CN111079299A - Method for calculating closing bounce electric contact mechanical property of electromagnetic relay under capacitive load - Google Patents
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Abstract
The invention discloses a method for calculating the closing bounce electrical contact mechanical property of an electromagnetic relay under capacitive load, which comprises the following steps: (1) and performing formulaic description on the action process, and establishing an electromagnetic force mathematical model, a contact force mathematical model and an electric repulsion force mathematical model of the electromagnetic relay. (2) And writing a calculation program by adopting MATLAB language to realize the coupling solution of the electromagnetic force mathematical model, the electric repulsion force mathematical model and the contact force mathematical model. In the coupling solving process, the contact bounce and the dynamic characteristic of the electromagnetic relay under the capacitive load are analyzed based on a four-order Runge-Kutta method. The invention provides an analysis method for solving and analyzing the bouncing characteristic of an electromagnetic relay, which can simultaneously solve the coupling equation of an electromagnetic field and a mechanical field for controlling the contact bouncing behavior of the electromagnetic relay, has strong universality, can be applied to different relays under various working conditions, and further improves the bouncing characteristic analysis efficiency of the electromagnetic relay.
Description
Technical Field
The invention relates to a method for calculating the bounce characteristic of a relay under a capacitive load, in particular to a method for simulating the dynamic motion process of a moving contact and an armature and acquiring the bounce parameter of the contact at the moment when the capacitive load is switched by the relay.
Background
The electromagnetic relay is widely applied to power control and power conversion circuits in the high-end equipment manufacturing industry, and the national urgent requirements of long service life and high reliability are met. The key factor influencing the dynamic characteristics of the electromagnetic relay is the contact bounce between the moving contact and the static contact and between the armature and the yoke. Many studies have shown that contact bounce can exacerbate contact wear and shorten the life of electromagnetic relays. In controlling the electrical circuit, switching the capacitive load is an unavoidable task. During the closing process of the moving contact, surge current can be generated under capacitive load, which directly increases the contact bounce possibility of the electromagnetic relay. The contact bounce characteristic in electromagnetic relay applications under capacitive loading has therefore been a concern in recent years for relay manufacturers and users.
At present, the research on the contact characteristics of the traditional relay mainly focuses on two aspects of simulation and experimental research. Few researchers have used theoretical methods to study the bounce characteristics of relays under capacitive loads. In addition, since the experimental study of the contact characteristics of the electromagnetic relay is extremely complicated and time-consuming in structural design, and the mechanism of contact bounce cannot be clearly revealed. Therefore, a simpler, more practical and more universal method is needed to be provided to realize the bounce characteristic analysis of the electromagnetic relay under the capacitive load.
In view of the facts, the theoretical analysis method for effectively evaluating the bounce of the relay under the capacitive load has important significance for improving the dynamic characteristics and the contact reliability of the relay. In addition, the calculation method and the research idea of the bouncing characteristic have good reference effects on the dynamic characteristic evaluation, the contact bouncing inhibition and the performance improvement of the similar electrical appliance structure.
Disclosure of Invention
The invention aims to provide a method for calculating the closing bounce electrical contact mechanical property of an electromagnetic relay under capacitive load, which can simulate the motion-contact-motion process and the bounce property of a contact and an armature in a simple and effective mode.
The purpose of the invention is realized by the following technical scheme:
a method for calculating the closing bounce electrical contact mechanical property of an electromagnetic relay under capacitive load comprises the following steps:
step one, establishing an electromagnetic force mathematical model:
where V is the volume of the solution domain, WmIs the total energy of the magnetic field, H represents the magnetic field strength vector, B represents the magnetic flux density vector, y1Representing the actual displacement of the armature, FmRepresents an electromagnetic force;
step two, establishing a contact force mathematical model:
(1) establishing a mathematical expression of contact force between the moving contact and the static contact:
wherein, FmsExpressing the nonlinear contact force between the static contact and the moving contact, k expressing the contact rigidity coefficient, n being the contact index, kcExpressing the contact damping coefficient, δ is the penetration distance of the moving contact into the stationary contact, y2Actual displacement of the moving contact, ydIndicating an open distance;
(2) establishing a contact force expression between the armature and the yoke:
wherein, FayRepresenting the non-linear contact force between the armature and the yoke, k representing the contact stiffness coefficient, n being the contact index, kcExpressing the contact damping coefficient, δ is the moving contact indentation staticPenetration distance of the state contact, y1Representing the actual displacement of the armature, yxIs an air gap;
step three, establishing an electric repulsion force mathematical model:
(1) a work load circuit of an equivalent electromagnetic relay;
(2) the introduction of the contact bridge model gives an expression of electrodynamic repulsion:
electric repulsive force F on movable contactrEqual to Hall force FhHall force FhComprises the following steps:
where μ is the permeability, imIs surge current, R1Represents the measured contact radius, P represents the contact force, ξ is the contact coefficient of the contact surface, H is the brinell hardness of the contact material;
step four, solving the electro-magnetic-motion field by coupling:
(1) transforming a motion differential equation of a contact model of the electromagnetic relay:
the kinematic differential equation of the electromagnetic relay contact model is expressed in the following vector form:
wherein:
in the formula, M1Mass of armature and connecting rod, M2Is the mass of the moving contact c1Is return spring damping, c2Is contact spring damping, k1Denotes the return spring rate, k2Representing the contact spring stiffness;
armature andresultant force F of moving contact1，F2And F3Expressed as:
F1＝Fm+Ff,F2＝Fm+Ff+Fc+Fay,F3＝Fc+Fms+Fr；
in the formula, FfIs the return spring pre-pressure, FcIs the pre-pressure of the contact spring;
(2) solving a motion differential equation of a contact model of the electromagnetic relay based on a fourth-order Runge-Kutta method to obtain the response of a moving contact and an armature of the relay in a time domain.
Compared with the prior art, the invention has the following advantages:
(1) the invention can simulate the dynamic contact process of the electromagnetic relay and obtain the contact bounce parameter in a simple and effective mode.
(2) The mathematical equation is formulated: a mathematical equation capable of describing the whole action process of the electromagnetic relay under the capacitive load is given, and an electromagnetic force mathematical model, a contact force mathematical model and an electric repulsion force mathematical model of the electromagnetic relay under the capacitive load are established.
(2) The invention realizes the coupling solution of an electromagnetic force mathematical model, a contact force mathematical model and an electric repulsion force mathematical model by using MATLAB language.
(3) The invention realizes the analysis of the contact bounce and the dynamic characteristics of the electromagnetic relay under the capacitive load based on a four-order Runge-Kutta method.
(4) The invention allows the bounce characteristic of the electromagnetic relay under capacitive load to be analyzed, and the time domain response of the moving contact and the armature under corresponding parameters can be obtained only by modifying and operating the MATLAB program under corresponding parameters. The single running time is only 5s, and compared with simulation and experimental research under the same condition, the invention greatly saves the time for designing the device through simulation and experiment.
(5) The invention forms a method for analyzing the action process and the bouncing characteristic of the contact and the armature, and compared with the traditional simulation and experiment methods, the method allows the dynamic process of the armature and the moving contact to be simulated in a simple and effective mode and collects the contact bouncing parameter.
(6) The invention discloses physical mechanisms of contact bounce and armature bounce of an electromagnetic relay. Through establishing a coupling equation of an electro-magnetic-structure in the electromagnetic relay system and describing a differential equation of the motion-contact-motion process of a contact and an armature, the capacitive load circuit is connected with an instantaneous surge current transient equation to realize the bounce characteristic analysis of the electromagnetic relay system.
(7) The invention provides an analysis method for solving and analyzing the bouncing characteristic of an electromagnetic relay, which can simultaneously solve the electromagnetic field and the structural field coupling equation for controlling the contact bouncing behavior of the electromagnetic relay, has strong universality, can be applied to different relays under various working conditions, and further improves the bouncing characteristic analysis efficiency of the electromagnetic relay.
(8) The invention supports and analyzes the influence of the bouncing characteristics of a moving contact and an armature on the bouncing characteristics of the moving contact and the armature, such as ampere-turns, air gap, opening distance, over-travel spring pre-pressure, over-travel spring rigidity, return spring pre-pressure, return spring rigidity, load voltage, contact resistance and the like.
Drawings
FIG. 1 is a work load circuit of an electromagnetic relay;
FIG. 2 is a schematic structural diagram of an electromagnetic relay, 1-fixed contact, 2-connecting rod, 3-return spring, 4-coil, 5-moving contact, 6-contact spring, 7-yoke, 8-magnetic shell, 9-armature;
FIG. 3 is a plot of coil current versus time;
FIG. 4 is a graph showing the variation of the displacement of the movable contact with time;
FIG. 5 is a graph showing the relationship between the bounce displacement of the movable contact and the time under different over travel spring stiffness;
FIG. 6 is a curve of the relationship between the bounce displacement of the movable contact and the time under different pre-pressures of the return spring;
FIG. 7 is a graph showing the relationship between the bouncing displacement of the movable contact and the time under different contact resistances;
fig. 8 is a curve of the relationship between the bounce amplitude and the opening distance of the movable contact under different surge currents.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and modifications or equivalent substitutions may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.
The invention provides a method for calculating the closing bounce electric contact mechanical property of an electromagnetic relay under capacitive load, which comprises the following steps: (1) and performing formulaic description on the action process, and establishing an electromagnetic force mathematical model, a contact force mathematical model and an electric repulsion force mathematical model of the electromagnetic relay. (2) And writing a calculation program by adopting MATLAB language to realize the coupling solution of the electromagnetic force mathematical model, the electric repulsion force mathematical model and the contact force mathematical model. In the coupling solving process, the contact bounce and the dynamic characteristic of the electromagnetic relay under the capacitive load are analyzed based on a fourth-order Runge-Kutta method.
The specific execution steps are as follows:
1. and (5) establishing an electromagnetic force mathematical model. The specific operation process is as follows:
the first step is as follows: the transient electromagnetic field is evaluated by simplified maxwell's equations.
Where H and E represent magnetic field and electric field strength vectors, B represents magnetic flux density vectors, J is current density vectors, J ═ IN/S where I is coil current, N and S represent number of coil turns and surface area, and t represents time.
The magnetic flux and field strength vectors B and H are represented as:
where A is the magnetic vector potential and μ is the magnetic permeability.
Based on equations (1) and (2), the control equation can be derived as:
wherein, JeAnd JsIs the eddy current and source current density vector, and σ is the conductivity.
The second step is that: and solving the electromagnetic force of the electromagnetic relay according to the virtual work principle.
The electromagnetic force of the electromagnetic relay can be calculated by the following formula:
where V is the volume of the solution domain, WmIs the total energy of the magnetic field, y1Representing the actual displacement of the armature, FmRepresenting an electromagnetic force.
2. And (5) establishing a contact force mathematical model. The specific operation process is as follows:
the first step is as follows: the mathematical expression of the contact force between the moving contact and the static contact.
Nonlinear contact force F between static contact and moving contactmsThe following can be evaluated by the Kelvin-Voigt viscoelastic contact model:
wherein k represents a contact stiffness coefficient, n is a contact index, kcExpressing the contact damping coefficient, δ is the penetration distance of the moving contact into the stationary contact, y2Actual displacement of the moving contact, ydIndicating the open distance. To prevent discontinuity of the damping force during contact, a step function is introduced in the calculation, which can be expressed as:
wherein Δ ═ yd–y2+δ)/δ。
The second step is that: contact force expression between the armature and the yoke.
Armature ironAnd the non-linear contact force F between the yokeayThe following can also be evaluated by the Kelvin-Voigt viscoelastic contact model:
wherein k represents a contact stiffness coefficient, n is a contact index, kcExpressing the contact damping coefficient, δ is the penetration distance of the moving contact into the stationary contact, y1Representing the actual displacement of the armature, yxIs an air gap. To prevent discontinuity of the damping force during the contact, a step function is also introduced in the calculation, which can be expressed as:
wherein Δ ═ yx–y2+δ)/δ。
3. And (5) establishing an electric repulsion force mathematical model. The specific operation process is as follows:
the first step is as follows: the working load circuit of the equivalent electromagnetic relay.
Fig. 1 shows a work load circuit of an electromagnetic relay. In FIG. 1, usIs the supply voltage, CsAnd CmRepresenting the stationary and moving contacts, asRepresenting the auxiliary switch, C and R representing the total equivalent capacitance and resistance of the load circuit, im，icAnd irIs the inrush current, the instantaneous current of the capacitor branch and the current of the resistor branch. As can be seen from fig. 1, the capacitor needs to be charged through a resistance and generate a surge current until a steady state voltage is reached in the load circuit.
The second step is that: the introduction of the contact bridge model gives an expression for electrodynamic repulsion.
Generally, the electrodynamic repulsive force acting on the movable contact includes a hall force caused by current contraction and a lorentz force generated by the conductive circuit. As can be seen from fig. 2, there are no other conductive circuits in the load circuit. Thus, the electric repulsive force F on the movable contactrEqual to Hall force Fh. Therefore, the Hall force F is calculated by introducing a contact bridge modelhThe following assumptions were made:
(1) there is only one conductive spot in the center of the contact inner surface, or all conductive spots are concentrated on the center, forming one larger conductive spot.
(2) The conductive points on the contact surface are superconducting cylinders.
Based on the above assumptions, the Hall force F between the moving and stationary contactshCan be expressed as:
where a is the radius of the superconducting cylinder, R1Representing the measured contact radius. The radius a of the superconducting cylinder can be estimated by the following empirical formula:
P＝ξHπa2(10)；
where P represents the contact force, ξ is the contact coefficient of the contact surface, H is the Brinell hardness of the contact material, based on equations (9) and (10), a Hall force F can be obtainedhComprises the following steps:
surge current i through the load circuit when the movable contact of the electromagnetic relay is closedmThe differential equation is calculated as:
wherein u iscIs the voltage of the capacitor, RrIs the contact resistance.
4. The coupling of the electro-magnetic-motion field is solved. The specific operation process is as follows:
the first step is as follows: and converting a motion differential equation of the contact model of the electromagnetic relay.
Based on the above description of steps 1, 2 and 3, the kinematic differential equation of the contact model of the electromagnetic relay can be uniformly expressed in the form of the following vectors:
wherein:
in the formula, M1Mass of armature and connecting rod, M2Is the mass of the moving contact c1Return spring damping, c2Is contact spring damping, k1Denotes the return spring rate, k2Indicating the contact spring rate.
Wherein the resultant force F of the armature and the moving contact1，F2And F3Expressed as:
F1＝Fm+Ff,F2＝Fm+Ff+Fc+Fay,F3＝Fc+Fms+Fr. (17)；
in the formula, FfIs the return spring pre-pressure, FcIs the contact spring pre-pressure.
The second step is that: solving the equation (14) based on the fourth-order Runge-Kutta method.
In order to analyze the contact bounce and the dynamic characteristics of the electromagnetic relay under the capacitive load, the response of a moving contact and an armature of the relay in a time domain is obtained by solving an equation (14) based on a fourth-order Runge-Kutta method.
Example (b):
1. example of computing
The structure of the electromagnetic relay is shown in fig. 2. The relevant parameters of the relay are as follows: m1＝12.9g,M2＝ 7g,k1＝0.37N/mm,k2＝13N/mm,yx＝2.68mm,yd＝1.7mm,Ff＝6N,Fc＝7N,k＝ 5.3×105N/mm,kc＝1N/(mm/s),n＝1.5,δ＝0.1mm.The circuit and electrical contact parameters are:I＝0.7A,N＝2100,S＝430mm2；us＝1V,C＝220μF,R＝ 22Ω,Rr＝0.32mΩ,μ0＝4π×10–10H/mm,ξ＝0.45,H＝91N/mm2,R15.5mm and P10N.
2. Calculation process
(1) And (4) establishing a step based on the electromagnetic force mathematical model to complete the electromagnetic force mathematical model of the electromagnetic relay.
(2) And establishing a step according to the contact force mathematical model to finish the contact force mathematical model of the electromagnetic relay.
(3) And (3) establishing a step by utilizing the electric repulsion force mathematical model to finish the electric repulsion force mathematical model of the electromagnetic relay.
(4) And according to the coupling solving step of the electric-magnetic-motion field, completing the motion differential equation conversion and solving of the contact model of the electromagnetic relay.
(5) Verifying and analyzing influence factors of bounce:
the calculated current and measured value obtained by calculation are shown in fig. 3, and the moving contact displacement and measured value are shown in fig. 4. The curve of the bound displacement and the time change of the moving contact displacement along with the change of the stiffness of the contact spring is shown in figure 5, and the curve of the bound displacement and the time change of the moving contact displacement along with the change of the pre-pressure of the return spring is shown in figure 6. The curve of the bounce amplitude of the moving contact under different load voltages and the change of the time is shown in fig. 7, and the bounce amplitude of the gap between the moving contact and the contact under different surge currents is shown in fig. 8.
3. Calculating the profit
The invention provides an effective theoretical method for calculating the dynamic response behavior of an electromagnetic relay under a capacitive load. Compared with the traditional simulation and experiment methods, the method provided by the invention can be used for analyzing the bouncing characteristic of the structure, and the physical mechanism of the contact bounce of the electromagnetic relay is disclosed. The results obtained by the theoretical method were verified by comparison with experimental results. According to the method, the influence of the structural parameters and the electrical parameters of the load circuit on the bounce characteristics of the contact is researched, and the obtained beneficial conclusion can provide good guidance for designing a relay which can switch a capacitive load more reliably, and the specific conclusion is as follows:
(1) the theoretical model provided by the invention can effectively predict the dynamic characteristics of the electromagnetic relay under the capacitive load. In addition, it can optimize the design of a complex electromagnetic relay by conducting a large amount of parameter studies in a short time.
(2) The reduction in the stiffness of the return spring cannot reduce the bound amplitude of the structure, but can significantly reduce the initial closing moment of the electromagnetic relay.
(3) The bounce amplitude of the electromagnetic relay can be effectively reduced by increasing the rigidity of the contact spring. However, the stiffness of the contact spring has little effect on the initial closing time of the structure.
(4) To a certain extent, the increase in contact resistance is advantageous for reducing the contact bounce of the moving contact of the electromagnetic relay under capacitive load.
(5) The electromagnetic relay under capacitive load has an optimal opening distance, and the value of the opening distance is equal to 2.1 mm.
Claims (5)
1. A method for calculating the closing bounce electrical contact mechanical property of an electromagnetic relay under capacitive load is characterized by comprising the following steps:
step one, establishing an electromagnetic force mathematical model:
where V is the volume of the solution domain, WmIs the total energy of the magnetic field, H represents the magnetic field strength vector, B represents the magnetic flux density vector, y1Representing the actual displacement of the armature, FmRepresents an electromagnetic force;
step two, establishing a contact force mathematical model:
(1) establishing a mathematical expression of contact force between the moving contact and the static contact:
wherein, FmsExpressing the nonlinear contact force between the static contact and the moving contact, k expressing the contact rigidity coefficient, n being the contact index, kcExpressing the contact damping coefficient, δ is the penetration distance of the moving contact into the stationary contact, y2Actual displacement of the moving contact, ydIndicating an open distance;
(2) establishing a contact force expression between the armature and the yoke:
wherein, FayRepresenting the non-linear contact force between the armature and the yoke, k representing the contact stiffness coefficient, n being the contact index, kcExpressing the contact damping coefficient, δ is the penetration distance of the moving contact into the stationary contact, y1Representing the actual displacement of the armature, yxIs an air gap;
step three, establishing an electric repulsion force mathematical model:
(1) a work load circuit of an equivalent electromagnetic relay;
(2) the introduction of the contact bridge model gives an expression of electrodynamic repulsion:
electric repulsive force F on movable contactrEqual to Hall force FhHall force FhComprises the following steps:
where μ is the permeability, imIs surge current, R1Represents the measured contact radius, P represents the contact force, ξ is the contact coefficient of the contact surface, H is the brinell hardness of the contact material;
step four, solving the electro-magnetic-motion field by coupling:
(1) transforming a motion differential equation of a contact model of the electromagnetic relay:
the kinematic differential equation of the electromagnetic relay contact model is expressed in the following vector form:
wherein:
in the formula, M1Mass of armature and connecting rod, M2Is the mass of the moving contact c1Is return spring damping, c2Is contact spring damping, k1Denotes the return spring rate, k2Representing the contact spring stiffness;
resultant force F of armature and moving contact1，F2And F3Expressed as:
F1＝Fm+Ff,F2＝Fm+Ff+Fc+Fay,F3＝Fc+Fms+Fr；
in the formula, FfIs the return spring pre-pressure, FcIs the pre-pressure of the contact spring;
(2) solving a motion differential equation of a contact model of the electromagnetic relay based on a fourth-order Runge-Kutta method to obtain the response of a moving contact and an armature of the relay in a time domain.
2. The method for calculating the closing bounce electrical contact mechanical property of the electromagnetic relay under the capacitive load according to claim 1, wherein the magnetic flux and magnetic field strength vectors B and H are expressed as:
where A is the magnetic vector potential and μ is the magnetic permeability.
3. The method for calculating the closing bounce electrical contact mechanical property of the electromagnetic relay under the capacitive load according to claim 1, wherein in the mathematical expression of the contact force between the moving contact and the static contact, the step function is expressed as:
wherein Δ ═ yd–y2+δ)/δ。
4. The method for calculating the closing bounce electrical contact mechanical property of the electromagnetic relay under the capacitive load according to claim 1, wherein in the contact force expression between the armature and the yoke, the step function is expressed as:
wherein Δ ═ yx–y2+δ)/δ。
5. The method for calculating the closing bounce electrical contact mechanical property of the electromagnetic relay under the capacitive load according to claim 1, wherein i ismThe differential equation of (a) is calculated as:
wherein u iscIs the voltage of the capacitor, RrIs the contact resistance.
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