Grinding three-dimensional surface decomposition method based on typical imaginary surface characteristics

Abstract

The invention discloses a grinding three-dimensional surface decomposition method based on typical additive surface characteristics. The method is characterized by comprising the following steps: step 1, analyzing a demand and determining a target; 2, establishing a plurality of hypothetical surface mathematical models; and 3, according to the model in the step 2, coupling a plurality of hypothetical surfaces, and searching an optimal coupling mode. And 4, solving an empirical formula of grinding machining parameters according to the coupling mode. And 5, performing simulation and experiment according to the data obtained in the step 4, and measuring and comparing the data. And step 6, performing similarity discrimination according to the data, and drawing a normal vector cumulative distribution curve (NVCDC). The method has important guiding significance on the controllable machining technology of the grinding machining surface.

Description

Technical Field

[0001] The invention relates to a grinding process technology, in particular to the technical field of grinding process parameter research, specifically to a grinding three-dimensional surface decomposition method based on typical added surface features. Background Art

[0002] The design and manufacturing of domestic aircraft hydraulic system seals are mainly based on two-dimensional surface morphology indicators. However, two-dimensional morphology indicators cannot fully reflect the performance of dynamic seal structures. Two-dimensional morphology indicators only reflect the characteristics of a certain linear direction of the surface, and the surface information they can reflect has great limitations. In the field of aerospace, three-dimensional morphology indicators not only cover the roughness that can be described by two-dimensional roughness, but also consider the ups and downs and concavities of the surface in different directions. A more accurate description is crucial for the fluid dynamics, aerodynamic performance and combustion characteristics of the aircraft surface. Therefore, the design and production of dynamic seal structures abroad are already based on a three-dimensional surface characterization system. Due to the monopoly of technology, the domestic academic and industrial circles currently lack a systematic and in-depth understanding of the theory and technology of the design method of the three-dimensional surface characterization system of seals, the intrinsic connection between three-dimensional morphology and sealing performance, and the three-dimensional surface creation processing.

[0003] With the development of my country's economy, the transportation network is becoming increasingly developed, and air transportation accounts for an increasingly larger proportion in transportation. Many cities in my country have established relatively complete trunk airports and branch airports. The demand for large aircraft is increasing day by day, bringing huge benefits to the relevant industrial chain. 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 parts is also increasing year by year. Therefore, investing in the research and development and manufacturing of high-end aviation hydraulic parts is of strategic significance.

[0004] After years of exploration and technical accumulation, the design level of my country's high-end aviation hydraulic parts has gradually caught up with the international advanced level, but the main reason restricting its development is the gap in manufacturing level. Products manufactured based on two-dimensional surface morphology standards can no longer fully measure the dynamic sealing performance, and there is no in-depth research in China on the design method of three-dimensional surface characterization system and the theory and technology of three-dimensional morphology creation processing, which is an urgent problem to be solved. At the same time, there are fewer studies on the three-dimensional roughness of typical imaginary surface grinding, and there is no relevant application for the research on the three-dimensional morphology and roughness index of the workpiece surface associated with grinding. Therefore, in order to build a connection between the three and save time and cost for enterprises to conduct in-depth research, it is necessary to provide a method for decomposing the surface of the grinding workpiece into an imaginary surface complex. Summary of the invention

[0005] The purpose of the present invention is to address the problem that the existing seals affect the hydraulic sealing performance due to the lack of three-dimensional surface feature design technology. A grinding three-dimensional surface decomposition method based on typical hypothetical surface features is invented. It establishes an association model between key indicators of the three-dimensional morphology of the sealing surface and processing parameters through a typical hypothetical surface model, and finally realizes the three-dimensional roughness prediction of the ground surface through numerical simulation and experimental verification.

[0006] The technical solution of the present invention is:

[0007] A grinding three-dimensional surface decomposition method based on typical added surface features is characterized in that it comprises the following steps:

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

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

[0010] Step 3: According to the model in step 2, multiple hypothetical surfaces are coupled to find the optimal coupling method.

[0011] Step 4: Calculate the empirical formula of 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: Perform similarity judgment based on the data and draw the normal vector cumulative distribution curve (NVCDC) curve.

[0014] The three-dimensional morphological parameters mentioned in this article are mainly the arithmetic mean height, skewness, and kurtosis, and their expressions are:

[0015] ①Arithmetic mean height:

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

[0017] ② Skewness:

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

[0019] ③ Kurtosis:

[0020] Different three-dimensional surface morphology characteristics can be obtained based on the calculation formula of the three-dimensional roughness key index.

[0021] The specific steps of step 2 are:

[0022] Step 2.1: For different typical hypothetical surfaces, establish a mathematical model of their height function.

[0023] For typical hypothetical surfaces, they can be divided into two categories: linear and nonlinear. Linear waviness is sinusoidal waviness, and its height function expression in a single extension direction is:

[0024] z(x)=A m sin(2πf(x))

[0025] Among them A m is the ripple amplitude, and f is the ripple frequency.

[0026] The nonlinear waviness can be divided into three categories according to the step coefficient c: sawtooth (c = 0), step (c∈(0,1)) and rectangular c = 1. The specific expressions are as follows:

[0027]

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

[0029] The sinusoidal corrugation surface has symmetry, and its three-dimensional roughness expression is:

[0030]

[0031] The three-dimensional roughness expression of step 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:

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

[0036] Step 3.2: Change the value of the step coefficient c in the coupling, draw the curve of the three-dimensional roughness parameter changing with c, and perform target optimization. The expression of 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 is the slope of each point. x is a column vector composed of the three-dimensional roughness parameter values ​​at each point.

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

[0040] In step 4, the empirical formula is expressed as:

[0041]

[0042] Where C is the correction factor, V s is the grinding wheel speed, V w is the feed speed, a p Depth of cut

[0043] The specific steps of step 5 are:

[0044] Step 5.1: Establish the grinding wheel surface topography, including the size, position and distribution density of the abrasive particles. The position of each abrasive particle is expressed by the following formula:

[0045]

[0046] Among them, G i,j is the position of each abrasive particle center in the two-dimensional unfolding plane, They represent the position 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, which are equal to the abrasive grain spacing L, and their values ​​are related to the grinding wheel structural parameter S.

[0047] Step 5.2: According to the grinding motion relationship, the abrasive particle trajectory curve is established in combination with the grinding principle. The surface morphology of the grinding wheel and the workpiece is represented by a matrix. The generated morphology of the workpiece surface can be regarded as the process of i abrasive particles on j xoz sections successively scratching it. The motion trajectory of the abrasive particle can be expressed as:

[0048]

[0049] Where R is the radius of the grinding wheel, n s is the grinding wheel speed, v w is the platform feed speed, and h(i,j) is the workpiece surface morphology 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 value z of the grinding trajectory of multiple abrasive particles at that position. ij (m,n), that is, x ij (t) = m, y ij (t) = n. The final workpiece surface height is as follows:

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

[0052] The specific steps of step 6 are:

[0053] Step 6.1: Calculate the normal vector of the three-dimensional surface. The actual surface can be regarded as irregular discrete points arranged on a plane with equal spacing and different heights. The surface morphology can be obtained by connecting the height values ​​of each position. Using the principle of determining a plane with three points, four three-dimensional planes can be constructed through point m and its surrounding four points, where point m is the common point where these planes intersect. The normal vector n of each small plane 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 By adding the four normal vectors and normalizing them, we can get the unit normal vector n=(n x ,n y ,n z ), and then the angles α, β, and γ between the normal vector and the three-dimensional coordinate axes can be obtained by inverse trigonometric functions.

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

[0057]

[0058] Step 6.3: Use λ / n as the horizontal coordinate, S λ As the ordinate, the junction point (λ / δ, S λ ) Draw the cumulative distribution curve of the normal vector. Comparing the NVCDC curves of two three-dimensional surfaces can clarify their similarity. Let the two surface distribution curves be δ and η, and use the area difference between the curve and the horizontal axis to measure their difference, as shown in the following formula:

[0059]

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

[0061] The smaller D(δ,η), the more similar the three-dimensional surfaces corresponding to the two curves are, that is, the smaller the difference in morphology. If D(δ,η)≥20%, it means that there is no relationship between the two surfaces.

[0062] The above 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 the present invention are:

[0064] The present invention starts with a typical hypothetical surface to clarify the relationship between three-dimensional roughness values ​​and surface parameters. Through single-factor grinding numerical simulation and orthogonal experiments, the optimal combination of processing parameters is selected based on the three-dimensional roughness key value as the evaluation index and actual processing verification is carried out. At the same time, the three-dimensional morphology and roughness value of the workpiece and the typical hypothetical surface are judged for similarity, 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 surface of aviation hydraulic parts sealing workpieces. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a flow chart of the present invention.

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

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

[0068] Figure 4 A schematic diagram is generated for the grinding machined surface of the present invention.

[0069] Figure 5 It is a three-dimensional topographic point cloud diagram of the imaginary coupling surface and the actual processing surface of the present invention.

[0070] Figure 6 NVCDC curve diagrams of two three-dimensional morphology point cloud diagrams of the present invention. DETAILED DESCRIPTION

[0071] The present invention will be further described below in conjunction with 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 present invention.

[0072] like Figure 1-6 shown.

[0073] A grinding 3D surface decomposition method based on typical additive surface features, such as Figure 1As shown, it includes the following steps:

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

[0075] This example requires that the surface integrity be relatively optimal, that is, the state in which Sa, Ssk, and Sku are overall minimal.

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

[0077] Step 2.1: For different typical hypothetical surfaces, establish a mathematical model of their height function.

[0078] For typical hypothetical surfaces, they can be divided into two categories: linear and nonlinear. Linear waviness is sinusoidal waviness, and its height function expression in a single extension direction is:

[0079] z(x)=A m sin(2πf(x))

[0080] Among them A m is the ripple amplitude, and f is the ripple frequency.

[0081] The nonlinear waviness can be divided into three categories according to the step coefficient c: sawtooth (c = 0), step (c∈(0,1)) and rectangular c = 1. The specific expressions are as follows:

[0082]

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

[0084] The sinusoidal corrugation surface has symmetry, and its three-dimensional roughness expression is:

[0085]

[0086] The three-dimensional roughness expression of step 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: According to the model in step 2, multiple hypothetical surfaces are coupled to find the optimal coupling method.

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

[0091] Step 3.2: Change the value of the step coefficient c in the coupling, draw the curve of the three-dimensional roughness parameter changing with c, and perform target optimization. The expression of target optimization is:

[0092] min:a T x

[0093] Where a is a column vector containing the coefficients of each key indicator in the objective function, and its value is the slope of each point. x is a column vector composed of the three-dimensional roughness parameter values ​​at each point. It can be calculated that the overall morphological characteristic parameters obtained when the step parameter is 0.1 in various combinations are the smallest.

[0094] Step 3.3: Based on the above coupled surfaces, rotate the angles of two pure waviness surfaces to find the optimal coupling mode. Figure 2 A m =1μm, f=1Hz, and three-dimensional morphology images of different coupling angles of c=0.1.

[0095] Under multiple extension directions, the overall lower three-dimensional roughness values ​​under different pure waviness are the coupling cases of step-shaped 0° (step coefficient is 0.1) + sinusoidal 90° + sawtooth 60°.

[0096] Step 4: Calculate the empirical formula of grinding parameters according to the coupling method. The expression of the empirical formula is:

[0097]

[0098] Where C is the correction factor, V s is the grinding wheel speed, V w is the feed speed, a p Depth of cut

[0099] The empirical formulas of the three process parameters of grinding obtained by calculation are:

[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 the simulation and experiment of this example 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 grinding wheel surface topography, including the size, position and distribution density of the abrasive particles. The position of each abrasive particle is expressed by the following formula:

[0104]

[0105] Among them, Gi,j is the position of each abrasive particle center in the two-dimensional unfolding plane, They represent the position of the center of the first abrasive particle on the x and y axes respectively, Δx and Δy are the offset distances of each abrasive particle relative to the previous abrasive particle on the x and y axes, which are equal to the abrasive particle spacing L. Figure 4 Shown is the resulting grinding wheel surface morphology.

[0106] Step 5.2: According to the grinding motion relationship, the abrasive particle trajectory curve is established in combination with the grinding principle. The grinding wheel and the workpiece surface morphology are represented by a matrix. The workpiece surface morphology can be regarded as a process in which i abrasive particles on j xoz sections successively scratch it. The principle is as follows: Figure 5 The motion trajectory of the abrasive particles can be expressed as:

[0107]

[0108] Where R is the radius of the grinding wheel, n s is the grinding wheel speed, v w is the platform feed speed, and h(i,j) is the workpiece surface morphology 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 value z of the grinding trajectory of multiple abrasive particles at that position. ij (m,n), that is, x ij (t) = m, y ij (t) = n. The final workpiece surface height is as follows:

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

[0111] Step 6: Perform similarity judgment based on the data and draw the normal vector cumulative distribution curve (NVCDC) curve.

[0112] Step 6.1: Calculate the normal vector of the three-dimensional surface. The actual surface can be regarded as irregular discrete points arranged on a plane with equal spacing and different heights. The surface morphology can be obtained by connecting the height values ​​of each position. Using the principle of determining a plane with three points, four three-dimensional planes can be constructed through point m and its surrounding four points, where point m is the common point where these planes intersect. The normal vector n of each small plane 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 By adding the four normal vectors and normalizing them, we can get the unit normal vector n=(n x ,n y ,n z ), and then the angles α, β, and γ between the normal vector and the three-dimensional coordinate axes can be obtained by inverse trigonometric functions.

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

[0116]

[0117] Step 6.3: Use λ / n as the horizontal coordinate, S λ As the ordinate, the junction point (λ / n,S λ )Draw the cumulative distribution curve of the normal vector. The cumulative distribution curve drawn is as follows Figure 6 As shown. Comparing the NVCDC curves of two three-dimensional surfaces can clarify their similarity. Assume that the two surface distribution curves are δ and η, and use the area difference between the curve and the horizontal axis to measure their difference, as shown in the following formula:

[0118]

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

[0120] In this example, we calculate the data D(δ,η)=6.78%.

[0121] The smaller D(δ,η), the more similar the three-dimensional surfaces corresponding to the two curves are, that is, the smaller the difference in morphology. If D(δ,η)≥20%, it means that there is no relationship between the two surfaces.

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

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features therein may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

[0124] The present invention does not involve parts that are the same as the prior art or can be implemented by using the prior art.

Claims

1. A grinding three-dimensional surface decomposition method based on typical added surface features, characterized in that it The following steps are involved: Step 1: Analyze needs and determine goals; Step 2: Establish multiple imaginary surface mathematical models; Step 3: Couple multiple hypothetical surfaces according to the model in step 2 to find the optimal coupling method; Step 4: Calculate the empirical formula of grinding parameters according to the coupling method; Step 5: Perform simulation and experiments based on the data obtained in step 4, measure and compare the data; Step 6: Perform similarity judgment based on the data and draw the normal vector cumulative distribution curve (NVCDC) curve; The three-dimensional morphological parameters are the arithmetic mean height, skewness and kurtosis, and their expressions are as follows: ①Arithmetic mean height: Where A is the area of ​​the sampling region; |z (x,y) | is the height function of each point in the region; ②Slope: Where Sq is the root mean square height, and the specific calculation expression is: ③ degree: Different three-dimensional surface morphology characteristics are finally obtained based on the calculation formula of the three-dimensional roughness key indicators.

2. The method according to claim 1, characterized in that: The method of establishing multiple imaginary surface mathematical models comprises the following steps: Step 2.1: For different typical hypothetical surfaces, establish a mathematical model of their height function; For typical hypothetical surfaces, there are two categories: linear and nonlinear. Linear waviness is sinusoidal waviness, and its height function expression in a single extension direction is: z(x)=A m sin(2πf(x)) Among them A m is the ripple amplitude, f is the ripple frequency; The nonlinear waviness is divided into three categories according to the step coefficient c: sawtooth (c = 0), step (c∈(0,1)) and rectangular c = 1. The specific expressions are as follows: Step 2.2: Calculate the three-dimensional roughness parameters of the imaginary surface based on its height function: The sinusoidal corrugation surface has symmetry, and its three-dimensional roughness expression is: Ssk=0,Sku=1.5 The three-dimensional roughness expression of step waviness is: Step 2.3: Expand the single pure waviness surface to different extension directions and calculate its surface roughness parameter function.

3. The method according to claim 1, characterized in that: The specific steps of step 3 are: Step 3.1: Couple the three pure wavinesses with different extension directions, different extension angles and different types of pure waviness hypothetical surfaces; analyze and calculate the three-dimensional roughness values ​​under different coupling modes; Step 3.2: Change the value of the step coefficient c in the coupling, draw the curve of the three-dimensional roughness parameter changing with c, and perform target optimization; the expression of 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 of each point; x is a column vector composed of the three-dimensional roughness parameter values ​​at each point; Step 3.3: Based on the above coupled surfaces, rotate the angles of two pure waviness surfaces to find the optimal coupling mode; In step 4, the empirical formula is expressed as: Where C is the correction factor, V s is the grinding wheel speed, V w is the feed speed, a p is the cutting depth.

4. The method according to claim 1, characterized in that: The specific steps of step 5 are: Step 5.1: Establish the surface morphology of the grinding wheel, including the size, position and distribution density of the abrasive particles; the position of each abrasive particle is expressed by the following formula: Among them, G i,j is the position of each abrasive particle center in the two-dimensional unfolding plane, Respectively represent the position of the center of the first abrasive grain on the x and y axes, Δx and Δy are the offset distances of each abrasive grain relative to the previous abrasive grain on the x and y axes, which are equal to the abrasive grain spacing L, and its value is related to the grinding wheel structural parameter S; Step 5.2: According to the grinding motion relationship and the grinding principle, the abrasive particle trajectory curve is established; the surface morphology of the grinding wheel and the workpiece is represented by a matrix; the generated surface morphology of the workpiece is divided into the process of i abrasive particles on j xoz sections successively scratching it; the motion trajectory of the abrasive particles is expressed as: Where R is the radius of the grinding wheel, n s is the grinding wheel speed, v w is the platform feed speed, h(i,j) is 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 value z of the grinding trajectory of multiple abrasive particles at that position ij (m,n), that is, x ij (t) = m, y ij (t) = n; the final workpiece surface height is as follows: h(m,n)=min(z ij (m,n))。 5. The method according to claim 1, characterized in that: The specific steps of step 6 are: Step 6.1: Calculate the normal vector of the three-dimensional surface. The actual surface is an irregular discrete point arranged in a plane with equal spacing and different heights. The surface morphology can be obtained by connecting the height value of each position. Using the principle of three points to determine a plane, four three-dimensional planes are constructed through point m and its surrounding four points, where point m is the common point where these planes intersect. The normal vector n of each small plane 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 of point m; add the four normal vectors and normalize them to obtain the unit normal vector n=(n x ,n y ,n z ), and then the angles α, β, and γ between the normal vector and the three-dimensional coordinate axis can be obtained by inverse trigonometric functions; Step 6.2: Select half of the three-dimensional space and divide it into n equal parts according to the angle. Then calculate the probability distribution P of the normal vectors of different subspaces, sort them from small to large, 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 horizontal coordinate, S λ As the ordinate, the junction point (λ / δ, S λ ) Draw the cumulative distribution curve of the normal vector; compare the NVCDC curves of two three-dimensional surfaces to clarify their similarity; let the two surface distribution curves be δ and η respectively, and use the area difference between the curve and the horizontal axis to measure their difference, as shown in the following formula: in and are the sequences corresponding to curves δ and η respectively; The smaller D(δ,η) is, the more similar the three-dimensional surfaces corresponding to the two curves are, that is, the smaller the morphological difference is; if D(δ,η) ≥ 20%, it means that there is no relationship between the two surfaces.

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