CN112621771A - Cold spraying robot track planning method based on geodesic line - Google Patents

Cold spraying robot track planning method based on geodesic line Download PDF

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CN112621771A
CN112621771A CN202011414347.2A CN202011414347A CN112621771A CN 112621771 A CN112621771 A CN 112621771A CN 202011414347 A CN202011414347 A CN 202011414347A CN 112621771 A CN112621771 A CN 112621771A
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curve
geodesic
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陈伟
郭碧宇
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Jiangsu University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J11/00—Manipulators not otherwise provided for
    • B25J11/0075—Manipulators for painting or coating
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Application Of Or Painting With Fluid Materials (AREA)

Abstract

The invention relates to the technical field of robot spraying, in particular to a cold spraying robot track planning method based on geodesic wires, which is a curved surface spraying track planning method used in a robot off-line programming system and comprises the following steps: step one, selecting an initial curve; secondly, constructing a series of new scanning curves by using a curve discrete algorithm and discrete points; and step three, generating the target point robot track by using the curves, wherein the selected initial curve is helpful for minimizing the geodesic curvature of the offset curve according to Gauss-Bonnet theorem, so that the uniform full-coverage track is ensured. And constructing a series of new orthogonal planes by using a curve discrete algorithm and discrete points, and generating a scanning curve by intersecting curved surfaces so as to generate a target point for the robot track. And the material consumption can be reduced while the coating uniformity is ensured.

Description

Cold spraying robot track planning method based on geodesic line
Technical Field
The invention relates to the technical field of robot spraying, in particular to a cold spraying robot track planning method based on geodesic lines, which is a curved surface spraying track planning method used in a robot offline programming system.
Background
With the ever-increasing demands of manufacturing, various complex free-form surfaces have found widespread use in cold spray applications. The off-line programming transfers the robot program created by the simulation to the actual robot cell. It does not interfere with the production of the robot program and is prepared on an external computer outside the production environment. Despite the advances made today in off-line programming of cold spray applications, there are still a number of unresolved problems. For example, it is very difficult to manually select an appropriate trace point in a graphical environment of off-line programming software, and it is difficult to ensure the programming accuracy of a complex industrial workpiece. The currently developed offline program packages mainly focus on the trajectory generation method. The cold spray coating has no fluidity and is more sensitive to trajectory accuracy and cold spray parameters (such as scanning steps, spray distance, etc.).
Although there are many good trajectory planning methods in the field of thermal spraying, there is little in-depth analysis of trajectory generation within the framework of differential geometry. In fact, the geodesic curvature of the start curve and the offset curve has a significant effect on the uniformity of material deposition. Currently, the operator is too much dependent on selecting a start curve (cutting method) or selecting a boundary curve (grid method) as the start curve.
Disclosure of Invention
An optimal spray trajectory is not only to ensure uniform coverage of the entire coating surface, but also to ensure that the length of the trajectory is minimized when the coating surface is covered. Aiming at the problems that cold spraying is more sensitive to track precision and spraying parameters and the selection of proper track points manually in the graphic environment of off-line programming software is very difficult, the invention provides a track planning method based on geodesic lines, which combines the Gauss-Bonnet theorem to select an optimal initial curve and an optimal offset curve, wherein the curves are dispersed by a constant value, the operation can obtain new points to generate a plurality of orthogonal curved surfaces, then the track points are extracted from the intersection line between the orthogonal curved surfaces and the coating surface, and the optimal track is generated under the condition of considering the scanning speed.
The invention adopts the following specific technical scheme:
a cold spraying robot track planning method based on geodesic lines comprises the following steps:
step one, selecting an initial curve;
secondly, constructing a series of new scanning curves by using a curve discrete algorithm and discrete points;
and step three, generating a target point robot track by using the curves.
When a complex curved surface is sprayed, firstly, CAD data of the surface of a workpiece is obtained, the curved surface is triangulated, the curved surface is modeled by using a corresponding method, and the complex curved surface is segmented according to a curved surface topological structure, so that the complex curved surface is decomposed into simpler curved surfaces.
The selection of the start curves is crucial to the track generation process, since different start curves may lead to different offset curves, which together affect the total length of the covered track. Self-intersection results in discontinuities in the tangent line on the offset curve and may hinder coating thickness uniformity. The task of trajectory planning is therefore to find a geodesic curve on the curved surface Q, which curve minimizes the geodesic curvature of the offset curve.
Q is represented by curve C1Curve C2And two orthogonal geodesic lines g1And g2And (4) forming. Let L be a smooth curve, connect endpoint B and endpoint D on curved surface Q. Then region Q1From L and curve C1、AB(AB∈g1) Defining; similarly, region Q2From C2、DE(DE∈g2) And L.
Obtaining:
θ1+θ2+θ3＝θ4+θ5+θ6pi (formula 1)
Figure BDA0002819683600000021
Figure BDA0002819683600000022
KgDenotes geodesic curvature of BD on Q, K denotes gaussian curvature of BD on Q; then, according to Gauss-Bonnet theorem, we get:
Figure BDA0002819683600000023
Figure BDA0002819683600000024
suppose Q1And Q2The surrounding counterclockwise region is the positive direction, then we have:
Figure BDA0002819683600000031
Figure BDA0002819683600000032
due to g1And g2If it is a geodesic curve, then:
Figure BDA0002819683600000033
add equations 6 and 7 to obtain:
Figure BDA0002819683600000034
substituting equation 9 into the equation obtained by adding equation 4 and equation 5 yields:
Figure BDA0002819683600000035
the following can be concluded from equation 1:
Figure BDA0002819683600000036
finally, assume C1Is a geodesic curve; then, we get:
Figure BDA0002819683600000037
where K represents the gaussian curvature of the toric surface Q.
On a curved surface Q, CsAnd C1Represents curve C2First and last offset curves, Q, on each side+Is CsAnd C2Boundary region therebetween, similarly, Q-Is C1And C2The boundary region therebetween.
Then, the following steps are obtained:
Figure BDA0002819683600000038
Figure BDA0002819683600000039
adding equation 13 and equation 14 yields:
Figure BDA00028196836000000310
when in use
Figure BDA0002819683600000041
When the temperature of the water is higher than the set temperature,
Figure BDA0002819683600000042
and
Figure BDA0002819683600000043
the maximum value in between is minimal. When curve C2When the curved surface Q is divided into two disjoint regions, the integral of the geodetic curvature on the offset curve is minimal. Therefore, the geodesic line is selected as the starting curve.
The off-line programming software robottstudio is built on the ABB virtual controller, which is an exact copy of the real control software, allowing real simulation. In the trajectory planning process, the kinematic parameters of the robot have important influence on the coating quality, including the spraying distance, the scanning speed and the scanning step. In order to achieve a uniform deposition on the coating surface, the scanning step of the cold spray should first be evaluated at the desired coating thickness.
The cold spraying should be performed on a trapezoidal curved surface. Generally, the trajectory of a typical cold spraying robot is a Z-shaped scan, the path curves are connected according to the spatial position sequence, the scan moves alternately from left to right and then from right to left, the number of scanning steps is constant, and the full coverage of the coating surface is realized. According to the actual engineering requirements, the intersection curve of the plane is always close to the geodesic line, and the task is completed in the geometric model based on Boolean operation. Selecting midpoint P1And P2As an intersection curve passing through these two points, and the gaussian curvature of the curved surface Q can be approximately divided.
The start curve C is then obtained by intersecting the target surface with an orthogonal plane2. Good deposition uniformity is obtained by specifying a constant velocity motion of the track gap distance with one standard deviation of the gaussian distribution, which means that the scan step between adjacent path profiles is preferably kept within a certain value.
On this basis, the starting curve is equally divided, and then discrete points are extracted from the starting curve according to the scanning step size. This operation results in the generation of a new orthogonal plane and scan curve, resulting in a series of numbered trace points.
The robot trajectory is then generated by rearranging the code references of the trajectory points. The method helps to maintain a constant scan step between adjacent path curves, thereby optimizing deposition uniformity and ensuring short full coverage trajectories on curved surfaces in cold spray applications.
The invention has the beneficial effects that: according to the Gauss-Bonnet theorem, the selected initial curve is helpful for minimizing the geodesic curvature of the offset curve, so that a uniform full-coverage track is ensured. And constructing a series of new orthogonal planes by using a curve discrete algorithm and discrete points, and generating a scanning curve by intersecting curved surfaces so as to generate a target point for the robot track. And the material consumption can be reduced while the coating uniformity is ensured.
Drawings
FIG. 1 is a graph in which a curved surface Q is defined by a curve C1Curve C2And two orthogonal geodesic lines AB and DE.
FIG. 2 is a schematic diagram of midpoint selection in an embodiment of the present invention.
FIG. 3 is a schematic diagram of discrete points on a cross-sectional curve in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a new orthogonal plane in an embodiment of the invention.
FIG. 5 is a schematic view of a scanning curve in an embodiment of the present invention.
FIG. 6 is a diagram of a series of numbered tracks in an embodiment of the present invention.
Fig. 7 is a schematic diagram of a robot trajectory in an embodiment of the present invention.
Detailed Description
For the purpose of enhancing the understanding of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and examples, which are provided for the purpose of illustration only and are not intended to limit the scope of the present invention.
Example (b): a cold spraying robot track planning method based on geodesic lines is also the most important step firstly, and an initial curve is selected; secondly, a series of new scanning curves are constructed by using a curve discrete algorithm and discrete points; third, target point robot trajectories are generated using these curves.
When a complex curved surface is sprayed, firstly, CAD data of the surface of a workpiece is obtained, the curved surface is triangulated, the curved surface is modeled by using a corresponding method, and the complex curved surface is segmented according to a curved surface topological structure, so that the complex curved surface is decomposed into simpler curved surfaces, as shown in figure 1.
The selection of the start curves is crucial to the track generation process, since different start curves may lead to different offset curves, which together affect the total length of the covered track. Self-intersection results in discontinuities in the tangent line on the offset curve and may hinder coating thickness uniformity. The task of trajectory planning is therefore to find a geodesic curve on the curved surface Q, which curve minimizes the geodesic curvature of the offset curve.
Q is represented by curve C1Curve C2And two orthogonal geodesic lines g1And g2And (4) forming. Let L be a smooth curve, connect endpoint B and endpoint D on curved surface Q. Then region Q1From L and curve C1、AB(AB∈g1) Defining; similarly, region Q2From C2、DE(DE∈g2) And L.
Q1And Q2The interior angle of (a) is shown in fig. 1; then, we get:
(1)θ1+θ2+θ3＝θ4+θ5+θ6＝π
(2)
Figure BDA0002819683600000051
(3)
Figure BDA0002819683600000052
Kgdenotes geodesic curvature of BD on Q, K denotes gaussian curvature of BD on Q; then, according to Gauss-Bonnet theorem, we get:
(4)
Figure BDA0002819683600000061
(5)
Figure BDA0002819683600000062
suppose Q1And Q2The surrounding counterclockwise region is the positive direction, then we have:
(6)
Figure BDA0002819683600000063
(7)
Figure BDA0002819683600000064
due to g1And g2If it is a geodesic curve, then:
(8)
Figure BDA0002819683600000065
add equations 6 and 7 to obtain:
(9)
Figure BDA0002819683600000066
substituting formula 9 into formula 4 and formula 5 to obtain:
Figure BDA0002819683600000067
from equation 1, the following conclusions can be drawn:
(11)
Figure BDA0002819683600000068
finally, assume C1Is a geodesic curve; then, we get:
(12)
Figure BDA0002819683600000069
where K represents the gaussian curvature of the toric surface Q.
On a curved surface Q, CsAnd C1Represents curve C2First and last offset curves, Q, on each side+Is CsAnd C2Boundary region therebetween, similarly, Q-Is C1And C2The boundary region therebetween.
Then, the following steps are obtained:
(13)
Figure BDA00028196836000000610
(14)
Figure BDA0002819683600000071
adding equation 13 and equation 14 yields:
(15)
Figure BDA0002819683600000072
when in use
Figure BDA0002819683600000073
When the temperature of the water is higher than the set temperature,
Figure BDA0002819683600000074
the maximum value in between is minimal. When curve C2When the curved surface Q is divided into two disjoint regions, the integral of the geodetic curvature on the offset curve is minimal. Therefore, the geodesic line is selected as the starting curve.
The off-line programming software robottstudio is built on the ABB virtual controller, which is an exact copy of the real control software, allowing real simulation. In the trajectory planning process, the kinematic parameters of the robot have important influence on the coating quality, including the spraying distance, the scanning speed and the scanning step. In order to achieve a uniform deposition on the coating surface, the scanning step of the cold spray should first be evaluated at the desired coating thickness.
Cold spraying should be performed on a trapezoidal curved surface (as shown in fig. 2). Generally, the trajectory of a typical cold spraying robot is a Z-shaped scan, the path curves are connected according to the spatial position sequence, the scan moves alternately from left to right and then from right to left, the number of scanning steps is constant, and the full coverage of the coating surface is realized. According to the actual engineering requirements, the intersection curve of the plane is always close to the geodesic line, and the task is completed in the geometric model based on Boolean operation. In FIG. 2, midpoint P is selected1And P2As an intersection curve passing through these two points, and the gaussian curvature of the curved surface Q can be approximately divided.
The start curve C is then obtained by intersecting the target surface with an orthogonal plane2. By specifying a standard deviation having a Gaussian distributionThe constant velocity movement of the track gap distance to obtain good deposition uniformity means that the scanning step between adjacent path profiles is preferably kept within a certain value.
On this basis, the start curve is equally divided, and then discrete points are extracted from the start curve according to the scanning step size, as shown in fig. 3. This operation results in the generation of a new orthogonal plane (as shown in fig. 4) and a sweep curve (as shown in fig. 5), resulting in a series of numbered trace points (as shown in fig. 6).
The robot trajectory is then generated by rearranging the code references of the trajectory points (as shown in fig. 7). The method helps to maintain a constant scan step between adjacent path curves, thereby optimizing deposition uniformity and ensuring short full coverage trajectories on curved surfaces in cold spray applications.
In order to compare the geodesic-based trajectory planning method with the conventional cutting method, two types of robot trajectories are generated in robottstudio, wherein the scanning step length is 6mm, and the relative speeds of the spray gun and the curved surface to be sprayed are both kept at 45 mm/s. Under the same conditions, the total length of the geodesic-based robot trajectory is 2760mm, consisting of 21 path curves, and the time of the trajectory is 55.5 s. The total length of the robot track of the cutting method is 2790mm, the robot track consists of 22 path curves, and the total time of the track is 56.5 s.
Small changes in the robot trajectory during cold spraying may result in a wavy coating surface after two adjacent gaussian distributed material deposits accumulate. If the track gap is greater than one standard deviation, the difference in the flatness of the coating surface may be large. In the experiment, a curved surface with the same shape as that of fig. 1 is adopted, and the placing position of the workpiece and the mounting position of the spray gun are calibrated to be consistent with the simulation robot station, so that simulation is performed. Therefore, the trajectory of the simulation robot can be completed quickly without using a complicated spatial rotation-translation operation. A test was conducted on polished aluminum parts using a self-refrigerating spray gun, copper powder was selected as the spraying material, and a spherical nozzle having an expansion ratio of 8:8 and a divergence length of 125mm was used. Compressed air is used as driving gas, the temperature is 762k, the pressure is 2.8mpa, argon is used as powder carrier gas, and the pressure is 3 mpa. The spray distance from the nozzle outlet to the curved surface was maintained at 30mm, and the scanning speed and the spray angle were set at 45mm/s and 90 °, respectively. During the spraying process, the spray gun is mounted at the end of the robot shaft and moves along with the movement of the robot. To keep the measurement simple, only one coating is applied to the prepared surface. The performance of the coating after the coating is sprayed by using a cold spraying system is measured, and cross-section microstructures at different positions are sampled for about 30 times by using an optical microscope. For the geodesic-based method, the mean coating thickness calculated for the geodesic trace was 430.10 μm with a standard deviation of 15.72 μm under the same experimental parameters. The average coating thickness calculated by the cutting method was 408.46 μm with a standard deviation of 20.91. mu.m.
Through the comparison results, the improvement in standard deviation indicates that the surface coating based on the geodesic method is more uniform; therefore, the choice of the path profile has a significant impact on the deposition uniformity. As previously mentioned, by limiting the distance between adjacent scan curves to approach a constant value, optimal coating uniformity can be achieved. The proposed trajectory generation method improves uniformity by offsetting the distance between adjacent trajectory curves, which also demonstrates that the technique can form an almost uniform, full coverage deposit on the coating surface.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. A cold spraying robot track planning method based on geodesic lines is characterized by comprising the following steps:
step one, selecting an initial curve;
secondly, constructing a series of new scanning curves by using a curve discrete algorithm and discrete points;
and step three, generating a target point robot track by using the curves.
2. The geodesic-based cold spray robot trajectory planning method of claim 1, wherein when spraying a complex surface, first obtaining workpiece surface CAD data, triangulating the surface, modeling the surface using a corresponding method, and slicing the complex surface according to a surface topology.
3. The geodesic-based cold spray robot trajectory planning method of claim 2, characterized in that the curved surface Q is set from the curve C1Curve C2And two orthogonal geodesic lines g1And g2The composition is that L is a smooth curve, an end point B and an end point D are connected on a curved surface Q, and then an area Q is formed1From L and curve C1、AB(AB∈g1) Defining; similarly, region Q2From C2、DE(DE∈g2) And L is defined by the following components,
obtaining:
θ1+θ2+θ3＝θ4+θ5+θ6pi (formula 1)
Figure FDA0002819683590000011
Figure FDA0002819683590000012
KgDenotes geodesic curvature of BD on Q, K denotes gaussian curvature of BD on Q; then, according to Gauss-Bonnet's theorem,
obtaining:
Figure FDA0002819683590000013
Figure FDA0002819683590000021
set Q1And Q2The surrounding counterclockwise region is the positive direction, then, there is:
Figure FDA0002819683590000022
Figure FDA0002819683590000023
due to g1And g2If it is a geodesic curve, then:
Figure FDA0002819683590000024
add equations 6 and 7 to obtain:
Figure FDA0002819683590000025
substituting equation 9 into the equation obtained by adding equation 4 and equation 5 yields:
Figure FDA0002819683590000026
the following can be concluded from equation 1:
Figure FDA0002819683590000027
finally, set C1Is a geodesic curve; then:
Figure FDA0002819683590000028
wherein K represents the gaussian curvature of the toric surface Q;
set on a curved surface Q, CsAnd C1Represents curve C2First and last offset curves, Q, on each side+Is CsAnd C2Boundary region therebetween, similarly, Q-Is C1And C2In the region of the boundary between them,
then, the following steps are obtained:
Figure FDA0002819683590000029
Figure FDA00028196835900000210
adding equation 13 and equation 14 yields:
Figure FDA0002819683590000031
when in use
Figure FDA0002819683590000034
When the temperature of the water is higher than the set temperature,
Figure FDA0002819683590000032
and
Figure FDA0002819683590000033
the maximum value therebetween is minimal; when curve C2When the curved surface Q is divided into two disjoint areas, the integral of the geodesic curvature on the offset curve is minimal, and therefore, the geodesic line is selectedThe initial curve is shown.
4. A geodesic-based cold spray robot trajectory planning method according to claim 3, characterized in that the scanning step of cold spray is estimated at the expected coating thickness: firstly, the track of the cold spraying robot is Z-shaped scanning, the path curves are connected according to the spatial position sequence, the scanning is from left to right and then alternately moves from right to left, the scanning steps are constant, the full coverage of the coating surface is realized, according to the actual engineering requirement, because the plane intersection curve is always close to the geodesic line, the task is completed in a geometric model based on Boolean operation, and the midpoint P is selected1And P2As an intersecting curve passing through these two points, and the gaussian curvature of the curved surface Q can be approximately divided; the start curve C is then obtained by intersecting the target surface with an orthogonal plane2Good deposition uniformity is obtained by specifying a constant velocity motion of the track gap distance with one standard deviation of the gaussian distribution; on the basis, equally dividing the initial curve, and extracting discrete points from the initial curve according to the scanning step length; and finally generating the robot track by rearranging the code reference of the track points.
CN202011414347.2A 2020-12-07 2020-12-07 Cold spraying robot track planning method based on geodesic line Pending CN112621771A (en)

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CN116371696A (en) * 2023-04-12 2023-07-04 福州大学 Curved surface spraying method and system of planar pattern based on industrial robot
CN117201685A (en) * 2023-11-06 2023-12-08 中国民航大学 Surface coverage scanning method, device, equipment and medium for three-dimensional object

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023050866A1 (en) * 2021-09-30 2023-04-06 深圳迈塔兰斯科技有限公司 Metasurface of curved substrate, and preparation method for metasurface
CN116371696A (en) * 2023-04-12 2023-07-04 福州大学 Curved surface spraying method and system of planar pattern based on industrial robot
CN116371696B (en) * 2023-04-12 2023-11-07 福州大学 Curved surface spraying method and system of planar pattern based on industrial robot
CN117201685A (en) * 2023-11-06 2023-12-08 中国民航大学 Surface coverage scanning method, device, equipment and medium for three-dimensional object
CN117201685B (en) * 2023-11-06 2024-01-26 中国民航大学 Surface coverage scanning method, device, equipment and medium for three-dimensional object

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