Method for predicting material removal rate of a vibratory air grinder

Abstract

The application discloses a vibration type air grinder polishing material removal rate prediction method, comprising the following steps: S1, sequentially extracting track points in a polishing track, and taking a currently extracted track point as a current initial contact point; S2, calculating a maximum contact depth h0 corresponding to a constant polishing force F at the current initial contact point, and then calculating the size of a current polishing area; and S3, calculating a material removal rate under the current constant polishing force F and the polishing area, wherein the removal rate represents a removal thickness. According to the method, the maximum contact depth of a polishing disc and a workpiece to be polished in a polishing process is used to represent polishing force and material removal rate, the polishing force size is calculated by using contact area equivalence, and the method is suitable for polishing of vibration polishing discs with different shapes.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of workpiece processing, and more particularly, relates to a polishing material removal rate prediction method for a vibration type air grinder. BACKGROUND

[0002] Polishing is polishing and polishing of a workpiece, removing a uniform layer on the surface of the workpiece, and having certain requirements for the final surface quality and precision, and the surface characteristics directly affect the use characteristics of the processed workpiece.

[0003] For polishing of a free-form surface, such as a hub surface, an aircraft blade, and the like, a uniform layer of oxide needs to be removed on the free-form surface, and since a workpiece polished by an industrial robot instead of manual polishing does not have as good an effect as a skilled worker, the workpiece is currently mainly polished by manual polishing.

[0004] A large amount of dust and noise is generated during polishing, which causes irreparable damage to the worker's body, the consistency of the workpiece surface after polishing is related to the worker's proficiency, and the quality of the polished workpiece is difficult to control and difficult to meet the needs of modern industrial production. SUMMARY

[0005] The present application provides a polishing material removal rate prediction method for a vibration type air grinder, which aims to improve the above problems.

[0006] The present application is implemented as follows: a polishing material removal rate prediction method for a vibration type air grinder, the method specifically comprising the following steps:

[0007] S1, sequentially extracting trajectory points in a polishing trajectory, and taking the currently extracted trajectory point as a current initial contact point;

[0008] S2, calculating a maximum contact depth h0 corresponding to a constant polishing force F at the current initial contact point, and further calculating the size of the current polishing area;

[0009] S3, calculating the material removal rate under the current constant polishing force F and the polishing area, and the removal rate representing the removal thickness per unit time.

[0010] Further, the maximum contact depth h0 under the constant polishing force F is calculated according to the following formula:

[0011]

[0012] wherein, is the elastic modulus of the polishing disc, H is the thickness of the polishing disc, β is the nonlinear index of the contact between the polishing disc and the workpiece, m is the radius of the polishing disc, θ is the included angle between the normal direction of the polishing disc and the normal direction of the workpiece at the initial contact point O, and b -1 is the radius of curvature of the initial contact point O on the surface of the workpiece along the Y-axis direction.

[0013] Further, the width w of the current polishing area is calculated as follows:

[0014]

[0015] where h0 is the maximum contact depth under constant polishing force F, m is the radius of the polishing disc, b is the radius of curvature of the initial contact point O on the workpiece surface along the Y-axis, and θ is the angle between the normal direction of the polishing disc and the normal direction of the workpiece. -1

[0016] Further, the length l of the current polishing area is calculated as follows:

[0017]

[0018] where h0 is the maximum contact depth under constant polishing force F, and θ is the angle between the normal direction of the polishing disc and the normal direction of the workpiece.

[0019] Further, the material removal rate MR is calculated as follows:

[0020]

[0021] where r is the vibration radius of the polishing disc, K is the wear coefficient of the workpiece to be polished, which is determined through prior experiments, v is the polishing feed speed of the polishing disc, v is the vibration speed of the polishing disc during polishing, which is equal to the polishing speed between the polishing disc and the free-form surface, and y is the coordinate of the current initial contact point on the Y-axis. w m

[0022] Further, the constant polishing force of the current initial contact point is set based on the curvature b of the current initial contact point.

[0023] Further, when , the constant polishing force is calculated as follows:

[0024]

[0025] When , the constant polishing force is calculated as follows:

[0026]

[0027] where c is a proportional coefficient.

[0028] Further, the proportional coefficient c is calculated as follows:

[0029]

[0030] where​​​ E is the elastic modulus of the polishing pad, H is the thickness of the polishing pad, and β is the nonlinear index of the contact between the polishing pad and the workpiece.

[0031] Further, when When the free-form surface to be polished is concave and has a large curvature, the polishing process cannot be performed.

[0032] The vibration type air grinder polishing material removal rate prediction method provided by the present application has the following beneficial technical effects: (1) a method for predicting material removal in vibration polishing is provided, which can realize offline prediction of the material removal rate in the vibration polishing process; (2) a method for representing the polishing force and the material removal rate according to the maximum contact depth of the contact between the polishing pad and the workpiece to be polished, which uses the contact area to calculate the polishing force, and is suitable for polishing of polishing pads of different shapes; (3) a method for dividing the free-form surface according to the curvature, which divides the regions according to the curvature of the surface, and uses different polishing force planning strategies in different regions, which can be better applied to polishing of workpieces with different curvatures. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 A vibration type air grinder polishing material removal rate prediction method flowchart is provided for the embodiment of the present application.

[0034] Figure 2 A polishing pad and workpiece surface contact schematic diagram is provided for the embodiment of the present application.

[0035] Figure 3 A Figure 2 projection schematic diagram of the contact area in the XY plane. DETAILED DESCRIPTION

[0036] The specific embodiments of the present application will be further described below with reference to the drawings, and the description of the embodiments will help those skilled in the art to have a more complete, accurate and in-depth understanding of the inventive concept and technical solutions of the present application.

[0037] Figure 1 A vibration type air grinder polishing material removal rate prediction method flowchart is provided for the embodiment of the present application, and the method includes the following steps:

[0038] S1, sequentially extracting the track points in the polishing track, and taking the currently extracted track point as the current initial contact point;

[0039] The Figure 2As shown in the schematic diagram of the contact between the polishing disc and the workpiece surface, the polishing disc with an equivalent radius of m initially contacts the workpiece at point O, and an orthogonal coordinate system O-XYZ is established on the workpiece surface according to the following rules: the feeding direction f of the polishing disc is the X axis, the normal direction n of the surface is aligned and perpendicular to the workpiece surface at the initial contact point O, the direction of the Z axis is perpendicular to the workpiece surface, and the Y axis is given by the unit vector n x f. The local deformation of the polishing disc at the initial contact point O is shown as a gray area after the polishing disc is pressed into the workpiece at an inclination angle θ, and the initial contact point O is the maximum contact depth in the contact area.

[0040] S2, the maximum contact depth h0 corresponding to the constant polishing force F at the current initial contact point is calculated, and then the size of the current polishing area is calculated;

[0041] In the embodiment of the application, the maximum contact depth h0 under the constant polishing force F is calculated based on the following formula:

[0042]

[0043] wherein, is the elastic modulus of the polishing disc, H is the thickness of the polishing disc, β is the nonlinear index of the contact between the polishing disc and the workpiece, m is the radius of the polishing disc, θ is the angle between the normal direction of the polishing disc and the normal of the workpiece at the initial contact point O, and b -1 is the radius of curvature of the initial contact point O of the workpiece surface along the Y axis direction.

[0044] In the embodiment of the application, the size of the maximum contact depth h0, i.e. the width w and the length l of the current polishing area, Figure 3 is Figure 2 the projection of the contact area in the XY plane, i.e. the polishing area, C1 in the figure represents the shape of the polishing disc, and the polishing disc can be circular, triangular, rectangular or other shapes with different shapes. The formula (1) can be used to calculate the relationship between the polishing force F and the maximum contact depth h0 for the above shapes, and the shape of C2 is determined by the curvature b of the workpiece surface. The calculation formula of the polishing area is as follows:

[0045]

[0046]

[0047] S3, the material removal rate under the current constant polishing force F and the polishing area is calculated, and the removal rate represents the removal thickness per unit time.

[0048] In the embodiment of the application, according to the Preston equation, a material removal rate model is established, and the calculation formula of the material removal rate MR is as follows:

[0049]

[0050] wherein r is the vibration radius of the polishing disc, K is the wear coefficient of the workpiece to be polished, determined through prior experiments, v w is the polishing feed speed of the polishing disc, v m is the vibration speed of the polishing disc during polishing, equal to the polishing speed between the polishing disc and the free-form surface, and y is the coordinate of the current initial track point on the Y axis.

[0051] When the inclination angle of the polishing disc is small, sinθ is approximately equal to θ and tanθ is approximately equal to θ, b<0 indicates that the free-form surface is concave, b>0 indicates that the polished surface is convex, and b=0 indicates a polishing plane. In the embodiment of the present application, the constant polishing force of the current initial contact point is set according to the curvature b of the polishing area, and the setting method of the constant polishing force is as follows:

[0052] (1) When , i.e., the curvature radius of the free-form surface to be polished is much larger than the radius m of the polishing disc, the calculation formula of the constant polishing force is as follows:

[0053]

[0054] (2) When , i.e., the curvature radius at the contact surface is much smaller than the radius of the polishing disc, the size of the polishing force during polishing is no longer related to the radius of the polishing disc, and the curvature radius is used to calculate the size of the polishing force, i.e.,

[0055]

[0056] wherein c is a proportional coefficient, and the calculation formula of c is as follows:

[0057]

[0058] The size of β is related to the material of the workpiece contacted by the polishing disc and the elastic deformation capacity of the polishing disc, and β is larger when the elastic deformation per unit length is larger. When the elastic deformation is greater than 20%, the value of β is generally 0.8, and at this time,

[0059] (3) When , it indicates that the free-form surface is seriously concave inward and cannot be polished.

[0060] The vibration-type air grinder polishing material removal rate prediction method provided by the present application has the following beneficial technical effects:

[0061] (1) A method for predicting the material removal of vibration polishing is provided, which can realize offline prediction of the material removal rate in the vibration polishing process.

[0062] (2) according to the polishing process polishing disc and the maximum contact depth of the contact with the workpiece to be polished, the polishing force and the material removal rate are expressed, the polishing force size is calculated by using the contact area, and the polishing is suitable for polishing of polishing discs with different shapes;

[0063] (3) a method for dividing a free-form surface according to the curvature size, regions are divided according to the curvature size of the surface, and different polishing force planning strategies are used on different regions, so that the polishing is better suitable for workpieces with different curvatures.

[0064] The application is described exemplarily, and it is obvious that the specific implementation of the application is not limited by the above methods, as long as various non-essential improvements are made by using the method concept and technical scheme of the application, or the concept and technical scheme of the application are directly applied to other occasions without improvement, all of which are within the protection scope of the application.

Claims

1. A method for predicting the material removal rate of a vibratory air mill polishing material, characterized in that, The method specifically includes the following steps: S1. Sequentially extract the trajectory points in the grinding trajectory, and take the currently extracted trajectory point as the current initial contact point; S2. Calculate the maximum contact depth h0 corresponding to the constant grinding force F at the current initial contact point, and then calculate the size of the current grinding area; S3. Calculate the current constant grinding force F and the material removal rate in the grinding area. The removal rate represents the thickness removed per unit time. The formula for calculating the maximum contact depth h0 under a constant grinding force F is as follows: in, Let H be the elastic modulus of the grinding disc, H be the thickness of the grinding disc, β be the nonlinearity index of the contact between the grinding disc and the workpiece, m be the radius of the grinding disc, θ be the angle between the normal direction of the grinding disc and the normal direction of the workpiece at the initial contact point O, and b be the elastic modulus of the grinding disc. -1 It is the radius of curvature along the Y-axis at the initial contact point O on the workpiece surface, and h0 is the maximum contact depth under a constant grinding force F. The formula for calculating the material removal rate (MR) is as follows: Where r is the vibration radius of the grinding disc, K is the wear coefficient of the workpiece to be ground, determined through prior experiments, and v w v is the feed speed for polishing the grinding disc. m The vibration speed of the polishing disc during polishing is v. m It equals the polishing speed between the polishing disc and the freeform surface, y is the coordinate of the current initial trajectory point on the Y-axis, and w represents the width of the current polishing area.

2. The method for predicting the material removal rate of a vibratory air mill as described in claim 1, characterized in that, The formula for calculating the width w of the current grinding area is as follows: Where h0 is the maximum contact depth under constant grinding force F, m is the radius of the grinding disc, and b -1 It is the radius of curvature along the Y-axis at the initial contact point O on the workpiece surface, and θ is the angle between the normal direction of the grinding disc and the normal direction of the workpiece.

3. The method for predicting the material removal rate of a vibratory air mill as described in claim 1, characterized in that, The formula for calculating the length l of the current grinding area is as follows: Where h0 is the maximum contact depth under constant grinding force F, and θ is the angle between the normal direction of the grinding disc and the normal direction of the workpiece.

4. The method for predicting the material removal rate of a vibratory air mill as described in claim 1, characterized in that, The constant grinding force at the current initial contact point is set based on the curvature b of the current initial contact point.

5. The method for predicting the material removal rate of a vibratory air mill as described in claim 4, characterized in that, exist The specific formula for calculating a constant grinding force F is as follows: exist The specific formula for calculating a constant grinding force F is as follows: Where c is the proportionality coefficient, m is the radius of the grinding disc, and b -1 θ is the radius of curvature along the Y-axis at the initial contact point O on the workpiece surface, h0 is the maximum contact depth under constant grinding force F, and θ is the angle between the normal direction of the grinding disc and the normal direction of the workpiece at the initial contact point O.

6. The method for predicting the material removal rate of a vibratory air mill as described in claim 5, characterized in that, The formula for calculating the proportionality coefficient c is as follows: in, Let β be the elastic modulus of the grinding disc, H be the thickness of the grinding disc, and β be the nonlinearity index of the contact between the grinding disc and the workpiece.

7. The method for predicting the material removal rate of a vibratory air mill as described in claim 5, characterized in that, exist At that time, the free-form surface to be polished was severely concave and could not be polished. Where m is the radius of the grinding disc, b -1 It is the radius of curvature along the Y-axis at the initial contact point O on the workpiece surface.

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