent the axial, radial, and circumferential thermal resistances, respectively. , , These represent the one-dimensional thermal conduction compensation thermal resistance of the axial, radial, and circumferential heat source nodes, respectively. The formula for calculating the thermal resistance of a solid cylindrical structure is: in R Indicates the radius of a solid cylinder; The formula for calculating contact thermal resistance is: in, The contact gap length, For the thermal conductivity of the contact gap, Contact area; The formulas for calculating the heat capacity of each component of the motor are as follows: in, For the specific heat capacity of motor components, For the mass density of motor components, This refers to the volume of the motor components; (3) Connect the hot nodes through contact thermal resistance and convection thermal resistance to obtain a complete three-dimensional thermal network of synchronous reluctance motor.

3. The method as described in claim 1, characterized in that, In step S3, the steady-state solution equation for the hot node is: in, Represents the thermal conductivity matrix. Represents the node temperature rise matrix. This represents the node heat source matrix.

4. The method as described in claim 2, characterized in that, In step S4, the finite difference algorithm is used to solve the three-dimensional subdomain temperature field model. The steady-state heat conduction equation of the subdomain temperature field in cylindrical coordinates is: in, r Represents radial coordinates, T Represents the three-dimensional temperature distribution. Indicates the heat source; The subdomain heat conduction equation is discretized as follows: Substituting the convective heat transfer boundary and the temperature boundary, the three-dimensional subdomain temperature field distribution can be obtained, where i, j, and k represent the node indices in the radial, circumferential, and axial directions, respectively.

5. The method as described in claim 1, characterized in that, In step S5, the formula for calculating the average temperature compensation thermal resistance of the heat source node is expressed as follows: in, , These represent the average component temperatures obtained by the subdomain method and the thermal network method, respectively. This indicates component wear and tear.

6. The method as described in claim 1, characterized in that, In step S6, for a synchronous reluctance motor, the formula for calculating winding copper losses considering temperature effects is: in, Indicates the number of phases of the motor. Indicates phase current, Indicates the initial temperature The phase resistance below, This represents the temperature coefficient of resistance of the winding conductor. This represents the winding temperature obtained through magnetothermal coupling iteration.

7. The method as described in claim 5, characterized in that, In step S7, the formula for calculating the maximum temperature-compensated thermal resistance is: in, This represents the maximum temperature of the component obtained by the subdomain method. The transient equations of the hot nodes are solved using the state-space method: heat capacity matrix The node temperature with heat capacity is called the state variable. Node temperatures that do not have heat capacity are called non-state variables. This allows for the block representation of the nodal admittance matrix: The equation of state for the heat capacity node temperature and the non-heat capacity node temperature is expressed as: The transient solution equation for the state variable, namely the temperature at the heat capacity node, is derived as follows: 。

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