CN115203886A - Intermittent fusion welding small-load relay electric contact characteristic analysis method - Google Patents
Intermittent fusion welding small-load relay electric contact characteristic analysis method Download PDFInfo
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Abstract
The invention discloses an intermittent fusion welding small-load relay electrical contact characteristic analysis method, which comprises the following steps: step 1, constructing an equivalent contact dynamic model of an intermittent fusion welding relay; step 2, deducing a contact dynamics differential equation; step 3, matrixing a contact dynamic motion partial differential equation; step 4, determining forced thrust of the relay; step 5, determining impact force; step 6, determining Hall force; step 7, determining welding force; step 8, according to the steps 1 to 7, the moving contact displacement y is obtained by utilizing the Longge Kutta method, and if y is more than or equal to d 0 Then the electric contact parameters of the contacts are output, so that the dynamic response of the movable contact of the relay can be obtained,otherwise, returning to the step 4. The invention formulates and matriculates different natures at the contact position, flexibly and efficiently obtains the bounce time, the bounce times and the bounce amplitude data of the relay under different parameters, and provides data support for the optimization of the reliability of the whole service life of the relay.
Description
Technical Field
The invention relates to a relay electrical contact characteristic analysis method, in particular to a method capable of formulaically evaluating the intermittent closing-opening-closing process of a relay movable contact under the condition of non-welding failure.
Background
Contact weld failure is a common failure mode for small load relays. In the process of power control, signal conversion and load protection of the relay, a contact point electrifying loop is actually composed of a plurality of contact spots and bears load current. When a large current flows through the contacts, the current density in the actual contact area between the contacts suddenly increases, joule heating heats the contact area and causes the nearby contact material to melt and soften. When the molten microscopic liquid metal in the contact area is cooled and solidified, the relay contact pairs are welded together. When the contact area of the relay is melted and softened, the natural damping of the contact material can be increased, the original mechanical action relation on the contact surface is seriously damaged, the contact state of the contact is further changed, the reliability of the relay is directly reduced, and the bottleneck for improving the reliability of the relay with a small load is formed.
Breaking the fusion weld between the two contacts and thereby opening the relay contacts again requires that the separation force on the contacts be higher than the maximum weld force of the contact area. The force on the contact of the small-load relay mainly comprises four parts: the forced pushing force acting on the contact, the impact force generated by the contact collision of the two contacts, the Hall force generated by the contraction of the current line in the contact area and the welding force in the melting area. In recent years, contact fusion welding research has mainly focused on experimental studies of the characteristics of contact welding, the arcing that induces welding, and the failure modes. The on-load switching process and the bouncing characteristic analysis of the relay are also researched by a method for developing the instantaneous impulse brought to the contact by surrounding the load access. Very little research is currently being conducted to link and kinetically analyze the contact impact phenomenon during relay contact action with intermittent fusion welding in the event of non-weld failure. The parameters that affect the fusion welding and reopening of the contacts are numerous and are interrelated. Thus, the electrical contact characteristics of a relay in the event of a non-welded failure is a very complex phenomenon. However, there is little specific study on the calculation of the dynamic characteristics of the relay in which intermittent fusion welding currently occurs and the analysis of the mechanism of the influence of welding force on the contact action.
Disclosure of Invention
The invention provides an intermittent fusion welding small-load relay electric contact characteristic analysis method aiming at a fusion welding phenomenon often accompanied with the small-load relay electric contact characteristic. The method can effectively evaluate the conditions of magnetizer magnetization, electromagnetic force generation, forced movement of the movable contact, contact impact between contact pairs, heating softening of a contact area and local resultant force of the relay coil after the relay coil is electrified, can quickly acquire the electric contact performance of the relay under the condition of changing input parameters, structure and material parameters, effectively counts contact bounce parameter data of the whole contact action process, and can directly use an analysis theory and the obtained data to construct a relay reliability optimization model and degrade parameter analysis.
The purpose of the invention is realized by the following technical scheme:
an intermittent fusion welding small-load relay electrical contact characteristic analysis method comprises the following steps:
constructing an equivalent contact dynamic model of the relay according to the working principle of the small-load relay;
Obtaining a contact dynamics motion partial differential equation of the relay according to the equivalent contact dynamics model of the intermittent fusion welding relay established in the step 1:
wherein E and I are respectively the elastic modulus and the moment of inertia of the structure, and ρ is the material of the structureMaterial density, A s Is the cross-sectional area of the structure, c s Is the structural damping coefficient, x is the abscissa, t is the structural movement time, y (x, t) represents the contact movement displacement, p (x, t) is the load per unit length of the movable spring;
Substituting the displacement expression of the movable spring into a contact dynamics motion partial differential equation of the relay to obtain a partial differential equation:
wherein i =1,2 \ 8230n, N and N represent the number of truncated modes, ξ i (x) Representing the ith modal function, g, of the movable spring i (t) represents the ith generalized coordinate function, L 1 Indicating the distance, L, of the push rod from the fixed end of the movable spring 2 The distance from the movable contact to the fixed end of the movable spring is shown;
multiplying xi to the left and right of partial differential equation based on orthogonality of main mode function j (x) J =1,2, \8230n, which is then integrated from 0 to L, and thus the partial differential equations can be discretized into N sets of ordinary differential equations which are expressed in matrix form as shown below:
wherein g = [ g ] 1 ,g 2 ,…,g N ] T Expressing a generalized coordinate vector, M expressing a mass matrix, C expressing a damping matrix, K expressing a rigidity matrix and Q expressing an external force vector; element M in mass, damping and stiffness matrix and external force vector ij 、C ij 、K ij And Q i Respectively expressed as:
Where ψ is the flux linkage u, i c And R is the voltage, current and resistance of the input end coil respectively; omega x Is the angular velocity, T, of the armature m Is an electromagnetic torque, T f Is a counter moment, I m Is the moment of inertia, α is the angle of rotation of the armature, L 3 Is the length of the push rod, beta is the initial angle of the push rod;
In the formula, k c Denotes the contact stiffness, d 0 Representing initial opening distance, n representing a non-linear coefficient, c c Represents the contact damping, Δ c is a function that ensures the continuity of the damping force during a collision;
In the formula, μ represents permeability, i b Representing the current flowing through the contact, r 1 Denotes the contact radius of the contact point, P denotes the contact pressure, ζ denotes the contact coefficient, H denotes the brinell hardness of the contact material;
Where r is the tensile strength, d w Is the cross-sectional diameter of the ablation pit;
Compared with the prior art, the invention has the following advantages:
(1) The invention constructs an electric contact dynamic model for evaluating contact bounce of the contact under the condition of intermittent fusion welding of the small-load relay. Compared with the traditional small-load relay electric contact analysis method, the dynamic model provided by the invention fully considers the contact motion, impact, heating softening and melting contact processes, and more truly reflects the dynamic contact behavior of the contact in the small-load relay switching process.
(2) The invention defines the criterion of the critical contact bounce of the relay under the non-welding failure condition, and effectively discloses the physical law that the bounce of the contact can be effectively controlled by adjusting the distance between the movable contact and the fixed end and the voltage parameter of the input end; however, under the condition of different distance parameters between the movable contact and the fixed end, the influence rule change of the input end voltage on the contact bounce characteristic is different, and a foundation is laid for predicting the contact fault of the relay under the working condition with the load.
(3) The invention provides a method for simplifying and simulating the welding contact area after the metal softening deformation of a contact area by a half test method, and carries out the welding force calculation of the complete physical process from heating to melting deformation of a microcosmic contact area, thereby realizing the quantitative analysis of the electric contact influence rule of a relay.
(4) The invention discloses a general electric contact dynamic characteristic evaluation method for an intermittent fusion welding relay, which is characterized in that different properties at a contact position are formulated and matrixed, the bounce time, the bounce times and the bounce amplitude data of the relay under different parameters are flexibly and efficiently obtained, and data support is provided for the optimization of the whole service life reliability of the relay.
(5) The invention discloses a simulation method and steps of a common problem of contact bounce in an intermittent fusion welding process of a relay. Based on the method, the main key factors influencing the contact bounce of the contact are the width, the thickness and the material density of the movable spring leaf; the initial closing time, the bounce amplitude and the bounce time of the contact of the relay can be obviously reduced by reducing the values of the three.
(6) According to the working principle of the relay, a series of motion differential equations are deduced, and the processes of excitation, motion, collision, fusion welding and bouncing in an electromagnetic system and a contact system of the relay are formulated for representation. The method can be popularized and applied to dynamic characteristic analysis and product optimization of similar electrical appliances with contacts. The method can be used for determining the influence of intermittent fusion welding on the electric contact performance of the relay, effectively explaining the contact bounce mechanism under the change of the surface morphological characteristics of the contact, and efficiently assisting in developing methods and measures for controlling contact bounce and contact failure.
(7) The dynamic characteristic of a commercial relay is analyzed by the method of the invention, and the error between the calculated coil current and the measured value is 3 percent (figure 5, J in the figure) 1 The time of the current suction at the input end), the error between the displacement of the moving contact and the measured data is calculated to be 7 percent (figure 6, J in the figure) 2 Representing the initial closing time of the movable contact), the calculation error is within an allowable range, and the accuracy of the method is well verified.
Drawings
FIG. 1 is an equivalent contact dynamics model of an intermittent fusion welded relay, (a) initial state, (b) initial contact between a movable spring and a normally open contact lever, (c) contact between the movable spring and the normally open contact lever, and (d) over travel contact between the movable spring and the normally open contact lever;
FIG. 2 is an equivalent electrical contact bridge model;
FIG. 3 is a contact ablation profile for intermittent fusion welding;
FIG. 4 is a schematic diagram of a solution topology;
FIG. 5 is a comparison of calculated coil current and measured values;
FIG. 6 is a comparison of the moving contact displacement with the actual measurement;
FIG. 7 is a commercial light load relay contact system;
FIG. 8 shows the distance L between the moving contact and the fixed end 2 The contact bounce displacement of the lower movable contact changes along with the time;
FIG. 9 shows the spring width b of different movable springs w The contact bounce displacement of the lower movable contact changes along with the time;
FIG. 10 is a graph of contact bounce displacement versus time for different movable spring material densities ρ movable contact;
FIG. 11 is a graph of contact bounce displacement versus time for different movable spring elastic moduli Emovable contacts;
in the figure: 1-fixed end, 2-normally open contact rod, 3-movable spring, 4-push rod, 5-normally closed contact rod, 6-base, 7-lead leading-out end and 8-movable reverse spring.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a relay electric contact characteristic analysis method capable of flexibly simulating the intermittent fusion bonding phenomenon based on the actual on-load switching requirement of a certain commercial small-load relay, aiming at elaborating the action mechanism of the fusion welding condition on the contact state of a contact and the influence of the fusion welding condition on the final welding failure of the contact, and defining the action rule of input parameters, structures and material parameters on the contact bounce characteristic, and data generated in the analysis process can be directly used for constructing a relay contact reliability and electric service life optimization model. The technical key points of the invention are as follows:
(1) The invention aims at a type of contact with a fusion welding area, and constructs a mathematical model suitable for evaluating the intermittent fusion contact dynamic characteristics of a small-load relay.
(2) The invention deduces the mechanical action relationship and the displacement complete differential equation of a series of motion behaviors of motion, contact, deformation, welding and bounce of the relay contact, and clarifies the contact bounce mechanism under the melting contact.
(3) The invention simulates the dynamic process of intermittent molten contact of the relay, collects parameter data which can be used for guiding engineering design and provides data for bounce suppression and electrical contact reliability optimization of similar electrical products.
(4) The invention defines the key parameters and effective measures for reducing the contact bounce condition and improving the contact reliability and the electric service life of the relay.
Analyzing the action process of a small-load relay with intermittent fusion welding contact, carrying out stress analysis on the contact and decomposing the stress analysis into the following stages: 1) The moving contact is forced to push force F p Starting to move under the action; the movable contact contacts with the normally open contact and generates an impact force F c (ii) a The current line contracts in the actual contact area of the contact to generate Hall force F e When the closed contact is subjected to large current impact, the current density of the actual contact area of the relay contact is rapidly increased, and the contact is heated by joule heat and the material near the contact area is heated, softened and even melted; the molten microscopic liquid metal in the contact areas causes the microscopic contact areas between the moving and stationary contacts to join together, producing a welding force F w . Because the input end of the relay is continuously acted by the forced thrust, the mechanical action relation of the contact area of the contact can be changed in real time. When the separating force of the movable contact is larger than the welding force on the contacts, the two contacts are opened again, the movable contact is far away from the normally open contact, and the movable contact bounces. Therefore, the core of the solution of the small-load relay electrical contact bounce process of intermittent fusion welding is actually a contact area stress analysis process under the condition of fusion welding. The specific implementation steps are as follows:
According to the working principle of the small-load relay, namely the whole action process of the relay comprises a free stroke stage, a contact process and an over-stroke stage, the invention provides the equivalent contact dynamic model of the relay shown in FIG. 1. In the model shown in fig. 1, the moving contact is equivalent to "a", the normally open contact is equivalent to "B", the movable spring is equivalent to an euler-bernoulli beam to complete the dynamic characteristic analysis, and the solving process follows the linear stress-strain theory. The model shown in fig. 1 considers the rigid large displacement linear motion of the movable spring of the relay in the free stroke stage (fig. 1 (b)), and the flexible small distance nonlinear motion of the movable spring in the overtravel stage (fig. 1 (d)), in the process, the movable contact collides with the normally open contact and continues to move until the deformation of the movable spring reaches the maximum value. Contact bounce can occur before the moving contact kinetic energy is completely dissipated. Meanwhile, in the contact process of two contacts of the free relay, the model shown in fig. 1 fully considers the initial movement of the movable spring of the relay under the action of forced thrust (fig. 1 (a)), the impact when the movable contact and the normally open contact are contacted and the welding force when the movable contact is not stably contacted (fig. 1 (c)).
According to the equivalent contact dynamics model of the intermittent fusion welding relay established in the step 1, a contact dynamics motion partial differential equation can be given:
where E and I are the modulus of elasticity and moment of inertia, respectively, of the structure, ρ is the material density of the structure, A s Is the cross-sectional area of the structure, c s Is the structure damping coefficient, x is the abscissa, t is the structure movement time, y (x, t) represents the contact movement displacement, p (x, t) is the load per unit length of the movable spring, which can be expressed as equation (2), where δ (x) is the dirac function, and where F is r ＝F c +F e +F w 。
p(x,t)＝F p δ(x-L 1 )-F r δ(x-L 2 ) (2)；
In the formula, L 1 Indicating the distance, L, of the push rod from the fixed end of the movable spring 2 Indicating the distance of the moving contact from the fixed end of the movable spring, F p To be forced, F r Is on the contact F c ，F e And F w A resultant force of the three, and F c ，F e And F w Respectively, impact force, hall force and welding force on the contact.
The requirement formula (1) needs to disperse the partial differential motion equation of the relay into an ordinary differential equation, and then the contact bounce behavior of the movable contact of the relay is solved. According to the Galerkin method, the displacement of the moving contact is assumed to be the following equation:
in the formula, i =1,2 \8230n, xi i (x) Representing the ith modal function, g, of the movable spring i (t) represents the ith generalized coordinate function, and N represents the number of truncated modes. Mode function xi i (x) Can be obtained by solving the free vibration equation of the movable spring, which can be expressed in the form of equation (4).
The contact motion displacement y (x, t) is assumed and made y (x, t) = ξ (x) t (t), after which y (x, t) is substituted into equation (4). According to the split variant method, equation (4) can be converted into the following expression:
ξ(x)＝C 1 sin(λx)+C 2 cos(λx)+C 3 sh(λx)+C 4 ch(λx) (5)；
wherein λ is a constant coefficient and has 4 ＝ρA s ω 2 I,. Omega.represents the natural frequency of the movable spring, C 1 、C 2 、C 3 And C 4 Is the undetermined coefficient. According to the equivalent contact dynamics model of the intermittent fusion welding relay in the figure 1 established in the step 1, the deflection of the fixed end of the movable spring is knownThe degree and the corner are zero, and the bending moment and the shearing force of the free end are also equal to zero. Thus, the boundary condition of the movable spring can be expressed as:
y| x＝0 ＝y′| x＝0 ＝y″| x＝L ＝y″′| x＝L ＝0 (6)；
in the formula, L represents the length of the movable spring.
By substituting formula (5) for formula (6), it is possible to obtain:
the condition that equation (7) has a non-zero solution is:
expanding and simplifying equation (8), the movable spring frequency equation of the relay can be given by:
cos(λL)ch(λL)+1＝0 (9)。
solving equation (9) can calculate the value of λ. Then substituting the value of lambda into a formula (7) to further determine the undetermined coefficient C 1 、C 2 、C 3 And C 4 And obtaining the mode function of the movable spring.
Substituting the displacement expression (3) of the movable spring in the step 2 into the partial differential equation (1), the following partial differential equation can be obtained:
based on the orthogonality of the principal mode functions, xi is multiplied around equation (10) j (x) J =1,2, \8230;, N, which is then integrated from 0 to L, and then equation (10) may be discretized into N sets of ordinary differential equations, which may be expressed in a matrix form as shown in equation (11):
wherein g = [ g ] 1 ,g 2 ,…,g N ] T The generalized coordinate vector is represented, the mass matrix is represented by M, the damping matrix is represented by C, the rigidity matrix is represented by K, and the external force vector is represented by Q. Element M in mass, damping and stiffness matrix and external force vector ij 、C ij 、K ij And Q i Can be expressed as:
After the relay coil is electrified, the magnetizer in the electromagnetic system is magnetized to generate electromagnetic attraction. The electromagnetic attraction drives the push rod to push the movable contact to move towards the normally open contact side. According to the moment equilibrium equation, the forced thrust force F acting on the relay contact p The evaluation can be made by equation (16):
where ψ is the flux linkage u, i c And R is the voltage, current and resistance of the input end coil respectively; omega x Is prepared fromAngular velocity of iron, T m Is an electromagnetic torque, T f Is a counter moment, I m Is the moment of inertia, alpha is the angle of rotation of the armature, L 3 Is the length of the push rod and beta is the initial angle of the push rod.
Impact force F when Impact function method Impact is used for making collision contact between moving contact and normally open contact of model in figure 1 c And (4) performing calculation. The impact force between the movable contact and the normally open contact comprises two parts, one is an elastic force generated by the mutual cut-in of the two contacts when the contacts are in collision contact, and the other is a damping force generated by the relative speed. Thus, F between the movable contact and the normally open contact can be obtained c ：
In the formula, k c Denotes contact stiffness, d 0 Denotes the initial opening distance, n denotes the non-linear coefficient, c c Representing contact damping, ac is a function that ensures the continuity of the damping force during a collision, namely:
in the formula, delta s Indicating the depth of penetration.
The Impact function Impact can be used for conveniently solving the problem of collision between the movable contact and the normally open contact, but the derivation formula (17) shows that the selection of the calculation parameters has great influence on the accuracy of the calculation result, and the selection is also the difficult point and the key point for accurately and quickly solving the problem of contact collision by using the formula (17).
To evaluate Hall force F e The equivalent electrical contact bridge model shown in fig. 2 is presented. Since the contact surface between the contacts is formed by a plurality of micro-convex bodies from the microscopic level, the invention simplifies the calculation by combining the movable contact and the constant contact of the relayThe contact between the open contacts is equivalent to the contact of a single large cylinder. Wherein, r in FIG. 2 c Is the radius of the circular cross-section of the contact patch, a r And b r Respectively the length and width of the contact cross-section i b Is the load current. The contact bridge model in fig. 2 satisfies: (1) The contact micro-convex bodies between the moving contact and the normally open contact are converged at the center to form an equivalent conductive cylinder, and the conductive cylinder is positioned at the center of the contact area; (2) The conductive cylinder is made of the same material as the contact and the movable contact and the normally open contact. The holm force is generated by the contraction of the current lines at the contact surfaces of the contacts, and therefore exists only during the time period when the movable contact and the normally open contact are maintained in a metal contact state, i.e., during the overtravel phase of the relay. Accordingly, the hall force generated in the relay contact area can be expressed as follows:
in the formula, μ represents a magnetic permeability, r 1 Denotes the contact radius of the contact point, P denotes the contact pressure, ζ denotes the contact coefficient, and H denotes the brinell hardness of the contact material. The Hall force calculation formula (19) is arranged to obtain a more intuitive expression of the Hall force:
the contact pressure of the relay movable contact and the normally open contact is continuously reduced in the disjunction time period. While equation (20) clearly illustrates that the hall force of a relay is closely related to the pressure on the contacts. Thus, the Hall force varies with the instantaneous current through the contacts and the contact force, and after the moving contact separates from the normally open contact, the force is not present.
The molten metal in the contact area is pressed to the outside of the contact area under the combined action of the contact pressure, atmospheric pressure, and surface tension, and the contact position is locally deformed. The position of the edge of the initial contact area of the contact has a certain annular appearance in the process of gradually solidifying the molten liquid metal, and the annular appearance area has small contribution to fusion welding between the movable contact and the normally open contact and belongs to an ineffective fusion welding area. The continuous increase of the bounce heat of the contact area of the relay creates a certain condition for the formation of a melting bridge.
The relay contact is observed under an electron microscope, and the ablation morphology of the contact obtained by intermittent fusion welding is shown in figure 3, wherein Y in the figure s Indicating a molten zone. Since the welding area is 20 to 40% of the melting area for the same material, the area of the contact where the melting welding occurs can be estimated. Welding force F between moving contact and normally open contact w Given by:
where r is the tensile strength, d w Is the cross-sectional diameter of the ablation pit.
The steps 1 to 7 are formulated to describe the forced thrust F of microcosmic contact spots of the contacts of the intermittent fusion welding relay in the mutual contact process p Impact force F c Hall force F e And a welding force F w The dynamic process of transition from elastic deformation to plastic deformation is carried out under the action of the elastic deformation. The specific solving topological diagram of the method is shown in FIG. 4, and the specific solving method comprises the following steps:
(1) Constructing an intermittent fusion welding relay contact dynamic model according to the step 1;
(2) Deducing a relay contact dynamics differential equation based on the step 2 and formulating;
(3) Performing matrixing on the relay contact dynamics differential equation according to the step 3;
(4) Determining forced thrust F of relay by using step 4 p ；
(5) Determining the impact force F of the relay based on step 5 c ；
(6) Determining the Hall force F of the relay according to step 6 e ；
(7) Determining the welding force F of the relay according to step 7 w ；
(8) According to the steps 1 to 7, a Runge Kutta electrical contact characteristic solving program can be written according to the solving topology shown in FIG. 4, the numerical solution of the generalized coordinate vector g in the formula (11) can be accurately and rapidly solved, and then the dynamic response of the relay moving contact can be obtained by combining the formula (3).
The embodiment is as follows:
1. example of computing
A commercial, low-load relay having the contact system of fig. 7 was selected for example analysis, with the operating parameters of the relay as shown in table 1.
TABLE 1 operating parameters of the Relay
2. Calculation process
(1) Constructing an intermittent fusion welding relay contact dynamic model according to the step 1;
(2) Deriving and formulating a contact dynamics differential equation of the commercial relay of fig. 7 based on the step 2;
(3) Matrixing the commercial relay contact dynamics differential equation of fig. 7 according to step 3;
(4) Determination of the forced thrust force F of the commercial Relay of FIG. 7 Using step 4 p ；
(5) Determining the impact force F of the commercial relay of FIG. 7 based on step 5 c ；
(6) Determining the Hall force F of the commercial relay of FIG. 7 according to step 6 e ；
(7) Determination of the welding force F of the commercial relay of FIG. 7 according to step 7 w ；
(8) Following fig. 4, a lunger stota electrical contact characteristic solver is written to solve for the dynamic response of the contacts, pursuant to step 8.
3. Calculating the profit
(1) The intermittent fusion welding contact dynamic model of the commercial relay in FIG. 7 constructed according to the method of the invention accurately simulates the electrical contact process of the relay, and the calculation error is controlled within 7%;
(2) A relay coupling equation for controlling the action of the contact system is cooperatively and quickly solved, a contact motion displacement curve is output in real time, and the contact bounce duration, bounce amplitude and bounce times are effectively collected;
(3) Analysis of a certain commercial relay in the relay in fig. 7 shows that the trend of contact separation and bounce in the electric contact process depends on the resultant force and impact effect of the contact area, and the contact separation mechanism of the relay in fig. 7 is effectively disclosed;
(4) Analyzing the calculation results of fig. 8, 9, 10 and 11, it is found that reducing the width and material density of the movable spring of the relay can significantly reduce the initial closing time, bounce amplitude and bounce time of the relay. Meanwhile, the elastic modulus of the relay contact material is reasonably selected, and the distance from the relay contact to the fixed end is controlled, so that the purpose of effectively controlling the relay to stabilize the electric contact process can be achieved;
(5) The relay parameters of the figure 7 which can be flexibly and widely changed subsequently by utilizing the method of the invention comprise: the influence and action rule of the change of each parameter on the electric contact state of the relay are researched by input end parameters (the number of turns of a coil, control voltage), structural parameters (the length of a movable spring) and contact parameters (contact rigidity and contact damping), and the obtained data can be directly used for the reliability optimization design of the relay.
Claims (6)
1. An intermittent fusion welding small-load relay electrical contact characteristic analysis method is characterized by comprising the following steps:
step 1, constructing an equivalent contact dynamic model of an intermittent fusion welding relay;
constructing an equivalent contact dynamic model of the relay according to the working principle of the small-load relay;
step 2, deducing a contact dynamics differential equation
Obtaining a contact dynamics motion partial differential equation of the relay according to the equivalent contact dynamics model of the intermittent fusion welding relay established in the step 1:
where E and I are the modulus of elasticity and the moment of inertia, respectively, of the structure, ρ is the material density of the structure, A s Is the cross-sectional area of the structure, c s Is the structural damping coefficient, x is the abscissa, t is the structural movement time, y (x, t) represents the contact movement displacement, p (x, t) is the load per unit length of the movable spring;
step 3, matrixing contact dynamics motion partial differential equation
Substituting the displacement expression of the movable spring into partial differential equation (1), the following partial differential equation can be obtained:
based on the orthogonality of the principal mode functions, xi is multiplied around equation (10) j (x) J =1,2, \8230;, N, which is then integrated from 0 to L, and then equation (10) may be discretized into N sets of ordinary differential equations, which may be expressed in a matrix form as shown in equation (11):
wherein g = [ g ] 1 ,g 2 ,…,g N ] T Expressing a generalized coordinate vector, M expressing a mass matrix, C expressing a damping matrix, K expressing a rigidity matrix and Q expressing an external force vector;
step 4, determining forced thrust F of the relay p ：
Where ψ is the flux linkage u, i c And R is the voltage, current and resistance of the input end coil respectively; omega x Is the angular velocity, T, of the armature m Is an electromagnetic torque, T f Is a counter moment, I m Is the moment of inertia, alpha is the angle of rotation of the armature, L 3 Is the length of the push rod, and beta is the initial angle of the push rod;
step 5, determining the impact force F c ：
In the formula, k c Denotes the contact stiffness, d 0 Representing initial opening distance, n representing a non-linear coefficient, c c Represents the contact damping, Δ c is a function that ensures the continuity of the damping force during a collision;
step 6, determining Hall force F e ：
In the formula, μ represents a magnetic permeability, i b Representing the current flowing through the contact, r 1 Denotes the contact radius of the contact point, P denotes the contact pressure, ζ denotes the contact coefficient, H denotes the brinell hardness of the contact material;
step 7, determining welding force F w ：
Where r is the tensile strength, d w Is the cross-sectional diameter of the ablation pit;
step 8, according to the steps 1 to 7, the movement is obtained by using the Longge Kutta methodThe contact displacement y is equal to or larger than d 0 And (4) outputting the contact point electric contact parameters to obtain the dynamic response of the relay moving contact, and otherwise, returning to the step (4).
2. The intermittent fusion welded small load relay electrical contact characteristic analysis method according to claim 1, characterized in that p (x, t) is expressed as:
p(x,t)＝F p δ(x-L 1 )-F r δ(x-L 2 ) (2)；
wherein δ (x) is the Dirac function, L 1 Indicating the distance, L, of the push rod from the fixed end of the movable spring 2 Indicating the distance of the moving contact from the fixed end of the movable spring, F p To be forced, F r Is on the contact F c 、F e And F w Resultant force of the three, F c 、F e And F w Respectively impact force, holm force and welding force on the contacts.
3. The intermittent fusion welded small load relay electrical contact characteristic analysis method according to claim 1, wherein the displacement expression of the movable spring is:
4. the intermittent fusion welded small load relay electrical contact characteristic analysis method as claimed in claim 1, characterized in that the mode function ξ i (x) Can be obtained by solving the free vibration equation of the movable spring, which can be expressed in the form of equation (4):
assuming the contact motion displacement y (x, t) and letting y (x, t) = ξ (x) t (t), then substituting y (x, t) into equation (4), equation (4) can be converted into the following expression according to the split-variable method:
ξ(x)＝C 1 sin(λx)+C 2 cos(λx)+C 3 sh(λx)+C 4 ch(λx) (5)；
wherein λ is a constant coefficient and has 4 ＝ρA s ω 2 the/EI, omega denotes the natural frequency of the movable spring, C 1 、C 2 、C 3 And C 4 Is a undetermined coefficient;
according to the equivalent contact dynamics model of the intermittent fusion welding relay established in the step 1, the deflection and the corner of the fixed end of the movable spring are zero, the bending moment and the shearing force of the free end are also equal to zero, and the boundary conditions of the movable spring can be expressed as follows:
y| x＝0 ＝y′| x＝0 ＝y″| x＝L ＝y″′| x＝L ＝0 (6)；
wherein L represents the length of the movable spring;
by substituting formula (5) for formula (6), one can obtain:
the condition that equation (7) has a non-zero solution is:
expanding and simplifying equation (8), the movable spring frequency equation of the relay can be given by:
cos(λL)ch(λL)+1＝0 (9)；
the value of lambda can be obtained by calculating by solving the formula (9), then the value of lambda is substituted into the formula (7), and the undetermined coefficient C is further determined 1 、C 2 、C 3 And C 4 And obtaining the mode function of the movable spring.
5. The method of claim 1The method for analyzing the electric contact characteristics of the intermittent fusion welded small-load relay is characterized in that the mass matrix, the damping matrix, the rigidity matrix and the element M in the external force vector ij 、C ij 、K ij And Q i Can be expressed as:
6. the intermittent fusion welded small load relay electrical contact characteristic analysis method as claimed in claim 1, wherein the expression of Δ c is:
in the formula, delta s Indicating the depth of penetration.
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