Surface topography prediction method for oblique-axis polishing using cerium oxide polishing slurry with spherical polishing head

Abstract

The invention discloses a method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing. The method starts from the force of a single cerium oxide abrasive grain in the cerium oxide polishing liquid and combines the pressing condition of the cerium oxide abrasive grain on the surface of a workpiece to obtain the motion trajectory of a single cerium oxide abrasive grain in the polishing head-workpiece contact surface under the drive of the polishing head during the oblique axis polishing process of the spherical polishing head, obtain the motion footprint of the single cerium oxide abrasive grain, and realize the prediction of the processing surface morphology by setting the effective cerium oxide abrasive grain number on the polishing head-workpiece contact surface and the superposition strategy of the motion footprint of the cerium oxide abrasive grain. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing provided by the invention combines the force of the cerium oxide abrasive grain, the motion of the cerium oxide abrasive grain, the effective cerium oxide abrasive grain number and the superposition condition of the cerium oxide abrasive grain, and improves the accuracy of the prediction result.

Description

Technical Field

[0001] The invention relates to the field of high-end equipment precision machining, and in particular to a method for predicting the surface morphology of a spherical polishing head during cerium oxide polishing liquid oblique-axis polishing machining. Background Art

[0002] The polishing process is usually the last step to ensure that the surface quality and accuracy meet the requirements of use. However, the quality of the polished surface is the result of the combined action of the polishing pad, abrasive particles and the workpiece. Due to the complex mechanism of action between the polishing pad-abrasive particles-workpiece surface, this is a process that is difficult to achieve quantitative material removal. In order to meet the finishing accuracy of the components, it is often necessary to repeatedly detect whether the surface morphology of the machined surface meets the accuracy requirements, and then adjust the processing parameters, and repeat this process until the requirements are met, which seriously affects the processing efficiency of the workpiece. To this end, by establishing an analysis model to achieve quantitative material removal, and then simulating the surface morphology according to the processing parameters, and adjusting the process parameters through feedback, it is of great significance to improve the processing quality and improve the processing efficiency.

[0003] However, most of the existing polishing surface prediction models are based on Preston's empirical equations, which are limited to studying the effects of macro process parameters (pressure and rotation speed) on surface morphology and roughness, and the material removal coefficients for different workpieces need to be obtained through preliminary experiments during the prediction simulation process. There are few studies on the microscopic contact between abrasive particles and workpieces, especially the analysis of the motion trajectory of cerium oxide abrasive particles during oblique axis polishing, which is crucial for accurately predicting the polishing surface morphology, because the final surface is formed by the superposition of multiple abrasive particle motion footprints on the workpiece surface. Summary of the invention

[0004] The present invention overcomes the shortcomings of the prior art and provides a method for predicting the surface morphology of a spherical polishing head during oblique-axis polishing with a cerium oxide polishing liquid. The method combines the force on cerium oxide abrasive particles, the movement of cerium oxide abrasive particles, the number of effective cerium oxide abrasive particles and the superposition of cerium oxide abrasive particles to realize the method for predicting the surface morphology of a spherical polishing head during oblique-axis polishing with a cerium oxide polishing liquid, thereby improving the accuracy of the prediction results.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for predicting the surface morphology of a workpiece surface subjected to oblique-axis polishing by a spherical polishing head and a cerium oxide polishing liquid, the method comprising the following steps:

[0006] Obtaining polishing operation data, wherein the polishing operation data includes polishing parameters of a spherical polishing head, a cerium oxide abrasive polishing liquid, and a workpiece morphology;

[0007] According to the polishing operation data, based on a pre-trained polishing surface morphology prediction model, a polishing surface morphology prediction process is performed to obtain a spherical polishing head cerium oxide polishing liquid oblique axis polishing surface morphology profile;

[0008] Wherein, the training of the polishing surface morphology prediction model includes:

[0009] S1. Use electron microscope scanning to obtain the morphological information of the polishing head. Through the image binarization processing in the image processing algorithm, identify and calculate the pixel ratio to obtain the surface porosity of the polishing head. ;

[0010] Specifically, the electron microscope includes a laser confocal microscope or a white light interferometer.

[0011] S2. Based on the Hertz contact theory, determine the contact area between the polishing head and the workpiece when the spherical polishing head is vertically fed, and determine the contact pressure at any radial position from the contact center in the contact area between the polishing head and the workpiece;

[0012] S3, the surface porosity of the polishing head obtained according to step S1 The polishing head-workpiece effective contact area is determined by combining the polishing head-workpiece contact area obtained in step S2; and the number N of effective cerium oxide abrasive particles in the polishing head-workpiece effective contact area is obtained according to the polishing head-workpiece effective contact area, the concentration of cerium oxide polishing liquid and the average particle size of cerium oxide abrasive particles.

[0013] S4. Use a uniform distribution function and repeatedly propose the motion footprint of a single cerium oxide abrasive generated at any position in the polishing head-workpiece contact plane for N times, generate the coordinates of N cerium oxide abrasives on the polishing head-workpiece contact surface, obtain the footprints of the cerium oxide abrasives under the action of N cerium oxide abrasives, superimpose them in the vertical direction, and obtain the surface morphology profile of the oblique axis polishing process of the spherical polishing head cerium oxide polishing liquid.

[0014] Specifically, the uniform distribution function used is the Matlab uniform distribution function unifrnd.

[0015] In a preferred embodiment of the present invention, the motion footprint of a single cerium oxide abrasive grain generated at any position in the contact plane between the polishing head and the workpiece is calculated, comprising the following steps:

[0016] S41, taking the center of the effective contact area between the polishing head and the workpiece as the coordinate origin O, establishing an OXYZ coordinate system, defining the coordinates of a cerium oxide abrasive grain generated at any position in the contact plane between the polishing head and the workpiece as (x, y, 0), and mapping the coordinates of the generated cerium oxide abrasive grain downward to the surface of the polishing head, and the mapped coordinates of the cerium oxide abrasive grain are (x, y, z);

[0017] S42, take the center of the polishing head as the coordinate origin O1, the plane passing through O1 and parallel to the XOY plane as the X1O1Y1 plane, the direction perpendicular to the X1O1Y1 plane upward as the positive direction of the Z1 axis, and establish the O1X1Y1Z1 coordinate system; rotate the polishing head around the O1X1 axis in the O1X1Y1Z1 coordinate system θ Angle, get the posture of the polishing head for oblique axis polishing, at this time the inclination angle of the polishing head is θ ;

[0018] S43, based on spatial geometry, calculate the coordinates (x, y, z) of the cerium oxide abrasive grains in the coordinate system OXYZ in step S4 to rotate around the O1X1 axis in the coordinate system O1X1Y1Z1 in step S42 θ The distance R' of the polishing head rotation axis O1Z1' after the angle is determined, and the motion trajectory (x, y, z) of the cerium oxide abrasive grain at the coordinate position (x, y, z) of the polishing head surface during the oblique axis polishing process is determined based on the distance R'. 1’ ,y 1’ ,z 1’ ), the angle division of the polar coordinate system is , the algorithm of the motion trajectory of the polishing head surface is:

[0019] ;

[0020] S44, the coordinates (x, y, z) determined in step S43 are transformed by a rotation and a translation of the movement trajectory of the cerium oxide abrasive grains on the surface of the polishing head during the oblique axis polishing of the cerium oxide abrasive grains, wherein the rotation matrix is: , the translation matrix is , 0, ly, lz are the displacements of the coordinate values ​​in the x, y, and z directions respectively. The coordinates in the OXYZ coordinate system are used to represent the motion trajectory of the cerium oxide abrasive particles during the oblique axis polishing process:

[0021] ;

[0022] The Z-axis coordinate is set to zero, and the trajectory is projected onto the XOY plane to obtain the actual motion trajectory of the cerium oxide abrasive grains at the coordinate (x, y, z) position in the polishing head-workpiece contact area;

[0023] ;

[0024] S45. Combine the contact pressure at each position in the contact area obtained in step S2 with the coordinates of the actual motion trajectory of the cerium oxide abrasive at the coordinate position (x, y, z) in the polishing head-workpiece contact area in step S44, discretize the motion trajectory, and determine the indentation depth and indentation of the cerium oxide abrasive at each discrete motion trajectory point based on the Hertz basic theory to obtain the motion footprint of a single cerium oxide abrasive and the scratch mark produced by a single cerium oxide abrasive on the workpiece surface.

[0025] In a preferred embodiment of the present invention, in step S41, the method for establishing the OXYZ coordinate system is: taking the center of the polishing head-workpiece effective contact area as the coordinate origin O, determining the contact area of ​​the polishing head-workpiece effective contact area as the XOY plane, and the vertical contact plane upward as the positive direction of the Z axis, and establishing the OXYZ coordinate system.

[0026] In a preferred embodiment of the present invention, in step S41, the cerium oxide abrasive particles in the polishing head-workpiece contact area are uniformly distributed, and a cerium oxide abrasive particle is generated at any position in the polishing head-workpiece contact plane. The coordinates of the generated cerium oxide abrasive particle are (x, y, 0). The coordinates of the generated cerium oxide abrasive particle are mapped downward to the surface of the polishing head. According to the equation of the ball of the polishing head without contact deformation, the coordinates of the cerium oxide abrasive particle after mapping are (x, y, z).

[0027] In a preferred embodiment of the present invention, in step S2, the polishing head is vertically fed to the polishing head-workpiece contact area contact radius for: ;in, is the radius of the spherical polishing head, is the vertical feed distance of the polishing head;

[0028] The contact area S is: ; Radial position of the contact area from the contact center r Contact pressure for: ;in, Contact center pressure, contact center pressure is the maximum pressure in the contact area, ;in, is the equivalent elastic modulus.

[0029] In a preferred embodiment of the present invention, step S3 comprises: according to the porosity of the polishing head surface obtained in step 1 The effective number N of cerium oxide abrasive particles is obtained by combining the polishing head-workpiece contact area S obtained in step 2 with the concentration of cerium oxide polishing liquid and the average particle size of cerium oxide abrasive particles.

[0030] In a preferred embodiment of the present invention, the polishing head-workpiece effective contact area for: ;

[0031] Surface mass density of cerium oxide polishing liquid at the polishing head-workpiece contact surface for: ; Among them, m v is the volume mass density of the polishing liquid, h is the height of the polishing liquid, m v / h is the surface mass density of the polishing liquid per unit height, d is the average particle size of cerium oxide abrasive particles in the cerium oxide polishing liquid, and d is set as the average distance between the polishing head and the workpiece contact area.

[0032] In a preferred embodiment of the present invention, the mass M of the cerium oxide abrasive grains in the contact area between the spherical polishing head and the workpiece is s for: ; The effective number of cerium oxide abrasive particles N is .

[0033] In a preferred embodiment of the present invention, a computer device comprises: a memory for storing computer programs / instructions; a processor for executing the computer programs / instructions to implement the steps of a method for predicting surface morphology during oblique-axis polishing of a spherical polishing head using cerium oxide polishing liquid.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention discloses a method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process. The prediction method of the present invention starts from the force on a single cerium oxide abrasive in the cerium oxide polishing liquid, analyzes the pressing of the cerium oxide abrasive on the workpiece surface under the action of the polishing head, and analyzes the movement trajectory of a single cerium oxide abrasive in the polishing head-workpiece contact surface under the drive of the polishing head during the spherical polishing head oblique axis polishing process, thereby obtaining the movement footprint of a single cerium oxide abrasive (i.e., the scratch mark generated on the workpiece surface), and finally realizes the prediction of the processing surface morphology by the effective cerium oxide abrasive number on the polishing head-workpiece contact surface and setting the cerium oxide abrasive movement footprint superposition strategy. Since the factors such as the force on the cerium oxide abrasive, the movement of the cerium oxide abrasive, the effective number of the cerium oxide abrasive, and the superposition of the cerium oxide abrasive are comprehensively considered, the prediction result is accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0037] Figure 1 A schematic flow chart of a method for predicting surface topography during oblique-axis polishing of a spherical polishing head using cerium oxide polishing liquid provided by the present invention;

[0038] Figure 2 A schematic diagram of analyzing the contact between a polishing head and a workpiece in a method for predicting the surface morphology during oblique-axis polishing of a spherical polishing head by a cerium oxide polishing liquid provided by the present invention;

[0039] Figure 3 A schematic diagram of analyzing the number of effective cerium oxide abrasive grains between a polishing head and a workpiece in a method for predicting surface morphology during oblique-axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention;

[0040] Figure 4Schematic diagram of the motion mode analysis of cerium oxide abrasive particles in the surface morphology prediction method for oblique axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention Figure 1 ;

[0041] Figure 5 Schematic diagram of the motion mode analysis of cerium oxide abrasive particles in the surface morphology prediction method for oblique axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention Figure 2 ;

[0042] Figure 6 Schematic diagram of the motion mode analysis of cerium oxide abrasive particles in the surface morphology prediction method for oblique axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention Figure 3 ;

[0043] Figure 7 Schematic diagram of the motion mode analysis of cerium oxide abrasive particles in the surface morphology prediction method for oblique axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention Figure 4 ;

[0044] Figure 8 A schematic diagram of the analysis of the sweeping cross-section model of the sliding motion of cerium oxide abrasive particles in the surface morphology prediction method for oblique-axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention (pressure distribution states at different positions (radial distances r and r' as an example) on the same trajectory);

[0045] Fig. 9 A schematic diagram of the analysis of the rolling motion cerium oxide abrasive grain indentation model in the surface morphology prediction method for oblique axis polishing of a spherical polishing head cerium oxide polishing liquid provided by the present invention (different positions (resulting in different pressure indentation cross-sectional profiles);

[0046] Among them, 1. spherical polishing head, 2. polishing head pores, 3. cerium oxide abrasives, 4. effective cerium oxide abrasives, 6. polishing head rotation axis, 8. workpiece, 9. polishing head-workpiece contact area. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0048] The term "and / or" is only a description of the association relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects are in an "or" relationship. Embodiment 1

[0049] like Figure 1 As shown, the present invention discloses a method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing, and the method for predicting the surface morphology of a workpiece 8 by oblique axis polishing using a spherical polishing head 1 and a cerium oxide abrasive polishing liquid comprises the following steps:

[0050] Obtaining polishing operation data, wherein the polishing operation data includes polishing parameters of the spherical polishing head 1, the cerium oxide abrasive polishing liquid, and the workpiece morphology;

[0051] According to the polishing operation data, based on a pre-trained polishing surface morphology prediction model, a polishing surface morphology prediction process is performed to obtain a spherical polishing head cerium oxide polishing liquid oblique axis polishing surface morphology profile.

[0052] Among them, the training of the polishing surface morphology prediction model includes:

[0053] S1. Use electron microscope scanning to obtain the morphological information of the polishing head. Through image processing algorithms such as image binarization, identify and calculate the pixel ratio to obtain the surface porosity of the polishing head. ;

[0054] Specifically, the electron microscope includes a laser confocal microscope or a white light interferometer.

[0055] S2, such as Figure 2 As shown, based on the Hertz contact theory, the polishing head-workpiece contact area 9 is determined when the spherical polishing head 1 is vertically fed, and the contact pressure at any radial position from the contact center in the polishing head-workpiece contact area 9 is determined;

[0056] Specifically, Figure 2 As shown, the polishing head vertically feeds the polishing head-workpiece contact area 9 contact radius for: ;in, is the radius of the spherical polishing head, is the vertical feed distance of the polishing head;

[0057] The contact area S is: ; Radial position from the contact center in the contact area r Contact pressure for: ;in, Contact center pressure, contact center pressure is the maximum pressure in the contact area, ;in, is the equivalent elastic modulus.

[0058] S3, such as Figure 3As shown, the surface porosity of the polishing head obtained in step S1 is The polishing head-workpiece effective contact area is determined by the polishing head-workpiece contact area 9 obtained in step S2; the effective cerium oxide abrasive number N of the effective cerium oxide abrasive particles 4 within the polishing head-workpiece effective contact area is obtained based on the polishing head-workpiece effective contact area combined with the cerium oxide polishing liquid concentration and the average particle size of the cerium oxide abrasive particles 3.

[0059] The acquisition of the number N of effective cerium oxide abrasive grains of the effective cerium oxide abrasive grains 4 includes:

[0060] According to the polishing head surface porosity obtained in step 1 The effective cerium oxide abrasive number N of the effective cerium oxide abrasive particles 4 is obtained by combining the polishing head-workpiece contact area S obtained in step 2 with the cerium oxide polishing liquid concentration and the average particle size of the cerium oxide abrasive particles.

[0061] Polishing head-workpiece effective contact area for: .

[0062] Surface mass density of cerium oxide polishing liquid at the polishing head-workpiece contact surface for: ; Among them, m v is the volume mass density of the polishing liquid, h is the height of the polishing liquid, m v / h is the surface mass density of the polishing liquid per unit height, and d is the average particle size of the cerium oxide abrasive particles in the cerium oxide polishing liquid (the average distance between the set polishing head and the workpiece contact area 9).

[0063] The mass M of the cerium oxide abrasive grains in the spherical polishing head-workpiece contact area 9 s for: ; The effective cerium oxide abrasive grain number N of the effective cerium oxide abrasive grain 4 is .

[0064] S4. Use Matlab uniform distribution function unifrnd to repeatedly propose the motion footprint of a single cerium oxide abrasive generated at any position in the contact plane between the polishing head and the workpiece N times (repeat steps S41-S45 N times, N is the number of effective cerium oxide abrasives obtained in step S3), generate the coordinates of N cerium oxide abrasives on the contact surface between the polishing head and the workpiece, obtain the footprints of the cerium oxide abrasives under the action of N cerium oxide abrasives, superimpose them in the vertical direction, and obtain the surface morphology profile of the oblique axis polishing process of the spherical polishing head cerium oxide polishing liquid.

[0065] Specifically, the motion footprint of a single cerium oxide abrasive grain generated at any position in the contact plane between the polishing head and the workpiece is formulated, including the following steps:

[0066] S41, such as Figure 4As shown, an OXYZ coordinate system is established with the center of the effective contact area between the polishing head and the workpiece as the coordinate origin O, and the coordinates of a cerium oxide abrasive generated at any position in the contact plane between the polishing head and the workpiece are defined as (x, y, 0). The coordinates of the generated cerium oxide abrasive are mapped downward to the surface of the polishing head, and the mapped coordinates of the cerium oxide abrasive are (x, y, z).

[0067] Specifically, the method for establishing the OXYZ coordinate system is as follows: taking the center of the polishing head-workpiece effective contact area as the coordinate origin O, determining the contact area of ​​the polishing head-workpiece effective contact area as the XOY plane, and the vertical contact plane upward as the positive direction of the Z axis, and establishing the OXYZ coordinate system.

[0068] The cerium oxide abrasive is uniformly distributed in the polishing head-workpiece contact area 9, and a cerium oxide abrasive is generated at any position in the polishing head-workpiece contact plane. The coordinates of the generated cerium oxide abrasive are (x, y, 0). The coordinates of the generated cerium oxide abrasive are mapped downward to the surface of the polishing head. According to the equation of the ball of the polishing head without contact deformation, the coordinates of the cerium oxide abrasive after mapping are (x, y, z).

[0069] S42, such as Figure 5 As shown, the center of the polishing head is taken as the coordinate origin O1, the plane passing through O1 and parallel to the XOY plane is the X1O1Y1 plane, and the positive direction of the Z1 axis is perpendicular to the X1O1Y1 plane. The O1X1Y1Z1 coordinate system is established; the polishing head is rotated around the O1X1 axis in the O1X1Y1Z1 coordinate system. θ Angle, get the polishing head posture of oblique axis polishing, at this time the polishing head tilt angle is θ .

[0070] S43, such as Figure 6 As shown, based on the spatial geometry, the coordinates (x, y, z) of the cerium oxide abrasive grains in the coordinate system OXYZ in step S4 are calculated to rotate around the O1X1 axis in the coordinate system O1X1Y1Z1 in step S42 θ The polishing head rotation axis 6 after the angle is O1Z1', and the motion trajectory (x, y, z) of the cerium oxide abrasive grain at the coordinate position (x, y, z) of the polishing head surface during the oblique axis polishing process is determined based on the distance R'. 1’ ,y 1’ ,z 1’ ), the angle division of the polar coordinate system is , the algorithm of the motion trajectory of the polishing head surface is:

[0071] .

[0072] S44, such as Figure 7As shown, the movement trajectory of the cerium oxide abrasive grains on the surface of the polishing head during the oblique axis polishing of the cerium oxide abrasive grains at the coordinates (x, y, z) determined in step S43 is subjected to a rotation and a translation coordinate transformation, wherein the rotation matrix is , the translation matrix is , 0, ly, lz are the displacements of the coordinate values ​​in the x, y, and z directions respectively. The OXYZ coordinates are used to represent the motion trajectory of the cerium oxide abrasive particles during the oblique axis polishing process:

[0073] ;

[0074] The Z-axis coordinate is set to zero, and the trajectory is projected onto the XOY plane to obtain the actual motion trajectory of the cerium oxide abrasive grain at the coordinate (x, y, z) position in the polishing head-workpiece contact area 9;

[0075] .

[0076] Furthermore, steps S41 to S44 are mainly used to determine the motion trajectory of the cerium oxide abrasive grains in the polishing head-workpiece contact area 9 in the XOY plane during the oblique axis polishing process. ; In step S41, the coordinates of the cerium oxide abrasive grains at any position in the contact surface between the polishing head and the workpiece are mapped to the surface of the polishing head to obtain the position coordinates (x, y, z) of the cerium oxide abrasive grains on the spherical surface; step S42 determines the oblique axis (inclination angle θ ) The polishing head rotation axis 6 is at the O1X1 position; Step S43 determines the distance R' from the mapped cerium oxide abrasive coordinates (x, y, z) to the oblique axis polishing rotation axis, and further determines the motion trajectory of the cerium oxide abrasive in the oblique axis coordinate system with the oblique axis rotation center; Step S44, through a rotation and a translation coordinate change, the initial cerium oxide abrasive motion trajectory in the OXYZ coordinate system is further projected onto the XOY plane to obtain the cerium oxide abrasive motion trajectory in the polishing head-workpiece contact plane. .

[0077] S45, such as Figure 8 , Fig. 9 As shown, combined with the contact pressure at each position in the polishing head-workpiece contact area 9 obtained in step S2 and the coordinates of the actual motion trajectory of the cerium oxide abrasive at the coordinate (x, y, z) position in the polishing head-workpiece contact area 9 in step S44, the motion trajectory is discretized, and the indentation depth and indentation of the cerium oxide abrasive at each discrete motion trajectory point are determined based on the Hertz basic theory to obtain the motion footprint of a single cerium oxide abrasive, and the scratch mark produced by a single cerium oxide abrasive on the surface of the workpiece 8 is obtained.

[0078] Further, first, the movement trajectory of the cerium oxide abrasive particles in the polishing head-workpiece contact area 9 obtained in S41-S45 is Discretize into trajectory points, and calculate the distance from each trajectory point to the contact center of the polishing head-workpiece; then, based on the contact pressure at any radial position of the contact center within the contact area 9 obtained by Hertz contact theory in S2 , determine the pressure state of the cerium oxide abrasive at each discrete trajectory point, and further determine the indentation produced by the cerium oxide abrasive at each discrete trajectory point under the rotation drive of the spherical polishing head 1 based on the Hertz basic theory and the equation of the ball, and obtain the motion footprint of a single cerium oxide abrasive (that is, the scratch mark produced by a single cerium oxide abrasive on the surface of the workpiece 8 under the drive of the polishing head). Embodiment 2

[0079] A computer device, comprising:

[0080] Memory, for storing computer programs / instructions;

[0081] The processor is used to execute the computer program / instructions to implement the steps of the method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process of the first embodiment.

[0082] Working principle:

[0083] The present invention discloses a method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing, which predicts the surface morphology of a workpiece 8 by analytical method. In the process of establishing the model, the number of effective cerium oxide abrasive grains in the effective contact area under the polishing head porosity of the polishing head pore 5, the movement trajectory of cerium oxide abrasive grains in the contact surface between the polishing head and the workpiece under the driving of the oblique rotation of the polishing head, and the influence of the dynamic change of the contact force in the movement trajectory of the cerium oxide abrasive grains on the footprint of the cerium oxide abrasive grains on the machined surface are comprehensively considered.

[0084] Since the polishing process is a precision process, the movement of the cerium oxide abrasive particles under the driving of the tilted rotation of the polishing head produces scratches on the surface of the workpiece 8, which are finally superimposed to form the surface morphology. From a microscopic perspective, the prediction of the movement trajectory of the cerium oxide abrasive particles on the polishing head-workpiece contact surface has a great influence on the surface accuracy of the workpiece 8; secondly, considering that the movement trajectory is a non-circular trajectory, the distance from the center of the contact area changes dynamically with the movement position of the cerium oxide abrasive particles, and then the force state of the cerium oxide abrasive particles changes dynamically, and the scratch and indentation morphology changes dynamically, which in turn affects the polishing accuracy prediction. Therefore, the prediction results of the prediction method provided by the present invention are more accurate, and at the same time provide a reference for the parameter setting of the oblique axis polishing process of the spherical polishing head cerium oxide polishing liquid, thereby improving the polishing efficiency.

[0085] Based on the ideal embodiment of the present invention, through the above description, relevant personnel can make various changes and modifications without departing from the technical concept of the present invention. The technical scope of the present invention is not limited to the content in the specification, and the technical scope must be determined according to the scope of the claims.

Claims

1. A method for predicting the surface morphology of a spherical polishing head by cerium oxide polishing liquid oblique axis polishing, characterized in that: A method for predicting the surface morphology of a workpiece surface by oblique-axis polishing using a spherical polishing head and a cerium oxide abrasive polishing liquid comprises the following steps: Obtaining polishing operation data, wherein the polishing operation data includes polishing parameters of a spherical polishing head, a cerium oxide abrasive polishing liquid, and a workpiece morphology; According to the polishing operation data, based on a pre-trained polishing surface morphology prediction model, a polishing surface morphology prediction process is performed to obtain a spherical polishing head cerium oxide polishing liquid oblique axis polishing surface morphology profile; Wherein, the training of the polishing surface morphology prediction model includes: S1. Use electron microscope scanning to obtain the morphological information of the polishing head. Through the image binarization processing in the image processing algorithm, identify and calculate the pixel ratio to obtain the surface porosity of the polishing head. ; S2. Based on the Hertz contact theory, determine the contact area between the polishing head and the workpiece when the spherical polishing head is vertically fed, and determine the contact pressure at any radial position from the contact center in the contact area between the polishing head and the workpiece; S3, the surface porosity of the polishing head obtained according to step S1 The polishing head-workpiece effective contact area is determined by combining the polishing head-workpiece contact area obtained in step S2; and the number N of effective cerium oxide abrasive particles in the polishing head-workpiece effective contact area is obtained according to the polishing head-workpiece effective contact area, the concentration of cerium oxide polishing liquid and the average particle size of cerium oxide abrasive particles. S4. Use a uniform distribution function and repeatedly propose the motion footprint of a single cerium oxide abrasive generated at any position in the polishing head-workpiece contact plane for N times, generate the coordinates of N cerium oxide abrasives on the polishing head-workpiece contact surface, obtain the footprints of the cerium oxide abrasives under the action of N cerium oxide abrasives, superimpose them in the vertical direction, and obtain the surface morphology profile of the oblique axis polishing process of the spherical polishing head cerium oxide polishing liquid.

2. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 1, characterized in that: The motion footprint of a single cerium oxide abrasive grain generated at any position in the contact plane between the polishing head and the workpiece is proposed, including the following steps: S41, taking the center of the effective contact area between the polishing head and the workpiece as the coordinate origin O, establishing an OXYZ coordinate system, defining the coordinates of a cerium oxide abrasive grain generated at any position in the contact plane between the polishing head and the workpiece as (x, y, 0), and mapping the coordinates of the generated cerium oxide abrasive grain downward to the surface of the polishing head, and the mapped coordinates of the cerium oxide abrasive grain are (x, y, z); S42, take the center of the polishing head as the coordinate origin O1, the plane passing through O1 and parallel to the XOY plane as the X1O1Y1 plane, the direction perpendicular to the X1O1Y1 plane upward as the positive direction of the Z1 axis, and establish the O1X1Y1Z1 coordinate system; rotate the polishing head around the O1X1 axis in the O1X1Y1Z1 coordinate system θ Angle, get the posture of the polishing head for oblique axis polishing, at this time the inclination angle of the polishing head is θ ; S43, based on spatial geometry, calculate the coordinates (x, y, z) of the cerium oxide abrasive grains in the coordinate system OXYZ in step S4 to rotate around the O1X1 axis in the coordinate system O1X1Y1Z1 in step S42 θ The distance R' of the polishing head rotation axis O1Z1' after the angle is determined, and the motion trajectory (x, y, z) of the cerium oxide abrasive grain at the coordinate position (x, y, z) of the polishing head surface during the oblique axis polishing process is determined based on the distance R'. 1’ ,y 1’ ,z 1’ ), the angle of the polar coordinate system is divided into , the algorithm of the motion trajectory of the polishing head surface is: ； S44, the coordinates (x, y, z) determined in step S43 are subjected to a rotation and a translation coordinate transformation on the movement trajectory of the cerium oxide abrasive grains on the surface of the polishing head during the oblique axis polishing of the cerium oxide abrasive grains, wherein the rotation matrix is: , the translation matrix is , 0, ly, lz are the displacements of the coordinate values ​​in the x, y, and z directions respectively. The coordinates in the OXYZ coordinate system are used to represent the motion trajectory of the cerium oxide abrasive particles during the oblique axis polishing process: ； The Z-axis coordinate is set to zero, and the trajectory is projected onto the XOY plane to obtain the actual motion trajectory of the cerium oxide abrasive grains at the coordinate (x, y, z) position in the polishing head-workpiece contact area; ； S45. Combine the contact pressure at each position in the contact area obtained in step S2 with the coordinates of the actual motion trajectory of the cerium oxide abrasive at the coordinate position (x, y, z) in the polishing head-workpiece contact area in step S44, discretize the motion trajectory, and determine the indentation depth and indentation of the cerium oxide abrasive at each discrete motion trajectory point based on the Hertz basic theory to obtain the motion footprint of a single cerium oxide abrasive and the scratch mark produced by a single cerium oxide abrasive on the workpiece surface.

3. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 2, characterized in that: In step S41, the method for establishing the OXYZ coordinate system is: taking the center of the polishing head-workpiece effective contact area as the coordinate origin O, determining the contact area of ​​the polishing head-workpiece effective contact area as the XOY plane, and the vertical contact plane upward as the positive direction of the Z axis, and establishing the OXYZ coordinate system.

4. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 3, characterized in that: In step S41, the cerium oxide abrasive is uniformly distributed in the polishing head-workpiece contact area, and a cerium oxide abrasive is generated at any position in the polishing head-workpiece contact plane. The coordinates of the generated cerium oxide abrasive are (x, y, 0). The coordinates of the generated cerium oxide abrasive are mapped downward to the surface of the polishing head. According to the equation of the ball of the polishing head without contact deformation, the coordinates of the cerium oxide abrasive after mapping are (x, y, z).

5. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 3, characterized in that: In step S2, the polishing head is vertically fed to the contact radius of the polishing head-workpiece contact area. for: ;in, is the radius of the spherical polishing head, is the vertical feed distance of the polishing head; The contact area S is: ; Radial position of the contact area from the contact center r Contact pressure for: ;in, Contact center pressure, contact center pressure is the maximum pressure in the contact area, ;in, is the equivalent elastic modulus.

6. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 3, characterized in that: The step S3 comprises: according to the porosity of the polishing head surface obtained in step 1 The effective number N of cerium oxide abrasive particles is obtained by combining the polishing head-workpiece contact area S obtained in step 2 with the concentration of cerium oxide polishing liquid and the average particle size of cerium oxide abrasive particles.

7. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 6, characterized in that: Polishing head-workpiece effective contact area for: ; Surface mass density of cerium oxide polishing liquid at the polishing head-workpiece contact surface for: ; Among them, m v is the volume mass density of the polishing liquid, h is the height of the polishing liquid, m v / h is the surface mass density of the polishing liquid per unit height, d is the average particle size of cerium oxide abrasive particles in the cerium oxide polishing liquid, and d is set as the average distance between the polishing head and the workpiece contact area.

8. The method for predicting the surface morphology of a spherical polishing head cerium oxide polishing liquid oblique axis polishing process according to claim 7, characterized in that: The mass M of cerium oxide abrasive grains in the contact area between spherical polishing head and workpiece s for: ; The effective cerium oxide abrasive number N is .

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