Mobile interval-based 8-shaped coil electromagnetic force analysis method and system

Abstract

The application provides a mobile interval-based 8-shaped coil electromagnetic force analysis method and system, which comprises the following steps: dividing a track into a plurality of calculation intervals, the lengths of the plurality of calculation intervals are equal, and the length of any calculation interval is equal to the length of a set number of sequentially arranged ground 8-shaped coils; determining a current calculation interval corresponding to a superconducting magnet according to the position of the superconducting magnet on the track; and calculating and obtaining the electromagnetic force of the superconducting magnet according to the induced current of the plurality of ground 8-shaped coils and the superconducting magnet coil in the current calculation interval. The technical scheme of the application is used to solve the technical problems of long calculation period and low efficiency of electromagnetic force in the prior art.

Description

Technical Field

[0001] This invention relates to the field of magnetic levitation technology, and in particular to a method and system for analyzing the electromagnetic force of a figure-eight coil based on a moving section. Background Technology

[0002] The magnetic track relationship differs from the traditional wheel-rail relationship; it refers to the propulsion, levitation, and guidance effects of the ground coil on the vehicle coil due to electromagnetic forces. Modeling the magnetic track relationship requires considering the topology, geometry, positional relationships, and relevant magnetoelectric parameters of both the ground and vehicle coils. The theoretical modeling process for the magnetic track relationship is complex and computationally intensive. This study proposes a combined approach of analytical modeling and finite element verification to obtain the transient and static three-dimensional forces acting on the magnetic track under different system operating parameters, exploring the coupled modeling, simulation, and analysis process of the analytical model and the dynamic analytical model of the magnetic track.

[0003] Foreign research institutions have conducted several theoretical and experimental studies on the figure-eight coil-based levitation system in electric levitation schemes. Major research institutions include the Japan Railway Technical Research Institute and Argonne Laboratory in the United States. Shunsuke Ohashi established a dynamic model of the levitation train including the relationship between the magnetic track and the levitation system, and carried out simulation and design optimization of the vehicle body dynamics [Shunsuke Ohashi, Research on the Motion of Superconducting Magnetically Levitated Vehicles, University of Tokyo, Doctoral Dissertation, 1997]. Toshiaki Murai et al. used numerical optimization algorithms to optimize the magnetic track design parameters [Toshiaki Murai, Shunsuke Fujiwara, Design of Coil Elements in Superconducting Magnetically Levitation Using Optimization Methods, Electric Theory, 117, 7, 1997; Toshiaki Murai, Katsumi Iwamatsu, Hiroshi Yoshioka, Optimization of Elements of the Figure-Eight Coil in Superconducting Magnetically Levitation, Electric Theory, 123, 1, 2003]. Kotaro Higashi et al. studied the dynamic damping characteristics of bogies using a circuit composed of coil resistance and inductance [Kotaro Higashi, Shunsuke Ohashi, Hiroyuki Osaki, Eisuke Masada, Magnetic Damping of Electromagnetically Inductive Superconducting Magnetically Levitation System, Electric Theory, 117, 8, 1997]. Toshiaki Murai et al. conducted related research on collector coils and analyzed the influence of collector coils on the magnetic track relationship [Hidaru Hasegawa, Toshiaki Murai, Takamitsu Yamamoto, Real Vehicle Tests of Distributed Inductive Collectors, Electric Theory, 123, 2, 2003; Yasuaki Sakamoto, Toshiaki Murai, Takayuki Kashiwagi, Eriko Suzuki, Katsuya Yamamoto, Development of Inductive Collector System with Added Magnetic Damping Function, Electric Theory, 126, 2, 2006; Toshiaki Murai, Yasuaki Sakamoto, High Power Coefficient Converter Control of Linear Generator in Magnetically Levitation Train System through Instantaneous Single-Phase Current, Electric Theory, 126, 2, 2006]. He and Coffey conducted analytical modeling and numerical simulation of figure-eight coil electro-levitation [He, Coffey, Rote, Analysis of combined Maglev levitation, propulsion, and guidance system, IEEE Transactions on Magnetics, 31, 2, 1995; He, Rote, Coffey, Applicates of the dynamic ciruite theory to Maglev suspension systems, IEEE Transactions on Magnetics, 29, 6, 1993].Cai et al. conducted research on the dynamic characteristics of levitation systems [Cai, Rote, Dynamic stability of Maglev Systems, Argonne National Laboratory, Technical Report, 1992; Cai, Chen, Dynamic characteristics of magnetically-levitated vehicle systems, Applied Mechanics Review, 50, 11, 1997]. Compared with foreign countries, there are fewer mechanistic studies on figure-eight coil-based electro-levitation systems conducted in China, and corresponding simulation models and related experimental data are lacking.

[0004] According to the laws of electromagnetism, when a superconducting magnet moves relative to a figure-eight coil on the ground, an induced current is generated inside the figure-eight coil. This induced current interacts with the background magnetic field of the superconducting magnet, generating three-dimensional forces (levitation force, guiding force, and magnetic reluctance) on the magnet. According to electromagnetic theory, the induced current in the figure-eight coil obeys Ferrari's law of electromagnetic induction and the differential equations of the circuit, and the three-dimensional forces acting on the superconducting magnet can also be determined by the induced current and mutual inductance coefficient. Analytical modeling based on the figure-eight coil aims to establish differential equations describing this physical process and use computer and numerical methods to calculate the induced current and three-dimensional forces. Existing analytical algorithms based on continuous-state figure-eight coils present nonlinear functional relationships between the levitation force, guiding force, and magnetic reluctance acting on the superconducting magnet and the levitation height, lateral clearance, and forward velocity.

[0005] Solving for the damping of a suspension system, or coupling existing analytical algorithms for figure-eight coil magnetic tracks based on continuous states with vehicle and bridge dynamics modules, requires long-period numerical simulations. This increases the solution distance and the number of figure-eight coils needed. The dimensions of the current state matrix, self-inductance state matrix, and mutual inductance state matrix in the program also increase, reducing the solution speed and creating technical difficulties for practical solutions. Due to computational resource limitations, currently only finite-length tracks within the pole pitch range of 500 figure-eight coils can be solved. Summary of the Invention

[0006] This invention provides a method and system for analyzing the electromagnetic force of a figure-eight coil based on a moving interval, which can solve the technical problems of long calculation cycles and low efficiency in the prior art.

[0007] According to one aspect of the present invention, a method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval is provided. The method includes: dividing the track into multiple calculation intervals, all of which have equal lengths, and the length of any calculation interval being equal to the length of a predetermined number of sequentially arranged ground figure-eight coils; determining the current calculation interval corresponding to the superconducting magnet based on the position of the superconducting magnet on the track; and calculating the electromagnetic force of the superconducting magnet based on the induced currents of the multiple ground figure-eight coils and the superconducting magnet coil within the current calculation interval.

[0008] Furthermore, dividing the track into multiple calculation intervals specifically includes: taking the track length corresponding to the first coil to the s-th coil as the first calculation interval; shifting the first calculation interval by one coil along the train's direction of movement to the track length corresponding to the second coil to the (s+1)-th coil as the second calculation interval; shifting the second calculation interval by one coil along the train's direction of movement to the track length corresponding to the third coil to the (s+2)-th coil as the third calculation interval; repeating the above process to sequentially obtain the fourth calculation interval, the fifth calculation interval, ..., the J-th calculation interval, where the length of the J-th calculation interval is equal to the track length corresponding to the ns-th to n-th coils.

[0009] Furthermore, when the center of the superconducting magnet is in the first operational range, the electromagnetic force of the figure-eight coil can be determined according to... Calculated and obtained, where p = [L T H T D T d T ], p is the geometric parameter of the figure-eight coil, L T H is the length of the figure-eight coil. T D is the height of the figure-eight coil. T d represents the pole pitch between any two adjacent figure-eight coils. T The thickness of the figure-eight coil is q = [L] S H S d S ], q is the geometric parameter of the superconducting magnet coil, L S H is the length of the superconducting magnet coil. S d is the height of the superconducting magnet coil. S Let be the thickness of the superconducting magnet coil, x be the levitation height of the superconducting magnet coil, y be the propulsion displacement of the superconducting magnet coil, z be the guiding displacement of the superconducting magnet coil, and v be the thickness of the superconducting magnet coil. x Let v be the vibration velocity in the levitation direction of the superconducting magnet coil. y v is the propulsion velocity of the superconducting magnet coil. z R is the vibration velocity in the guiding direction of the superconducting magnet coil, R is the resistance matrix, L is the self-inductance matrix of the ground figure-eight coil, and I is the vibration velocity in the guiding direction of the superconducting magnet coil. TFor the current matrix of the ground figure-eight coil, I S Let f be the current matrix of the superconducting magnet coil. x For levitation force, f y For magnetic resistance, f z The guiding force is G(x,y,z,p,q), which is the mutual inductance coefficient matrix between the superconducting magnet coil and the ground figure-eight coil.

[0010] Furthermore, when the center of the superconducting magnet is in the second operational range, the electromagnetic force of the figure-eight coil can be determined according to... The calculation yields the induced current I of the ground figure-eight coil. j In (i,t), the superscript j is the calculation interval number, i is the ground figure-eight coil number, and D... T The pole spacing of the figure-eight coil on the ground.

[0011] Furthermore, when the center of the superconducting magnet is located in the j-th operational interval, the electromagnetic force of the figure-eight coil can be determined according to... The calculation yields the result, where j = 3, 4, ..., J.

[0012] Furthermore, the length of any calculation interval can be calculated based on the displacement of the superconducting magnet along the track when the induced current of the figure-eight coil and the superconducting electromagnetic force tend to stabilize.

[0013] Furthermore, the length D of any calculation interval can be determined by D = S + kD. T The calculation yields the result, where S is the induced current of the figure-eight coil and the displacement of the superconducting magnet along the track when the superconducting electromagnetic force tends to stabilize, k is a coefficient, and D is the displacement of the superconducting magnet along the track. T The pole pitch of the figure-eight coil.

[0014] According to another aspect of the present invention, a figure-eight coil electromagnetic force analysis system based on a moving interval is provided, wherein the figure-eight coil electromagnetic force analysis system based on a moving interval uses the figure-eight coil electromagnetic force analysis method based on a moving interval as described above to perform electromagnetic force analysis.

[0015] The present invention provides a method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval. This method divides the track into multiple calculation intervals. When performing electromagnetic force analysis calculations, the current calculation interval corresponding to the superconducting magnet is determined according to the position of the superconducting magnet on the track. Only the figure-eight coil within the current calculation interval is selected for calculation. This reduces the order of matrices such as current state quantity I, self-inductance state quantity L, and mutual inductance state quantity G, thereby reducing the amount of calculation and greatly improving the calculation speed and efficiency of the electromagnetic force of the superconducting magnet, while shortening the calculation cycle. Attached Figure Description

[0016] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0017] Figure 1 A schematic diagram of an analytical method for electromagnetic force analysis of a figure-eight coil based on a moving interval, according to a specific embodiment of the present invention, is shown.

[0018] Figure 2 A schematic diagram of the levitation force acting on a superconducting magnet according to a specific embodiment of the present invention is shown;

[0019] Figure 3 A schematic diagram showing the positional relationship between a superconducting magnet coil and a ground coil according to a specific embodiment of the present invention is shown;

[0020] Figure 4 A schematic diagram of the levitation force generated by each ground coil according to a specific embodiment of the present invention is shown;

[0021] Figure 5 A schematic diagram of the induced current generated by each ground coil according to a specific embodiment of the present invention is shown;

[0022] Figure 6 A schematic diagram of the derivative of the mutual inductance coefficient between each superconducting magnet coil and the ground coil with respect to the X direction, according to a specific embodiment of the present invention, is shown.

[0023] Figure 7 A comparative schematic diagram of three different methods for solving levitation force according to a specific embodiment of the present invention is shown;

[0024] Figure 8 A comparative schematic diagram of three different methods for solving magnetic drag provided according to specific embodiments of the present invention is shown;

[0025] Figure 9 A comparative schematic diagram of three different methods for solving the guiding force according to a specific embodiment of the present invention is shown;

[0026] Figure 10 A comparative schematic diagram of solving levitation force using the continuous state method and the moving interval method according to a specific embodiment of the present invention is shown;

[0027] Figure 11 A schematic diagram of a magnetic track module according to a specific embodiment of the present invention is shown;

[0028] Figure 12 This illustrates m superconducting magnet coils provided according to a specific embodiment of the present invention, moving at a speed v. y A schematic diagram using n figure-eight coils. Detailed Implementation

[0029] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0031] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0032] like Figures 1 to 11As shown, according to a specific embodiment of the present invention, a method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval is provided. This method includes: dividing the track into multiple calculation intervals, all of which have equal lengths, and the length of any calculation interval being equal to the length of a predetermined number of sequentially arranged ground figure-eight coils; determining the current calculation interval corresponding to the superconducting magnet based on its position on the track; and calculating the electromagnetic force of the superconducting magnet based on the induced current of the multiple ground coils within the current calculation interval.

[0033] This configuration provides a method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval. This method divides the track into multiple calculation intervals. When performing electromagnetic force analysis calculations, the current calculation interval corresponding to the superconducting magnet is determined based on the position of the superconducting magnet on the track. Only the figure-eight coil within the current calculation interval is selected for calculation. This reduces the order of matrices such as current state quantity I, self-inductance state quantity L, and mutual inductance state quantity G, thereby reducing the amount of calculation and greatly improving the calculation speed and efficiency of the electromagnetic force of the superconducting magnet, while shortening the calculation cycle.

[0034] Specifically, in this invention, the analytical algorithm for figure-eight coil magnetic tracks based on continuous states requires an increasing number of figure-eight coils as the solution distance increases. This increases the dimensions of the current state matrix, self-inductance state matrix, and mutual inductance state matrix, reducing the solution speed and creating technical difficulties for practical solutions. Therefore, it can only solve for track lengths with limited distances. However, the magnitude of the mutual inductance coefficient and the induced current are related to the relative distance between the center of the superconducting magnet coil and the ground-based figure-eight coil. When the relative distance exceeds the range of three figure-eight coil pole pitches, the mutual inductance coefficient is almost zero. The induced current in the figure-eight coil near the center of the superconducting magnet coil is relatively large, gradually decreasing to zero as the relative distance increases. Therefore, the figure-eight coils within a certain relative distance range contribute to the electromagnetic force of the superconducting magnet. This relative distance is defined as the calculation interval. This invention selects only the figure-eight coils within the calculation interval for calculation, achieving order reduction of the matrices for current state, current state I, self-inductance L, and mutual inductance G, reducing the computational load and improving the calculation speed. By continuously shifting the calculation interval, the solution for infinitely long tracks with increased speed was achieved.

[0035] As a specific embodiment of the present invention, a continuous-state magnetic track relationship model is used to solve for the number of superconducting magnet coils m=4, the number of ground figure-eight coils n=30, and the state input quantity of the superconducting magnet coils. The superconducting magnet coil moves along the track, and the figure-eight coil on the ground begins to generate an induced current. Figure 2 At t = 0.05s, the induced current of the figure-eight coil on the ground tends to stabilize, and the levitation force on the superconducting magnet also tends to stabilize.

[0036] Figure 3 The table shows the positional relationship between the superconducting magnet coil and the ground coil at t = 0.1 s. The levitation force on the superconducting magnet is 117319 N, and the contribution of each ground figure-eight coil to the levitation force is shown in Table 1. Figure 4 As shown, coils 9 through 20 contribute to the levitation force, while the contributions of the other coils to the electromagnetic force are negligible.

[0037] Table 1. Suspension force generated by each ground figure-eight coil.

[0038] Coil number Suspension force (N) Coil number Suspension force (N) 1 0 16 16880 2 0 17 5153 3 0 18 8538 4 0 19 12719 5 0 20 2934 6 0 21 2.7 7 6.67 22 0 8 4.66 23 0 9 10529 24 0 10 15866 25 0 11 4606.5 26 0 12 9912 27 0 13 14609 28 0 14 3921 29 0 15 3921 30 0

[0039] Superconducting current I S Since the levitation force is constant, its magnitude is determined by the derivative of the induced current and the mutual inductance coefficient. Figure 5 The induced current of each ground coil at t = 0.1s is given. The induced currents of ground coils 9 through 20 near the superconducting magnet coil are relatively large. As the distance between the superconducting center and the ground coils increases, the induced currents of ground coils 8 through 1 decrease sequentially. The induced currents of coils 21 through 30 are almost zero. Figure 6 The derivative values ​​of the mutual inductance coefficient between each superconducting magnet coil and the ground coil are given at t = 0.1 s. Within the range of the three ground coils at the center of the superconducting magnet coil, the derivative value of the mutual inductance coefficient is relatively large. Beyond this range, the derivative value of the mutual inductance coefficient is almost zero. Therefore, for a single superconducting magnet coil, only the three ground coils in its vicinity contribute to the electromagnetic force it experiences. At m = 4, the 12 ground coils (numbered 9 to 20) near the superconducting center contribute to the electromagnetic force it experiences. Therefore, the figure-eight coils within a finite distance range near the superconducting magnet contribute to the electromagnetic force; this finite distance L is defined as the calculation interval.

[0040] Therefore, only the current state quantities of the s ground figure-eight coils within the calculation interval need to be solved for the calculation of superconducting electromagnetic force. In this way, the solution size of the circuit equation 1 matrix is ​​reduced from n×n to s×s, effectively reducing the amount of computation and improving the calculation speed.

[0041] Furthermore, in this invention, as Figure 1As shown, dividing the track into multiple calculation intervals specifically includes: taking the track length corresponding to the first coil to the s-th coil as the first calculation interval; shifting the first calculation interval by one coil along the train's direction of movement to the track length corresponding to the second coil to the (s+1)-th coil as the second calculation interval; shifting the second calculation interval by one coil along the train's direction of movement to the track length corresponding to the third coil to the (s+2)-th coil as the third calculation interval; repeating the above process to sequentially obtain the fourth calculation interval, the fifth calculation interval, ..., the J-th calculation interval, where the length of the J-th calculation interval is equal to the track length corresponding to the ns-th to the lowest n-th coils.

[0042] Furthermore, in this invention, to ensure computational accuracy and efficiency, the length of any computational interval can be calculated based on the displacement of the superconducting magnet along the track when the induced current of the figure-eight coil and the superconducting electromagnetic force tend to stabilize. In this invention, the length D of any computational interval can be determined using the formula D = S + kD. T The calculation yields the result, where S is the induced current of the figure-eight coil and the displacement of the superconducting magnet along the track when the superconducting electromagnetic force tends to stabilize, k is a coefficient, and D is the displacement of the superconducting magnet along the track. T The pole pitch of the figure-eight coil. In a specific embodiment of the present invention, k takes the value of 2 to 3.

[0043] Specifically, in this invention, such as Figure 12 As shown, the origin of the coordinate system is selected at the midpoint of the upper and lower rectangles of the first figure-eight coil. Consider m rectangular superconducting magnets moving at a given velocity v. y Through n figure-eight coils. (x, y, z) T The rectangle representing the center point of the first superconducting magnet coil. The main geometric parameters of the ground figure-eight coil: p = [L] T H T D T d T ], where L T H is the length of the figure-eight coil. T D is the height of the figure-eight coil. T d represents the pole pitch between any two adjacent figure-eight coils. T This refers to the thickness of the figure-eight coil. The geometric parameters of the superconducting magnet coil are q = [L]. S H S d S ], where L S H is the length of the superconducting magnet coil. S d is the height of the superconducting magnet coil. S N represents the thickness of the superconducting magnet coil. T N represents the number of turns of the figure-eight coil on the ground. SThe number of turns represents the superconducting magnet coil, where the subscripts T and S represent the figure-eight coil (also known as the T-coil) and the superconducting magnet coil (also known as the S-coil), respectively. In the continuous-state magnetic track relationship model, the induced current of the figure-eight coil is first solved according to the circuit equation and the displacement equation, and then the electromagnetic forces in the three directions of levitation, magnetic reluctance, and guidance experienced by the superconducting magnet are obtained from the induced current.

[0044] The circuit equation for the ground figure-eight coil is:

[0045] The equation for displacement in the heading direction is:

[0046] The electromagnetic force equations for the superconducting magnet in the three directions of levitation, magnetic reluctance, and guidance are as follows: Among them, f x For levitation force, f y For magnetic resistance, f z For guiding force.

[0047] The initial condition for equation (1) is I T (0)=0(6)

[0048] The initial condition for equation (2) is y(0) = 0 (7)

[0049] In formula (1), This is a resistance matrix, a diagonal matrix with constant coefficients. The values ​​on the diagonal are the resistances of the ground figure-eight coils. The matrix dimensions are determined by the number of ground figure-eight coils, n, and its size is:

[0050]

[0051] The self-inductance matrix of the ground figure-eight coil is a constant coefficient matrix. The dimension of the matrix is ​​determined by the number of ground figure-eight coils, n. The size of the matrix elements is determined by the geometric parameters p of the figure-eight coils.

[0052] Let be the current matrix of the superconducting magnet coils, which is a constant coefficient matrix. The matrix dimension is determined by the number of superconducting magnet coils, m.

[0053] This is the current matrix of the ground figure-eight coils. The matrix dimensions are determined by the number of ground figure-eight coils, n. The current magnitudes are obtained from the circuit equations.

[0054] The matrix represents the mutual inductance coefficients between m superconducting magnet coils and n ground-based figure-eight coils. The partial derivative matrix in the X, Y, and Z directions. The size of the matrix elements is related to the state variables x, y, z, p, and q. The dimensions of the matrix are determined by the number of ground coils n and the number of superconducting magnet coils m.

[0055] Formula (1) is a nonlinear differential equation. Under initial conditions (6)-(7), the given state input is the propulsion velocity v of the superconducting magnet. y Vibration velocity v in the suspension direction x Vibration velocity v in the guiding direction z The levitation height x and guide displacement z can be used to calculate the propulsion displacement y and the induced current I of the figure-eight coil. T levitation force f x Magnetic resistance f y Guiding force f z Output quantities for different states.

[0056] Based on the location of the superconducting center, the infinitely long orbit is divided into different calculation intervals, such as... Figure 1 As shown. The calculation interval is L, consisting of s ground figure-eight coils. Two coordinate systems are defined: the global coordinate system OXgYg, with its origin located at the middle of the figure-eight coil at the beginning of the track; and the local coordinate system OXjYj, with its origin located at the middle of the figure-eight coil at the beginning of the calculation interval. Under OXgYg, It is the longitudinal displacement y of the superconducting center on the track. g Solve equations (1)-(5) under OXjYj.

[0057] (1) When the first calculation interval (i.e., interval j=1) is

[0058] like Figure 1 As shown, the positions of the center of the superconducting magnet coil on the track are y1, y2, y3…y J And the calculation interval 1, 2, 3…J, where position y1 represents the displacement of the superconducting magnet on the track when the induced current of the ground coil and the superconducting electromagnetic force tend to stabilize; position y2 refers to the displacement of the superconducting magnet on the track when the current of the first ground coil decays to 0; position y3 refers to the displacement of the superconducting magnet on the track when the current of the second ground coil decays to 0, and so on, position y…J ... J It refers to the displacement of the superconducting magnet on the track when the current decay of the (J-1)th ground coil is 0.

[0059] Displacement y of the superconducting center on the orbit g When y1 < y1, given initial condition I T (0)=0, y g (0) = 0, the superconducting magnet is at a velocity v y It begins to move along the Y direction. The figure-eight coil on the ground begins to generate an induced current. Position 1 (t = t1, yg When y = 1), the induced current in the ground coil and the superconducting electromagnetic force tend to stabilize. At position 2 (t = t2, y = t1), the induced current in the ground coil and the superconducting electromagnetic force tend to stabilize. g When y = 2), due to the increase in distance, the current of ground coil 1 decreases to 0. The calculation interval switches from 1 to 2. When the center of the superconducting magnet is in the first calculation interval, the electromagnetic force of the figure-eight coil can be calculated according to the electromagnetic force equations in three directions as follows: Calculated and obtained, where p = [L T H T D T d T ], p is the geometric parameter of the figure-eight coil, L T H is the length of the figure-eight coil. T D is the height of the figure-eight coil. T d represents the pole pitch between any two adjacent figure-eight coils. T The thickness of the figure-eight coil is q = [L] S H S d S ], q is the geometric parameter of the superconducting magnet coil, L S H is the length of the superconducting magnet coil. S d is the height of the superconducting magnet coil. S Let be the thickness of the superconducting magnet coil, x be the levitation height of the superconducting magnet coil, y be the propulsion displacement of the superconducting magnet coil, z be the guiding displacement of the superconducting magnet coil, and v be the thickness of the superconducting magnet coil. x Let v be the vibration velocity in the levitation direction of the superconducting magnet coil. y v is the propulsion velocity of the superconducting magnet coil. z R is the vibration velocity in the guiding direction of the superconducting magnet coil, R is the resistance matrix, L is the self-inductance matrix of the ground figure-eight coil, and I is the vibration velocity in the guiding direction of the superconducting magnet coil. T For the current matrix of the ground figure-eight coil, I S Let f be the current matrix of the superconducting magnet coil. x For levitation force, f y For magnetic resistance, f z The guiding force is G(x,y,z,p,q), which is the mutual inductance coefficient matrix between the superconducting magnet coil and the ground figure-eight coil.

[0060] (2) When the second calculation interval (i.e., interval j=2)

[0061] Position 2 (t = t2, y gWhen t2 = y2), the current of ground coil 1 decays to 0. Therefore, the figure-eight coil at the beginning of calculation interval 1 can be removed. Simultaneously, a figure-eight coil is added at the end. Thus, the calculation space 2 of the same dimension is formed by the 2nd to s+1th ground coils. At time t2, the current value of the i-th figure-eight coil in calculation interval 2, i = 1, 2, ..., s-1, depends on the current state value of the (i+1)-th figure-eight coil in calculation interval 1. The current value of the s-th figure-eight coil in calculation interval 2 is initialized to 0. Induced current I j The superscript j in (i,t) is used to denote the calculation interval number, and i is used to denote the ground coil number. Then:

[0062] I 2 (1,t2)=I 1 (2,t2),I 2 (2,t2)=I 1 (3,t2),…,I 2 (s-1,t2)=I 1 (s,t2),I 2 (s,t2)=0(8)

[0063] Displacement state quantity y j The superscript j in (t) is used to denote the interval number. At time t2, the displacement state variable y under OX2Y2... 2 Size: y 2 (t2)=y 1 (t2)-D T (9)

[0064] The initial conditions (6) and (7) of the circuit equation (1) and displacement equation (2) within interval 2 are updated to equations (8) and (9). The superconducting center displacement y1 < y g When y < 2, combining equations 1-5 and 8-9, we obtain the electromagnetic force on the superconducting magnet within interval 2. Position 3 (t = t3, y g When y = 3), the calculation interval switches from 2 to 3.

[0065] When the center of the superconducting magnet is in the second operational range, the electromagnetic force of the figure-eight coil can be determined according to... The calculation yields the induced current I of the ground figure-eight coil. j In (i, t), the superscript j is the calculation interval number, i is the ground figure-eight coil number, and D... T The pole spacing of the figure-eight coil on the ground.

[0066] (3) As the calculation interval is continuously switched and updated (j = 3, 4, ..., J), the solution of infinitely long orbits is realized.

[0067] When calculating interval switching, the current state variables and displacement state variables need to be updated before being given. However, the continuous state equations 1-2 encapsulated in Simulink cannot update the state variables during the calculation process. Therefore, it is necessary to discretize equations (1)-(2). The form is as follows: The continuous state equations can be written in discrete state form using the second-order Rogon-Kutta method:

[0068] a1=f(t k y k )

[0069] a2=f(t k +Δt, y k +k1Δt)

[0070]

[0071] Equations 1 and 2 can be written in the form of discrete state equations as follows:

[0072]

[0073] When Δt is sufficiently small or when a higher-order Runge-Kutta method is used for discretization, the error of the discrete state solution relative to the solutions of equations (1) and (2) is smaller.

[0074] To facilitate object-oriented use, the above solution process is encapsulated using Simulink. The magnetic track module interface is as follows: Figure 11 As shown. When the center of the superconducting magnet is in the j-th operational interval, the electromagnetic force of the figure-eight coil can be determined according to... Calculated and obtained.

[0075] According to another aspect of the present invention, a figure-eight coil electromagnetic force analysis system based on a moving interval is provided, which uses the figure-eight coil electromagnetic force analysis method based on a moving interval as described above to perform electromagnetic force analysis.

[0076] This configuration provides a figure-eight coil electromagnetic force analysis system based on a moving interval. By dividing the track into multiple calculation intervals, the system determines the current calculation interval corresponding to the superconducting magnet based on its position on the track during electromagnetic force analysis calculations. Only the figure-eight coil within the current calculation interval is selected for calculation. This reduces the order of matrices such as current state quantity I, self-inductance state quantity L, and mutual inductance state quantity G, thereby reducing the computational load and greatly improving the calculation speed and efficiency of the electromagnetic force of the superconducting magnet, while shortening the calculation cycle.

[0077] To gain a further understanding of the present invention, the following description is provided in conjunction with... Figures 7 to 10 The electromagnetic force analysis method of the figure-eight coil based on the moving interval provided by the present invention will be described in detail.

[0078] To more clearly demonstrate the advantages of the figure-eight coil electromagnetic force analysis method provided by this invention in electromagnetic force analysis, three different methods are used below for solving the problem. The magnitude of the electromagnetic force was determined. Example 1 uses the continuous state method, with 150 figure-eight coils on the ground. Examples 2 and 3 use the moving interval method with s=12 and s=30, respectively. The calculation time is 0.4s, and the orbital advance displacement is 40m. The calculation results are as follows: Figures 7-9 As shown.

[0079] After stabilization, f x (t),f y (t),f z (t) exhibits some fluctuation on the time axis, let f x (t),f y (t),f z (t) is the average value over the time interval [T1,T2], where T1 and T2 are as follows: Figure 9 As shown. The statistical error relative to Example 1 is:

[0080]

[0081] n = 2, 3, representing examples 2 and 3. m = 1, 2, 3, ..., K, representing the number of electromagnetic force sampling points within the time interval [T1, T2].

[0082] The number of coils, *s*, within the moving interval has a significant impact on the solution results. When *s* is 12, the electromagnetic force calculation result can reach an error of 25%. When *s* is 30, the solution errors for levitation force, magnetic reluctance, and guiding force are 0, 1.11%, and 0.5%, respectively, which are basically consistent with the solution results of the continuous state method. The solution time is significantly reduced by using the moving interval method.

[0083] Comparing the solution times, the MAGNET electromagnetic finite element software cannot solve for a 40-meter track length. The solution time for the continuous state method is 234 minutes. Example 3's solution time is 16 minutes, a reduction of 69%. Therefore, using the moving interval method (number of coils S>=30) can both ensure the accuracy of the electromagnetic force solution and effectively reduce the computation time.

[0084] Table 2 Comparison of solution results from different algorithms

[0085]

[0086]

[0087] Figure 9At t = 0.72s, the displacement of the superconducting center on the track is 72m, exceeding the length of 150 figure-eight coils on the ground. The induced current and the derivative of the mutual inductance gradually decay to zero, and the levitation force also decreases to zero. Therefore, using the continuous state equation, when the number of coils is fixed, only electromagnetic forces over finite distances can be solved. The moving interval method is not limited by the solution distance. By continuously moving the calculation interval, solutions for infinitely long tracks can be obtained.

[0088] As can be seen from this embodiment, in order to ensure the accuracy and efficiency of electromagnetic force calculation, it is necessary to reasonably determine the length of the calculation interval. In this invention, the calculation interval can be calculated based on the induced current of the figure-eight coil and the displacement of the superconducting magnet along the track when the superconducting electromagnetic force tends to stabilize.

[0089] In summary, this invention provides an analytical method for electromagnetic force analysis of a figure-eight coil based on a moving interval. This method divides the track into multiple calculation intervals. When performing electromagnetic force analysis calculations, the current calculation interval corresponding to the superconducting magnet is determined based on the position of the superconducting magnet on the track. Only the figure-eight coil within the current calculation interval is selected for calculation. This achieves order reduction of matrices such as current state quantity I, self-inductance state quantity L, and mutual inductance state quantity G, reducing the amount of calculation and greatly improving the calculation speed and efficiency of the electromagnetic force of the superconducting magnet, while shortening the calculation cycle.

[0090] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention; the directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0091] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0092] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0093] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., 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 method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval, characterized in that, The electromagnetic force analysis method for the figure-eight coil based on the moving interval includes: The track is divided into multiple calculation intervals, all of which have the same length. The length of any one of the calculation intervals is equal to the length of a set number of sequentially arranged figure-eight ground coils. The current calculation interval corresponding to the superconducting magnet is determined based on its position on the track. The electromagnetic force of the superconducting magnet is calculated based on the induced current of multiple ground figure-eight coils and the superconducting magnet coil within the current calculation interval. The track is divided into multiple calculation intervals, specifically including: The track lengths corresponding to the first coil to the s-th coil are taken as the first calculation interval; The second calculation interval is the track length corresponding to the second coil corresponding to the first coil and the (s+1)th coil, which is shifted one coil along the direction of train movement. The second calculation interval is shifted along the direction of train movement by one coil to the track length corresponding to the third coil to the (s+2)th coil, which is taken as the third calculation interval; Repeat the above process to obtain the fourth calculation interval, the fifth calculation interval, and so on. The J-th calculation interval, the length of which is equal to the track length corresponding to the ns-th to n-th coils, when the center of the superconducting magnet is in the first calculation interval, the electromagnetic force of the figure-eight coil is based on... , calculated and obtained, where, , The geometric parameters of the figure-eight coil are... The length of the figure-eight coil. The height of the figure-eight coil. The pole spacing is the distance between any two adjacent figure-eight coils. The thickness of the figure-eight coil. , For the geometric parameters of the superconducting magnet coil, The length of the superconducting magnet coil. The height of the superconducting magnet coil, The thickness of the superconducting magnet coil. The levitation height of the superconducting magnet coil. This represents the propulsion displacement of the superconducting magnet coil. For the guiding displacement of the superconducting magnet coil, The vibration velocity in the levitation direction of the superconducting magnet coil is denoted as . The propulsion speed of the superconducting magnet coil. The vibration velocity in the guiding direction of the superconducting magnet coil. It is a resistance matrix. For the self-inductance matrix of the ground figure-eight coil, The current matrix of the ground figure-eight coil. This is the current matrix of the superconducting magnet coil. For levitation force, For magnetic resistance, As a guiding force, This is the mutual inductance matrix between the superconducting magnet coil and the ground-based figure-eight coil. When the center of the superconducting magnet is within the second operational interval, the electromagnetic force of the figure-eight coil is determined according to... The calculation yielded the induced current of the ground figure-eight coil. superscript To calculate the interval number, Number the figure-eight coils on the ground. The figure-eight coil pole pitch is the distance between the poles of the ground-based superconducting magnet and the poles of the figure-eight coil. During the calculation interval, the electromagnetic force of the figure-eight coil is based on ， Calculation and acquisition, where, .

2. The method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval as described in claim 1, characterized in that, The length of any of the calculation intervals is calculated based on the displacement of the superconducting magnet along the track when the induced current of the figure-eight coil and the superconducting electromagnetic force tend to stabilize.

3. The method for analyzing the electromagnetic force of a figure-eight coil based on a moving interval as described in claim 2, characterized in that, Length of any of the calculated intervals according to Calculation and acquisition, where, The displacement of the superconducting magnet along the track when the induced current and superconducting electromagnetic force of the figure-eight coil tend to stabilize is given. For coefficients, The pole pitch of the figure-eight coil is given.

4. A figure-eight coil electromagnetic force analysis system based on a moving interval, characterized in that, The figure-eight coil electromagnetic force analysis system based on the moving interval uses the figure-eight coil electromagnetic force analysis method based on the moving interval as described in any one of claims 1 to 3 to perform electromagnetic force analysis.

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