Method for optimizing a magnetic levitation track structure and use thereof

Abstract

The application relates to the technical field of magnetic suspension track optimization, and discloses a magnetic suspension track structure optimization method and application, which comprises the following steps: (A) analyzing the force conditions of a vehicle-mounted magnet and a magnetic track magnet, and establishing a mechanical expression of a magnetic suspension force; the structure of the magnet is a Halbach array; (B) adopting a quantitative analysis method and / or a coupling optimization method to analyze and obtain the numerical value of w when the maximum value is taken; or the numerical value of z when the maximum value is taken; or the numerical value of y when the maximum value is taken; or the numerical value of d when the maximum value is taken; the numerical values of w, z, y and d obtained are optimization values. The method can optimize the permanent magnetic suspension track structure size, improve the suspension efficiency of rare earth permanent magnet materials, and thus reduce the suspension cost of the permanent magnetic suspension or superconducting magnetic suspension.

Description

Technical Field

[0001] This invention relates to the field of magnetic levitation track optimization technology, specifically to an optimization method and application for magnetic levitation track structure. Background Technology

[0002] Maglev rail transit technology is an important direction for the future development of rail transit technology. Its characteristic of no mechanical contact, with friction primarily arising from air resistance, makes ultra-high speeds possible for maglev trains. Currently, conventional electromagnetic levitation (EMS) and electro-hydraulic levitation (EDS) are the two most mature levitation modes for maglev rail transit. However, EMS suffers from high levitation energy consumption, and EDS cannot achieve levitation operation at static or low speeds, significantly hindering the further development of maglev rail transit technology. Adopting permanent magnet levitation or hybrid levitation modes is an important approach to solving the problems of high energy consumption in conventional electromagnetic levitation and the inability of electro-hydraulic levitation to achieve low-speed operation. Against this backdrop, several new levitation modes have been proposed, namely permanent magnet levitation (PMS) and high-temperature superconducting levitation (HTSCM). Compared with EMS and EDS, PMS and HTSCM have advantages such as low levitation energy consumption, static levitation capability, and low operation and maintenance costs.

[0003] Permanent magnet tracks are a crucial component of PMS and HTSCM technologies, both requiring permanent magnet levitation tracks to provide fundamental levitation force. The Halbach array is a novel type of permanent magnet array where different magnetization directions are arranged in a specific order, resulting in a more concentrated magnetic field—a significant increase in magnetic field strength on one side and a significant decrease on the other. Figure 1 As shown, Halbach arrays have important applications in the field of magnetic levitation. The emergence of Halbach arrays and the invention of powerful permanent magnets have made permanent magnet levitation and superconducting levitation possible. Neodymium iron boron (NdFeB) permanent magnets are the most commonly used permanent magnet materials in the field of magnetic levitation due to their strong magnetic force, high magnetic energy, mature technology, and relatively low cost. However, rare earth permanent magnet materials are non-renewable resources, and their prices are constantly rising. Furthermore, the levitation force generated by a Halbach-structured magnetic track is closely related to its spatial structure and geometric dimensions. How to achieve the levitation design goals (levitation gap, levitation weight) with the minimum amount of magnets is a worthwhile engineering problem to consider. Against this backdrop, optimizing the structural dimensions of permanent magnet levitation tracks to improve the levitation efficiency of rare earth permanent magnet materials (i.e., the levitation force provided per unit volume) and providing technical support for the application and promotion of permanent magnet levitation and superconducting levitation technologies has significant practical engineering implications. Summary of the Invention

[0004] The purpose of this invention is to overcome the problem of low levitation efficiency of rare earth permanent magnet materials in the existing technology, and to provide a method and application for optimizing magnetic levitation track structure. This method can improve the levitation efficiency of rare earth permanent magnet materials and provide a levitation force greater than the weight of the levied object with the fewest permanent magnets.

[0005] To achieve the above objectives, the present invention provides a method for optimizing a magnetic levitation track structure, the method comprising the following steps:

[0006] (A) Analyze the forces acting on the vehicle-mounted magnet and the magnetic track magnet, and establish a mechanical expression for the magnet's levitation force; the magnet's structure is a Halbach array, and the mechanical expression is...

[0007]

[0008]

[0009] Among them, F z B represents the levitation force of the Halbach array magnet along the z-axis. Z B represents the component of the magnetic flux density along the Z-axis. r denoted as remanence of the permanent magnet, μ0 as vacuum permeability, k as the number of wavelengths in the Halbach array magnetic group, d as the thickness of a unit magnetic block, w as the width of a unit magnetic block, z as the levitation gap between the vehicle-mounted magnet and the magnetic track magnet, n as the number of magnetic blocks per unit wavelength, m1 and m2 as magnetic induction intensity correction coefficients, and y as the length of a unit magnetic block.

[0010] (B) Analyze using quantitative analysis and / or coupled optimization methods.

[0011] Find The value of w when it reaches its maximum value; or

[0012] Find The value of z when it reaches its maximum value; or

[0013] Find The value of y when it reaches its maximum value; or

[0014] Find The value of d is taken when it reaches its maximum value; the calculated values ​​of w, z, y, and d are the optimized values.

[0015] The second aspect of this invention provides the application of the magnetic levitation track structure optimization method described in this invention in linear magnetic levitation tracks.

[0016] Through the above technical solutions, the method of the present invention can optimize the structural dimensions of permanent magnet maglev track and improve the suspension efficiency of rare earth permanent magnet materials, thereby reducing the suspension cost of permanent magnet maglev or superconducting maglev. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0018] Figure 1 This is a diagram of the magnetic field density distribution of the Halbach array;

[0019] Figure 2 This is a schematic diagram of the Halbach magnetic track levitation structure;

[0020] Figure 3 This is a diagram showing the vertical force analysis of the vehicle-mounted magnet;

[0021] Figure 4 This is a graph showing the variation of the levitation force of the vehicle-mounted magnet with the levitation air gap z.

[0022] Figure 5 This is a graph showing the variation of the levitation force of the vehicle-mounted magnet with the length y of the magnetic track.

[0023] Figure 6 This is a graph showing the variation of the levitation force of the vehicle-mounted magnet with the thickness d of the magnetic track.

[0024] Figure 7 The levitation force F generated per unit thickness of the magnet d Curve showing the variation of magnetic track thickness d;

[0025] Figure 8 This is a graph showing the variation of the levitation force of the vehicle-mounted magnet with the width w of the magnetic track.

[0026] Figure 9 The levitation force F generated per unit width of the magnet w Curve showing the variation of magnetic track thickness w;

[0027] Figure 10 This is a three-dimensional graph showing the variation of the levitation force of the vehicle-mounted magnet with the width w and thickness d of the magnetic track. Detailed Implementation

[0028] The endpoints and any values ​​of the ranges disclosed herein are not limited to the precise ranges or values, and these ranges or values ​​should be understood to include values ​​close to these ranges or values. For numerical ranges, the endpoint values ​​of the various ranges, the endpoint values ​​of the various ranges and individual point values, and individual point values ​​can be combined with each other to obtain one or more new numerical ranges, which should be considered as specifically disclosed herein.

[0029] This invention provides a method for optimizing the structure of a magnetic levitation track, the method comprising the following steps:

[0030] (A) Analyze the forces acting on the vehicle-mounted magnet and the magnetic track magnet, and establish a mechanical expression for the magnet's levitation force; the magnet's structure is a Halbach array, and the mechanical expression is...

[0031] Among them, F z B represents the levitation force of the Halbach array magnet along the z-axis. Z B represents the component of the magnetic flux density along the Z-axis. r denoted as remanence of the permanent magnet, μ0 as vacuum permeability, k as the number of wavelengths in the Halbach array magnetic group, d as the thickness of a unit magnetic block, w as the width of a unit magnetic block, z as the levitation gap between the vehicle-mounted magnet and the magnetic track magnet, n as the number of magnetic blocks per unit wavelength, m1 and m2 as magnetic induction intensity correction coefficients, and y as the length of a unit magnetic block.

[0032] (B) Analyze using quantitative analysis and / or coupled optimization methods.

[0033] Find The value of w when it reaches its maximum value; or

[0034] Find The value of z when it reaches its maximum value; or

[0035] Find The value of y when it reaches its maximum value; or

[0036] Find The value of d is taken when it reaches its maximum value; the calculated values ​​of w, z, y, and d are the optimized values.

[0037] According to a particularly preferred embodiment of the present invention, the magnet is a permanent magnet selected from one or more of neodymium iron boron magnets, samarium cobalt magnets, and permanent ferrite magnets, preferably neodymium iron boron permanent magnets.

[0038] The levitation force mechanical expression of this invention can be derived from the levitation force mathematical model, as follows:

[0039] During the magnetization process of a magnetically conductive material, the magnetization current density at any point inside the magnetized body can be expressed as:

[0040]

[0041] In equation (1), The current density of the magnetized permanent magnet. The magnetization intensity of the magnetized permanent magnet. This is the symbol for curl calculation.

[0042] During the magnetization process of a permanent magnet, the magnetization intensity is usually constant, therefore the current density of the magnetized body is zero. At the boundary between the interior of the permanent magnet and the external vacuum region, there is a difference in magnetization intensity, resulting in a surface current of a certain intensity at the boundary. The surface current density can be expressed as…

[0043]

[0044] In equation (2), The surface current density of the magnetized body. It is the normal vector pointing to the vacuum position.

[0045]

[0046] In equation (3), μ0 is the free permeability, μ0 = 4π × 10 -7 H / m, μ r The relative permeability of the medium in a permanent magnet. is the magnetic field strength vector.

[0047] The magnetic force exerted by an airborne magnetic field on a magnetically conductive material within that field can be expressed as:

[0048]

[0049] In equation (4), V is the magnetic force exerted by the air magnetic field on the magnetically conductive material within the magnetic field, V is the volume of the suspended magnetically conductive material, and S is the surface area of ​​the magnetized current.

[0050] Substituting equation (3) into equation (4) and performing vector operations, we get

[0051]

[0052] Equation (5) can be obtained by using the vector gradient integral formula.

[0053]

[0054] The permanent magnet described in this invention has a Halbach array structure. According to the research results in the literature (Peng Shuhua, Li Huade. Sliding mode variable structure control of electric servo motors with uncertain parameters [J]. Journal of Electrical Machines and Control, 2009, 13(1):128-132.), the reinforcing side magnetic induction intensity of the Halbach array permanent magnet assembly can be expressed as:

[0055]

[0056] In equation (7), B r (take B) r=1.35T) is the remanence of the permanent magnet, k is the number of wavelengths in the Halbach array magnetic group, k = 2π / λ, λ is the wavelength of the permanent magnet, and λ = nw, that is, k = 2π / (nw), n is the number of magnetic blocks per unit wavelength, z is the levitation gap between the vehicle magnet and the magnetic track magnet, m1 and m2 are both magnetic induction intensity correction coefficients, taken as m1 = 1.732, m2 = 0.500, B0 is the magnetic induction intensity on the reinforced side, B x To enhance the lateral magnetic flux density along the X-axis component of the Halbach array, B z The component of the lateral magnetic induction intensity along the Z-axis is enhanced for the Halbach array.

[0057] In practical engineering applications, to maintain the integrity of the Halbach array wavelength, an additional unit magnetic block is usually added to the end of the array, making the total width of the array (n+1)w. Combining equations (6) and (7), the levitation force along the z-axis on the reinforced side of the array can be calculated as follows:

[0058]

[0059] In equation (8), F z To enhance the levitation force along the z-axis of the Halbach array magnet, d is the thickness of the unit magnet, w is the width of the unit magnet, and y is the length of the unit magnet.

[0060] That is, equation (8) is the mechanical expression in step (A) of the present invention.

[0061] In this invention, n is a positive integer greater than or equal to 2, preferably 2, 4, or 6.

[0062] In equation (8), when n = 4, the levitation force expressions for the 5 Halbach array levitation systems can be obtained as follows:

[0063]

[0064] When n=2, the levitation force expressions for the three Halbach array levitation systems can be obtained as follows:

[0065]

[0066] When n=6, the levitation force expression for the 7 Halbach array levitation systems can be obtained as follows:

[0067]

[0068] According to equation (9), the magnitude of the levitation force is related not only to the material of the permanent magnet itself, but also to the thickness, width, length of the permanent magnet, and the levitation gap between the vehicle magnet and the magnetic track magnet.

[0069] The quantitative analysis method of this invention includes the following steps: using one of the parameters z, w, d, or y as a variable, fixing the other parameters, and substituting them into the mechanical expression to obtain... The value of w when it reaches its maximum value; or calculate the value of w. The value of z when it reaches its maximum value; or find the value of z. The value of y when it reaches its maximum value; or calculate the value of y. The value of d when the maximum value is reached.

[0070] According to a particularly preferred embodiment of the present invention, the quantitative analysis method includes the following steps: fixing z as z0, y as y0, and w as w0, and calculating... Find the value of d when it reaches its maximum value; or fix z as z0, y as y0, and d as d0, and calculate... The value of w when it reaches its maximum value.

[0071] According to equation (9), with the suspension gap z as the variable, and w, d, and y fixed (take w = 30mm, d = 25mm, l = 600mm), the curve of the levitation force changing with the suspension gap z can be plotted, as follows: Figure 4 As shown. Figure 4 As shown, the levitation force decreases exponentially as the levitation gap increases.

[0072] According to equation (9), with length y as the variable and w, d, and z fixed (take w = 30mm, d = 25mm, z = 15mm), the curve of levitation force changing with the levitation gap l can be plotted, as follows: Figure 5 As shown. Figure 5 As shown, the magnitude of the levitation force is linearly proportional to the length of the magnet.

[0073] In the engineering magnetic circuit design of magnetic tracks, the on-board magnet cannot be infinitely long due to the constraints of actual route selection (such as small turns and large gradients). The length of the magnet must be determined in combination with the size of the curves and gradients. Therefore, the length of the magnet is often not considered in the optimization design of magnetic tracks.

[0074] As can be seen from equation (9), the levitation force of the Halbach array is affected by multiple parameters, and there are also mutual influences between different parameters. Therefore, size optimization cannot be analyzed from a single factor.

[0075] The coupling optimization method of the present invention includes the following steps: taking at least two parameters of z, w, d or y as variables, fixing other parameters, substituting them into the mechanical expression, and calculating the value of the variable when the unit variable parameter magnet levitation force takes the maximum value.

[0076] According to a particularly preferred embodiment of the present invention, the coupling optimization method includes the following steps: fixing z as z0 and y as y0, and calculating... The values ​​of width w and thickness d when the maximum value is obtained.

[0077] The magnitude of the levitation force is directly proportional to the length along the y-axis. Therefore, in practical magnetic circuit design for engineering applications, the length along the y-axis is often not considered. The core optimization objective is to achieve a predetermined levitation force F with the minimum number of magnets at a fixed levitation gap z0. z0 Therefore, the target parameters for optimizing the permanent magnet track size in Halbach are w and d.

[0078] Another aspect of the present invention provides the application of the magnetic levitation track structure optimization method described herein in linear magnetic levitation tracks.

[0079] The method of this invention can optimize the structural dimensions of permanent magnet maglev track and improve the suspension efficiency of rare earth permanent magnet materials, thereby reducing the suspension cost of permanent magnet maglev or superconducting maglev.

[0080] The present invention will be described in detail below through embodiments. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the embodiments of the present invention.

[0081] In the following embodiments, to better illustrate the invention, a repulsive-type 5-group (n=4) Halbach array permanent magnet levitation system is used as an example to illustrate the advantages of the invention, but the invention is not limited thereto. The material used is NdFeB sintered permanent magnet of grade N45. The permanent magnet levitation system structure and the magnetization direction of the unit magnetic blocks are as follows... Figure 2 As shown, it includes the vehicle-mounted magnet and the magnetic track magnet. The vertical force analysis of the vehicle-mounted magnet is as follows. Figure 3 As shown, when the levitation force on the vehicle-mounted magnet is equal to its weight (F... z =mg), the vehicle-mounted magnet is suspended above the magnetic track.

[0082] Example 1

[0083] With fixed levitation gap z0, magnet length y0 and width w0, optimize thickness d.

[0084] To optimize the thickness d of the permanent magnet, a quantitative analysis method is used. In addition to d, we take w = w0, y = y0, z = z0, and substitute them into root (9) to obtain

[0085]

[0086] To optimize the permanent magnet thickness d and enhance the impact of a unit volume of permanent magnet on levitation force, the levitation force generated per unit magnetic track thickness can be expressed as:

[0087]

[0088] In order to obtain F d The maximum value can be obtained by differentiating equation (13).

[0089]

[0090] Let w0 = 0.030, y0 = 0.600, z0 = 0.015 (Note: w0, y0, z0 can be any values), substitute them into equations (12), (13), and (14), and a two-dimensional curve can be drawn from equation (12), as follows. Figure 6 As shown, the levitation force F can be seen. z The levitation force increases with increasing d, but the increase in levitation force gradually decreases with increasing d.

[0091] Command Solving for d, we get d = 0.0240. Based on equation (13), we can draw... Figure 7 ,like Figure 7 As shown, F d It first increases and then decreases; when d = 0.0240, F d Take the maximum value, F dmax = 771494 N / m, that is, when w = 30 mm, z = 15 mm, and d = 24 mm, the levitation force F generated per unit magnet thickness is 771494 N / m. d Maximum, F d The larger the permanent magnet, the higher its utilization rate, while still meeting the levitation target. F d Take the maximum value and then calculate the corresponding thickness d according to equation (13) to achieve the goal of optimizing the magnet thickness.

[0092] Example 2

[0093] With fixed suspension gap z0, magnet length y0 and thickness d0, the permanent magnet width w is optimized.

[0094] To optimize the width w of the permanent magnet, a quantitative analysis method is used. Besides w, we take d = d0, y = y0, and z = z0. Substituting these values ​​into equation (9), we obtain...

[0095]

[0096] To optimize the permanent magnet width w and enhance the impact of a unit volume of permanent magnet on levitation force, the levitation force generated per unit magnetic track width can be expressed as:

[0097]

[0098] In order to obtain F w Maximum, put Substituting (5 Halbach arrays, n=4) into equation (16) and taking the derivative, we get

[0099]

[0100] Let d0 = 0.025, y0 = 0.600, z0 = 0.015 (Note: d0, y0, z0 can be any value), substitute them into equations (15), (16), and (17), and we can draw the result from equation (15). Figure 8 Two-dimensional curves. For example... Figure 8 As shown, the levitation force F can be seen. z The levitation force increases with increasing w, but the increase in levitation force gradually decreases as w increases.

[0101] Command Solving for w, we get w = 0.0268. Based on equation (16), we can draw... Figure 9 ,like Figure 9 As shown, F w It first increases and then decreases; when w = 0.0268, F w Take the maximum value F wmax That is, when d = 25mm, z = 15mm, and w = 26.8mm, the levitation force F generated per unit magnet width is... w Maximum, F wmax = 649307 N / m, F w The larger the permanent magnet, the higher its utilization rate, while still meeting the levitation target. F w Take the maximum value, and then calculate the corresponding width w according to formula (16) to achieve the magnet width optimization goal.

[0102] Example 3

[0103] With the levitation gap z0 and the magnet length y0 fixed, the permanent magnet width w and thickness d are optimized.

[0104] To optimize the width w and thickness d of the permanent magnet, besides w and d, we take z = z0. Substituting this into equation (9) yields...

[0105]

[0106] To optimize the width and thickness of permanent magnets and enhance their impact on levitation force per unit volume, the levitation force generated per unit magnet volume can be expressed as:

[0107]

[0108] To achieve the goal of optimizing w and d, that is, to satisfy the levitation objective (i.e. Find F under the condition z = z0, y = y0. wd The maximum value can be obtained from equation (9).

[0109]

[0110] Substituting equation (20) into equation (19) yields

[0111]

[0112] To find F wd To find the maximum value, substitute k = 2π / (nw) into equation (21) and differentiate with respect to w. ,make

[0113]

[0114] Let z0 = 0.015, y0 = 0.600, (Note: z0, y0, F z0 (Any option can be arbitrarily substituted into equations (18), (19), (20), (21), and (22). A three-dimensional curve can be drawn from equation (18), such as... Figure 10 As shown. From Figure 10 It can be seen that the levitation force increases nonlinearly with the increase of w and d.

[0115] Using MATLAB numerical calculation formula (22), we obtain w = 0.0236. Substituting w = 0.0236 into formula (20), we get d = 0.0189. That is, without considering the change of y (y = 600 mm), when we want to achieve a suspension gap z0 = 0.015 m, w = 23.6 mm, and d = 18.8 mm, F wd Take the maximum value, F wdmax = 4403199428 N / m 3 .

[0116] Example 4

[0117] A repulsive type 3-group Halbach array permanent magnet levitation system, n=2, the magnetic force expression is Equation (23).

[0118]

[0119] According to the quantitative analysis method, when w0 = 30mm, y0 = 600mm, and z0 = 15mm, the optimized result of d is d = 20.4mm; when d0 = 25mm, y0 = 600mm, and z0 = 15mm, the optimized result of w is w = 33.5mm.

[0120] According to the coupled optimization method, when z0 = 15mm and y0 = 600mm, the optimization results are w = 23.6mm and d = 18.9mm, corresponding to the levitation force F. z It is 3.5352 kN.

[0121] Comparative Example 1

[0122] The method is the same as in Example 1, except that d = 0.030 is taken, and substituting it into equation (13) yields F. d =756691, take d=0.020, substitute into equation (13) to get F d =762122 N / m, the result is less than F dmax The utilization rate of permanent magnets is low.

[0123] Comparative Example 2

[0124] The method is the same as in Example 2, except that w = 0.020 is taken, and substituting it into equation (16) yields F. w =601749 N / m, take w = 0.030, substitute into equation (16) to get F w =642501 N / m, which is less than F wmax The utilization rate of permanent magnets is low.

[0125] Comparative Example 3

[0126] The method is the same as in Example 3, except that d = 0.025 and w = 0.030 are used. Substituting into equation (19), we can obtain F. wd = 4283341639 N / m 3 The result is much smaller than F. wdmax The utilization rate of permanent magnets is low.

[0127] The preferred embodiments of the present invention have been described in detail above; however, the present invention is not limited thereto. Within the scope of the inventive concept, various simple modifications can be made to the technical solutions of the present invention, including combinations of various technical features in any other suitable manner. These simple modifications and combinations should also be considered as the content disclosed in the present invention and are all within the protection scope of the present invention.

Claims

1. A method for optimizing the structure of a magnetic levitation track, characterized in that, The method includes the following steps: (A) Analyze the forces acting on the vehicle-mounted magnet and the magnetic track magnet, and establish a mechanical expression for the magnet's levitation force; the magnet's structure is a Halbach array, and the mechanical expression is... Among them, F z B represents the levitation force of the Halbach array magnet along the z-axis. Z B represents the component of the magnetic flux density along the Z-axis. r denoted as remanence of the permanent magnet, μ0 as vacuum permeability, k as the number of wavelengths in the Halbach array magnetic group, d as the thickness of a unit magnetic block, w as the width of a unit magnetic block, z as the levitation gap between the vehicle-mounted magnet and the magnetic track magnet, n as the number of magnetic blocks per unit wavelength, m1 and m2 as magnetic induction intensity correction coefficients, and y as the length of a unit magnetic block. (B) Analyze using quantitative analysis and / or coupled optimization methods. Find The value of w when it reaches its maximum value; or Find The value of z when it reaches its maximum value; or Find The value of y when it reaches its maximum value; or Find The value of d is taken when it reaches its maximum value; the calculated values ​​of w, z, y, and d are the optimized values.

2. The optimization method according to claim 1, wherein, The quantitative analysis method includes the following steps: Using one of the parameters z, w, d, or y as a variable, and fixing the values ​​of the other parameters, substitute them into the mechanical expression to obtain the result. The value of w when it reaches its maximum value; or Find The value of z when it reaches its maximum value; or Find The value of y when it reaches its maximum value; or Find The value of d when the maximum value is reached.

3. The optimization method according to claim 2, wherein, The quantitative analysis method includes the following steps: fixing z as z0, y as y0, and w as w0, calculating... The value of d when it reaches its maximum value; or With z as z0, y as y0, and d as d0, find The value of w when it reaches its maximum value.

4. The optimization method according to claim 1, wherein, The coupling optimization method includes the following steps: With z fixed as z0 and y as y0, find The values ​​of width w and thickness d when the maximum value is obtained.

5. The optimization method according to any one of claims 1-4, wherein, n is an even number greater than or equal to 2.

6. The optimization method according to claim 5, wherein, n is 2, 4, or 6; When n is 2, the mechanical expression is: When n is 4, the mechanical expression is: When n is 6, the mechanical expression is:

7. The optimization method according to any one of claims 1-6, wherein, The magnet is a permanent magnet.

8. The optimization method according to claim 7, wherein, The magnet is selected from one or more of neodymium iron boron permanent magnets, samarium cobalt permanent magnets, and permanent magnet ferrite permanent magnets.

9. The optimization method according to claim 8, wherein, The magnet is a neodymium iron boron permanent magnet.

10. The application of the magnetic levitation track structure optimization method according to any one of claims 1-9 in a linear magnetic levitation track.

Images