CN104607367B

CN104607367B - A kind of electrostatic coating machine people's variate spray method on curved surface

Info

Publication number: CN104607367B
Application number: CN201510047332.XA
Authority: CN
Inventors: 李发忠; 赵德安; 季松林
Original assignee: CHANGZHOU BIAOMA INDUSTRIAL ROBOT SYSTEM ENGINEERING Co Ltd; Jiangsu University
Current assignee: CHANGZHOU BIAOMA INDUSTRIAL ROBOT SYSTEM ENGINEERING Co Ltd; Jiangsu University
Priority date: 2015-01-26
Filing date: 2015-01-26
Publication date: 2016-08-31
Anticipated expiration: 2035-01-26
Also published as: CN104607367A

Abstract

The invention discloses a variable spraying method of an electrostatic spraying robot on a curved surface. Firstly, a variable spraying model on the curved surface is established; then the curved surface workpiece is geometrically analyzed to determine the initial spraying path; The coating consistency and the stability of the spraying system are the goals, and the variable spraying trajectory is obtained by optimizing the spray gun moving speed and electrostatic voltage; on the basis of the optimized variable spraying trajectory, by optimizing the path spacing, electrostatic voltage and moving rate, etc. The parameters improve the consistency of coating thickness between trajectories; on the basis of ensuring the coating thickness requirements, the optimization scheme with the least number of path segments is selected to improve the spraying efficiency. The invention can obtain variable spraying tracks by optimizing parameters such as path spacing, electrostatic voltage and moving speed, thereby improving economic benefits and spraying efficiency, and reducing environmental pollution.

Description

A Variable Spraying Method of Electrostatic Spraying Robot on Curved Surface

技术领域technical field

本发明属于机器人喷涂技术领域，具体涉及一种曲面上的静电喷涂机器人变量喷涂方法。The invention belongs to the technical field of robot spraying, and in particular relates to a variable spraying method of an electrostatic spraying robot on a curved surface.

背景技术Background technique

高压静电旋杯式喷涂机器人是一种重要的涂装生产装备，广泛应用于国内外汽车等产品的涂装生产线。产品表面的色泽在相当程度上取决于涂层厚度的一致性，如果表面的涂层厚度不一致，会引起表面不光洁，并出现边缘涂料的流挂和涂料桔皮现象，而且涂层过厚的地方在使用过程中会出现皲裂倾向。另外，汽车及其零部件的涂装一直是汽车制造过程中能耗最高且产生三废最多的环节之一。在保证最小涂层厚度的情况下，均匀的涂层厚度可以减少涂料总量，降低喷涂成本。因此，如何通过优化喷涂机器人的运动轨迹、达到涂层厚度均匀，是值得进一步深入研究的问题。The high-voltage electrostatic rotary cup spraying robot is an important coating production equipment, which is widely used in the coating production lines of automobiles and other products at home and abroad. The color of the surface of the product depends on the consistency of the coating thickness to a considerable extent. If the coating thickness of the surface is inconsistent, it will cause the surface to be rough, and there will be edge paint sagging and paint orange peel phenomenon, and the coating is too thick. Areas have a tendency to crack during use. In addition, the painting of automobiles and their parts has always been one of the links in the automobile manufacturing process that consumes the most energy and produces the most three wastes. In the case of ensuring the minimum coating thickness, the uniform coating thickness can reduce the total amount of coating and reduce the cost of spraying. Therefore, how to achieve uniform coating thickness by optimizing the trajectory of the spraying robot is a problem worthy of further study.

曲面上的静电喷涂机器人变量喷涂技术是一种新型的喷涂技术，它是根据工件的形状，结合静电电压对喷涂图形的影响，优化喷涂轨迹，提高现有喷涂机器人在喷涂曲面时的质量和效率。Electrostatic spraying robot variable spraying technology on curved surfaces is a new type of spraying technology, which optimizes the spraying trajectory according to the shape of the workpiece, combined with the influence of electrostatic voltage on the spraying pattern, and improves the quality and efficiency of existing spraying robots when spraying curved surfaces .

发明内容Contents of the invention

本发明的目的在于利用静电喷涂机器人的静电电压对喷涂图形、涂层生长率和涂料转移率等的影响，提出一种专门针对曲面的静电喷涂机器人变量喷涂方法，以提高曲面工件的喷涂质量和效率。The purpose of the present invention is to utilize the influence of the electrostatic voltage of the electrostatic spraying robot on the spraying pattern, coating growth rate and paint transfer rate, etc., to propose a variable spraying method for the electrostatic spraying robot specially for curved surfaces, so as to improve the spraying quality and quality of curved surface workpieces. efficiency.

本发明采用的技术方案是：The technical scheme adopted in the present invention is:

一种曲面上的静电喷涂机器人变量喷涂方法，根据工件的形状，结合静电电压、喷枪移动速度和路径间距等喷涂参数获得机器人的最佳变量喷涂轨迹，具体步骤为：An electrostatic spraying robot variable spraying method on a curved surface, according to the shape of the workpiece, combined with electrostatic voltage, spray gun moving speed and path spacing and other spraying parameters to obtain the robot's optimal variable spraying trajectory, the specific steps are:

步骤1，建立曲面上的变量喷涂模型；Step 1, establishing a variable spraying model on the surface;

步骤2，确定起始喷涂路径，沿起始路径方向通过优化喷枪移动速度和静电电压获取变量喷涂轨迹，在已优化变量喷涂轨迹的基础上通过优化路径间距、静电电压和喷枪移动速度等参数提高轨迹间的涂层厚度一致性；Step 2, determine the initial spraying path, obtain the variable spraying trajectory by optimizing the spray gun moving speed and electrostatic voltage along the initial path direction, and improve the parameters by optimizing the path spacing, electrostatic voltage and spray gun moving speed on the basis of the optimized variable spraying trajectory Coating thickness consistency between tracks;

步骤3，在保证涂层厚度要求的基础上选取路径段数最少的优化方案，减少喷涂过程中喷枪的转折次数，提高喷涂效率。Step 3: On the basis of ensuring the coating thickness requirements, select the optimization scheme with the least number of path segments, reduce the number of turning times of the spray gun during the spraying process, and improve the spraying efficiency.

进一步，所述步骤2的变量喷涂轨迹优化的过程包括：Further, the process of the variable spray trajectory optimization of the step 2 includes:

步骤2.1，喷涂起始曲线的选择；Step 2.1, the selection of the spraying initial curve;

步骤2.2，沿路径方向的变量喷涂轨迹优化；Step 2.2, variable spray trajectory optimization along the path direction;

步骤2.3，垂直路径方向的变量喷涂轨迹优化；Step 2.3, variable spray trajectory optimization in the vertical path direction;

步骤2.4，变量喷涂轨迹综合优化。Step 2.4, comprehensive optimization of variable spraying trajectory.

进一步，所述步骤2.1中喷涂起始曲线的选择方法是：首先将曲面展开成平面，然后求取平面工件的最低高度ALT_min，以与ALT_min曲线垂直的边沿曲线中最长的边作为起始轨迹曲线。Further, the selection method of the spraying starting curve in the step 2.1 is: first, the curved surface is developed into a plane, and then the minimum height ALT _min of the plane workpiece is obtained, and the longest side of the edge curve perpendicular to the ALT _min curve is used as the starting point. start track curve.

进一步，所述步骤2.2中沿路径方向的变量喷涂轨迹优化方法是：在轨迹优化过程中采用喷枪移动速度和静电电压同时优化的方法提高沿轨迹方向的涂层一致性和喷涂系统的稳定性；建立了以喷枪移动速度(函数中用移动固定长度路径的时间代替)和静电电压为优化参数的沿路径方向的变量喷涂轨迹优化目标函数 Further, the variable spraying trajectory optimization method along the path direction in the step 2.2 is: in the trajectory optimization process, the method of simultaneously optimizing the spray gun moving speed and electrostatic voltage is used to improve the consistency of the coating along the trajectory direction and the stability of the spraying system; A variable spraying trajectory optimization objective function along the path direction is established with the spray gun moving speed (replaced by the time of moving a fixed-length path in the function) and electrostatic voltage as optimization parameters

进一步，所述步骤2.3中垂直路径方向的变量喷涂轨迹优化方法是：在已优化的路径上根据曲率变化取m个标记点，过标记点作一条与该点路径直交的索引曲线，沿着索引曲线结合喷枪移动速度和静电电压的优化确定最优的曲面间距d_i，根据m个曲面间距即可拟合得待优化路径，建立了以喷枪移动速度、路径间距和静电电压为优化参数的垂直路径方向的变量喷涂轨迹优化目标函数 Further, the variable spraying trajectory optimization method in the vertical path direction in the step 2.3 is: on the optimized path, m mark points are taken according to the curvature change, and an index curve perpendicular to the point path is made through the mark point, and along the index The curve is combined with the optimization of spray gun moving speed and electrostatic voltage to determine the optimal surface distance d _i , and the path to be optimized can be fitted according to m surface distances. Optimal function of variable spraying trajectory in path direction

本发明的技术效果为：本发明首先建立曲面上的变量喷涂模型；然后对曲面工件进行几何分析，确定起始喷涂路径；沿起始路径方向，以提高沿路径方向的涂层一致性和喷涂系统的稳定性为目标，采用优化喷枪移动速度和静电电压的方法获取变量喷涂轨迹；在已优化的变量喷涂轨迹的基础上通过优化路径间距、静电电压和移动速率等参数提高轨迹间的涂层厚度一致性；在保证涂层厚度要求的基础上，选取路径段数最少的优化方案提高喷涂效率。本发明既可提高曲面工件的喷涂质量，又可提高喷涂效率。The technical effect of the present invention is: firstly, the present invention establishes the variable spraying model on the curved surface; then performs geometric analysis on the curved surface workpiece to determine the initial spraying path; along the initial path direction, to improve the coating consistency and spraying along the path direction The stability of the system is the goal, and the variable spraying trajectory is obtained by optimizing the moving speed of the spray gun and the electrostatic voltage; on the basis of the optimized variable spraying trajectory, the coating between the trajectory is improved by optimizing the parameters such as path spacing, electrostatic voltage and moving speed. Thickness consistency; on the basis of ensuring the coating thickness requirements, select the optimization scheme with the least number of path segments to improve the spraying efficiency. The invention can not only improve the spraying quality of curved surface workpieces, but also improve the spraying efficiency.

附图说明Description of drawings

图1为静电电压与转移率的关系示意图；Figure 1 is a schematic diagram of the relationship between electrostatic voltage and transfer rate;

图2为平面上的涂料空间分布示意图；Fig. 2 is the schematic diagram of the spatial distribution of coating on the plane;

图3为旋转径向厚度剖面所得涂料空间分布示意图；Fig. 3 is a schematic diagram of the spatial distribution of the paint obtained by rotating the radial thickness profile;

图4为静态分布模型的平移示意图；Fig. 4 is the translation schematic diagram of static distribution model;

图5为平移模型的截面厚度示意图；Fig. 5 is the schematic diagram of the section thickness of translational model;

图6为曲面上的涂层生长模型；Fig. 6 is the coating growth model on the curved surface;

图7为最小高度代表最小的路径转折数示意图；Fig. 7 is a schematic diagram of the minimum path turning number represented by the minimum height;

图8为沿路径方向的变量喷涂轨迹优化示意图；Fig. 8 is a schematic diagram of variable spray trajectory optimization along the path direction;

图9为垂直路径方向的变量喷涂轨迹优化示意图；Fig. 9 is a schematic diagram of variable spray trajectory optimization in the vertical path direction;

图10为曲面上的变量喷涂轨迹优化步骤示意图。Fig. 10 is a schematic diagram of the optimization steps of the variable spray trajectory on the curved surface.

具体实施方式detailed description

下面结合附图进一步说明书本发明的具体实施方式，具体步骤如下：Further illustrate the specific embodiment of the present invention below in conjunction with accompanying drawing, concrete steps are as follows:

一、建立变量喷涂模型1. Establish variable spraying model

1.1静电电压与涂料转移率的关系1.1 The relationship between electrostatic voltage and paint transfer rate

如图1所示，涂料转移率是指沉积到工件表面的涂料与从喷枪喷出的涂料之比，静电电压的增加有助于提高喷涂过程中雾粒的荷质比，同时增加电场力对雾粒的作用，减少漂浮到工件外的涂料量，促进涂料在工件表面的沉积，提高涂料的沉积率。当间距、涂料流量恒定时，静电电压和涂料在工件上的转移率如图1所示，拟合得到喷涂转移率：As shown in Figure 1, the paint transfer rate refers to the ratio of the paint deposited on the surface of the workpiece to the paint sprayed from the spray gun. The increase of the electrostatic voltage helps to improve the charge-to-mass ratio of the mist particles during the spraying process, and at the same time increases the electric field force on the spray gun. The effect of fog particles reduces the amount of paint floating out of the workpiece, promotes the deposition of paint on the surface of the workpiece, and improves the deposition rate of paint. When the spacing and paint flow are constant, the electrostatic voltage and the transfer rate of the paint on the workpiece are shown in Figure 1, and the spray transfer rate is obtained by fitting:

g(u)＝-888100u^-2.563+99.5 (1)g(u)＝-888100u ^-2.563 +99.5 (1)

式中u为静电电压。where u is the electrostatic voltage.

1.2静电电压与喷涂图形的关系1.2 The relationship between electrostatic voltage and spray pattern

喷涂时，涂料的雾化是由旋杯高速旋转产生的离心力、高压静电的电场力和整形空气的惯性力共同完成的，它所产生的涂料空间分布是环形，不同于空气喷枪的圆锥形。如图2a所示，当静电电压、间距、旋杯转速、涂料流量和涂料的粘度等参数保持一定的情况下，喷枪垂直于工件表面定点喷涂一段时间所形成的涂料空间分布为中空的环形，可以近似看成一个内直径为D₂和外直径为D₁的圆环。如图2所示，随着静电电压的变化，雾化后的带电雾粒所受电场力也发生变化，在其他参数不变的情况下，试验得到涂料空间分布图形的内、外径均随静电电压的增加而变小。拟合得到外半径R₁(u)和内半径R₂(u)：When spraying, the atomization of the paint is completed by the centrifugal force generated by the high-speed rotation of the rotary cup, the electric field force of the high-voltage static electricity and the inertial force of the shaping air. The spatial distribution of the paint produced by it is ring-shaped, which is different from the conical shape of the air spray gun. As shown in Figure 2a, when the parameters such as electrostatic voltage, spacing, rotating cup speed, paint flow rate and paint viscosity are kept constant, the spray gun is perpendicular to the surface of the workpiece and sprayed at a fixed point for a period of time to form a hollow ring. It can be approximated as _a ring with inner diameter _D2 and outer diameter D1. As shown in Figure 2, as the electrostatic voltage changes, the electric field force on the atomized charged mist particles also changes. Under the condition that other parameters remain unchanged, the test shows that the inner and outer diameters of the spatial distribution pattern of the paint change with the electrostatic force. decrease with increasing voltage. Fitting results in outer radius R ₁ (u) and inner radius R ₂ (u):

${R R}_{11} ((u u)) = = k k ((- - \frac{88 {u u}^{33}}{11211121} + + \frac{881881 {u u}^{22}}{481481} - - 157.95 157.95 u u + + 50215021)) - - - - - - ((22))$

${R R}_{22} ((u u)) = = k k ((- - \frac{{u u}^{33}}{808808} + + \frac{297297 {u u}^{22}}{895895} - - \frac{13101310 u u}{4343} + + 10661066)) - - - - - - ((33))$

式中u为静电电压，k为与旋杯口径对应的比例系数。In the formula, u is the electrostatic voltage, and k is the proportional coefficient corresponding to the diameter of the rotary cup.

1.3平面上的变量喷涂模型1.3 Variable spraying model on plane

如图3a所示，平面上的涂料空间分布为环形，涂料空间分布的径向剖面h(r)为图3b所示曲线，图中R₁为涂料空间分布的外半径，R₂为内半径。将径向剖面绕过圆心的沉积平面法线旋转一周即得涂料空间分布，在各个工况参数不变的情况下，单位时间内工件上沉积的涂料量为As shown in Figure 3a, the spatial distribution of the paint on the plane is circular, and the radial section h(r) of the spatial distribution of the paint is the curve shown in Figure _3b . In the figure, R1 is the outer radius of the spatial distribution _of the paint, and R2 is the inner radius . The spatial distribution of the paint can be obtained by rotating the normal line of the deposition plane with the radial section around the center of the circle for a circle. Under the condition that the parameters of each working condition remain unchanged, the amount of paint deposited on the workpiece per unit time is

$q q = = {&Integral; &Integral;}_{00}^{22 π π} {&Integral; &Integral;}_{{R R}_{22}}^{{R R}_{11}} h h ((r r)) rdrdθ rdrdθ - - - - - - ((44))$

设单位时间内旋杯喷出的涂料流量为Q，算上喷涂转移率则有Let Q be the paint flow rate sprayed by the rotary cup per unit time, and calculate the spraying transfer rate as follows:

q＝gQ (5)q=gQ (5)

如图4所示，当固定的喷涂沉积模型沿x方向以恒定速度移动，在平面上形成一个条纹沉积模型，沿平移方向的涂膜生长速率是一致的。图4的条纹涂膜沿A-A方向的典型横截面如图5所示，它表示剖面厚度在y方向的变化函数H(y)。As shown in Figure 4, when the fixed spray deposition model moves at a constant speed along the x direction, a stripe deposition model is formed on the plane, and the growth rate of the coating film along the translation direction is consistent. The typical cross-section of the striped coating film in Figure 4 along the A-A direction is shown in Figure 5, which represents the variation function H(y) of the section thickness in the y direction.

设平移速度为v，如图4所示，若旋杯沿x方向平移，在平面上沿平移方向的涂层生长速率是一致的，而沿y方向的涂层生长速率H(y)为沿x方向的涂料厚度积分Assuming that the translation velocity is v, as shown in Figure 4, if the rotary cup translates along the x direction, the coating growth rate along the translation direction on the plane is consistent, while the coating growth rate H(y) along the y direction is Coating thickness integral in the x direction

$H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r)) dx dx - - - - - - ((66))$

其中，既然，静态径向厚度剖面为半径r的函数，半径是x的函数，假设y在弦上的值保持不变，而且x是随着y的变化而变化的函数，那么in, Since, the static radial thickness profile is a function of radius r, and radius is a function of x, assuming that the value of y on the chord remains constant, and that x is a function that varies with y, then

$H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r ((x x)))) dx dx - - - - - - ((77))$

为了得到弦上厚度值，有必要从圆柱坐标系转换到直角坐标系，由r的恒等式演化得：In order to obtain the thickness value on the chord, it is necessary to convert from the cylindrical coordinate system to the rectangular coordinate system, which is evolved from the identity of r:

$H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r ((x x)))) dx dx = = \frac{22}{v v} {&Integral; &Integral;}_{y the y}^{{R R}_{11}} \frac{rg r g ((r r))}{\sqrt{{r r}^{22} - - {y the y}^{22}}} dr dr - - - - - - ((88))$

至此，在获得单位时间内高压静电旋杯在平面静态喷涂模型的径向厚度剖面数据后，即可由式(8)得到高压静电旋杯移动过程中在平面上沉积的涂层厚度分布数据。So far, after obtaining the radial thickness profile data of the high-voltage electrostatic rotary cup on the plane static spraying model per unit time, the coating thickness distribution data deposited on the plane during the high-voltage electrostatic rotary cup movement can be obtained by formula (8).

1.4曲面上的涂层厚度数学模型的建立1.4 Establishment of mathematical model of coating thickness on curved surface

曲面上的涂层生长模型如图6所示，在保持涂料总量不变的前提下，根据微分几何的面积放大定理，平面上某一点s的涂层累积速率乘以面积放大系数得到曲面上点s₁的涂层累积速率。The coating growth model on the curved surface is shown in Figure 6. On the premise of keeping the total amount of coating constant, according to the area magnification theorem of differential geometry, the coating accumulation rate at a certain point s on the plane is multiplied by the area magnification factor to obtain Coating accumulation rate at point _s1 .

平面P为参考平面，P₂为过点s₁且与P平行的平面，c为P上以s为圆心的圆，c₁为c映射到过点s₁的切平面上的圆，h为喷射点e到参考平面P之间的距离，h₁为e到平面P₂的距离，θ为直线es₁与喷枪中轴线之间的夹角，β为e到圆c的最大张角(β→0)，α为s₁的法向量与es₁的夹角。c₁和c的面积Sc₁与Sc的关系：Plane P is the reference plane, P ₂ is the plane passing through point s ₁ and parallel to P, c is the circle on P with s as the center, c ₁ is the circle mapped from c to the tangent plane passing through point s ₁ , h is The distance between the injection point e and the reference plane P, h ₁ is the distance from e to the plane P ₂ , θ is the straight line es ₁ and the central axis of the spray gun The angle between , β is the maximum angle from e to circle c (β→0), α is the normal vector of s ₁ Angle with es ₁ . The relationship between c ₁ and the area Sc ₁ of c and Sc:

$\frac{{s the s}_{{c c}_{11}}}{{s the s}_{c c}} = = {((\frac{{h h}_{11} cos cos θ θ}{h h cos cos α α}))}^{22}$

已知平面上某点s的涂层厚度q，则曲面上点s₁涂层厚度数学表达式为Knowing the coating thickness q of a certain point s on the plane, the mathematical expression of the coating thickness at point s ₁ on the curved surface is

二、变量喷涂轨迹优化方法2. Optimization method of variable spraying trajectory

2.1起始曲线的选择2.1 Selection of starting curve

根据机器人的特性，喷涂轨迹转折越少效率越高。同一工件，轨迹起始曲线取不同的方向，产生的轨迹段数不同，对应的喷涂效率也不同。曲面工件所需的路径段数可以由工件的最低高度ALT_min代替，图7说明了平面工件的ALT_min和转折数的关系，曲面工件的ALT_min可以将曲面展开成平面后求取。得到曲面的ALT_min后，选取与ALT_min曲线垂直的边沿曲线中最长的边作为起始轨迹曲线。According to the characteristics of the robot, the less turning the spraying trajectory, the higher the efficiency. For the same workpiece, the starting curve of the trajectory takes different directions, the number of trajectory segments generated is different, and the corresponding spraying efficiency is also different. The number of path segments required for a curved surface workpiece can be replaced by the minimum height ALT _min of the workpiece. Figure 7 illustrates the relationship between the ALT _min of a flat workpiece and the number of turns. The ALT _min of a curved surface workpiece can be obtained after unfolding the curved surface into a plane. After obtaining the ALT _min of the surface, select the longest edge among the edge curves perpendicular to the ALT _min curve as the initial trajectory curve.

2.2沿路径方向的变量喷涂轨迹优化2.2 Variable spray trajectory optimization along the path direction

由式(9)、(10)知，沿轨迹方向曲面曲率变化导致涂层厚度不均，采用调节喷枪移动速度(v)的方法可以提高沿轨迹方向的涂层一致性。然而，v的大幅度变化同时带来喷涂系统的不稳定，由图1、2知，静电电压(u)越高涂层生长速率越大，轨迹优化过程中可以采用v和u同时优化的方法提高沿轨迹方向的涂层一致性和喷涂系统的稳定性。From equations (9) and (10), it is known that the variation of surface curvature along the track direction leads to uneven coating thickness, and the method of adjusting the moving speed (v) of the spray gun can improve the coating consistency along the track direction. However, a large change in v also brings about the instability of the spraying system. As shown in Figures 1 and 2, the higher the electrostatic voltage (u), the greater the growth rate of the coating, and the simultaneous optimization of v and u can be used in the trajectory optimization process. Improves coating consistency along the trajectory and stability of the spray system.

如图8所示，在给定喷枪路径的两侧构建若干条子偏移(sub-offset)路径，沿子偏移路径计算涂层厚度的标准方差，优化目标为所有标准方差之和最小。优化方法如下：As shown in Figure 8, several sub-offset paths are constructed on both sides of a given spray gun path, and the standard deviation of the coating thickness is calculated along the sub-offset paths. The optimization goal is to minimize the sum of all standard deviations. The optimization method is as follows:

将给定路径分为n段，设在第i段路径长为s_i，喷枪速度v_i，喷涂时间t_i＝s_i/v_i，速度向量为V＝{v_i:i∈[1,n]}，电压向量为U＝{u_i:i∈[1,n]}。可以把V的优化问题转化为T＝{t_i:i∈[1,n]}的优化问题。定义子偏移路径j上的涂层生长速率矩阵HP_j＝{d_ef:e,f∈[1,n]}，其中d_ef为喷枪在第f段的中间时，第e段的涂层生长速率。则涂层厚度标准方差为||(HP_jT-k_j)/k_j||，其中HP_jT代表子偏移路径j上的涂层厚度，s_j表示向量HP_jT所有元素之和，k_j＝s_j/n为涂层平均厚度，k_j为元素恒等于k_j的n维向量。Divide the given path into n sections, set the i-th section path length as s _i , spray gun speed v _i , spraying time t _i =s _i /v _i , and velocity vector as V={v _i :i∈[1, n]}, the voltage vector is U={u _i :i∈[1,n]}. The optimization problem of V can be transformed into an optimization problem of T={t _i :i∈[1,n]}. Define the coating growth rate matrix HP _j ={d _ef :e,f∈[1,n]} on the sub-offset path j, where d _ef is the coating of the e-th segment when the spray gun is in the middle of the f-th segment growth rate. Then the standard deviation of the coating thickness is ||(HP _j Tk _j )/k _j ||, where HP _j T represents the coating thickness on the sub-offset path j, s _j represents the sum of all elements of the vector HP _j T, k _j = s _j /n is the average thickness of the coating, and k _j is an n-dimensional vector whose elements are always equal to k _j .

定义第j条子偏移路径的标准方差在目标函数中的加权系数w_j＝k_j/Σ_ik_i，则优化问题表示为Define the weight coefficient w _j = k _j /Σ _i k _i of the standard deviation of the jth sub-offset path in the objective function, then the optimization problem is expressed as

$\underset{((T T,, U u))}{min min} \underset{j j}{Σ Σ} \frac{{w w}_{j j}}{{k k}_{j j}} | | | | H h {P P}_{j j} T T - - {K K}_{j j} | | | | - - - - - - ((1111))$

电压、速度和加速度约束条件为The voltage, velocity and acceleration constraints are

u_min≤u_i≤u_max u _min ≤ u _i ≤ u _max

s_i/v_max≤t_i≤s_i/v_min s _i /v _max ≤t _i ≤s _i /v _min

$- - {a a}_{max max} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} \leq \leq {s the s}_{i i + + 11} {t t}_{i i} - - {s the s}_{i i} {t t}_{i i + + 11} \leq \leq {a a}_{max max} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}}$

2.3垂直路径方向的变量喷涂轨迹优化2.3 Variable spray trajectory optimization in vertical path direction

在曲面上，沿路径方向的变量优化并不能解决由曲率变化造成的轨迹间涂层厚度不均匀问题，还须优化路径间距。间距优化方法如图9所示，根据曲率变化在当前路径上取m个标记点，过标记点作一条与该点路径直交的索引曲线，沿着索引曲线确定最优的曲面间距d_i，根据m个曲面间距D＝{d_i:i∈[1,m]}即可拟合得待优化路径。On curved surfaces, variable optimization along the path direction cannot solve the problem of uneven coating thickness between trajectories caused by curvature changes, and path spacing must also be optimized. The distance optimization method is shown in Figure 9. According to the curvature change, m mark points are selected on the current path, and an index curve perpendicular to the path is made through the mark points, and the optimal surface distance d _i is determined along the index curve. According to The distance between m surfaces D={d _i :i∈[1,m]} can be fitted to obtain the path to be optimized.

在当前路径的标记点(A)和待优化路径的标记点(A1)之间取g个观测点，由2.2节可知观测点的涂层厚度，两条路径间共有m×g个观测点。定义索引曲线观测点的涂层生长速率矩阵HV＝{d_ef:e∈[1,m],f∈[1,g]}，第e条索引曲线上的涂层厚度标准方差为||(HV_et_e-k_e)/k_e||，其中t_e表示喷枪在第e条索引曲线上停留的时间，HV_et_e第e条索引曲线上各个观测点的涂层厚度，s_e表示向量HV_et_e所有元素之和，k_e＝s_e/g为涂层平均厚度，k_e为元素恒等于k_e的g维向量。Take g observation points between the mark point (A) of the current path and the mark point (A1) of the path to be optimized. The coating thickness of the observation point can be known from Section 2.2. There are m×g observation points between the two paths. Define the coating growth rate matrix HV of the observation point of the index curve ={d _ef :e∈[1,m],f∈[1,g]}, the standard deviation of the coating thickness on the e-th index curve is ||( HV _e t _e -k _e )/k _e ||, where t _e represents the time the spray gun stays on the index curve e, the coating thickness of each observation point on the index curve e of HV _e t _e , s _e Indicates the sum of all elements of the vector HV _e t _e , _ke = s _e /g is the average thickness of the coating, and _ke is the g-dimensional vector whose elements are equal to _ke .

则垂直路径方向的优化问题表示为Then the optimization problem in the direction of the vertical path is expressed as

$\underset{((T T,, U u,, D D.))}{min min} \frac{11}{m m} \underset{e e}{Σ Σ} | | | | ((H h {V V}_{e e} {t t}_{e e} - - {k k}_{e e})) / / {k k}_{e e} | | | | - - - - - - ((1212))$

u_min≤u_i≤u_max u _min ≤ u _i ≤ u _max

s_i/v_max≤t_i≤s_i/v_min s _i /v _max ≤t _i ≤s _i /v _min

$- - {a a}_{max max} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} \leq \leq {s the s}_{i i + + 11} {t t}_{i i} - - {s the s}_{i i} {t t}_{i i + + 11} \leq \leq {a a}_{max max} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} . .$

为了提高喷涂效率，在保证涂层厚度要求的基础上，路径段数越少越优。In order to improve the spraying efficiency, on the basis of ensuring the coating thickness requirements, the fewer the number of path segments, the better.

2.4变量喷涂轨迹综合优化2.4 Comprehensive optimization of variable spraying trajectory

前面的两种优化方法是从两个不同的方向对轨迹进行分步优化，那么对整个工件而言，难免出现局部喷涂效果相对较差的结果。针对此问题，还需对轨迹进行全局优化，即对整个工件的轨迹喷涂效果进行总体评估，然后针对存在的问题对喷涂参数进行局部微调，以达到全局最优。The previous two optimization methods are to optimize the trajectory step by step from two different directions, so for the entire workpiece, it is inevitable that the local spraying effect will be relatively poor. To solve this problem, global optimization of the trajectory is also required, that is, an overall evaluation of the trajectory spraying effect of the entire workpiece, and then local fine-tuning of the spraying parameters for the existing problems to achieve the global optimum.

三、变量喷涂轨迹优化流程3. Variable spraying trajectory optimization process

对曲面进行变量喷涂轨迹优化，如附图10所示：Perform variable spray trajectory optimization on the curved surface, as shown in Figure 10:

第一步、确定变量喷涂模型，通过实验确定静电电压与涂料转移率和喷涂图形的关系，然后将相应的参数代入平面上的变量喷涂模型和曲面上的涂层厚度数学模型。The first step is to determine the variable spraying model, determine the relationship between electrostatic voltage, paint transfer rate and spraying pattern through experiments, and then substitute the corresponding parameters into the variable spraying model on the plane and the mathematical model of coating thickness on the curved surface.

第二步、起始曲线的选择，计算曲面工件所的最低高度ALT_min，沿曲面边沿规划与ALT_min曲线垂直的曲线作为起始轨迹曲线。The second step is the selection of the starting curve. Calculate the minimum height ALT _min of the workpiece on the curved surface, and plan a curve perpendicular to the ALT _min curve along the edge of the surface as the starting trajectory curve.

第三步、沿路径方向的变量喷涂轨迹优化，采用调节喷枪移动速度(v)和静电电压(u)的方法提高沿轨迹方向的涂层一致性和喷涂系统的稳定性。The third step is to optimize the variable spraying trajectory along the path direction. The method of adjusting the spray gun moving speed (v) and electrostatic voltage (u) is used to improve the coating consistency along the trajectory direction and the stability of the spraying system.

第四步、垂直路径方向的变量喷涂轨迹优化，在已优化路径的基础上通过优化路径间的间距以及喷涂时的v和u提高轨迹间的涂层厚度一致性，且在保证涂层厚度要求的基础上，采用最少路径段数方案。The fourth step is to optimize the variable spraying trajectory in the direction of the vertical path. On the basis of the optimized path, by optimizing the distance between paths and v and u during spraying, the coating thickness consistency between the paths is improved, and the coating thickness requirements are guaranteed. On the basis of , the scheme with the least number of path segments is adopted.

第五步、全部轨迹的综合优化，对整个工件的轨迹喷涂效果进行总体评估，然后针对存在的问题对喷涂参数进行局部微调，以达到全局最优。The fifth step is the comprehensive optimization of all trajectories. The overall evaluation of the trajectory spraying effect of the entire workpiece is carried out, and then local fine-tuning of the spraying parameters is carried out according to the existing problems to achieve the global optimum.

第六步、优化结束，输出喷涂机器人末端轨迹位姿、静电电压和喷枪移动速度等数据。Step 6: After the optimization is completed, output the data such as the end trajectory pose of the spraying robot, the electrostatic voltage, and the moving speed of the spray gun.

应理解上述施例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。It should be understood that the above-mentioned embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading the present invention, those skilled in the art all fall into the appended claims of the present application to the amendments of various equivalent forms of the present invention limited range.

Claims

1. An electrostatic spraying robot variable spraying method on a curved surface is characterized in that: according to the shape of the workpiece, the optimal variable spraying track of the robot is obtained in conjunction with the spraying parameters of electrostatic voltage, spray gun moving speed and path spacing, and the concrete steps are:

Step 1, establishing a variable spraying model on the surface;

1.1 The relationship between electrostatic voltage and paint transfer rate: paint transfer rate refers to the ratio of the paint deposited on the surface of the workpiece to the paint sprayed from the spray gun. Increase the effect of the electric field force on the mist particles, reduce the amount of paint floating out of the workpiece, promote the deposition of the paint on the surface of the workpiece, and increase the deposition rate of the paint; when the distance and the flow of paint are constant, the spraying transfer rate is obtained by fitting:

g(u)＝-888100u ^-2.563 +99.5 (1)

where u is the electrostatic voltage;

1.2 The relationship between electrostatic voltage and spraying pattern: when spraying, the atomization of the paint is completed by the centrifugal force generated by the high-speed rotation of the rotary cup, the electric field force of the high-voltage static electricity and the inertial force of the shaping air, and the spatial distribution of the paint produced by it is circular. , which is different from the conical shape of the air spray gun; when the electrostatic voltage, spacing, rotating cup speed, paint flow and paint viscosity parameters are kept constant, the paint space formed by spraying the spray gun perpendicular to the surface of the workpiece for a period of time is hollow. Ring, which can be approximated as _a ring with an inner diameter of D2 and an outer diameter of D1 _; as the electrostatic voltage changes, the electric field force on the atomized charged mist particles also changes, and when other parameters remain unchanged Under the following conditions, the test shows that the inner and outer diameters of the paint spatial distribution pattern become smaller with the increase of the electrostatic voltage; the outer radius R ₁ (u) and inner radius R ₂ (u) are obtained by fitting:

{R R}_{11} ((u u)) = = k k ((- - \frac{88 {u u}^{33}}{11211121} + + \frac{881881 {u u}^{22}}{481481} - - 157.95 157.95 u u + + 50215021)) - - - - - - ((22))

{R R}_{22} ((u u)) = = k k ((- - \frac{{u u}^{33}}{808808} + + \frac{297297 {u u}^{22}}{895895} - - \frac{13101310 u u}{4343} + + 10661066)) - - - - - - ((33))

In the formula, u is the electrostatic voltage, and k is the proportional coefficient corresponding to the diameter of the rotary cup;

1.3 Variable spraying model on the plane: the spatial distribution of the paint on the plane is circular, the radial section h(r) of the spatial distribution of the paint is a curve, and the spatial distribution of the paint can be obtained by rotating the radial section around the normal of the deposition plane at the center of the circle. , when the parameters of each working condition are constant, the amount of paint deposited on the workpiece per unit time is

q q = = {&Integral; &Integral;}_{00}^{22 π π} {&Integral; &Integral;}_{{R R}_{22}}^{{R R}_{11}} h h ((r r)) r r d d r r d d θ θ - - - - - - ((44))

Let Q be the paint flow rate sprayed by the rotary cup per unit time, and calculate the spraying transfer rate as follows:

q=gQ (5)

When the fixed spray deposition model moves at a constant speed along the x direction, a fringe deposition model is formed on the plane, and the growth rate of the coating film along the translation direction is consistent; if the translation speed is v, if the rotary cup translates along the x direction, in The coating growth rate along the translation direction on the plane is consistent, and the coating growth rate H(y) along the y direction is the integral of the coating thickness along the x direction

H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r)) d d x x - - - - - - ((66))

in, The static radial thickness profile is a function of radius r, which is a function of x, assuming that the value of y on the chord remains constant, and that x is a function that varies with y, then

H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r ((x x)))) d d x x - - - - - - ((77))

In order to obtain the thickness value on the chord, it is necessary to convert from the cylindrical coordinate system to the rectangular coordinate system, which is evolved from the identity of r:

H h ((y the y)) = = \frac{22}{v v} {&Integral; &Integral;}_{00}^{s the s ((y the y))} h h ((r r ((x x)))) d d x x = = \frac{22}{v v} {&Integral; &Integral;}_{y the y}^{{R R}_{11}} \frac{r r h h ((r r))}{\sqrt{{r r}^{22} - - {y the y}^{22}}} d d r r - - - - - - ((88))

So far, after obtaining the radial thickness profile data of the high-voltage electrostatic rotary cup on the plane static spraying model per unit time, the coating thickness distribution data deposited on the plane during the movement of the high-voltage electrostatic rotary cup can be obtained by formula (8);

1.4 Establishment of the mathematical model of coating thickness on the curved surface: under the premise of keeping the total amount of coating unchanged, according to the area magnification theorem of differential geometry, the point on the surface is obtained by multiplying the coating accumulation rate at a certain point s on the plane by the area magnification factor s ₁ coating accumulation rate;

Plane P is the reference plane, P ₂ is the plane passing through point s ₁ and parallel to P, c is the circle on P with s as the center, c ₁ is the circle mapped from c to the tangent plane passing through point s ₁ , h is The distance between the injection point e and the reference plane P, h ₁ is the distance from e to the plane P ₂ , θ is the straight line es ₁ and the central axis of the spray gun The angle between , β is the maximum angle from e to circle c (β→0), α is the normal vector of s ₁ The angle with es ₁ ; the relationship between the area Sc ₁ and Sc of c ₁ and c:

\frac{{s the s}_{{c c}_{11}}}{{s the s}_{c c}} = = {((\frac{{h h}_{11} cos cos θ θ}{h h c c o o s the s α α}))}^{22} - - - - - - ((99))

Knowing the coating thickness q of a certain point s on the plane, the mathematical expression of the coating thickness at point s ₁ on the curved surface is

Step 2, determine the initial spraying path, obtain the variable spraying trajectory by optimizing the spray gun moving speed and electrostatic voltage along the initial path direction, and improve the trajectory by optimizing the path spacing, electrostatic voltage and spray gun moving speed parameters on the basis of the optimized variable spraying trajectory Coating thickness consistency between;

Step 3, on the basis of ensuring the coating thickness requirements, select the optimization scheme with the least number of path segments, reduce the number of turning times of the spray gun during the spraying process, and improve the spraying efficiency;

The process of the variable spray trajectory optimization of the step 2 includes:

Step 2.1, the selection of the spraying initial curve;

Step 2.2, variable spray trajectory optimization along the path direction;

Step 2.3, variable spray trajectory optimization in the vertical path direction;

Step 2.4, comprehensive optimization of variable spray trajectory;

The selection method of the spraying starting curve in the step 2.1 is: firstly, the curved surface is developed into a plane, and then the minimum height ALT _min of the plane workpiece is calculated, and the longest side among the edge curves perpendicular to the ALT _min curve is used as the starting track curve;

The variable spraying trajectory optimization method along the path direction in the step 2.2 is: in the trajectory optimization process, the method of simultaneously optimizing the moving speed of the spray gun and the electrostatic voltage is used to improve the consistency of the coating along the trajectory direction and the stability of the spraying system; The objective function of variable spraying trajectory optimization along the path direction with spray gun moving speed and electrostatic voltage as optimization parameters Among them, the given path is divided into n sections, assuming that the path length of the i-th section is s _i , the spray gun speed v _i , the spraying time t _i =s _i /v _i , and the velocity vector is V={v _i : i∈[ 1, n]}, the voltage vector is U={u _i : i∈[1,n]}; the optimization problem of V can be transformed into the optimization problem of T={t _i : i∈[1,n]}; Define the coating growth rate matrix HP _j = {d _ef : e, f ∈ [1, n]} on the sub-offset path j, where d _ef is the coating of the e-th segment when the spray gun is in the middle of the f-th segment growth rate; then the standard deviation of the coating thickness is ||(HP _j Tk _j )/k _j ||, where HP _j T represents the coating thickness on the sub-offset path j, and s _j represents the value of all elements of the vector HP _j T And, _kj=sj _/ n is the coating average thickness, and _kj is the n-dimensional vector whose element is equal to _kj ;

Define the weighting coefficient w _j =k _j /∑ _i k _i of the standard deviation of the jth sub-offset path in the objective function, and the voltage, velocity and acceleration constraints are

u _min ≤ u _i ≤ u _max

s _i /v _max ≤t _i ≤s _i /v _min

- - {a a}_{m m a a x x} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} \leq \leq {s the s}_{i i + + 11} {t t}_{i i} - - {s the s}_{i i} {t t}_{i i + + 11} \leq \leq {a a}_{m m a a x x} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}}

The variable spraying trajectory optimization method in the vertical path direction in the step 2.3 is: get m mark points according to the curvature change on the optimized path, pass the mark point to make an index curve perpendicular to the path of this point, and combine along the index curve The optimization of spray gun moving speed and electrostatic voltage determines the optimal surface distance d _i , and the path to be optimized can be fitted according to m surface distances, and the vertical path direction with spray gun moving speed, path distance and electrostatic voltage as optimization parameters is established The variable spraying trajectory optimization objective function of Among them, the coating growth rate matrix HV={d _ef : e∈[1, m], f∈[1, g]} defining the observation points of the index curve, the standard deviation of the coating thickness on the e-th index curve is | |(HV _e t _e -k _e )/k _e ||, where t _e represents the time the spray gun stays on the e index curve, the coating thickness of each observation point on the e index curve of HV _e t _e , s _e represents the sum of all elements of the vector HV _e t _e , _ke = s _e /g is the average thickness of the coating, and _ke is the g-dimensional vector whose elements are equal to _ke ;

Then the optimization problem in the direction of the vertical path is expressed as

\underset{((T T,, U u,, D D.))}{m m i i n no} \frac{11}{m m} \underset{e e}{Σ Σ} | | | | (({HV HV}_{e e} {t t}_{e e} - - {k k}_{e e})) / / {k k}_{e e} | | | | - - - - - - ((1212))

The voltage, velocity and acceleration constraints are

u _min ≤ u _i ≤ u _max

s _i /v _max ≤t _i ≤s _i /v _min

- - {a a}_{m m a a x x} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} \leq \leq {s the s}_{i i + + 11} {t t}_{i i} - - {s the s}_{i i} {t t}_{i i + + 11} \leq \leq {a a}_{m m a a x x} \frac{{s the s}_{i i + + 11} {s the s}_{i i}^{22}}{{v v}_{max max}^{33}} . .