A constant-conductance high-speed maglev transportation precise and fast electromagnetic force calculation method

Abstract

The application discloses a kind of normal high-speed maglev traffic accurate fast electromagnetic force calculation method, belong to the technical field of high-speed normal magnetic levitation suspension system, including the equivalent magnetic circuit model of suspension electromagnet and guide rail being constructed by combining finite element analysis method and equivalent magnetic circuit method;The magnetic resistance of each component in the equivalent magnetic circuit model is calculated;According to the magnetic resistance of each component obtained by calculation, the five nonlinear equations of the equivalent magnetic circuit model are constructed;Based on the solution of five nonlinear equations, the electromagnet magnetic force is calculated.The application first obtains the equivalent magnetic circuit of electromagnet and track based on equivalent magnetic circuit method;Secondly, the magnetic circuit calculation equation set considering the nonlinear magnetic resistance of ferromagnetic material is established, the magnetic circuit magnetic flux can be obtained through the equation set, and then the electromagnet magnetic force is obtained, the electromagnetic force obtained by the electromagnetic force calculation method of the application is compared with the finite element simulation result, the maximum relative error of suspension force calculation result is 4.6%, and the calculation accuracy is higher than that of traditional electromagnetic force calculation formula.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high-speed normal-conducting maglev suspension systems, and particularly relates to a normal-conducting high-speed maglev transportation precise and rapid electromagnetic force calculation method. BACKGROUND

[0002] The normal-conducting high-speed maglev train realizes suspension / guiding by using non-contact electromagnetic attraction, has high running safety, good ride comfort, strong line adaptability, small running noise and low maintenance cost, and has been widely applied and developed in the world in the past two decades.

[0003] The electromagnetic system of the normal-conducting high-speed maglev train needs active control to realize stable suspension, and the force between the electromagnet and the guide rail is the magnetic field force distributed in three-dimensional space. However, it is difficult to theoretically analyze the irregular three-dimensional magnetic field, and the numerical solution efficiency is low, so in addition to the special electromagnetic iron structure design and optimization, the existing suspension / guiding control and dynamics research of the maglev vehicle almost all use the analytical method to calculate the one-dimensional electromagnetic force. The analytical solution of the one-dimensional magnetic force usually assumes that the magnetic permeability of the electromagnet pole, the magnetic yoke and the ferromagnetic guide rail is infinite, the magnetic potential is uniformly dropped 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 force 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), and is suitable for the initial scheme design and performance pre-evaluation of the maglev vehicle. However, the engineering practice of the normal-conducting maglev transportation shows that when the maglev train passes through the track beam with light mass per unit length and small structural damping, the coupled vibration is often severe, and even the suspension fails. The phenomena such as dropping points and smashing rails often occur during high-speed operation. In these cases, the gap and current of the electromagnet have deviated greatly from the rated design value, and the traditional analytical method cannot accurately solve the magnetic force. Existing researches have pointed out that under the condition of large fluctuations of the gap and current, the analytical value of the suspension electromagnetic force of the high-speed maglev vehicle is obviously different from the finite element calculation value and the indoor measured value, and the relative error is more than 100% in the extreme case. Obviously, if the dynamics model continues to use the analytical formula under severe working conditions, the simulation results will be far from the actual situation, and it is difficult to reveal the dynamics performance evolution mechanism of the high-speed maglev train.

[0004] In summary, the accurate static magnetic-track relationship is the cornerstone of the suspension / guiding control design and the dynamics design of the maglev transportation system. Although the magnetic field is solved based on the finite element method, the calculation efficiency is low, and it is difficult to adapt to the dynamics simulation calculation. Therefore, it is necessary to explore a magnetic force calculation method which can meet the simulation accuracy of the electromagnet under the whole working state and can be quickly solved to provide a solid foundation for the dynamics research of the maglev transportation. SUMMARY

[0005] The present application aims at the above-mentioned deficiencies in the prior art, and provides a constant-conductance high-speed maglev transportation precise and rapid electromagnetic force calculation method to solve the problem that the calculation error of the classical electromagnetic force analytical formula is large, so that the dynamic simulation result deviates from the actual situation.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present application is:

[0007] A constant-conductance high-speed maglev transportation precise and rapid electromagnetic force calculation method, comprising the following steps:

[0008] S1, constructing an equivalent magnetic circuit model of the suspension electromagnet and the guide rail by combining the finite element analysis method and the equivalent magnetic circuit method;

[0009] S2, calculating the magnetic resistance of each component part in the equivalent magnetic circuit model;

[0010] S3, constructing a five-element nonlinear equation set of the equivalent magnetic circuit model according to the calculated magnetic resistance of each component part;

[0011] S4, calculating the electromagnet magnetic force based on the solution of the five-element nonlinear equation set.

[0012] Further, the step S1 of constructing the equivalent magnetic circuit model of the suspension electromagnet and the guide rail comprises:

[0013] The magnetic field distribution of the electromagnet and the track is obtained by using the finite element analysis method, and the magnetic induction line distribution is simplified;

[0014] Based on the simplified magnetic induction line distribution, the equivalent magnetic circuit method is used to construct the equivalent magnetic circuit model of the suspension electromagnet and the guide rail.

[0015] Further, the equivalent magnetic circuit model comprises the electromagnet, the long stator and the air gap therebetween.

[0016] Further, according to the stator piece tooth slot structure, the equivalent magnetic circuit model at the suspension gap is divided into a main magnetic circuit and an auxiliary magnetic circuit.

[0017] Further, the step S2 of calculating the magnetic resistance of each component part in the equivalent magnetic circuit model comprises:

[0018] The main magnetic circuit air magnetic resistance R k is:

[0019]

[0020] The auxiliary magnetic circuit air magnetic resistance R l is:

[0021]

[0022] Wherein, δ is the suspension gap; S k , Sl respectively are the cross-sectional area of the main magnetic circuit and the cross-sectional area of the auxiliary magnetic circuit; μ0is the air permeability;

[0023] The B-H curves of the magnetic pole and the stator material are fitted, respectively, to obtain:

[0024]

[0025] where B e and B s are the magnetic induction in the magnetic pole and the stator, respectively, H is the magnetic field intensity, a e and b e are the fitting coefficients of the B-H curve of the magnetic pole material, a s and b s are the fitting coefficients of the B-H curve of the stator material;

[0026] Therefore:

[0027] The magnetic reluctance R e of the magnetic pole material is:

[0028]

[0029] The magnetic reluctance R s of the stator material is:

[0030]

[0031] where l e is the equivalent magnetic circuit length of the magnetic pole material in the magnetic circuit; 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 magnetic pole area of the stator material; and Φ is the total magnetic flux of the magnetic circuit.

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

[0033]

[0034] where Φ k and Φ l are the main magnetic flux and the auxiliary magnetic flux, respectively, N is the number of turns, and I is the excitation current.

[0035] The Newton iteration method is used to solve the nonlinear equations G(Φ,Φ k ,Φ l , R s , R e ), and 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 For 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 circuit flux Φ l .

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

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

[0043] Based on the main magnetic circuit magnetic induction intensity B k and the secondary magnetic circuit magnetic induction intensity B 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 we can get the electromagnetic force of a standard levitation electromagnet:

[0047]

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

[0049] The constant-conductance high-speed maglev transportation precise and rapid electromagnetic force calculation method provided by the application has the following beneficial effects:

[0050] The application first obtains the equivalent magnetic circuit of the electromagnet and the track based on the equivalent magnetic circuit method; secondly, a magnetic circuit calculation equation set considering the nonlinear magnetic resistance of the ferromagnetic material is established, and the magnetic circuit magnetic flux can be obtained through the equation set, and then the electromagnetic force of the electromagnet is obtained.

[0051] At present, the calculation of electromagnetic force mostly does not consider the magnetic resistance of the electromagnet and the track, and only considers the air magnetic resistance. When the excitation current is small, the magnetic resistance of the ferromagnetic material is small, and at this time, 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, and if it is still ignored, it will significantly affect the calculation result. The application fully considers the magnetic resistance of the ferromagnetic material, and thus obtains more accurate one-dimensional electromagnetic force calculation results. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is the magnetic field distribution of the electromagnet and the track of the application.

[0053] Figure 2 is the simplified magnetic induction line diagram of the application.

[0054] Figure 3 is the equivalent magnetic circuit model of the application.

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

[0056] Figure 5 is the comparison of the three magnetic forces of the application, wherein, Figure 5 (a) is the comparison of the three magnetic forces of the suspension gap of 8mm, and (b) is the comparison of the three magnetic forces of the suspension gap of 10mm.

[0057] Figure 6 is the flowchart of the constant-conductance high-speed maglev transportation precise and rapid electromagnetic force calculation method of the application. DETAILED DESCRIPTION

[0058] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0059] Embodiment 1

[0060] The present embodiment provides a constant-conductance high-speed maglev transportation precise and rapid electromagnetic force calculation method, which refers to Figure 6 , and specifically includes the following contents:

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

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

[0063] The magnetic induction line distribution is simplified, as shown in Figure 2 ;

[0064] Based on the equivalent magnetic circuit method, the equivalent magnetic circuit of the electromagnet and the track is obtained, as shown in Figure 3 , and the stator piece tooth slot structure is considered, and the magnetic circuit at the suspension gap is divided into main magnetic circuit and auxiliary magnetic circuit.

[0065] As can be seen from Figure 1 , Figure 2 and Figure 3 , the equivalent magnetic circuit model is composed of the electromagnet, the long stator and the air gap therebetween.

[0066] Many laws in the magnetic field are extremely similar to those in the electric field, and the concept of magnetic circuit is derived from the electric circuit. The path through which the magnetic flux passes through the magnetic medium is called the magnetic circuit. Similar to the current in the electric circuit, the magnetic flux preferentially passes through the medium with high magnetic permeability. The electromagnet and the track are both magnetic conductive materials with high magnetic permeability, so the magnetic flux preferentially passes through the electromagnet, the track and the air gap therebetween, thereby 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] The main magnetic circuit air magnetic resistance R k is:

[0069]

[0070] The auxiliary magnetic circuit air magnetic resistance R l is:

[0071]

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

[0073] The air permeance μ0 is a constant value, the permeance of the magnetic material is determined by its own B-H curve, and the magnetization characteristic curve of the magnetic pole and the stator material is shown in Fig. 1. Figure 4

[0074] The fitting formula of the B-H curve of the magnetic pole material is:

[0075]

[0076] The fitting formula of the B-H curve of the stator material is:

[0077]

[0078] wherein, B e and B s are the magnetic induction intensity in the magnetic pole and the stator respectively, H is the magnetic field intensity, a e and b e are the fitting coefficients of the B-H curve of the magnetic pole material, a s and b s are the fitting coefficients of the B-H curve of the stator material.

[0079] The magnetic induction intensity B can be expressed as the ratio of the magnetic flux and the cross-sectional area of the magnetic circuit, i.e.

[0080] Thus, the magnetic resistance R e of the magnetic pole material and the magnetic resistance R s of the stator material can be further obtained, respectively:

[0081]

[0082] wherein, l e is the equivalent magnetic circuit length of the magnetic pole material in the magnetic circuit; 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 magnetic pole area of the stator material; and Φ is the total magnetic flux of the magnetic circuit.

[0083] Step S3, according to the magnetic resistance of each component obtained by calculation, a five-element nonlinear equation set of the equivalent magnetic circuit model is constructed, which specifically includes the following contents:

[0084] ​According to the magnetic flux continuity principle and the magnetic circuit ohm law, five nonlinear equations are established:

[0085]

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

[0087] Since the above formula is a nonlinear equation group, the analytical solution cannot be obtained, so the Newton method is used for iterative solution, and 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] wherein, J(G(x (k) )) -1 is the Jacobian matrix of the equation group G(x (k) );

[0091] (3) Take x (0) =(0.003, 0.0017, 0.0047, 12442, 334), and bring it into the above formula for iterative solution;

[0092] (4) When the iteration error max(x (k+1) -x (k) )≤1×10 -5 , the iterative solution is ended, and the main magnetic circuit magnetic flux Φ k and the auxiliary magnetic circuit magnetic flux Φ l are solved.

[0093] Step S4, based on the solution of the five nonlinear equations, the electromagnet magnetic force is calculated.

[0094] Based on the ratio of the main magnetic circuit magnetic flux Φ k to the main magnetic circuit cross-sectional area S k , and the ratio of the auxiliary magnetic circuit magnetic flux Φ l to the auxiliary magnetic circuit cross-sectional area S l , the main magnetic circuit magnetic induction intensity B k and the auxiliary magnetic circuit magnetic induction intensity B l are obtained respectively;

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

[0096]

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

[0098] Thus, the electromagnetic force of a standard levitation electromagnet is:

[0099]

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

[0101] Embodiment 2

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

[0103] This embodiment is used to further illustrate the accuracy of the electromagnetic force calculation formula (hereinafter referred to as the magnetic resistance correction formula) of the present application. The magnetic resistance correction formula is compared with the traditional classical formula and the finite element result, and the results are as follows:

[0104] Reference Figure 5 The magnetic resistance correction magnetic force model calculation result, the classical magnetic force model calculation result and the finite element calculation result are compared in the current range of 0-60A when the levitation gap is 8 and 10mm. The results show that the calculation result of the magnetic resistance correction magnetic force model is in good agreement with the finite element model simulation result, and the maximum relative deviation is only 4.6%. Under the same levitation gap condition, the magnetic force calculation values of both increase rapidly at first and then increase slowly with the increase of current, which reflects the magnetic saturation characteristics of ferromagnetic materials. The electromagnetic force obtained by the classical magnetic force model increases with the increase of current, and the increase rate becomes larger and larger, and the difference with the finite element calculation value also becomes larger and larger with the increase of current, and the maximum relative deviation is 161.5%. From the comparison, it can be seen that the electromagnetic force calculation method in the present application has obviously higher accuracy than the existing classical algorithm.

[0105] Although the specific embodiments of the application are described in detail with reference to the accompanying drawings, it should not be understood as limiting the protection scope of the patent. Various modifications and variations made by those skilled in the art within the scope described in the claims are still within the protection scope of the 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 the finite element analysis method and the equivalent magnetic circuit method to construct an equivalent magnetic circuit model of the levitation electromagnet and the guide rail; S2. Calculate the magnetic resistance of each component in the equivalent magnetic circuit model; S3. Based on the calculated magnetic resistance of each component, a five-variable nonlinear equation system of the equivalent magnetic circuit model is constructed; S4. Based on the solution of the five-variable nonlinear equations, the magnetic force of the electromagnet is calculated; The five-variable nonlinear equation group of the equivalent magnetic circuit model in S3 includes: in, and are the main magnetic circuit flux and the auxiliary magnetic circuit flux respectively, N is the number of coil turns, I is the excitation current; R e is the magnetic pole material reluctance; R s is the magnetic reluctance of the stator material; is the total magnetic flux of the magnetic circuit; Air reluctance is the main magnetic circuit; is the air reluctance of the auxiliary magnetic circuit; a e and b e Is the magnetic pole material B - H The fitting coefficient of the curve, a s and b s Stator material B - H The fitting coefficient of the curve; l e is the equivalent magnetic path length of the magnetic pole material in the magnetic circuit; 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; Solving nonlinear equations using Newton's iteration method , the steps are as follows: (1) Order ; （2） in, J ( G ( x (k) )) -1 For 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 is obtained and the secondary magnetic circuit flux .

2. The method for calculating the precise and rapid electromagnetic force of 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: Finite element analysis 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 levitation electromagnet and guide rail is constructed using the equivalent magnetic circuit method.

3. The method for calculating the precise and rapid electromagnetic force of 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 method for calculating the precise and rapid electromagnetic force of 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 method for calculating the precise and rapid electromagnetic force of conventional high-speed maglev transportation according to claim 1 is characterized in that: The calculation of the magnetic resistance of each component in the equivalent magnetic circuit model in S2 includes: Air reluctance of the main magnetic circuit for: Auxiliary magnetic circuit air reluctance for: in, 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; For pole and stator materials B - H The curves are fitted and the following are obtained: therefore: Pole material reluctance R e for: Stator material reluctance R s for: in, B e and B s are the magnetic induction intensities in the poles and stator, H is the magnetic field strength.

6. The method for calculating the precise and rapid electromagnetic force of conventional high-speed maglev transportation according to claim 1 is characterized in that: The calculation of the electromagnet magnetic force in S4 includes: Based on the main magnetic circuit flux The cross-sectional area of ​​the main magnetic circuit S k The ratio of the auxiliary magnetic flux and the secondary magnetic circuit cross-sectional area S l The ratio of the main magnetic circuit magnetic induction intensity is obtained. B k and the magnetic induction intensity of the secondary magnetic circuit B l ; Based on the magnetic induction intensity of the main magnetic circuit B k and the magnetic induction intensity of the secondary magnetic circuit B l , calculate the total electromagnetic force of the U-shaped unit F m : in, F mk Is the main magnetic circuit electromagnetic force; F ml is the electromagnetic force of the secondary magnetic circuit; From this we can get the electromagnetic force of a standard levitation electromagnet: in, For the i The electromagnetic force of a U-shaped unit.

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