A rough surface morphology generation method considering contact stress deformation performance requirements

Abstract

The application discloses a rough surface morphology generation method considering contact stress deformation performance requirements. The application comprises the following steps: firstly, according to the contact stress deformation performance requirements of the rough surface morphology, the target stress deformation curve and the height value range of the rough surface morphology are determined; then the number of control points of the Bezier curve is determined and the abscissa values of all the control points are determined; then the ordinate values of all the control points are taken as optimization variables, the maximum deviation between the contact stress deformation curve and the target stress deformation curve of the rough surface morphology is minimized as an optimization target, an optimization model of the rough surface morphology is constructed and solved, the optimal ordinate values of all the control points are obtained, and then the height probability density distribution of the rough surface morphology is obtained, so that the rough surface morphology is generated. The application provides a theoretical guidance for improving the contact deformation performance between product parts by optimizing the height probability density distribution of the rough surface morphology at the microscale.

Description

Technical Field

[0001] This invention relates to a method for generating rough surface morphology at the microscale, specifically a method for generating rough surface morphology that takes into account the requirements of contact stress deformation performance. Background Technology

[0002] The deformation caused by the contact between the rough surface morphologies of product parts has a significant impact on product performance, such as friction, heat transfer, electrical conductivity, sealing, and assembly accuracy. To ensure the final product meets given performance requirements, it is necessary to generate the rough surface morphologies of product parts during the design phase, ensuring that the parts meet the given contact stress deformation requirements.

[0003] The rough surface morphology of product parts is characterized by its microscopic and random nature. Most existing studies use four parameters—mean, root mean square, skewness, and kurtosis—to describe the probability density distribution of the rough surface height, and generate the rough surface morphology by designing the values ​​of these four parameters. However, when the values ​​of skewness and kurtosis are large, existing methods based on Johnson transform systems using these four height parameters cannot generate rough surface morphologies that satisfy these skewness and kurtosis values. To address this problem, a more universal method for describing the probability density distribution of the rough surface height and for generating rough surface morphologies is proposed, which has significant practical implications. Summary of the Invention

[0004] To address the problems and needs in the background technology, this invention proposes a method for generating rough surface morphology that considers the requirements of contact stress deformation performance. This method uses a Bézier curve to describe the height probability density distribution of the rough surface morphology, and uses the ordinates of all control points of the Bézier curve describing the height probability density distribution as optimization variables. The optimization objective is to minimize the maximum deviation between the contact stress deformation curve of the rough surface morphology and the given target stress deformation curve, thus establishing an optimization model. By solving the established optimization model, the optimal values ​​of the coordinates of the control points of the Bézier curve describing the height probability density distribution of the rough surface morphology are obtained, generating the corresponding Bézier curve to obtain the height probability density distribution of the rough surface morphology, and directly using this height probability density distribution to generate the rough surface morphology.

[0005] The technical solution of the present invention includes the following steps:

[0006] I. A method for generating rough surface morphology considering contact stress deformation performance requirements

[0007] Step 1: Determine the target stress-deformation curve F of the rough surface morphology based on the contact stress-deformation performance requirements. obj(d) and the range of values ​​for the height of the rough surface morphology;

[0008] Step 2: Determine the number N of control points for the Bézier curve p(t). h The abscissa values ​​of all control points in the Bézier curve p(t) are determined based on the range of height values ​​of the rough surface morphology.

[0009] Step 3: Using the ordinate values ​​of all control points of the Bézier curve p(t) as optimization variables, and the contact stress-deformation curve describing the rough surface morphology based on the Bézier curve p(t) with a high probability density distribution, and the given target stress-deformation curve F... obj The optimization objective is to minimize the maximum deviation between (d) and construct an optimization model for rough surface morphology.

[0010] Step 4: Use the particle swarm optimization algorithm to solve the optimization model of the rough surface morphology and obtain the optimal ordinate values ​​of all control points in the Bézier curve p(t);

[0011] Step 5: Based on the x-coordinate values ​​of all control points in the Bézier curve p(t) and the corresponding optimal y-coordinate values, generate an initial Bézier curve p′(t). Then, linearly scale the y-coordinate values ​​of the initial Bézier curve p′(t) to obtain a scaled Bézier curve p″(t). Use the scaled Bézier curve p″(t) as the height probability density distribution p(h) of the rough surface morphology to generate the rough surface morphology.

[0012] The formula for the Bézier curve p(t) is as follows:

[0013]

[0014] Among them, B i Let represent the i-th control point of the Bézier curve p(t), and t represent the parametric coordinates of the Bézier curve. In step three, the formula for the optimization model minimizeJ(p(t)) of the rough surface morphology is as follows:

[0015] minimizeJ(p(t))=max(|F obj (d)-F(d, p(t))|)

[0016] The optimized model satisfies the following constraints:

[0017] p(t)≥0

[0018]

[0019] Where max() represents the maximum value operation, || represents the absolute value operation, F(d, p(t)) represents the contact force deformation curve of the rough surface morphology corresponding to the Bézier curve p(t), d represents the displacement of the rigid plane relative to the rough surface morphology caused by the external force F, and h min h max These are the minimum height and maximum height of the rough surface, respectively.

[0020] The contact force deformation curve F(d, p(t)) of the rough surface morphology corresponding to the Bézier curve p(t) satisfies the following four formulas:

[0021]

[0022]

[0023]

[0024]

[0025] Where x and y represent the two positional coordinates of the rough surface morphology, h(x) represents the height of the undeformed rough surface morphology, u(x) represents the deformation of the rough surface morphology, F represents the external force applied to the rigid plane, d represents the displacement of the rigid plane relative to the rough surface morphology caused by the external force F, and p con (x) and p con (y) represents the contact pressure between the rigid plane and the rough surface at coordinates x and y, respectively; v represents the Poisson's ratio of the rough surface material; E represents the Young's modulus of the rough surface material; ||2 represents the 2-norm operation; h max ε represents the maximum height of the rough surface, H represents the material hardness of the rough surface morphology, and ε represents the rough surface morphology region where no contact occurs. This represents the rough surface morphology region where contact has occurred. Represents the total region and satisfies

[0026] In step four, the particle position vector z of the particle swarm optimization algorithm is composed of the ordinate values ​​of all control points in the Bézier curve p(t), satisfying... And set p i ∈[0,1]; After obtaining the particle position vector z each time, firstly, a corresponding Bézier curve p(t) is generated based on the ordinate value of the control point corresponding to the particle position vector z. Then, the ordinate value of the generated Bézier curve p(t) is linearly scaled so that the scaled Bézier curve p(t) satisfies h min h maxThese are the minimum height and maximum height of the rough surface, respectively.

[0027] In step five, the scaled Bézier curve p″(t) satisfies h min h max These are the minimum height and maximum height of the rough surface, respectively.

[0028] II. A computer device

[0029] The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method.

[0030] III. A computer-readable storage medium

[0031] A computer program is stored on a computer-readable storage medium, which, when executed by a processor, implements the steps of the method.

[0032] The beneficial effects of this invention are:

[0033] Compared to the traditional method of describing the height probability density distribution of rough surface morphology based on height mean, root mean square, skewness, and kurtosis, the method of directly describing the height probability density distribution of rough surface morphology using Bézier curves is simpler and easier to understand. Using the coordinates of the control points of the Bézier curve as optimization variables allows for more precise design and adjustment of the height probability density distribution of rough surface morphology.

[0034] The height probability density distribution of rough surface morphology is directly described by Bézier curves, and rough surface morphology that satisfies the height probability density distribution is directly generated based on the height probability density distribution curve. This overcomes the shortcomings of traditional methods that use the mean, root mean square, skewness and kurtosis of height to generate rough surface morphology based on Johnson transform system, which cannot generate rough surface morphology that satisfies large skewness and large kurtosis values.

[0035] The problem of designing the height probability density distribution of rough surface morphology is constructed into an optimization problem, which facilitates obtaining the optimal design result of the height probability density distribution of rough surface morphology that meets the requirements of contact stress deformation performance, and promotes the automation of the rough surface morphology generation process. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a rigid plane pressing against a rough surface morphology.

[0037] Figure 2 This is a flowchart of the method of the present invention.

[0038] Figure 3 These are schematic diagrams of the force-deformation curves of different types of targets in embodiments of the present invention; wherein (a) is a schematic diagram of the force-deformation curve of the first target, (b) is a schematic diagram of the force-deformation curve of the second target, (c) is a schematic diagram of the force-deformation curve of the third target, and (d) is a schematic diagram of the force-deformation curve of the fourth target.

[0039] Figure 4 This is a schematic diagram of the height probability density distribution obtained by the method of the present invention for different types of target deformation curves in an embodiment of the present invention; wherein (a) is the height probability density distribution obtained based on the first target deformation curve, (b) is the height probability density distribution obtained based on the second target deformation curve, (c) is the height probability density distribution obtained based on the third target deformation curve, and (d) is the height probability density distribution obtained based on the fourth target deformation curve.

[0040] Figure 5 These are comparison diagrams between different types of target stress-deformation curves in embodiments of the present invention and contact stress-deformation curves of rough surface morphology generated based on the height probability density distribution obtained by the method of the present invention, wherein (a) is a comparison diagram obtained based on the first target stress-deformation curve, (b) is a comparison diagram obtained based on the second target stress-deformation curve, (c) is a comparison diagram obtained based on the third target stress-deformation curve, and (d) is a comparison diagram obtained based on the fourth target stress-deformation curve.

[0041] Figure 6 These are comparison diagrams of the height probability density distributions obtained by the method of this invention and the traditional method based on the height parameter for different types of target stress deformation curves in this embodiment of the invention; wherein (a) is a comparison diagram obtained based on the first target stress deformation curve, (b) is a comparison diagram obtained based on the second target stress deformation curve, (c) is a comparison diagram obtained based on the third target stress deformation curve, and (d) is a comparison diagram obtained based on the fourth target stress deformation curve.

[0042] Figure 7 These are comparison diagrams of different types of target stress-deformation curves in embodiments of the present invention, specifically the contact stress-deformation curve of a rough surface morphology generated based on the high probability density distribution obtained by the method of the present invention and the contact stress-deformation curve of a rough surface morphology generated based on the high probability density distribution obtained by the conventional method. Among them, (a) is a comparison diagram obtained based on the first target stress-deformation curve, (b) is a comparison diagram obtained based on the second target stress-deformation curve, (c) is a comparison diagram obtained based on the third target stress-deformation curve, and (d) is a comparison diagram obtained based on the fourth target stress-deformation curve. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0044] The rough surface morphology generation method proposed in this invention, which considers the contact stress-deformation performance requirements, includes: determining the target stress-deformation curve F of the rough surface morphology based on the contact stress-deformation performance requirements. obj (d) Set the range of values ​​for the height of the rough surface morphology [h] min h max Set the number of control points N for the Bézier curve p(t). h and control point B i x-coordinate h i The values ​​of are determined, the optimization model minimizeJ(p(t)) is constructed, and the control points B of the Bézier curve p(t) are obtained by solving the optimization model minimizeJ(p(t)) using the particle swarm optimization algorithm. i The ordinate p i The value of is selected, and the Bézier curve p(t) is generated to obtain the high probability density distribution p(h) of the rough surface morphology. The rough surface morphology is generated based on p(h).

[0045] like Figure 2 As shown, Figure 2 The flowchart above is a flowchart of the rough surface morphology generation method proposed in this invention, which considers the requirements of contact stress deformation performance. This invention includes the following steps:

[0046] Step 1: Determine the target stress-deformation curve F of the rough surface morphology based on the contact stress-deformation performance requirements. obj (d) and the range of values ​​for the height of the rough surface morphology [h] min h max ],in max(d) is the target force-deformation curve F. obj The maximum value of the x-coordinate of (d), h min h max These are the minimum height and maximum height of the rough surface, respectively; where, for example... Figure 1 As shown, the target force-deformation curve F of the rough surface morphology obj (d) describes the relationship between the applied external force F and the displacement d of the rigid plane relative to the rough surface caused by the external force when a rigid plane presses against a rough surface, which is input as a known quantity. Embodiments of the present invention use four different types of curves as the target force-deformation curve F. obj (d), such as Figure 3 of (a), Figure 3 (b) Figure 3 (c) and Figure 3 As shown in (d).

[0047] The four different types of target stress-deformation curves used in this embodiment are defined by the formulas (a)-(d) shown below, and are respectively denoted as the first to fourth target stress-deformation curves, where H is the material hardness and A is the surface area of ​​the matrix to which the rough surface morphology belongs.

[0048]

[0049]

[0050]

[0051]

[0052] The rough surface morphology used in this embodiment is established on a rectangular plane with A = 100 μm × 100 μm. The material properties of this rough surface morphology are shown in Table 1.

[0053] Table 1 shows the material properties of the rough surface morphology in this embodiment.

[0054]

[0055] Step 2: Use the Bézier curve p(t) to describe the height probability density distribution p(h) of the rough surface morphology, and determine the number N of control points for the Bézier curve p(t). h Based on the height range of the rough surface morphology determined in step one [h], min h max Determine the x-coordinate values ​​of all control points in the Bézier curve p(t), where the i-th control point B... i Satisfy B i =[h i p i ], h i p i These are its x-coordinate and y-coordinate values, respectively, with the x-coordinate value being h. i satisfy

[0056] In step two, according to B i The formula for generating the Bézier curve p(t) is as follows:

[0057]

[0058] Where t represents the parametric coordinates of the Bézier curve.

[0059] according to Figure 3 The range of values ​​for d shown is given. The range of values ​​for the height of the rough surface morphology is set to [-3μm, 3μm]. The number of control points N for the Bézier curve p(t) is set. hIf the value is 35, then control point B i =[h i p i x-coordinate

[0060] Step 3: Calculate the ordinate values ​​p of all control points of the Bézier curve p(t) describing the probability density distribution of the rough surface morphology. i As optimization variables, the contact stress-deformation curve of the rough surface morphology, which is described by the Bezier curve p(t) based on the probability density distribution, and the given target stress-deformation curve F are used. obj The optimization objective is to minimize the maximum deviation between (d) and construct an optimization model for rough surface morphology.

[0061] In step three, the formula for the optimization model of rough surface morphology, minimizeJ(p(t)), is as follows:

[0062] minimizeJ(p(t))=max(|F obj (d)-F(d, p(t))|)

[0063] In the optimization model, F(d, p(t)) describes the relationship between the applied external force F and the displacement d of the rigid plane relative to the rough surface morphology caused by the external force when a rigid plane presses against a rough surface morphology that satisfies the height probability density distribution described by p(t).

[0064] The optimized model satisfies the following constraints:

[0065] p(t)≥0

[0066]

[0067] Where max() represents the maximum value operation, || represents the absolute value operation, and F(d, p(t)) represents the contact force deformation curve of the rough surface morphology corresponding to the Bézier curve p(t).

[0068] The contact force-deformation curve F(d, p(t)) of the rough surface morphology corresponding to the Bézier curve p(t) satisfies the following four formulas:

[0069]

[0070]

[0071]

[0072]

[0073] Where x and y represent the two positional coordinates of the rough surface morphology, h(x) represents the height of the undeformed rough surface morphology, u(x) represents the deformation of the rough surface morphology, F represents the external force applied to the rigid plane, d represents the displacement of the rigid plane relative to the rough surface morphology caused by the external force F, and p con (x) and p con (y) represents the contact pressure between the rigid plane and the rough surface at coordinates x and y, respectively; v represents the Poisson's ratio of the rough surface material; E represents the Young's modulus of the rough surface material; ||2| represents the 2-norm operation; H represents the hardness of the rough surface material; and ε represents the rough surface region where no contact occurs. This represents the rough surface morphology region where contact has occurred. Represents the total region and satisfies

[0074] Step 4: Use the particle swarm optimization algorithm to solve the optimization model of the rough surface morphology, minimizeJ(p(t)), and obtain the optimal ordinate values ​​of all control points in the Bézier curve p(t) that describes the height probability density distribution p(h) of the rough surface morphology.

[0075] In step four, the particle position vector z of the particle swarm optimization algorithm consists of the ordinate values ​​of all control points in the Bézier curve p(t), satisfying... And set p i ∈[0,1]; After obtaining the particle position vector z each time, firstly, a corresponding Bézier curve p(t) is generated based on the ordinate value of the control point corresponding to the particle position vector z. Then, the ordinate value of the generated Bézier curve p(t) is linearly scaled so that the scaled Bézier curve p(t) satisfies

[0076] Step 5: Based on the x-coordinate values ​​of all control points in the Bézier curve p(t) determined in Step 2 and the optimal y-coordinate values ​​of the corresponding control points in the Bézier curve p(t) obtained in Step 4, an initial Bézier curve p′(t) is generated. Then, the y-coordinate values ​​of the initial Bézier curve p′(t) are linearly scaled to obtain the scaled Bézier curve p″(t). The scaled Bézier curve p″(t) is used as the height probability density distribution p(h) of the rough surface morphology, as follows... Figure 4 of (a), Figure 4 (b) Figure 4 (c) and Figure 4 As shown in (d), this generates a rough surface morphology.

[0077] In step five, the scaled Bézier curve p″(t) satisfies

[0078] Figure 5 This is a comparison diagram between the target stress-deformation curve and the contact stress-deformation curve of the rough surface morphology generated based on the height probability density distribution obtained by the method of this invention. Figure 5 of (a), Figure 5 (b) Figure 5 (c) and Figure 5 As can be seen from (d), for the four different types of target stress-deformation curves, the deviation between the contact stress-deformation curve of the rough surface morphology generated based on the height probability density distribution obtained by the present invention and the corresponding target stress-deformation curve is very small, which verifies the effectiveness of the method proposed in the present invention.

[0079] For four different types of target stress-deformation curves, the proposed method of using Bézier curves to describe the height probability density distribution of rough surface morphology and the traditional method of using height mean, root mean square, skewness, and kurtosis to describe the height probability density distribution of rough surface morphology were respectively used. The control points of the corresponding Bézier curves and the corresponding height mean, root mean square, skewness, and kurtosis values ​​were obtained respectively. Then, the corresponding height probability density distribution curve was generated as the design result of the height probability density distribution p(h) of the rough surface morphology. A comparison of the height probability density distribution p(h) obtained by the two methods is provided. Figure 6 of (a), Figure 6 (b) Figure 6 (c) and Figure 6 As shown in (d), a comparison is made between the contact force-deformation curve of the rough surface morphology generated based on the height probability density distribution p(h) obtained by the two methods described above and the target force-deformation curve. Figure 7 As shown.

[0080] observe Figure 6 and Figure 7 It can be seen that for the target stress-deformation curves defined by formulas (a)-(c), the solution results of the method of this invention and the traditional method are almost identical. However, for the target stress-deformation curve defined by formula (d), the traditional method cannot obtain the height probability density distribution of the rough surface morphology consistent with the target stress-deformation curve, while the method of this invention can still obtain good results. Therefore, considering the requirements of contact stress-deformation performance for rough surface morphology, compared with the traditional method of using height mean, root mean square, skewness, and kurtosis to describe the height probability density distribution of rough surface morphology, the method of using Bézier curves to describe the height probability density distribution of rough surface morphology proposed in this invention has a wider range of applications.

[0081] The above embodiments are merely specific examples of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the present invention, and should all be covered within the scope of protection of the present invention.

Claims

1. A method for generating rough surface morphology considering contact stress deformation performance requirements, characterized in that, Includes the following steps: Step 1: Based on the contact stress-deformation performance requirements of the rough surface morphology, determine the target stress-deformation curve F for the rough surface morphology. obj (d) and the range of values ​​for the height of the rough surface morphology; Step 2: Determine the number N of control points for the Bézier curve p(t). h The abscissa values ​​of all control points in the Bézier curve p(t) are determined based on the range of height values ​​of the rough surface morphology. Step 3: Using the ordinate values ​​of all control points of the Bézier curve p(t) as optimization variables, and the contact stress-deformation curve describing the rough surface morphology based on the Bézier curve p(t) with a high probability density distribution, and the given target stress-deformation curve F... obj The optimization objective is to minimize the maximum deviation between (d) and construct an optimization model for the rough surface morphology. Step 4: Use the particle swarm optimization algorithm to solve the optimization model of the rough surface morphology and obtain the optimal ordinate values ​​of all control points in the Bézier curve p(t); Step 5: Based on the x-coordinate values ​​of all control points in the Bézier curve p(t) and the corresponding optimal y-coordinate values, generate an initial Bézier curve p′(t). Then, linearly scale the y-coordinate values ​​of the initial Bézier curve p′(t) to obtain a scaled Bézier curve p″(t). Use the scaled Bézier curve p″(t) as the height probability density distribution p(h) of the rough surface morphology to generate the rough surface morphology.

2. The method for generating rough surface morphology considering contact stress deformation performance requirements according to claim 1, characterized in that, The formula for the Bézier curve p(t) is as follows: Among them, B i Let p(t) represent the i-th control point of the Bézier curve p(t), and t represent the parametric coordinates of the Bézier curve.

3. The method for generating rough surface morphology considering contact stress deformation performance requirements according to claim 1, characterized in that, In step three, the formula for the optimization model of rough surface morphology, minimize J(p(t)), is as follows: minimize J(p(t))=max(|F obj (d)-F(d,p(t))|) The optimized model satisfies the following constraints: p(t)≥0 Where max() represents the maximum value operation, || represents the absolute value operation, F(d,p(t)) represents the contact force deformation curve of the rough surface morphology corresponding to the Bézier curve p(t), d represents the displacement of the rigid plane relative to the rough surface morphology caused by the external force F, and h min ,h max These are the minimum height and maximum height of the rough surface, respectively.

4. The method for generating a rough surface morphology considering contact stress deformation performance requirements according to claim 3, characterized in that, The contact force deformation curve F(d,p(t)) of the rough surface morphology corresponding to the Bézier curve p(t) satisfies the following four formulas: Where x and y represent the coordinates of two positions of the rough surface morphology, h(x) represents the height of the undeformed rough surface morphology, u(x) represents the deformation of the rough surface morphology, F represents the external force applied to the rigid plane, d represents the displacement of the rigid plane relative to the rough surface morphology caused by the external force F, and p con (x) and p con (y) represents the contact pressure between the rigid plane and the rough surface at coordinates x and y, respectively; v represents the Poisson's ratio of the rough surface material; E represents the Young's modulus of the rough surface material; ‖‖2 indicates the 2-norm operation; h max ε represents the maximum height of the rough surface, H represents the material hardness of the rough surface morphology, and ε represents the rough surface morphology region where no contact occurs. This represents the rough surface morphology region where contact has occurred. Represents the total region and satisfies 5. The method for generating a rough surface morphology considering contact stress deformation performance requirements according to claim 1, characterized in that, In step four, the particle position vector z of the particle swarm optimization algorithm is composed of the ordinate values ​​of all control points in the Bézier curve p(t), satisfying... And set p i ∈[0,1]; After obtaining the particle position vector z each time, firstly, a corresponding Bézier curve p(t) is generated based on the ordinate value of the control point corresponding to the particle position vector z. Then, the ordinate value of the generated Bézier curve p(t) is linearly scaled so that the scaled Bézier curve p(t) satisfies h min h max These are the minimum height and maximum height of the rough surface, respectively.

6. The method for generating a rough surface morphology considering contact stress deformation performance requirements according to claim 1, characterized in that, In step five, the scaled Bézier curve p″(t) satisfies h min ,h max These are the minimum height and maximum height of the rough surface, respectively.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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