Polishing surface roughness prediction method based on robot flexible ball tool

Abstract

The application relates to the technical field of optical processing, in particular to a polishing surface roughness prediction method based on a robot flexible ball head tool, which comprises the following steps: firstly, a micro contact model of the flexible ball head tool and a workpiece is established, and a first pressure distribution of a contact area between the flexible ball head tool and the workpiece is determined; vibration of the flexible ball head tool is converted into pressure fluctuation of the flexible ball head tool, and a total pressure distribution during processing is obtained, and then a second pressure distribution is formed; a relative speed model during processing of the flexible ball head tool is combined with the second pressure distribution, and a material removal rate model during processing of the flexible ball head tool is obtained; path integration is performed on the material removal rate model, and surface height variation of the workpiece during processing is obtained; and the original surface height of the workpiece and the surface height variation are combined, and the surface roughness of the workpiece after processing is obtained. The application discloses a quantitative relationship between vibration parameters and surface roughness, and provides a theoretical basis for optimizing polishing process parameters and controlling surface quality.

Description

Technical Field

[0001] The invention belongs to the technical field of optical processing, and in particular relates to a polishing surface roughness prediction method based on a robot flexible ball head tool. Background Art

[0002] In recent years, robotic polishing has gained widespread attention in ultra-precision manufacturing due to its advantages such as high flexibility, wide workspace, cost-effectiveness and suitability for complex surface processing. However, the inherent structural vibration of the robotic system significantly affects the uniformity of material removal and surface quality during the polishing process, and has become a key limiting factor in high-precision applications. Current research on the influence of vibration on the polishing process mainly focuses on the description of experimental phenomena, and lacks the establishment of theoretical models and quantitative relationships to reveal the influence of vibration on micro-scale material removal. The existing Preston equation, as the basis of polishing theory, cannot accurately characterize the material removal unevenness caused by dynamic pressure changes under vibration conditions. Although some scholars have proposed various vibration suppression technologies, such as constant force control and active vibration suppression systems, these methods are mainly based on empirical engineering improvements, and lack theoretical analysis and quantitative prediction models to describe the relationship between vibration and material removal, which limits the further development of robotic polishing technology in the field of ultra-precision machining.

[0003] The existing technology has the following major disadvantages:

[0004] (1) Lack of theoretical model: There is a lack of theoretical model for microscopic material removal under vibration conditions, which makes it impossible to quantitatively describe the relationship between vibration parameters and surface roughness;

[0005] (2) Insufficient prediction ability: The traditional Preston equation fails in a vibration environment and cannot accurately predict the effect of dynamic pressure changes on material removal uniformity;

[0006] (3) The vibration suppression effect is difficult to quantify: the existing vibration suppression technology lacks a quantitative evaluation method, and it is impossible to scientifically evaluate the suppression effect;

[0007] (4) Difficulty in surface quality control: Due to the lack of in-depth understanding of the formation mechanism of surface micromorphology under vibration conditions, it is difficult to achieve precise surface quality control. Summary of the Invention

[0008] In light of this, the present invention aims to provide a method for predicting polished surface roughness using a robotic flexible ball-end tool. This method establishes a theoretical model for microscale surface roughness under vibration conditions, reveals the quantitative relationship between vibration parameters and surface roughness, and provides a theoretical basis for optimizing polishing process parameters and controlling surface quality. This approach also provides a scientific basis for high-efficiency, high-precision manufacturing in the field of ultra-precision optical processing.

[0009] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0010] A method for predicting polishing surface roughness based on a robot flexible ball head tool, comprising:

[0011] S1: establishing a microscopic contact model between the flexible ball-end tool and the workpiece, and determining a first pressure distribution in a contact area between the flexible ball-end tool and the workpiece based on the microscopic contact model;

[0012] S2: converting the vibration of the flexible ball head tool during machining of the workpiece into pressure fluctuations of the flexible ball head tool to obtain a total pressure distribution during machining, and substituting the total pressure distribution into the first pressure distribution obtained in step S1 to form a second pressure distribution;

[0013] S3: combining the second pressure distribution obtained in step S2 and the relative velocity model of the flexible ball head tool during machining to obtain a material removal rate model during machining with the flexible ball head tool;

[0014] S4: performing path integration on the material removal rate model obtained in step S3 to obtain the surface height change of the workpiece during the machining process; combining the original surface height of the workpiece and the surface height change to obtain the surface roughness of the workpiece after machining.

[0015] Furthermore, in step S1:

[0016] The microscopic contact model is:

[0017] ;

[0018] Where a represents the radius of the contact area of ​​the flexible ball head tool when machining the workpiece, R represents the spherical radius of the flexible ball head tool, It represents the equivalent elastic modulus when the flexible ball head tool is machining the workpiece, and F represents the total pressure distribution when the flexible ball head tool is machining the workpiece;

[0019] The first pressure distribution is:

[0020] ;

[0021] Wherein, p1(r) represents the first pressure distribution, and r represents the radial distance from any point in the contact area to the center of the contact area.

[0022] Furthermore, the equivalent elastic modulus is obtained by the following formula:

[0023] ;

[0024] in, represents the Poisson's ratio of the workpiece material, represents the Poisson's ratio of the flexible ball head tool material, represents the elastic modulus of the workpiece material, Represents the elastic modulus of the tool material.

[0025] Furthermore, in step S2, the process of converting the vibration of the flexible ball-end tool into pressure fluctuations of the flexible ball-end tool includes:

[0026] The vibration of the flexible ball-end tool is expressed by the following formula:

[0027] ;

[0028] Where h(t) represents the vibration displacement generated by the flexible ball head tool at time t, h0 represents the vibration amplitude of the flexible ball head tool when processing the workpiece, and f v Indicates the vibration frequency of the flexible ball head tool when processing the workpiece;

[0029] According to Hertz contact theory, the relationship between the contact deformation generated when the workpiece is machined and the spherical radius of the flexible ball head tool is:

[0030] ;

[0031] Where δ represents the contact deformation;

[0032] The relationship between contact deformation and total pressure distribution is further obtained as follows:

[0033] ;

[0034] Taking the derivative of the contact deformation in the above formula, we can get the normal stiffness of the contact area, which is:

[0035] ;

[0036] Among them, K n represents the normal stiffness;

[0037] Combining the normal stiffness and contact deformation analysis, the pressure change caused by vibration during machining of the flexible ball head tool is obtained by the following formula:

[0038] ;

[0039] Wherein, ΔF(t) represents the pressure change of the flexible ball head tool at time t, and F0 represents the reference static pressure of the workpiece processed by the flexible ball head tool.

[0040] Furthermore, the total pressure distribution in step S2 is:

[0041] ;

[0042] Where F(s) represents the total pressure of the flexible ball head tool under the path distance s of the workpiece, v feed represents the moving speed of the flexible ball head tool when machining the workpiece, A represents the pressure fluctuation amplitude coefficient; ΔF(s) represents the pressure change of the flexible ball head tool under the path distance s, which is obtained by the following formula:

[0043] ;

[0044] The pressure fluctuation amplitude coefficient A is obtained by the following formula:

[0045] .

[0046] Furthermore, the material removal rate model in step S3 is:

[0047] ;

[0048] Where MRR represents the material removal rate, p2(r,s) represents the second pressure distribution, θ represents the angle between the line connecting any point in the contact area and the center point of the contact area and the horizontal, and k represents the Preston constant.

[0049] Furthermore, in step S4, the surface height change is obtained by the following formula:

[0050] ;

[0051] Where Δz(x, y) represents the surface height change at the (x, y) position on the workpiece after machining, and C represents the motion trajectory of the flexible ball head tool.

[0052] Furthermore, in step S4, the surface roughness is obtained by the following formula:

[0053] ;

[0054] Where Ra represents the surface roughness, L represents the evaluation length, z0(x) represents the original surface height at position x on the workpiece, represents the original average surface height of the workpiece, Indicates the average surface height variation of the workpiece.

[0055] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0056] The present invention proposes a method for predicting polished surface roughness using a robotic flexible ball-end tool. This method establishes a theoretical model for surface roughness at the microscale that accounts for vibration factors. This model fills a gap in ultraprecision polishing theory and provides a theoretical basis for understanding the formation mechanism of surface microtopography under vibration. A quantitative relationship between vibration parameters and surface roughness characteristics is established, which can be used to predict and control surface quality during polishing, providing theoretical guidance for high-precision machining. The established theoretical model for microscopic surface roughness can be further extended to other ultraprecision machining areas, such as robotic chemical mechanical polishing and robotic magnetorheological polishing, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0058] Figure 1 The present invention is a flowchart of a method for predicting the polishing surface roughness based on a robot flexible ball head tool according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0060] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0061] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0062] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0063] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0064] like Figure 1 As shown, the polishing surface roughness prediction method based on the robot flexible ball head tool described in the embodiment of the present invention includes:

[0065] S1: establishing a microscopic contact model between the flexible ball head tool and the workpiece, and determining a first pressure distribution in the contact area between the flexible ball head tool and the workpiece based on the microscopic contact model.

[0066] In step S1, when a flexible ball-tip tool with a spherical radius of R contacts the workpiece with a total pressure F, a circular contact area with a radius of a is formed. At this time, the microscopic contact model between the flexible ball-tip tool and the workpiece is described as follows:

[0067] ;

[0068] in, It represents the equivalent elastic modulus of the flexible ball head tool when processing the workpiece, which is obtained by the following formula:

[0069] ;

[0070] in, represents the Poisson's ratio of the workpiece material, represents the Poisson's ratio of the flexible ball head tool material, represents the elastic modulus of the workpiece material, The elastic modulus of the tool material is the elastic modulus of the workpiece material and the tool material. The elastic modulus of the workpiece material and the tool material are inherent properties of the material and can be measured. In the embodiment of the present invention, the total pressure F is the force in the normal direction acting on any point in the contact area, and the workpiece to be processed is a planar workpiece.

[0071] In the contact area, the first pressure distribution p1(r) follows a semi-ellipsoidal distribution, and the first pressure distribution p1(r) is obtained as:

[0072] ;

[0073] Where p0 represents the maximum pressure at the center of the contact area, and r represents the radial distance from any point in the contact area to the center of the contact area. The relationship between the maximum pressure p0 and the total pressure F is:

[0074] ;

[0075] Combining the relationship between the maximum pressure p0 and the total pressure F with the formula of the first pressure distribution p1(r), the first pressure distribution p1(r) is obtained as:

[0076] .

[0077] S2: Convert the vibration of the flexible ball head tool when processing the workpiece into pressure fluctuations of the flexible ball head tool to obtain the total pressure distribution during processing, and substitute the total pressure distribution into the first pressure distribution obtained in step S1 to form a second pressure distribution.

[0078] In an embodiment of the present invention, the vibration of the flexible ball-end tool is expressed as a displacement function, namely:

[0079] ;

[0080] Where h(t) represents the vibration displacement generated by the flexible ball head tool at time t, h0 represents the vibration amplitude of the flexible ball head tool when processing the workpiece, and f v Indicates the vibration frequency of the flexible ball head tool when processing the workpiece.

[0081] Normal stiffness K of the contact area n It is defined as the derivative of the total pressure distribution F with respect to the contact deformation δ generated when the workpiece is machined:

[0082] ;

[0083] According to Hertz contact theory, the relationship between the contact deformation δ and the spherical radius R of the flexible ball head tool is:

[0084] ;

[0085] Substituting the microscopic contact model into the above relationship, the relationship between the contact deformation δ and the total pressure distribution F is obtained as follows:

[0086] .

[0087] Taking the derivative of the contact deformation δ in the above formula, we can get the normal stiffness K of the contact area. n ,Right now:

[0088] .

[0089] Combining the normal stiffness and contact deformation analysis, the pressure change caused by vibration during machining of the flexible ball head tool is obtained by the following formula:

[0090] ;

[0091] Wherein, ΔF(t) represents the pressure change of the flexible ball head tool at time t, and F0 represents the reference static pressure of the workpiece processed by the flexible ball head tool.

[0092] At this time, the total pressure distribution F is expressed as:

[0093] ;

[0094] Where F(t) represents the total pressure of the flexible ball head tool when machining the workpiece at time t, and A represents the pressure fluctuation amplitude coefficient.

[0095] Let the flexible ball head tool move at a constant speed v feed Moving, the relationship between time t and path distance s is:

[0096] ;

[0097] At this time, the pressure change ΔF(t) of the flexible ball head tool at the path distance s is obtained as follows:

[0098] ;

[0099] At the same time, the relationship between time t and path distance s is substituted into the total pressure distribution F, and the total pressure distribution F along the path is obtained as:

[0100] ;

[0101] Among them, the pressure fluctuation amplitude coefficient A is:

[0102] .

[0103] S3: Combining the second pressure distribution obtained in step S2 and the relative velocity model during machining with the flexible ball head tool, a material removal rate model during machining with the flexible ball head tool is obtained:

[0104] ;

[0105] Where MRR represents the material removal rate, p2(r,s) represents the second pressure distribution, θ represents the angle between the line connecting any point in the contact area and the center point of the contact area and the horizontal, and k represents the Preston constant.

[0106] S4: performing path integration on the material removal rate model obtained in step S3 to obtain the surface height change of the workpiece during the machining process; combining the original surface height of the workpiece and the surface height change to obtain the surface roughness of the workpiece after machining.

[0107] The evolution of the workpiece surface during the polishing process can be regarded as the cumulative effect of material removal. For any point (x, y), the change in the surface height of the workpiece can be expressed as:

[0108] ;

[0109] Where Δz(x,y) represents the surface height change at the (x,y) position on the workpiece after processing, [t start ,t end ] indicates the time range during which the point is polished.

[0110] Considering the motion trajectory of the tool, the time integral can be converted into a path integral:

[0111] .

[0112] Where C represents the motion trajectory of the flexible ball head tool. The surface microscopic height of the workpiece after processing is:

[0113] ;

[0114] Where z(x,y) represents the surface height at position (x,y) on the workpiece after machining, and z0(x,y) represents the original surface height at position (x,y) on the workpiece, which is the basic surface morphology of the workpiece in the absence of vibration.

[0115] Surface roughness Ra is defined as the average deviation of surface height, that is:

[0116] ;

[0117] Where Ra represents the surface roughness, L represents the evaluation length, represents the average surface height of the machined workpiece, and z(x) represents the surface height at position x on the machined workpiece. The evaluation length L is the range of surface roughness measurement and is an essential parameter for measuring surface roughness.

[0118] Combined with the formula of the surface height z(x,y) of the processed workpiece, the surface roughness Ra is further obtained as:

[0119] ;

[0120] Where z0(x) represents the original surface height at position x on the workpiece, represents the original average surface height of the workpiece, Indicates the average surface height variation of the workpiece.

[0121] The method provided by the present invention can be applied to the scenarios of chemical mechanical polishing (CMP), robotic magnetorheological polishing, ultrasonic assisted polishing, online quality monitoring and multi-scale surface optimization. Specifically, in chemical mechanical polishing, the method provided by the present invention can be applied to the polishing process of semiconductors using chemical reagents and flexible ball head tools, and predict the surface roughness after the chemical mechanical polishing process; in robotic magnetorheological polishing, the method provided by the present invention can be applied to the process of polishing optical elements using magnetorheological as the polishing medium and the flexible ball head tool as the polishing head, and predict the surface roughness after the robotic magnetorheological polishing, thereby completing surface quality prediction and control; in ultrasonic assisted polishing, the method provided by the present invention can be applied to polishing elements using ultrasonic assisted flexible ball head tools, and predict the surface roughness after ultrasonic assisted polishing, thereby achieving real-time prediction and control of surface roughness during the polishing process; in online quality monitoring, the method provided by the present invention combines online monitoring technology to achieve real-time prediction and control of surface roughness during the polishing process. For example, the change in polishing force can be measured using the Kislter real-time force sensor, and the state of optical surface roughness can be predicted by the formula in this article.

[0122] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0123] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for predicting polishing surface roughness based on a robot flexible ball head tool, characterized in that: include: S1: establishing a microscopic contact model between the flexible ball head tool and the workpiece, and determining a first pressure distribution in the contact area between the flexible ball head tool and the workpiece based on the microscopic contact model; S2: converting the vibration of the flexible ball head tool during machining of the workpiece into pressure fluctuations of the flexible ball head tool to obtain a total pressure distribution during machining, and substituting the total pressure distribution into the first pressure distribution obtained in step S1 to form a second pressure distribution; S3: combining the second pressure distribution obtained in step S2 and the relative velocity model of the flexible ball head tool during machining to obtain a material removal rate model during machining with the flexible ball head tool; S4: performing path integration on the material removal rate model obtained in step S3 to obtain the surface height change of the workpiece during the machining process; combining the original surface height of the workpiece and the surface height change to obtain the surface roughness of the workpiece after machining.

2. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 1 is characterized in that: In step S1: The microscopic contact model is: ； Where a represents the radius of the contact area of ​​the flexible ball head tool when machining the workpiece, R represents the spherical radius of the flexible ball head tool, It represents the equivalent elastic modulus when the flexible ball head tool is machining the workpiece, and F represents the total pressure distribution when the flexible ball head tool is machining the workpiece; The first pressure distribution is: ； Wherein, p1(r) represents the first pressure distribution, and r represents the radial distance from any point in the contact area to the center of the contact area.

3. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 2 is characterized in that: The equivalent elastic modulus is obtained by the following formula: ； in, represents the Poisson's ratio of the workpiece material, represents the Poisson's ratio of the flexible ball head tool material, represents the elastic modulus of the workpiece material, Represents the elastic modulus of the tool material.

4. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 2 is characterized in that: The process of converting the vibration of the flexible ball-tip tool into pressure fluctuations of the flexible ball-tip tool in step S2 includes: The vibration of the flexible ball-end tool is expressed by the following formula: ； Where h(t) represents the vibration displacement generated by the flexible ball head tool at time t, h0 represents the vibration amplitude of the flexible ball head tool when processing the workpiece, and f v Indicates the vibration frequency of the flexible ball head tool when processing the workpiece; According to Hertz contact theory, the relationship between the contact deformation generated when the workpiece is machined and the spherical radius of the flexible ball head tool is: ； Where δ represents the contact deformation; The relationship between contact deformation and total pressure distribution is further obtained as follows: ； Taking the derivative of the contact deformation in the above formula, we can get the normal stiffness of the contact area, which is: ； Among them, K n represents the normal stiffness; Combining the normal stiffness and contact deformation analysis, the pressure change caused by vibration during machining of the flexible ball head tool is obtained by the following formula: ； Wherein, ΔF(t) represents the pressure change of the flexible ball head tool at time t, and F0 represents the reference static pressure of the workpiece processed by the flexible ball head tool.

5. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 4 is characterized in that: The total pressure distribution in step S2 is: ； Where F(s) represents the total pressure of the flexible ball head tool under the path distance s of the workpiece, v seed represents the moving speed of the flexible ball head tool when machining the workpiece, A represents the pressure fluctuation amplitude coefficient; ΔF(s) represents the pressure change of the flexible ball head tool under the path distance s, which is obtained by the following formula: ； The pressure fluctuation amplitude coefficient A is obtained by the following formula: 。 6. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 5 is characterized in that: The material removal rate model in step S3 is: ； Where MRR represents the material removal rate, p2(r,s) represents the second pressure distribution, θ represents the angle between the line connecting any point in the contact area and the center point of the contact area and the horizontal, and k represents the Preston constant.

7. The method for predicting polishing surface roughness based on a robot flexible ball head tool according to claim 6, characterized in that: In step S4, the surface height change is obtained by the following formula: ； Where Δz(x, y) represents the surface height change at the (x, y) position on the workpiece after machining, and C represents the motion trajectory of the flexible ball head tool.

8. The polishing surface roughness prediction method based on a robot flexible ball head tool according to claim 6, characterized in that: In step S4, the surface roughness is obtained by the following formula: ； Where Ra represents the surface roughness, L represents the evaluation length, z0(x) represents the original surface height at position x on the workpiece, represents the original average surface height of the workpiece, Indicates the average surface height variation of the workpiece.

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