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CN111013887A - Method for optimizing irregular plane variable-inclination-angle spraying track based on boundary constraint - Google Patents

Method for optimizing irregular plane variable-inclination-angle spraying track based on boundary constraint Download PDF

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CN111013887A
CN111013887A CN201911413643.8A CN201911413643A CN111013887A CN 111013887 A CN111013887 A CN 111013887A CN 201911413643 A CN201911413643 A CN 201911413643A CN 111013887 A CN111013887 A CN 111013887A
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spraying
path
coating thickness
coating
spray
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CN111013887B (en
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曾勇
于永庆
肖海宁
周临震
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Jiangsu Juyuan Robot System Engineering Co ltd
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Yancheng Institute of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
    • B05B—SPRAYING APPARATUS; ATOMISING APPARATUS; NOZZLES
    • B05B13/00—Machines or plants for applying liquids or other fluent materials to surfaces of objects or other work by spraying, not covered by groups B05B1/00 - B05B11/00
    • B05B13/02—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work
    • B05B13/04—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work the spray heads being moved during spraying operation
    • B05B13/0431—Means for supporting work; Arrangement or mounting of spray heads; Adaptation or arrangement of means for feeding work the spray heads being moved during spraying operation with spray heads moved by robots or articulated arms, e.g. for applying liquid or other fluent material to 3D-surfaces
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
    • B05B—SPRAYING APPARATUS; ATOMISING APPARATUS; NOZZLES
    • B05B12/00—Arrangements for controlling delivery; Arrangements for controlling the spray area
    • B05B12/08—Arrangements for controlling delivery; Arrangements for controlling the spray area responsive to condition of liquid or other fluent material to be discharged, of ambient medium or of target ; responsive to condition of spray devices or of supply means, e.g. pipes, pumps or their drive means
    • B05B12/084—Arrangements for controlling delivery; Arrangements for controlling the spray area responsive to condition of liquid or other fluent material to be discharged, of ambient medium or of target ; responsive to condition of spray devices or of supply means, e.g. pipes, pumps or their drive means responsive to condition of liquid or other fluent material already sprayed on the target, e.g. coating thickness, weight or pattern

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

Abstract

本发明公开了一种基于边界约束的不规则平面变倾角喷涂轨迹的优化方法。该方法在基于边界约束生成的相对较短的喷涂路径基础上，将喷涂倾角作为喷枪的可控参数，考虑到喷涂路径可能是自由曲线的形式，基于圆弧逼近思想，建立喷枪在单条圆弧喷涂路径动态喷涂的涂层厚度模型，并进一步给出圆弧路径两侧涂层厚度分布的优化方法；以整个工件表面上的涂层均匀度为优化目标，通过建立生成喷涂路径每条截交线上两相邻喷涂路径间的涂层厚度叠加模型，给出整个工件表面上喷枪变倾角喷涂轨迹参数的全局优化算法，最终达到涂层均匀度、喷涂效率和涂料利用率的同时提升。本发明方法在减少涂料浪费和喷涂时间的同时，还能保证均匀的喷涂效果。

Figure 201911413643

The invention discloses a method for optimizing the spraying trajectory of irregular plane with variable inclination angle based on boundary constraints. Based on the relatively short spraying path generated based on boundary constraints, the method takes the spraying inclination as a controllable parameter of the spraying gun. Considering that the spraying path may be in the form of a free curve, based on the idea of arc approximation, the spray gun is established on a single arc. The coating thickness model of the dynamic spraying of the spraying path, and further gives the optimization method of the coating thickness distribution on both sides of the arc path; with the coating uniformity on the entire workpiece surface as the optimization goal, each interception of the spraying path is generated by establishing The coating thickness superposition model between two adjacent spraying paths on the line provides a global optimization algorithm for the parameters of the spraying trajectory parameters of the spray gun with variable inclination on the entire workpiece surface, and finally achieves the simultaneous improvement of coating uniformity, spraying efficiency and coating utilization. The method of the invention can ensure uniform spraying effect while reducing paint waste and spraying time.

Figure 201911413643

Description

Method for optimizing irregular plane variable-inclination-angle spraying track based on boundary constraint
Technical Field
The invention relates to the technical field of robots, in particular to an optimization method of irregular plane variable-inclination-angle spraying tracks based on boundary constraint.
Background
The off-line programming track planning mode of the spraying robot has the advantages of not occupying the working time of the robot, being capable of planning complex tracks, freeing workers from toxic environments and the like, and is increasingly applied to the fields such as automobiles, ships, aerospace and the like. The spraying track optimization result directly influences the spraying quality, the spraying efficiency and the paint utilization rate after spraying, and has important significance for coating production. For the spraying of plane workpieces with irregular boundary shapes, for the sake of simplicity, the conventional spraying path planning method without considering the workpiece boundary constraint has the defects of long path and easy overspray at the boundary, so that unnecessary waste of coating and longer spraying time are caused, and the improvement of the coating utilization rate and the spraying efficiency is not facilitated. Considering the spraying path generated by the boundary constraint of the workpiece, although the path length is shortened to some extent and the overspray is reduced, because the generated spraying path is a free curve type, the uniformity of the coating generated by the traditional spray gun in a vertical posture along the path by dynamic spraying is not as good as the condition without the boundary constraint, the uniformity of the coating, the spraying efficiency and the utilization rate of the coating are difficult to be considered, and the new standard requirement of the current spraying operation can not be met.
Application number 201810316359.8 discloses a curved surface spraying track generation method and system based on curved surface parameterization, wherein the method comprises the following steps: s1, acquiring curved surface information to be sprayed, and acquiring a coating accumulation model and a plurality of gradient flow lines of the spray gun according to the curved surface information; s2, obtaining spray gun optimization parameters by combining the coating accumulation model and a preset optimization target; s3, acquiring the track information of the spray gun and the height information of the spray gun on each gradient flow line by combining the gradient flow lines and the spray gun optimization parameters; and S4, acquiring the track pose parameters of the spray gun by combining the curved surface information, the spray gun track information and the spray gun height information, thereby generating a curved surface spraying track. The method can be suitable for free curved surfaces with irregular shapes and relatively complex shapes, has uniform spraying and optimized paths, improves the efficiency and quality of curved surface spraying, and can be widely applied to the technical field of robots. However, the method does not consider the influence of the geodesic curvature of the generated spraying path on the uniformity of film thickness distribution, and when the generated spraying path is a curve, the geodesic curvature of the spraying path can cause the asymmetric distribution of the film thickness at the two sides of the path, thereby seriously influencing the uniformity of the film after spraying.
Disclosure of Invention
Aiming at the defects of the prior art in the spraying of the plane workpiece with irregular boundary, the method is based on the planned boundary constraint spraying path, and provides an optimization method of the irregular plane variable-inclination angle spraying track based on the boundary constraint. On the basis of a relatively short spraying path generated based on boundary constraint, a spraying inclination angle is used as a controllable parameter of a spray gun, a coating thickness model of the spray gun in dynamic spraying of a single arc spraying path is established based on an arc approximation thought in consideration of the fact that the spraying path may be in a free curve form, and an optimization method of coating thickness distribution on two sides of the arc path is further provided; by taking the coating uniformity on the surface of the whole workpiece as an optimization target, a coating thickness superposition model between two adjacent spraying paths on each intersection line of the spraying paths is established and generated, a global optimization algorithm of variable-inclination spraying track parameters of a spray gun on the surface of the whole workpiece is given, and the coating uniformity, the spraying efficiency and the coating utilization rate are improved at the same time.
In order to solve the problems of the prior art, the invention adopts the technical scheme that:
an optimization method of irregular plane variable-inclination spraying track based on boundary constraint comprises the following steps:
step1, based on the existing static vertical spraying coating growth rate model, establishing a static variable-inclination spraying coating growth rate model by using a differential geometry principle and taking a spraying inclination angle as a controllable parameter of a spray gun;
step2, according to the arc approximation idea, the free curve type spraying path generated based on the boundary constraint is equivalent to be composed of a plurality of arc sections, wherein a straight line can be regarded as an arc with infinite curvature radius;
step3, based on the established static variable-inclination-angle spraying coating growth rate model, establishing a coating thickness model for dynamic spraying of a spray gun on a single arc path, and further establishing an optimization model of coating thickness distribution on two sides of the single path to obtain a functional relation among the spraying speed, the spraying inclination angle and the spraying height;
and 4, considering the track parameter optimization of the overall spraying path on the irregular plane workpiece, establishing a coating thickness superposition model between two adjacent spraying paths on each section intersection line of the generated spraying path based on the established coating thickness model of the dynamic spraying of the spray gun on the single arc path, and establishing an optimization model by taking the coating uniformity between the two adjacent spraying paths as an optimization target so as to achieve the aim of optimizing the spraying effect.
The improvement is that the method for establishing the growth rate model of the static variable-inclination spraying coating in the step1 is as follows:
101. let the static vertical spray coating growth rate model of a spray gun be a parabolic model, which can be expressed as
Figure BDA0002350623940000021
(unit: mum/s, A is constant), the space shape of the spray torch is a cone, and the flare angle of the cone is phi;
102. based on the static vertical spraying coating growth rate model, considering the spraying inclination angle α and the spraying height H of the spray gun as controllable parameters, adopting a differential geometric theory to establish the static spraying coating growth rate model of the spray gun at any point (x, y) in the spraying amplitude range:
Figure BDA0002350623940000031
if the spray gun is used for spraying at an inclined angle, the formed spray width range is an ellipse, and the expressions of the major axis and the minor axis a and b of the ellipse are respectively as follows:
Figure BDA0002350623940000032
Figure BDA0002350623940000033
wherein, in formula (2) and formula (3):
Figure BDA0002350623940000034
Figure BDA0002350623940000035
as an improvement, the step3 of establishing a coating thickness model for the dynamic spraying of the spray gun on the single arc path, and further establishing an optimization model for the coating thickness distribution on both sides of the single path to obtain a functional relationship between the spraying speed, the spraying inclination angle and the spraying height comprises the following steps:
301, setting the curvature radius of the arc path as ρ, the curvature center of the arc path as P, when the spray gun sprays along the dynamic inclination of the arc path track, the speed direction of the spray gun is the tangential direction of the arc path, the dynamic spraying speed of the spray gun on the arc path track is v, and the spraying speed of the spray gun on any point S in the swept spraying range is vSThe radius of curvature of the arc in which the point S is located is rhoSEstablishing a rectangular coordinate system by taking the curvature radius direction of the circular arc path as an X axis and the speed direction of the spray gun as a Y axis, wherein
Figure BDA0002350623940000036
The arc length of a point S swept by the spray gun in the spray amplitude range is represented, and based on the formula (1), by integrating the time t, a coating thickness model of the spray gun dynamic spraying on a single arc path can be represented as follows:
Figure BDA0002350623940000037
the speed of any point swept by the spray gun along the direction of the curvature radius of the path in the spray amplitude range is different, and the speed is in direct proportion to the curvature radius of the circular arc track where the point is located, so that the spray velocity on any point S in the spray amplitude range is vSCan be expressed as:
Figure BDA0002350623940000041
the y-axis coordinate value of the point S is as follows:
Figure BDA0002350623940000042
arc length of point S swept by the lance
Figure BDA0002350623940000043
And the elapsed time t may be expressed as:
Figure BDA0002350623940000044
Figure BDA0002350623940000045
in formula (9):
ρs＝ρ-x (11)
Figure BDA0002350623940000046
in equation (12):
Figure BDA0002350623940000047
in equation (13):
Figure BDA0002350623940000048
in equation (14):
d＝|a1-a2|
substituting the formula (8) and the formula (10) into the formula (6) to establish a coating thickness model expression of the dynamic spraying of the spray gun on the single arc path;
302, dynamically spraying the coating along a curved path track by a spray gun in a posture vertical to the surface of a workpiece, wherein for a single spraying path, the reason that the coating uniformity effect of the surface of the whole workpiece is poor is that the peak value of the coating is not on the spraying path, the peak value of the coating is deviated to one side of the path which is concave inwards, the uneven thickness of the two sides is more obvious along with the increase of the curvature of an arc, and the uniformity effect of the sprayed coating is poorer; the coating thickness peak value appears on the concave side of the arc path, so the direction of the spraying dip angle is deviated to the convex side of the path, the size of the spraying dip angle needs to be calculated and determined on the spraying path according to the set coating thickness peak value, and the target value of the coating thickness can be determined according to the dynamic spraying coating thickness model solving spraying speed;
setting the target value of the coating thickness as TdWhen the coating thickness peak value appears on the spraying path, namely at the original point of the X axis, firstly, the formula (6) is derived to obtain the coordinate value X of the X axis where the coating thickness peak value is located0Let x again0And this is taken into equation (6), specifically expressed as follows:
Figure BDA0002350623940000051
from the above equation, v and α are functions of H, and if the spray height H is known, the optimized spray velocity v and spray inclination angle α can be obtained by solving the above equation system.
As an improvement, in step4, the establishing generates a coating thickness superposition model between two adjacent spraying paths on each cross-sectional line of the spraying paths, and establishes an optimization model with the coating uniformity between the two adjacent spraying paths as an optimization target, including the following steps:
step 401, according to the requirements of the target coating thickness and the peak position of the coating thickness, by optimizing the dynamic dip angle spraying tracks of the free curve path, a rate function and a dip angle function on each spraying track relative to the spraying height H can be obtained, so that the peak value of the coating thickness on each spraying track reaches a target value, but the overall optimization of the coating uniformity among the spraying tracks on the whole workpiece surface is not yet performed, because the generated spraying path based on the boundary constraint is generated by adopting a series of bisection line bisection methods, the distance between two adjacent paths on each bisection line is determined and equal, and because the spraying height and the path distance have a direct relation, the spraying height at the position of the spraying path where each intersecting line is located can be solved through optimization, so that the coating thickness superposition among the adjacent paths reaches uniformity;
and (3) setting n cross-sectional lines for generating the spraying paths, wherein m coating thickness superposition intervals exist in the spraying paths, and according to the coating thickness superposition principle between adjacent paths, the coating thickness model of any point S in the jth superposition interval on the ith cross-sectional line can be represented as follows:
Figure BDA0002350623940000061
step 402, after a coating thickness superposition model between two adjacent spraying paths on each intersection line of the generated spraying paths is established, an optimization function is established according to the minimum variance between the coating thickness and the target coating thickness value at any point on each intersection line and in each superposition interval, and the optimization function is expressed as follows:
Figure BDA0002350623940000062
in the above formula HminAnd HmaxRespectively representing the minimum value and the maximum value of the allowable spraying height, wherein n multiplied by m variables are needed to be solved, and a mode search method can be adopted to solve the optimization problem with constrained multivariable.
The specific steps for solving the pattern search method are as follows:
step1 gives the initial point x(1)＝(1,1,…,1)TN coordinate directions e1,e2,…,enThe initial step λ is 1, the acceleration factor ζ is 1, the reduction rate τ is 0.25, the allowable error ∈ is 0.1, and y is set(1)＝x(1)，k＝1，j＝1；
Step2 if E (y)(j)+λej)＜E(y(j)) Then let y(j+1)＝y(j)+λejPerforming step 4; otherwise, step3 is carried out;
step3 if E (y)(j)-λej)＜E(y(j)) Then let y(j+1)＝y(j)-λejPerforming step 4; otherwise, let y(j+1)＝y(j)Performing step 4;
step4, if j is less than n, setting j to j +1, and turning to Step 2; otherwise, step5 is carried out;
step5 if E (y)(n+1))＜E(x(k)) Step6 is performed; otherwise, step7 is carried out;
step6 place x(k+1)＝y(n+1)Let y(1)＝x(k+1)+ξ(x(k+1)-x(k)) Setting k to k +1 and j to 1, and switching to step 2;
step7, if lambda is less than or equal to epsilon, stopping iteration to obtain a point x(k)(ii) a Otherwise, let λ ═ τ λ, y(1)＝x(k)，x(k+1)＝x(k)K +1 and j 1, step 2.
Has the advantages that:
compared with the prior art, the method for optimizing the irregular plane variable-inclination spraying track based on the boundary constraint has the following advantages: for a plane workpiece with an irregular boundary, a spraying path generated based on boundary constraint has the advantages of less coating waste and shorter spraying time, but the uniformity effect of the sprayed coating is poor, and the uniformity effect of the coating dynamically sprayed by a spray gun along a free curve path can be effectively improved by adopting a spraying track optimization method with a variable inclination angle, so that the coating waste and the spraying time are reduced, and meanwhile, the better spraying effect can be ensured.
Drawings
FIG. 1 is a space model of a torch of the spray gun;
FIG. 2 is a schematic view of a spray gun for dynamic spray coating along a circular arc path trajectory;
fig. 3 shows the overall optimization principle of the spray trajectory.
Detailed Description
The invention is further described with reference to specific examples.
An optimization method of irregular plane variable-inclination spraying track based on boundary constraint,
the method comprises the following specific steps:
step1, based on the existing static vertical spraying coating growth rate model, establishing a static variable-inclination spraying coating growth rate model by using a differential geometry principle and taking a spraying inclination angle as a controllable parameter of a spray gun;
step2, according to the arc approximation idea, the free curve type spraying path generated based on the boundary constraint is equivalent to be composed of a plurality of arc sections, wherein a straight line can be regarded as an arc with infinite curvature radius;
step3, based on the established static variable-inclination-angle spraying coating growth rate model, establishing a coating thickness model for dynamic spraying of a spray gun on a single arc path, and further establishing an optimization model of coating thickness distribution on two sides of the single path to obtain a functional relation among the spraying speed, the spraying inclination angle and the spraying height;
and 4, considering the track parameter optimization of the overall spraying path on the irregular plane workpiece, establishing a coating thickness superposition model between two adjacent spraying paths on each section intersection line of the generated spraying path based on the established coating thickness model of the dynamic spraying of the spray gun on the single arc path, and establishing an optimization model by taking the coating uniformity between the two adjacent spraying paths as an optimization target so as to achieve the aim of optimizing the spraying effect.
In step1, the method for establishing the growth rate model of the static variable-inclination spray coating specifically comprises the following steps:
101. let a static vertical spray coating growth rate model of a spray gun be a parabolic model, which can be expressed as:
Figure BDA0002350623940000086
(unit: μm/s, A is constant), the space shape of the spray torch is a cone, and the flare angle of the cone is phi, as shown in figure 1;
102. based on the static vertical spraying coating growth rate model, considering the spraying inclination angle α and the spraying height H of the spray gun as controllable parameters, adopting a differential geometric theory to establish the static spraying coating growth rate model of the spray gun at any point (x, y) in the spraying amplitude range:
Figure BDA0002350623940000081
if the spray gun is used for spraying at an inclined angle, the formed spray width range is an ellipse, and the expressions of the major axis and the minor axis a and b of the ellipse are respectively as follows:
Figure BDA0002350623940000082
Figure BDA0002350623940000083
wherein, in formula (2) and formula (3):
Figure BDA0002350623940000084
Figure BDA0002350623940000085
step3, establishing a coating thickness model for the dynamic spraying of the spray gun on the single arc path, and further establishing an optimization model for the coating thickness distribution on two sides of the single arc path to obtain a functional relation among the spraying speed, the spraying inclination angle and the spraying height, and the method comprises the following steps:
301. as shown in fig. 2, let ρ be the radius of curvature of the circular arc path, P be the center of curvature of the circular arc path, when the spray gun performs dynamic dip coating along the circular arc path trajectory, the velocity direction of the spray gun is the tangential direction of the circular arc path, v is the dynamic coating velocity of the spray gun on the circular arc path trajectory, v is the coating velocity of the spray gun at any point S in the swept spray width rangeSThe radius of curvature of the arc in which the point S is located is rhoSThe arc path curvature radius direction is taken as an X axis, and the spray gunA rectangular coordinate system is established for the Y axis in the speed direction, wherein
Figure BDA0002350623940000099
The arc length of a point S swept by the spray gun within the spray amplitude range is represented, and based on formula (1), a coating thickness model of the spray gun dynamic spraying on a single arc path by integrating the time t can be represented as follows:
Figure BDA0002350623940000091
as can be seen from FIG. 2, the speed at which any point in the spray width range is swept by the spray gun along the direction of the radius of curvature of the path is different, and the speed is in direct proportion to the radius of curvature of the circular arc track where the point is located, so that the spraying speed at any point S in the spray width range is vSCan be expressed as:
Figure BDA0002350623940000092
the y-axis coordinate value of the point S is as follows:
Figure BDA0002350623940000093
arc length of point S swept by the lance
Figure BDA0002350623940000094
And the elapsed time t may be expressed as:
Figure BDA0002350623940000095
Figure BDA0002350623940000096
in formula (9):
ρs＝ρ-x (11)
Figure BDA0002350623940000097
in equation (12):
Figure BDA0002350623940000098
in equation (13):
Figure BDA0002350623940000101
in equation (14):
d＝|a1-a2|
substituting the formula (8) and the formula (10) into the formula (6) to establish a coating thickness model expression of the dynamic spraying of the spray gun on the single arc path;
302. the spray gun dynamically sprays along a curved path track in a posture vertical to the surface of a workpiece, for a single spraying path, the fact that the coating uniformity effect of the surface of the whole workpiece is poor is that the coating thickness peak value is not on the spraying path, the coating thickness peak value is deviated to one side with the concave path, the uneven thickness of the two sides is more remarkable along with the increase of the curvature of the arc, and the uniformity effect of the sprayed coating is poor. Therefore, the characteristic that the position of the peak value of the coating thickness can be changed by utilizing the spraying inclination angle is utilized, and the direction and the size of the spraying inclination angle are reasonably adjusted, so that the peak value of the coating thickness after the spray gun dynamically sprays along the track of the arc path appears on the spraying path, the uniform distribution of the coating thickness at the two sides of the path is realized, and the aim of improving the spraying effect is finally achieved. The coating thickness peak value appears on the concave side of the arc path, so the spraying dip angle direction is deviated to the convex side of the path, the spraying dip angle needs to be calculated and determined on the spraying path according to the set coating thickness peak value, and the coating thickness target value can be determined according to the dynamic spraying coating thickness model solving spraying speed.
Setting the target value of the coating thickness as TdWhen the coating thickness peak value appears on the spraying path, namely at the original point of the X axis, firstly, the formula (6) is derived to obtain the coordinate value X of the X axis where the coating thickness peak value is located0Let x again0And this is taken into equation (6), specifically expressed as follows:
Figure BDA0002350623940000102
from the above equation, v and α are functions of H, and if the spray height H is known, the optimized spray velocity v and spray inclination angle α can be obtained by solving the above equation system.
In step4, the building generates a coating thickness superposition model between two adjacent spraying paths on each section line of the spraying paths, and builds an optimization model by taking the coating uniformity between the two adjacent spraying paths as an optimization target, and the building method comprises the following steps:
401. according to the requirements of the target coating thickness and the position of the peak value of the coating thickness, by optimizing the dynamic dip angle spraying tracks of the free curve path, a speed function and a dip angle function related to the spraying height H on each spraying track can be obtained, so that the peak value of the coating thickness on each spraying track reaches a target value, but the coating uniformity among the spraying tracks on the whole workpiece surface is not globally optimized. Because the generated spraying paths based on the boundary constraint are generated by adopting a series of bisection line bisection methods, the distance between two adjacent paths on each bisection line is determined and equal, as shown in fig. 3, and because the spraying height and the path distance have a direct ratio relationship, the spraying height at the position of the spraying path where each bisection line is located can be solved through optimization, so that the coating thickness superposition between the adjacent paths is uniform.
And (3) setting n cross-sectional lines for generating the spraying paths, wherein m coating thickness superposition intervals exist in the spraying paths, and according to the coating thickness superposition principle between adjacent paths, the coating thickness model of any point S in the jth superposition interval on the ith cross-sectional line can be represented as follows:
Figure BDA0002350623940000111
402. after the coating thickness superposition model between adjacent paths is established, an optimization function is established by the minimum variance between the coating thickness and the target coating thickness value at any point on each intersection line and in each superposition interval, and the optimization function is expressed as follows:
Figure BDA0002350623940000112
in the above formula HminAnd HmaxRespectively representing the minimum value and the maximum value of the allowable spraying height, wherein n multiplied by m variables are needed to be solved, and for the optimization problem with constrained multivariable, a mode search method can be adopted for solving, and the algorithm steps are as follows:
step1 gives the initial point x(1)＝(1,1,…,1)TN coordinate directions e1,e2,…,enThe initial step λ is 1, the acceleration factor ζ is 1, the reduction rate τ is 0.25, the allowable error ∈ is 0.1, and y is set(1)＝x(1)，k＝1，j＝1；
Step2 if E (y)(j)+λej)＜E(y(j)) Then let y(j+1)＝y(j)+λejPerforming step 4; otherwise, step3 is carried out;
step3 if E (y)(j)-λej)＜E(y(j)) Then let y(j+1)＝y(j)-λejPerforming step 4; otherwise, let y(j+1)＝y(j)Performing step 4;
step4, if j is less than n, setting j to j +1, and turning to Step 2; otherwise, step5 is carried out;
step5 if E (y)(n+1))＜E(x(k)) Step6 is performed; otherwise, step7 is carried out;
step6 place x(k+1)＝y(n+1)Let y(1)＝x(k+1)+ξ(x(k+1)-x(k)) Setting k to k +1 and j to 1, and switching to step 2;
step7, if lambda is less than or equal to epsilon, stopping iteration to obtain a point x(k)(ii) a Otherwise, let λ ═ τ λ, y(1)＝x(k)，x(k+1)＝x(k)K +1 and j 1, step 2.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention. Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

1.一种基于边界约束的不规则平面变倾角喷涂轨迹的优化方法，其特征在于，包括以下步骤：1. an optimization method based on the irregular plane variable inclination spraying trajectory of boundary constraint, is characterized in that, comprises the following steps: 步骤1，基于已有的静态垂直喷涂涂层生长率模型，将喷涂倾角作为喷枪的可控参数，运用微分几何原理建立静态变倾角喷涂涂层生长率模型；Step 1, based on the existing static vertical spray coating growth rate model, the spray inclination angle is used as a controllable parameter of the spray gun, and the differential geometry principle is used to establish a static variable inclination spray coating growth rate model; 步骤2，根据圆弧逼近思想，将基于边界约束生成的自由曲线型喷涂路径等效成若干圆弧段的组成，其中直线可看作是曲率半径无穷大的圆弧；Step 2, according to the idea of arc approximation, the free curve spraying path generated based on boundary constraints is equivalent to the composition of several arc segments, wherein the straight line can be regarded as an arc with an infinite radius of curvature; 步骤3，基于建立的静态变倾角喷涂涂层生长率模型，建立单条圆弧路径上喷枪动态喷涂的涂层厚度模型，并进一步建立单条路径两侧涂层厚度分布的优化模型，获得喷涂速率、喷涂倾角与喷涂高度的函数关系；Step 3: Based on the established static variable inclination spray coating growth rate model, establish a coating thickness model dynamically sprayed by a spray gun on a single arc path, and further establish an optimization model for the coating thickness distribution on both sides of a single path to obtain the spraying rate, The functional relationship between spraying inclination and spraying height; 步骤4，考虑不规则平面工件上全局喷涂路径的轨迹参数优化，基于建立的单条圆弧路径上喷枪动态喷涂的涂层厚度模型，建立生成喷涂路径每条截交线上两相邻喷涂路径间的涂层厚度叠加模型，并以两相邻喷涂路径间涂层均匀度为优化目标建立优化模型，以达到优化喷涂效果的目的。Step 4: Considering the optimization of the trajectory parameters of the global spraying path on the irregular plane workpiece, based on the established coating thickness model of the dynamic spraying of the spray gun on a single arc path, establish the interval between two adjacent spraying paths on each intersecting line of the generated spraying path. The coating thickness stacking model was established, and the optimization model was established with the coating uniformity between two adjacent spraying paths as the optimization goal to achieve the purpose of optimizing the spraying effect. 2.根据权利要求1所述的一种基于边界约束的不规则平面变倾角喷涂轨迹的优化方法，其特征在于，步骤1中建立静态变倾角喷涂涂层生长率模型的方法如下：2. the optimization method of a kind of irregular plane variable inclination spraying trajectory based on boundary constraint according to claim 1, is characterized in that, in step 1, the method for establishing static variable inclination spray coating growth rate model is as follows: 101、设一喷枪的静态垂直喷涂涂层生长率模型为一抛物线模型，可表示为
Figure FDA0002350623930000011
(单位：μm/s，A为常量)，其喷炬空间形状为圆锥体，圆锥体张角为φ；101. Set the static vertical spray coating growth rate model of a spray gun as a parabolic model, which can be expressed as
Figure FDA0002350623930000011
(unit: μm/s, A is a constant), the spatial shape of the torch is a cone, and the cone opening angle is φ; 102、基于上述静态垂直喷涂涂层生长率模型，考虑喷枪的喷涂倾角α和喷涂高度H为可控参数，采用微分几何理论建立喷幅范围内任意点(x,y)上喷枪的静态喷涂涂层生长率型：102. Based on the above static vertical spray coating growth rate model, considering the spraying inclination α of the spray gun and the spraying height H as controllable parameters, the differential geometry theory is used to establish the static spray coating of the spray gun on any point (x, y) within the spray width range. Layer Growth Rate Type:
Figure FDA0002350623930000012
Figure FDA0002350623930000012
 若喷枪为倾角喷涂，则形成的喷幅范围是椭圆形，椭圆的长短轴a和b的表达式分别为：If the spray gun is sprayed at an inclination angle, the formed spray width is an ellipse, and the expressions of the major and minor axes a and b of the ellipse are:
Figure FDA0002350623930000013
Figure FDA0002350623930000013
Figure FDA0002350623930000014
Figure FDA0002350623930000014
 其中，式(2)和式(3)中：Among them, in formula (2) and formula (3):
Figure FDA0002350623930000021
Figure FDA0002350623930000021
Figure FDA0002350623930000022
Figure FDA0002350623930000022
 3.根据权利要求1所述的一种基于边界约束的不规则平面变倾角喷涂轨迹的优化方法，其特征在于，步骤3中所述的建立单条圆弧路径上喷枪动态喷涂的涂层厚度模型，并进一步建立单条路径两侧涂层厚度分布的优化模型，获得喷涂速率、喷涂倾角与喷涂高度的函数关系，包括如下步骤：3. the optimization method of a kind of irregular plane variable inclination spraying trajectory based on boundary constraint according to claim 1, is characterized in that, the coating thickness model of spray gun dynamic spraying on single arc path of setting up described in step 3 , and further establish an optimization model of coating thickness distribution on both sides of a single path to obtain the functional relationship between spraying rate, spraying inclination and spraying height, including the following steps: 301，设圆弧路径的曲率半径为ρ，圆弧路径所在曲率中心为P，当喷枪沿圆弧路径轨迹动态倾角喷涂时，喷枪速率方向为圆弧路径的切线方向，喷枪在圆弧路径轨迹上的动态喷涂速率为v，喷枪在扫掠过喷幅范围内任意一点S上的喷涂速率为vS，点S所在圆弧的曲率半径为ρS，以圆弧路径曲率半径方向为X轴，喷枪速率方向为Y轴建立直角坐标系，其中
Figure FDA0002350623930000023
表示喷幅范围内点S被喷枪扫掠过的弧长，基于式(1)，通过对时间t求积分，单条圆弧路径上喷枪动态喷涂的涂层厚度模型可表示为：301. Set the radius of curvature of the arc path as ρ, and the center of curvature where the arc path is located as P. When the spray gun is spraying with a dynamic inclination along the arc path trajectory, the speed direction of the spray gun is the tangent direction of the arc path, and the spray gun is in the arc path trajectory. The dynamic spraying rate on is v, the spraying rate of the spray gun at any point S within the range of the spray width is v S , the radius of curvature of the arc where the point S is located is ρ S , and the direction of the radius of curvature of the arc path is the X axis , the speed direction of the spray gun is the Y axis to establish a Cartesian coordinate system, where
Figure FDA0002350623930000023
Represents the arc length swept by the spray gun at the point S within the spray width range. Based on equation (1), by integrating the time t, the coating thickness model of the spray gun dynamic spraying on a single arc path can be expressed as:
Figure FDA0002350623930000024
Figure FDA0002350623930000024
 在喷幅范围内沿路径曲率半径方向上任意一点被喷枪扫掠过的速率各异，其速率与该点所在的圆弧轨迹曲率半径大小成正比关系，因此，喷幅范围内任意一点S上的喷涂速率为vS可表示为：In the spray width range, any point along the path curvature radius direction is swept by the spray gun at different speeds, and its speed is proportional to the radius of curvature of the arc trajectory where the point is located. Therefore, any point S within the spray width range The spraying rate v S can be expressed as:
Figure FDA0002350623930000025
Figure FDA0002350623930000025
 点S所在的y轴坐标值为：The y-axis coordinate value of point S is:
Figure FDA0002350623930000026
Figure FDA0002350623930000026
 点S被喷枪扫掠过的弧长
Figure FDA0002350623930000027
和所经历的时间t可分别表示为：The arc length of point S swept by the gun
Figure FDA0002350623930000027
and the elapsed time t can be expressed as:
Figure FDA0002350623930000031
Figure FDA0002350623930000031
Figure FDA0002350623930000032
Figure FDA0002350623930000032
 式(9)中：In formula (9): ρs＝ρ-x (11)ρ s = ρ-x (11)
Figure FDA0002350623930000033
Figure FDA0002350623930000033
 式(12)中：In formula (12):
Figure FDA0002350623930000034
Figure FDA0002350623930000034
 式(13)中：In formula (13):
Figure FDA0002350623930000035
Figure FDA0002350623930000035
 式(14)中：In formula (14): d＝|a1-a2|d=|a 1 -a 2 | 将公式(8)和公式(10)代入公式(6)中即可建立单条圆弧路径上喷枪动态喷涂的涂层厚度模型表达式；By substituting formula (8) and formula (10) into formula (6), the model expression of the coating thickness of the dynamic spraying of the spray gun on a single arc path can be established; 步骤302，喷枪以垂直于工件表面的姿态沿曲线路径轨迹动态喷涂，对于单条喷涂路径而言，涂层厚度峰值不在喷涂路径上是造成整个工件表面涂层均匀度效果较差的原因，涂层厚度峰值偏向于路径内凹的一侧，且随着圆弧曲率的增大，两侧的厚度不均也越显著，喷涂涂层均匀度效果也越差，为此，利用喷涂倾角可改变涂层厚度峰值位置的特性，通过合理调整喷涂倾角的方向和大小，使得喷枪沿圆弧路径轨迹动态喷涂后的涂层厚度峰值出现在喷涂路径上，从而实现路径两侧的涂层厚度较为均匀的分布，最终达到改善喷涂效果的目的；由于涂层厚度峰值出现在圆弧路径内凹的一侧，因此喷涂倾角方向应偏向于路径外凸的一侧，喷涂倾角大小需根据设定涂层厚度峰值在喷涂路径上为条件计算确定，而涂层厚度目标值可根据动态喷涂涂层厚度模型求解喷涂速率确定；In step 302, the spray gun sprays dynamically along the curved path trajectory in an attitude perpendicular to the surface of the workpiece. For a single spray path, the fact that the coating thickness peak is not on the spray path is the cause of the poor coating uniformity effect on the entire workpiece surface. The thickness peak is biased towards the concave side of the path, and with the increase of the arc curvature, the thickness unevenness on both sides is more significant, and the uniformity effect of the sprayed coating is also worse. Therefore, the spraying inclination can be used to change the coating. The characteristics of the peak position of the layer thickness, by reasonably adjusting the direction and size of the spraying inclination angle, the peak of the coating thickness after the dynamic spraying of the spray gun along the arc path trajectory appears on the spraying path, so that the coating thickness on both sides of the path is more uniform. distribution, and finally achieve the purpose of improving the spraying effect; since the peak of the coating thickness appears on the concave side of the arc path, the direction of the spraying inclination should be biased towards the convex side of the path, and the spraying inclination should be set according to the coating thickness. The peak value is determined by conditional calculation on the spraying path, and the target value of coating thickness can be determined by solving the spraying rate according to the dynamic spray coating thickness model; 设涂层厚度目标值为Td，令其出现在喷涂路径上，即在X轴原点处，首先通过对式(6)进行求导，获得涂层厚度峰值所在X轴的坐标值x0，再令x0＝0，并将其带入到式(6)中，具体表示如下：Set the target value of the coating thickness as T d , and make it appear on the spraying path, that is, at the origin of the X-axis, first obtain the coordinate value x 0 of the X-axis where the peak of the coating thickness is located by deriving the formula (6), Then let x 0 =0, and bring it into formula (6), the specific expression is as follows:
Figure FDA0002350623930000041
Figure FDA0002350623930000041
 由上式可知，v和α是H的函数，若已知喷涂高度H，通过求解上述方程组，即可获得经优化后喷涂速率v和喷涂倾角α。It can be seen from the above formula that v and α are functions of H. If the spraying height H is known, the optimized spraying rate v and spraying inclination α can be obtained by solving the above equations. 4.根据权利要求1所述的一种基于边界约束的不规则平面变倾角喷涂轨迹的优化方法，其特征在于，步骤4中，所述的建立生成喷涂路径每条截交线上两相邻喷涂路径间的涂层厚度叠加模型，并以两相邻喷涂路径间涂层均匀度为优化目标建立优化模型，包括如下步骤：4. a kind of optimization method based on the irregular plane variable inclination spraying trajectory of boundary constraint according to claim 1, is characterized in that, in step 4, described establishment generates two adjacent on each intersection of spraying path The coating thickness stacking model between the spraying paths is established, and the optimization model is established with the coating uniformity between two adjacent spraying paths as the optimization goal, including the following steps: 步骤401，根据目标涂层厚度和涂层厚度峰值位置要求，通过对自由曲线路径动态倾角喷涂轨迹优化，可获得每条喷涂轨迹上关于喷涂高度H的速率函数和倾角函数，使得每条喷涂轨迹上的涂层厚度峰值达到目标值，但尚未对整个工件表面上喷涂路径轨迹间的涂层均匀度进行全局优化。由于生成的基于边界约束的喷涂路径是采用一系列截交线的等分法生成的，在每条截交线上两相邻路径间的间距已确定且相等，如图3所示，又因为喷涂高度和路径间距存在正比关系，可通过优化求解每条截交线所在喷涂路径位置处的喷涂高度，使得相邻路径间的涂层厚度叠加达到均匀；Step 401, according to the target coating thickness and the coating thickness peak position requirements, by optimizing the dynamic dip angle spraying trajectory of the free curve path, the rate function and inclination angle function about the spraying height H on each spraying trajectory can be obtained, so that each spraying trajectory can be obtained. The peak coating thickness on the workpiece reaches the target value, but has not yet been globally optimized for coating uniformity between spray path trajectories across the workpiece surface. Since the generated spraying paths based on boundary constraints are generated by a series of intersecting lines, the distance between two adjacent paths on each intersecting line is determined and equal, as shown in Figure 3, and because There is a proportional relationship between the spraying height and the path spacing. The spraying height at the spraying path position where each intersection line is located can be optimized and solved, so that the coating thickness between adjacent paths can be superimposed uniformly; 设生成喷涂路径的截交线共有n条，喷涂路径中有m个涂层厚度叠加区间，根据相邻路径间涂层厚度叠加原理，其中第i条截交线上第j个叠加区间中任意一点S的涂层厚度模型可表示为：Suppose there are n intersecting lines for generating the spraying path, and there are m coating thickness superposition intervals in the spraying path. The coating thickness model for a point S can be expressed as:
Figure FDA0002350623930000042
Figure FDA0002350623930000042
 步骤402，在建立了相邻路径间涂层厚度叠加模型之后，以每条截交线上和每个叠加区间中任意点的涂层厚度与涂层厚度目标值间的方差最小建立优化函数，表示如下：Step 402, after establishing the coating thickness superposition model between adjacent paths, establish an optimization function with the minimum variance between the coating thickness at any point in each intersection line and each superposition interval and the coating thickness target value, It is expressed as follows:
Figure FDA0002350623930000051
Figure FDA0002350623930000051
 上式中Hmin和Hmax分别表示允许的喷涂高度最小值和最大值，需要求解的变量有n×m个，对于带约束多变量的优化问题，采用模式搜索法进行求解。In the above formula, H min and H max represent the minimum and maximum allowable spray heights, respectively, and there are n×m variables to be solved. For the optimization problem with constrained multi-variables, the pattern search method is used to solve it.
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