A method for grinding three-dimensional surface decomposition based on typical imaginary surface features

Abstract

The application discloses a grinding three-dimensional surface decomposition method based on typical additive surface features, and has the characteristics that it comprises the following steps: step 1, analyzing requirements to determine a target; step 2, establishing a plurality of imaginary surface mathematical models; step 3, coupling the plurality of imaginary surfaces according to the model of step 2, and searching for an optimal coupling mode; step 4, obtaining an empirical formula of grinding machining parameters according to the coupling mode; step 5, simulating and experimenting according to the data obtained in step 4, and measuring and comparing the data; and step 6, discriminating similarity according to the data, and drawing a normal vector cumulative distribution curve (NVCDC) curve. The application has important guiding significance for controllable machining technology of a ground surface.

Description

Technical Field

[0001] This invention relates to a grinding technology, and more particularly to a grinding process parameter research technology field, specifically a grinding three-dimensional surface decomposition method based on typical surface features. Background Technology

[0002] The design and manufacturing of hydraulic system seals in domestic aircraft are mainly based on two-dimensional surface topography indicators. However, two-dimensional topography indicators cannot fully reflect the performance of dynamic seal structures. They only reflect the characteristics of a surface in a single linear direction, and the surface information they can reflect is very limited. In the aerospace field, three-dimensional topography indicators not only cover the roughness that two-dimensional roughness can describe, but also consider the undulations and unevenness of the surface in different directions. A more accurate description is crucial for the hydrodynamic characteristics, aerodynamic performance, and combustion characteristics of aircraft surfaces. Therefore, the design and manufacturing of dynamic seal structures abroad are already based on three-dimensional surface characterization systems. Due to technological monopolies, the domestic academic and industrial communities currently lack a systematic and in-depth understanding of the design methods of three-dimensional surface characterization systems for seals, the intrinsic relationship between three-dimensional topography and sealing performance, and the theory and technology of three-dimensional surface creation and processing.

[0003] With the development of my country's economy and the increasingly advanced transportation network, air transport accounts for a larger and larger proportion of transportation. Many cities in my country have successively established relatively complete trunk and branch airports, and the demand for large aircraft is increasing day by day, bringing huge benefits to related industrial chains. Among them, the market size of aviation hydraulic systems will exceed 100 billion yuan. At the same time, my country's demand for high-end aviation hydraulic components is also increasing year by year. Therefore, investing in the research and development and manufacturing of high-end aviation hydraulic components is of strategic significance.

[0004] After years of exploration and technological accumulation, my country's design level of high-end aerospace hydraulic components has gradually caught up with international advanced levels. However, the main reason limiting its development is still the gap in manufacturing level. Products manufactured based on two-dimensional surface morphology standards can no longer fully measure dynamic sealing performance. Furthermore, there is a lack of in-depth research in China on the design methods of three-dimensional surface characterization systems and the theory and technology of three-dimensional morphology creation processing. This is an urgent problem to be solved. At the same time, research on the three-dimensional roughness of typical hypothetical surfaces is even scarcer, and there are no relevant applications for research on the correlation between the three-dimensional morphology and roughness index of the ground workpiece surface. Therefore, in order to establish the connection between these three aspects and save enterprises time and costs for in-depth research, a method is needed to decompose the surface of the ground workpiece into a hypothetical surface composite. Summary of the Invention

[0005] The purpose of this invention is to address the problem that the lack of three-dimensional surface feature design technology in existing seals affects the hydraulic sealing performance. This invention proposes a grinding three-dimensional surface decomposition method based on typical hypothetical surface features. It establishes a correlation model between the key indicators of the three-dimensional morphology of the sealing surface and the processing parameters through typical hypothetical surface models. Through numerical simulation and experimental verification, it ultimately achieves the prediction of the three-dimensional roughness of the grinding surface.

[0006] The technical solution of this invention is:

[0007] A grinding three-dimensional surface decomposition method based on typical surface features is characterized by comprising the following steps:

[0008] Step 1: Analyze needs and determine objectives.

[0009] Step 2: Establish mathematical models of various hypothetical surfaces.

[0010] Step 3: Based on the model in Step 2, couple multiple hypothetical surfaces to find the optimal coupling method.

[0011] Step 4: Determine the empirical formulas for grinding parameters based on the coupling method.

[0012] Step 5: Perform simulations and experiments based on the data obtained in Step 4, and measure and compare the data.

[0013] Step 6: Based on the data, perform similarity judgment and plot the cumulative normal vector distribution curve (NVCDC) curve.

[0014] The three-dimensional topographic parameters mentioned in this article mainly include three parameters: arithmetic mean height, skewness, and kurtosis. Their expressions are as follows:

[0015] ① Arithmetic average height:

[0016] Where A is the area of ​​the sampling region; |z (x,y) | is the height function for each point in the region.

[0017] ② Skewness:

[0018] Where Sq is the root mean square height, and the specific calculation expression is as follows:

[0019] ③Cumber:

[0020] The morphological characteristics of different three-dimensional surfaces can be obtained based on the calculation formula of the key index of three-dimensional roughness.

[0021] The specific steps of step 2 are as follows:

[0022] Step 2.1: Establish mathematical models of the height function for different typical hypothetical surfaces.

[0023] Typical hypothetical surfaces can be divided into two categories: linear and nonlinear. Linear waviness, also known as sinusoidal waviness, has the following expression for its height function in a single direction:

[0024] z(x) = A m sin(2πf(x))

[0025] Where A m denoted as , where f is the ripple amplitude and f is the ripple frequency.

[0026] Nonlinear waviness can be further classified into three types based on the step coefficient c: sawtooth (c=0), stepped (c∈(0,1)), and rectangular (c=1). Their specific expressions are as follows:

[0027]

[0028] Step 2.2: Calculate the three-dimensional roughness parameters of the hypothetical surface based on its height function.

[0029] A sinusoidal waviness surface exhibits symmetry, and its three-dimensional roughness expression is:

[0030]

[0031] The three-dimensional roughness expression for stepped waviness is:

[0032]

[0033] Step 2.3: Expand the single pure waviness surface to different extension directions and calculate its surface roughness parameter function.

[0034] The specific steps of step 3 are as follows:

[0035] Step 3.1: Couple the three types of pure waviness with different extension directions, extension angles, and types of pure waviness ideal surfaces. Analyze and calculate the three-dimensional roughness values ​​under different coupling methods.

[0036] Step 3.2: Change the value of the step coefficient c in the coupling process, plot the curve of the 3D roughness parameter as a function of c, and perform target optimization. The expression for target optimization is:

[0037] min:a T x

[0038] Where 'a' is a column vector containing the coefficients of each key indicator in the objective function, and its value represents the slope at each point. 'x' is a column vector consisting of the three-dimensional roughness parameter values ​​at each point.

[0039] Step 3.3: Based on the coupled surfaces described above, rotate the angles of the two pure waviness surfaces to find the optimal coupling method.

[0040] In step 4, the expression for the empirical formula is:

[0041]

[0042] Where C represents the correction factor, V s V is the speed of the grinding wheel. w For the feed rate, a p For cutting depth

[0043] The specific steps of step 5 are as follows:

[0044] Step 5.1: Establish the surface morphology of the grinding wheel, including the size, location, and distribution density of the abrasive grains. The location of each abrasive grain is represented by the following formula:

[0045]

[0046] Among them, G i,j The position of each abrasive grain center in the two-dimensional unfolded plane. Δx and Δy represent the positions of the center of the first abrasive grain on the x and y axes, respectively. Δx and Δy are the offset distances of each abrasive grain relative to the previous abrasive grain on the x and y axes, respectively, which are equal to the abrasive grain spacing L. The value of L is related to the grinding wheel structure parameter S.

[0047] Step 5.2: Based on the grinding motion relationship and the grinding principle, establish the abrasive grain trajectory curve. Represent the surface morphology of the grinding wheel and workpiece using a matrix. The formation of the workpiece surface morphology can be seen as a process of i abrasive grains on j xoz cross sections successively scratching it. The motion trajectory of the abrasive grains can be represented as:

[0048]

[0049] Where R is the radius of the grinding wheel, n s v is the grinding wheel speed. w h(i,j) represents the platform feed speed, and h(i,j) represents the workpiece surface topography matrix.

[0050] Step 5.3: Generate the workpiece surface morphology based on the contact between the grinding wheel and the workpiece. The height h(m,n) of each point on the workpiece surface corresponds to the grinding trajectory value z of multiple abrasive grains at that location. ij (m,n), i.e., x ij (t) = m, y ij (t) = n. The final workpiece surface height is given by the following formula:

[0051] h(m,n)=min(z ij (m,n))

[0052] The specific steps of step 6 are as follows:

[0053] Step 6.1: Calculate the 3D surface normal vector. The actual surface can be viewed as irregular discrete points arranged at equal intervals and different heights on a plane. Connecting the height values ​​at each location yields the surface topography. Using the principle that three points determine a plane, four 3D planes can be constructed using point m and its four surrounding points, where point m is the common intersection point of these planes. The normal vector n of each small plane is... i The calculation formula is:

[0054] n i =mm i ×mm i+1 =(x i -x,y i -y,z i -z)×(x i+1 -x,y i+1 -y,z i+1 -z)

[0055] Among them, mm i Point m points to m i The vectors. Adding the four normal vectors and normalizing them, we can obtain the unit normal vector n = (n... x ,n y ,n z Based on this, the angles α, β, and γ between the normal vector and the three-dimensional coordinate axes can be obtained using inverse trigonometric functions.

[0056] Step 6.2: Select half of the three-dimensional space and divide it into n subspaces by η equal parts according to the angle. Then calculate the probability distribution P of the normal vectors of different subspaces, sort them in ascending order, and define the sequence S. λ S0 = 0, when λ = n, S n =1,S λ The expression is:

[0057]

[0058] Step 6.3: Use λ / n as the x-axis, S λ As the ordinate, the connection point (λ / δ, S) λ Plot the cumulative distribution curve of the normal vectors. Comparing the NVCDC curves of two 3D surfaces can clarify their similarity. Let the distribution curves of the two surfaces be δ and η, respectively. The difference between the areas enclosed by the curves and the horizontal axis is used to measure their difference, as shown in the following formula:

[0059]

[0060] in and These are the sequences corresponding to curves δ and η, respectively.

[0061] The smaller the value of D(δ,η), the higher the similarity between the two curves and their corresponding three-dimensional surfaces, i.e., the smaller the difference in morphology. If D(δ,η) ≥ 20%, it indicates that the two surfaces are unrelated.

[0062] The above-mentioned technical features can be combined in various suitable ways or replaced by equivalent technical features, as long as the purpose of the present invention can be achieved.

[0063] The beneficial effects of this invention are:

[0064] This invention clarifies the relationship between three-dimensional roughness values ​​and surface parameters by starting with a typical hypothetical surface. Through single-factor and orthogonal experiments of grinding numerical simulation, the optimal combination of processing parameters is selected based on the key value of three-dimensional roughness as an evaluation index and verified by actual processing. At the same time, the similarity between the three-dimensional morphology and roughness value of the workpiece and the typical hypothetical surface is judged, and the relationship between "typical hypothetical surface - three-dimensional roughness value - processing parameters" is established, providing guidance for grinding the three-dimensional morphology of the sealing workpiece surface of aerospace hydraulic components. Attached Figure Description

[0065] Figure 1 This is a flowchart of the present invention.

[0066] Figure 2 These are three-dimensional topographic images of the present invention under different extension directions and coupling angles.

[0067] Figure 3 This is a simulation image of the grinding wheel morphology (M=120 mesh) of the present invention.

[0068] Figure 4 This is a schematic diagram illustrating the principle of surface generation in grinding processes according to the present invention.

[0069] Figure 5 This is a three-dimensional topographic point cloud diagram of the hypothetical coupled surface and the actual machined surface of the present invention.

[0070] Figure 6 The NVCDC curves are for two types of three-dimensional topographic point cloud maps of the present invention. Detailed Implementation

[0071] The present invention will be further described below with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the invention.

[0072] like Figure 1-6 As shown.

[0073] A grinding three-dimensional surface decomposition method based on typical surface features, such as Figure 1 As shown, it includes the following steps:

[0074] Step 1: Analyze needs and determine objectives.

[0075] This example aims to obtain the state with relatively optimal overall surface properties, that is, the state with the minimum overall Sa, Ssk, and Sku.

[0076] Step 2: Establish mathematical models of various hypothetical surfaces.

[0077] Step 2.1: Establish mathematical models of the height function for different typical hypothetical surfaces.

[0078] Typical hypothetical surfaces can be divided into two categories: linear and nonlinear. Linear waviness, also known as sinusoidal waviness, has the following expression for its height function in a single direction:

[0079] z(x) = A m sin(2πf(x))

[0080] Where A m denoted as , where f is the ripple amplitude and f is the ripple frequency.

[0081] Nonlinear waviness can be further classified into three types based on the step coefficient c: sawtooth (c=0), stepped (c∈(0,1)), and rectangular (c=1). Their specific expressions are as follows:

[0082]

[0083] Step 2.2: Calculate the three-dimensional roughness parameters of the hypothetical surface based on its height function.

[0084] A sinusoidal waviness surface exhibits symmetry, and its three-dimensional roughness expression is:

[0085]

[0086] The three-dimensional roughness expression for stepped waviness is:

[0087]

[0088] Step 2.3: Expand the single pure waviness surface to different extension directions and calculate its surface roughness parameter function.

[0089] Step 3: Based on the model in Step 2, couple multiple hypothetical surfaces to find the optimal coupling method.

[0090] Step 3.1: Couple the three types of pure waviness with different extension directions, extension angles, and types of pure waviness ideal surfaces. Analyze and calculate the three-dimensional roughness values ​​under different coupling methods.

[0091] Step 3.2: Change the value of the step coefficient c in the coupling process, plot the curve of the 3D roughness parameter as a function of c, and perform target optimization. The expression for target optimization is:

[0092] min:a T x

[0093] Where 'a' is a column vector containing the coefficients of each key index in the objective function, and its value represents the slope at each point. 'x' is a column vector composed of the three-dimensional roughness parameter values ​​at each point. Calculations show that the overall morphological feature parameters are minimized when the step parameter is set to 0.1 among various combinations.

[0094] Step 3.3: Based on the coupled surfaces described above, rotate the angles of the two pure waviness surfaces to find the optimal coupling method. Figure 2 The image shows A. m Three-dimensional topographic images of different coupling angles with f = 1 μm, f = 1 Hz, and c = 0.1.

[0095] In multiple extension directions, the case where the overall three-dimensional roughness value is relatively low under different pure waviness is the coupling case of step-shaped 0° (step coefficient is 0.1) + sinusoidal 90° + sawtooth 60°.

[0096] Step 4: Determine the empirical formulas for the grinding parameters based on the coupling method. The expression of the empirical formulas is:

[0097]

[0098] Where C represents the correction factor, V s V is the speed of the grinding wheel. w For the feed rate, a p For cutting depth

[0099] The empirical formulas for the three process parameters of grinding, obtained through calculation, are as follows:

[0100]

[0101] Step 5: Perform simulations and experiments based on the data obtained in Step 4, and measure and compare the data.

[0102] The grinding wheel used in this simulation and experiment is a white corundum grinding wheel with a mesh size of 120, a radius of 100 mm, a width of 10 mm, and a structural parameter of 7.

[0103] Step 5.1: Establish the surface morphology of the grinding wheel, including the size, location, and distribution density of the abrasive grains. The location of each abrasive grain is represented by the following formula:

[0104]

[0105] Among them, Gi,j The position of each abrasive grain center in the two-dimensional unfolded plane. Δx and Δy represent the positions of the center of the first abrasive grain on the x and y axes, respectively, and Δx and Δy are the offset distances of each abrasive grain relative to the previous abrasive grain on the x and y axes, respectively, which are equal to the abrasive grain spacing L. Figure 4 The image shows the surface morphology of the generated grinding wheel.

[0106] Step 5.2: Based on the grinding motion relationship and the grinding principle, establish the abrasive grain trajectory curve. Represent the surface morphology of the grinding wheel and workpiece using a matrix. The formation of the workpiece surface morphology can be seen as a process of i abrasive grains on j xoz cross sections successively scratching it, the principle of which is as follows: Figure 5 As shown. The trajectory of the abrasive grains can be represented as:

[0107]

[0108] Where R is the radius of the grinding wheel, n s v is the grinding wheel speed. w h(i,j) represents the platform feed speed, and h(i,j) represents the workpiece surface topography matrix.

[0109] Step 5.3: Generate the workpiece surface morphology based on the contact between the grinding wheel and the workpiece. The height h(m,n) of each point on the workpiece surface corresponds to the grinding trajectory value z of multiple abrasive grains at that location. ij (m,n), i.e., x ij (t) = m, y ij (t) = n. The final workpiece surface height is given by the following formula:

[0110] h(m,n)=min(z ij (m,n))

[0111] Step 6: Based on the data, perform similarity judgment and plot the cumulative normal vector distribution curve (NVCDC) curve.

[0112] Step 6.1: Calculate the 3D surface normal vector. The actual surface can be viewed as irregular discrete points arranged at equal intervals and different heights on a plane. Connecting the height values ​​at each location yields the surface topography. Using the principle that three points determine a plane, four 3D planes can be constructed using point m and its four surrounding points, where point m is the common intersection point of these planes. The normal vector n of each small plane is... i The calculation formula is:

[0113] n i =mm i ×mm i+1 =(x i -x,y i -y,z i -z)×(xi+1 -x,y i+1 -y,z i+1 -z)

[0114] Among them, mm i Point m points to m i The vectors. Adding the four normal vectors and normalizing them, we can obtain the unit normal vector n = (n... x ,n y ,n z Based on this, the angles α, β, and γ between the normal vector and the three-dimensional coordinate axes can be obtained using inverse trigonometric functions.

[0115] Step 6.2: Select half of the three-dimensional space and divide it into n subspaces by η equal parts according to the angle. Then calculate the probability distribution P of the normal vectors of different subspaces, sort them in ascending order, and define the sequence S. λ S0 = 0, when λ = n, S n =1,S λ The expression is:

[0116]

[0117] Step 6.3: Use λ / n as the x-axis, S λ As the ordinate, the connection point (λ / n, S) λ Plot the cumulative distribution curve of the normal vector. The cumulative distribution curve is shown in the figure. Figure 6 As shown. Comparing the NVCDC curves of two three-dimensional surfaces can clearly demonstrate their similarity. Let the two surface distribution curves be δ and η, respectively. The difference in area enclosed by the curves and the horizontal axis is used to measure their difference, as shown in the following formula:

[0118]

[0119] in and These are the sequences corresponding to curves δ and η, respectively.

[0120] In this example, the calculation is based on the data. D(δ,η) = 6.78%.

[0121] The smaller the value of D(δ,η), the higher the similarity between the two curves and their corresponding three-dimensional surfaces, i.e., the smaller the difference in morphology. If D(δ,η) ≥ 20%, it indicates that the two surfaces are unrelated.

[0122] In this example, the calculated D(δ,η) = 6.78%, which is much smaller than the set range of 20%, indicating that the ideal coupled surface and the actual processed surface have a similar relationship, proving the feasibility of the method of this invention.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

[0124] The parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A grinding three-dimensional surface decomposition method based on typical surface features, characterized in that it Includes the following steps: Step 1: Analyze needs and define objectives; Step 2: Establish mathematical models for various hypothetical surfaces; Step 3: Based on the model in Step 2, couple multiple hypothetical surfaces to find the optimal coupling method; Step 4: Determine the empirical formulas for grinding parameters based on the coupling method; Step 5: Perform simulations and experiments based on the data obtained in Step 4, and measure and compare the data; Step 6: Perform similarity judgment based on the data and plot the cumulative distribution curve of the normal vector (NVCDC). The establishment of various hypothetical surface mathematical models includes the following steps: Step 2.1: Establish mathematical models of the height function for different typical hypothetical surfaces; For typical hypothetical surfaces, they are divided into two categories: linear and nonlinear. Linear waviness, also known as sinusoidal waviness, has the following expression for its height function in a single direction of extension: z(x)=A m sin(2πf(x)) Where A m is the waviness amplitude, and f is the waviness frequency; Nonlinear waviness is classified into three types according to the step coefficient c: sawtooth (c=0), stepped (c∈(0,1)), and rectangular (c=1). The specific expressions are as follows: Step 2.2: Calculate the three-dimensional roughness parameters of the hypothetical surface based on its height function. A sinusoidal waviness surface exhibits symmetry, and its three-dimensional roughness expression is: The three-dimensional roughness expression for stepped waviness is: Step 2.3: Expand the single pure waviness surface to different extension directions and calculate its surface roughness parameter function; The specific steps of step 3 are as follows: Step 3.1: Couple the three types of pure corrugations with different extension directions, extension angles, and types of pure corrugated ideal surfaces; analyze and calculate the three-dimensional roughness values ​​under different coupling methods; Step 3.2: Change the value of the step coefficient c in the coupling process, plot the curve of the 3D roughness parameter as a function of c, and perform target optimization; the expression for target optimization is: min:a T x Where 'a' is a column vector containing the coefficients of each key indicator in the objective function, and its value is the slope at each point; 'x' is a column vector composed of the three-dimensional roughness parameter values ​​at each point. Step 3.3: Based on the coupled surfaces described above, rotate the angles of the two purely waviness surfaces to find the optimal coupling method; In step 4, the expression for the empirical formula is: Where C represents the correction factor, V s V is the speed of the grinding wheel. w For the feed rate, a p This refers to the depth of cut. The specific steps of step 5 are as follows: Step 5.1: Establish the surface morphology of the grinding wheel, including the size, location, and distribution density of the abrasive grains; the location of each abrasive grain is represented by the following formula: Among them, G i,j The position of each abrasive grain center in the two-dimensional unfolded plane. Δx and Δy represent the positions of the center of the first abrasive grain on the x and y axes, respectively. Δx and Δy are the offset distances of each abrasive grain relative to the previous abrasive grain on the x and y axes, respectively. They are equal to the abrasive grain spacing L, and their values ​​are related to the grinding wheel structure parameters S. Step 5.2: Based on the grinding motion relationship and combined with the grinding principle, establish the abrasive grain trajectory curve; use a matrix to represent the surface morphology of the grinding wheel and the workpiece; the workpiece surface morphology is generated by the process of i abrasive grains on j xoz sections successively engraving it; the motion trajectory of the abrasive grains is represented as: Where R is the radius of the grinding wheel, n s v is the grinding wheel speed. w h(i,j) represents the platform feed rate, and h(i,j) represents the workpiece surface topography matrix. Step 5.3: Generate the workpiece surface morphology based on the contact between the grinding wheel and the workpiece; the height h(m,n) of each point on the workpiece surface corresponds to the grinding trajectory value z of multiple abrasive grains at that position. ij (m,n), i.e., x ij (t) = m, y ij (t) = n; the final workpiece surface height is given by the following formula: h(m,n)=min(z ij (m,n)); The specific steps of step 6 are as follows: Step 6.1: Calculate the 3D surface normal vector; the actual surface is composed of irregular discrete points arranged at equal intervals and different heights on a plane. Connecting the height values ​​at each location yields the surface topography; using the principle that three points determine a plane, four 3D planes are constructed using point m and its four surrounding points, where point m is the common point where these planes intersect; the normal vector n of each small plane is... i The calculation formula is: n i =mm i ×mm i+1 =(x i -x,y i -y,z i -z)×(x i+1 -x,y i+1 -y,z i+1 -z) Among them, mm i Point m points to m i The vector; by adding the four normal vectors obtained and normalizing them, we can obtain the unit normal vector n = (n... x ,n y ,n z Based on this, the angles α, β, and γ between the normal vector and the three-dimensional coordinate axes can be obtained using inverse trigonometric functions; Step 6.2: Select half of the three-dimensional space and divide it into n subspaces by η equal parts according to the angle; then calculate the probability distribution P of the normal vectors of different subspaces, sort them in ascending order, and define the sequence S. λ S0 = 0, when λ = n, S n =1,S λ The expression is: Step 6.3: Use λ / n as the x-axis, S λ As the ordinate, the connection point (λ / δ, S) λ Plot the cumulative distribution curve of the normal vector; compare the NVCDC curves of the two 3D surfaces to determine their similarity; let the distribution curves of the two surfaces be δ and η, and use the area difference enclosed by the curve and the horizontal axis to measure their difference, as shown in the following formula: in and These are the sequences corresponding to curves δ and η, respectively; The smaller D(δ,η) is, the higher the similarity between the three-dimensional surfaces corresponding to the two curves, that is, the smaller the difference in morphology; if D(δ,η)≥20%, it means that there is no relationship between the two surfaces. Based on the calculation formula of the key three-dimensional roughness index, the morphological characteristics of different three-dimensional surfaces are finally obtained; The parameters of the three-dimensional surface topography feature are the arithmetic mean height, skewness, and kurtosis, and their expressions are as follows: ① Arithmetic average height: Where A is the area of ​​the sampling region; |z (x,y) | is the height function for each point in the region; ②Slope: Where Sq is the root mean square height, and the specific calculation expression is as follows: ③Cumber:

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