CN112084679B - Equivalent magnetic circuit modeling method of electromagnetic actuator considering eddy current distribution nonuniformity - Google Patents

Equivalent magnetic circuit modeling method of electromagnetic actuator considering eddy current distribution nonuniformity Download PDF

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CN112084679B
CN112084679B CN202011096156.6A CN202011096156A CN112084679B CN 112084679 B CN112084679 B CN 112084679B CN 202011096156 A CN202011096156 A CN 202011096156A CN 112084679 B CN112084679 B CN 112084679B
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赵建辉
卢相东
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Harbin Engineering University
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Abstract

The invention aims to provide an equivalent magnetic circuit modeling method of an electromagnetic actuator considering the nonuniformity of eddy current distribution, which comprises the following steps: dividing A-D according to the structure of the electromagnetic actuator, and defining the eddy current of the first layer and the nth layer on each zone as iR11And iR1nCalculating the eddy resistance corresponding to the first layer and the nth layer, and defining the equivalent current of an air gap part between an iron core and an armature of the electromagnetic actuator as igkThe equivalent inductance of the leakage part of the A-D region is defined as Lair1～Lair4And calculating the magnetic linkage between two adjacent thin layers in the areas A to D, and calculating the main circuit current i so as to obtain the magnetic flux phi of the electromagnetic actuator. The invention realizes that the existing method can not solve the nonlinear magnetization and magnetic saturation phenomena of the magnetic material of the iron core, in particular to the consideration of the eddy current effect in the magnetic field. The modeling method provided by the invention can be used for accurately predicting the dynamic performance of the electromagnetic actuator.

Description

Equivalent magnetic circuit modeling method of electromagnetic actuator considering eddy current distribution nonuniformity
Technical Field
The invention relates to an electromagnetic actuator, in particular to an electromagnetic actuator of a high-pressure common rail system.
Background
The high-speed electromagnetic actuator is a core control component of a high-pressure common rail system, and directly determines the injection characteristic of the common rail system, so that the dynamic property and the emission property of a diesel engine are influenced. Generally, a three-dimensional finite element method is adopted to carry out design optimization on an electromagnetic actuator, however, three-dimensional electromagnetic calculation is time-consuming and cannot realize rapid calculation comparison on different schemes. The more outstanding problem is that the three-dimensional finite element method cannot realize the coupling calculation of the electromagnetic actuator and the hydraulic component, the mechanical component and the like of the high-pressure common rail system, so that the influence of the dynamic performance of the electromagnetic actuator on the injection characteristic of the common rail system cannot be accurately predicted. Therefore, a one-dimensional electromagnetic model based on an equivalent magnetic circuit method with high calculation speed and high calculation accuracy is widely developed. When the invention patent 'permanent magnet synchronous linear motor modeling and characteristic analysis method based on an equivalent magnetic circuit method' is used for modeling, a permanent magnet synchronous motor magnetic circuit is divided into a linear motor primary part magnetic circuit, an air gap and a motor secondary part magnetic circuit, however, the model does not consider the magnetic saturation of an iron core, which is against the magnetic saturation characteristic existing in a real magnetic material. The invention discloses a permanent magnet synchronous motor field loss fault equivalent magnetic circuit model establishing method, which neglects the magnetic resistance of a stator core and the magnetic resistance of a rotor during modeling, and assumes that a silicon steel sheet of a permanent magnet synchronous motor is in an unsaturated state, thereby establishing a simplified equivalent magnetic circuit model. In fact, in an equivalent magnetic circuit model of an electromagnetic actuator such as a high-speed motor or a high-speed solenoid valve, it is necessary to consider the non-uniformity of eddy current distribution in the radial direction of the core material due to the saturation characteristic of the magnetic field and the skin effect.
Disclosure of Invention
The invention aims to provide an equivalent magnetic circuit modeling method of an electromagnetic actuator considering the eddy current distribution nonuniformity, which overcomes the defects that the magnetic property of an iron core, the eddy current property and the like are not considered in the conventional equivalent magnetic circuit method of the electromagnetic actuator.
The purpose of the invention is realized as follows:
the invention relates to an equivalent magnetic circuit modeling method of an electromagnetic actuator considering the nonuniformity of eddy current distribution, which is characterized by comprising the following steps:
(1) the method comprises the following steps of carrying out partition division according to the structure of an electromagnetic actuator, defining an inner magnetic pole part as an A area, an outer magnetic pole part as a B area, an area which is connected with the inner magnetic pole and the outer magnetic pole and is positioned above a coil winding as a C area, and an armature part as a D area; dividing the four defined areas into n layers of slices with equal thickness in the radial direction, and assuming that eddy currents in each layer of iron chip slice are uniformly distributed;
(2) defining the eddy current of the first layer and the nth layer on the A area as iR11And iR1nThe eddy resistance corresponding to the first layer and the nth layer is R11And R1nSimilarly, the eddy current in the B, C and D regions is i from the first layer to the n-th layerR21～iR2n、iR31～iR3n、iR41～iR4nEach sheet has a sheet eddy resistance of R11～R1n、R21～ R2n、R31～R3n、R41～R4nThe calculation formula of the in-sheet eddy resistance is as follows:
Figure BDA0002723810610000021
in the above formula, m is 1 to 4, q is 1 to n, ρ ismIs the resistivity of the material, N is the number of turns of the coil, lmqIs the flow distance of the vortex, SmqIs the flow area of the vortex;
(3) defining the equivalent current of an air gap part between an iron core and an armature of the electromagnetic actuator as igk：
Figure BDA0002723810610000022
In the above formula, k is 1 or 2, mu0Is the vacuum permeability, SgkAnd phigkRespectively the effective flux area and the flux of the air gap portion,/gkIs the distance of the flux in the air gap portion;
(4) when the leakage phenomenon of the electromagnetic actuator is considered, the equivalent inductance of the leakage part of the A-D region is defined as Lair1～Lair4The calculation formula is as follows:
Figure BDA0002723810610000023
in the above formula, x is 1 to 4, SmIs the area of the magnetic flux, /)mIs the magnetic flux distance; according to the relation between the inductance and the current in the four leakage magnetic regions, the effective current is calculated as follows:
Figure BDA0002723810610000024
in the above formula, E is a driving voltage loaded to the electromagnetic actuator, RR is a driving circuit trunk resistance, and i is a driving circuit trunk current;
(5) and calculating the magnetic linkage between two adjacent thin layers in the areas A to D, wherein the calculation formula is as follows:
ψmp＝∫iRmp·Rmp-iRm(p+1)·Rm(p+1)dt m＝1～4,p＝1～(n-1)
in the above formula, two adjacent thin layersVortex i ofRmpAnd iRm(p+1)Solving by kirchhoff's law; and calculating the magnetic induction intensity between two adjacent thin layers according to the magnetic linkage obtained by the formula:
Figure BDA0002723810610000031
in the above formula, SmpThe effective area through which the magnetic induction line passes; magnetic induction B in magnetization curve is obtained by data interpolation methodmpCorresponding magnetic field strength HmpFurther calculate the current I corresponding to the equivalent inductance between the two adjacent thin layersmp：
Figure BDA0002723810610000032
(6) According to kirchhoff's law, the formula
Figure BDA0002723810610000033
Figure BDA0002723810610000034
ψmp＝∫iRmp·Rmp-iRm(p+1)·Rm(p+1)dt m is 1-4, p is 1 to (n-1), and a main circuit current i is calculated, so that an electromagnetic actuator magnetic flux phi:
Figure BDA0002723810610000035
the invention has the advantages that: the invention realizes the consideration that the existing method can not solve the nonlinear magnetization and magnetic saturation phenomena of the magnetic material of the iron core, in particular the eddy current effect in the magnetic field. The modeling method provided by the invention can be used for accurately predicting the dynamic performance of the electromagnetic actuator.
Drawings
FIG. 1 is a schematic view of a partitioned layer of an electromagnetic actuator;
FIG. 2 is a schematic diagram of an equivalent magnetic circuit of a constructed electromagnetic actuator;
FIG. 3 is a flow chart of the present invention.
Detailed Description
The invention will now be described in more detail by way of example with reference to the accompanying drawings in which:
with reference to fig. 1-3, the specific steps of the present invention are as follows:
(1) the electromagnetic actuator is divided into regions according to the structure of the electromagnetic actuator, an inner magnetic pole part is defined as a region A, an outer magnetic pole part is defined as a region B, a region which is connected with the inner magnetic pole and the outer magnetic pole and is positioned above a coil winding is defined as a region C, and an armature part is defined as a region D. As shown in fig. 1, six layers of equal-thickness slices are divided in the radial direction for the four regions defined above, and assuming that the eddy current in each layer of iron chip is uniformly distributed, fig. 2 is a structural view of the equivalent magnetic circuit of the electromagnetic actuator constructed by dividing.
(2) Defining the eddy current of the first layer and the sixth layer on the A area as iR11And iR16And the first layer and the sixth layer have a corresponding eddy resistance R11And R16Similarly, the eddy current in the B, C and D regions is i from the first layer to the sixth layerR21～iR26、iR31～iR36、iR41～iR46Each sheet has a sheet eddy resistance of R11～R16、 R21～R26、R31～R36、R41～R46. The calculation formula of the in-sheet eddy resistance is as follows:
Figure BDA0002723810610000041
in the above formula, m is 1 to 4, q is 1 to 6, and rhomIs the resistivity of the material, N is the number of turns of the coil, lmqIs the flow distance of the vortex, SmqIs the flow area of the vortex.
(3) Defining the equivalent current of an air gap part between an iron core and an armature of the electromagnetic actuator as igkThe calculation formula is as follows:
Figure BDA0002723810610000042
in the above formula, k is 1 or 2, mu0Is the vacuum permeability, SgkAnd phigkRespectively the effective flux area and the flux of the air gap portion,/gkIs the distance of the flux in the air gap portion.
(4) When the leakage phenomenon of the electromagnetic actuator is considered, the equivalent inductance of the leakage part of the A-D region is defined as Lair1～Lair4The calculation formula is as follows:
Figure BDA0002723810610000043
in the above formula, x is 1 to 4, SmIs the area of the magnetic flux, /)mIs the flux distance. According to the relation between the inductance and the current in the four leakage magnetic regions, the effective current is calculated as follows:
Figure BDA0002723810610000044
in the above formula, E is a driving voltage applied to the electromagnetic actuator, and RR is a driving circuit trunk resistance. i is the main circuit current of the driving circuit.
(5) And calculating the magnetic linkage between two adjacent thin layers in the areas A to D, wherein the calculation formula is as follows:
ψmp＝∫iRmp·Rmp-iRm(p+1)·Rm(p+1)dt m＝1～4,p＝1～5 (5)
in the above formula, the eddy current i of two adjacent thin layersRmpAnd iRm(p+1)Calculated by kirchhoff's law. And calculating the magnetic induction intensity between two adjacent thin layers according to the flux linkage obtained by the formula (5) as follows:
Figure BDA0002723810610000051
in the above formula, SmpIs the effective area through which the magnetic induction line passes. Magnetic induction B in magnetization curve is obtained by data interpolation methodmpCorresponding magnetic field strength HmpFurther calculate the current I corresponding to the equivalent inductance between two adjacent thin layersmp：
Figure BDA0002723810610000052
(6) According to kirchhoff's law, calculating a main circuit current i by the formulas (3), (4) and (5) to obtain a magnetic flux phi of the electromagnetic actuator:
Figure BDA0002723810610000053

Claims (1)

1. an equivalent magnetic circuit modeling method of an electromagnetic actuator considering the nonuniformity of eddy current distribution is characterized by comprising the following steps:
the method comprises the following steps:
(1) the method comprises the following steps of carrying out partition division according to the structure of an electromagnetic actuator, defining an inner magnetic pole part as an A area, an outer magnetic pole part as a B area, an area which is connected with the inner magnetic pole and the outer magnetic pole and is positioned above a coil winding as a C area, and an armature part as a D area; dividing the four defined areas into n layers of slices with equal thickness in the radial direction, and assuming that the eddy current in each layer of iron chip slice is uniformly distributed;
(2) defining the eddy current of the first layer and the nth layer on the A area as iR11And iR1nThe eddy resistance corresponding to the first layer and the nth layer is R11And R1nSimilarly, the eddy current in the B, C and D regions is i from the first layer to the n-th layerR21～iR2n、iR31～iR3n、iR41～iR4nEach sheet has a sheet eddy resistance of R11～R1n、R21～R2n、R31～R3n、R41～R4nThe calculation formula of the in-sheet eddy resistance is as follows:
Figure FDA0003592976030000011
in the above formula, m is 1 to 4, q is 1 to n, ρ ismIs the resistivity of the material, N is the number of turns of the coil, lmqIs the flow distance of the vortex, SmqIs the flow area of the vortex;
(3) defining the equivalent current of an air gap part between an iron core and an armature of the electromagnetic actuator as igk：
Figure FDA0003592976030000012
In the above formula, k is 1 or 2, mu0Is the vacuum permeability, SgkAnd phigkRespectively the effective flux area and the flux of the air gap portion,/gkIs the distance of the flux in the air gap portion;
(4) when the leakage phenomenon of the electromagnetic actuator is considered, the equivalent inductance of the leakage part in the A-D area is defined as Lair1～Lair4The calculation formula is as follows:
Figure FDA0003592976030000013
in the above formula, j is 1 to 4, SjIs the area of magnetic flux,/jIs the magnetic flux distance; according to the relation between the inductance and the current of the four leakage parts, the effective current is calculated as follows:
Figure FDA0003592976030000024
in the above formula, E is a driving voltage loaded to the electromagnetic actuator, RR is a driving circuit trunk resistance, and i is a driving circuit trunk current;
(5) and calculating the magnetic linkage between two adjacent thin layers in the areas A to D, wherein the calculation formula is as follows:
ψdp＝∫iRdp·Rdp-iRd(p+1)·Rd(p+1)dt ③
in the above formula, d is 1 to 4, and p is 1 to (n-1)) Eddy currents of two adjacent layers iRdpAnd iRd(p+1)Solving by kirchhoff's law; and calculating the magnetic induction intensity between two adjacent thin layers according to the magnetic linkage obtained by the formula:
Figure FDA0003592976030000021
in the above formula, SdpThe effective area through which the magnetic induction line passes; magnetic induction B in magnetization curve is obtained by data interpolation methoddpCorresponding magnetic field strength HdpFurther calculate the current I corresponding to the equivalent inductance between two adjacent thin layersdp：
Figure FDA0003592976030000022
(6) According to kirchhoff's law, calculating to obtain a main circuit current i by formulas (i), (ii) and (iii), so as to obtain a magnetic flux phi of the electromagnetic actuator:
Figure FDA0003592976030000023
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