CN113567744B - Method for calculating contact resistance of electric connector under storage condition - Google Patents
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Abstract
The invention discloses a simulation method of an electric connector contact performance degradation process considering discrete stress, which comprises the following steps: s1, measuring the contact surface of an electric connector to obtain an initial value of a three-dimensional W-M function; s2, establishing two contact surface models based on a three-dimensional W-M function; s3, obtaining two section skeleton diagrams based on the two contact surface models; s4, respectively selecting two-dimensional curves at corresponding positions of the two profile skeleton diagrams based on preset components, and comparing the heights of the two-dimensional curves, so as to judge that the film resistance or the shrinkage resistance is generated on the contact surface; and determining the number and diameter of the contact spots and the oxide film spots; s5, repeatedly executing the step S4 until the selection of all two-dimensional curves in the X-axis interval range is completed, thereby determining the quantity of all oxide film spots and contact spots; and S6, calculating to obtain a contact resistance value based on the diameter of each contact spot and the oxide film spot and the number of all contact spots and oxide film spots.
Description
Technical Field
The invention relates to the technical field of electric connectors, in particular to a method for calculating contact resistance of an electric connector under the storage condition.
Background
The reliability of the electrical connector is critical as a component for mass use on model equipment. An electrical connector is the basic element for transmitting electrical energy, signal energy. The function of connection and disconnection plays a vital role for some types of equipment.
For some special reasons, for electrical connectors stored for a long period of time, it can be found through a large amount of empirical data whether the electrical connector has the same function and effect as before, and the main failure form of the electrical connector under the storage condition is contact failure, which is about 45.1% of the total failure number in the field, and the contact performance of the electrical connector inevitably has an irreversible gradual degradation trend during the long-term storage.
There are many types of reasons for electrical connector contact failure: the increase of oxide corrosion, stress relaxation of contact to reed, accumulation of contamination, severe wear of contact, etc. Under storage conditions, the electrical connector is stored in the warehouse for a long period of time and is not opened any more, so that the influence of pollutants and abrasion on the electrical connector is negligible under the conditions, and many students study that the influence of stress relaxation of the reed on the electrical connector is small, so that the main failure reason during storage can be considered as accumulation of contact surface oxidation corrosion, and the contact resistance is increased.
Therefore, the calculation of the contact resistance under the storage condition is an important index for judging the reliability of the electric connector, and at present, few people construct a calculation model of the contact resistance through a computer model, and the magnitude of the contact resistance is mainly obtained through the test of a traditional experiment.
Disclosure of Invention
In order to overcome the defects of the technology, the invention provides a method for simulating the formation process of the contact resistance based on the storage condition of the electric connector and creating a model to calculate the contact resistance.
The technical scheme adopted for overcoming the technical problems is as follows:
the invention provides a calculation method of contact resistance under the storage condition of an electric connector, which specifically comprises the following steps of S1, measuring the contact surface of the electric connector to obtain an initial parameter value of a three-dimensional W-M function; s2, establishing two contact surface models of the electric connector based on a three-dimensional W-M function determined by initial parameter values; s3, obtaining two section skeleton diagrams based on two contact surface models of the electric connector; s4, respectively selecting two-dimensional curves at corresponding positions of the two profile skeleton diagrams based on preset components, comparing the heights of the two-dimensional curves, judging that the contact surface generates a film resistance or a shrinkage resistance, and determining the number and the diameter of contact spots and oxide film spots; s5, repeatedly executing the step S4 until the selection of all two-dimensional curves in the X-axis interval range is completed, so as to determine the quantity of all oxide film spots and contact spots of the electric connection contact surface; and S6, calculating a film resistance value and a shrinkage resistance value based on the diameters of each contact spot and each oxide film spot and the number of all contact spots and oxide film spots, thereby obtaining the contact resistance value.
Further, the contact surface of the electrical connector is measured to obtain an initial value of a three-dimensional W-M function, which specifically includes: s11, measuring the height of the contact surface to obtain Z (x) curves of multiple sections, i.e. two-dimensional W-M functionsS12, carrying out Fourier transformation on the two-dimensional W-M function to obtain a power spectrum of the surface profile +.>S13, taking logarithms on two sides of the power spectrum to obtain +.>S14, calculating to obtain a fractal dimension D and a scale parameter G based on the linear relation of lgP (omega) and lgomega and the profile of the measured surface.
Further, in step S1, the contact surface of the electrical connector is measured to obtain an initial value of the three-dimensional W-M function, which specifically includes:
s11', measuring the roughness Ra of the contact surface;
s12' respectively obtaining a fractal dimension D and a scale parameter G based on the roughness Ra and the formula (1) and the formula (2),
further, in step S2, two contact surface models of the electrical connector are built based on the three-dimensional W-M function determining the initial parameter value, specifically including:
generating two contact surface micrographs based on a three-dimensional W-M function determined from initial parameter values for simulating a contact process for electrically connecting contact surfaces, wherein the three-dimensional W-M function isFor the sampling length, D is the fractal dimension in three dimensions, 2<D<3, G is a scale parameter, gamma is the randomness and frequency of curve phase, m is the number proportion of the convex and concave of the contact surface girth chart, n is a natural number sequence, phi m,n Is a random number subject to uniform distribution in the (0, 2 pi) interval.
Further, the step S3 specifically includes: cutting the two contact surface microscopic images along the X-axis cross section direction to obtain single line cross section skeleton diagrams of the first contact surface and the second contact surface
Further, the step S4 specifically includes: s41, respectively selecting two-dimensional curves of the same position on the X axis of a single line section skeleton diagram of the first contact surface and the second contact surface based on preset components; s42, calculating the height difference Δz=z of the two curves 1 (x,y)-z 2 (x, y) -lambda, wherein z 1 (x, y) is the height of the first curve, z 2 (x, y) is the height of the second curve, λ is the variation error amount, θ is the thickness of the oxide film covering the metal surface; s43, if the height difference is less than or equal to 2 theta, the contact spot and the oxide corrosion are considered to generate film resistance, if not, whether the height difference is greater than 0 is judged, if so, the contact spot part is considered to be shrinkage resistance, otherwise, the contact resistance is not generated.
Further, the step S6 specifically includes: the contact resistance value is obtained based on the formula (3),
wherein R is j Is a contact resistance，a sp Radius corresponding to the P-th contact spot; a, a bk For the radius corresponding to the kth oxide film spot, n is the number of contact spots, and m is the number of oxide film spots.
The beneficial effects of the invention are as follows:
1. and (3) analyzing the contact process of the two conductors from the microstructure and mechanism hierarchy, constructing a microcosmic contact surface model by using a W-M function, converting the three-dimensional contact surface into a two-dimensional intersection curve to distinguish the resistance types, and calculating the contact resistance.
2. The method reduces the manpower and material resources consumed by the traditional method-actual measurement, and can obtain the corresponding contact resistance by inputting the initial parameters of the corresponding materials, thereby realizing the process of numerically calculating the contact resistance.
3. In practical terms, the method provides a reference for accurately evaluating the storage life of the electric connector, optimizes the reliability evaluation process of the electric connector, and has important significance for prolonging the life of model equipment.
Drawings
FIG. 1 is a schematic view of the contact surface of an electrical connector;
FIG. 2 is a flow chart of a method for calculating contact resistance under storage conditions of an electrical connector according to an embodiment of the present invention;
FIG. 3 is a graph of W-M curves for different typing parameters D;
FIG. 4 is a graph of W-M curves for different scale parameters G;
FIG. 5 is a view showing the subtle aspects of the contact surfaces of an electrical connector;
fig. 6 is a contact surface model of the contact surface 1 according to an embodiment of the invention;
fig. 7 is a contact surface model of the contact surface 2 according to an embodiment of the invention;
fig. 8 is a single line cross-sectional skeleton view of the contact surface 1 of the embodiment of the present invention;
fig. 9 is a perspective view of a single line cross-sectional skeleton view of the contact surface 1 of the embodiment of the present invention;
FIG. 10 is a two-dimensional graph of contact surface according to an embodiment of the present invention;
FIG. 11 is a two-dimensional graph of contact surfaces labeled with points of intersection in accordance with an embodiment of the present invention;
FIG. 12 is a flow chart of contact resistance calculation;
FIG. 13 is a schematic diagram of a computer simulated contact resistance.
Detailed Description
The invention will now be described in further detail with reference to the drawings and the specific examples, which are given by way of illustration only and are not intended to limit the scope of the invention, in order to facilitate a better understanding of the invention to those skilled in the art.
First, terms involved in the embodiments of the present application will be described:
shrink resistance: it means that the electrical resistance generated at the current convergence is called the pinch resistance, since the contact surface is not perfectly flat from a microscopic point of view during processing, and in fact, the contact between a small portion of the hillocks during contact is as described in fig. 1, resulting in a convergence of the current. In the embodiment of the invention, the preconditions for the calculation of the shrink resistance are as follows:
1) The conductive spot is considered to be circular and its size should be much smaller than the size of the apparent area of the contact area, which can be regarded as "long shrink".
2) The materials of the two contact surfaces are consistent, and the resistivity of the two contact surfaces is the same.
3) The effect of temperature on resistivity was ignored.
4) The potential across the face was uniform in magnitude.
Thereby obtaining the contraction resistance of the contact surface and the contraction resistance of the contact surface at the other sideWherein ρ is the resistivity; a is the contact patch radius and the contact element's shrink resistance can be expressed as: />If there are n contact spots on the contact surface, the radius of the contact spot can be written as a sp The pinch resistance can be expressed as +.>
Film resistance: for some electric contact surfaces, a layer of metal oxide, dirt, dust and the like is generated on the surface due to the fact that the electric contact surfaces are exposed to the air, but the metal oxide is a semiconductor in general, and the resistance of the metal oxide is relatively high, so that the resistance of the metal oxide is often concerned when calculating the resistance of the film. For contact spots with a surface covered with a metal oxide, from the classical physical point of view, no current can pass through the film no matter how thick, but electrons, according to the quantum mechanics theory, can pass through the film as waves and conduct electricity, this effect is called tunneling, and the schrodinger equation shows that the film has a tunneling resistivity ofWherein U is the potential between the contact surfaces; j is the current density flowing through the membrane; the sheet resistance across a conductive surface of radius r can thus be calculated as: />If there are n conductive spots on the contact surface, the radius of each film spot can be written as a bk The total film resistance can be written as:
contact resistance: r is R j Comprises a shrink resistor R s And film resistance R b ，R j ＝R s +R b The nature of the contact resistance is such that the two conductors heat up during contact, due to the presence of resistance in the contact gap. In the embodiment of the application, two contact surfaces are contacted to simulate the process of contact under real conditions, so that the magnitude of contact resistance is calculated.
Two-dimensional Weierstrass-Mandelbrot function: the W-M function has special properties of continuity everywhere but no conduction everywhere, can be used for expressing random phenomena in nature, and is expressed as a common two-dimensional W-M function in the formula (1).
In an embodiment of the present application, Z (x) is the profile height, G is the scale parameter, D is the fractal parameter, where for the two-dimensional case 1<D<2，γ n The spatial phase and randomness of the profile is shown, typically taking γ=1.5 for a normal distribution of the surface profile.
As shown in fig. 2, a flowchart of a method for calculating a contact resistance under a storage condition of an electrical connector according to the present embodiment specifically includes:
s1, measuring the contact surface of an electric connector to obtain an initial parameter value of a three-dimensional W-M function;
s2, establishing two contact surface models of the electric connector based on a three-dimensional W-M function determined by initial parameter values;
s3, obtaining two section skeleton diagrams based on two contact surface models of the electric connector;
s4, respectively selecting corresponding two-dimensional curves at a certain position of X axes of the two profile skeleton diagrams based on a preset component, and comparing the heights of the two-dimensional curves, so as to judge that film resistance or shrinkage resistance is generated on the contact surface, and determining the number and the diameter of contact spots and oxide film spots;
s5, repeatedly executing the step S4 until the selection of all two-dimensional curves in the X-axis interval range is completed, so as to determine the quantity of all oxide film spots and contact spots of the electric connection contact surface;
and S6, calculating a film resistance value and a shrinkage resistance value based on the diameters of each contact spot and each oxide film spot and the number of all contact spots and oxide film spots, thereby obtaining the contact resistance value.
The method for calculating the contact resistance under the storage condition of the electric connector is described below with reference to the specific embodiment;
s1, measuring the contact surface of an electric connector to obtain an initial parameter value of a three-dimensional W-M function;
as shown in FIG. 3, the W-M curve graph corresponding to the different typing parameters D is shown in FIG. 3, and as D increases, more fluctuation is increased at a gentle place of the W-M curve graph, and the W-M function obtained by increasing D has more details.
The size of the fractal parameter D can be seen by fixing other parameters as shown in fig. 1. It can be seen from fig. 1 that the W-M graph increases with D, increasing more fluctuations at the flattening, and the greater D, the more detail of the W-M function.
As shown in fig. 4, the W-M curves corresponding to different typing parameters G are plotted, and as can be seen from fig. 4, the magnitude of the W-M curve decreases with decreasing G, and the smaller G, the smaller the peak value.
Therefore, the line type of the W-M curve can be changed by adjusting the fractal dimension D and the scale parameter G, so that the real simulation of the roughness of the rough surface is achieved.
However, the two dimensions only represent local features, and cannot clearly represent the features of a region, a three-dimensional W-M function model is introduced, and the representation formula of the three-dimensional W-M function is shown in a formula (2):
wherein L-characterizes the sampling length; fractal dimension in D-three-dimensional condition, its value is one-dimensional more than in two-dimensional condition, 2<D<3, and the complex fluctuation degree of the curve increases with the increase of the D value; the G-scale parameter is used for adjusting the amplitude of the curve; gamma-shows the randomness and frequency of the curve phase; m-selecting the three-dimensional graph to be generated with the number of the projections and the depressions being proportional, wherein the smaller m is, the smaller the proportion is; n-natural sequence; phi (phi) m,n -random numbers subject to a uniform distribution over the (0, 2 pi) interval; fig. 5 is a fine view of characterizing the contact surface of an electrical connector using a W-M three-dimensional surface.
In the embodiment of the invention, the initial parameter value of the three-dimensional W-M function is obtained by measuring the contact surface of the electric connector, and the fractal dimension D and the scale parameter G are obtained.
In some embodiments, a power spectral algorithm is employed. Firstly, measuring the height of a measured contact surface by using a pressure sensor to obtain Z (x) curves under a plurality of tangential planes, namely a W-M function under two dimensions, carrying out Fourier transformation on the formula (1) to obtain a power spectrum under a real surface profile, namely a formula (3), and taking logarithms from two sides of the power spectrum to obtain a formula (4).
lgP (ω) and lgω are linearly related, and a fractal dimension D, and a scale parameter G are calculated from the resulting profile of the measured surface.
In some embodiments, the roughness value Ra of the measured surface is measured by a roughness meter, and the fractal dimension and the scale parameters are obtained by the formula (5) and the formula (6), so as to obtain the W-M function curve.
S2, establishing two contact surface models of the electric connector based on a three-dimensional W-M function determined by initial parameter values;
the contact surface model of the contact surface 1 and the contact surface model of the contact surface 2, as shown in fig. 6 and 7, respectively, are generated based on the three-dimensional W-M function determining the fractal dimension and the dimensional parameter, and the contact process of the contact pair is simulated by means of both models.
In one embodiment of the present application, the initial parameter values are set to l=3, g=10+ (-7), d=2.2, y=1.5, m=9, nmax=20, where the selection of the coordinate axes of the contact surface model X and Y axes avoids 0 points. In the embodiment of the application, the X axis and the Y axis are positioned in the (1, 2) interval, and the indexing interval is 0.05. And the coordinate axes in the X, Y, Z direction are all in microns um.
In the embodiment of the present invention, the initial parameters may be unchanged, assuming that the roughness of the roughened surfaces of the insertion holes and pins is uniform, only a difference exists in a fine place. In addition, because of phi set by the formula (2) m,n The phase is a random number that is uniformly distributed on (0, 2 pi), and the randomness of the phase is used to express the randomness of the fine.
In some embodiments, fig. 6 and 7 are generated by the plot3 program in MATLAB, which can be viewed as generating a combination of two-dimensional W-M function curves at each x-axis spacing as a skeleton, and after sweeping the skeleton, the contact surface model shown in fig. 6 and 7 is obtained. The sweep process makes the peak position in the skeleton be the position of the highest point in the three-dimensional graph, and the model after sweep is generally only lower than the peak position in the original graph.
S3, respectively cutting the three-dimensional images in FIG. 6 and FIG. 7 along the X-axis section to obtain a single line section skeleton diagram shown in FIG. 8, and FIG. 9 is a perspective view of the single line section skeleton diagram.
S4, as shown in FIG. 10, after the contact surfaces of the contact surface 1 and the contact surface 2 are contacted according to the required contact size, a two-dimensional graph of a contact surface at a certain position on the X-axis component is selected. Wherein the solid line in the figure is the contact surface 1 and the dashed line is the contact surface 2.
In one embodiment of the present application, there is a machining error in the process of contact matching between two contact planes, and the contact cannot be perfectly fit according to the original dimensions, so a variation error amount λ=0.1 um is set, and some portions of the dotted line are located beyond the solid line, as can be seen in fig. 10, where it is considered that the two contact surfaces have made contact, and the microscopic appearance is that the hillock is intersected.
The contact surface and oxygen are fully contacted to generate an oxide film in the long-time storage and placement process of the electric connector, the thickness of the oxide film on a single contact surface is different along with the time, and the volume increase of the oxide film is a function of the time change, as shown in a formula (7).
In the formula (7), a and B are parameters related to materials, wherein a >1, which has an oxide film promoting effect according to the material, a <1, which is a material for suppressing the generation of an oxide film, and a=1 in the normal case.
In one embodiment of the present application, the oxide film is considered to be uniformly grown on the contact surface of the metal, so that the volume of the oxide film can be calculated according to the formula (7), and the thickness of the oxide film covering the metal surface can be calculated according to the formula (8).
The oxide etchant uniformly covers the metal surface, and the thickness theta of the etchant is calculated by the formula (8) according to the area of the surface covered by the film layer. X=1.2 in fig. 10
In one embodiment of the present application, θ=0.1 um is calculated. .
As shown in fig. 11, a schematic view of two-dimensional line contact of two contact surfaces is shown, in which two end points of the contact portion are labeled.
The resistance generated at a certain place is a film layer resistance or a shrinkage resistance by judging whether the oxide film is worn off in the process of contacting the two contact pairs or not in the process of judging the contact spots.
The height of the entire three-dimensional contact surface can be expressed by z (x, y) according to formula (1). The difference in height of the contact surface after contact can be expressed by formula (9),
Δz＝z 1 (x,y)-z 2 (x,y)-λ (9)
in one embodiment of the present invention, as the contact surface is covered with the oxide film, if the difference in height between the two points is smaller than 2θ=0.2 um, the oxide film is considered to be not broken during the contact process, the contact spot and the oxide corrosion generate the film resistance, otherwise, the oxide film is considered to be broken, and the contact between the contact surfaces generates the shrinkage resistance.
After judging whether the intersection is the shrink resistance or the film resistance, the contact surface at the intersection is considered to be circular here, so that the size of the contact spot and the diameter thereof are found and determined.
S5, repeatedly executing the step S4 until the number of all oxide film spots and the number of contact spots of the contact surface of the electrical connection are determined.
S6, FIG. 12 is a flow chart of the calculation of the contact resistance, in which Xi is represented by a two-dimensional W-M curve represented by the indexing interval of the X axis, and j is represented by the total number of intersecting positions of the surface 1 and the surface 2 on a certain Xi.
FIG. 13 is a schematic diagram showing the simulated film resistance and the shrink resistance of a computer program, wherein black spots are represented as oxide film spots and hollow spots are contact spots. Finally, the radius of each spot is calculated, and the contact resistance under the unit square of the contact surface can be obtained by taking the radius into a formula (10), wherein R j A is the contact resistance sp Radius corresponding to the P-th contact spot; a, a bk For the radius corresponding to the kth oxide film spot, n is the number of contact spots, and m is the number of oxide film spots.
The foregoing has described only the basic principles and preferred embodiments of the present invention, and many variations and modifications will be apparent to those skilled in the art in light of the above description, which variations and modifications are intended to be included within the scope of the present invention.
Claims (7)
1. A method for calculating contact resistance of an electrical connector under storage conditions, comprising:
s1, measuring the contact surface of an electric connector to obtain an initial parameter value of a three-dimensional W-M function;
s2, establishing two contact surface models of the electric connector based on a three-dimensional W-M function determined by initial parameter values;
s3, obtaining two section skeleton diagrams based on two contact surface models of the electric connector;
s4, respectively selecting two-dimensional curves at corresponding positions of the two profile skeleton diagrams based on preset components, comparing the heights of the two-dimensional curves, judging that the contact surface generates a film resistance or a shrinkage resistance, and determining the number and the diameter of contact spots and oxide film spots;
s5, repeatedly executing the step S4 until the selection of all two-dimensional curves in the X-axis interval range is completed, so as to determine the quantity of all oxide film spots and contact spots of the electric connection contact surface;
and S6, calculating a film resistance value and a shrinkage resistance value based on the diameters of each contact spot and each oxide film spot and the number of all contact spots and oxide film spots, thereby obtaining the contact resistance value.
2. The method for calculating the contact resistance under the storage condition of the electric connector according to claim 1, wherein in the step S1, the contact surface of the electric connector is measured to obtain an initial value of the three-dimensional W-M function, specifically comprising:
s11, measuring the height of the contact surface to obtain Z (x) curves of multiple sections, i.e. two-dimensional W-M functions
S12, carrying out Fourier transformation on the two-dimensional W-M function to obtain a power spectrum of the surface profile
S13, taking logarithms on two sides of the power spectrum to obtain
S14, calculating to obtain a fractal dimension D and a scale parameter G as initial values of a three-dimensional W-M function based on the linear relation of lgP (omega) and lgomega and the profile of the measured surface.
3. The method for calculating the contact resistance under the storage condition of the electric connector according to claim 1, wherein in the step S1, the contact surface of the electric connector is measured to obtain an initial value of the three-dimensional W-M function, specifically comprising:
s11', measuring the roughness Ra of the contact surface;
s12', respectively obtaining a fractal dimension D and a scale parameter G based on the roughness Ra and the formula (1) and the formula (2),
4. a method of calculating the contact resistance of an electrical connector according to any of claims 2 or 3, wherein in step S2, two contact surface models of the electrical connector are created based on a three-dimensional W-M function determining the initial parameter values, comprising in particular:
generating two contact surface micrographs based on a three-dimensional W-M function determined from initial parameter values for simulating a contact process for electrically connecting contact surfaces, wherein the three-dimensional W-M function is
L is the sampling length, D is the fractal dimension in three dimensions, 2<D<3, G is a scale parameter, gamma is the randomness and frequency of curve phase, m is the number proportion of the projections and the depressions of the contact surface girth chart, and n is a natural number sequence，φ m,n Is a random number subject to uniform distribution in the (0, 2 pi) interval.
5. The method of calculating contact resistance under storage conditions of an electrical connector as recited in claim 4, wherein step S3 specifically comprises: the two contact surface microscopic images are cut along the X-axis cross-section direction, so that single line cross-section skeleton diagrams of the first contact surface and the second contact surface are respectively obtained.
6. The method of calculating contact resistance under storage conditions of an electrical connector as recited in claim 4, wherein step S4 specifically comprises:
s41, respectively selecting two-dimensional curves of the same position on the X axis of a single line section skeleton diagram of the first contact surface and the second contact surface based on preset components;
s42, calculating the height difference Δz=z of the two curves 1 (x,y)-z 2 (x, y) -lambda, wherein z 1 (x, y) is the height of the first curve, z 2 (x, y) is the height of the second curve, λ is the variation error amount, θ is the thickness of the oxide film covering the metal surface;
s43, if the height difference is less than or equal to 2 theta, the contact spot and the oxide corrosion are considered to generate film resistance, if not, whether the height difference is greater than 0 is judged, if so, the contact spot part is considered to be shrinkage resistance, otherwise, the contact resistance is not generated.
7. The method for calculating contact resistance under storage conditions of an electrical connector according to claim 6: the step S6 specifically comprises the following steps: the contact resistance value is obtained based on the formula (3),
wherein R is j A is the contact resistance sp Radius corresponding to the P-th contact spot; a, a bk For the radius corresponding to the kth oxide film spot, n is the number of contact spots, and m is the number of oxide film spots.
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