A method, modeling method, system and application for predicting dynamic contact angle distribution

Abstract

This invention discloses a method, modeling method, system, and application for predicting dynamic contact angle distribution, belonging to the technical field of predicting dynamic contact angle distribution of micro-protrusions. The method for predicting dynamic contact angle distribution provided by this invention constructs a joint probability density function of horizontal distance and height difference based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface; derives the probability density function of the static micro-protrusion contact angle through integral transformation and Leibniz's differentiation rule; derives the first and second relations through cyclic load experiments; and constructs a probability density function model of the dynamic contact angle based on the first and second relations and the probability density function of the static contact angle. By integrating the static model and the dynamic relations, it achieves the prediction of contact angle distribution under different cycles, adapting to the evolution of contact characteristics under varying loads, and effectively solving the problem that traditional static models cannot reflect the dynamic evolution of the contact angle under cyclic loads.

Description

Technical Field

[0001] This invention relates to the field of predicting the dynamic contact angle distribution of micro-protrusions, and specifically to a method, modeling method, system, and application for predicting the dynamic contact angle distribution. Background Technology

[0002] Mechanical mating surfaces are the contact interfaces formed by two components in a mechanical system through bolted connections, interference fits, or direct contact. Their contact characteristics directly affect the stiffness, damping, accuracy retention, and dynamic response of the entire machine. In fields such as precision machinery, aerospace, and CNC machine tools, accurately characterizing the contact behavior of mating surfaces is crucial for improving equipment performance.

[0003] Contact on rough surfaces is essentially an interaction between micro-protrusions. Existing research indicates that contact between two rough surfaces primarily manifests as a lateral contact mode between the sidewalls of the micro-protrusions, rather than the peak-to-peak perpendicular contact assumed by traditional theory. The contact angle of the micro-protrusions is a key geometric parameter determining the normal and tangential deformation components of the contact area, directly affecting contact stiffness, friction coefficient, and energy dissipation characteristics.

[0004] However, existing contact mechanics models (such as the GW, CEB, and KE models) generally assume a contact angle of 0°, meaning that all micro-protrusion contacts are considered positive contacts, lacking consideration for the microscopic geometry of the actual surface. The contact angle distributions cited by Gorbatikh, Misra, and Hossein et al. have unclear sources, limiting the accuracy and applicability of their models. In reality, micro-protrusion contacts are mostly lateral contacts, with the contact angle determined by the horizontal distance and height difference between adjacent micro-protrusions. Currently, there is no effective method to obtain the contact angle distribution through experimental statistics. Furthermore, under cyclic loading, micro-protrusions undergo plastic deformation and surface reconstruction, leading to a dynamic evolution of the contact angle distribution. Traditional static contact angle assumptions cannot reflect this evolutionary process, making it difficult to predict changes in actual contact characteristics under repeated loading.

[0005] Therefore, how to overcome the limitations of traditional static assumptions and improve the accuracy of predicting the contact characteristics of rough surfaces has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method, modeling method, system, and application for predicting dynamic contact angle distribution, in order to overcome the problems of existing technologies where the source of contact angle distribution is unclear, static contact angle assumptions are generally used, and the dynamic evolution of contact angle distribution under cyclic loading cannot be reflected, making it difficult to accurately predict the true contact characteristics of mechanical mating surfaces under repeated loading.

[0007] The present invention solves the above-mentioned technical problems through the following technical solution: This invention provides a modeling method for predicting dynamic contact angle distribution, comprising the following steps: Based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface, a joint probability density function of the horizontal distance and height difference is constructed. ; By using integral transforms and Leibniz's differentiation rule, the probability density function of the contact angle of a static micro-convex body is derived. ; Through cyclic loading experiments, the first and second relationships were derived. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. Based on the first relation, the second relation, and the probability density function of the static contact angle. A probability density function model of the dynamic contact angle is constructed.

[0008] A further improvement of this invention lies in the joint probability density function of horizontal distance and height difference. Specifically:

[0009] in, Horizontal distance; The difference in height; The standard deviation of the horizontal distance; The standard deviation of the height difference; This represents the mean of the horizontal distances. This represents the average height difference.

[0010] A further improvement of this invention lies in the probability density function of the static contact angle. Specifically:

[0011] in, It represents the contact angle.

[0012] A further improvement of this invention is that the first relation is specifically as follows:

[0013] in, This is the proportionality coefficient; This represents the number of loop iterations. denoted as the standard deviation of the horizontal distance of the micro-protrusion after the k-th loading and unloading action; The standard deviation of the horizontal distance of the micro-protrusion after the (k-1)th loading and unloading action; The radius of curvature of the micro-convexity after the (k-1)th loading and unloading action; The radius of curvature of the micro-convex body after the (k-2)th loading and unloading action is denoted as .

[0014] A further improvement of this invention is that the second relation is specifically as follows:

[0015] in, The material attenuation factor; The residual deformation of the micro-protrusion after the k-th loading and unloading action; This represents the maximum deformation of the micro-protrusion after the k-th loading cycle. is the standard deviation of the height difference of the micro-protrusion after the kth loading and unloading action; The standard deviation of the height difference of the micro-protrusion after the (k-1)th loading and unloading action is given.

[0016] A further improvement of this invention is that the probability density function model of the dynamic contact angle is specifically as follows: .

[0017] The present invention also provides a modeling system for predicting dynamic contact angle distribution, comprising: The first module is used to construct the joint probability density function of horizontal distance and height difference based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface. ; The second module is used to derive the probability density function of the contact angle of a static micro-convex body through integral transform and Leibniz's differentiation rule. ; The third module is used to derive the first and second relationships through cyclic load experiments. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. The fourth module is used for the probability density function based on the first relation, the second relation, and the static contact angle. A probability density function model of the dynamic contact angle is constructed.

[0018] The present invention also provides a method for predicting dynamic contact angle distribution. Based on the probability density function model of dynamic contact angle in the modeling method for predicting dynamic contact angle distribution described above, the dynamic contact angle distribution of rough surface is obtained by plotting the probability density curve of dynamic contact angle under different working conditions.

[0019] This invention also provides an application of the method for predicting dynamic contact angle distribution as described above, for analysis and engineering design related to the contact characteristics of mechanical mating surfaces.

[0020] The present invention also provides a system for predicting dynamic contact angle distribution, comprising: The fifth module is used to analyze and obtain the dynamic contact angle distribution of rough surfaces by plotting the probability density function model of the dynamic contact angle in the modeling method for predicting dynamic contact angle distribution as described above, and by plotting the probability density curves of the dynamic contact angle of rough surfaces under different working conditions.

[0021] Compared with the prior art, the positive and progressive effects of the present invention are as follows: The modeling method for predicting dynamic contact angle distribution provided by this invention integrates the statistical characteristics of the surface geometry of micro-protrusions with the dynamic changes under cyclic loading to construct a probability density function model of dynamic contact angle, effectively solving the problem that traditional static models cannot reflect the dynamic evolution of contact angle under cyclic loading. Specifically, a joint probability density function of horizontal distance and height difference is constructed based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface. This considers the randomness and normal distribution law of surface roughness, truly reflecting the statistical characteristics of the actual geometric parameters of micro-protrusions, and providing an accurate geometric basis for subsequent derivations. The probability density function of the static micro-protrusion contact angle is derived through integral transformation and Leibniz's differentiation rule. Mathematical tools are used to efficiently derive the static contact angle distribution from the joint probability density function, ensuring the mathematical rigor of the model. The first and second relations are derived through cyclic load experiments. The influence of cyclic load on the geometric parameters of micro-protrusions is quantified by experimental means. The first relation captures the change of the standard deviation of horizontal distance with the number of cycles, and the second relation describes the change of the standard deviation of height difference, directly reflecting the dynamic process of plastic deformation and surface reconstruction. Based on the first and second relations and the probability density function of the static contact angle, a probability density function model of the dynamic contact angle is constructed. By integrating the static model and the dynamic relations, the prediction of the contact angle distribution under different number of cycles is realized, which can adapt to the evolution of contact characteristics under load changes.

[0022] The method for predicting dynamic contact angle distribution provided by this invention effectively solves the problems of visualization and prediction of dynamic contact angle distribution by utilizing the probability density function model of dynamic contact angle, plotting probability density curves, and performing analysis. Specifically, the probability density function model based on dynamic contact angle directly applies the model established in the referenced scheme. This model considers dynamic changes under cyclic loading, ensuring the accuracy and dynamic adaptability of the analysis results. By plotting the probability density curves of dynamic contact angle of rough surfaces under different working conditions, the model is visualized under different conditions, facilitating intuitive observation of the changing trend of contact angle. The analysis of the dynamic contact angle distribution of rough surfaces, through in-depth analysis of the curves, extracts actual distribution characteristics, providing a reliable basis for predicting the contact characteristics of mechanical mating surfaces. Through synergistic effects, the theoretical model is transformed into a practical application tool, improving the efficiency and practicality of the analysis. Attached Figure Description

[0023] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a MATLAB-reconstructed surface profile of the ground sample in an embodiment of the present invention; wherein... Figure 2 (a) in the figure is the reconstructed surface profile of the upper sample; Figure 2 (b) in the figure is the reconstructed surface profile of the lower sample; Figure 3 This is a two-dimensional contour curve of the rough surface of the present invention; Figure 4 A schematic diagram of the "three-point peak" sampling method for micro-convex bodies; Figure 5 This is a schematic diagram of the contact angle geometry of a micro-convex body. Figure 6 This is a theoretical curve of the contact angle probability density function of the micro-protrusion derived in this invention; wherein... Figure 6 In the table, (a), (b), (c), and (d) represent the standard deviation of the horizontal distance, respectively. Contact angle probability density function curves for 6.0, 6.5, 7.0, and 7.5 degrees Celsius; Figure 7 This is a trend graph showing the change of statistical parameters under cyclic loading as a function of the number of cycles in this invention. Figure 8 This is a dynamic contact angle distribution curve under the coupling effect of the number of cyclic loading and unloading cycles and the contact angle of the present invention; Figure 9 The graph shows a comparison between the model constructed in this invention and existing models. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0026] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0027] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0028] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0029] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0030] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This is an explanation of the present invention and not a limitation thereof.

[0031] See Figure 1 This invention provides a modeling method for predicting dynamic contact angle distribution, comprising the following steps: Based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface, a joint probability density function of the horizontal distance and height difference is constructed. ; By using integral transforms and Leibniz's differentiation rule, the probability density function of the contact angle of a static micro-convex body is derived. ; Through cyclic loading experiments, the first and second relationships were derived. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. Based on the first relation, the second relation, and the probability density function of the static contact angle. A probability density function model of the dynamic contact angle is constructed.

[0032] The modeling method for predicting dynamic contact angle distribution provided by this invention integrates the statistical characteristics of the surface geometry of micro-protrusions with the dynamic changes under cyclic loading to construct a probability density function model of dynamic contact angle, effectively solving the problem that traditional static models cannot reflect the dynamic evolution of contact angle under cyclic loading. Specifically, a joint probability density function of horizontal distance and height difference is constructed based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface. This considers the randomness and normal distribution law of surface roughness, truly reflecting the statistical characteristics of the actual geometric parameters of micro-protrusions, and providing an accurate geometric basis for subsequent derivations. The probability density function of the static micro-protrusion contact angle is derived through integral transformation and Leibniz's differentiation rule. Mathematical tools are used to efficiently derive the static contact angle distribution from the joint probability density function, ensuring the mathematical rigor of the model. The first and second relations are derived through cyclic load experiments. The influence of cyclic load on the geometric parameters of micro-protrusions is quantified by experimental means. The first relation captures the change of the standard deviation of horizontal distance with the number of cycles, and the second relation describes the change of the standard deviation of height difference, directly reflecting the dynamic process of plastic deformation and surface reconstruction. Based on the first and second relations and the probability density function of the static contact angle, a probability density function model of the dynamic contact angle is constructed. By integrating the static model and the dynamic relations, the prediction of the contact angle distribution under different number of cycles is realized, which can adapt to the evolution of contact characteristics under load changes.

[0033] Specifically, the joint probability density function of horizontal distance and height difference. Specifically:

[0034] in, Horizontal distance; The difference in height; The standard deviation of the horizontal distance; The standard deviation of the height difference; This represents the mean of the horizontal distances. This represents the average height difference.

[0035] The joint probability density function can accurately capture the geometric characteristics of adjacent micro-protrusions on a rough surface, ensuring that the static contact angle probability density function accurately reflects the true distribution, thereby improving the accuracy of subsequent dynamic models. Specifically, horizontal distance and height difference, as core variables, define the spatial relationship between micro-protrusions; the standard deviations of horizontal distance and height difference quantify the dispersion of the distribution; and the mean of horizontal distance and the mean of height difference characterize the central tendency of the distribution.

[0036] Specifically, the probability density function of the static contact angle. Specifically:

[0037] in, It represents the contact angle.

[0038] Specifically, the first relation is as follows:

[0039] in, This is the proportionality coefficient; This represents the number of loop iterations. denoted as the standard deviation of the horizontal distance of the micro-protrusion after the k-th loading and unloading action; The standard deviation of the horizontal distance of the micro-protrusion after the (k-1)th loading and unloading action; The radius of curvature of the micro-convexity after the (k-1)th loading and unloading action; The radius of curvature of the micro-convex body after the (k-2)th loading and unloading action is denoted as .

[0040] Specifically, the second relation is as follows:

[0041] in, The material attenuation factor; The residual deformation of the micro-protrusion after the k-th loading and unloading action; This represents the maximum deformation of the micro-protrusion after the k-th loading cycle. is the standard deviation of the height difference of the micro-protrusion after the kth loading and unloading action; The standard deviation of the height difference of the micro-protrusion after the (k-1)th loading and unloading action is given.

[0042] Specifically, the probability density function model for the dynamic contact angle is as follows: .

[0043] Based on the same inventive concept, the present invention also provides a modeling system for predicting dynamic contact angle distribution, comprising: The first module is used to construct the joint probability density function of horizontal distance and height difference based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface. ; The second module is used to derive the probability density function of the contact angle of a static micro-convex body through integral transform and Leibniz's differentiation rule. ; The third module is used to derive the first and second relationships through cyclic load experiments. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. The fourth module is used for the probability density function based on the first relation, the second relation, and the static contact angle. A probability density function model of the dynamic contact angle is constructed.

[0044] The modeling system for predicting dynamic contact angle distribution provided by this invention solves the problem of dynamic evolution of contact angle of micro-protrusions under cyclic loading, thereby improving the prediction accuracy of contact characteristics of rough surfaces. Specifically, the first module constructs a joint probability density function based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on the rough surface, utilizing the characteristic that the normal distribution can accurately describe the randomness of the geometric parameters of micro-protrusions, providing a statistical basis for subsequent models; the second module derives the probability density function of static contact angle through integral transformation and Leibniz's differentiation rule, applying mathematical tools to extract the contact angle distribution from the joint distribution, solving the problem of unclear source of static contact angle modeling; the third module derives the first and second relations through cyclic loading experiments, quantifying the influence of the number of cycles on the standard deviation through experimental data, capturing the dynamic evolution process; the fourth module constructs a dynamic contact angle probability density function model based on the first and second relations and the static contact angle probability density function, integrating static and dynamic factors, and realizing a comprehensive characterization of contact angle changes under cyclic loading.

[0045] Based on the same inventive concept, the present invention also provides a method for predicting dynamic contact angle distribution. Based on the probability density function model of dynamic contact angle in the modeling method for predicting dynamic contact angle distribution described above, the dynamic contact angle distribution of rough surface is obtained by plotting the probability density curve of dynamic contact angle under different working conditions.

[0046] The method for predicting dynamic contact angle distribution provided by this invention effectively solves the problems of visualization and prediction of dynamic contact angle distribution by utilizing the probability density function model of dynamic contact angle, combined with computer program plotting probability density curves and analysis. Specifically, the probability density function model based on dynamic contact angle directly applies the model established in the referenced scheme. This model considers the dynamic changes under cyclic loading, ensuring the accuracy and dynamic adaptability of the analysis results. By plotting the probability density curves of dynamic contact angle of rough surfaces under different working conditions, the model is visualized under different conditions, facilitating intuitive observation of the changing trend of contact angle. The obtained dynamic contact angle distribution of rough surfaces is further analyzed by deeply examining the curves to extract actual distribution characteristics, providing a reliable basis for predicting the contact characteristics of mechanical mating surfaces. Through synergistic effects, the theoretical model is transformed into a practical application tool, improving the efficiency and practicality of the analysis.

[0047] Based on the same inventive concept, the present invention also provides an application of the method for predicting dynamic contact angle distribution as described above, for analysis and engineering design related to the contact characteristics of mechanical mating surfaces.

[0048] Specifically, it is applied in practical scenarios such as microscopic morphology measurement, feature extraction, statistical analysis, contact characteristic calculation, and contact model construction under dynamic loads. Simultaneously, it provides key theoretical and parameter support for equipment development and performance optimization in fields such as precision machinery, aerospace, and CNC machine tools. For example, when analyzing the contact stiffness, damping characteristics, or design optimization of mechanical mating surfaces, a dynamic contact angle distribution model is used to evaluate the actual surface behavior, thereby overcoming the shortcomings of existing technologies where models are detached from practical applications and improving the accuracy and efficiency of engineering design.

[0049] Based on the same inventive concept, the present invention also provides a system for predicting dynamic contact angle distribution, comprising: The fifth module is used to analyze and obtain the dynamic contact angle distribution of rough surfaces by plotting the probability density function model of the dynamic contact angle in the modeling method for predicting dynamic contact angle distribution as described above, and by plotting the probability density curves of the dynamic contact angle of rough surfaces under different working conditions.

[0050] By analyzing the probability density curves to extract distribution features, contact angle distribution data that can be used for engineering design is output, supporting accurate prediction of mechanical interface characteristics.

[0051] The modeling method for predicting dynamic contact angle distribution provided by this invention is based on the following inventive concept: S1: Acquisition of three-dimensional topography data for rough surfaces: Taking a mating surface on a large shaft repair lathe as an example, due to its large size, the surface profile of this mating surface cannot be directly measured using a non-contact three-dimensional topography measurement device. Therefore, during the machining of this mating part, two surface samples are machined using the same material under the same machining conditions. These samples are then placed under a non-contact three-dimensional topography measurement device to sample profile data. The profile data of these samples is used to calculate the statistical parameters of the rough surface profile. Since the sample and the mating surface are made of the same material and have the same machining method, their surface profile statistical parameters can be considered to be identical.

[0052] A non-contact three-dimensional morphology measurement device was used to scan and measure the surfaces of the upper and lower samples of the same material and the same processing method at the bonding surface. and The sampling intervals in all directions are equal, each being 1 μm. The z-direction represents the true microscopic surface contour, and the sample size is 1 mm × 1 mm. This process acquires three-dimensional surface contour data containing X, Y, and Z coordinate information.

[0053] Non-contact three-dimensional topography measurement equipment uses a confocal interference microscope or a white light interferometer.

[0054] S2: Surface contour data preprocessing: After acquiring the 3D surface contour data, it is first preprocessed to extract the true microstructure data. The MAD method is used to detect outliers and eliminate systematic errors introduced by equipment tilt or sample installation. Then, a first-order polynomial linear fitting is used to eliminate linear deviations, forming a uniformly meshed digital surface model, thus obtaining the desired result. Figure 2 The surface profiles of the upper and lower samples, as shown in (a) and (b), are reconstructed using MATLAB.

[0055] S3: Extraction of statistical feature parameters of micro-convexity: Two-dimensional profile curve acquisition and statistical characterization: Based on the three-dimensional profile diagrams of the upper and lower samples obtained in step S2, six cross-sections are randomly selected along the x-direction from the surface profiles of the upper and lower samples. Specifically, x is randomly selected along the x-axis at values ​​of 150, 231, 415, 615, 802, and 972. By extracting the contour data from the cross-sections of the corresponding upper and lower specimens, we can obtain... Figure 3 The two-dimensional contour curve diagram shown is as follows. Figure 3 The sample x=231 is the value taken from the upper sample. Two-dimensional contour curve corresponding to the cross section; See Figure 4 This is a schematic diagram of the "three-point peak" sampling method for micro-convex bodies. The "three-point peak" method is used to extract the peak points of micro-convex bodies from a two-dimensional contour curve. The "three-point peak" method uses the micro-convex body peak as a reference and calculates the horizontal distance between the two nearest peaks on the left and right sides of the reference peak. (negative value) and (Positive value), and height difference (negative value) and (Positive value), the horizontal distance and height difference of the intermediate peak are defined as 0.

[0056] The identification criteria are as follows: when the height of the center point is greater than the heights of the two adjacent points on the left and right and the difference exceeds 0.5 μm, it is determined to be a valid micro-convex peak. The horizontal distance between the two nearest peaks on the left and right sides of the reference peak is calculated. (negative value) and (Positive value), and height difference (negative value) and (Positive value), the horizontal distance and height difference of the intermediate peak are defined as 0.

[0057] S4: Normal distribution test for the horizontal distance and height difference of the micro-convex body: Extracted horizontal distance and height difference Statistical analysis was performed, and the statistical parameters of the six groups of samples were calculated. See Tables 1 and 2 in the instruction manual for details.

[0058] Table 1 Statistical parameters of horizontal distance distribution of micro-protrusions

[0059] Table 2 Statistical parameters of the height difference distribution of micro-protrusions

[0060] Calculate skewness and kurtosis To verify its normality, when the test value is... and It is assumed that the distribution follows a normal distribution, and 1.96 is the two-sided critical value at the 95% confidence level of the standard normal distribution; use Perform a normality test on the distribution, null hypothesis The mean of the horizontal distance or height difference between the micro-convex bodies is 0, that is... Alternative Hypothesis The mean of the horizontal distance or height difference between micro-convexities is not zero, i.e. , The formula for calculating the statistic is:

[0061] in, Let be the sample standard deviation, and let be the relationship between and . , For sample size, Integrity level For details of the t-value test results, please refer to Table 3 in the instruction manual.

[0062] Table 3. t-value test for horizontal distance and height difference of micro-convex objects

[0063] Calculated for all groups The values ​​are all less than the degrees of freedom. of The critical value of the distribution (approximately 1.98) is sufficient to accept the null hypothesis. The horizontal distance and height difference are determined to follow a normal distribution with a mean of zero.

[0064] Based on the above statistical distribution characteristics, this invention provides a modeling method for predicting dynamic contact angle distribution, specifically including the following steps: Derivation of the contact angle probability density function: See Figure 5 A schematic diagram of the contact angle geometry of the micro-convex body is provided, establishing the horizontal distance. and height difference The probability density functions of the horizontal distance and height difference of the micro-convex bodies obtained statistically both follow a normal distribution, and their probability density functions are as follows:

[0065]

[0066] Based on the independence of horizontal distance and height difference (if two random variables are independent and each follows a normal distribution, then their joint probability density is equal to the product of the two marginal densities), the joint probability density function is obtained as follows:

[0067] Contact angle and , The geometric relationship is as follows: .

[0068] Next, we will analyze the contact angle. The probability is known. The goal is to calculate Because of the arctangent function Monotonically increasing, Equivalent to At this point, the probability needs to be transformed into an integral form, taking into account... The physical meaning, and from arrive Given the range of values ​​for , the cumulative distribution function can be obtained as follows:

[0069] Based on the relationship between the probability density function and the cumulative distribution function The above equation needs to be differentiated. Based on Leibniz's law, the probability density function of the contact angle can be obtained as follows:

[0070] In the formula: —The contact angle between the micro-protrusions ranges from 0° to 90°; —The mean values ​​of the horizontal distance and height difference of the micro-convexities; —Standard deviation of the horizontal distance and height difference of the micro-convexity.

[0071] Based on the hypothesis test results in the text, we can obtain The probability density function of the contact angle can be further simplified to

[0072] Due to indefinite integrals ,in ,so Substituting into the above equation, we can obtain the probability density function of the contact angle of the micro-convex body as follows:

[0073] Using the above integral transform and Leibniz's differentiation rule, the probability density function of the contact angle is derived:

[0074] In the formula, The contact angle between the micro-protrusions ranges from 0° to 90°. These are the standard deviations of the horizontal distance and height difference of the micro-convexities, respectively.

[0075] Calculate the mean standard deviation of the six sets of data. =6.7385μm, =2.4148μm. Since these six sets of data come from two-dimensional profile curve data obtained from different cross-sections, in order to verify the accuracy of the conclusion, the theoretical curve of the contact angle probability density function of this embodiment is taken when the horizontal distance and standard deviation are 6.0, 6.5, 7.0, 7.5 and the height difference standard deviation is 2.0, 2.5, 3.0, 3.5. Figure 6 As shown. The larger the standard deviation of the horizontal distance of the micro-protrusions, the smaller the standard deviation of the height difference, and the smaller the contact angle. , , The curve reaches its maximum value during (positive contact). This indicates that the contact angle of the grinding surface is mainly distributed in the range of 0° to 15°, which is consistent with the small-angle side contact characteristics.

[0076] Dynamic evolution of statistical parameters under cyclic loading: Establishing the iterative relationship between statistical parameters and the number of cycles, and the horizontal distance standard deviation. With the number of loops The standard deviation of the height difference increases slowly. With the number of loops Continuously decreasing; and satisfying the following respectively: The evolution of horizontal distance standard deviation:

[0077] Wherein, γ represents the amplification effect of the increase in residual radius of curvature on the standard deviation of horizontal distance. , The residual radius of curvature is obtained through surface topography measurement; The evolution of the standard deviation of height difference:

[0078] Where λ is the attenuation intensity of the flattening effect on the standard deviation of the height difference. Material attenuation factor Take 0.32, This represents the residual deformation of the micro-protrusion. This represents the maximum deformation of the micro-convexity. Figure 7 This demonstrates the trend of statistical parameters changing with the number of iterations. Follow Slowly increasing, Follow The contact angle continues to decrease, stabilizing after 15 cycles. Through rigorous statistical analysis and theoretical derivation, a contact angle probability density function is established, and the dynamic evolution law of the contact angle is revealed by combining cyclic loading and unloading.

[0079] Dynamic contact angle probability density function model: Substituting the statistical parameters of the dynamic evolution into the probability density function of step S5, the dynamic contact angle probability density function model is as follows:

[0080] Based on the dynamic contact angle probability density function model, the dynamic contact angle distribution models for the 1st, 5th, 10th, and 20th cycles can be obtained. .

[0081] Analysis and Verification of Dynamic Contact Angle Distribution Characteristics: The dynamic contact angle probability density function model was numerically calculated using MATLAB software, and the numerical calculation results were visualized using Origin software to plot the contact angles. Analyze the probability density function curves within the range of 0° to 90° for different... , Distribution characteristics under combination; plot 3D surface diagrams to show contact angle θ, number of cycles k, and probability density. The coupling relationship is investigated; the accuracy and superiority of the model are verified by comparing the contact angle distribution curves of this model with those of existing models.

[0082] Numerical calculations and data visualizations are performed using computer programs to plot contact angle probability density curves under different working conditions. Figure 8 The dynamic contact angle distribution surface under the coupling effect of cyclic loading / unloading and contact angle is shown. As the number of cycles increases, the probability density peak shifts towards smaller angles, and the distribution curve becomes sharper, indicating that the contact angle distribution tends to concentrate. Since the contact angle cannot be directly measured during the experiment, this invention uses numerical calculation methods to compare and verify the established contact angle probability density model with existing models. See [link to relevant documentation]. Figure 9 This paper presents a theoretical comparison curve of the contact angle probability density as a function of contact angle between the contact angle distribution model established in this invention and the Gorbatikh and Misra models. Figure 9As can be seen, the prediction trends of the model of this invention are basically consistent with those of the Gorbatikh and Misra models, demonstrating the rationality and accuracy of the model of this invention. Further analysis shows that, under any number of loading and unloading cycles, the contact probability of small-angle micro-protrusions is significantly higher than that of large-angle contacts. Furthermore, the loading and unloading curves of the 20th and 10th cycles almost overlap, indicating that after approximately 10 cycles, the contact state of the micro-protrusions tends to stabilize, and the influence of subsequent loading on the contact probability distribution is significantly weakened. With increasing loading cycles, the contact surface is gradually flattened, and the change in the contact angle distribution function tends to be gradual. It is worth noting that when the contact angle is 90°, the micro-protrusion contact probability predicted by the model of this invention is approximately 0.18, while the prediction result of the Gorbatikh and Misra models is 0, which is inconsistent with the actual physical situation. This further verifies that the contact angle distribution model established in this invention has a clearer physical meaning and higher prediction accuracy.

[0083] The modeling method provided by this invention starts from the statistical characteristics of surface morphology and establishes a contact angle distribution model through rigorous hypothesis testing and mathematical derivation. It has a solid theoretical foundation and clear physical meaning, overcoming the shortcomings of existing models that rely on empirical assumptions. It transforms the intangible contact angle into measurable horizontal distance and height difference, achieving indirect acquisition of the contact angle distribution through statistical transformation, thus solving the technical difficulties of experimental measurement. For the first time, a dynamic evolution model of the contact angle under cyclic loading is established, revealing the influence mechanism of the "flattening effect" on the contact angle distribution, filling the gap in dynamic contact mechanics modeling, and significantly improving the prediction accuracy of the model under cyclic loading conditions. It clarifies the relationship between the contact angle distribution and microscopic geometric parameters (…). , The quantitative relationship between the surface processing and the contact characteristics provides theoretical guidance for controlling contact characteristics through surface processing, which has important engineering application value; it provides key parameters for modeling the contact mechanics of rough surfaces dominated by small-angle side contact, and improves the accuracy of contact load and stiffness prediction.

[0084] Finally, it should be noted that the embodiments listed above are merely one or more specific manifestations of the technical solution of this invention. Their purpose is to clearly illustrate the concept, principle, and application of this invention through specific examples, and is by no means intended to limit the scope of protection of this invention to these specific embodiments. In fact, the true value of this invention lies in its proposed technical ideas and innovations, rather than its manifestations or implementation methods.

[0085] For those skilled in the art, after thoroughly reading and understanding the technical solution of this invention, they are fully capable of making various changes, modifications, or equivalent substitutions to the specific implementation of the invention based on their own professional knowledge and skills. These changes may include, but are not limited to: adjusting the range of technical parameters, optimizing the algorithm flow to improve efficiency, and replacing some technical components to achieve better compatibility or reduce costs. As long as these modified technical solutions substantially retain the technical features claimed by the original invention, that is, they can still achieve the core functions and effects of this invention, then these changes should be considered to fall within the scope of protection of the pending claims of this invention.

[0086] Furthermore, with the continuous progress and development of technology, new technical means and methods are constantly emerging, which provides ample space for further improvement and perfection of this invention. Therefore, the scope of protection of this invention should also include reasonable and foresightful improvements and extensions based on existing technology. As long as these improvements and extensions do not depart from the basic principles and core concepts of this invention, they should be considered equivalents of this invention and are equally protected by patent rights.

Claims

1. A modeling method of predicting dynamic contact angle distribution, characterized by, Includes the following steps: Based on the normal distribution law of horizontal distance and height difference between adjacent microconvexes of rough surface, a joint probability density function of horizontal distance and height difference is constructed ; By using integral transforms and Leibniz's differentiation rule, the probability density function of the contact angle of a static micro-convex body is derived. ; Through cyclic loading experiments, the first and second relationships were derived. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. Based on the first relation, the second relation, and the probability density function of the static contact angle. A probability density function model of the dynamic contact angle is constructed.

2. The modeling method for predicting dynamic contact angle distribution according to claim 1, characterized in that, Joint probability density function of horizontal distance and height difference Specifically: in, Horizontal distance; The difference in height; The standard deviation of the horizontal distance; The standard deviation of the height difference; This represents the mean of the horizontal distances. This represents the average height difference.

3. The modeling method for predicting dynamic contact angle distribution according to claim 2, characterized in that, probability density function of static contact angle Specifically: in, It represents the contact angle.

4. The modeling method for predicting dynamic contact angle distribution according to claim 3, characterized in that, The first relation is as follows: in, This is the proportionality coefficient; This represents the number of loop iterations. denoted as the standard deviation of the horizontal distance of the micro-protrusion after the k-th loading and unloading action; The standard deviation of the horizontal distance of the micro-protrusion after the (k-1)th loading and unloading action; The radius of curvature of the micro-convexity after the (k-1)th loading and unloading action; The radius of curvature of the micro-convex body after the (k-2)th loading and unloading action is denoted as .

5. The modeling method for predicting dynamic contact angle distribution according to claim 4, characterized in that, The second relation is as follows: in, The material attenuation factor; The residual deformation of the micro-protrusion after the k-th loading and unloading action; This represents the maximum deformation of the micro-protrusion after the k-th loading cycle. is the standard deviation of the height difference of the micro-protrusion after the kth loading and unloading action; The standard deviation of the height difference of the micro-protrusion after the (k-1)th loading and unloading action is given.

6. The modeling method for predicting dynamic contact angle distribution according to claim 5, characterized in that, The probability density function model for the dynamic contact angle is as follows: 。 7. A modeling system for predicting dynamic contact angle distribution, characterized in that, include: The first module is used to construct the joint probability density function of horizontal distance and height difference based on the normal distribution law of the horizontal distance and height difference between adjacent micro-protrusions on a rough surface. ; The second module is used to derive the probability density function of the contact angle of a static micro-convex body through integral transform and Leibniz's differentiation rule. ; The third module is used to derive the first and second relationships through cyclic load experiments. The first relationship is used to characterize the dynamic relationship between the standard deviation of the horizontal distance of the micro-protrusion and the number of cycles, and the second relationship is used to characterize the dynamic relationship between the standard deviation of the height difference of the micro-protrusion and the number of cycles. The fourth module is used for the probability density function based on the first relation, the second relation, and the static contact angle. A probability density function model of the dynamic contact angle is constructed.

8. A method for predicting dynamic contact angle distribution, characterized in that, Based on the probability density function model of the dynamic contact angle in the modeling method for predicting the dynamic contact angle distribution as described in any of claims 1 to 6, the dynamic contact angle distribution of the rough surface is obtained by plotting the probability density curves of the dynamic contact angle under different working conditions.

9. The application of the method for predicting dynamic contact angle distribution as described in claim 8, characterized in that, Used for analysis and engineering design related to the contact characteristics of mechanical mating surfaces.

10. A system for predicting dynamic contact angle distribution, characterized in that, include: The fifth module is used to analyze and obtain the dynamic contact angle distribution of a rough surface by plotting the probability density curves of the dynamic contact angle under different working conditions, based on the probability density function model of the dynamic contact angle in the modeling method for predicting the dynamic contact angle distribution as described in any of claims 1 to 6.

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