Robot variable spraying coating optimization method for convex and concave feature surface
By establishing vertical and variable inclination spraying models in the spraying robot and optimizing the spraying trajectory, the problem of poor coating uniformity during complex surface spraying is solved, and higher film thickness error accuracy and lower material waste are achieved.
Patent Information
- Application Number
- CN202411596629.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-11
- Publication Date
- 2025-02-25
AI Technical Summary
When spraying complex shaped surfaces with characteristics such as protrusions and depressions, it is difficult to meet the requirements of high film thickness error accuracy, resulting in poor uniformity of the coating, waste of materials and safety risks.
A robot variable spray coating optimization method for raised and sag feature surfaces is proposed. By establishing vertical static and dynamic spraying models and variable inclination static and dynamic spraying models, the impact of raised and sag geometric parameters on coating uniformity is explored, and a variable inclination spray trajectory optimization method is proposed to improve coating uniformity.
It effectively improves the coating uniformity of the raised and concave feature surfaces, solves the limitations of the traditional vertical spraying method when dealing with complex surfaces, reduces material waste and improves safety.
Smart Images
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Abstract
Description
Technical Field
[0001] The invention relates to a spraying method for convex and concave features, and in particular to a robot variable spraying coating optimization method for a convex and concave feature surface. Background Art
[0002] Spraying robots have been widely used in the coating process of industries such as automobiles and aviation due to their advantages such as stable spraying quality, high spraying efficiency and high degree of automation. However, there are still many spraying operations that require manual spraying due to their special working conditions. This causes the spraying results to be highly dependent on the workers' work proficiency and working status, making it difficult to guarantee the product effect and the spraying effect poor. In addition, it also leads to material waste and even endangers the personal safety of manual spraying workers. With the continuous improvement of the complexity of the appearance design of modern industrial products, the existing technology is difficult to meet the requirements of high film thickness error accuracy when spraying complex surfaces with features such as protrusions and depressions.
[0003] Therefore, optimizing the uniformity of spray coatings on complex surfaces has become a major technical challenge in the promotion and application of intelligent spray robots. Existing robotic spraying technologies for complex surface features such as protrusions and depressions mainly rely on vertical spray trajectory planning methods. These methods usually first establish a vertical static spraying model, and then use a vertical dynamic spraying model that includes spraying parameters such as spraying speed, spraying height, and trajectory spacing to calculate the optimal spraying parameters using an intelligent algorithm. The trajectory of the spraying robot is taught according to these parameters to achieve a more uniform coating thickness. However, when the curvature of a local area of a complex surface exceeds a specific range and forms an angular feature, the traditional vertical spraying method has obvious limitations in dealing with these features.
[0004] Specifically, as the height of protrusions and the depth of depressions on complex surfaces increase, the coating uniformity on the sides of the protrusions and depressions will gradually decrease, making it more difficult to optimize the spraying parameters and often making it impossible to find suitable teaching points for the spraying trajectory.
[0005] In addition, when spraying the outer corners of convex and concave features, the conical spray of the spray gun will be sprayed in large quantities into the air outside the surface, causing paint waste and environmental pollution; and when spraying the inner corners, the spraying quality of the sides of convex and concave features is difficult to guarantee, and often requires manual re-spraying. Existing methods lack effective spray trajectory optimization solutions when dealing with convex and concave features. Summary of the invention
[0006] Purpose of the invention: In order to solve the problem of poor coating uniformity when the traditional vertical spray trajectory planning method is applied to surfaces with raised or recessed features, the present invention proposes a robot variable spray coating optimization method for surfaces with raised or recessed features. First, based on the established vertical static and dynamic spraying models and variable inclination static and dynamic spraying models, the influence of the geometric parameters of the raised or recessed surfaces on the coating uniformity is obtained, and the range of raised height and recessed depth suitable for the vertical spraying method is discussed. Secondly, for raised or recessed features that are not suitable for vertical spraying, a variable inclination spray trajectory optimization method is proposed. Finally, by establishing a variable inclination dynamic spraying model and optimizing the objective function, the coating uniformity of surfaces with raised or recessed features is improved.
[0007] Technical solution: The robot variable spray coating optimization method for convex and concave feature surfaces of the present invention comprises the following steps:
[0008] (1) Set the vertical static spraying model as a parabolic model, and establish a vertical dynamic spraying model for convex and concave parts based on the vertical static spraying model:
[0009]
[0010] in:
[0011]
[0012] Among them, T S is the coating thickness at any point S in the convex or concave area, t c is half of the spraying time of the spray gun at point S, A is a constant determined according to the spraying equipment, R is the spraying radius, r S is the distance from point S to the axis of the spray gun, d2 is the height of the side of the convex concave part, H0 is the initial spraying height, is the distance from any point S on the side of the convex or concave part to the top surface of the convex or concave part. The spraying heights of the top, bottom and side surfaces of the convex or concave part are ψ is the angle between the top, side and bottom surfaces of the convex and concave parts, θ S is the angle between the line connecting point S and the spray gun nozzle and the spray gun axis, t is the time of spray gun movement, x is the straight-line distance from point S to the spray gun axis, v c It is the moving speed of the spray gun when spraying vertically on raised and recessed areas.
[0013] Take any point S on the top, bottom, or side of the convex or concave feature 1,2,3The optimization objective function is established by the minimum variance between the coating thickness and the ideal coating thickness, and the pattern search method is used to solve the optimal vertical spraying convex and concave movement speed of the spray gun at the convex and concave features, and the coating thickness of these feature surfaces is calculated; by judging whether the coating thickness meets the requirements under different convex heights or concave depths, the critical values of the convex height and concave depth suitable for the vertical spraying trajectory planning method are obtained. When the convex height or concave depth is greater than the critical value, the vertical spraying method is not applicable to the convex and concave features, and the variable inclination angle spraying trajectory planning method established in step (2) is used. The process is:
[0014] (2) When the height of the protrusion and the depth of the depression exceed the critical value, a variable-angle spraying trajectory planning method is established based on the variable-angle static spraying model. The variable-angle spraying trajectory of the protrusion and depression is divided into a vertical spraying trajectory segment and a variable-angle spraying trajectory segment, and a vertical dynamic spraying model and a variable-angle dynamic spraying model of the sampling points on each segment are constructed. On this basis, a variable-pose dynamic spraying model of any point S1, S2, S3 on the top, side, and bottom surfaces of the protrusion and depression is constructed; a multi-objective optimization function is constructed with coating uniformity as the goal to solve the optimal arc radius, optimal spraying height, and optimal spraying speed.
[0015] Step (2.1), set the spray gun movement direction as the X-axis direction, the vertical direction as the Y-axis direction, x and y as the positions of point S in the coordinate system, z as the position of the spray gun axis, d1 as the top surface of the convex and concave part, d2 as the side surface, d3 as the length of the bottom surface, the centers O2 and O3 of the variable-angle spraying trajectory at the outer and inner corners are located on the bisectors of the outer and inner corners respectively, the transition arc radii are R1 and R2 respectively, and the vertical height of the top surface of the convex and concave features is The vertical spraying height of the bottom surface is The maximum spraying angles at the outer and inner corners are The vertical distance between the center of the circle O3 and the side and bottom of the convex and concave parts is d0, then The variable-angle spraying trajectory at the protrusions and depressions is divided into the vertical spraying trajectory segments P1 and W6 on the top surface, the variable-angle spraying trajectory segments P2 and W5 at the outer corners of the top surface, the variable-angle spraying trajectory segments P3 and W4 at the outer corners of the side surfaces, the variable-angle spraying trajectory segments P4 and W3 at the inner corners of the side surfaces, the variable-angle spraying trajectory segments P5 and W2 at the inner corners of the bottom surface, and the vertical spraying trajectory segments P6 and W1 on the bottom surface. The method for establishing the vertical dynamic spraying model on the vertical spraying trajectory segments of the top and bottom surfaces is consistent with step (1). The variable-angle spraying trajectory segments at the outer and inner corners on the top, side, and bottom surfaces of the protrusions and depressions are equally divided into K segments, and the spraying heights on each segment are H1, H2, ..., H K The spraying inclination angles corresponding to each section are
[0016] The variable-angle dynamic spraying model on the variable-angle spraying trajectory segment at the outer and inner corners on the top, side and bottom surfaces of the convex and concave parts is:
[0017]
[0018] in:
[0019]
[0020] T P v is the coating thickness on the outer and inner corners of the top, side and bottom surfaces of the convex and concave parts at the variable angle spraying trajectory. b is the moving speed of the spray gun when spraying convex and concave parts at variable inclination angles, d l ' is the starting position of the current variable angle spraying trajectory segment, d l " is the end position of the current variable-angle spraying trajectory segment.
[0021] In step (1), any point S on the top, bottom, or side of the convex or concave feature is 1,2,3 The minimum square error between the coating thickness and the ideal coating thickness is used to establish the optimization objective function:
[0022]
[0023] Where: T d is the ideal coating thickness; the moving speed v of the spray gun at the vertical spraying convex and concave parts in equation (5) is solved by the parameters in equations (1) to (4): c The value of v c Substitute into formulas (1) to (4) to calculate the coating thickness on the top, bottom, and side surfaces of the convex and concave features.
[0024] Among them, in step (1.1), the vertical dynamic spraying model of point S1 on the top surface of the convex concave part is:
[0025]
[0026] Where: is the coating thickness at point S1 on the convex or concave part, and t1 is the time for the spray gun to move on the top surface of the convex or concave part.
[0027] Combined with step (1.1), a vertical dynamic spraying model of the bottom surface of the convex and concave parts is established. The spray gun is at a constant height. When spraying the bottom surface of the convex and concave part, the vertical dynamic spraying model of point S3 on the bottom surface is:
[0028]
[0029] Where: is the coating thickness of point S3 on the bottom surface of the convex and concave parts, and t3 is the time for the spray gun to move on the bottom surface of the convex and concave parts.
[0030] Combined with step (1.1), a vertical dynamic spraying model of the side of the convex and concave parts is established, and the spray gun is sprayed at a constant height. When spraying the side of the convex and concave part, the vertical dynamic spraying model of point S2 on the side is:
[0031]
[0032] Where: is the coating thickness of point S2 on the side of the convex or concave part, and t2 is the time for the spray gun to move on the side of the convex or concave part.
[0033] Solve the moving speed v of the spray gun in the vertical spraying convex and concave parts in formula (5): c The value of v c Substitute into equations (1) to (4) to calculate the coating thickness on the top, bottom, and side surfaces of the convex and concave features:
[0034] In step (1), the ideal coating thickness is set as T d , the coating thickness error is ΔT. When the height of the protrusion is d2 and the depth of the depression is d2, the vertical spraying method is adopted.
[0035] Increase the value of the convex height and concave depth d2, if it does not meet When the current value of d2 is set to the critical value d of the convex height and concave depth c .
[0036] When d2>d c When the vertical spraying trajectory planning method is not used at the current raised or recessed part, the variable inclination angle spraying trajectory planning method established in step (2) is used.
[0037] (2.2) When spraying the top surface of the depression, the spray gun is far away from the outer corner, which is the vertical spray trajectory segment P1. When the spray gun is close to the outer corner, it is the variable angle spray trajectory segment P2. The length of the trajectory segment is The expressions are:
[0038]
[0039]
[0040] When spraying the bottom surface of the protrusion, when the spray gun is far away from the inner corner, it is the vertical spray trajectory segment W1, and when the spray gun is close to the inner corner, it is the variable angle spray trajectory segment W2. The length of the trajectory segment is The expressions are:
[0041]
[0042] (2.3) Combined with step (2.1), establish a vertical dynamic spray model on the top surface of the depression and the bottom surface of the protrusion. Set the vertical spray speed on the top surface of the depression and the bottom surface of the protrusion to v1, then the vertical dynamic spray model of the sampling point S1 on the vertical spray trajectory segment P1 of the top surface of the depression is:
[0043]
[0044] in:
[0045]
[0046] The vertical dynamic spraying model of a sampling point S1 on the vertical spraying trajectory segment W1 at the bottom of the bulge is established as follows:
[0047]
[0048] in:
[0049]
[0050] (2.4) Combined with step (2.1), establish a variable-angle dynamic spraying model on the top and side surfaces of the outer corner of the concave feature. Set the maximum inclination angle of the spray gun on the arc transition variable-angle spraying trajectory segments P2 and P3 at the outer corner to The variable inclination angle trajectory is divided into i segments, and the spraying heights are H1, H2, ..., H i , and the corresponding spraying angles are The spraying speeds are v2 and v3 respectively. Then the variable-angle dynamic spraying model of a sampling point S1 on the variable-angle spraying trajectory segment P2 on the top surface of the depression is:
[0051]
[0052] in:
[0053]
[0054] j∈[1,i]
[0055] The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment P3 at the outer corner on the side of the depression is:
[0056]
[0057] in:
[0058]
[0059] j∈[1,i]
[0060] Combined with step (2.1), a variable-angle dynamic spraying model is established on the bottom and side surfaces of the inner corner of the convex feature. Set the spray gun inclination angle to The variable-angle dynamic spraying model of a sampling point S1 on the variable-angle spraying trajectory segment W2 at the bottom of the bulge is constructed as follows:
[0061]
[0062] in:
[0063]
[0064] j∈[1,i]
[0065] The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment W3 at the inner corner on the side of the bulge is:
[0066]
[0067] in:
[0068]
[0069]
[0070] j∈[1,i]
[0071] (2.5) Construct the variable-angle spraying trajectory segments P3 and P4 at the outer and inner corners on the side of the concave part. Set the variable-angle spraying trajectory at the outer and inner corners on the side of the concave part to be smoothly connected. Then the connection point S4 of the two spraying trajectories is at the intersection of the center line O2O3 and the spraying trajectory. The formula expression is:
[0072]
[0073] The length of the spraying track segments P3 and P4 on the side of the concave part when the outer and inner corners are sprayed at variable angles The expression is:
[0074]
[0075] Construct the variable-angle spraying trajectory segments W3 and W4 at the inner and outer corners on the side of the protrusion, and set the variable-angle spraying trajectory at the inner and outer corners on the side of the protrusion to be smoothly connected. Then the connection point S4 of the two spraying trajectories is at the intersection of the center line O2O3 and the spraying trajectory. The formula expression is:
[0076]
[0077] The length of the spraying track segments W3 and W4 on the side of the protrusion when the inner and outer corners are sprayed at variable angles The expression is:
[0078]
[0079] (2.6) Combined with step (2.1), establish a variable-angle dynamic spraying model on the side and bottom surfaces of the inner corner of the concave feature. Set the maximum inclination angle of the spray gun on the arc transition variable-angle spraying trajectory segments P4 and P5 at the inner corner to The variable inclination angle trajectory is divided into n segments, and the spraying heights are H1, H2, ..., H n , and the corresponding spraying angles are The spraying speeds are v4 and v5 respectively. The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment P4 at the inner corner on the side of the depression is:
[0080]
[0081] in:
[0082]
[0083] m∈[1,n]
[0084] The length of the variable angle spraying trajectory segment P5 at the inner corner on the bottom surface of the depression is expressed as follows: The variable inclination angle dynamic spraying model of a certain sampling point S3 is:
[0085]
[0086] in:
[0087]
[0088] m∈[1,n]
[0089] Combined with step (2.1), a variable-angle dynamic spraying model is established on the side and top surfaces of the outer corners of the convex feature. Set the spray gun inclination angle to The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment W4 at the outer corner on the side of the protrusion is constructed as follows:
[0090]
[0091] in:
[0092]
[0093]
[0094] m∈[1,n]
[0095] The length expression of the variable angle spraying track segment W5 at the outer corner on the top surface of the protrusion for The variable inclination angle dynamic spraying model of a certain sampling point S3 is:
[0096]
[0097] in:
[0098]
[0099] m∈[1,n]
[0100] (2.7) Combined with step (2.1), a vertical dynamic spraying model is established on the bottom surface of the depression and the top surface of the protrusion. When the bottom length of the depression d3>2d0, a vertical spraying trajectory segment P6 is established after the variable inclination trajectory segment P5, the spraying speed is v6, and the vertical spraying height is The length of its track segment The expression is The vertical dynamic spraying model of a sampling point S3 on the trajectory segment P6 is:
[0101]
[0102] in:
[0103]
[0104] When the top surface length d3 of the protrusion is greater than 2d0, a vertical spraying trajectory segment W6 is established after the variable inclination trajectory segment W5. The expression is The vertical dynamic spraying model of a certain sampling point S3 is:
[0105]
[0106] in:
[0107]
[0108] (2.8) When the spray gun sprays at the outer and inner corners, it will affect the coating thickness on the adjacent surfaces. When the variable-angle spraying is used at the outer corner on the top surface of the depression, it will affect the coating thickness on the side of the depression. The affected spraying distance is a2. Therefore, it is assumed that the influence of the spraying on the top surface of the depression on the side of the depression is regarded as the influence of the spray gun spraying on the extended surface of the side of the depression on the side of the depression. Then, the variable-angle dynamic spraying model formed on the side of the depression after the spray gun passes through the variable-angle spraying trajectory segment P2 at the outer corner on the top surface of the depression is:
[0109]
[0110] in:
[0111]
[0112] When variable-angle spraying is used at the inner corner on the bottom surface of the protrusion, the coating thickness on the side of the protrusion will be affected. The affected spraying distance is a1. Then, after the spray gun passes through the variable-angle spraying trajectory segment W2 at the inner corner on the bottom surface of the protrusion, the variable-angle dynamic spraying model formed on the side of the protrusion is:
[0113]
[0114] in:
[0115]
[0116] When variable-angle spraying is used at the outer corner on the side of the depression, the coating thickness on the top surface of the depression will be affected. The affected spraying distance is a2. Then, the variable-angle dynamic spraying model formed on the top surface of the depression after the spray gun passes through the variable-angle spraying trajectory segment P3 at the outer corner on the side of the depression is:
[0117]
[0118] in:
[0119]
[0120] When variable-angle spraying is used at the inner corner on the side of the protrusion, the coating thickness on the bottom surface of the protrusion will be affected. The affected spraying distance is a1. Then, the variable-angle dynamic spraying model formed on the bottom surface of the protrusion after the spray gun passes through the variable-angle spraying trajectory segment W3 at the inner corner on the side of the protrusion is:
[0121]
[0122] in:
[0123]
[0124] When variable-angle spraying is used at the inner corner on the side of the depression, the coating thickness on the bottom surface of the protrusion will be affected. The affected spraying distance is a1. Then, after the spray gun passes through the variable-angle spraying trajectory segment P4 at the inner corner on the side of the depression, the variable-angle dynamic spraying model formed on the bottom surface of the depression is:
[0125]
[0126] in:
[0127]
[0128] When variable-angle spraying is used at the outer corner on the side of the protrusion, the coating thickness on the top surface of the protrusion will be affected. The affected spraying distance is a2. Then, the variable-angle dynamic spraying model formed on the top surface of the protrusion after the spray gun passes through the variable-angle spraying trajectory segment W4 at the outer corner on the side of the protrusion is:
[0129]
[0130] in:
[0131]
[0132] When variable-angle spraying is used at the inner corner on the bottom surface of the depression, the coating thickness on the side of the depression will be affected. The affected spraying distance is a1. Then, after the spray gun passes through the variable-angle spraying trajectory segment P5 at the inner corner on the bottom surface of the depression, the variable-angle dynamic spraying model formed on the side of the depression is:
[0133]
[0134] in:
[0135]
[0136] When variable-angle spraying is used at the outer corner on the top surface of the protrusion, the coating thickness on the side of the protrusion will be affected. The affected spraying distance is a2. Then, after the spray gun passes through the variable-angle spraying trajectory segment W5 at the outer corner on the top surface of the protrusion, the variable-angle dynamic spraying model formed on the side of the protrusion is:
[0137]
[0138] in:
[0139]
[0140]
[0141] (2.9) Combined with steps (2.1) to (2.8), the variable posture dynamic spraying models of any point S1, S2, S3 on the top, side, and bottom surfaces of the depression are constructed as follows:
[0142]
[0143] The coating thickness expressions of points S1, S2, and S3 on the bottom, side, and top surfaces of the protrusion are:
[0144]
[0145]
[0146] (2.10) Taking coating uniformity as the goal, a multi-objective optimization function for concave and convex features is constructed, and a genetic algorithm is used to solve the optimal arc radius R1, R2 and the optimal spraying height of the variable inclination trajectory segment. And the optimal spraying speed v1, v2, ..., v6, the multi-objective optimization function is:
[0147]
[0148] Where: δ represents the track spacing, T d Indicates ideal coating thickness.
[0149] Working principle: The present invention establishes an optimization objective function with coating uniformity as the optimization target, adopts a pattern search method to solve the optimal spraying speed at the raised and recessed features, and calculates the coating thickness on the surface of the raised and recessed features; by judging whether the coating thickness meets the coating accuracy requirements under the conditions of different raised heights or recessed depths, the critical values of the raised height and recessed depth applicable to the vertical spraying trajectory planning method are obtained, so as to explore the height and depth range of the raised and recessed parts applicable to the vertical spraying method; when the raised height and recessed depth exceed the critical value, the size of the spraying inclination is optimized based on the variable spraying speed and the variable spraying height, and the variable inclination dynamic spraying model of the spray gun is studied; on this basis, a variable inclination spraying trajectory planning method is established, and a variable inclination dynamic spraying model of sampling points at raised and recessed features is constructed, and a multi-objective optimization function is constructed with coating uniformity as the target to solve the optimal arc radius, the optimal spraying height and the optimal spraying speed.
[0150] Beneficial effects: Compared with the prior art, the present invention has the following advantages:
[0151] (1) The present invention aims to optimize the coating uniformity of surfaces with raised or recessed features by spraying. First, the influence of the geometric parameters of raised or recessed surfaces on the coating uniformity during vertical spraying and variable-angle spraying is studied. Secondly, the range of raised height and recessed depth applicable to the vertical spraying method is explored. Finally, a variable-angle spraying trajectory optimization method using arc transition is proposed to improve the coating uniformity of surfaces with raised or recessed features.
[0152] (2) The present invention performs high-quality control on the spray coating at the convex and concave features, thereby solving the problem of low spraying accuracy when the traditional spraying method is applied to the convex and concave feature surfaces. BRIEF DESCRIPTION OF THE DRAWINGS
[0153] Figure 1 It is a schematic diagram of a vertical static spraying model of the present invention;
[0154] Figure 2 It is a schematic diagram of the vertical spraying depression feature of the present invention;
[0155] Figure 3It is a schematic diagram of the vertical spraying protrusion feature of the present invention;
[0156] Figure 4 It is a schematic diagram of a variable-angle static spraying model of the present invention;
[0157] Figure 5 It is a schematic diagram of the concave features of the variable inclination trajectory spraying of the present invention;
[0158] Figure 6 It is a schematic diagram of the convex features of the variable inclination trajectory spraying of the present invention;
[0159] Figure 7 This is a schematic diagram of the outer corner spraying of the present invention;
[0160] Figure 8 This is a schematic diagram of the inner corner spraying of the present invention;
[0161] Fig. 9 It is a schematic diagram of the coating at the junction of the outer corners of the present invention;
[0162] Fig.10 It is a schematic diagram of the coating at the inner corner junction of the present invention. DETAILED DESCRIPTION
[0163] like Figure 1 , Figure 2 and Figure 3 As shown, in this embodiment, a vertical dynamic spraying model of convex and concave features is established, and the height and depth range of the convex and concave features suitable for the vertical spraying method are explored, including the steps of:
[0164] (1.1) Select the existing parabolic model as the vertical static spraying model, such as Figure 1 As shown, the expression is:
[0165]
[0166] Where: R is the spraying radius, A is a constant, H is the spraying height, is the spray gun opening angle, θ S It is the angle between the line connecting point S and the spray gun nozzle and the axis of the spray gun, and r is the distance from a point S on the plane to the projection point of the center of the spray gun along the spraying direction.
[0167] The schematic diagrams of vertical spraying convex and concave features are as follows: Figure 2 , Figure 3 As shown in the figure, the vertical static spraying model is set as a parabolic model, and on this basis, a vertical dynamic spraying model at the convex and concave features is established. S is the coating thickness at any point S in the convex or concave area, t c is half of the spraying time of the spray gun at point S, A is a constant determined according to the spraying equipment, R is the spraying radius, rS is the distance from point S to the axis of the spray gun, d2 is the height of the side of the convex concave part, the initial spraying height is H0, and the distance from any point S on the side of the convex concave part to the top surface of the convex concave part is The spraying heights of the top, bottom and side surfaces of the convex and concave parts are ψ is the angle between the top, side and bottom surfaces of the convex and concave parts, θ S is the angle between the line connecting point S and the spray gun nozzle and the spray gun axis, t is the time of spray gun movement, x is the straight-line distance from point S to the spray gun axis, v c The optimal spraying speed in this article is the optimal moving speed of the spray gun for vertical spraying of convex and concave parts.
[0168] The vertical dynamic spraying model of the convex and concave parts is:
[0169]
[0170] in:
[0171]
[0172] (1.2) Combined with step (1.1), when vertical spraying is adopted on the top surface of the convex and concave part, the vertical dynamic spraying model of a point S1 on it is:
[0173]
[0174] Where: is the coating thickness at point S1 on the convex or concave part, and t1 is the time for the spray gun to move on the top surface of the convex or concave part.
[0175] (1.3) Combined with step (1.1), a vertical dynamic spraying model of the bottom surface of the convex and concave parts is established. The spray gun is at a constant height. When spraying the bottom surface of the convex concave part, the vertical dynamic spraying model of a point S3 on it is:
[0176]
[0177] Where: is the coating thickness of a point S3 on the bottom surface of the convex or concave part, and t3 is the time for the spray gun to move on the bottom surface of the convex or concave part.
[0178] (1.4) Combined with step (1.1), a vertical dynamic spraying model of the side of the convex and concave part is established. The distance between a point S2 on the side of the convex and concave part and the top surface of the convex and concave part is Spraying height The vertical dynamic spraying model of point S2 is:
[0179]
[0180] Where: is the coating thickness of a point S2 on the side of the convex or concave part, and t2 is the time for the spray gun to move on the side of the convex or concave part.
[0181] (1.5) Take any point S on the top, bottom, or side of the convex or concave feature 1,2,3 The variance between the coating thickness and the ideal coating thickness is minimized to establish the optimization objective function:
[0182]
[0183] Where: T d For the ideal coating thickness, the optimization objective function can be solved by pattern search method to obtain v c The optimal spraying speed v c Substitute into formulas (46) to (48) to calculate the coating thickness on the top, bottom, and side surfaces of the convex and concave features:
[0184] (1.6) Set the ideal coating thickness as T d , the coating thickness error is ΔT. When the current convex height and concave depth d2 are used, the vertical spraying method is adopted. Increase the value of the convex height and concave depth d2. When the When the current value of d2 is set to the critical value d of the convex height and concave depth c When d2>d c When the vertical spraying trajectory planning method is not used at the current raised or recessed part, the variable inclination angle spraying trajectory planning method established in step (2) is used.
[0185] (2) Figures 4 to 10 As shown, this embodiment establishes a variable-angle spraying trajectory planning method for a convex or concave feature surface, including the steps of:
[0186] (2.1) Select the existing variable-angle static spraying model, and its expression is:
[0187]
[0188] in:
[0189]
[0190] H s =H+xsinα
[0191] The spraying range of the spray gun under angle spraying is an ellipse. Figure 4 The major and minor axes a1(H,α) and a2(H,α) of the middle ellipse are:
[0192]
[0193] Set the spray gun movement direction as the X-axis direction, the vertical direction as the Y-axis direction, x and y as the positions of point S in the coordinate system, z as the position of the spray gun axis, d1, d2, and d3 as the lengths of the top, side, and bottom surfaces of the convex and concave parts, respectively, the centers O2 and O3 of the variable-angle spray trajectory at the outer and inner corners are located on the angular bisectors of the outer and inner corners, respectively, the transition arc radii are R1 and R2, and the vertical spray heights of the top and bottom surfaces of the concave features are The maximum spraying angles at the outer and inner corners are The vertical distance between the center of the circle O3 and the side and bottom of the convex and concave parts is d0, then The variable-angle spraying trajectory at the protrusion and depression is divided into the vertical spraying trajectory segment P1 and W6 on the top surface, the variable-angle spraying trajectory segment P2 and W5 at the outer corner of the top surface, the variable-angle spraying trajectory segment P3 and W4 at the outer corner of the side surface, the variable-angle spraying trajectory segment P4 and W3 at the inner corner of the side surface, the variable-angle spraying trajectory segment P5 and W2 at the inner corner of the bottom surface, and the vertical spraying trajectory segment P6 and W1 on the bottom surface. The method for establishing the vertical dynamic spraying model on the vertical spraying trajectory segments of the top and bottom surfaces is consistent with step (1). The variable-angle spraying trajectory segments at the outer and inner corners on the top, side, and bottom surfaces of the protrusion and depression are equally divided into K segments, and the spraying heights on each segment are H1, H2, ..., H K The spraying inclination angles corresponding to each section are The variable-angle dynamic spraying model on the variable-angle spraying trajectory segment at the outer and inner corners on the top, side and bottom surfaces of the convex and concave parts is:
[0194]
[0195] in:
[0196]
[0197] k∈[1,K]
[0198] Among them, T P v is the coating thickness on the outer and inner corners of the top, side and bottom surfaces of the convex and concave parts at the variable angle spraying trajectory. b is the moving speed of the spray gun when spraying convex and concave parts at variable inclination angles, d l ' is the starting position of the current variable angle spraying trajectory segment, d l ” The end position of the current variable-angle spraying trajectory segment.
[0199] (2.2) When spraying the top surface of the depression, the spray gun is far away from the outer corner, which is the vertical spray trajectory segment P1. When the spray gun is close to the outer corner, it is the variable angle spray trajectory segment P2. The length of the trajectory segment is The expressions are:
[0200]
[0201]
[0202] When spraying the bottom surface of the protrusion, when the spray gun is far away from the inner corner, it is the vertical spray trajectory segment W1, and when the spray gun is close to the inner corner, it is the variable angle spray trajectory segment W2. The length of the trajectory segment is The expressions are:
[0203]
[0204]
[0205] (2.3) Based on the existing vertical static spray model, the vertical dynamic spray model on the top surface of the depression and the bottom surface of the protrusion is established in combination with step (2.1). The vertical spray speed on the top surface of the depression is set to v1, and the vertical dynamic spray model of a sampling point S1 on the vertical spray trajectory segment P1 of the top surface of the depression is:
[0206]
[0207] in:
[0208]
[0209] A vertical dynamic spraying model on the bottom surface of the bulge is established. The vertical spraying speed on the bottom surface of the bulge is set to v1, and the vertical dynamic spraying model of a sampling point S1 on the vertical spraying trajectory segment W1 of the bottom surface of the bulge is:
[0210]
[0211] in:
[0212]
[0213] (2.4) Combined with step (2.1), establish a variable-angle spraying model at the outer corner of the top surface of the concave feature. Set the maximum inclination angle of the spray gun on the arc transition variable-angle spraying trajectory segments P2 and P3 at the outer corner to The variable inclination angle trajectory segment is divided into i segments, and the spraying height and spraying inclination angle on each segment are assumed to remain unchanged. The spraying heights are H1, H2, ..., H i , and the corresponding spraying angles are The spraying speeds are v2 and v3 respectively. Figure 7 As shown. Then the variable-angle dynamic spraying model of a sampling point S1 on the variable-angle spraying trajectory segment P2 on the top surface of the depression is:
[0214]
[0215] in:
[0216]
[0217] j∈[1,i]
[0218] The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment P3 at the outer corner on the side of the depression is:
[0219]
[0220] in:
[0221]
[0222]
[0223] j∈[1,i]
[0224] Combined with step (2.1), a variable-angle dynamic spraying model on the bottom and side surfaces of the inner corner of the convex feature is established. The maximum inclination angle of the spray gun in the variable-angle trajectory segments W2 and W3 at the inner corner is set to The variable inclination angle trajectory segment is divided into i segments, and the spraying height and spraying inclination angle on each segment are assumed to remain unchanged. The spraying heights are H1, H2, ..., H i , and the corresponding spraying angles are The spraying speed is v2, v3, such as Figure 8 As shown. Then the variable-angle dynamic spraying model of a sampling point S1 on the variable-angle spraying trajectory segment W2 at the bottom of the bulge is:
[0225]
[0226] in:
[0227]
[0228] j∈[1,i]
[0229] The variable-angle dynamic spraying model of a sampling point S2 on the variable-angle spraying trajectory segment W3 at the inner corner on the side of the bulge is:
[0230]
[0231] in:
[0232]
[0233]
[0234] j∈[1,i]
[0235] (2.5) Construct arc transition variable angle spraying trajectory segments P3 and P4 at the outer and inner corners on the side of the concave part, and set the variable angle spraying trajectory at the outer and inner corners to be smoothly connected. Then the connection point S4 of the two spraying trajectories is at the intersection of the center line O2O3 and the spraying trajectory. The formula expression is:
[0236]
[0237] The length of the spraying track segments P3 and P4 on the side of the concave part when the outer and inner corners are sprayed at variable angles The expression is:
[0238]
[0239] Construct arc transition variable angle spraying trajectory segments W3 and W4 at the inner and outer corners on the side of the bulge, and set the variable angle spraying trajectory at the inner and outer corners on the side to be smoothly connected. Then the connection point S4 of the two spraying trajectories is at the intersection of the center line O2O3 and the spraying trajectory. The formula expression is:
[0240]
[0241] The length of the spraying track segments W3 and W4 on the side of the protrusion when the inner and outer corners are sprayed at variable angles The expression is:
[0242]
[0243] (2.6) Combined with step (2.1), establish a variable-angle dynamic spraying model on the side and bottom surfaces of the inner corner of the concave feature. Set the maximum inclination angle of the spray gun on the arc transition variable-angle spraying trajectory segments P4 and P5 at the inner corner to The variable inclination angle trajectory segment is divided into n segments, and the spraying height and spraying inclination angle on each segment are assumed to remain unchanged. The spraying heights are H1, H2, ..., H n , and the corresponding spraying angles are The spraying speeds are v4 and v5 respectively. Then the coating thickness expression of a sampling point S2 on the variable angle spraying trajectory segment P4 at the inner corner on the side of the depression is:
[0244]
[0245] in:
[0246]
[0247] m∈[1,n]
[0248] A variable-angle dynamic spraying model at the inner corner of the concave feature bottom surface is established. When the spray gun is close to the inner corner of the concave bottom surface, it is the variable-angle spraying trajectory segment P5, and its trajectory segment length The expression is The coating thickness expression of a certain sampling point S3 is:
[0249]
[0250] in:
[0251]
[0252] m∈[1,n]
[0253] The variable inclination angle dynamic spraying model at the outer corner of the convex feature side is established. The maximum inclination angle of the spray gun on the arc transition variable inclination angle spraying trajectory segments W4 and W5 at the outer corner is set to The variable inclination angle trajectory segment is divided into n segments, and the spraying height and spraying inclination angle on each segment are assumed to remain unchanged. The spraying heights are H1, H2, ..., H n , and the corresponding spraying angles are The spraying speeds are v4 and v5 respectively. Then the coating thickness expression of a sampling point S2 on the variable angle spraying trajectory segment W4 at the outer corner on the side of the convex part is:
[0254]
[0255] in:
[0256]
[0257] m∈[1,n];
[0258] The variable-angle dynamic spraying model at the outer corner of the top surface of the convex feature is established. When the spray gun is close to the inner corner of the bottom surface of the concave part, it is the variable-angle spraying trajectory segment W5, and its trajectory segment length is The expression is The coating thickness expression of a certain sampling point S3 is:
[0259]
[0260] in:
[0261]
[0262] m∈[1,n]
[0263] (2.7) Combined with step (2.1), a vertical dynamic spraying model is established on the bottom surface of the depression and the top surface of the protrusion. When the bottom length of the depression d3>2d0, a vertical spraying trajectory segment P6 is established after the variable inclination trajectory segment P5, the spraying speed is v6, and the vertical spraying height is The length of its track segment The expression is The coating thickness expression of a sampling point S3 on the trajectory segment P6 is:
[0264]
[0265] in:
[0266]
[0267] A vertical spraying model for the top surface of the raised feature is established. When the top surface length d3 of the raised part is greater than 2d0, a vertical spraying trajectory segment W6 is established after the variable inclination trajectory segment W5, the spraying speed is v6, and the vertical spraying height is The length of its track segment The expression is The coating thickness expression of a sampling point S3 on the trajectory segment W6 is:
[0268]
[0269] in:
[0270]
[0271] (2.8) When the spray gun sprays at the outer and inner corners, it affects the coating thickness on the adjacent surfaces. When the outer corner on the top surface of the depression is sprayed with a variable angle, it will affect the coating thickness on the side of the depression. The affected spraying distance is a2. Therefore, it is assumed that the effect of spraying on the top surface of the depression on the side of the depression is regarded as the effect of spraying on the extended surface of the side of the depression by the spray gun on the side of the depression. Then, the variable angle dynamic spraying model formed on the side of the depression after the spray gun passes through the variable angle spraying trajectory segment P2 at the outer corner on the top surface of the depression is:
[0272]
[0273] in:
[0274]
[0275] When the inner corner on the bottom surface of the protrusion is sprayed with a variable angle, the coating thickness on the side of the protrusion will be affected. The affected spraying distance is a1. Therefore, it is assumed that the influence of the spraying on the bottom surface of the protrusion on the side of the protrusion is regarded as the influence of the spray gun spraying on the extended surface of the side of the protrusion on the side of the protrusion. Then, the variable angle dynamic spraying model formed on the side of the protrusion after the spray gun passes through the variable angle spraying trajectory segment W2 at the inner corner on the bottom surface of the protrusion is:
[0276]
[0277] in:
[0278]
[0279] When variable angle spraying is used at the outer corner of the side of the depression, the coating thickness on the top surface of the depression will be affected. The affected spraying distance is a2. Fig. 9 The variable-angle dynamic spraying model formed on the top surface of the concave part after the spray gun passes through the variable-angle spraying trajectory segment P3 at the outer corner on the side of the concave part is:
[0280]
[0281] in:
[0282]
[0283] When the inner corner of the side of the protrusion is sprayed with a variable angle, the coating thickness on the bottom surface of the protrusion will be affected. The affected spraying distance is a1. Fig.10 The variable-angle dynamic spraying model formed on the bottom surface of the protrusion after the spray gun passes through the variable-angle spraying trajectory segment W3 at the inner corner on the side of the protrusion is:
[0284]
[0285] in:
[0286]
[0287] When the inner corner on the side of the depression is sprayed with a variable angle, the coating thickness on the bottom surface of the depression will be affected. The affected spraying distance is a1. Then, the variable angle dynamic spraying model formed on the bottom surface of the depression after the spray gun passes through the variable angle spraying trajectory segment P4 at the inner corner on the side of the depression is:
[0288]
[0289] in:
[0290]
[0291]
[0292] When the outer corner on the side of the protrusion is sprayed with a variable angle, the coating thickness on the top surface of the protrusion will be affected. The affected spraying distance is a2. Then, the variable angle dynamic spraying model formed on the top surface of the protrusion after the spray gun passes through the variable angle spraying trajectory segment W4 at the outer corner on the side of the protrusion is:
[0293]
[0294] in:
[0295]
[0296] When the inner corner on the bottom surface of the depression is sprayed with a variable angle, the coating thickness on the side of the depression will be affected. The affected spraying distance is a1. After the spray gun passes through the variable angle spraying trajectory segment P5 at the inner corner on the bottom surface of the depression, the variable angle dynamic spraying model formed on the side of the depression is:
[0297]
[0298] in:
[0299]
[0300] When the outer corner on the top surface of the protrusion is sprayed with a variable angle, the coating thickness on the side of the protrusion will be affected. The affected spraying distance is a2. After the spray gun passes through the variable angle spraying trajectory segment W5 at the outer corner on the top surface of the protrusion, the variable angle dynamic spraying model formed on the side of the protrusion is:
[0301]
[0302] in:
[0303]
[0304] (2.9) Combined with steps (2.1) to (2.8), the coating thickness expressions of any point S1, S2, and S3 on the top, side, and bottom surfaces of the depression are constructed as follows:
[0305]
[0306] The coating thickness expressions of any point S1, S2, and S3 on the bottom, side, and top surfaces of the protrusion are constructed as follows:
[0307]
[0308] (2.10) Taking coating uniformity as the goal, the multi-objective optimization functions of concave and convex features are constructed as shown in formula (88), and the genetic algorithm is used to solve the optimal arc radius R1, R2 and the optimal spraying height of the variable inclination trajectory segment. And the optimal spraying speed v1, v2, ..., v6 is optimized, and the optimization objective function is:
[0309]
[0310] Where: δ represents the track spacing, T d Indicates ideal coating thickness.
Claims
1. A robot variable spray coating optimization method for convex and concave feature surfaces, characterized in that: The following steps are involved: (1) A vertical dynamic spraying model for convex and concave areas is established based on the vertical static spraying model: in: T S is the coating thickness at point S in the convex and concave areas, t c is half of the spraying time of the spray gun at point S, A is a constant, R is the spraying radius, r S is the distance from point S to the axis of the spray gun, d2 is the height of the side of the convex concave part, H0 is the initial spraying height, H is the distance between point S on the side of the convex or concave part and the top surface of the convex or concave part. c1 H is the spraying height of the top surface of the convex and concave parts, c2 is the bottom spraying height, H c3 is the spray height of the side, ψ is the angle between the top, side and bottom of the convex and concave parts, θ S is the angle between the line connecting point S and the spray gun nozzle and the spray gun axis, t is the time of spray gun movement, x is the straight-line distance from point S to the spray gun axis, v c The moving speed of the spray gun for vertical spraying of convex and concave areas; The optimization objective function is established with the minimum variance between the coating thickness of the points on the top, bottom and side surfaces of the convex and concave features and the ideal coating thickness: the optimal spraying speed at the convex and concave features is solved, and the coating thickness on the surface of the convex and concave features is calculated; by judging the coating thickness at different convex heights or concave depths, the critical values of the convex height and concave depth for vertical spraying are obtained; (2) When the height of the protrusion and the depth of the depression exceed the critical value, the variable-angle spraying trajectory of the protrusion and depression is divided into a vertical spraying trajectory segment and a variable-angle spraying trajectory segment, and a vertical dynamic spraying model and a variable-angle dynamic spraying model of the sampling point are constructed; a variable-pose dynamic spraying model of the top surface point S1, the side point S2, and the bottom surface point S3 of the protrusion and depression is constructed; a multi-objective optimization function is constructed to solve the optimal arc radius, the optimal spraying height, and the optimal spraying speed; The variable-angle dynamic spraying model on the variable-angle spraying trajectory segment at the outer and inner corners on the top, side and bottom surfaces of the convex and concave parts is: in: k∈[1,K] T P v is the coating thickness on the outer corner and inner corner of the top, side and bottom surfaces of the convex and concave parts at the variable angle spraying trajectory. b is the moving speed of the spray gun when spraying convex and concave parts at variable inclination angles, d l ' is the starting position of the current variable angle spraying trajectory segment, d l " is the end position of the current variable-angle spraying trajectory segment; x, y are the positions of point S in the coordinate system, z is the position of the spray gun axis, is the maximum spraying angle at the outer corner, It is the maximum spraying inclination angle at the inner corner.
2. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1 is characterized in that: In step (1), the vertical dynamic spraying model of point S1 on the top surface of the convex concave part is: Where: is the coating thickness at point S1 of the convex and concave part, and t1 is the time of the spray gun movement on the top surface of the convex and concave part; The spray gun is at a constant height H c3 When spraying the bottom surface of the convex and concave part, the vertical dynamic spraying model of point S3 on the bottom surface is: is the coating thickness of point S3 on the bottom surface of the convex and concave part, and t3 is the time of the spray gun movement on the bottom surface of the convex and concave part; The spray gun is at a constant height H c2 When spraying the side of the convex and concave part, the vertical dynamic spraying model of point S2 on the side is: Where: is the coating thickness of point S2 on the side of the convex and concave part, and t2 is the time of the spray gun movement on the side of the convex and concave part; Solve the moving speed v of the spray gun in the vertical spraying convex and concave parts in formula (5): c The value of v c Substitute into equations (1) to (4) to calculate the coating thickness on the top, bottom, and side surfaces of the convex and concave features:
3. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (1), the ideal coating thickness is set to T d , the coating thickness error is ΔT, when When , the vertical spraying method is adopted at the current protrusion height and depression depth d2.
4. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (1), the current value of d2 is set to the critical value d of the protrusion height and the depression depth. c ; When d2>d c When the variable inclination angle spraying trajectory planning method of step (2) is used at the current raised or recessed part.
5. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (2), assuming that the vertical spraying speed on the top surface of the concave part and the bottom surface of the convex part is v1, the vertical dynamic spraying model of the sampling point S1 on the vertical spraying trajectory segment P1 on the top surface of the concave part is: in:
6. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: The vertical dynamic spraying model of the sampling point S1 on the vertical spraying trajectory segment W1 at the bottom of the bulge is established as follows: in:
7. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (2), the variable posture dynamic spraying model of point S1 on the top surface of the depression, point S2 on the side surface, and point S3 on the bottom surface is constructed as follows:
8. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (2), a multi-objective optimization function for concave and convex features is constructed with coating uniformity as the goal to solve the optimal arc radius R1, R2 of the variable inclination trajectory segment and the optimal spraying height H z0 , H z1 And the optimal spraying speed v1, v2, ..., v6, the multi-objective optimization function is: Where: δ represents the track spacing, T d Indicates ideal coating thickness.
9. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (2), the coating thickness expressions of point S1 on the bottom surface of the protrusion, point S2 on the side surface, and point S3 on the top surface are:
10. The robot variable spray coating optimization method for convex and concave feature surfaces according to claim 1, characterized in that: In step (1), the optimization objective function is established based on the minimum square error between the coating thickness of points on the top, bottom, and side surfaces of the convex and concave features and the ideal coating thickness: Where: T d is the ideal coating thickness; v c The moving speed of the spray gun for vertical spraying of convex and concave areas; It is the coating thickness on the top, bottom and side surfaces of raised and recessed features.