Method for simulating micro-convex rough surface abrasion process based on fractal theory

Abstract

The invention discloses a method for simulating a micro-convex rough surface abrasion process based on a fractal theory, and belongs to the field of software secondary development. According to the fractal dimension D, the fractal roughness G, the contour space frequency gamma and the standard deviation sigma of the rough surface, based on a W-M logic function in the fractal theory, a rough surface set model is established, a finite element method is combined, the concept of the normal elastic-plastic contact load and the friction coefficient standard deviation is introduced, and the dynamic mesh technology is utilized to calculate the fractal roughness of the rough surface. And establishing a method for simulating the micro-convex rough surface wear process based on the fractal theory.

Description

Technical Field

[0001] The invention discloses a method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, and belongs to the field of software secondary development. Background Art

[0002] At present, friction and wear are inevitable and common phenomena in the field of industrial production. With the rapid development of industry, researchers are paying more and more attention to wear and wear. The British "Jost Report" pointed out that the resources consumed by friction and wear account for 1 / 3 to 1 / 2 of the total resources in the world. Wear and tear will reduce the life of parts and even make them fail. Avoiding serious friction and wear of mechanical equipment as much as possible will greatly reduce economic losses.

[0003] The finite element model of friction and wear is generally divided into the Archard model and the energy model, and these two models are widely used to this day. In previous simulation studies, the Archard model and the energy model mostly assumed that the surface of the grinding block was an ideal surface. The new surface updated after each wear of the grinding block is different from the original surface, and the impact on the simulation results will also be greatly biased. Therefore, the fractal theory is introduced to refine the surface conditions of the grinding block calculated by each wear model, and accurately grasp the surface state of the grinding block after each wear, which can greatly improve the accuracy of the friction and wear model and greatly improve the error between the simulation data and the experimental data. Summary of the invention

[0004] 1. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that the simulation process includes the following steps:

[0005] (1) Based on the rough surface waviness, the value ranges of fractal dimension D, fractal roughness G, profile spatial frequency γ, and standard deviation σ are obtained;

[0006] (2) According to the value range of the fractal dimension D, fractal roughness G, spatial frequency γ of the profile, and standard deviation σ obtained in step (1), a geometric model of the rough surface of the micro-convex body is established by Matlab based on the WM fractal function, and the material parameters of the rough surface are set, including: Poisson's ratio v, friction coefficient μ, yield strength σ, wear coefficient K, contact stiffness Kc, and hardness H;

[0007] (3) dividing the fractal calculation area of ​​the rough surface of the micro-asperity according to the geometric model of the rough surface of the micro-asperity established in step (2);

[0008] (4) In each fractal calculation region, according to the fractal dimension D and fractal roughness G obtained in step (1), combined with the Hertz contact theory, the normal elastic contact load f of the rough surface in each fractal region is calculated respectively. e With normal plastic contact load f p ;

[0009] (5) According to the normal elastic load f in each fractal region described in step (4) e With normal plastic contact load f p , the normal load F considering the elastic-plastic deformation of the micro-convex body is calculated i And the standard deviation of the friction coefficient Δμ i , where the subscript i represents the fractal calculation area of ​​the rough surface of the micro-convex body;

[0010] (6) The material friction coefficient μ set in step (2) and the friction coefficient standard deviation Δμ obtained in step (5) are i The friction coefficient μ in the fractal calculation area of ​​the rough surface of the micro-convex body is obtained by adding i ;

[0011] (7) According to the normal load F described in step (5) i And the friction coefficient μ in step (6) i , relying on the finite element calculation method, the wear amount W in the parting area is obtained i And reconstruct the grid in the classification area through dynamic mesh;

[0012] (8) Repeat steps (4), (5), (6), (7) until the calculation iteration step N is reached, at which time the total wear amount W and surface morphology after rough surface wear are obtained;

[0013] (9) The method for calculating the total wear amount W and the surface morphology is a method for simulating the wear of the rough surface of micro-convex bodies based on fractal theory.

[0014] 2. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: the WM fractal function in step (2) is:

[0015]

[0016] Where: ρ and θ are the surface points and plane polar coordinates at height z, γ is the spatial frequency of the profile, D is the fractal dimension, which represents the irregularity and complexity of the profile at different scales, k0 is the wave number related to the sample length, M is the number of superimposed ridges, and for each index m there is an angle corresponding to the direction of the surface ripples, which are evenly spaced in the interval [0, π], and the amplitude A m As m changes, the surface becomes anisotropic and takes a random phase is uniformly distributed in [0, 2π], where all m values ​​are G is a frequency-independent height standard parameter that affects the profile height and represents the profile flatness and roughness at a unit scale.

[0017] 3. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: in step (4), the Hertz contact theory, the function is:

[0018]

[0019] Where: Where E * is the equivalent elastic modulus, E1, E2, v1, and v2 are the elastic modulus and Poisson's ratio of the contact body and the contacted body, respectively, where:

[0020]

[0021] Where a′ is the ideal contact area of ​​the micro-asperity without considering elastic contact, and r is the actual contact area of ​​the micro-asperity.

[0022] 4. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: the normal elastic contact load f in step (4) is e With normal plastic contact load f p The calculation formula is:

[0023]

[0024] f p =Ha′

[0025] Where: r′ is the ideal contact radius of the micro-convex body without considering elastic contact, and H is the hardness of the material.

[0026] 5. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: the normal load F in step (5) i And the standard deviation of the friction coefficient Δμ i The calculation formula is:

[0027]

[0028] Where: is the normal elastic load, is the normal plastic load, a′ c 、a l ′ are the minimum and maximum critical contact areas, n(a′) is the number of contact points, and the calculation formula is:

[0029]

[0030] Where: Q i The calculation formula for the standard deviation of friction force in the fractal calculation area of ​​the rough surface of the micro-convex body is:

[0031]

[0032] 6. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: the wear amount W in step (7) is i , the calculation formula is:

[0033]

[0034] Where: K is the wear coefficient, S i The sliding distance within the fractal calculation area of ​​the rough surface of the micro-asperity is calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart

[0036] Figure 2 Schematic diagram of convex body contact DETAILED DESCRIPTION

[0037] In order to make the technical scheme and technical description of the present invention clearer, the present invention will be further described in detail with reference to the accompanying drawings and embodiments.

[0038] Example:

[0039] A method for simulating the wear process of micro-convex rough surface based on fractal theory, the flow chart is as follows Figure 1 As shown, it specifically includes the following steps:

[0040] (1) Based on the surface waviness of the material to be measured, the value ranges of the fractal dimension D, fractal roughness G, profile spatial frequency γ, and standard deviation σ of the material are obtained;

[0041] (2) The fractal dimension D, fractal roughness G, profile spatial frequency γ and standard deviation σ of the material are assigned to the WM fractal function model established in Matlab, and a rough surface geometric model of a micro-convex body is established as the grinding block, and another rough surface geometric model of a micro-convex body is established as the counter grinding block. The two grinding blocks are set to contact. The schematic diagram of the micro-convex contact is shown in Figure 2 As shown, the calculation grid is divided;

[0042] (3) The geometric model of the rough surface of the micro-convex body is imported into Abaqus, and the material parameters and boundary conditions of the rough surface are set. The contact type between the two grinding blocks is friction contact, and the normal contact behavior and the tangential contact behavior are defined by penalty functions to improve convergence;

[0043] (4) The bottom surface of the grinding block is fixed, the grinding block reciprocates along the x-axis direction, and a reference point is set at the top of the grinding block, and a concentrated load perpendicular to the grinding surface is applied to the reference point;

[0044] (5) The contact surfaces of the counter abrasive block and the abraded block are defined as the main surface and the secondary surface respectively, so as to achieve the purpose of simultaneous wear of the two abrasive blocks;

[0045] (6) Enable ALE dynamic mesh technology, set the dynamic mesh control area, set the ALE adaptive mesh control frequency to 1, and set the number of mesh sweeps to 3 for each incremental step to improve the accuracy of mesh updates;

[0046] (7) During the sliding process between the two grinding blocks, the contact pressure and relative sliding distance of each node in the contact surface are calculated using finite element method. In each calculation sub-step, the program control calculates the normal elastic contact load of the rough surface in each fractal area based on the Hertz contact theory. Plastic contact load with normal Normal elastic contact load calculated for each fractal region Plastic contact load with normal Calculate the normal load F considering the elastic-plastic deformation of the micro-convex body in the fractal region i And the standard deviation of the friction coefficient Δμ i , the standard deviation of the friction coefficient in each fractal region Δμ i Adding the friction coefficient of the material to obtain the friction coefficient μ in the fractal calculation area of ​​the rough surface of the micro-convex body i , and the normal load F is obtained i And the friction coefficient μ i The wear amount W in the parting area is calculated i The mesh in the parting area is reconstructed by moving the mesh, and the wear amounts of all sub-steps in the i-th iteration cycle are superimposed to obtain the i-th iteration wear amount. In order to improve the calculation efficiency, when the surface mesh moves to the lower mesh, the change is the single iteration wear amount multiplied by the expansion coefficient μ; the node position of each incremental step is adjusted by the arbitrary Lagrangian Euler technique.

[0047] (8) Through the above steps, the wear amount of the two rough surfaces and the surface morphology changes that are closer to the actual change process are simulated.

Claims

1. A method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory, characterized in that: The simulation process includes the following steps: (1) Based on the rough surface waviness, the value ranges of fractal dimension D, fractal roughness G, profile spatial frequency γ, and standard deviation σ are obtained; (2) According to the value range of the fractal dimension D, fractal roughness G, spatial frequency γ of the profile, and standard deviation σ obtained in step (1), a geometric model of the rough surface of the micro-convex body is established by Matlab based on the WM fractal function, and the material parameters of the rough surface are set, including: Poisson's ratio v, material friction coefficient μ, yield strength σ, wear coefficient K, contact stiffness Kc, and hardness H; (3) dividing the fractal calculation area of ​​the rough surface of the micro-asperity according to the geometric model of the rough surface of the micro-asperity established in step (2); (4) In each fractal calculation region, according to the fractal dimension D and fractal roughness G obtained in step (1), combined with the Hertz contact theory, the normal elastic contact load f of the rough surface in each fractal region is calculated respectively. e With normal plastic contact load f p ; (5) According to the normal elastic load f in each fractal region described in step (4) e With normal plastic contact load f p , the normal load F considering the elastic-plastic deformation of the micro-convex body is calculated i And the standard deviation of the friction coefficient Δμ i , where the subscript i represents the fractal calculation area of ​​the rough surface of the micro-convex body; (6) The material friction coefficient μ set in step (2) and the friction coefficient standard deviation Δμ obtained in step (5) are i The friction coefficient μ in the fractal calculation area of ​​the rough surface of the micro-convex body is obtained by adding i ; (7) According to the normal load F described in step (5) i And the friction coefficient μ in step (6) i , relying on the finite element calculation method, the wear amount W in the parting area is obtained i And reconstruct the grid in the classification area through dynamic mesh; (8) Repeat steps (4), (5), (6), (7) until the calculation iteration step N is reached, at which time the total wear amount W and surface morphology after rough surface wear are obtained; (9) The method for calculating the total wear amount W and the surface morphology is a method for simulating the wear of the rough surface of micro-convex bodies based on fractal theory.

2. The method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory according to claim 1, characterized in that: The WM fractal function in step (2) is: Where: ρ and θ are the surface points and plane polar coordinates at height z, γ is the spatial frequency of the profile, D is the fractal dimension, which represents the irregularity and complexity of the profile at different scales, k0 is the wave number related to the sample length, M is the number of superimposed ridges, and for each index m there is an angle corresponding to the direction of the surface ripples, which are evenly spaced in the interval [0, π], and the amplitude A m As m changes, the surface becomes anisotropic and takes a random phase is uniformly distributed in [0, 2π], where all m values ​​are G is a frequency-independent height standard parameter that affects the profile height and represents the profile flatness and roughness at a unit scale.

3. The method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory according to claim 1, characterized in that: In step (4), the Hertz contact theory function is: Where: Where E * is the equivalent elastic modulus, E1, E2, v1, and v2 are the elastic modulus and Poisson's ratio of the contact body and the contacted body, respectively, where: Where a′ is the ideal contact area of ​​the micro-asperity without considering elastic contact, and r is the actual contact area of ​​the micro-asperity.

4. The method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory according to claim 1, characterized in that: The normal elastic contact load f in step (4) is e With normal plastic contact load f p The calculation formula is: f p =Ha′ Where: r′ is the ideal contact radius of the micro-convex body without considering elastic contact, and H is the hardness of the material.

5. The method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory according to claim 1, characterized in that: Step (5) The normal load F i And the standard deviation of the friction coefficient Δμ i The calculation formula is: Where: is the normal elastic load, is the normal plastic load, a′ c 、a l ′ are the minimum and maximum critical contact areas, n(a′) is the number of contact points, and the calculation formula is: Where: Q i The calculation formula for the standard deviation of friction force in the fractal calculation area of ​​the rough surface of the micro-convex body is:

6. The method for simulating the wear process of a rough surface of a micro-convex body based on fractal theory according to claim 1, characterized in that: The wear amount W in step (7) i , the calculation formula is: Where: K is the wear coefficient, S i The sliding distance within the fractal calculation area of ​​the rough surface of the micro-asperity is calculated.

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