A temperature-based contact resistance prediction method

Abstract

The application discloses a temperature-based contact resistance prediction method, which predicts the contact resistance change trend when external load is unchanged in a theoretical calculation form by measuring basic parameters of a contact interface, and assists researchers in eliminating the influence of temperature on the measured value of the contact resistance, and provides a correction basis for analyzing the contact characteristics of the interface.

Description

Technical Field

[0001] This invention belongs to the field of contact resistance measurement technology, specifically a temperature-based method for predicting contact resistance. Background Technology

[0002] In engineering structural systems, when the contact characteristics (contact force, etc.) of the interface change, the contact resistance also changes. The contact resistance of the interface can be measured in real time by passing a direct current through both sides of the interface, thereby obtaining and analyzing the contact characteristics of the interface. However, the direct current passing through the interface generates temperature, which also causes changes in the measured value of the contact resistance. This makes it impossible for researchers to distinguish whether the change in the measured value of the contact resistance is caused by changes in external operating conditions or by temperature. For some engineering applications that require long-term online monitoring of interface contact characteristics, the temperature-induced changes in contact resistance can greatly affect researchers' evaluation of the interface contact characteristics. Summary of the Invention

[0003] The purpose of this invention is to provide a temperature-based method for predicting contact resistance, in order to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a temperature-based method for predicting contact resistance, comprising the following steps:

[0005] S1: Obtain the basic parameters of the contact interface by consulting literature or measurement. The basic parameters include: the DC current used for measuring the contact resistance. Initial contact resistance Equivalent thermal resistance Thermal time constant Maximum breakdown rate Breakdown threshold temperature rise Threshold smoothness Temperature coefficient of resistivity Equivalent heat capacity Number of unconducted pathways Number of initially activated pathways Contact thermal softening coefficient ;

[0006] S2: Establish a set of equations to predict temperature and breakdown ratio over time. The set of equations is as follows:

[0007] In the formula, The integration time interval, The duration of DC power supply. for The amount of temperature change at the contact interface at any given time. for Constantly monitor the temperature change at the interface. for Breakdown ratio at any given moment for The percentage of breakdowns at any given moment;

[0008] S3: Through the system of equations ;calculate time and In the formula, for Contact resistance at any given moment;

[0009] S4: The result calculated in step S3 time and Substituting into the system of equations established in step S2, the following calculations are obtained. time and ;

[0010] S5: The result calculated in step S4 and Substitute into the formula: In the middle; you can get Contact resistance at any given moment;

[0011] S6: Using the calculation results in steps S4 and S5 as known quantities for calculating the parameter value at the next moment, repeat the calculations in steps S3-S5 to obtain the contact resistance at any moment.

[0012] Preferably, in step S2, the integration time interval .

[0013] Compared with the prior art, the beneficial effects of the present invention are:

[0014] For certain engineering applications that require long-term online monitoring of interface contact characteristics, this invention establishes a temperature-based method for predicting contact resistance changes. This method can predict the trend of contact resistance changes when the external load remains constant, helping researchers to eliminate the influence of temperature from the measured values ​​of contact resistance and providing a basis for correcting the analysis of interface contact characteristics. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of current contraction provided in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of the calibration experiment provided in the embodiment of the present invention;

[0017] Figure 3 This is the contact resistance decay curve provided in the embodiment of the present invention;

[0018] Figure 4 This is a temperature difference curve provided in an embodiment of the present invention;

[0019] Figure 5 This is a breakdown ratio curve provided in an embodiment of the present invention;

[0020] Figure 6 This is a comparison chart of the predicted contact resistance and the measured contact resistance provided by the temperature-based contact resistance prediction method in this embodiment of the invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention provides a technical solution:

[0023] Example 1

[0024] A temperature-based method for predicting contact resistance is proposed, and its derivation is as follows:

[0025] 1. Contact Interface Resistance Formula

[0026] When two interfaces come into contact, due to surface roughness, actual contact only occurs at the high points (protrusions) of the surface micromorphology; these micro-protrusions are called micro-protrusions. When a current is passed through them, the current can only pass through these discrete conductive spots (micro-protrusions), and the current stream contracts near the conductive spots (e.g., Figure 1 As shown in the figure, this leads to a longer current path, a smaller equivalent conductive area, and a contraction of the current line, which increases the current density and generates an additional resistive component, i.e., contraction resistance.

[0027] (1);

[0028] In the formula, The shrinkage resistance of a single micro-convexity. Resistivity The contact radius of the micro-protrusion is given when both exist on the interface. Each of the "conductive" micro-contact points (each with approximately the same resistance) They are connected in parallel, meaning the total shrinkage resistance is:

[0029] (2);

[0030] In the formula, The total interface shrinkage resistance is given. In addition, there may be film resistance on the micro-protrusion. Film resistance is an additional resistance caused by non-conductive / low-conductive film layers (such as oxide film, oil, dust, etc.) formed by oxidation, contamination or deposition on the contact surface, which hinder the passage of current. Generally speaking, film resistance is very large and can be regarded as an open circuit.

[0031] 2. Temperature effect

[0032] 2.1 Thermal softening effect

[0033] A common engineering approximation used in rough metal contacts is: when plasticity dominates, the actual contact area... With total normal load satisfy:

[0034] (3);

[0035] In the formula, This represents the actual contact area. For the total load, Assuming material hardness, the actual contact area is considered to be composed of... The load is shared by individual micro-protrusions, and the average area of ​​each micro-protrusion is taken:

[0036] (4);

[0037] In the formula, The area of ​​each micro-protrusion, This represents the number of micro-protrusions, with each micro-protrusion having an approximately circular contact surface:

[0038] (5);

[0039] As temperature increases, hardness decreases; this is expressed exponentially.

[0040] (6);

[0041] In the formula, The initial hardness of the material. The contact thermal softening coefficient, This refers to the temperature difference.

[0042] 2.2 Temperature Effect of Resistivity

[0043] As temperature increases, the amplitude of atomic vibrations within the metal increases, leading to a higher probability of collisions between free electrons and atoms. These collisions create resistance during electron movement, making electron flow more difficult and thus increasing resistivity. Here, we consider a linear relationship between resistivity and temperature:

[0044] (7);

[0045] In the formula, The initial resistivity, is the temperature coefficient of resistivity.

[0046] 3. The influence of the number of conduction paths

[0047] Due to the Joule heating effect of the current, the temperature of the oxide film increases, thereby increasing the conductivity of the oxide film and causing breakdown. After the oxide film breaks down, the originally open circuit micro-protrusions form a circuit, thus... The number of conduction paths in a micro-convex body can be written as:

[0048] (8);

[0049] In the formula, The initial number of conductive paths. The breakdown ratio is the proportion of a previously unconnected circuit that has now become a connected circuit. To simplify the formula, we divide both sides of equation (8) by the number of potential pathways initially separated by the oxide film (i.e., the number of unconducted pathways). ,have to:

[0050] (9);

[0051] In the formula, Defined as the maximum path gain intensity.

[0052] Substituting equations (5), (6), (7), and (9) into equation (2), we obtain the complete expression for the shrinkage resistance:

[0053] (10);

[0054] Since total contact resistance = contraction resistance + film resistance, but the film resistance is abnormally high and considered an open circuit, it is not considered. Therefore, in this method, total contact resistance is assumed to equal contraction resistance.

[0055] (11);

[0056] Analyzing formula (11), it can be seen that formula (11) introduces the contact resistance formula for temperature and breakdown. The right half of the equation is the equation for temperature and breakdown. So, removing the right half (removing the influence of temperature and breakdown) leaves the initial contact resistance (the contact resistance unaffected by temperature and breakdown), that is, the contact resistance at the initial moment. Then the contact resistance is:

[0057] (12);

[0058] The contact resistance can be seen from formula (12). With temperature difference and breakdown ratio Related to the next step, regarding temperature difference and breakdown ratio Perform the analysis.

[0059] 4. Temperature rise equation

[0060] When current flows through a contact interface, electrical energy is converted into heat energy due to the contact resistance, and the amount of heat follows Joule's law:

[0061] (13);

[0062] In the formula, Joule heat power, It represents electric current.

[0063] Treating the interface as a "total heat capacity", through an interface equivalent resistance Heat dissipation to the environment, according to the energy balance equation:

[0064] (14);

[0065] In the formula, For equivalent heat capacity, Equivalent thermal resistance (equivalent heat capacity refers to the measure of temperature change caused by the absorption or release of heat by a substance under certain conditions; equivalent thermal resistance is a comprehensive physical quantity reflecting the ability of a material or interface to impede heat transfer). Divide both sides by... have to:

[0066] (15);

[0067] Define a thermal time constant Define steady-state temperature rise have to:

[0068] (16).

[0069] 5. Breakdown equation

[0070] After the current is applied, the Joule heating will cause the temperature to rise. This temperature rise will break down the oxide layer. We consider the breakdown to be a "rate-dependent transformation process," that is:

[0071] (17);

[0072] In the formula, To determine the breakdown rate, and furthermore, since the oxide layer only undergoes significant breakdown when the threshold temperature rise is reached, a smoothed version of the sigmoid function is used to define the breakdown equation:

[0073] (18);

[0074] In the formula, For the maximum breakdown rate, For threshold smoothness, The temperature rise is to break down the threshold.

[0075] 6. Methods for calculating differential equations

[0076] This method involves the calculation of differential equations (16) and (17). We first write equations (16) and (17) as the temperature difference equation and the breakdown ratio equation at any given time, that is:

[0077] (19);

[0078] Equation (12) can be written as the contact resistance equation at any given time, i.e.:

[0079] (20);

[0080] In the formula, for In equation (16) at time , for In equation (16) at time , for In equation (16) at time , for In equation (17) of time , for In equation (17) of time , for In equation (17) of time , for Contact resistance at any given moment.

[0081] The calculation is performed using the explicit Euler method, i.e.:

[0082] (twenty one);

[0083] In the formula, for Temperature difference at any time , for Temperature difference at any time , The minimum time interval, for Breakdown ratio at any time , for Breakdown ratio at any time ,when At the initial moment, the initial temperature difference and breakdown ratio are: Substituting into equation (19) yields (Initial time) and ,Will and and Substituting into equation (21) yields Moment and ,Will Moment and Substituting into equation (20) yields Contact resistance at any moment .Will Moment , , Substituting into equation (19) again yields Moment , ;Will , as well as , Substituting into equation (21) yields ,Will Substituting into equation (20) again, we can obtain Contact resistance at any moment By substituting the calculation results into equations (19) to (20) in turn, the predicted contact resistance based on temperature changes at any given time can be obtained. This helps researchers eliminate the influence of temperature from the measured value of the contact resistance and provides a basis for correcting the analysis of the interface contact characteristics.

[0084] Example 2

[0085] The calculation steps in this embodiment are as follows:

[0086] S1: Obtain the basic parameters of the contact interface by consulting literature or measurement. The basic parameters include: the DC current used for measuring the contact resistance. Initial contact resistance Equivalent thermal resistance Thermal time constant Maximum breakdown rate Breakdown threshold temperature rise Threshold smoothness Temperature coefficient of resistivity Equivalent heat capacity Number of unconducted pathways Number of initially activated pathways Contact thermal softening coefficient The basic parameters of the obtained interface are shown in the table below:

[0087] Table 1 Basic Parameters of Contact Interface

[0088] .

[0089] This embodiment describes the measurement methods for some parameters:

[0090] Initial contact resistance R0: The initial contact resistance is measured experimentally. For specific measurement experiments, please refer to the literature [Ta W, Qiu S, Wang Y, et al. Volumetric contact theory to electrical contact between random rough surfaces. Tribology International, 2021(3): 107007.].

[0091] Maximum path gain intensity m ox Using the Sensofor-neox three-dimensional optical surface testing instrument to measure the contact surface, the roughness profile of the contact surface can be obtained. With the roughness profile, parameter data on the rough surface can be obtained, and the number of initially conductive paths can be counted. (Number of micro-protrusions not covered by oxide film) and number of unconducted pathways (The number of micro-protrusions covered by the oxide film), using Divide by The maximum path gain intensity is obtained.

[0092] Equivalent thermal resistance R th Measured using the ASTM D5470 standard test method.

[0093] Equivalent heat capacity C th The thermal constant was measured using a Hot Disk thermal constant analyzer.

[0094] Maximum breakdown rate k0, breakdown threshold temperature rise Threshold smoothness The calibration experiment was conducted, and the experimental data was fitted using a formula. The specific calibration experimental steps were as follows: a current source and a nanovoltmeter were placed on the upper and lower surfaces of the contacting metal plates. The contact resistance was continuously collected over a certain period of time. The data was normalized (i.e., the contact resistance at any given time was divided by the initial contact resistance) to obtain the contact resistance decay curve. The data could then be fitted using this decay curve. A schematic diagram of the calibration experiment is shown below. Figure 2 As shown.

[0095] In this embodiment, the calibration experiment method is as follows: Two 100*100*10 mm metal plates of the same material are stacked one on top of the other. An M81 in-situ detector and a CZ225 small high-precision intelligent temperature control box are used. Four probes are arranged on the upper and lower surfaces and the sides of the metal plates near the contact interface. The probes on the upper and lower surfaces of the metal plates are connected to the current source of the M81 in-situ detector using wires, and the probes on the sides of the metal plates near the contact interface are connected to the M81 in-situ detector using wires, with a current of 0.1 A flowing through them. A special-grade T-type thermocouple is attached to the contact surface of the metal plates and connected to the CZ225 small high-precision intelligent temperature control box. Contact resistance and temperature changes are continuously collected over a period of 60 seconds at a sampling frequency of 5 Hz, resulting in 300 measured contact resistance and temperature data points within 60 seconds. Dividing each of these 300 contact resistance data points by the first contact resistance data point yields the contact resistance decay data. The contact resistance decay curve is shown below. Figure 3 As shown, the temperature difference curve is as follows Figure 4 As shown. Substituting the contact resistance attenuation data and temperature difference data into equation (21), and then substituting the resistivity temperature coefficient, contact thermal softening coefficient, and maximum path gain intensity, the breakdown ratio data can be obtained. The breakdown ratio curve is shown in Figure 1. Figure 5 As shown.

[0096] By fitting the breakdown ratio data with equations (17) and (18) in Origin software, the maximum breakdown rate k0 and the breakdown threshold temperature rise can be obtained. Threshold smoothness .

[0097] S2: Establish a set of equations to predict temperature and breakdown ratio over time. The set of equations is as follows:

[0098] In the formula, The integration time interval, The duration of DC power supply. for The amount of temperature change at the contact interface at any given time. for Constantly monitor the temperature change at the interface. for Breakdown ratio at any given moment for The percentage of breakdown at any given moment.

[0099] S3: Through the system of equations ;calculate time and In the formula, for Contact resistance at any given moment;

[0100] S4: The result calculated in step S3 time and Substituting into the system of equations established in step S2, the following calculations are obtained. time and ;

[0101] S5: The result calculated in step S4 and Substitute into the formula: In the middle; you can get Contact resistance at any given moment;

[0102] S6: Using the calculation results in steps S4 and S5 as known quantities for calculating the parameter value at the next moment, repeat the calculations in steps S3-S5 to obtain the contact resistance at any moment.

[0103] This embodiment compares the calculation results of the established model with the experimental results in the literature [Zhai C, Hanaor D, Proust G, et al. Stress-dependent electrical contact resistance at fractal rough surfaces[J]. Journal of Engineering Mechanics, 2017, 143(3): B4015001.]. The comparison results are as follows: Figure 6 As shown, the calculated resistance results are in good agreement with the measured results, thus verifying the accuracy of the present invention.

[0104] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A temperature-based method for predicting contact resistance, characterized in that, Includes the following steps: S1: Obtain the basic parameters of the contact interface by consulting literature or measurement. The basic parameters include: the DC current used for measuring the contact resistance. Initial contact resistance Equivalent thermal resistance Thermal time constant Maximum breakdown rate Breakdown threshold temperature rise Threshold smoothness Temperature coefficient of resistivity Equivalent heat capacity Number of unconducted pathways Number of initially activated pathways Contact thermal softening coefficient ; S2: Establish a set of equations to predict temperature and breakdown ratio over time. The set of equations is as follows: In the formula, The integration time interval, The duration of DC power supply. for The amount of temperature change at the contact interface at any given time. for Constantly monitor the temperature change at the interface. for Breakdown ratio at any given moment for The percentage of breakdowns at any given moment; S3: Through the system of equations ;calculate time and In the formula, for Contact resistance at any given moment; S4: The result calculated in step S3 time and Substituting into the system of equations established in step S2, the following calculations are obtained. time and ; S5: The result calculated in step S4 and Substitute into the formula: In the middle; you can get Contact resistance at any given moment; S6: Using the calculation results in steps S4 and S5 as known quantities for calculating the parameter value at the next moment, repeat the calculations in steps S3-S5 to obtain the contact resistance at any moment.

2. The temperature-based contact resistance prediction method according to claim 1, characterized in that, In step S2, the integration time interval .

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