CN112257239A - High-speed electromagnetic actuator dynamic performance calculation method considering eddy current effect - Google Patents

High-speed electromagnetic actuator dynamic performance calculation method considering eddy current effect Download PDF

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CN112257239A
CN112257239A CN202011096141.XA CN202011096141A CN112257239A CN 112257239 A CN112257239 A CN 112257239A CN 202011096141 A CN202011096141 A CN 202011096141A CN 112257239 A CN112257239 A CN 112257239A
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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 a method for calculating the dynamic performance of a high-speed electromagnetic actuator by considering an eddy current effect, which comprises the following steps of: dividing A-D according to the structure of the electromagnetic actuator, defining eddy current and eddy resistance on the A, B, C and D regions, 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～Lair4Calculating the flux linkage between two adjacent thin layers in the areas A to D, calculating the magnetic flux phi of the electromagnetic actuator, calculating the electromagnetic force, solving the armature motion equation of the electromagnetic actuator, outputting the curve of the armature lift along with the change of the driving time, and obtaining the opening response time and the closing response time of the electromagnetic actuator. The method can realize accurate prediction of dynamic performances of different high-speed electromagnetic actuators, and can realize coupling calculation with multiple physics such as a mechanical sports field, a hydraulic field and the like, so that the method is really usedThe prediction calculation of the high-speed electromagnetic actuator in the hydraulic system is realized in a meaning.

Description

High-speed electromagnetic actuator dynamic performance calculation method considering eddy current effect
Technical Field
The invention relates to an electromagnetic actuator, in particular to a performance calculation method of the electromagnetic actuator.
Background
The high-speed electromagnetic actuator is a core component in the hydraulic system, and the high-speed electromagnetic actuator is controlled to control the cutting or communication of an oil way, so that the established motion law of the hydraulic system is realized. Although the design of the electromagnetic actuator can be developed by adopting three-dimensional electromagnetic finite element software, the calculation time is too long, and only the calculation and analysis of the dynamic characteristics of the 'dry valve' without considering the hydraulic environment can be carried out, so that the working characteristics of the high-speed electromagnetic actuator in the 'hydraulic environment' of the hydraulic system cannot be accurately predicted. The invention patent "a control method for reducing closing time delay of a high-speed switch electromagnetic valve" (No. CN110094565B, granted date 2020.08.07) discloses a control method for reducing closing time of a high-speed switch electromagnetic valve, according to response requirements of the electromagnetic valve in work, a controller outputs PWM signals with different duty ratios to control the closing of the electromagnetic valve in different time periods when the electromagnetic valve is opened, and therefore closing time of the switch electromagnetic valve is shortened. This method is valuable for engineering applications, but does not guide the predictive design of solenoid valves. The Chinese invention patent 'a multi-objective optimization method for dynamic response characteristics of a high-speed electromagnetic valve' (application number CN201910594428.6, application date 20190703) provides a multi-objective optimization method for dynamic response characteristics of a high-speed electromagnetic valve, electromagnetic force test data obtained by static characteristic experiments are adopted, a polynomial fitting method is adopted, electromagnetic force numerical values under continuous air gaps and current changes are indirectly obtained, and optimization of parameters is realized based on a genetic algorithm. However, this method requires testing the electromagnetic force of the sample piece of the solenoid valve in advance, so that the proposed method cannot really realize the predictive design of the high response characteristic of the solenoid valve.
Disclosure of Invention
The invention aims to provide a simple and high-precision one-dimensional method for calculating the dynamic performance of a high-speed electromagnetic actuator by considering the eddy current effect.
The purpose of the invention is realized as follows:
the invention relates to a method for calculating the dynamic performance of a high-speed electromagnetic actuator by considering an eddy current effect, which is characterized by comprising the following steps of:
(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, and carrying out n layers of slice division with equal thickness on the four defined areas in the radial direction;
(2) defining the first layer and the n-th layer on the A regionEddy currents are respectively 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 BDA0002723810080000021
in the above formula, m is 1 to 4, q is 1 to n, and 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 BDA0002723810080000022
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) considering the leakage phenomenon of the electromagnetic actuator, the equivalent inductance of the leakage part of the A-D region is defined as Lair1～Lair4：
Figure BDA0002723810080000023
In the above formula, x is 1 to 4, SmIs the area of magnetic flux,/mFor the magnetic flux distance, the effective current is calculated according to the relationship between the inductance and the current in the four leakage magnetic regions as follows:
Figure BDA0002723810080000024
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, the eddy current i of two adjacent thin layersRmpAnd iRm(p+1)The magnetic induction intensity between two adjacent thin layers is obtained by the kirchhoff law according to the magnetic flux linkage obtained by the formula:
Figure BDA0002723810080000031
in the above formula, SmpObtaining the magnetic induction intensity B in the magnetization curve by using a data interpolation method for the effective area through which the magnetic induction line passesmpCorresponding magnetic field strength HmpFurther calculate the current I corresponding to the equivalent inductance between two adjacent thin layersmp：
Figure BDA0002723810080000032
(6) According to kirchhoff's law, the formula
Figure BDA0002723810080000033
Figure BDA0002723810080000034
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 BDA0002723810080000035
(7) after the magnetic flux of the electromagnetic actuator is obtained, the air gap magnetic flux phi is obtained according to the law of conservation of full magnetic fluxg1And phig2Equal to φ, the electromagnetic force calculated from the electromagnetic force formula is:
Figure BDA0002723810080000036
(8) carrying out stress analysis on the movement of the armature of the high-speed electromagnetic actuator, constructing a dynamic response model of the electromagnetic actuator, and analyzing the stress condition of the armature, wherein F is defined as electromagnetic force, and FfrIs the frictional resistance during movement of the armature, FmassIs the weight to which the armature is subjected, FsprIs spring elastic force, and oil-fired power F is between armature and iron corehydAccording to Newton's second law, the armature moving upwards is taken as the positive direction, and the armature motion equation of the electromagnetic actuator is solved:
Figure BDA0002723810080000037
in the above formula, c is the damping coefficient, MarmIs armature mass, varmIs the armature movement speed, aarmIs the acceleration of armature movement, xarmIs the armature displacement;
(9) and outputting a curve of the armature lift of the high-speed electromagnetic actuator along with the change of the driving time to obtain the opening response time and the closing response time of the electromagnetic actuator.
The invention has the advantages that: the calculation method provided by the invention can realize accurate prediction of dynamic performances of different high-speed electromagnetic actuators, and can realize coupling calculation with multiple physics such as a mechanical sports field, a hydraulic field and the like, thereby realizing prediction calculation of the high-speed electromagnetic actuators in the hydraulic system in a real sense.
Drawings
FIG. 1 is a schematic view of an electromagnetic actuator of the present invention in a partitioned and layered configuration;
FIG. 2 is a structural diagram of an equivalent magnetic circuit of a constructed electromagnetic actuator;
FIG. 3 is a diagram of the armature force of the high-speed electromagnetic actuator;
FIG. 4 is a graph comparing predicted armature lift and experimental data;
FIG. 5 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. 1-5, the specific process of the present invention is:
(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 BDA0002723810080000041
in the above formula, m is 1 to 4, q is 1 to 6, and ρ ismIs the resistivity of the material, N is the number of turns of the coil, lmqIs the flow distance of the vortex, SmqFlow 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 BDA0002723810080000042
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 BDA0002723810080000051
in the above formula, x is 1 to 4, SmIs the area of 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 BDA0002723810080000052
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 (3) calculating the magnetic induction intensity between two adjacent thin layers according to the magnetic linkage obtained by the formula (5) as follows:
Figure BDA0002723810080000053
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 BDA0002723810080000054
(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 BDA0002723810080000055
(7) after the magnetic flux of the electromagnetic actuator is obtained, the air gap magnetic flux phi is obtained according to the law of conservation of full magnetic fluxg1And phig2Equal to φ, the electromagnetic force calculated from the electromagnetic force formula is:
Figure BDA0002723810080000056
(8) carrying out stress analysis on the movement of the armature of the high-speed electromagnetic actuator to construct a dynamic response model of the electromagnetic actuator, wherein the stress condition is shown as figure 3, F is electromagnetic force, and FfrIs the frictional resistance during movement of the armature, FmassIs the weight to which the armature is subjected, FsprIs spring elastic force, and oil-fired power F is between armature and iron corehyd. According to Newton's second law, the armature moving upwards is taken as the positive direction, and the armature motion equation of the electromagnetic actuator is solved:
Figure BDA0002723810080000061
in the above formula, c is the damping coefficient，MarmIs armature mass, varmIs the armature movement speed, aarmIs the acceleration of armature movement, xarmIs the armature displacement.
(9) The output variable is the armature lift curve result of the high-speed electromagnetic actuator of time.
Fig. 4 shows that the calculated data and the experimental data of the armature dynamic response have good consistency, the total error range of the time when the armature reaches the maximum lift and the time when the armature completely closes does not exceed 5%, and the error range accords with the error range of engineering application, so that the accuracy and the reliability of the method for calculating the dynamic performance of the electromagnetic actuator of the high-pressure common rail system considering the non-uniformity of eddy current distribution provided by the invention are demonstrated.

Claims (1)

1. A high-speed electromagnetic actuator dynamic performance calculation method considering eddy current effect 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, and carrying out n layers of slice division with equal thickness on the four defined areas in the radial direction;
(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 FDA0002723810070000011
in the above formula, m is 1 to 4, q is 1 to n, and ρ ismIs the resistivity of the material, N being the turns of the coilNumber, 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 FDA0002723810070000012
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) considering the leakage phenomenon of the electromagnetic actuator, the equivalent inductance of the leakage part of the A-D region is defined as Lair1～Lair4：
Figure FDA0002723810070000013
In the above formula, x is 1 to 4, SmIs the area of magnetic flux,/mFor the magnetic flux distance, the effective current is calculated according to the relationship between the inductance and the current in the four leakage magnetic regions as follows:
Figure FDA0002723810070000014
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, the eddy current i of two adjacent thin layersRmpAnd iRm(p+1)Obtained by kirchhoff's law, and the magnetic linkage obtained by the formula is calculated to obtain the space between two adjacent thin layersThe magnetic induction intensity of (a) is:
Figure FDA0002723810070000021
in the above formula, SmpObtaining the magnetic induction intensity B in the magnetization curve by using a data interpolation method for the effective area through which the magnetic induction line passesmpCorresponding magnetic field strength HmpFurther calculate the current I corresponding to the equivalent inductance between two adjacent thin layersmp：
Figure FDA0002723810070000022
(6) According to kirchhoff's law, the formula
Figure FDA0002723810070000023
Figure FDA0002723810070000024
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 FDA0002723810070000025
(7) after the magnetic flux of the electromagnetic actuator is obtained, the air gap magnetic flux phi is obtained according to the law of conservation of full magnetic fluxg1And phig2Equal to φ, the electromagnetic force calculated from the electromagnetic force formula is:
Figure FDA0002723810070000026
(8) carrying out stress analysis on the armature motion of the high-speed electromagnetic actuator, constructing a dynamic response model of the electromagnetic actuator, and analyzing the stress condition of the armatureBy definition F is an electromagnetic force, FfrIs the frictional resistance during movement of the armature, FmassIs the weight to which the armature is subjected, FsprIs spring elastic force, and oil-fired power F is between armature and iron corehydAccording to Newton's second law, the armature moving upwards is taken as the positive direction, and the armature motion equation of the electromagnetic actuator is solved:
Figure FDA0002723810070000031
in the above formula, c is the damping coefficient, MarmIs armature mass, varmIs the armature movement speed, aarmIs the acceleration of armature movement, xarmIs the armature displacement;
(9) and outputting a curve of the armature lift of the high-speed electromagnetic actuator along with the change of the driving time to obtain the opening response time and the closing response time of the electromagnetic actuator.
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CN105334477A (en) * 2015-11-04 2016-02-17 中国北方发动机研究所(天津) High-speed solenoid valve electromagnetic force static and dynamic testing apparatus
CN105448459A (en) * 2015-12-10 2016-03-30 哈尔滨工程大学 Multi-permanent magnet high-speed two-way electromagnet
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