Linear eddy current braking system applied to electric high-speed magnetic levitation and having normal force restraining and braking force lifting effects

Abstract

The invention relates to the field of high-speed magnetic levitation electromagnetic braking, and particularly discloses a linear eddy current braking system applied to electric high-speed magnetic levitation and having normal force restraining and braking force improving effects, and the linear eddy current braking system comprises the steps that S1, a PHE-LECB system is constructed, and a two-dimensional simplified model of a pair of poles of the PHE-LECB system is established; s2, establishing a magnetic vector potential partial differential model according to the two-dimensional simplified model of the pair of poles of the PHE-LECB system established in the step S1; s3, sub-domain magnetic field boundary condition analysis is carried out after the magnetic vector potential partial differential model established in the S2; s4, establishing a flux density distribution and electromagnetic force model according to S2 and S3, and obtaining total braking force and normal force of the system; and S5, establishing a finite element model of the PHE-LECB system, and verifying the correctness of the analytical model. According to the method, eddy current normal force is effectively restrained, stable suspension of the EDS maglev train during emergency braking is guaranteed, eddy current braking force is further improved, shorter emergency braking time can be brought to the train, and operation safety is effectively guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed magnetic levitation electromagnetic braking, and in particular to a linear eddy current braking system for electric high-speed magnetic levitation with normal force suppression and braking force enhancement functions. Background Art

[0002] Speed ​​is an important pursuit in the field of transportation technology. The pursuit of higher speeds for transportation tools runs through the entire history of transportation technology development. In the field of rail transportation, the pursuit of high speed is also long-standing. The maximum operating speed of trains is an important basis for judging whether a country's railway technology and railway-related equipment and facilities are superior.

[0003] In order to fill the gap of higher operating speed, high-speed maglev trains that have gotten rid of the limitation of wheel-rail adhesion have received extensive attention from academia and engineering circles. The emergence of high-speed maglev trains is considered a great revolution in the history of human transportation. It has enriched and improved the transportation network and has changed the development pattern of world transportation to a certain extent. It is precisely because of the advantages of maglev rail transit, such as wide speed range, strong climbing, low noise, good stability, high safety, environmental protection and energy saving, low maintenance cost and strong adaptability, that it stands out in rail transit and becomes a highly competitive green ground transportation tool. Therefore, people's exploration and research on maglev technology has been in the ascendant and has achieved a series of research results.

[0004] When developing a means of transportation, especially a high-efficiency, high-capacity train like a maglev train, safety is the primary consideration for researchers. Because the safety of the train directly affects the safety of passengers' lives and property, and the reliability of the braking system largely determines the safety of the train, the safe and stable operation of the train is closely related to its braking system. Research and analysis of the braking system of high-speed maglev trains is of great significance.

[0005] For high-speed or ultra-high-speed rail transit vehicles, they must be equipped with an emergency braking system independent of conventional braking methods. There are currently three types of high-speed emergency braking methods available: the first is magnetic rail braking. Its essence is still friction braking, but the dynamic friction coefficient will continue to decrease with the increase of relative movement speed. Therefore, the higher the relative movement speed, the smaller the friction resistance, and the poor braking effect. The second is wind resistance braking. The higher the speed, the better the braking effect. However, it can only provide a deceleration that meets the braking requirements of the train above 300km / h. The braking effect in the low-speed domain is obviously insufficient and is not suitable for use alone. The last is eddy current braking. Eddy current braking can provide braking force that meets the requirements in the full braking speed range, and is considered to be the best choice for emergency braking of future high-speed or ultra-high-speed rail transit vehicles. At present, linear eddy current braking devices have been applied to the German ICE-3 high-speed EMU and the Shanghai high-speed maglev train.

[0006] At present, there are many research results on eddy current braking systems. First, the secondary induction plate is divided into a series of units and described as an equivalent circuit with resistance and inductance parameters. The Runge-Kutta method is used to solve the state equation composed of the circuit equation and the Newton equation, so as to obtain the dynamic performance of the linear electromagnetism eddy current braking system. Second, for the electromagnetism eddy current braking system, the two-dimensional electromagnetic field theory is used to analyze different magnetic field boundary conditions to obtain the analytical formula between different parameters and eddy current braking force, and the correctness of the analytical calculation is proved by finite element simulation. Third, a mathematical model of the braking force of the rotating eddy current braking system under the condition of air resistance is established, and the braking system under constant magnetic flux and alternating magnetic flux is experimentally verified. Fourth, by distributing the braking torque to multiple electromagnets, a high volume density eddy current braking device is proposed, and the influence of different excitation inputs is analyzed based on finite element modeling. Fifth, the subdomain method considering the skin effect of the induction plate is used to derive the analytical formula of the eddy current braking force, and the electromagnetic characteristics and parameter influence of the peak braking force and critical speed are analyzed in detail. Sixth, an analytical model of a linear permanent magnet eddy current brake device was established, and the time domain signal of the braking force was processed by fast Fourier transform to obtain the optimal parameters of the permanent magnet, and the rationality was verified by the finite element model. Seventh, considering the heating effect of the eddy current brake, a multi-field coupling and bidirectional data transmission model of the coil temperature field and transient electromagnetic field was established, and the change law of the braking torque over time under continuous braking conditions was analyzed.

[0007] At present, most of the research on eddy current braking focuses on the analytical calculation of a single eddy current braking system, system parameter analysis, and system thermal effects. In view of the particularity of the EDS high-speed maglev track structure, the eddy current braking system is more suitable for installation on the underbody suspension frame. In this application context, there is little research in the academic community on issues such as the dynamic matching of vehicle braking and the destruction of stable suspension by the normal force of eddy current braking, and these issues need to be urgently addressed in engineering.

[0008] Although the existing LECB system can provide reliable braking deceleration in the full speed range of train braking, when applied to EDS maglev trains, the eddy current normal force generated during braking will seriously destroy the stable suspension state of the EDS maglev train, and may even cause the car body to become unstable and hit the track, endangering the lives and property of passengers. Summary of the invention

[0009] In view of the above-mentioned problems in the prior art, the present invention provides a linear eddy current braking system with normal force suppression and braking force enhancement functions for use in electric high-speed maglev, which can effectively suppress the eddy current normal force, ensure the stable suspension of the EDS maglev train during emergency braking, and further enhance the eddy current braking force, which can bring a shorter emergency braking time to the train and effectively ensure operational safety.

[0010] The technical solution adopted by the present invention is as follows:

[0011] A linear eddy current braking system with normal force suppression and braking force enhancement functions applied to an electric high-speed magnetic levitation, the steps are as follows:

[0012] S1. Construct the PHE-LECB system and use the generalized plane space subdomain method to establish a two-dimensional simplified model of a pair of poles of the PHE-LECB system;

[0013] S2, according to the two-dimensional simplified model of a pair of poles of the PHE-LECB system established in step S1, a partial differential model of magnetic vector potential is established, and the magnetic flux density distribution and electromagnetic force model of the system are analyzed;

[0014] S3, after the partial differential model of magnetic vector potential established in S2, the sub-domain magnetic field boundary condition analysis is performed;

[0015] S4. Establish the magnetic flux density distribution and electromagnetic force model according to S2 and S3 to obtain the total braking force and normal force of the system;

[0016] S5. After obtaining the analytical model of the key parameters of the braking force and normal force of the PHE-LECB system, a finite element model of the PHE-LECB system is established to verify the correctness of the analytical model.

[0017] Preferably, the magnetic field system involved in the operation of the PHE-LECB system is mainly divided into the main magnetic flux magnetic field, the air gap magnetic flux magnetic field and the eddy current magnetic flux magnetic field. The PHE-LECB system carries out force analysis with the secondary induction plate as the analysis object.

[0018] Preferably, in S1, the two-dimensional simplified model of a pair of poles of the PHE-LECB system established includes four regions, wherein region I is the primary eddy current brake, including the excitation coil, permanent magnet block, magnetic core and yoke; region II is the brake air gap, which is regarded as a vacuum environment; region III is the secondary induction plate of ferromagnetic material; and region IV is the vacuum environment outside the induction plate.

[0019] Preferably, in S1, the magnetic flux leakage caused by field diffusion at the edge of the magnetic pole, the thermal expansion of the components, the temperature rise effect and the hysteresis effect, the influence of the lateral edge effect are ignored, and the air gap magnetic resistance is increased by the stator slotting, and the Carter coefficient k is introduced. C , the change of air gap reluctance is equivalent to the increase of air gap length, and the equivalent air gap length is the air gap coefficient and k C The product of:

[0020]

[0021] Where τ is the eddy current brake pole pitch, δ is the air gap thickness, b p is the brake pole width, and γ is the air gap coefficient.

[0022] Preferably, in S2, by establishing a partial differential model of magnetic vector potential, analyzing the magnetic density distribution and electromagnetic force model of the system, and introducing the magnetic vector A as the field function to be solved, the solution process is as follows:

[0023] S21. According to the fact that the magnetic induction intensity of each subdomain in the two-dimensional plane of the electromagnetic field has only the components in the x and y directions, the electromagnetic field intensity B is obtained, and combined with the electromagnetic field conclusion, the Poisson equation of the system is obtained, where the electromagnetic field intensity expression is:

[0024] B (i) =(B x (x,y),B y (x,y),0)i=I,II,III,IV;

[0025] The Poisson equation for the system is:

[0026]

[0027] Where μ0 is the vacuum magnetic permeability, μ r is the relative magnetic permeability of the material, J is the current density;

[0028] S22. According to the Poisson equation obtained in S21, the magnetic vector potential A has only a component in the z direction, and according to the Maxwell equations, the constraint conditions satisfied by the magnetic vector potential A are obtained, where the component expression of the magnetic vector potential A in the z direction is:

[0029] A (i) =(0,0,A z (x,y))i=I,II,III,IV;

[0030] The constraint expression satisfied by the magnetic vector potential A is:

[0031]

[0032] Among them, ▽ is a differential operator in vector form;

[0033] S23. The magnetic vector potential A changes periodically with respect to x. The general solution of A in the z direction is obtained by separation of variables method. The formula is as follows:

[0034]

[0035] Where n is the harmonic order, G(y) n is the function of y to be determined, j is the imaginary unit, and k is the intermediate variable;

[0036] S24. According to the eddy current braking principle, calculate the eddy current in the induction plate of region III and calculate the eddy current density J w , whose expression is:

[0037] J w =σvB (III)y ;

[0038] In the formula, B (III)y is the normal component of the magnetic induction intensity in region III, v is the relative motion velocity between the primary and secondary, and σ is the conductivity of the secondary induction plate;

[0039] S25. According to the equations obtained in the above steps S21-24, the partial differential equations satisfied by the magnetic vector potential in each subdomain space are obtained by combining them, and the partial differential equations are solved to obtain the nth harmonic expression of the magnetic vector potential, wherein the expression of the partial differential equation satisfied by the magnetic vector potential in each subdomain space is:

[0040]

[0041] The nth harmonic expression of the magnetic vector potential is:

[0042]

[0043] Where C (i)n , D (i)n is the unknown coefficient, i represents the area number, α is the intermediate variable, and its expression is:

[0044] Preferably, in S3, the process of solving the undetermined coefficients of the nth harmonic expression of the magnetic vector potential is as follows:

[0045] S31, transforming the connection conditions on the interfaces of different regions into the form of magnetic vector potential, wherein the connection conditions on the interfaces of different regions are:

[0046]

[0047] In the formula, B y is the normal component of the magnetic flux density, H x is the tangential component of the magnetic field strength, K z is the z-component of the line density on the regional interface;

[0048] The magnetic vector potential is in the form of:

[0049]

[0050] S32. Perform Fourier decomposition on the line current density distribution curve of the interface between region I and region II to obtain the only odd harmonic components in the expression of the periodic square wave function, and the expression is:

[0051]

[0052] in,

[0053] S33, introduce the conditions that the equivalent line electric density constant b1 and line electric density constant b2 of permanent magnets meet:

[0054]

[0055] Where N is the number of turns of the excitation coil, I is the excitation current, and b is c 、h m is the device structure parameter, H C is its own magnetic coercivity;

[0056] S34. According to the Euler formula, the nth harmonic of the line density at the interface between area I and area II is expressed as follows:

[0057] K (I)(II)zn =a n e jnkx n=1,3,5...;

[0058] In the formula,

[0059] S35. According to the equations obtained in the above steps S31-S34, the boundary condition equation is obtained, and the boundary condition equation is brought into step S25 to solve and obtain the nth harmonic expression of the magnetic vector potential. After simplification, the undetermined coefficients of the magnetic vector potential function are obtained, and the expression is:

[0060]

[0061] In the formula, L, M, and N are quantities introduced to simplify the results. The expressions are as follows:

[0062]

[0063] Preferably, in S4, the process of solving the total braking force and normal force of the system is as follows:

[0064] S41. According to the definition of magnetic vector potential function A, the expression of magnetic induction intensity B with respect to A is obtained and combined with the nth harmonic expression of magnetic vector potential obtained in S25, the nth harmonic expression of air gap magnetic induction intensity is obtained, wherein the expression of magnetic induction intensity B with respect to A is:

[0065]

[0066] The nth harmonic expression of the air gap magnetic induction intensity is:

[0067]

[0068] S42. According to the obtained nth harmonic expression of the air gap magnetic induction intensity, let y = δ, and substitute the undetermined coefficients to obtain the expression of the magnetic induction intensity at the surface of the induction plate:

[0069]

[0070] S43. The Maxwell stress method is used to solve the eddy current braking force and normal force of the system. The nth harmonic calculation formula of the eddy current brake braking force and normal force is:

[0071]

[0072] Wherein, w is the vertical depth of the eddy current brake device on the paper surface, and p is the number of pole pairs;

[0073] S44, calculating and arranging the nth harmonic calculation formula obtained in S43 to obtain the nth harmonic analytical expressions of the braking force and the normal force, which are:

[0074]

[0075] In the formula, C is the quantity introduced to simplify the calculation results. The expression of C is:

[0076] S45. The total braking force and normal force of the system are obtained by sorting out the nth harmonic analytical expression obtained according to S44, which are:

[0077]

[0078] Preferably, in S35, the boundary conditions obtained are divided into four types, which are specifically classified as follows:

[0079] S351, when y→-∞, according to the nth harmonic expression of the magnetic vector potential obtained in S25, A (I)zn =0, then D (I)n =0; when y→+∞, due to A (IV)zn =0, C (IV)n =0.

[0080] S352. When y = 0, the relative magnetic permeability of the ferromagnetic region I is infinite, H (I)xn =0, the expression of magnetic vector potential obtained according to S31 can be obtained:

[0081]

[0082] S353, when y = δ, there is no line current on the interface, and using the natural boundary conditions, the expression of the magnetic vector potential obtained in S31 can be obtained:

[0083]

[0084] S354, when y=δ+b g When there is no line current on the interface, the natural boundary condition is also used:

[0085]

[0086] A device of a linear eddy current braking system with normal force suppression and braking force enhancement functions applied to electric high-speed magnetic levitation, wherein the mechanism consists of a primary brake and a rigid single-layered graded induction plate, wherein the primary brake includes adjacent oppositely excited excitation windings and parallel magnetized neodymium iron boron permanent magnets, wherein the mechanism adopts a parallel magnetic circuit structure, and the magnetic circuit of the device is a magnetic concentrating structure.

[0087] Preferably, the normal force on the device is divided into two parts: the normal attraction force between the main magnetic flux of the magnetic circuit and the induction plate, and the normal repulsion force between the eddy current of the induction plate and the air gap magnetic flux.

[0088] The present invention has the following characteristics and advantages:

[0089] (1) The proposed PHE-LECB system can effectively suppress the eddy current normal force and ensure the stable suspension of the EDS maglev train during emergency braking;

[0090] (2) The proposed PHE-LECB system can further enhance the eddy current braking force, which can provide the train with a shorter emergency braking time.

[0091] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments, but the embodiments should not be construed as limiting the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 This is a schematic diagram of the EDS high-speed maglev track structure;

[0093] Figure 2 It is the structure diagram of the electrically excited linear LECB;

[0094] Figure 3 It is a schematic diagram of static eddy current braking magnetic lines of force;

[0095] Figure 4 It is a schematic diagram of the magnetic lines of force of dynamic eddy current braking;

[0096] Figure 5 It is a three-dimensional magnetic density model diagram of the electrically excited LECB system;

[0097] Figure 6 are the characteristic curves of eddy current braking force and normal force generated by the LECB system, where (a) is the braking force curve, and (b) is the eddy current electromagnetic force-speed characteristic curve;

[0098] Figure 7It is the vertical force curve of a single carriage;

[0099] Figure 8 is a schematic diagram of a four-module Halbach array;

[0100] Fig. 9 is a comparison diagram of the braking force and normal force under two excitation modes, where (a) is a braking force-speed curve diagram, and (b) is a normal force-speed curve diagram;

[0101] Fig.10 It is a three-dimensional model diagram of the PHE-LECB system;

[0102] Fig.11 is the magnetic field line distribution diagram of the PHE-LECB system, where (a) is the diagram without electrical excitation input, and (b) is the diagram with electrical excitation input;

[0103] Fig.12 It is the magnetic density cloud diagram of PHE-LECB system, among which (a) is the diagram of electric excitation eddy current braking system, and (b) is the diagram of parallel hybrid excitation eddy current braking system;

[0104] Fig.13 is a comparison diagram of electromagnetic force characteristics, where (a) is a braking force curve diagram, and (b) is a normal force curve diagram;

[0105] Fig.14 It is a schematic diagram of a pair of poles of the PHE-LECB system;

[0106] Fig.15 is the line current density distribution curve of the interface between regions Ⅰ and Ⅱ;

[0107] Fig.16 is the comparison curve between the analytical solution and the simulation solution of eddy current electromagnetic force, where (a) is the braking force curve and (b) is the normal force curve;

[0108] Fig.17 This is the PHE-LECB system structure diagram. DETAILED DESCRIPTION

[0109] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0110] For the EDS high-speed maglev train, the side wall of the train and the track involves the suspension / guiding magnetic field interaction system between the superconducting magnet and the "8"-shaped coil, as well as the propulsion magnetic field interaction system of the long stator linear synchronous motor. The electromagnetic relationship on the side is particularly complex. However, there is ample space at the bottom of the train and the track and there are no other electromagnetic mechanisms. At the same time, the impact of the above-mentioned magnetic field system on the bottom space is also relatively weak. Therefore, the primary brake of the eddy current braking system is only convenient to install under the car body suspension frame, and the secondary induction plate is laid between the two wheel treads on the bottom surface of the track. The primary and secondary are distributed vertically. The specific structural form can be seen in Figure 1 .

[0111] Technical solution of prior art 1

[0112] like Figure 2 As shown in the figure, the electric excitation linear LECB system mainly includes a primary electromagnet and a ferromagnetic induction plate. First, direct current is passed through the coil of the excitation electromagnet. When the relative speed between the excitation electromagnet and the induction plate is 0, the magnetic flux enters the induction plate through the air gap from the electromagnet. Since there is no relative motion, no eddy current is induced in the induction plate. Figure 3 The figure shows the distribution of eddy current braking magnetic lines of force when stationary. As shown in the figure, the magnetic lines of force are symmetrically distributed along the direction of relative motion between the primary and secondary, and the main magnetic field will not be distorted. In this case, only a normal force will be generated between the excitation electromagnet and the induction plate, and no force will be generated in the direction of relative motion between the primary and secondary.

[0113] When relative motion occurs between the excitation electromagnet and the induction plate, according to Lenz's law, the magnetic flux of the electromagnet enters the induction plate through the air gap. As the magnetic flux changes continuously, eddy current is induced in the induction plate. The eddy current magnetic field generated by this eddy current interacts with the main magnetic field, causing a certain distortion of the main magnetic field, such as Figure 3 As shown in the figure, the magnetic field in the air gap at the front end of the electromagnet in the direction of motion is weakened, and the magnetic field in the air gap at the rear end of the electromagnet is strengthened. The magnetic lines of force in the air gap are inclined. Therefore, in addition to the normal force, the electromagnetic force between the electromagnet and the induction plate also has a braking force along the direction of relative motion.

[0114] Although the currently widely used electrically excited LECB system can provide appropriate train braking deceleration, the resulting eddy current normal force will seriously destroy the stable suspension state of the EDS maglev train, and may even cause the car body to become unstable and hit the track, endangering the lives and property of passengers. Figure 5The three-dimensional magnetic flux density model of the electrically excited LECB system established by ANSYS-Maxwell is shown. The magnetic field distribution of each part of the LECB system can be clearly observed from the figure. The system magnetic flux passes through the air gap and the secondary induction plate from the primary brake to form a closed magnetic circuit. Based on the fact that the system eddy current braking force can meet the braking requirements of the vehicle body, the actual impact of the eddy current normal force on the EDS maglev train is analyzed.

[0115] Figure 6 The characteristic curve of eddy current braking force and normal force generated by the LECB system. Figure 6 As shown in (a), during the braking process, as the relative speed continues to decrease, the braking force generated by the eddy current braking gradually increases and reaches a peak value at a speed of about 100 km / h. After that, as the relative speed further decreases, the braking force decreases rapidly. Figure 6 (b) shows that when the relative speed between the primary and secondary is high, the normal force generated by eddy current braking manifests as a repulsive force. As the speed continues to decrease, the repulsive force continues to decrease and its rate of change continues to accelerate. When the relative speed drops to a certain value, the normal force changes from a repulsive force to an attractive force and increases rapidly as the speed decreases. The reversal point of the normal force appears at around 300 km / h.

[0116] Since the EDS maglev train's suspension method is passive suspension based on the principle of zero magnetic flux, the system's suspension force is sufficient to support the weight of the vehicle body only when the train speed is higher than 100km / h. Otherwise, it needs to rely on wheels to support its operation.

[0117] like Figure 7 As shown in the figure, for a single carriage, the eddy current normal force is superimposed on the body weight and compared with the body suspension force. As can be seen from the figure, when the train activates eddy current braking, as the speed of the train continues to decrease, after the eddy current normal force passes the reversal point, the normal gravity will appear as a vertical load function that is negatively correlated with the train speed. In the subsequent braking process, the suspension force that can be provided by the 8-shaped coil is obviously insufficient, which seriously affects the stable suspension operation of the train and even causes instability and collision with the rails. It can be seen that the destruction of the suspension state of EDS trains by the eddy current normal force has become the primary problem restricting the promotion and application of linear eddy current braking devices.

[0118] Technical solution of prior art 2

[0119] Permanent magnet linear eddy current brake system used in rail transit. The permanent magnet of the permanent magnet eddy current brake device adopts a four-module Halbach array, and its magnetization direction is as follows: Figure 8 This array form has the characteristics of strong side magnetic field strength, few harmonic components, and relatively ideal sinusoidal characteristics, and has high engineering application value.

[0120] Adjust the excitation parameters of the electric excitation LECB system to make it roughly equal to the air gap flux density generated by the permanent magnet LECB system, such as Fig. 9 As shown in the figure. It can be seen from the figure that the eddy current brake air gap magnetic flux waveforms of the two excitation methods are basically the same, and the peak-to-peak value of the electric excitation LECB is slightly larger. Due to the asymmetric arrangement characteristics of the Halbach array, the edge peak of one side of the permanent magnet LECB is significantly smaller than that of the electric excitation LECB. Except for the two waveforms at both ends, the period and peak value of the other waveforms are basically the same. Under this condition, the eddy current electromagnetic force performance of the two is compared as shown in the figure. Fig. 9 shown.

[0121] Depend on Fig. 9 From (a) in the figure, it can be seen that in the same air gap magnetic density environment, the braking force of the permanent magnet LECB system is much greater than that of the electromagnetic eddy current braking, and the peak speed point of the permanent magnet LECB system is slightly delayed relative to the electric excitation LECB system. The maximum value of the eddy current braking force of the permanent magnet LECB system is about 3.3 times that of the electric excitation LECB system. Fig. 9 (b) in the figure shows that at low speed, the normal attraction of the permanent magnet eddy current brake is significantly greater than the attraction of the electromagnetic LECB system, which undoubtedly further aggravates the degree of damage caused by the normal force of the LECB system to the stable suspension of the EDS maglev train.

[0122] Although the permanent magnet LECB system can greatly improve the braking force of LECB, the normal force it generates is also further increased, which aggravates the degree of damage to the stable suspension of EDS maglev train caused by the normal force of the LECB system. Therefore, an eddy current braking system, the PHE-LECB system, is proposed, which can effectively suppress the normal force while providing a greater eddy current braking force.

[0123] A linear eddy current braking system with normal force suppression and braking force enhancement functions applied to an electric high-speed magnetic levitation vehicle comprises the following steps:

[0124] S1. Construct the PHE-LECB system and use the generalized plane space subdomain method to establish a two-dimensional simplified model of a pair of poles of the PHE-LECB system;

[0125] S2, according to the two-dimensional simplified model of a pair of poles of the PHE-LECB system established in step S1, a partial differential model of magnetic vector potential is established, and the magnetic flux density distribution and electromagnetic force model of the system are analyzed;

[0126] S3, after the partial differential model of magnetic vector potential established in S2, the sub-domain magnetic field boundary condition analysis is performed;

[0127] S4. Establish the magnetic flux density distribution and electromagnetic force model according to S2 and S3 to obtain the total braking force and normal force of the system;

[0128] S5. After obtaining the analytical model of the key parameters of the braking force and normal force of the PHE-LECB system, a finite element model of the PHE-LECB system is established to verify the correctness of the analytical model.

[0129] From the system level, the magnetic field system involved in the operation of the LECB system is mainly the main magnetic flux magnetic field, the air gap magnetic flux magnetic field and the eddy current magnetic flux magnetic field. In order to analyze the intrinsic relationship between the electromagnetic force of the system and the main magnetic field system, the force analysis is carried out with the secondary induction plate as the analysis object.

[0130] As for the eddy current braking force, its mechanism is that the primary and secondary relative motion generates eddy currents in the conductor induction plate, and the eddy currents, under the action of the air gap magnetic field, make the induction plate act on the Ampere force, which eventually manifests as resistance that hinders the direction of relative motion. Its microscopic essence is the force of the air gap magnetic field on the charged particles in the induction plate. The normal force on the device is actually composed of two parts: one is the normal attraction between the main magnetic flux of the magnetic circuit and the induction plate. The larger the main magnetic flux, the greater the attraction generated. The second is the normal repulsion between the eddy current of the induction plate and the air gap magnetic flux. The larger the values ​​of the two, the greater the repulsion generated.

[0131] According to Faraday's law of electromagnetic induction, normal gravity becomes the main manifestation in the low-speed domain. Considering the essential relationship between the magnetic field systems of the system and the eddy current braking force and normal force, the following is constructed: Fig.10 The PHE-LECB system shown.

[0132] Structurally, the mechanism consists of a primary brake and a rigid single-layer cascade induction plate. The primary includes adjacent oppositely excited excitation windings and parallel magnetized NdFeB permanent magnets. As a hybrid excitation device, the mechanism combines the advantages of electric excitation and permanent magnet eddy current brakes. Compared with the permanent magnet type, it has the function of adjusting the air gap magnetic field, and compared with electric excitation, it has the advantages of high efficiency and large air gap magnetic density. At the same time, compared with the series magnetic circuit, the parallel magnetic circuit structure does not include permanent magnets in the magnetic flux path of the excitation winding, the magnetic resistance of the excitation circuit is small, and the magnetic circuit of the device is a magnetic concentrating structure, so the braking force density is higher.

[0133] The fundamental reason why the PHE-LECB mechanism can meet the design requirements can be clearly explained from the system magnetic circuit characteristics of the PHE-LECB. Fig.11 As shown in the figure, when the system has no excitation input, that is, the permanent magnet works alone, ideally the permanent magnet flux only passes through the primary core yoke closure, and does not pass through the air gap, so no braking force is generated (but in actual situations there will be leakage magnetic flux); when the system inputs excitation, the permanent magnet flux is divided into two paths through the parallel magnetic circuit to improve the overall performance of the system magnetic circuit: on the one hand, it passes through the core in the opposite direction of the main magnetic flux, greatly reducing the magnetic saturation of the core. Fig.12From the magnetic density cloud diagram shown, the magnetic core density of the parallel hybrid excitation mechanism is lighter in color and smaller in value than that of the electric excitation mechanism. This means that for the same core material, the new mechanism can withstand a larger external excitation current without saturation. On the other hand, part of the permanent magnet flux will pass through the air gap via the secondary induction plate to form a new closed magnetic circuit, which strengthens the air gap flux on the basis of the original main magnetic field.

[0134] Combined with the interaction between the electromagnetic force and magnetic field system of the eddy current brake system, for the electrically excited LECB system under the same input excitation conditions, the braking force of the PHE-LECB system is naturally increased under the premise that the air gap magnetic flux is strengthened. Fig.13 (a) in the figure. As for the normal force, since the PHE-LECB system does not change the DC excitation input of the system, the system attraction will not change significantly. However, if the air gap flux density and eddy current size increase, the repulsive force will increase in the full speed range. Therefore, the normal force of the PHE-LECB system, such as Fig.13 (b) in the figure shows, on a macroscopic level, that the low-speed attraction is suppressed while the high-speed repulsion is enhanced.

[0135] Therefore, it can be proved that the PHE-LECB system proposed in the present invention has the practical effects of suppressing the eddy current normal force and enhancing the line braking force.

[0136] like Fig.14 As shown in the figure, a two-dimensional simplified model of a pair of poles of the PHE-LECB system is established. Among them, region I is the primary eddy current brake, which includes the excitation coil, permanent magnet block, magnetic core and yoke; region II is the brake air gap, which is regarded as a vacuum environment; region III is the secondary induction plate of ferromagnetic material; region IV is the vacuum environment outside the induction plate. The interaction between various physical quantities in the eddy current braking process is very complex, and its electromagnetic characteristics are affected by many factors. Therefore, the following assumptions are made in the theoretical modeling: the parallel magnetic flux is only distributed in the relative air gap and induction plate, and the leakage magnetic flux caused by field diffusion at the edge of the magnetic pole is ignored; the electrical conductivity and magnetic permeability of each component of the system are constants; the thermal expansion, temperature rise and hysteresis effect of the components are ignored; the two-dimensional model of the system is analyzed, and the influence of lateral edge effects is ignored.

[0137] Fig.14 Where τ is the eddy current brake pole pitch, δ is the air gap thickness, and b p is the brake pole width, b c is the primary slot width, h m is the width of the permanent magnet, b g is the thickness of the sensing plate, and w is the stack thickness of the device.

[0138] Considering that stator slotting will increase the air gap magnetic resistance, the Carter coefficient k is introduced C, the change of air gap reluctance can be equivalent to the increase of air gap length. The equivalent air gap length is the product of air gap coefficient and k C The product of:

[0139]

[0140] In S2, by establishing the partial differential model of magnetic vector potential, analyzing the magnetic density distribution and electromagnetic force model of the system, and introducing the magnetic vector A as the field function to be solved, the solution process is as follows:

[0141] S21. According to the fact that the magnetic induction intensity of each subdomain in the two-dimensional plane of the electromagnetic field has only the components in the x and y directions, the electromagnetic field intensity B is obtained, and combined with the electromagnetic field conclusion, the Poisson equation of the system is obtained, where the electromagnetic field intensity expression is:

[0142] B (i) =(B x (x,y),B y (x,y),0)i=I,II,III,IV;

[0143] The Poisson equation for the system is:

[0144]

[0145] Where μ0 is the vacuum magnetic permeability, μ r is the relative magnetic permeability of the material, J is the current density;

[0146] S22. According to the Poisson equation obtained in S21, the magnetic vector potential A has only a component in the z direction. According to the Maxwell equations, the constraint conditions satisfied by the magnetic vector potential A are obtained. The form of the constraint conditions can be given arbitrarily. The component expression of the magnetic vector potential A in the z direction is:

[0147] A (i) =(0,0,A z (x,y))i=I,II,III,IV;

[0148] The constraint expression satisfied by the magnetic vector potential A is:

[0149]

[0150] Among them, ▽ is a differential operator in vector form;

[0151] S23. The magnetic vector potential A changes periodically with respect to x. The general solution of A in the z direction is obtained by separation of variables method. The general solution is as follows:

[0152]

[0153] In the formula, n is the harmonic order, G(y)n is the function of y to be determined, j is the imaginary unit, and k is the intermediate variable;

[0154] exist Fig.14 According to the principle of equal magnetic potential, the excitation winding and permanent magnet in region I are equivalent to the linear current density on the interface between region I and region II. This will cause the magnetic field calculation results in region I to be distorted, but will not affect the magnetic field calculations in regions II and III, thus ensuring the correctness of the eddy current electromagnetic force solution results.

[0155] S24. According to the eddy current braking principle, calculate the eddy current in the induction plate of region III and calculate the eddy current density J w , whose expression is:

[0156] J w =σvB (III)y ;

[0157] In the formula, B (III)y is the normal component of the magnetic induction intensity in region III, v is the relative motion velocity between the primary and secondary, and σ is the conductivity of the secondary induction plate;

[0158] S25. According to the equations obtained in the above steps S21-24, the partial differential equations satisfied by the magnetic vector potential in each subdomain space are obtained by combining them, and the partial differential equations are solved to obtain the nth harmonic expression of the magnetic vector potential, wherein the expression of the partial differential equation satisfied by the magnetic vector potential in each subdomain space is:

[0159]

[0160] The nth harmonic expression of the magnetic vector potential is:

[0161]

[0162] Where C (i)n , D (i)n is the unknown coefficient, i represents the area number, α is the intermediate variable, and its expression is:

[0163] In S3, the process of solving the unknown coefficients of the nth harmonic expression of the magnetic vector potential is as follows:

[0164] S31, transforming the connection conditions on the interfaces of different regions into the form of magnetic vector potential, wherein the connection conditions on the interfaces of different regions are:

[0165]

[0166] In the formula, B y is the normal component of the magnetic flux density, H x is the tangential component of the magnetic field strength, K z is the z-component of the line density on the regional interface;

[0167] The magnetic vector potential is in the form of:

[0168]

[0169] The line current density at the interface between region I and region II concentrates the external excitation of the entire system. The line current density distribution curve is shown in Fig.15 shown.

[0170] The expressions of the horizontal coordinate values ​​of the curve are shown in Table 1.

[0171] Table 1 Line density curve horizontal coordinate expression

[0172] parameter expression <![CDATA[x1]]> <![CDATA[(τ-b c ) / 2]]> <![CDATA[x2]]> <![CDATA[(τ-h m ) / 2]]> <![CDATA[x3]]> <![CDATA[(τ+h m ) / 2]]> <![CDATA[x4]]> <![CDATA[(τ+b c ) / 2]]> <![CDATA[x5]]> τ

[0173] S32, yes Fig.15 The line current density distribution curve of the interface between region I and region II in the Fourier decomposition is performed to obtain the only odd harmonic components in the expression of the periodic square wave function, and its expression is:

[0174]

[0175] in,

[0176] S33, introduce the conditions that the equivalent line electric density constant b1 and line electric density constant b2 of permanent magnets meet:

[0177]

[0178] Where N is the number of turns of the excitation coil, I is the excitation current, and b is c 、h m is the device structure parameter, H C is its own magnetic coercivity;

[0179] S34. According to the Euler formula, the nth harmonic of the line density at the interface between area I and area II is expressed as follows:

[0180] K (I)(II)zn =a n e jnkx n=1,3,5...;

[0181] In the formula,

[0182] S35. According to the equations obtained in the above steps S31-34, boundary condition equations are obtained. The obtained boundary conditions are divided into four types, which are specifically classified as follows:

[0183] S351, when y→-∞, according to the nth harmonic expression of the magnetic vector potential obtained in S25, A (I)zn =0, then D (I)n=0; when y→+∞, due to A (IV)zn =0, C (IV)n =0.

[0184] S352. When y = 0, the relative magnetic permeability of the ferromagnetic region I is infinite, H (I)xn =0, the expression of magnetic vector potential obtained according to S31 can be obtained:

[0185]

[0186] S353, when y = δ, there is no line current on the interface, and using the natural boundary conditions, the expression of the magnetic vector potential obtained in S31 can be obtained:

[0187]

[0188] S354. When y = δ + bg, there is no line current on the interface, and the natural boundary condition is also used:

[0189]

[0190] Substitute the boundary condition equation into step S25 to solve the nth harmonic expression of the magnetic vector potential, and simplify to obtain the undetermined coefficient of the magnetic vector potential function, which is expressed as follows:

[0191]

[0192] In the formula, L, M, and N are quantities introduced to simplify the results. The expressions are as follows:

[0193]

[0194] In S4, the solution process for obtaining the total braking force and normal force of the system is as follows:

[0195] S41. According to the definition of magnetic vector potential function A, the expression of magnetic induction intensity B with respect to A is obtained and combined with the nth harmonic expression of magnetic vector potential obtained in S25, the nth harmonic expression of air gap magnetic induction intensity is obtained, wherein the expression of magnetic induction intensity B with respect to A is: The nth harmonic expression of the air gap magnetic induction intensity is:

[0196] S42. According to the obtained nth harmonic expression of the air gap magnetic induction intensity, let y = δ, and substitute the undetermined coefficients to obtain the expression of the magnetic induction intensity at the surface of the induction plate:

[0197]

[0198] The Maxwell stress method is used to solve the eddy current braking force and normal force of the system, that is, the equivalent magnetic tension is used to replace the volume force, and the resultant force and moment in the magnetic mass of a given volume are equivalent to the calculation method of the resultant force of each tension on the surrounding surface. It is more effective in determining the electromagnetic force on the interface.

[0199] S43. The Maxwell stress method is used to solve the eddy current braking force and normal force of the system. The nth harmonic calculation formula of the eddy current brake braking force and normal force is:

[0200]

[0201] Wherein, w is the vertical depth of the eddy current brake device on the paper surface, and p is the number of pole pairs;

[0202] S44, calculating and arranging the nth harmonic calculation formula obtained in S43 to obtain the nth harmonic analytical expressions of the braking force and the normal force, which are:

[0203]

[0204] In the formula, C is the quantity introduced to simplify the calculation results. The expression of C is:

[0205] S45. The total braking force and normal force of the system are obtained by sorting out the nth harmonic analytical expression obtained according to S44, which are:

[0206]

[0207] In order to verify the correctness of the analytical model, a finite element model of the PHE-LECB system was established. The main parameters of the system are shown in Table 2.

[0208] Table 2 Main parameters of PHE-LECB system

[0209]

[0210]

[0211] In ANSYS Maxwell, a transient solver is used for simulation and the motion condition is set as the primary brake moves parallel to the secondary induction plate, with a maximum relative motion speed of 600 km / h. Fig.16 This is a comparison curve between the simulation solution and the analytical solution of the system's eddy current electromagnetic force changing with speed.

[0212] Depend on Fig.16It can be seen that the calculation results of the analytical model are basically consistent with the finite element simulation results, and the peak point of the braking force and the reversal point of the normal force are consistent. From the calculation results of the full-speed domain, the finite element simulation solution is slightly higher than the analytical solution, especially in the low-speed domain. This is mainly due to the neglect of the influence of the hysteresis effect during the analytical modeling process. The magnetization state of the induction plate is related to the history of the external magnetic field. Under low-speed conditions, the frequency of alternating changes in the direction of the magnetic field is low, and the hysteresis effect is more significant, which will affect the establishment and attenuation of the magnetic field, resulting in the electromagnetic force predicted by the mathematical model being smaller than the actual situation.

[0213] In summary, the PHE-LECB system proposed in the present invention can effectively suppress the eddy current normal force, ensure the stable suspension of the EDS maglev train during emergency braking, and provide the train with a shorter emergency braking time.

[0214] The embodiments described above are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A linear eddy current braking system with normal force suppression and braking force enhancement functions applied to electric high-speed magnetic levitation, characterized in that: Here are the steps: S1. Construct the PHE-LECB system and use the generalized plane space subdomain method to establish a two-dimensional simplified model of a pair of poles of the PHE-LECB system; S2, according to the two-dimensional simplified model of a pair of poles of the PHE-LECB system established in step S1, a partial differential model of magnetic vector potential is established, and the magnetic flux density distribution and electromagnetic force model of the system are analyzed; S3, after the partial differential model of magnetic vector potential established in S2, the sub-domain magnetic field boundary condition analysis is performed; S4. Establish the magnetic flux density distribution and electromagnetic force model according to S2 and S3 to obtain the total braking force and normal force of the system; S5. After obtaining the analytical model of the key parameters of the braking force and normal force of the PHE-LECB system, a finite element model of the PHE-LECB system is established to verify the correctness of the analytical model.

2. According to claim 1, a linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation, characterized in that: The magnetic field system involved in the operation of the PHE-LECB system is mainly divided into the main magnetic flux magnetic field, the air gap magnetic flux magnetic field and the eddy current magnetic flux magnetic field. The PHE-LECB system carries out force analysis with the secondary induction plate as the analysis object.

3. According to claim 1, a linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation, characterized in that: In S1, the two-dimensional simplified model of a pair of poles of the PHE-LECB system established includes four regions, among which region I is the primary eddy current brake, including the excitation coil, permanent magnet block, magnetic core and yoke; region II is the brake air gap, which is regarded as a vacuum environment; region III is the secondary induction plate of ferromagnetic material; and region IV is the vacuum environment outside the induction plate.

4. A linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation according to claim 1, characterized in that: In S1, the magnetic flux leakage caused by field diffusion at the edge of the magnetic pole, the thermal expansion of the components, the temperature rise effect and the hysteresis effect are ignored, the influence of the lateral edge effect is ignored, and the stator slotting will increase the air gap magnetic resistance, and the Carter coefficient k is introduced C , the change of air gap reluctance is equivalent to the increase of air gap length, and the equivalent air gap length is the air gap coefficient and k C The product of: Where τ is the eddy current brake pole pitch, δ is the air gap thickness, b p is the brake pole width, and γ is the air gap coefficient.

5. The linear eddy current braking system with normal force suppression and braking force enhancement functions applied to electric high-speed magnetic levitation according to claim 1, characterized in that: In S2, by establishing the partial differential model of magnetic vector potential, analyzing the magnetic density distribution and electromagnetic force model of the system, and introducing the magnetic vector A as the field function to be solved, the solution process is as follows: S21. According to the fact that the magnetic induction intensity of each subdomain in the two-dimensional plane of the electromagnetic field has only the components in the x and y directions, the electromagnetic field intensity B is obtained, and combined with the electromagnetic field conclusion, the Poisson equation of the system is obtained, where the electromagnetic field intensity expression is: B (i) =(B x (x,y), B y (x,y),0)i=I,II,III ,IV 4 The Poisson equation for the system is: Where μ0 is the vacuum magnetic permeability, μ r is the relative magnetic permeability of the material, J is the current density; S22. According to the Poisson equation obtained in S21, the magnetic vector potential A has only a component in the z direction, and according to the Maxwell equations, the constraint conditions satisfied by the magnetic vector potential A are obtained, where the component expression of the magnetic vector potential A in the z direction is: A (i) (0,0,A z (x,y))i(I,II,III,IV); The constraint expression satisfied by the magnetic vector potential A is: Among them, ▽ is a differential operator in vector form; S23. The magnetic vector potential A changes periodically with respect to x. The general solution of A in the z direction is obtained by separation of variables method. The formula is as follows: Where n is the harmonic order, G(y) n is the function of y to be determined, j is the imaginary unit, and k is the intermediate variable; S24. According to the eddy current braking principle, calculate the eddy current in the induction plate of region III and calculate the eddy current density J w , whose expression is: J w =σvB (III)y ; In the formula, B (III)y is the normal component of the magnetic induction intensity in region III, v is the relative motion speed between the primary and secondary, and σ is the conductivity of the secondary induction plate; S25. According to the equations obtained in the above steps S21-24, the partial differential equations satisfied by the magnetic vector potential in each subdomain space are obtained by combining them, and the partial differential equations are solved to obtain the nth harmonic expression of the magnetic vector potential, wherein the expression of the partial differential equation satisfied by the magnetic vector potential in each subdomain space is: The nth harmonic expression of the magnetic vector potential is: Where C (i)n , D (i)n is the unknown coefficient, i represents the region number, α is the intermediate variable, and its expression is:

6. A linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation according to claim 1, characterized in that: In S3, the process of solving the unknown coefficients of the nth harmonic expression of the magnetic vector potential is as follows: S31, transforming the connection conditions on the interfaces of different regions into the form of magnetic vector potential, wherein the connection conditions on the interfaces of different regions are: In the formula, B y is the normal component of the magnetic flux density, H x is the tangential component of the magnetic field strength, K z is the z-component of the line density on the regional interface; The magnetic vector potential is in the form of: S32. Perform Fourier decomposition on the line current density distribution curve of the interface between region I and region II to obtain the only odd harmonic components in the expression of the periodic square wave function, and the expression is: in, S33, introduce the conditions that the equivalent line electric density constant b1 and line electric density constant b2 of permanent magnets meet: Where N is the number of turns of the excitation coil, I is the excitation current, and b is c 、h m is the device structure parameter, H C is its own magnetic coercivity; S34. According to the Euler formula, the nth harmonic of the line density at the interface between area I and area II is expressed as follows: K (I)(II)zn =a n e jnkx n=1,3,5...; S35. According to the equations obtained in the above steps S31-S34, the boundary condition equation is obtained, and the boundary condition equation is brought into step S25 to solve and obtain the nth harmonic expression of the magnetic vector potential. After simplification, the undetermined coefficients of the magnetic vector potential function are obtained, and the expression is: In the formula, L, M, and N are quantities introduced to simplify the results. The expressions are as follows:

7. A linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation according to claim 1, characterized in that: In S4, the solution process of the total braking force and normal force of the system is as follows: S41. According to the definition of magnetic vector potential function A, the expression of magnetic induction intensity B with respect to A is obtained and combined with the nth harmonic expression of magnetic vector potential obtained in S25, the nth harmonic expression of air gap magnetic induction intensity is obtained, wherein the expression of magnetic induction intensity B with respect to A is: The nth harmonic expression of the air gap magnetic induction intensity is: S42. According to the obtained nth harmonic expression of the air gap magnetic induction intensity, let y = δ, and substitute the undetermined coefficients to obtain the expression of the magnetic induction intensity at the surface of the induction plate: S43. The Maxwell stress method is used to solve the eddy current braking force and normal force of the system. The nth harmonic calculation formula of the eddy current brake braking force and normal force is: Wherein, w is the vertical depth of the eddy current brake device on the paper surface, and p is the number of pole pairs; S44, calculating and arranging the nth harmonic calculation formula obtained in S43 to obtain the nth harmonic analytical expressions of the braking force and the normal force, which are: In the formula, C is the quantity introduced to simplify the calculation results. The expression of C is: S45. The total braking force and normal force of the system are obtained by sorting out the nth harmonic analytical expression obtained according to S44, which are:

8. A linear eddy current braking system with normal force suppression and braking force enhancement functions for electric high-speed magnetic levitation according to claim 6, characterized in that: In S35, the boundary conditions obtained are divided into four types, which are specifically classified as follows: S351, when y→-∞, according to the nth harmonic expression of the magnetic vector potential obtained in S25, A (I)zn =0, then D (I)n =0; when y→+∞, due to A (IV)zn =0, C (IV)n =0. S352. When y = 0, the relative magnetic permeability of the ferromagnetic region I is infinite, H (I)xn =0, the expression of magnetic vector potential obtained according to S31 can be obtained: S353, when y = δ, there is no line current on the interface, and using the natural boundary conditions, the expression of the magnetic vector potential obtained in S31 can be obtained: S354, when y=δ+b g When there is no line current on the interface, the natural boundary condition is also used:

9. A linear eddy current braking system device with normal force suppression and braking force enhancement functions applied to electric high-speed magnetic levitation as claimed in any one of claims 1 to 8, characterized in that: The mechanism consists of a primary brake and a rigid single-layered induction plate. The primary brake includes adjacent oppositely excited excitation windings and parallel magnetized NdFeB permanent magnets. The mechanism adopts a parallel magnetic circuit structure, and the device magnetic circuit is a magnetic concentrating structure.

10. The device of the linear eddy current braking system with normal force suppression and braking force enhancement functions applied to electric high-speed magnetic levitation according to claim 9, characterized in that: The normal force on the device is divided into two parts: the normal attraction between the main magnetic flux of the magnetic circuit and the induction plate, and the normal repulsion between the eddy current of the induction plate and the air gap magnetic flux.

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