CN112084679B - A Modeling Method of Equivalent Magnetic Circuit of Electromagnetic Actuator Considering Inhomogeneity of Eddy Current Distribution - Google Patents

Abstract

The purpose of the present invention is to provide a method for modeling the equivalent magnetic circuit of an electromagnetic actuator considering the inhomogeneity of eddy current distribution, including the following steps: dividing A to D according to the structure of the electromagnetic actuator, and defining the first layer and the first layer in each area. The eddy currents of the n layers are i _R11 and i _{R1n respectively} , calculate the eddy resistances corresponding to the first layer and the nth layer, define the equivalent current of the air gap between the electromagnetic actuator core and the armature as i _gk , define A～D The equivalent inductance of the leakage magnetic part of the area is L _air1 ～L _air4 , calculate the flux linkage between the two adjacent thin layers in the A～D area, calculate the main circuit current i, and obtain the magnetic flux φ of the electromagnetic actuator. The invention realizes that the existing methods cannot solve the nonlinear magnetization and magnetic saturation phenomena of the iron core magnetic material, especially the consideration of the eddy current effect in the magnetic field. The modeling method proposed by the invention can be used for accurate prediction of the dynamic performance of the electromagnetic actuator.

Description

A Modeling Method of Equivalent Magnetic Circuit of Electromagnetic Actuator Considering Inhomogeneity of Eddy Current Distribution

technical field

The invention relates to an electromagnetic actuator, in particular to an electromagnetic actuator of a high-voltage common rail system.

Background technique

The high-speed electromagnetic actuator is the core control component of the high-pressure common rail system, which directly determines the injection characteristics of the common rail system, thereby affecting the power and emission performance of the diesel engine. Usually, the 3D finite element method is used to optimize the design of electromagnetic actuators. However, the 3D electromagnetic calculation takes a long time, and it is impossible to achieve rapid calculation and comparison of different schemes. The more prominent problem is that the three-dimensional finite element method cannot realize the coupling calculation of the electromagnetic actuator and the hydraulic components and mechanical components of the high-pressure common rail system, which makes it impossible to accurately predict the influence of the dynamic performance of the electromagnetic actuator on the injection characteristics of the common rail system. Therefore, the one-dimensional electromagnetic model based on the equivalent magnetic circuit method with fast calculation speed and high calculation accuracy has been widely developed. The invention patent "Modeling and Characteristic Analysis Method of Permanent Magnet Synchronous Linear Motor Based on Equivalent Magnetic Circuit Method" When modeling, the magnetic circuit of permanent magnet synchronous motor is divided into the primary part of the linear motor, the air gap, and the secondary part of the motor. The magnetic circuit, however, the model does not take into account the magnetic saturation of the iron core, which violates the magnetic saturation characteristics that exist in real magnetic materials. The invention patent "A Method for Establishing an Equivalent Magnetic Circuit Model of Permanent Magnet Synchronous Motor Loss of Field Failure" ignores the reluctance of the stator core and the rotor reluctance when modeling, and assumes that the silicon steel sheet of the permanent magnet synchronous motor is in an unsaturated state, Therefore, a simplified equivalent magnetic circuit model is established. This assumption makes the above model unable to accurately predict the working characteristics of the permanent magnet motor under magnetic saturation, and the model has certain limitations. In fact, in the equivalent magnetic circuit model of electromagnetic actuators such as high-speed motors or high-speed solenoid valves, it is necessary to take into account the saturation characteristics of the magnetic field and the uneven distribution of eddy currents in the radial direction of the core material caused by the skin effect. sex.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for modeling the equivalent magnetic circuit of an electromagnetic actuator considering the inhomogeneity of the eddy current distribution, which overcomes the shortcomings of the existing electromagnetic actuator equivalent magnetic circuit method that does not consider the iron core magnetic characteristics and eddy current characteristics.

The object of the present invention is achieved in this way:

A method for modeling an equivalent magnetic circuit of an electromagnetic actuator considering the inhomogeneity of eddy current distribution in the present invention is characterized in that:

(1) According to the structure of the electromagnetic actuator, the division is carried out, and the inner magnetic pole part is defined as the A area, the outer magnetic pole part is defined as the B area, the area on the coil winding connecting the inner and outer magnetic poles is the C area, and the armature part is the D area; The defined four regions are divided into n layers of equal thickness slices in the radial direction, and it is assumed that the eddy current in each layer of iron core slices is uniformly distributed;

(2) Define the eddy currents of the first layer and the nth layer on the A area as i _R11 and i _{R1n respectively} , and the eddy resistances corresponding to the first layer and the nth layer are R ₁₁ and R _1n respectively. Similarly, the B area, C The eddy currents in zone and D zone from the first layer to the nth layer are i _R21 ～i _R2n , i _R31 ～i _R3n , i _R41 ～i _R4n , and the eddy resistances of each thin layer are R ₁₁ ～R _1n , R ₂₁ ～ R _2n , R ₃₁ ～R _3n , R ₄₁ ～R _4n , the calculation formula of the eddy resistance in the thin layer is:

In the above formula, m=1～4, q=1～n, ρ _m is the resistivity of the material, N is the number of turns of the coil, l _mq is the circulation distance of the eddy current, and S _mq is the circulation area of the eddy current;

(3) Define the equivalent current of the air gap between the electromagnetic actuator core and the armature as i _gk :

In the above formula, k=1 or 2, μ ₀ is the vacuum permeability, S _gk and φ _gk are the effective magnetic flux area and magnetic flux of the air gap part, respectively, and l _gk is the distance of the magnetic flux of the air gap part;

(4) When considering the magnetic flux leakage phenomenon of electromagnetic actuators, define the equivalent inductances of the magnetic flux leakage parts of the A to D regions as L _air1 ～L _air4 , and the calculation formula is:

In the above formula, x=1～4, S _m is the magnetic flux area, and l _m is the magnetic flux distance; according to the relationship between the inductance and current in the above four magnetic leakage regions, the effective current is calculated as:

In the above formula, E is the driving voltage loaded on the electromagnetic actuator, RR is the main circuit resistance of the driving circuit, and i is the main circuit current of the driving circuit;

(5) Calculate the magnetic linkage between the two adjacent thin layers in the A-D area, and the calculation formula is:

ψ _mp =∫i _Rmp ·R _mp -i _Rm(p+1) ·R _m(p+1) dt m=1～4,p=1～(n-1)

In the above formula, the eddy currents i _Rmp and i _Rm(p+1) of two adjacent thin layers are obtained by Kirchhoff's law; the magnetic induction between two adjacent thin layers can be obtained by calculating the flux linkage obtained by the above formula. The strength is:

In the above formula, S _mp is the effective area that the magnetic field line passes through; the magnetic field intensity H _mp corresponding to the magnetic field intensity B _mp in the magnetization curve is obtained by the data interpolation method, and then the equivalent inductance corresponding to the two adjacent thin layers is calculated. The current _Imp :

ψ_mp＝∫i_Rmp·R_mp-i_Rm(p+1)·R_m(p+1)dt m＝1～4,p＝1～(n-1)计算得到干路电流i，从而得到电磁执行器磁通φ：(6) According to Kirchhoff's law, the formula

ψ _mp =∫i _Rmp ·R _mp -i _Rm(p+1) ·R _m(p+1) dt m=1～4,p=1～(n-1) The main circuit current i is obtained by calculating Electromagnetic actuator magnetic flux φ:

The advantages of the present invention are: the present invention realizes the non-linear magnetization and magnetic saturation phenomena of the iron core magnetic material which cannot be solved by the existing methods, especially the consideration of the eddy current effect in the magnetic field. The modeling method proposed by the invention can be used for accurate prediction of the dynamic performance of the electromagnetic actuator.

Description of drawings

Fig. 1 is the schematic diagram of electromagnetic actuator partition and layering;

Figure 2 is a schematic diagram of the equivalent magnetic circuit of the constructed electromagnetic actuator;

Figure 3 is a flow chart of the present invention.

Detailed ways

The present invention will be described in more detail below in conjunction with the accompanying drawings:

1-3, the specific steps of the present invention are as follows:

(1) According to the structure of the electromagnetic actuator, the division is divided, and the inner magnetic pole part is defined as the A area, the outer magnetic pole part is the B area, the area above the coil winding connecting the inner and outer magnetic poles is the C area, and the armature part is D area. As shown in Figure 1, the above-defined four regions are divided into six layers of equal thickness in the radial direction, and it is assumed that the eddy current in each layer of the core sheet is uniformly distributed. Figure 2 shows the electromagnetic implementation constructed after the division. Equivalent magnetic circuit structure diagram of the device.

(2) Define the eddy currents of the first layer and the sixth layer on the A area as i _R11 and i _R16 respectively, and the eddy resistances corresponding to the first layer and the sixth layer are R ₁₁ and R ₁₆ respectively. Similarly, the B area, The eddy currents on the C area and the D area from the first layer to the sixth layer are i _R21 ～i _R26 , i _R31 ～i _R36 , i _R41 ～i _R46 , and the eddy resistance of each thin layer is R ₁₁ ～R ₁₆ , R ₂₁ ～ R ₂₆ , R ₃₁ to R ₃₆ , and R ₄₁ to R ₄₆ . The formula for calculating the eddy resistance in the thin layer is:

In the above formula, m=1～4, q=1～6, ρ _m is the resistivity of the material, N is the number of turns of the coil, l _mq is the circulation distance of the eddy current, and S _mq is the circulation area of the eddy current.

(3) Define the equivalent current of the air gap between the electromagnetic actuator core and the armature as i _gk , and its calculation formula is:

In the above formula, k=1 or 2, μ ₀ is the vacuum permeability, S _gk and φ _gk are the effective magnetic flux area and magnetic flux of the air gap part, respectively, and l _gk is the distance of the magnetic flux of the air gap part.

(4) When considering the magnetic flux leakage phenomenon of electromagnetic actuators, define the equivalent inductances of the magnetic flux leakage parts of the A to D regions as L _air1 ～L _air4 , and the calculation formula is:

In the above formula, x=1～4, S _m is the magnetic flux area, and l _m is the magnetic flux distance. According to the relationship between the inductance and the current in the above four magnetic leakage regions, the effective current is calculated as:

In the above formula, E is the driving voltage loaded on the electromagnetic actuator, and RR is the main circuit resistance of the driving circuit. i is the main circuit current of the drive circuit.

(5) Calculate the magnetic linkage between the two adjacent thin layers in the A-D area, and the calculation formula is:

ψ _mp =∫i _Rmp ·R _mp -i _Rm(p+1) ·R _m(p+1) dt m=1～4,p=1～5 (5)

In the above formula, the eddy currents i _Rmp and i _Rm(p+1) of two adjacent thin layers are obtained by Kirchhoff's law. According to the flux linkage obtained by formula (5), the magnetic induction intensity between two adjacent thin layers is calculated as:

In the above formula, S _mp is the effective area through which the magnetic field lines pass. The data interpolation method is used to obtain the magnetic field intensity H _mp corresponding to the magnetic induction intensity B _mp in the magnetization curve, and then the current I _mp corresponding to the equivalent inductance between two adjacent thin layers is calculated:

(6) According to Kirchhoff's law, the main circuit current i is calculated by formulas (3), (4) and (5), so as to obtain the magnetic flux φ of the electromagnetic actuator:

Claims (1)

1. A method for modeling an equivalent magnetic circuit of an electromagnetic actuator considering the inhomogeneity of eddy current distribution, characterized in that: Include the following steps: (1) According to the structure of the electromagnetic actuator, the division is carried out, and the inner magnetic pole part is defined as the A area, the outer magnetic pole part is defined as the B area, the area on the coil winding connecting the inner and outer magnetic poles is the C area, and the armature part is the D area; The defined four regions are divided into n layers of equal thickness slices in the radial direction, and it is assumed that the eddy current in each layer of iron core slices is uniformly distributed; (2) Define the eddy currents of the first layer and the nth layer on the A area as i _R11 and i _{R1n respectively} , and the eddy resistances corresponding to the first layer and the nth layer are R ₁₁ and R _1n respectively. Similarly, the B area, C The eddy currents in the zone and D zone from the first layer to the nth layer are i _R21 ～i _R2n , i _R31 ～i _R3n , i _R41 ～i _R4n , and the eddy resistances of each thin layer are R ₁₁ ～R _1n , R ₂₁ ～R _2n , R ₃₁ ～R _3n , R ₄₁ ～R _4n , the calculation formula of the eddy resistance in the thin layer is:

In the above formula, m=1～4, q=1～n, ρ _m is the resistivity of the material, N is the number of turns of the coil, l _mq is the circulation distance of the eddy current, and S _mq is the circulation area of the eddy current; (3) Define the equivalent current of the air gap between the electromagnetic actuator core and the armature as i _gk :

In the above formula, k=1 or 2, μ ₀ is the vacuum permeability, S _gk and φ _gk are the effective magnetic flux area and magnetic flux of the air gap part, respectively, and l _gk is the distance of the magnetic flux of the air gap part; (4) When considering the magnetic flux leakage phenomenon of electromagnetic actuators, define the equivalent inductances of the magnetic flux leakage parts of the A to D regions as L _air1 ～L _air4 , and the calculation formula is:

In the above formula, j=1～4, S _j is the magnetic flux area, l _j is the magnetic flux distance; according to the relationship between the inductance and the current in the above four leakage magnetic parts, the effective current is calculated as:

In the above formula, E is the driving voltage loaded on the electromagnetic actuator, RR is the main circuit resistance of the driving circuit, and i is the main circuit current of the driving circuit; (5) Calculate the magnetic linkage between the two adjacent thin layers in the A-D area, and the calculation formula is: ψ _dp = _{∫i Rdp} ·R _dp -i _Rd(p+1) ·R _d(p+1) dt ③ In the above formula, d=1～4, p=1～(n-1), the eddy currents i _Rdp and i _Rd(p+1) of two adjacent thin layers are obtained by Kirchhoff’s law; The obtained flux linkage is calculated to obtain the magnetic induction intensity between two adjacent thin layers as:

In the above formula, S _dp is the effective area that the magnetic field line passes through; the magnetic field intensity H _dp corresponding to the magnetic field intensity B _dp in the magnetization curve is obtained by the data interpolation method, and then the equivalent inductance corresponding to the two adjacent thin layers is calculated. The current I _dp :

(6) According to Kirchhoff's law, the main circuit current i is calculated from the formulas ①, ②, and ③, so as to obtain the magnetic flux φ of the electromagnetic actuator:

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