Method and system for calculating the equivalent thermal conductivity of an electric propulsion motor winding

Abstract

The application discloses a kind of equivalent thermal conductivity calculation method and system of electric propulsion motor winding, it is related to electric propulsion motor temperature field calculation field, wherein the equivalent thermal conductivity calculation method of electric propulsion motor winding includes the following steps: according to the arrangement state of entire winding in electric propulsion motor in slot, winding is divided into multiple unit circular structure;Establish the Laplace equation of the temperature of insulating layer subdomain in multiple unit circular structure, and the Poisson equation of the temperature of winding layer subdomain;According to the boundary condition in multiple unit circular structure, the temperature rise of each subdomain is solved, and the total temperature rise of multiple unit circular structure is solved, the entire winding is equivalent to circular heating body, and the total temperature rise of multiple unit circular structure is taken as the temperature rise of circular heating body;Equivalent thermal conductivity of entire winding is calculated.The winding equivalent model based on the analytical method proposed in the application obtains more accurate winding temperature;The method also provides a reference for temperature solution of other types of motor.

Description

Technical Field

[0001] This invention relates to the field of temperature field calculation for electric propulsion motors, specifically to a method and system for calculating the equivalent thermal conductivity of electric propulsion motor windings. Background Technology

[0002] Electric propulsion motors require high power density, but high-power-density motors have small heat dissipation areas, leading to concentrated heat generation. Motor losses primarily accumulate in the windings, resulting in large temperature gradients within the slots and threatening the winding insulation. Winding temperature directly affects motor lifespan, and consequently, the safety of electric aircraft. Therefore, accurate calculation of winding temperature is crucial.

[0003] There are many methods for calculating winding temperature, which can be divided into two categories: the thermal circuit method and the finite element method (FEM). Compared to the thermal circuit method, the FEM can obtain the temperature distribution of the winding and describe the winding temperature more accurately. However, the calculation accuracy of the FEM is related to the level of refinement of the winding model. Real windings are unevenly distributed and have no discernible pattern, making it difficult to establish a winding temperature field model that accurately reflects the actual situation. To facilitate calculation, an equivalent winding model is usually used to solve this problem. However, the traditional equivalent winding model treats the winding as an insulation layer and a winding layer. This method has low refinement, and the simulated temperature rise is concentrated on the insulation layer. It not only fails to reflect the temperature gradient from the slot core to the slot wall but also overestimates the calculated winding temperature, making it unsuitable for high-power-density motors. An accurate temperature field winding model requires a reasonable configuration of the model structure to accurately reflect the winding temperature gradient; on the other hand, it requires refined calculation of the thermal conductivity. Therefore, research on the thermal equivalent model of the winding of an electric propulsion motor for electric aircraft has significant practical value. Summary of the Invention

[0004] To address the problem of inaccurate calculation results from the traditional equivalent model of temperature field windings mentioned in the background art, this invention proposes a method and system for calculating the equivalent thermal conductivity of electric propulsion motor windings.

[0005] This invention provides a method for calculating the equivalent thermal conductivity of an electric propulsion motor winding, comprising the following steps:

[0006] Based on the arrangement of the entire winding in the slot in the electric propulsion motor, the winding is divided into a multi-unit circular structure. Each unit consists of an insulation layer and a winding layer, and the insulation layer and winding layer in each unit are a subdomain.

[0007] In the polar coordinate system, thermal differential equations are established for the multi-unit circular structure, namely, the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain.

[0008] Based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of the various subdomains in the multi-unit circular structure, the thermal differential equation of the multi-unit circular structure is solved to obtain the temperature rise of each subdomain.

[0009] The total temperature rise of the multi-unit circular structure is calculated based on the temperature rise of each subdomain. The entire winding is equivalent to a circular heating element, and the total temperature rise of the multi-unit circular structure is taken as the temperature rise of the circular heating element.

[0010] The equivalent thermal conductivity of the entire winding is calculated based on the temperature rise of the circular heating element.

[0011] Furthermore, the formula for calculating the number of units in the multi-unit circular structure is as follows:

[0012]

[0013] Where n is the number of units;

[0014] A w The area of ​​the bare wire is expressed as:

[0015]

[0016] Where t w t represents the winding layer thickness. i This refers to the winding layer thickness.

[0017] Where the winding layer thickness t w Insulation layer thickness t i The relationship between the number of units n and the number of units can be expressed as:

[0018] n(t w +t i ) = r n,2 (3)

[0019] Where r n,2 Let n be the outer diameter of the nth insulating layer, and its expression is:

[0020]

[0021] Where A s It is the area of ​​the groove.

[0022] Furthermore, the Laplace equation for the temperature of the established insulating subdomain is expressed as follows:

[0023]

[0024] The expression for the Poisson equation of the temperature of the winding layer subdomain is as follows:

[0025]

[0026] Where T is temperature; q is heat flux density; and λ is thermal conductivity.

[0027] Furthermore, based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of the various subdomains in the multi-unit circular structure, the thermal differential equation of the multi-unit circular structure is solved to obtain the temperature rise of each subdomain, including:

[0028] Solve for the temperature rise T of the nth winding layer subdomain. n,1 'and heat φ n,1 Their expressions are as follows:

[0029]

[0030] Where T n-1,2 ' represents the temperature rise of the insulating subdomain of the (n-1)th unit;

[0031] λ n,1 Let be the thermal conductivity of the winding layer of the nth unit;

[0032] r i,j The radius of the winding layer j=1 or the insulation layer j=2 of the i-th unit;

[0033] L is the axial length of the motor core;

[0034] r n,1 The radius of the winding layer of the nth unit;

[0035] r n-1,2 The radius of the insulating layer of the (n-1)th unit;

[0036] Solve for the temperature rise T of the nth insulating subdomain. n,2 'and heat φ n,2 Their expressions are as follows:

[0037]

[0038] Where r n,2 Let be the radius of the insulating layer of the nth unit;

[0039] λ n,2 Let be the thermal conductivity of the insulating layer of the nth unit.

[0040] Furthermore, the step of calculating the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain includes:

[0041] The total temperature rise of the multi-unit circular structure can be calculated using the following expression:

[0042]

[0043] Where T0' is the temperature at the center of the circle;

[0044] λ i,j Let be the thermal conductivity of the winding layer j=1 or the insulation layer j=2 of the i-th unit;

[0045] r k,p Let be the radius of the winding layer p=1 or the insulation layer p=2 of the k-th unit.

[0046] Furthermore, the calculation of the equivalent thermal conductivity of the entire winding based on the temperature rise of the circular heating element includes:

[0047] The expression for the temperature rise of the circular heating element is:

[0048]

[0049] Where λ e The equivalent thermal conductivity of the circular heating element;

[0050] q e The heat flux density of the heating element is expressed as:

[0051]

[0052] Based on the total temperature rise expression (9) for the multi-unit circular structure and the temperature rise expression (10) for the circular heating element, the equivalent thermal conductivity of the entire winding is calculated as follows:

[0053]

[0054] Y is an intermediate variable.

[0055] This invention provides a system for calculating the equivalent thermal conductivity of an electric propulsion motor winding, comprising:

[0056] The layered structure construction module is used to divide the winding into a multi-unit circular structure according to the arrangement of the entire winding in the slot in the electric propulsion motor. Each unit consists of an insulation layer and a winding layer, and the insulation layer and winding layer in each unit are a subdomain.

[0057] The temperature equation establishment module is used to establish thermal differential equations for multi-unit circular structures in polar coordinates, namely, to establish the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain.

[0058] The thermal resistance and temperature rise solution module is used to solve the thermal differential equation of the multi-unit circular structure based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interface of each subdomain in the multi-unit circular structure, and to obtain the temperature rise of each subdomain.

[0059] The equivalent thermal conductivity calculation module is used to calculate the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain. The entire winding is equivalent to a circular heating element, and the total temperature rise of the multi-unit circular structure is taken as the temperature rise of the circular heating element. Based on the temperature rise of the circular heating element, the equivalent thermal conductivity of the entire winding is calculated.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] This invention proposes a method and system for calculating the equivalent thermal conductivity of an electric propulsion motor winding. The method first divides the winding into multiple layers, solves for the thermal resistance and temperature rise of each layer using thermal differential equations, and then treats the winding as a single heating element. Using the results of the layered solution, the equivalent thermal conductivity of the heating element is calculated, thereby establishing a thermal equivalent model of the motor winding. By treating the winding as a single heating element, the number of subdivision units is reduced, improving calculation speed. Furthermore, the winding equivalent model based on analytical methods proposed in this invention provides more accurate winding temperature results. The proposed method also provides a reference for temperature calculation in other types of motors. Attached Figure Description

[0062] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0063] Figure 1 This is a flowchart illustrating a method for calculating the equivalent thermal conductivity of an electric propulsion motor winding, as proposed in this invention.

[0064] Figure 2 This is a schematic diagram of the solution process for the calculation method of the equivalent thermal conductivity of the winding of an electric propulsion motor proposed in this invention.

[0065] Figure 3 This is a schematic diagram of the region division of the entire winding in an electric propulsion motor, based on the method for calculating the equivalent thermal conductivity of the winding of an electric propulsion motor proposed in this invention. Detailed Implementation

[0066] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. However, it should be understood that the scope of protection of the present invention is not limited to the specific implementation.

[0067] Example 1

[0068] like Figure 1-3 As shown, the present invention provides a method for calculating the equivalent thermal conductivity of an electric propulsion motor winding, comprising the following steps:

[0069] Step S1: Based on the arrangement of the entire winding in the slot in the electric propulsion motor, the winding is divided into a multi-unit circular structure. Each unit consists of an insulation layer and a winding layer. The insulation layer and the winding layer in each unit are a subdomain.

[0070] Step S2: In the polar coordinate system, establish the thermal differential equation for the multi-unit circular structure, that is, establish the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain.

[0071] Step S3: Based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of each subdomain in the multi-unit circular structure, solve the thermal differential equation of the multi-unit circular structure to obtain the temperature rise of each subdomain.

[0072] Step S4: Solve for the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain. Treat the entire winding as an equivalent circular heating element and take the total temperature rise of the multi-unit circular structure as the temperature rise of the circular heating element. Calculate the equivalent thermal conductivity of the entire winding based on the thermal resistance and temperature rise of the circular heating element.

[0073] In step S1, the formula for calculating the number of units in the multi-unit circular structure is:

[0074]

[0075] Where n is the number of units;

[0076] A w The area of ​​the bare wire is expressed as:

[0077]

[0078] Where t w t represents the winding layer thickness. i This refers to the winding layer thickness.

[0079] Where the winding layer thickness t w Insulation layer thickness t i The relationship between the number of units n and the number of units can be expressed as:

[0080] n(t w +t i ) = r n,2 (3)

[0081] Where r n,2 Let n be the outer diameter of the nth insulating layer, and its expression is:

[0082]

[0083] Where A s It is the area of ​​the groove.

[0084] In step S2, the Laplace equation for the temperature of the established insulating subdomain is expressed as follows:

[0085]

[0086] The expression for the Poisson equation of temperature in the winding layer subdomain is as follows:

[0087]

[0088] Where T is temperature; q is heat flux density; and λ is thermal conductivity.

[0089] In step S3, based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of each subdomain in the multi-unit circular structure, the thermal differential equation of the multi-unit circular structure is solved to obtain the temperature rise of each subdomain, including:

[0090] Solve for the temperature rise T of the nth winding layer subdomain. n,1 'and thermal resistance φ n,1 Their expressions are as follows:

[0091]

[0092] Where T n-1,2 ' represents the temperature rise of the insulating subdomain of the (n-1)th unit;

[0093] λ n,1 Let be the thermal conductivity of the winding layer of the nth unit;

[0094] r i,j The radius of the winding layer j=1 or the insulation layer j=2 of the i-th unit;

[0095] L is the axial length of the motor core;

[0096] r n,1 The radius of the winding layer of the nth unit;

[0097] r n-1,2 The radius of the insulating layer of the (n-1)th unit;

[0098] Solve for the temperature rise T of the nth insulating subdomain. n,2 'and thermal resistance φ n,2 Their expressions are as follows:

[0099]

[0100] Where r n,2 Let be the radius of the insulating layer of the nth unit;

[0101] λ n,2 Let be the thermal conductivity of the insulating layer of the nth unit.

[0102] In step S4, the total temperature rise of the multi-unit circular structure is calculated based on the temperature rise of each subdomain, including: calculating the total temperature rise of the multi-unit circular structure, the expression of which is:

[0103]

[0104] Among them, the temperature of the center of circle T0';

[0105] λ i,j Let be the thermal conductivity of the winding layer j=1 or the insulation layer j=2 of the i-th unit;

[0106] r k,p Let be the radius of the winding layer p=1 or the insulation layer p=2 of the k-th unit.

[0107] Based on the temperature rise of the circular heating element, the equivalent thermal conductivity of the entire winding is calculated, including:

[0108] The expression for the temperature rise of the circular heating element is:

[0109]

[0110] Where λ e The equivalent thermal conductivity of the circular heating element;

[0111] q e The heat flux density of the heating element is expressed as:

[0112]

[0113] Based on the total temperature rise expression (9) for the multi-unit circular structure and the temperature rise expression (10) for the circular heating element, the equivalent thermal conductivity of the entire winding is calculated as follows:

[0114]

[0115] Y is an intermediate variable.

[0116] Example 2

[0117] This invention provides a system for calculating the equivalent thermal conductivity of an electric propulsion motor winding, comprising:

[0118] The layered structure construction module is used to divide the winding into a multi-unit circular structure according to the arrangement of the entire winding in the slot in the electric propulsion motor. Each unit consists of an insulation layer and a winding layer, and the insulation layer and winding layer in each unit are a subdomain.

[0119] The temperature equation establishment module is used to establish thermal differential equations for multi-unit circular structures in polar coordinates, namely, to establish the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain.

[0120] The thermal resistance and temperature rise solution module is used to solve the thermal differential equation of the multi-unit circular structure based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interface of each subdomain in the multi-unit circular structure, and to obtain the temperature rise of each subdomain.

[0121] The equivalent thermal conductivity calculation module is used to calculate the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain. The entire winding is equivalent to a circular heating element, and the total temperature rise of the multi-unit circular structure is taken as the temperature rise of the circular heating element. Based on the temperature rise of the circular heating element, the equivalent thermal conductivity of the entire winding is calculated.

[0122] Finally, it should be noted that the above-disclosed embodiment is only one specific embodiment of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for calculating the equivalent thermal conductivity of an electric propulsion motor winding, characterized in that, Includes the following steps: Based on the arrangement of the entire winding in the slot in the electric propulsion motor, the winding is divided into a multi-unit circular structure. Each unit consists of an insulation layer and a winding layer, and the insulation layer and winding layer in each unit are a subdomain. In the polar coordinate system, thermal differential equations are established for the multi-unit circular structure, namely, the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain. Based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of the various subdomains in the multi-unit circular structure, the thermal differential equation of the multi-unit circular structure is solved to obtain the temperature rise of each subdomain. The total temperature rise of the multi-unit circular structure is calculated based on the temperature rise of each subdomain. The entire winding is equivalent to a circular heating element, and the total temperature rise of the multi-unit circular structure is taken as the temperature rise of the circular heating element. The equivalent thermal conductivity of the entire winding is calculated based on the temperature rise of the circular heating element. The formula for calculating the number of units in the multi-unit circular structure is as follows: （1） in, n Number of units; A w The area of ​​the bare wire is expressed as: （2） in tw This refers to the winding layer thickness; ti This refers to the thickness of the insulation layer. Among them, the winding layer thickness tw Insulation layer thickness ti With unit number n The relationship between them can be represented as: （3） in rn, 2 is the first n The outer diameter of each insulating layer is expressed as follows: （4） in A s It is the area of ​​the groove.

2. The method for calculating the equivalent thermal conductivity of an electric propulsion motor winding according to claim 1, characterized in that: The Laplace equation for the temperature of the established insulating subdomain is expressed as follows: （5） The expression for the Poisson equation of the temperature of the winding layer subdomain is as follows: （6） in T For temperature; q Heat flux density; λ is the thermal conductivity.

3. The method for calculating the equivalent thermal conductivity of an electric propulsion motor winding according to claim 2, characterized in that: Based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interfaces of the various subdomains in the multi-unit circular structure, the thermal differential equation of the multi-unit circular structure is solved to obtain the temperature rise of each subdomain, including: Solve the first n Temperature rise of each winding layer subdomain Tn ,1 ' and calories Their expressions are as follows: （7） in Tn -1,2 ' For the first n -1 unit of insulation layer subdomain temperature rise; λn ,1 is the first n Thermal conductivity of the winding layer of the unit; ri , j is No. i Unit winding layer j =1 or insulation layer j =2 radius; L This refers to the axial length of the motor core. rn ,1 is the first n The radius of the winding layer of each unit; rn -1,2 is the first n -1 unit radius of the insulation layer; Solve the first n Temperature rise of each insulating subdomain Tn ,2 ' and calories Their expressions are as follows: （8） in rn ,2 is the first n The radius of the insulating layer of each unit; λ n,2 For the first n The thermal conductivity of the unit's insulating layer.

4. The method for calculating the equivalent thermal conductivity of an electric propulsion motor winding according to claim 3, characterized in that: The method of calculating the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain includes: The total temperature rise of the multi-unit circular structure can be calculated using the following expression: （9） in T 0 ' Temperature at the center; λ i,j For the first i Unit winding layer j =1 or insulation layer j Thermal conductivity = 2; r k,p For the first k Unit winding layer p =1 or insulation layer p =2 radius.

5. The method for calculating the equivalent thermal conductivity of an electric propulsion motor winding according to claim 4, characterized in that: The calculation of the equivalent thermal conductivity of the entire winding based on the temperature rise of the circular heating element includes: The expression for the temperature rise of the circular heating element is: （10） in λe The equivalent thermal conductivity of the circular heating element; q e The heat flux density of the heating element is expressed as: （11） Based on the total temperature rise expression (9) for the multi-unit circular structure and the temperature rise expression (10) for the circular heating element, the equivalent thermal conductivity of the entire winding is calculated as follows: （12） in Y It is an intermediate variable.

6. A system for calculating the equivalent thermal conductivity of an electric propulsion motor winding, characterized in that, include: The layered structure construction module is used to divide the winding into a multi-unit circular structure according to the arrangement of the entire winding in the slot in the electric propulsion motor. Each unit consists of an insulation layer and a winding layer, and the insulation layer and winding layer in each unit are a subdomain. The temperature equation establishment module is used to establish thermal differential equations for multi-unit circular structures in polar coordinates, namely, to establish the Laplace equation for the temperature of the insulation layer subdomain and the Poisson equation for the temperature of the winding layer subdomain. The thermal resistance and temperature rise solution module is used to solve the thermal differential equation of the multi-unit circular structure based on the boundary conditions that the heat flow and radial temperature gradient are equal at the interface of each subdomain in the multi-unit circular structure, and to obtain the temperature rise of each subdomain. The equivalent thermal conductivity calculation module is used to calculate the total temperature rise of the multi-unit circular structure based on the temperature rise of each subdomain. The entire winding is equivalent to a circular heating element, and the total temperature rise of the multi-unit circular structure is taken as the temperature rise of the circular heating element. Based on the temperature rise of the circular heating element, the equivalent thermal conductivity of the entire winding is calculated. The formula for calculating the number of units in the multi-unit circular structure is as follows: （1） in, n Number of units; A w The area of ​​the bare wire is expressed as: （2） in tw This refers to the winding layer thickness. ti The thickness of the insulation layer; Among them, the winding layer thickness tw Insulation layer thickness ti With unit number n The relationship between them can be represented as: （3） in rn, 2 is the first n The outer diameter of each insulating layer is expressed as follows: （4） in A s It is the area of ​​the groove.

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