Accurate and rapid electromagnetic force calculation method for normal-conducting high-speed maglev traffic

Abstract

The invention discloses an accurate and rapid electromagnetic force calculation method for normal-conducting high-speed maglev traffic, which belongs to the technical field of high-speed normal-conducting maglev suspension systems, and comprises the following steps: constructing an equivalent magnetic circuit model of a suspension electromagnet and a guide rail by combining a finite element analysis method and an equivalent magnetic circuit method; calculating the magnetic resistance of each component in the equivalent magnetic circuit model; according to the calculated magnetic resistance of each component, constructing a five-element nonlinear equation set of the equivalent magnetic circuit model; and calculating to obtain the magnetic force of the electromagnet based on the solution of the quinary nonlinear equation set. Firstly, an equivalent magnetic circuit of an electromagnet and a track is obtained based on an equivalent magnetic circuit method; secondly, a magnetic circuit calculation equation set considering ferromagnetic material nonlinear magnetic resistance is established, magnetic circuit magnetic flux can be obtained through the equation set, then the electromagnet magnetic force is obtained, the electromagnetic force obtained through the electromagnetic force calculation method is compared with a finite element simulation result, the maximum relative error of the suspension force calculation result is 4.6%, and the maximum relative error of the suspension force calculation result is 4.6%. The calculation precision is higher than that of a traditional electromagnetic force calculation formula.

Description

Technical Field

[0001] The invention belongs to the technical field of high-speed conventional magnetic levitation suspension systems, and in particular relates to a precise and rapid electromagnetic force calculation method for conventional high-speed magnetic levitation transportation. Background Art

[0002] The Changdao high-speed maglev train uses contactless electromagnetic suction to achieve suspension / guidance. It has the advantages of high operating safety, good riding comfort, strong line adaptability, low operating noise and low maintenance cost. It has been widely used and developed around the world in the past two decades.

[0003] The electromagnetic system of a conventional high-speed maglev train requires active control to achieve stable suspension. The force between the electromagnet and the guide rail is a magnetic field force distributed in three-dimensional space. However, the theoretical analysis of irregular three-dimensional magnetic fields is difficult and the numerical solution efficiency is low. Therefore, in addition to the special design and optimization of the electromagnet structure, almost all existing studies on the suspension / guidance control and dynamics of maglev vehicles use analytical methods to calculate one-dimensional electromagnetic forces. The analytical solution of one-dimensional magnetic force usually assumes that the magnetic permeability of the electromagnet poles, yokes and ferromagnetic guide rails is infinite, the magnetic potential falls evenly on the air gap, the magnetic field is a uniform field perpendicular to the pole surface, and the leakage flux is ignored. The one-dimensional magnetic force analytical formula can accurately reflect the magnetic characteristics of the electromagnet near the rated working state (inversely proportional to the square of the gap and proportional to the square of the coil current), which is suitable for the initial design of maglev vehicles and their performance pre-evaluation. However, the practice of conventional maglev transportation projects shows that when maglev trains pass through track beams with a relatively light mass per linear meter and small structural damping, coupled vibrations often occur violently or even suspension failures. Point drops and rail smashing often occur during high-speed operation. In these cases, the gap and current of the electromagnet have greatly deviated from their rated design values, and traditional analytical methods can no longer accurately solve the magnetic force. Studies have pointed out that when the gap and current fluctuate greatly, the analytical value of the electromagnetic force of the suspension of high-speed maglev vehicles is significantly different from the finite element calculation value and the indoor measured value. In extreme cases, the relative error exceeds 100%. Obviously, if the dynamic model continues to use this analytical formula under harsh working conditions, the simulation results will be far from the actual situation, and it will be difficult to reveal the evolution mechanism of the dynamic performance of high-speed maglev trains.

[0004] In summary, accurate static magnet-track relationship is the cornerstone of suspension / guidance control design and maglev transportation system dynamics design. Although the finite element method is highly accurate in solving magnetic fields, its computational efficiency is low and it is difficult to adapt to dynamic simulation calculations. Therefore, it is necessary to explore a magnetic force calculation method that can not only meet the simulation accuracy of the electromagnet under full working conditions, but also solve quickly, providing a solid foundation for the study of maglev transportation dynamics. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the electromagnetic force of a conventional high-speed maglev transportation accurately and quickly in view of the above-mentioned deficiencies in the prior art, so as to solve the problem that the calculation error of the classical electromagnetic force analytical formula is large, causing the dynamic simulation results to deviate from the actual situation.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for calculating the electromagnetic force of a conventional high-speed maglev transportation system accurately and quickly comprises the following steps:

[0008] S1. Combine finite element analysis method and equivalent magnetic circuit method to construct an equivalent magnetic circuit model of the suspension electromagnet and guide rail;

[0009] S2. Calculate the magnetic resistance of each component in the equivalent magnetic circuit model;

[0010] S3. Construct a set of five nonlinear equations of an equivalent magnetic circuit model based on the calculated magnetic resistance of each component;

[0011] S4. Based on the solution of the five-variable nonlinear equation group, the magnetic force of the electromagnet is calculated.

[0012] Furthermore, an equivalent magnetic circuit model of the suspension electromagnet and the guide rail is constructed in S1, including:

[0013] The finite element analysis method is used to obtain the magnetic field distribution of the electromagnet and the track, and the distribution of magnetic flux lines is simplified;

[0014] Based on the simplified distribution of magnetic flux lines, the equivalent magnetic circuit model of the suspension electromagnet and guide rail is constructed using the equivalent magnetic circuit method.

[0015] Furthermore, the equivalent magnetic circuit model includes an electromagnet, a long stator and an air gap therebetween.

[0016] Furthermore, according to the tooth structure of the stator, the equivalent magnetic circuit model at the suspension gap is divided into a main magnetic circuit and a secondary magnetic circuit.

[0017] Furthermore, S2 calculates the magnetic resistance of each component in the equivalent magnetic circuit model, including:

[0018] Air reluctance of main magnetic circuit R k for:

[0019]

[0020] Auxiliary magnetic circuit air reluctance R l for:

[0021]

[0022] Where δ is the suspension gap; S k , Sl are the cross-sectional areas of the main magnetic circuit and the auxiliary magnetic circuit of the suspension gap respectively; μ0 is the magnetic permeability of air;

[0023] The BH curves of the pole and stator materials are fitted to obtain:

[0024]

[0025] Among them, B e and B s are the magnetic induction intensity in the pole and stator respectively, H is the magnetic field intensity, a e and b e is the fitting coefficient of the BH curve of the magnetic pole material, a s and b s is the fitting coefficient of the BH curve of the stator material;

[0026] therefore:

[0027] Magnetic pole material reluctance R e for:

[0028]

[0029] Stator material reluctance R s for:

[0030]

[0031] Among them, l e is the equivalent magnetic path length of the magnetic pole material in the magnetic path; l s is the equivalent magnetic circuit length of the stator material in the magnetic circuit; S e is the equivalent magnetic pole area of ​​the magnetic pole material; S s is the equivalent pole area of ​​the stator material; Φ is the total magnetic flux of the magnetic circuit.

[0032] Furthermore, the five-variable nonlinear equations of the equivalent magnetic circuit model in S3 include:

[0033]

[0034] Among them, Φ k and Φ l are the main magnetic circuit flux and the auxiliary magnetic circuit flux respectively, N is the number of coil turns, and I is the excitation current;

[0035] Newton iteration method is used to solve the nonlinear equation system G(Φ,Φ k ,Φ l ,R s ,R e ), the steps are as follows:

[0036] (1) Let x = (Φ, Φ k ,Φl ,R e ,R s );

[0037] (2)x (k+1) =x (k) -J(G(x (k) )) -1 G(x (k) ), k = 0, 1, 2…

[0038] Among them, J(G(x (k) )) -1 The system of equations G(x (k) )’s Jacobian matrix;

[0039] (3) Take x (0) =(0.003, 0.0017, 0.0047, 12442, 334), substitute into the above formula and iterate to solve;

[0040] (4) When the iteration error max(x (k+1) -x (k) )≤1×10 -5 When , the iterative solution ends, and the main magnetic flux Φ is obtained. k and the secondary magnetic flux Φ l .

[0041] Furthermore, the electromagnetic force is calculated in S4, including:

[0042] Based on the main magnetic flux Φ k The cross-sectional area of ​​the main magnetic circuit S k The ratio of the secondary magnetic flux Φ l The cross-sectional area of ​​the secondary magnetic circuit S l The ratio of the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l ;

[0043] Based on the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l , calculate the total electromagnetic force F of the U-shaped unit m :

[0044]

[0045] Among them, F mk is the main magnetic circuit electromagnetic force; F ml is the electromagnetic force of the secondary magnetic circuit;

[0046] From this, the electromagnetic force of a standard suspension electromagnet can be obtained as:

[0047]

[0048] Among them, F mi is the electromagnetic force of the i-th U-shaped unit.

[0049] The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation provided by the present invention has the following beneficial effects:

[0050] The present invention first obtains the equivalent magnetic circuit of the electromagnet and the track based on the equivalent magnetic circuit method; secondly, a group of magnetic circuit calculation equations considering the nonlinear magnetic resistance of ferromagnetic materials is established, through which the magnetic circuit flux can be obtained, and then the magnetic force of the electromagnet can be obtained. The electromagnetic force obtained by the electromagnetic force calculation method of the present invention is compared with the finite element simulation result. The maximum relative error of the suspension force calculation result is 4.6%, and the calculation accuracy is higher than that of the traditional electromagnetic force calculation formula.

[0051] At present, most calculations of electromagnetic force do not consider the magnetic resistance of the electromagnet and the track, but only consider the magnetic resistance of the air. When the excitation current is small, the magnetic resistance of the ferromagnetic material is small, and the accuracy of the traditional calculation formula basically meets the requirements; however, when the excitation current is large, the magnetic resistance of the ferromagnetic material will also increase. If it is still ignored, it will significantly affect the calculation results. The present invention fully considers the magnetic resistance of the ferromagnetic material, thereby obtaining a more accurate one-dimensional electromagnetic force calculation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Magnetic field distribution of the electromagnet and track of the present invention.

[0053] Figure 2 The magnetic flux line diagram is simplified for the present invention.

[0054] Figure 3 It is the equivalent magnetic circuit model of the present invention.

[0055] Figure 4 is the magnetization characteristic curve of the magnetic pole material and the stator material of the present invention, wherein: Figure 4 (a) is the magnetization characteristic curve of the pole material, and (b) is the magnetization characteristic curve of the stator material.

[0056] Figure 5 This is a comparison of three magnetic results of the present invention, among which, Figure 5 (a) is a comparison of three magnetic force results with a suspension gap of 8 mm, and (b) is a comparison of three magnetic force results with a suspension gap of 10 mm.

[0057] Figure 6 The present invention is a flow chart of the accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation. DETAILED DESCRIPTION

[0058] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0059] Example 1

[0060] This embodiment provides a method for calculating the electromagnetic force of a conventional high-speed maglev transportation system accurately and quickly. Figure 6 , which specifically includes the following:

[0061] Step S1, combining finite element analysis method and equivalent magnetic circuit method to construct an equivalent magnetic circuit model of the suspension electromagnet and the guide rail, which specifically includes the following contents:

[0062] First, the finite element analysis method is used to obtain the magnetic field distribution of the electromagnet and the track, such as Figure 1 As shown;

[0063] The distribution of magnetic flux lines is simplified, such as Figure 2 As shown;

[0064] Based on the equivalent magnetic circuit method, the equivalent magnetic circuit of the electromagnet and the track is obtained, such as Figure 3 As shown, and considering the tooth structure of the stator, the magnetic circuit at the suspension gap is divided into a main magnetic circuit and a secondary magnetic circuit.

[0065] Depend on Figure 1 , Figure 2 and Figure 3 It can be seen that the equivalent magnetic circuit model consists of an electromagnet, a long stator and the air gap between them.

[0066] Many laws in magnetic fields are very similar to those in electric fields. The concept of magnetic circuit comes from the circuit. The path through which magnetic flux passes through the magnetic medium is called a magnetic circuit. Similar to the fact that the current in a circuit preferentially passes through a path with high conductivity, magnetic flux preferentially passes through a medium with high magnetic permeability. Both the electromagnet and the track are made of magnetic conductive materials with high magnetic permeability, so the magnetic flux preferentially passes through the electromagnet, the track, and the air gap between the two, thus forming a magnetic circuit.

[0067] Step S2, calculating the magnetic resistance of each component in the equivalent magnetic circuit model, which specifically includes the following contents:

[0068] Air reluctance of main magnetic circuit R k for:

[0069]

[0070] Auxiliary magnetic circuit air reluctance R l for:

[0071]

[0072] Where δ is the suspension gap; S k , S l are the cross-sectional areas of the main magnetic circuit and the auxiliary magnetic circuit of the suspension gap respectively; μ0 is the magnetic permeability of air.

[0073] The air permeability μ0 is a constant, the magnetic material permeability is determined by its own BH curve, and the magnetization characteristic curves of the pole and stator materials are as follows: Figure 4 shown.

[0074] The BH curve fitting formula of magnetic pole material is:

[0075]

[0076] The fitting formula of the stator material BH curve is:

[0077]

[0078] Among them, B e and B s are the magnetic induction intensity in the pole and stator respectively, H is the magnetic field intensity, a e and b e is the fitting coefficient of the BH curve of the magnetic pole material, a s and b s is the fitting coefficient of the BH curve of the stator material.

[0079] The magnetic induction intensity B can be expressed as the ratio of magnetic flux to the cross-sectional area of ​​the magnetic circuit, that is,

[0080] Therefore, the magnetic pole material reluctance R can be further obtained e and stator material reluctance R s They are:

[0081]

[0082] Among them, l e is the equivalent magnetic path length of the magnetic pole material in the magnetic path; l s is the equivalent magnetic circuit length of the stator material in the magnetic circuit; S e is the equivalent magnetic pole area of ​​the magnetic pole material; S s is the equivalent pole area of ​​the stator material; Φ is the total magnetic flux of the magnetic circuit.

[0083] Step S3: construct a five-variable nonlinear equation group of the equivalent magnetic circuit model according to the calculated magnetic resistance of each component, which specifically includes the following contents:

[0084] According to the flux continuity principle and Ohm's law of magnetic circuit, a set of five nonlinear equations is established:

[0085]

[0086] Among them, Φ k and Φ l They are the main magnetic circuit flux and the auxiliary magnetic circuit flux respectively, N is the number of coil turns, and I is the excitation current.

[0087] Since the above equation is a nonlinear system of equations, it is impossible to find an analytical solution, so the Newton method is used for iterative solution. The solution process is as follows:

[0088] (1) Let x = (Φ, Φ k ,Φ l ,R e ,R s );

[0089] (2)x (k+1) =x (k) -J(G(x (k) )) -1 G(x (k) ), k = 0, 1, 2…

[0090] Among them, J(G(x (k) )) -1 The system of equations G(x (k) )’s Jacobian matrix;

[0091] (3) Take x (0) =(0.003, 0.0017, 0.0047, 12442, 334), substitute into the above formula and iterate to solve;

[0092] (4) When the iteration error max(x (k+1) -x (k) )≤1×10 -5 When , the iterative solution ends, and the main magnetic flux Φ is obtained. k and the secondary magnetic flux Φ l .

[0093] Step S4: Based on the solution of the five-variable nonlinear equation group, the magnetic force of the electromagnet is calculated.

[0094] Based on the main magnetic flux Φ k The cross-sectional area of ​​the main magnetic circuit S k The ratio of the secondary magnetic flux Φ l The cross-sectional area of ​​the secondary magnetic circuit S l The ratio of the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l ;

[0095] Based on the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l , calculate the total electromagnetic force F of the U-shaped unit m :

[0096]

[0097] Among them, F mk is the main magnetic circuit electromagnetic force; F ml is the electromagnetic force of the secondary magnetic circuit;

[0098] From this, the electromagnetic force of a standard suspension electromagnet can be obtained as:

[0099]

[0100] Among them, F mi is the electromagnetic force of the i-th U-shaped unit.

[0101] Example 2

[0102] This embodiment is used to verify the electromagnetic force calculated in Embodiment 1, and specifically includes the following contents:

[0103] In order to further illustrate the accuracy of the electromagnetic force calculation formula (hereinafter referred to as the magnetic resistance correction formula) of the present invention, this embodiment compares the magnetic resistance correction formula with the traditional classical formula and the finite element results, and the results are as follows:

[0104] refer to Figure 5 , the calculation results of the reluctance-corrected magnetic model, the calculation results of the classical magnetic model and the finite element calculation results were compared when the suspension gap was 8 and 10 mm and the current range was 0 to 60 A. The results show that the calculation results of the reluctance-corrected magnetic model are in good agreement with the simulation results of the finite element model, with the maximum relative deviation being only 4.6%. Under the same suspension gap conditions, the magnetic force calculation values ​​of both increase rapidly with the increase of current, and then the growth rate slows down, reflecting the magnetic saturation characteristics of ferromagnetic materials. The electromagnetic force obtained by the classical magnetic model increases with the increase of current, and its growth rate continues to increase. The difference with the finite element calculation value also increases with the increase of current, with a maximum relative deviation of 161.5%. From this comparison, it can be seen that the accuracy of the electromagnetic force calculation method in the present invention is significantly higher than that of the existing classical algorithm.

[0105] Although the specific implementation of the invention is described in detail in conjunction with the drawings, it should not be understood as limiting the scope of protection of this patent. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still fall within the scope of protection of this patent.

Claims

1. A method for calculating the electromagnetic force of a conventional high-speed maglev transportation system, characterized in that: The following steps are involved: S1. Combine finite element analysis method and equivalent magnetic circuit method to construct an equivalent magnetic circuit model of the suspension electromagnet and guide rail; S2. Calculate the magnetic resistance of each component in the equivalent magnetic circuit model; S3. Construct a set of five nonlinear equations of an equivalent magnetic circuit model based on the calculated magnetic resistance of each component; S4. Based on the solution of the five-variable nonlinear equation group, the magnetic force of the electromagnet is calculated.

2. The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation according to claim 1 is characterized in that: The equivalent magnetic circuit model of the suspension electromagnet and the guide rail is constructed in S1, including: The finite element analysis method is used to obtain the magnetic field distribution of the electromagnet and the track, and the distribution of magnetic flux lines is simplified; Based on the simplified distribution of magnetic flux lines, the equivalent magnetic circuit model of the suspension electromagnet and guide rail is constructed using the equivalent magnetic circuit method.

3. The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation according to claim 2 is characterized in that: The equivalent magnetic circuit model includes an electromagnet, a long stator and an air gap therebetween.

4. The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation according to claim 2 is characterized in that: According to the tooth structure of the stator, the equivalent magnetic circuit model at the suspension gap is divided into the main magnetic circuit and the auxiliary magnetic circuit.

5. The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation according to claim 1 is characterized in that: The magnetic resistance of each component in the equivalent magnetic circuit model is calculated in S2, including: Air reluctance of main magnetic circuit R k for: Auxiliary magnetic circuit air reluctance R l for: Where δ is the suspension gap; S k , S l are the cross-sectional areas of the main magnetic circuit and the auxiliary magnetic circuit of the suspension gap respectively; μ0 is the magnetic permeability of air; The BH curves of the pole and stator materials are fitted to obtain: Among them, B e and B s are the magnetic induction intensity in the pole and stator respectively, H is the magnetic field intensity, a e and b e is the fitting coefficient of the BH curve of the magnetic pole material, a s and b s is the fitting coefficient of the BH curve of the stator material; therefore: Magnetic pole material reluctance R e for: Stator material reluctance R s for: Among them, l e is the equivalent magnetic path length of the magnetic pole material in the magnetic path; l s is the equivalent magnetic circuit length of the stator material in the magnetic circuit; S e is the equivalent magnetic pole area of ​​the magnetic pole material; S s is the equivalent pole area of ​​the stator material; Φ is the total magnetic flux of the magnetic circuit.

6. The accurate and fast electromagnetic force calculation method for conventional high-speed maglev transportation according to claim 5 is characterized in that: The five-variable nonlinear equation group of the equivalent magnetic circuit model in S3 includes: Among them, Φ k and Φ l are the main magnetic circuit flux and the auxiliary magnetic circuit flux respectively, N is the number of coil turns, and I is the excitation current; Newton iteration method is used to solve the nonlinear equation system G(Φ,Φ k ,Φ l ,R s ,R e ), the steps are as follows: (1) x=(Φ,Φ) k ,F l ,R e ,R s ); (2)x (k+1) =x (k) -J(G(x (k) )) -1 G(x (k) ),k=0,1,2… Among them, J(G(x (k) )) -1 The system of equations G(x (k) )’s Jacobian matrix; (3) Take x (0) =(0.003, 0.0017, 0.0047, 12442, 334), substitute into the above formula and iterate to solve; (4) When the iteration error max(x (k+1) -x (k) )≤1×10 -5 When , the iterative solution ends, and the main magnetic flux Φ is obtained. k and the secondary magnetic flux Φ l .

7. The method for calculating the precise and rapid electromagnetic force of conventional high-speed maglev transportation according to claim 6 is characterized in that: The calculation of the electromagnet magnetic force in S4 includes: Based on the main magnetic flux Φ k The cross-sectional area of ​​the main magnetic circuit S k The ratio of the secondary magnetic flux Φ l The cross-sectional area of ​​the secondary magnetic circuit S l The ratio of the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l ; Based on the main magnetic circuit magnetic induction intensity B k and the magnetic induction intensity B of the secondary magnetic circuit l , calculate the total electromagnetic force F of the U-shaped unit m : Among them, F mk is the main magnetic circuit electromagnetic force; F ml is the electromagnetic force of the secondary magnetic circuit; From this, the electromagnetic force of a standard suspension electromagnet can be obtained as: Among them, F mi is the electromagnetic force of the i-th U-shaped unit.

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