A method for generating simulated coating thickness based on spray trajectory

Abstract

A method for generating simulated coating thickness of a spraying trajectory relates to the technical field of robot spraying. In order to solve the problems of large integral calculation amount and low coating analysis efficiency in the existing technology, the method comprises the following steps: step 1: modeling a coating thickness accumulation model: w is the spraying thickness, (x, y) is the thickness point to be sprayed at {C i}, v is the movement speed of the spray gun, γ is the angle with l, and is the angle between the normal vector of m at point P and l; Step 2: Generate an intersection segment based on a triangular mesh point cloud; Step 3: Generate a simulated coating for a single trajectory; Step 4: Generate a simulated coating for multiple trajectories; Use the established coating thickness accumulation model to generate intersection segments through the posture information of the trajectory points and the mesh model, and calculate the coating thickness. Use the topological relationship of the mesh model to traverse and calculate the thickness values ​​of the points between the intersection segments, and store the generated simulated coatings corresponding to the trajectory. There is no need to perform individual integral calculations for each point, which speeds up the generation of simulated coatings.

Description

Technical Field

[0001] The present invention relates to the technical field of robot spraying, and in particular to a method for generating a simulated coating thickness of a spraying trajectory. Background Art

[0002] With the widespread application of robots, more and more industrial spraying is carried out by autonomous robot spraying, which places very high demands on spraying thickness and uniformity. For workpieces that have been sprayed but the coating does not meet the standards, a second spraying is required. Research on the generation method of simulated coatings for evaluating coating quality can improve the pass rate of one-time trajectory planning and effectively reduce the waste of manpower and material resources caused by secondary spraying.

[0003] The Chinese patent publication number is "CN 108549759 A", and the patent name is "A method for calculating and simulating the coating thickness of parts for automated spraying processes". This method provides a method for calculating and simulating the coating thickness of parts for automated spraying processes. It uses the "spraying method" to establish a spray thickness accumulation rate model for a spray gun at a certain point on an arbitrary surface, and then extracts the grid points for spray thickness calculation on the workpiece surface. The spray gun motion trajectory is then input and the trajectory is discretized. According to the spray gun motion trajectory and the spray thickness accumulation rate model, the cumulative thickness of the grid points on the surface is calculated. After that, three-dimensional display software is used to realize a visual simulation display of the spray accumulation thickness on the part surface. Finally, the thickness display value of each grid point is displayed in the software, the spray thickness is simulated and displayed, and the spray quality is analyzed. The paint film thickness at each point in this method needs to be calculated by time integration of the spray thickness accumulation rate model, which requires a large amount of calculation and has low coating analysis efficiency. Summary of the Invention

[0004] In order to solve the problems of large integral calculation amount and low coating analysis efficiency in the prior art, the present invention proposes a method for generating simulated coating thickness of a spraying trajectory.

[0005] The technical solution of the present invention to solve the technical problem is as follows:

[0006] A method for generating a simulated coating thickness of a spraying trajectory, the method comprising the following steps:

[0007] Assume that the world coordinate system is {B}, the robot end coordinate system is {E}, and the spray gun coordinate system of the i-th track point of a single track is {C i}, take the center point of the paint outlet of the spray gun as {C i Origin O i , its X-axis, Z-axis and Y-axis directions are the same as {E} direction, and the spray gun is pointed to For its Y axis, For its Z axis, is its X axis;

[0008] Step 1: Modeling the coating thickness accumulation model;

[0009] Assume that any point on the triangular mesh model m of the sprayed surface is P, and the coating thickness at P is:

[0010]

[0011] In formula (1), w is the spraying thickness, (x, y) is the thickness point to be sprayed at {C i}, v is the speed of the spray gun, γ is The angle with l, is the normal vector of m at point P The angle with l;

[0012] Step 2: Generate intersection line segments based on the triangular mesh point cloud;

[0013] Constructed with O i As the trajectory point spray gun coordinate system {C i The trajectory point of the origin is in the spray gun coordinate system. The known position information of the trajectory point is:

[0014]

[0015] In the formula O i At the spatial position under {B}, point P on the mesh model is in the spray gun coordinate system {C i}The following expression is:

[0016]

[0017] By {C i Origin O i and Z axis The set of intersection points of the point-normal plane XOY and the triangle mesh is B P i ={p1,p2…p k}, obtained by the formula in {C i}The intersection point set in the coordinate system Connecting the intersection points in sequence will form several intersection segments;

[0018] Step 3: Generate a simulated coating of a single track;

[0019] The generation of the simulated coating is to store the corresponding thickness of the spray coverage area of ​​the trajectory point, process the area between the two intersection segments generated by adjacent trajectory points, and calculate the thickness on the intersection segment by formula (1). The point on the area is searched through the topological relationship between points in the grid model, and the thickness value at the point is obtained by distance weighted averaging; let this point be N, and the thickness of the paint film coating at point N is calculated as shown in formula (4):

[0020]

[0021] In the formula w N is the thickness value at point N, with the position information at point N and Construct a point-normal plane and intersect two line segments at points c1 and c2. w1 and w2 are the coating thickness values ​​at c1 and c2 respectively. d1 is the thickness from N to p. l The distance from N to p is d2. r θ1 is the angle between the straight line determined by c1 and N and the straight line determined by c1 and c2; θ2 is the angle between the straight line determined by c2 and N and the straight line determined by c1 and c2;

[0022] Step 4: Generate multiple tracks of simulated coating;

[0023] The cumulative thickness of multiple coatings passing through a certain point N by n trajectories is calculated by formula (5):

[0024]

[0025] In the formula is the thickness of the paint film coating caused by the j-th trajectory to point N. The thickness value obtained by superimposing multiple spraying trajectories is calculated to generate a simulated coating after superimposing multiple trajectories.

[0026] The beneficial effects of the present invention are as follows: the present invention uses an established coating thickness accumulation model, generates intersection line segments through the posture information of the trajectory points and the grid model, and calculates the coating thickness. The topological relationship of the grid model is used to traverse and calculate the thickness values ​​of the points between the intersection line segments, and stores the generated trajectory corresponding to the simulated coating. There is no need to perform individual integral calculations on each point, which speeds up the generation of the simulated coating. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the spray gun coordinate system;

[0028] Figure 2 This is a flow chart of a method for generating a simulated coating thickness of a spray trajectory according to the present invention;

[0029] Figure 3 Schematic diagram of the spraying experiment;

[0030] Figure 4 Calculation principle diagram for coating thickness accumulation model;

[0031] Figure 5 Generate schematic diagrams for the intersection segments of the mesh model;

[0032] Figure 6 Generate schematics for simulated coatings;

[0033] Figure 7 Schematic diagram of the thickness point diffusion process of the grid model;

[0034] Figure 8 Schematic diagram for calculating the paint film thickness at a certain point;

[0035] Figure 9 This is a simulation of the paint film coating effect of a single track;

[0036] Figure 10 This is the effect diagram of the superposition of multiple track simulated paint film coatings. DETAILED DESCRIPTION

[0037] The present invention will be further described in detail below with reference to the accompanying drawings.

[0038] like Figure 1 As shown, establish the coordinate system relationship, set the world coordinate system as {B}, the robot end coordinate system as {E}, and set the spray gun coordinate system of the i-th track point of a single track as {C i}, take the center point of the paint outlet of the spray gun as {C i Origin O i , its X-axis, Z-axis and Y-axis directions are the same as {E} direction, and the spray gun is pointed to For its Y axis, For its Z axis, is its X axis.

[0039] like Figure 2 As shown, a method for generating a simulated coating thickness of a spraying trajectory includes the following steps:

[0040] Step 1: Modeling the coating thickness accumulation model;

[0041] First, according to the modeling method of the 3D coating thickness accumulation model based on inclined spraying, the model with the distance x between the measurement point and the spray gun axis and the spraying distance y of the measurement point as input parameters and the coating thickness w as output can be obtained:

[0042] w=T(x,y) (6)

[0043] Wherein the distance between the measuring point and the spray gun axis x and the spray distance y of the measuring point can be transformed into the coordinates of the thickness measuring point under {B} under {C i}The coordinate values ​​in the X-axis and Y-axis directions are represented.

[0044] Then, if Figure 3 As shown in the figure, through the spraying experiment, the Z-axis direction of the spray gun coordinate system is used as the trajectory direction, different spraying speeds v and the same spraying height h0 are used to spray along the trajectory direction. The coating thickness w at the same position x and different speeds v is fitted with the inverse proportional function using the least squares method, and formula (7) can be obtained:

[0045] w=a / v+b (7)

[0046] Where a and b are the coefficients of the inverse proportional function. Formula (6) can be used to obtain the relationship between different spraying positions and coating thickness at spraying speed v0. The ratio of the coating thickness at different speeds v to the coating thickness at v0 is obtained, and the ratio is recorded as k, and we get:

[0047]

[0048] From (8), we can derive the coating thickness accumulation model of the factors affecting coating thickness, spraying position and spraying speed. The model expression is:

[0049] w=F(T(x,y),v) (9)

[0050] Finally, if Figure 4 As shown, according to the differential geometry amplification principle, any point on the surface m is denoted as P, and a perpendicular line is established at P. Let plane S2 be the plane perpendicular to the line l determined by points O and P, and S3 be the tangent plane passing through P on m, then we can deduce the following relationship:

[0051]

[0052] γ is The angle with l, is the normal vector of point P The angle with l.

[0053] The paint in the S1 area on the reference plane will all be accumulated on the surface.

[0054] w1S1=wS3 (11)

[0055] Where w1 is the coating thickness in the S1 region, and w is the coating thickness in the S3 region, that is, the coating thickness at point P on the surface. Combining equations (9), (10), and (11), we can obtain equation (1), that is, the coating thickness accumulation model at point P is:

[0056]

[0057] Step 2: Generate intersection line segments based on the triangular mesh point cloud;

[0058] Constructed with O i As the trajectory point spray gun coordinate system {C i The trajectory point of the origin is in the spray gun coordinate system. The known position information of the trajectory point is:

[0059]

[0060] In the formula O i At the spatial position under {B}, point P on the mesh model is in the spray gun coordinate system {C i}The following expression is:

[0061]

[0062] like Figure 5 As shown, by {C i Origin O i and Z axis The set of intersection points of the point-normal plane XOY and the triangle mesh is B P i ={p1,p2…p k}, from formula (3) we can get i}The intersection point set in the coordinate system Connecting the intersection points in sequence will form several intersection segments;

[0063] Step 3: Generate a simulated coating of a single track;

[0064] like Figure 6 As shown, the generation of the simulated coating corresponding to the spraying trajectory is to process the area between the two intersection segments generated by adjacent trajectory points. First, calculate {C i}The corresponding point p on the intersection segment j Thickness value.

[0065] From formula (13), we can get cosγ j :

[0066]

[0067] In the formula for Relative to the gun coordinate system {C i}, for Relative to the gun coordinate system {C i}, For p j The local normal vector of . (x j ,y j ,zj ) is p j Relative to the gun coordinate system {C i}, then p j The coating thickness values ​​on are:

[0068]

[0069] Diffusion process such as Figure 7 As shown in the figure, the length of the intersection segment generated by two adjacent trajectory points is used as a constraint condition, and the topological relationship between the points on the intersection segment and the grid model is used to perform a breadth-first search for the next point whose thickness has not been calculated until the constraint condition is met and the diffusion process ends.

[0070] like Figure 8 As shown, the thickness is calculated for the points in the area between adjacent intersection segments. Let this point be N, and the thickness of the paint film coating at point N is calculated as shown in formula (4):

[0071]

[0072] In the formula w N is the thickness value at point N, with the position information at point N and Construct a point-normal plane and intersect two line segments at points c1 and c2. w1 and w2 are the coating thickness values ​​at c1 and c2 respectively. d1 is the thickness from N to p. l The distance from N to p is d2. r , θ1 is the angle between the straight line determined by c1 and N and the straight line determined by c1 and c2, and θ2 is the angle between the straight line determined by c2 and N and the straight line determined by c1 and c2.

[0073] At this point, the simulation coating corresponding to a single trajectory is generated, and the simulation paint film coating effect is as follows Figure 9 As shown, the green vector represents the Y axis of the spray gun coordinate system of the spray trajectory point, the red vector represents the Z axis of the spray gun coordinate system of the spray trajectory point, and the blue vector represents the X axis of the spray gun coordinate system of the spray trajectory point. The three are perpendicular to each other; the color gradient area is the simulated paint film coating area of ​​the current single trajectory.

[0074] Step 4: Generate multiple tracks of simulated coating;

[0075] The cumulative thickness of the multi-coating from n trajectories passing through a certain point N is calculated by formula (5):

[0076]

[0077] In the formula is the paint film coating thickness value caused by the j-th trajectory to point N.

[0078] The effect of the simulated paint film with multiple layers superimposed is as follows Figure 10 As shown in the figure, the red gradient area is the simulated paint film coating area where multiple trajectories are currently superimposed.

Claims

1. A method for generating a simulated coating thickness of a spraying trajectory, characterized in that: The method comprises the following steps: Assume that the world coordinate system is {B}, the robot end coordinate system is {E}, and the spray gun coordinate system of the i-th track point of a single track is {C i }, take the center point of the paint outlet of the spray gun as {C i Origin O i , its X-axis, Z-axis and Y-axis directions are the same as {E} direction, and the spray gun is pointed to For its Y axis, For its Z axis, is its X axis; Step 1: Modeling the coating thickness accumulation model; First, according to the modeling method of the 3D coating thickness accumulation model based on inclined spraying, the model with the distance x between the measurement point and the spray gun axis and the spraying distance y of the measurement point as input parameters and the coating thickness w as output can be obtained: w=T(x,y) (6) Wherein the distance between the measuring point and the spray gun axis is x, and the spray distance y is transformed from the thickness measuring point coordinates under {B} to {C i }The coordinate values ​​in the X-axis and Y-axis directions are represented; Then, through the spraying experiment, the Z-axis direction of the spray gun coordinate system is used as the trajectory direction, different spraying speeds v and the same spraying height h0 are used to spray along the trajectory direction. The coating thickness w at the same position x and different speeds v is fitted with the inverse proportional function using the least squares method, and formula (7) can be obtained: w=a / v+b (7) Where a and b are the coefficients of the inverse proportional function. The relationship between different spraying positions and coating thickness at the spraying speed v0 is obtained from formula (6); the ratio of the coating thickness at different speeds v to the coating thickness at v0 is obtained, and the ratio is recorded as k, and the result is: From (8), the coating thickness accumulation model of the factors affecting the coating thickness, spraying position and spraying speed is obtained. The model expression is: w=F(T(x,y),v) (9) Finally, according to the differential geometry amplification principle, any point on the surface m is denoted as P, and a perpendicular line is established at P. Let plane S1 be the plane perpendicular to the line l defined by points O and P, and let plane S2 be the plane tangent to point m through P. Then we can deduce the following relationship: γ is The angle with l, is the normal vector of point P The angle with l, The paint in the S1 region on the reference plane will all be accumulated on the surface, and we can get: w1S1=wS3 (11) Where w1 is the coating thickness in the S1 region, and w is the coating thickness in the S3 region, that is, the coating thickness at point P on the surface. Combining equations (9), (10), and (11), we can obtain equation (1), that is, the coating thickness accumulation model at point P is: Step 2: Generate intersection line segments based on the triangular mesh point cloud; Constructed with O i As the trajectory point spray gun coordinate system {C i The trajectory point of the origin is in the spray gun coordinate system. The known position information of the trajectory point is: In the formula O i At the spatial position under {B}, point P on the mesh model is in the spray gun coordinate system {C i }The following expression is: By {C i Origin O i and Z axis The set of intersection points of the point-normal plane XOY and the triangle mesh is B P i ={p1,p2…p k }, obtained by the formula in {C i }The intersection point set in the coordinate system Connecting the intersection points in sequence will form several intersection segments; Step 3: Generate a simulated coating of a single track; The generation of the simulated coating is to store the corresponding thickness of the spray coverage area of ​​the trajectory point, process the area between the two intersection segments generated by adjacent trajectory points, and calculate the thickness on the intersection segment by formula (1). The point on the area is searched through the topological relationship between points in the grid model, and the thickness value at the point is obtained by distance weighted averaging; let this point be N, and the thickness of the paint film coating at point N is calculated as shown in formula (4): In the formula w N is the thickness value at point N, with the position information at point N and Construct a point-normal plane and intersect two line segments at points c1 and c2. w1 and w2 are the coating thickness values ​​at c1 and c2 respectively. d1 is the thickness from N to p. l The distance from N to p is d2. r θ1 is the angle between the straight line determined by c1 and N and the straight line determined by c1 and c2; θ2 is the angle between the straight line determined by c2 and N and the straight line determined by c1 and c2; Step 4: Generate multiple tracks of simulated coating; The cumulative thickness of multiple coatings passing through a certain point N by n trajectories is calculated by formula (5): In the formula is the thickness of the paint film coating caused by the j-th trajectory to point N. The thickness value obtained by superimposing multiple spraying trajectories is calculated to generate a simulated coating after superimposing multiple trajectories.

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