A method for forming a surface with anisotropic friction properties by numerically controlled milling.

Abstract

A method for forming a surface having anisotropic friction properties by numerically controlled milling is disclosed. [Solution] In this method, machining simulations of milling are performed for combinations of multiple tool orientation parameters, and a height matrix is ​​constructed from the obtained three-dimensional point cloud data. Then, the contact region is extracted, the surface gradient and gradient amplitude values ​​are calculated, and the sets of gradient amplitude values ​​at the contact leading edge during forward and reverse sliding are extracted. Furthermore, the coefficient of friction for forward and reverse sliding is calculated, and an anisotropy evaluation index is calculated based on these. In addition, an anisotropy evaluation index heat map is created, and a ridge line indicating the direction of sensitivity to changes in the anisotropy evaluation index is generated, thereby enabling quantitative prediction and evaluation of the surface friction behavior. This makes it possible to inversely calculate tool orientation parameters under predetermined cutting parameters based on the anisotropy requirements related to the surface micromorphology. By performing milling according to the parameter combination obtained by this method and predetermined cutting parameters, a viscoelastic material workpiece that satisfies the requirements for friction characteristics or sealing function according to the sliding direction can be obtained. The present invention is useful in satisfying the requirements for friction characteristics and sealing function according to the sliding direction in a seal pair.

Description

Technical Field

[0001] The present invention relates to the technical fields of surface friction and milling, and particularly to a method for forming a surface having anisotropic friction characteristics by numerical control milling.

Background Art

[0002] In the manufacture of precision machinery, the shape of the workpiece surface formed by milling not only affects the fitting accuracy of parts, but also directly determines the friction performance of the contact interface. In core parts such as the fitting surface of a cylinder-piston, the seal pair of a shaft sleeve, and various precision seal connection structures, the requirement for the directionality of surface friction performance is strict. Along the assembly direction, it is necessary to have the characteristics of low frictional resistance and easy assembly. On the other hand, along the vibration direction during the operation of the device and the part removal direction, it is necessary to achieve anti-loosening and vibration resistance due to high friction damping. Thereby, it is possible to reduce the difficulty of the assembly operation, reduce the damage to the seal member structure caused by the assembly force, prevent loosening or displacement of parts due to vibration under operating conditions, and thus maintain the uniformity of the contact pressure distribution of the seal pair, avoid leakage of the sealing medium, and ensure the sealing performance of the seal interface and the long-term stability of the structure.

[0003] Existing methods for optimizing milling process parameters often take reducing surface roughness as a single goal and ignore the complex influence of the gradient distribution of the surface texture on the friction behavior. In the conventional surface shape evaluation criteria, it is difficult to accurately describe the contribution of the complex three-dimensional shape formed by the interaction of parameters such as the feed rate and cutting interval of milling to the frictional resistance of viscoelastic materials in each direction. Therefore, the gradient of the milling shape cannot represent the control effect on the contact pressure distribution of the seal pair and the dynamic friction characteristics of the cylinder fitting surface. At present, there is also a lack of a systematic method for directly predicting the macroscopic friction coefficient in each direction starting from the gradient of the microscopic surface shape and inversely calculating the processing process parameters for realizing the desired friction characteristics based on this.

[0004] Therefore, developing a method that can quantitatively express the anisotropy of friction characteristics starting from the microscopic shape of the surface and inversely calculate process parameters is of great significance in realizing an integrated closed-loop control of "design-manufacturing-performance" for high-performance surfaces, and in particular in meeting the requirements for friction characteristics and sealing function according to the sliding direction in cylinder / piston and shaft sleeve seal pairs. [Overview of the project]

[0005] In view of the shortcomings of the prior art, the object of the present invention is to provide a method for forming a surface having anisotropic friction properties by numerically controlled milling.

[0006] The technical means employed in this invention are as follows:

[0007] The method for forming a surface having anisotropic friction properties by numerically controlled milling according to the present invention specifically includes the following steps.

[0008] S1: For each of the predetermined cutting parameters and multiple parameter combinations, a milling simulation is performed on the simulation workpiece, and three-dimensional point cloud data showing the shape of the milled surface of the simulation workpiece after the machining simulation is output. The parameter combination consists of a lateral tilt angle α and a forward tilt angle β. The coordinates of each grid point in the three-dimensional point cloud data are represented in a three-dimensional Cartesian coordinate system, in which the coordinate axes X and Y are located within the milled surface of the simulation workpiece, the direction of the coordinate axis X is aligned with the feed direction, the direction of the coordinate axis Y is aligned with the cutting row spacing direction, and the coordinate axis Z of the three-dimensional Cartesian coordinate system is aligned with the height direction.

[0009] S2: Based on the height data Zgrid(xi,yj) of each grid point (i,j) on the milled surface of the simulated workpiece, a height matrix Zgrid is constructed that records the height data of all grid points on the milled surface of the simulated workpiece. Here, xi and yj are the X and Y coordinates of the grid point (i,j), respectively.

[0010] S3: Based on the shape of the milled surface, the contact area that comes into contact with the contact member is extracted.

[0011] S4: Based on the height matrix Zgrid, the surface gradient and gradient amplitude values ​​corresponding to each grid point are calculated, and a surface gradient field is constructed based on the surface gradients of all grid points.

[0012] S5: Extract the set of gradient amplitude values ​​at the contact leading edge during forward sliding and the set of gradient amplitude values ​​at the contact leading edge during reverse sliding.

[0013] S6: Calculate the coefficient of friction for sliding in the forward direction and the coefficient of friction for sliding in the reverse direction.

[0014] S7: The anisotropy evaluation index Q is the percentage obtained by dividing the absolute value of the difference between the forward sliding friction coefficient and the reverse sliding friction coefficient by a reference value. The reference value is either the forward sliding friction coefficient or the reverse sliding friction coefficient, or the smaller of the two.

[0015] S8: Based on the anisotropy evaluation index Q obtained for each of the predetermined cutting parameters and the plurality of parameter combinations, the parameter combination that maximizes the anisotropy evaluation index Q is determined as the optimal parameter combination.

[0016] S9: Milling is performed according to the predetermined cutting parameters and the optimal parameter combination.

[0017] Preferably, the cutting parameters include spindle speed, feed rate per tooth, cutting row interval, and cutting depth.

[0018] Preferably, the specific process for extracting the contact area is based on the highest point height Zmax and the displacement distance δ in the shape of the milled surface of the simulated workpiece, using the formula

number

[0019] Preferably, the element values ​​corresponding to each grid point (i,j) on the milled surface are given by the formula

number

[0020] Preferably, step S4 uses the central difference method to obtain the partial derivatives of the height of the grid point (i,j) with respect to the coordinate axes X and Y, based on the height matrix Zgrid, using the equation

number

number

[0021] Preferably, in the step S5, when the simulation workpiece slides in the positive direction of the coordinate axis X, grid points that belong to the contact area during the sliding process and satisfy ∂z / ∂x < 0 are recorded in the point set ΩF. When the simulation workpiece slides in the negative direction of the coordinate axis X, grid points that belong to the contact area during the sliding process and satisfy ∂z / ∂x > 0 are recorded in the point set ΩB. The gradient amplitude values of each grid point included in the point set ΩF are extracted and recorded in the gradient amplitude value set Spos at the contact leading edge during forward sliding, and the gradient amplitude values of each grid point included in the point set ΩB are extracted and recorded in the gradient amplitude value set Sneg at the contact leading edge during reverse sliding.

[0022] Preferably, in the step S6, the friction coefficient μ is calculated by the formula

Equation

[0023] Preferably, before performing step S9, an anisotropy evaluation index heatmap is created, and a ridge line is generated in the anisotropy evaluation index heatmap that reflects the sensitivity direction and passes through points corresponding to the optimal parameter combination. In step S9, milling is performed according to the predetermined cutting parameters and the optimal parameter combination, or, instead, based on the target anisotropy evaluation index, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated using the ridge line, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters.

[0024] More preferably, contour lines connecting parameter combinations having the same anisotropy evaluation index Q are superimposed and displayed on the anisotropy evaluation index heatmap. In step S9, milling is performed according to the predetermined cutting parameters and the optimal parameter combination, or, instead, based on the target anisotropy evaluation index, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated using the ridge line and the contour lines, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters.

[0025] More preferably, the specific process of creating the anisotropy evaluation index heatmap and generating the ridgeline in the anisotropy evaluation index heatmap is to create the anisotropy evaluation index heatmap based on each parameter combination and the corresponding anisotropy evaluation index Q, wherein the two coordinate axes of the anisotropy evaluation index heatmap represent the forward tilt angle and the lateral tilt angle, respectively, and the grayscale value represents the anisotropy evaluation index Q, and extract a set of neighboring gradient vectors centered on the peak point in the anisotropy evaluation index heatmap, and analyze the gradient field of the anisotropy evaluation index Q using principal component analysis. The method includes determining the principal direction, taking a plurality of discrete points on the straight line where the principal direction is located, and if the lateral tilt angle and forward tilt angle of the selected discrete points are not included in the parameter combination, calculating an anisotropy evaluation index for the discrete points by bilinear interpolation, then performing a smoothing process by cubic spline interpolation on each discrete point arranged sequentially along the principal direction and the value of the anisotropy evaluation index corresponding to each discrete point, and generating the ridge line based on the data obtained by the cubic spline interpolation, with the discrete points as the horizontal axis and the anisotropy evaluation index Q as the vertical axis.

[0026] The advantageous effects of the present invention are as follows:

[0027] In this invention, machining simulations of milling are performed for each combination of tool position parameters, surface data is gridded, contact areas are extracted, surface gradients and gradient amplitude values ​​are calculated, sets of gradient amplitude values ​​at the contact leading edge during forward and reverse sliding are extracted, the coefficient of friction for forward and reverse sliding is calculated, and an anisotropy evaluation index is calculated. Then, an anisotropy evaluation index heatmap is created and ridge lines indicating the sensitivity direction are generated. This makes it possible to quantitatively predict and evaluate the friction behavior of the surface, and furthermore, based on the friction performance requirements, it is possible to calculate tool position parameters that are highly sensitive to the surface shape after milling of viscoelastic materials. As a result, it is possible to obtain the optimal combination of tool position parameters corresponding to the maximum value of the anisotropy evaluation index, or various combinations of tool position parameters that can achieve the target anisotropy evaluation index. Therefore, according to this invention, tool position parameters can be calculated under predetermined cutting parameters based on the anisotropy requirements related to the surface micromorphology. Furthermore, by performing milling according to the parameter combination and predetermined cutting parameters recommended by the present invention, a viscoelastic material workpiece that satisfies the requirements for friction characteristics or sealing function according to the sliding direction can be obtained. In addition, by introducing a ridge line, the control rules for the milled surface function based on tool position parameters can be shown intuitively and with high sensitivity. This enables more flexible parameter selection while ensuring anisotropy of friction characteristics. Here, high sensitivity means that the change in the anisotropy evaluation index is fastest and more adjustable near the peak point on the ridge line, that is, the anisotropy evaluation index can be adjusted even when the change in tool position parameters is small. The present invention realizes an integrated closed-loop control of "design-manufacturing-performance" for high-performance surfaces, and is of particular significance in meeting the requirements for friction characteristics and sealing function according to the sliding direction in cylinder / piston and shaft sleeve seal pairs. [Brief explanation of the drawing]

[0028] [Figure 1] This is a flowchart of the present invention. [Figure 2] These are anisotropy evaluation index heatmaps and ridgeline diagrams obtained when a simulated workpiece is milled while being fed along one direction selected in the embodiment of the present invention. [Figure 3] These are anisotropy evaluation index heatmaps and ridgeline diagrams obtained when a simulated workpiece is milled while being fed along the other direction selected in the embodiment of the present invention. [Modes for carrying out the invention]

[0029] The present invention will be further described below with reference to the drawings.

[0030] As shown in Figure 1, the method for forming a surface with anisotropic friction characteristics by numerically controlled milling specifically includes the following steps.

[0031] S1: Perform a machining simulation of milling and output three-dimensional point cloud data showing the shape of the milled surface of the simulated workpiece after the machining simulation. Specifically, this is done as follows: Set cutting parameters including spindle speed N, feed rate fz per tooth, cutting row spacing fp, and cutting depth ap, and change tool posture parameters including lateral tilt angle α and forward tilt angle β. The lateral tilt angle α is the inclination angle that the tool axis makes with respect to the vertical axis in a plane parallel to the feed direction, and the forward tilt angle β is the inclination angle that the tool axis makes with respect to the vertical axis in a plane perpendicular to the feed direction. This obtains multiple sets of different parameter combinations consisting of lateral tilt angle α and forward tilt angle β. Here, the range of values ​​for the lateral tilt angle α is [αmin, αmax], and the range of values ​​for the forward tilt angle β is [βmin, βmax]. In this embodiment, αmin=2°, αmax=22°, βmin=2°, and βmax=22°. For each of the predetermined cutting parameters and multiple parameter combinations, a milling simulation is performed on the simulation workpiece in the simulation environment, i.e., simulation software, and three-dimensional point cloud data showing the shape of the milled surface of the simulation workpiece after the machining simulation is output. As a result of the analysis by milling simulation, for the viscoelastic material targeted in this embodiment, the sensitivity of the cutting parameters to the surface shape after machining simulation is not as high as the sensitivity of the tool position parameters to the surface shape after machining simulation. Therefore, in this embodiment, different surface shapes after milling simulation are obtained for the viscoelastic material by setting the cutting parameters and changing the tool position parameters. The coordinates of each grid point in the three-dimensional point cloud data are represented in a three-dimensional Cartesian coordinate system. In this embodiment, since the milling process simulation is performed only on the horizontal surface of the simulation workpiece, the coordinate axes X and Y are set within the milling surface of the simulation workpiece in a three-dimensional Cartesian coordinate system. The direction of the coordinate axis X is aligned with the feed direction, i.e., the friction sliding direction of the simulation workpiece after the milling process simulation, the direction of the coordinate axis Y is aligned with the cutting row spacing direction, and the coordinate axis Z of the three-dimensional Cartesian coordinate system is aligned with the height direction.Furthermore, the anisotropy index of friction characteristics after performing a milling machining simulation on the horizontal surface of the simulated workpiece can be directly applied to the anisotropy of friction characteristics after performing a milling machining simulation on any surface of the simulated workpiece. Moreover, viscoelastic materials can be made to have surface shapes with anisotropy in friction characteristics that change significantly in response to changes in tool position parameters along many directions. The important thing is to find the tool position parameters that impart strong anisotropy in friction characteristics to the viscoelastic material. Therefore, in this embodiment, it is sufficient to select and examine any one direction of the viscoelastic material, and if anisotropy in friction characteristics that changes significantly in response to tool position parameters cannot be obtained in that direction, it can always be found by trying multiple directions.

[0032] S2: Based on the three-dimensional point cloud data showing the shape of the milled surface of the simulated workpiece after the milling machining simulation, the height data Zgrid(xi,yj) of each grid point (i,j) on the milled surface of the simulated workpiece is identified. The value of this height data is equal to the Z coordinate of the grid point (i,j). Here, xi and yj are the X and Y coordinates of the grid point (i,j), respectively. Then, a height matrix Zgrid is constructed that records the height data of all grid points on the milled surface of the simulated workpiece.

[0033] S3: The purpose of this process is to extract the contact area where physical contact actually occurs with the contacting member from the complex shape of the milled surface. Specifically, the depth threshold Zt is calculated based on the highest point height Zmax and the displacement distance δ in the shape of the milled surface of the simulated workpiece. That is,

number

[0034] Preferably, to more directly distinguish contact areas and facilitate data processing, the physical contact state of the surface is converted into a binarized logical matrix. In the logical matrix, the element values ​​corresponding to the grid points (i,j) are defined as follows:

number

[0035] S4: Based on the height matrix Zgrid, the partial derivatives of the height of the grid point (i,j) with respect to the coordinate axes X and Y are calculated using the central difference method as follows.

number

[0036] Furthermore, the surface gradient (∂z / ∂x, ∂z / ∂y) corresponding to each grid point is obtained, and the gradient amplitude value of the surface gradient is calculated using the following formula.

number

[0037] A surface gradient field is constructed based on the surface gradient of all grid points. The surface gradient field represents the magnitude and directional distribution of the microscopic geometric slope of the milled texture.

[0038] S5: In order to accurately calculate the coefficient of friction, the set of gradient amplitude values ​​at the contact leading edge during forward sliding and the set of gradient amplitude values ​​at the contact leading edge during reverse sliding are extracted based on the contact mask obtained in step S3 and the surface gradient field obtained in step S4. Specifically, this is done as follows.

[0039] When the simulation workpiece slides in the positive direction of the coordinate axis X, that is, in applications where the seal member is assembled to create an anti-slip effect on the surface, when the seal member slides in the direction of frictional sliding against the contact member during removal, the grid points that belong to the contact region during the sliding process, i.e., grid points in the contact mask, and satisfying ∂z / ∂x < 0 are recorded in the point set ΩF. When the simulation workpiece slides in the negative direction of the coordinate axis X, the grid points that belong to the contact region during the sliding process and satisfying ∂z / ∂x > 0 are recorded in the point set ΩB. The point sets ΩF and ΩB record all leading edge points that come into contact with the contact member when the simulation workpiece slides in the positive and negative directions of the coordinate axis X, respectively. Here, the partial derivative of the height with respect to the coordinate axis Y is not involved in the determination of leading edge points, but is used only for calculating the gradient amplitude value.

[0040] The gradient amplitude values ​​of each grid point included in the point set ΩF are extracted and recorded in the gradient amplitude value set Spos at the contact leading edge during forward sliding. Similarly, the gradient amplitude values ​​of each grid point included in the point set ΩB are extracted and recorded in the gradient amplitude value set Sneg at the contact leading edge during reverse sliding. The gradient amplitude value set Spos at the contact leading edge during forward sliding and the gradient amplitude value set Sneg at the contact leading edge during reverse sliding are expressed by the following equations.

number

[0041] Data cleaning is performed by applying preprocessing, such as noise reduction, to the data in the set of gradient amplitude values ​​at the contact leading edge during forward sliding (Spos) and the set of gradient amplitude values ​​at the contact leading edge during reverse sliding (Sneg), thereby removing outliers.

[0042] S6: Calculate the forward sliding friction coefficient μf and the reverse sliding friction coefficient μb. Specifically, the process is as follows:

[0043] The coefficient of friction μ is calculated using the following formula.

number

[0044] The formula for calculating the friction coefficient μ is based on conventional technology and is obtained by calculating the energy dissipation when a viscoelastic material slides against a contact member in a simulation work, i.e., based on hysteresis friction theory, and quantitatively predicting the resistance experienced by surface friction. Here, C is a dimensionless coefficient and is obtained by calibration experiments. In this example, since a viscoelastic material is used, C can be approximately set to 1. tanδ is the material loss coefficient, and the material loss coefficient under different operating conditions can be measured by friction characteristic experiments of the viscoelastic material. <∇f> is the average value of the gradient amplitude values ​​of all grid points involved in the calculation of the friction coefficient μ. The average value of each gradient amplitude value included in the set of gradient amplitude values ​​Spos at the contact leading edge during forward sliding can be found and substituted into <∇f>, and the forward sliding friction coefficient μf can be calculated using the above friction coefficient calculation formula. Furthermore, the average value of each gradient amplitude value included in the set of gradient amplitude values ​​Sneg at the contact leading edge during reverse sliding can be calculated and substituted into <∇f>, and the coefficient of friction μb for reverse sliding can be calculated using the aforementioned formula for calculating the coefficient of friction μ.

[0045] S7: The anisotropy evaluation index Q is calculated using either the forward sliding friction coefficient μf or the reverse sliding friction coefficient μb, or the smaller of the two, as the reference value μ0. That is, the anisotropy evaluation index Q is calculated as the percentage obtained by dividing the absolute value of the difference between the forward sliding friction coefficient and the reverse sliding friction coefficient by the reference value. Here, the absolute value is the absolute value of the difference.

number

[0046] The anisotropy evaluation index Q quantitatively represents the degree of relative difference in the texture of the milled surface of a simulated workpiece when friction occurs along two directions: the positive and negative directions of the coordinate axis X. When the value of Q is close to 0, the surface shape of the simulated workpiece after machining simulation exhibits isotropy along the coordinate axis X direction in terms of friction performance, meaning that the coefficient of friction is close during the reciprocating motion process, making it suitable for friction scenarios involving reciprocating motion. Conversely, when the value of Q is large, the surface shape of the simulated workpiece after machining simulation exhibits significant anisotropy, making it suitable for requirements that provide anti-slip or anti-loosening effects on the surface after the assembly of sealing members.

[0047] S8: After performing a milling simulation on the simulation workpiece for each of the predetermined cutting parameters and multiple parameter combinations, the optimal parameter combination that maximizes the anisotropy evaluation index Q is obtained based on the calculated corresponding anisotropy evaluation index Q. That is, the optimal forward tilt angle and lateral tilt angle of the tool along the coordinate axis X direction are determined. By performing cutting along the coordinate axis X direction according to the predetermined cutting parameters and the optimal parameter combination, an optimal directional friction texture can be formed.

[0048] S9: An anisotropy evaluation index heatmap is created, and a ridgeline is generated in the anisotropy evaluation index heatmap that reflects the sensitivity direction and passes through points corresponding to the optimal parameter combination. Specifically, an anisotropy evaluation index heatmap is created based on each parameter combination and the corresponding anisotropy evaluation index Q. The two coordinate axes of the anisotropy evaluation index heatmap represent the forward tilt angle β and the lateral tilt angle α, respectively, and the grayscale value represents the anisotropy evaluation index Q. A smaller grayscale value indicates a smaller anisotropy evaluation index Q. A set of neighboring gradient vectors is extracted centered on the peak point in the anisotropy evaluation index heatmap, and the principal direction of the gradient field of the anisotropy evaluation index Q is determined by principal component analysis (PCA). This obtains the sensitivity direction in which the change in the anisotropy evaluation index is most pronounced. Multiple discrete points (αk, βk) are taken on the line where the principal direction is located, and αk and βk are the lateral tilt angle and forward tilt angle of the k-th discrete point, respectively. If the lateral and forward tilt angles of the selected discrete points are not included in the parameter combination, an anisotropy evaluation index for these discrete points is calculated by bilinear interpolation. Then, a smoothing process is performed by cubic spline interpolation on each discrete point arranged sequentially along the principal direction and the value of the anisotropy evaluation index corresponding to each discrete point. Then, a smooth and continuous ridge line is generated based on the data obtained by the cubic spline interpolation, with the discrete points on the horizontal axis and the anisotropy evaluation index Q on the vertical axis. This ridge line reflects the sensitivity direction in which the change in the anisotropy evaluation index is most pronounced in the anisotropy evaluation index heatmap and passes through the point corresponding to the optimal parameter combination. The purpose of this process is to intuitively and sensitively show the control rules for the milling surface function by tool posture parameters by constructing a map showing the correspondence between "tool posture parameters - anisotropy evaluation index" and introducing a ridge line. This makes it possible to select parameters more flexibly while ensuring the anisotropy of friction characteristics. Here, "high sensitivity" means that the anisotropy evaluation index changes most rapidly and is more adjustable near the peak point on the ridgeline, that is, the anisotropy evaluation index can be adjusted even when the change in tool position parameters is small.

[0049] Figure 2(a) shows an anisotropy evaluation index heatmap obtained when the simulated workpiece is milled while being fed along one direction 1 selected in this embodiment. The positions indicated by circles in the figure are peak points, and the straight lines are the straight lines where the principal direction is located. Figure 2(b) shows the ridge line, each discrete point and the anisotropy evaluation index corresponding to each discrete point, as well as the shape of the milled surface of the simulated workpiece corresponding to multiple discrete points. Figure 3(a) shows an anisotropy evaluation index heatmap obtained when the simulated workpiece is milled while being fed along direction 2 selected in this embodiment, i.e., a direction perpendicular to direction 1. Similarly, Figure 3(b) shows the ridge line, each discrete point and the anisotropy evaluation index corresponding to each discrete point, as well as the shape of the milled surface of the simulated workpiece corresponding to multiple discrete points.

[0050] Preferably, contour lines are superimposed on the anisotropy evaluation index heatmap to show multiple parameter combinations having the same anisotropy evaluation index Q. This allows for the selection of parameter combinations for the side tilt angle α and the forward tilt angle β while maintaining the anisotropy of the friction characteristics and considering processing efficiency.

[0051] S10: Milling is performed according to the predetermined cutting parameters and the optimal parameter combination. Alternatively, based on the target anisotropy evaluation index, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated in reverse using the ridge line, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters. Alternatively, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated in reverse using the ridge line and contour lines, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters.

Claims

1. A method for forming a surface having anisotropic friction properties by numerically controlled milling, Step S1 is a process in which a milling simulation is performed on a simulation workpiece for each of the predetermined cutting parameters and multiple parameter combinations, and three-dimensional point cloud data showing the shape of the milled surface of the simulation workpiece after the machining simulation, wherein the parameter combination consists of a lateral tilt angle α, which is the tilt angle that the tool axis makes with respect to the vertical axis in a plane parallel to the feed direction, and a forward tilt angle β, which is the tilt angle that the tool axis makes with respect to the vertical axis in a plane perpendicular to the feed direction, and each grid point coordinate of the three-dimensional point cloud data is represented in a three-dimensional Cartesian coordinate system, and in the three-dimensional Cartesian coordinate system, the coordinate axes X and Y are located within the milled surface of the simulation workpiece, the direction of the coordinate axis X is along the feed direction, the direction of the coordinate axis Y is along the cutting row spacing direction, and the coordinate axis Z of the three-dimensional Cartesian coordinate system is along the height direction, Step S2 is a step of constructing a height matrix Zgrid that records the height data of all grid points on the milled surface of the simulated workpiece, based on the height data Zgrid(xi, yj) of each grid point (i, j) on the milled surface of the simulated workpiece, wherein xi and yj are the X coordinate and Y coordinate of the grid point (i, j), respectively. Step S3 involves extracting a contact area that comes into contact with a contact member based on the shape of the milled surface, Step S4 involves calculating the surface gradient and gradient amplitude values ​​corresponding to each grid point based on the height matrix Zgrid, and constructing a surface gradient field based on the surface gradients of all grid points. Step S5 involves extracting a set of gradient amplitude values ​​at the contact leading edge during forward sliding and a set of gradient amplitude values ​​at the contact leading edge during reverse sliding. Step S6 is to calculate the forward sliding friction coefficient and the reverse sliding friction coefficient, Step S7 is a step in which the anisotropy evaluation index Q is defined as the percentage obtained by dividing the absolute value of the difference between the forward sliding friction coefficient and the reverse sliding friction coefficient by a reference value, wherein the reference value is either one or the smaller of the forward sliding friction coefficient and the reverse sliding friction coefficient. Step S8: Based on the anisotropy evaluation index Q obtained for each of the predetermined cutting parameters and the plurality of parameter combinations, the parameter combination that maximizes the anisotropy evaluation index Q is determined as the optimal parameter combination. A method comprising step S9 of performing milling according to the predetermined cutting parameters and the optimal parameter combination.

2. The method according to claim 1, wherein the cutting parameters include spindle speed, feed rate per cutting edge, cutting row interval, and cutting depth.

3. The specific process for extracting the contact region is based on the highest point height Zmax and the displacement distance δ in the shape of the milled surface of the simulated workpiece, [Math 1] The method according to claim 1, wherein a depth threshold Zt is calculated from the above, where the displacement distance δ is the height difference between the highest point in the shape of the milled surface of the simulated workpiece and the lowest point of the contact member, and grid points that are higher in height than the threshold plane are selected from the shape of the milled surface of the simulated workpiece, and the region consisting of these grid points is defined as the contact region.

4. The element values ​​corresponding to each grid point (i, j) on the milled surface are given by the formula [Math 2] The method according to claim 1, wherein a logical matrix defined by is constructed, and the region consisting of all lattice points corresponding to Mcontact(i,j) = 1 is defined as the contact region.

5. In step S4, based on the height matrix Zgrid, the partial derivatives of the height of the grid point (i, j) with respect to the coordinate axes X and Y are calculated using the central difference method, as shown in the equation [Math 3] The calculation is performed by the following formula, where x, y, and z represent the X, Y, and Z coordinates of the grid point, respectively, and Δx and Δy are the difference in the X coordinates of two adjacent grid points along the X axis and the difference in the Y coordinates of two adjacent grid points along the Y axis, respectively. Furthermore, the surface gradient (∂z / ∂x, ∂z / ∂y) corresponding to each grid point is obtained, and the gradient amplitude value of the surface gradient is calculated using the formula [Math 4] The method according to claim 1, wherein a surface gradient field is constructed based on the surface gradient of all grid points, calculated by [method].

6. The method according to claim 1, wherein in step S5, when the simulation workpiece slides in the positive direction of the coordinate axis X, the grid points that belong to the contact region during the sliding process and satisfy ∂z / ∂x < 0 are recorded in the point set ΩF; when the simulation workpiece slides in the negative direction of the coordinate axis X, the grid points that belong to the contact region during the sliding process and satisfy ∂z / ∂x > 0 are recorded in the point set ΩB; the gradient amplitude values ​​of each grid point included in the point set ΩF are extracted and recorded in the gradient amplitude value set Spos at the contact leading edge during positive sliding; and the gradient amplitude values ​​of each grid point included in the point set ΩB are extracted and recorded in the gradient amplitude value set Sneg at the contact leading edge during reverse sliding.

7. In step S6, the coefficient of friction μ is given by the formula [Math 5] The coefficient of friction μ is calculated as follows, where C is a dimensionless coefficient, tanδ is the material loss coefficient, and <∇f> is the average value of the gradient amplitude values ​​of all grid points involved in the calculation of the coefficient of friction μ. The average value of each gradient amplitude value included in the set of gradient amplitude values ​​Spos at the contact leading edge during forward sliding is obtained and substituted into <∇f>, and the coefficient of friction μf for forward sliding is calculated using the formula for calculating the coefficient of friction μ. The method according to claim 6, wherein the average value of each gradient amplitude value included in the set of gradient amplitude values ​​Sneg at the contact leading edge during reverse sliding is obtained and substituted into <∇f>, and the coefficient of friction μb for reverse sliding is calculated using the formula for calculating the coefficient of friction μ.

8. Before executing step S9, an anisotropy evaluation index heatmap is created, and in the anisotropy evaluation index heatmap, a ridgeline is generated that reflects the sensitivity direction in which the change in the anisotropy evaluation index Q is most pronounced and passes through the point corresponding to the optimal parameter combination. In step S9, milling is performed according to the predetermined cutting parameters and the optimal parameter combination, or, instead, The method according to claim 1, wherein, based on a target anisotropy evaluation index, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated in reverse using the ridge line, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters.

9. On the anisotropy evaluation index heatmap, contour lines connecting parameter combinations having the same anisotropy evaluation index Q are superimposed and displayed. In step S9, milling is performed according to the predetermined cutting parameters and the optimal parameter combination, or, instead, The method according to claim 8, wherein, based on a target anisotropy evaluation index, a plurality of parameter combinations capable of achieving the target anisotropy evaluation index are calculated in reverse using the ridge line and the contour lines, and milling is performed according to one of the plurality of parameter combinations and the predetermined cutting parameters.

10. The process of creating the anisotropy evaluation index heatmap and generating the ridgeline in the anisotropy evaluation index heatmap involves creating the anisotropy evaluation index heatmap based on each of the multiple parameter combinations used in step S1 and the corresponding anisotropy evaluation index Q, wherein the two coordinate axes of the anisotropy evaluation index heatmap represent the forward tilt angle and the lateral tilt angle, respectively, and the grayscale value represents the anisotropy evaluation index Q. The process involves extracting a set of neighboring gradient vectors centered on the peak point in the anisotropy evaluation index heatmap, and determining the principal directions of the gradient field of the anisotropy evaluation index Q using principal component analysis. If multiple discrete points are taken on the straight line in which the principal direction is located, and the lateral tilt angle and forward tilt angle of the selected discrete point are not included in any of the multiple parameter combinations used in step S1, then an anisotropy evaluation index of the discrete point is calculated by bilinear interpolation. Subsequently, smoothing is performed on each discrete point arranged sequentially along the principal direction and the values ​​of the anisotropy evaluation index corresponding to each discrete point by cubic spline interpolation. The method according to claim 8 or 9, further comprising generating the ridgeline based on the data obtained by the cubic spline interpolation, with the discrete points on the horizontal axis and the anisotropy evaluation index Q on the vertical axis.

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