CN112241584A - A Setting Method of Boundary Constraint Distance Value for Boundary Constraint Spraying Trajectory Planning - Google Patents

A Setting Method of Boundary Constraint Distance Value for Boundary Constraint Spraying Trajectory Planning Download PDF

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CN112241584A
CN112241584A CN202010890859.XA CN202010890859A CN112241584A CN 112241584 A CN112241584 A CN 112241584A CN 202010890859 A CN202010890859 A CN 202010890859A CN 112241584 A CN112241584 A CN 112241584A
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曾勇
于永庆
赵雪雅
刘毅
刘德志
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Yancheng Institute of Technology
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Abstract

本发明公开一种边界约束喷涂轨迹规划边界约束距离值的设定方法。该方法包括以下步骤：基于建立的喷枪变位姿静态喷涂模型，构建喷枪沿圆弧路径的动态喷涂模型；以工件边界处满足允许的最低涂膜厚度为要求，对边界约束距离进行定义，并分别阐明边界曲线的曲率半径、喷涂高度和喷涂倾角对边界约束距离的影响规律；根据待喷涂工件表面的边界曲线形状，设定统一边界约束距离值，以确保边界处的涂膜厚度质量处处都满足要求。本发明可在离线编程规划边界约束喷涂轨迹时，快速设定边界约束距离值，再通过对待喷涂工件表面规划边界约束喷涂轨迹，并对喷涂过程中的喷涂速率、喷涂高度和倾角进行优化，可实现喷涂质量、喷涂效率和涂料利用率的同时提升。

Figure 202010890859

The invention discloses a method for setting the boundary constraint distance value of boundary constraint spraying trajectory planning. The method includes the following steps: constructing a dynamic spraying model of the spraying gun along the arc path based on the static spraying model of the established spraying gun; The influence of the radius of curvature of the boundary curve, the spraying height and the spraying inclination on the boundary constraint distance are respectively clarified; according to the shape of the boundary curve of the surface of the workpiece to be sprayed, a uniform boundary constraint distance value is set to ensure that the coating film thickness and quality at the boundary are everywhere. fulfil requirements. The invention can quickly set the boundary constraint distance value when planning the boundary constraint spraying trajectory in offline programming, and then plan the boundary constraint spraying trajectory on the surface of the workpiece to be sprayed, and optimize the spraying rate, spraying height and inclination angle during the spraying process. Achieve simultaneous improvement in spray quality, spray efficiency and paint utilization.

Figure 202010890859

Description

Method for setting boundary constraint distance value of boundary constraint spraying track planning
Technical Field
The invention discloses a method for setting a boundary constraint distance value of a boundary constraint spraying track planning, particularly relates to an off-line programming spraying track planning of a spraying robot, and belongs to the technical field of automatic control.
Background
The off-line programming method of the spraying robot has the advantages of short programming period, capability of planning complex spraying tracks and the like, and is increasingly applied to robot spraying track planning in the fields of automobiles, ships, aerospace and the like. The spraying path planning result in the off-line programming system is a key factor for determining the spraying effect, the spraying efficiency and the paint utilization rate, and has important significance for production.
The traditional spray path planning method only pursues to meet the spray quality once, and often neglects the boundary constraint of the workpiece surface when pursuing to plan the spray path, so that the phenomenon of overspray at the workpiece boundary is serious, a large amount of paint is wasted when a spray gun sprays at the workpiece boundary, and the spray efficiency is not high. And the key point of planning the boundary constraint spraying path is to reasonably set a boundary constraint distance value according to the shape of the boundary curve of the surface of the workpiece so as to ensure that the thickness of a coating film at the boundary meets the quality requirement.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for setting a boundary constraint distance value for planning a boundary constraint spraying track, which is used for ensuring that the film thickness of the generated boundary constraint spraying track at the boundary meets the quality requirement, firstly establishing a dynamic spraying model of a spray gun along a curve path, then clarifying the influence rule of the curve shape of the boundary, the pose (spraying height and spraying inclination angle) of the spray gun on the boundary constraint distance according to the quality requirement of the film thickness, realizing the prediction of the value range of the boundary constraint distance, and finally setting the uniform value of the boundary constraint distance according to the curve shape of the surface boundary of a workpiece and taking the film thickness quality at the boundary as the requirement.
A setting method of a boundary constraint distance value of a boundary constraint spraying track planning comprises the following steps:
step 1, constructing a dynamic spraying model of a spray gun along an arc path based on an established static spraying model of the spray gun with a variable pose, wherein the space shape of a spraying torch of the spray gun is a cone;
step 2, defining a boundary constraint distance by taking the minimum allowable coating thickness at the boundary of the workpiece as a requirement, and respectively clarifying the influence rules of the curvature radius, the spraying height and the spraying inclination angle of a boundary curve on the boundary constraint distance;
and 3, setting a unified boundary constraint distance value according to the shape of the boundary curve of the surface of the workpiece to be sprayed so as to ensure that the coating thickness quality at the boundary meets the requirements everywhere.
As an improvement, in step 1, based on the established static spraying model of the spray gun with the position changed, a dynamic spraying model of the spray gun along an arc path is established, and the specific steps are as follows:
101. based on a parabolic model with a space shape of a spray torch as a cone, the parabolic model is expressed as:
Figure RE-GDA0002825338550000021
assuming that the spray gun is spraying the coating material flow qvAnd the conical opening angle phi of the spray gun is unchanged, the position and posture of the spray gun relative to the spraying surface are considered as controllable parameters, the position and posture are the spraying height H and the spraying inclination angle alpha, and after the static spraying of the position and posture change of the spray gun on the plane, a paint deposition model of any point (x, y) in the spraying amplitude range can be expressed as
Figure RE-GDA0002825338550000022
Wherein A is a constant;
when the spray gun sprays at a static inclination angle, the spray width formed on the plane is in an ellipse, wherein the major axis a and the minor axis b of the ellipse are respectively as follows:
Figure RE-GDA0002825338550000023
Figure RE-GDA0002825338550000024
wherein, a1(H,α),a2(H, α) are respectively:
Figure RE-GDA0002825338550000025
Figure RE-GDA0002825338550000026
102. when the spray gun dynamically sprays along the track of the circular arc path, the radius of the circular arc path is set as r, the curvature center of the circular arc is set as O', the speed direction of the spray gun is the tangential direction of the circular arc path, the dynamic spraying speed of the spray gun on the track of the circular arc path is set as v, and the spraying speed at any point S in the spraying range is set as vsThe radius of curvature of the arc on which the point S is located is rSEstablishing 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 RE-GDA0002825338550000027
The arc length of a point S swept by the spray gun in the spray amplitude range is represented, the spraying speed of the spray gun in the tangential direction on the same arc is unchanged, and if the spray gun is fixed, the spraying process can be regarded as uniform-speed circular motion of any point S around an O' point in the elliptical spray amplitude range, so that the time of the any point S passing through the elliptical spray amplitude range is
Figure RE-GDA0002825338550000028
By integrating the formula (1), a film thickness model of any point S in the spray amplitude range after the spray gun dynamically sprays along the circular arc path track is established as follows:
Figure RE-GDA0002825338550000029
in the formula (6), the spraying rate at any point S and the coordinate value of the y axis where the spraying rate is located are respectively:
Figure RE-GDA0002825338550000031
Figure RE-GDA0002825338550000032
arc length of point S swept by the lance
Figure RE-GDA0002825338550000033
Comprises the following steps:
Figure RE-GDA0002825338550000034
r in formulae (7), (8) and (9)s、
Figure RE-GDA0002825338550000035
And p are each:
rS＝r-x (10)
Figure RE-GDA0002825338550000036
Figure RE-GDA0002825338550000037
q and j in formula (12) are respectively:
Figure RE-GDA0002825338550000038
Figure RE-GDA0002825338550000039
by substituting formula (8) for formula (6), a model of the coating film thickness at any point S in the spray width range can be obtained.
The improvement is that in the step 2, the boundary constraint distance is defined by taking the minimum allowable coating thickness at the workpiece boundary as a requirement, and the influence rules of the curvature radius of the boundary curve, the spraying height and the spraying inclination angle on the boundary constraint distance are respectively clarified, and the method comprises the following steps:
201. assuming that the target value of the thickness of the coating film is TdObtaining a coordinate value X of the X axis on which the peak value of the thickness of the coating film is located by deriving X in the formula (6)0Specifically, the following are shown:
Figure RE-GDA00028253385500000310
according to the formula (15), the spraying speed v, the spraying inclination angle alpha and the spraying height H meet a specific functional relationship, and if one parameter is known, the other two parameters can be obtained by solving the equation set;
202. the boundary constraint spraying path is generated by retracting a certain boundary constraint distance value towards the inner part of the surface of the workpiece based on a workpiece boundary curve, the boundary curve is larger than the spraying path in curvature radius by a boundary constraint distance value, and the reasonable setting of the value directly influences whether the coating thickness quality at the boundary meets the requirement or not;
the requirement of the thickness of a coating film at any point on the surface of a workpiece is set to meet TS∈[Tmin,Tmax]For this purpose, the spray path point at the boundary is defined here in the direction of the radius of curvature of the boundary curve to just meet the minimum film thickness (T)min) The distance between the boundaries is required to be boundary constraint distance, and the boundary constraint distance is divided into left and right parts according to the position relation of the boundary constraint distance relative to the spraying path, and the left and right parts are respectively d1And d2The value of which is influenced by the pose of the lance and the radius of curvature of the boundary curve, based on the numerical valueSimulating, namely clarifying the influence rule by adopting an orthogonal experiment method; according to the orthogonal experiment principle, two of H, r and alpha parameters are respectively fixed, the third parameter is used as an independent variable, the boundary constraint distance is used as a function, the influence rules of the position and the curvature radius of the spray gun and the spray path on the boundary constraint distance are respectively analyzed, and the spray path at the boundary is generated by contracting a boundary constraint distance in a boundary curve, so that the influence of the curvature radius of the spray path on the boundary constraint distance is equal to the influence of the boundary curve on the boundary constraint distance.
Has the advantages that:
compared with the prior art, the method has the following technical effects:
the invention can rapidly set a reasonable boundary constraint distance value when planning the boundary constraint spraying track in an off-line programming way so as to achieve the purpose of ensuring that the thickness of a coating film at the boundary meets the quality requirement.
Drawings
FIG. 1 is a space model of a torch and a paint deposition model, (a) a space model of a torch, (b) a paint deposition model;
FIG. 2 is a trajectory of a spray gun for dynamic spray along a circular arc path trajectory;
FIG. 3 is a graph showing the influence of the pose of the spray gun and the radius of curvature of the spray trajectory on the boundary constraint distance, where (a) is the spray inclination angle, (b) is the spray height, and (c) is the radius of curvature of the spray trajectory;
FIG. 4 is a graph showing the variation of the boundary constraint distance with the curvature radius of the boundary curve, where (a) is d1Is (b) is d2A change in (c);
FIG. 5 is a graph showing the variation of the boundary constraint distance with the spray inclination angle, where (a) is d1Is (b) is d2A change in (c);
FIG. 6 is a graph showing the variation of the boundary constraint distance with the height of the sprayed material, where (a) is d1Is (b) is d2A change in (c);
FIG. 7 is a graph showing the change rule of boundary constraint distance with spraying height and inclination angle under different boundary curve curvature radii.
Detailed Description
A setting method of a boundary constraint distance value of a boundary constraint spraying track planning comprises the following steps:
step 1, constructing a dynamic spraying model of a spray gun along an arc path based on an established static spraying model of the spray gun with a variable pose, wherein the space shape of a spraying torch of the spray gun is a cone;
step 2, defining a boundary constraint distance by taking the minimum allowable coating thickness at the boundary of the workpiece as a requirement, and respectively clarifying the influence rules of the curvature radius of the boundary curve, the spraying height and the spraying inclination angle on the boundary constraint distance;
and 3, setting a unified boundary constraint distance value according to the shape of the boundary curve of the surface of the workpiece to be sprayed so as to ensure that each point of the coating thickness quality at the boundary meets the requirement.
And (2) constructing a dynamic spraying model of the spray gun along the arc path based on the established static spraying model of the spray gun with the posture changing in the step 1, and specifically comprising the following steps:
101. based on a parabolic model with a spray torch space shape as a cone, the parabolic model is as follows:
Figure RE-GDA0002825338550000051
assuming that the spray gun is spraying the coating material flow qvAnd the conical opening angle phi of the spray gun is unchanged, the pose of the spray gun relative to the spraying surface is considered as a controllable parameter, the pose is the spraying height H and the spraying inclination angle alpha, and as shown in figure 1(a), after the static spraying of the spray gun with the changed pose on a plane, the paint deposition model of any point (x, y) in the spraying width range can be represented as follows:
Figure RE-GDA0002825338550000052
where a is a constant (the value of a is different for spray guns with different flow rates, and a is a fixed value for a certain spray gun with a fixed flow rate), and the paint deposition model is shown in fig. 1 (b).
When the spray gun sprays at a static inclination angle, the spray width formed on the plane is in an ellipse, wherein the major axis a and the minor axis b of the ellipse are respectively as follows:
Figure RE-GDA0002825338550000053
Figure RE-GDA0002825338550000054
wherein, a1(H,α),a2(H, α) are respectively:
Figure RE-GDA0002825338550000055
Figure RE-GDA0002825338550000056
102. in fig. 2, let the radius of the circular arc path be r, the center of curvature of the circular arc be O', when the spray gun is dynamically spraying along the circular arc path trajectory, the speed direction of the spray gun is the tangential direction of the circular arc path, the dynamic spraying speed of the spray gun on the circular arc path trajectory is v, and the spraying speed at any point S in the spray width range is vsThe radius of curvature of the arc on which the point S is located is rSEstablishing 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 RE-GDA0002825338550000061
Indicating the arc length swept by the lance at point S over the range of the spray pattern.
When the spray gun is used for dynamically spraying along the path track of the circular arc, the spraying speed of the spray gun in the tangential direction on the same circular arc is constant, so that the spray gun is assumed to be fixed, and the spraying process can be regarded as uniform-speed circular motion of any point S around the point O' in the elliptical spraying range, so that any point S can be freely movedThe time when the intention point S passes through the elliptical spray amplitude range is
Figure RE-GDA0002825338550000062
By integrating the formula (1), after the spray gun is established to dynamically spray along the circular arc path track, the film thickness model of any point S in the spray amplitude range is as follows:
Figure RE-GDA0002825338550000063
in the formula (6), the spraying rate at any point S and the coordinate value of the y axis where the spraying rate is located are respectively:
Figure RE-GDA0002825338550000064
Figure RE-GDA0002825338550000065
arc length of point S swept by the lance
Figure RE-GDA0002825338550000066
Comprises the following steps:
Figure RE-GDA0002825338550000067
r in formulae (7), (8) and (9)s、
Figure RE-GDA0002825338550000068
And p are each:
rS＝r-x (10)
Figure RE-GDA0002825338550000069
Figure RE-GDA00028253385500000610
q and j in formula (12) are respectively:
Figure RE-GDA00028253385500000611
Figure RE-GDA00028253385500000612
the formula (8) is substituted into the formula (6), and a specific expression of the coating thickness of any point S in the spray width range can be obtained.
The static dip spraying mentioned above means that the spray gun forms a certain dip angle with a plane and then is statically sprayed relative to the plane, and the dynamic spraying along the arc means that the spray gun moves relative to the surface.
In step 2, defining the boundary constraint distance by taking the minimum allowable coating thickness at the boundary of the workpiece as a requirement, and respectively clarifying the influence rules of the curvature radius of the boundary curve, the spraying height and the spraying inclination angle on the boundary constraint distance, wherein the method comprises the following steps:
201. assuming that the target value of the thickness of the coating film is TdObtaining a coordinate value X of the X axis on which the peak value of the thickness of the coating film is located by deriving X in the formula (6)0Specifically, the following are shown:
Figure RE-GDA0002825338550000071
according to the formula (15), the spraying speed v, the spraying inclination angle alpha and the spraying height H meet a specific functional relationship, and if one parameter is known, the other two parameters can be obtained by solving the equation set;
202. the boundary constraint spraying path is generated based on a certain boundary constraint distance value of a workpiece boundary curve inwards shrinking towards the inner part of the surface of the workpiece, the boundary curve is larger than the spraying path in curvature radius by a boundary constraint distance value, and the reasonable setting of the value directly influences whether the coating thickness quality at the boundary meets the requirement or not.
The requirement of the thickness of a coating film at any point on the surface of a workpiece is set to meet TS∈[Tmin,Tmax]For this purpose, in the direction of the radius of curvature of the boundary curve, the point of the spray path at the boundary is defined so as to just meet the minimum film thickness (T)min) The distance between the boundaries is required to be boundary constraint distance, and the boundary constraint distance is divided into left and right parts according to the position relation of the boundary constraint distance relative to the spraying path, and the left and right parts are respectively made to be d1And d2The value of the curve is influenced by the pose of the spray gun and the curvature radius of the boundary curve, and the influence rule is clarified by adopting an orthogonal experiment method based on numerical simulation as shown in figure 3.
At a target coating film thickness TdTaking the cone opening angle phi of the spray gun spray torch as an example of 28 degrees, different coating film thickness distribution states can be obtained by respectively taking different parameter values of H, alpha and r to substitute in the formula (15) in the variable ranges of the position and posture parameters of the spray gun H and alpha (the variable ranges are related to the spray gun), and boundary constraint distance values under different coating film thickness distribution states are measured according to the definition of the boundary constraint distance.
According to the orthogonal experiment principle, respectively fixing H, r and two of three parameters alpha, respectively analyzing the influence rules of the pose of the spray gun and the curvature radius of the spraying path on the boundary constraint distance by taking the third parameter as an independent variable and the boundary constraint distance as a function, wherein the spraying path at the boundary is generated by contracting the boundary constraint distance in a boundary curve, and the curvature radius of the boundary curve is set as rdSatisfy rdTherefore, the influence of the curvature radius of the boundary curve on the boundary constraint distance can be obtained by analyzing the influence rule of the curvature radius of the spraying track on the boundary constraint distance.
Fig. 4, 5 and 6 show the influence rule curves of the curvature radius of the boundary curve, the spraying inclination angle and the spraying height on the boundary constraint distance respectively.
As can be seen from fig. 4, 5 and 6, under the premise that the posture of the lance is fixed, the boundary constraint distance is in a power function change relationship with the curvature radius of the boundary curve as a whole, wherein when the curvature radius of the boundary curve is greater than 400mm, the boundary constraint distance is in an almost linear change relationship with the curvature radius of the boundary curve. On the premise that the spraying height and the curvature radius of the boundary curve are fixed and unchanged, the boundary constraint distance is in a linear change relation with the spraying inclination angle. On the premise that the spraying inclination angle and the curvature radius of the boundary curve are fixed and unchanged, the boundary constraint distance is in a linear change relation with the spraying height.
According to fig. 4, 5 and 6, the rule of influence of the pose of the spray gun on the boundary constraint distance under different boundary curve curvature radii can be clarified, as shown in fig. 7, so that the minimum value and the maximum value of the boundary constraint distance at any curvature radius boundary on an irregular plane can be predicted within the variable range of the pose of the spray gun, and are respectively set as di minAnd di maxBoundary constraint distance value of
Figure RE-GDA0002825338550000081
diWhen the value is taken in the range, the coating thickness effect meeting the spraying quality requirement can be obtained at the boundary by optimizing the position and posture of the spray gun in the range of the position and posture variable of the spray gun.
For any irregular plane, the boundary curve can be approximately regarded as the combination of a plurality of straight line segments and circular arc segments, and the analysis shows that if the boundary curve has N boundary segments with different curvature radiuses, under the premise that the posture of the spray gun is fixed, N boundary constraint distance values theoretically exist, and in order to generate a smooth and continuous spraying path at the boundary, a uniform boundary constraint distance value can be obtained at the boundary.
In order to ensure that the thickness of the coating film at any position of the boundary can meet the quality requirement, on the basis of obtaining the value range of the boundary constraint distance values of all the boundary segments, the minimum value is taken as a uniform boundary constraint distance value, as shown in the following formula:
Figure RE-GDA0002825338550000082
in the direction of curvature radius of the boundary curve, the boundary curve of the patch is uniformly biased to be bound to the inside of the patchDistance d0And obtaining a boundary constraint range closed curve for generating a boundary constraint spraying path, thereby finally finishing the setting of the boundary constraint distance value.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited thereto, and any simple modifications or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention are within the scope of the present invention.

Claims (4)

1.一种边界约束喷涂轨迹规划边界约束距离值的设定方法，其特征在于，包括以下步骤：1. a setting method of boundary constraint spraying trajectory planning boundary constraint distance value, is characterized in that, comprises the following steps: 步骤1，基于建立的喷枪变位姿静态喷涂模型，构建喷枪沿圆弧路径的动态喷涂模型，所述喷枪的喷炬空间形状为圆锥体；Step 1, based on the established static spraying model of the spray gun with variable pose, build a dynamic spraying model of the spray gun along the arc path, and the spray torch space shape of the spray gun is a cone; 步骤2，以工件边界处满足允许的最低涂膜厚度为要求，对边界约束距离进行定义，并分别阐明边界曲线的曲率半径、喷涂高度和喷涂倾角对边界约束距离的影响规律；Step 2: The boundary constraint distance is defined based on the requirement of the minimum allowable coating film thickness at the workpiece boundary, and the influence of the curvature radius of the boundary curve, the spraying height and the spraying inclination on the boundary constraint distance is clarified respectively; 步骤3，根据待喷涂工件表面的边界曲线形状，设定统一边界约束距离值，以确保边界处的涂膜厚度质量处处都满足要求。Step 3, according to the boundary curve shape of the surface of the workpiece to be sprayed, set a uniform boundary constraint distance value to ensure that the thickness and quality of the coating film at the boundary meet the requirements everywhere. 2.根据权利要求1所述的一种边界约束喷涂轨迹规划边界约束距离值的设定方法，其特征在于，步骤1中基于建立的喷枪变位姿静态喷涂模型，构建喷枪沿圆弧路径的动态喷涂模型，具体步骤如下：2. the setting method of a kind of boundary constraint spraying trajectory planning boundary constraint distance value according to claim 1, it is characterized in that, in step 1, based on the spray gun change posture static spray model of establishing, build spray gun along the arc path. Dynamic spray model, the specific steps are as follows: 101、基于一种喷炬空间形状为圆锥体的抛物线模型，所述抛物线模型表示为：
Figure FDA0002656945380000011
假设喷枪喷涂时涂料流量qv和喷炬圆锥张角φ不变，考虑喷枪相对于喷涂表面的位姿为可控参数，所述位姿为喷涂高度H和喷涂倾角α，喷枪在平面上变位姿静态喷涂后，在喷幅范围内任意点(x,y)的涂料沉积模型可表示为101. Based on a parabolic model in which the spatial shape of the torch is a cone, the parabolic model is expressed as:
Figure FDA0002656945380000011
Assuming that the paint flow q v and the torch cone opening angle φ remain unchanged when the spray gun is spraying, the pose of the spray gun relative to the spraying surface is considered as a controllable parameter, and the pose is the spraying height H and the spraying inclination α. After static spraying in pose, the paint deposition model at any point (x, y) within the spray width can be expressed as
Figure FDA0002656945380000012
Figure FDA0002656945380000012
 其中，A为常量；Among them, A is a constant; 当喷枪以静态倾角喷涂时，在平面上形成的喷幅形状为椭圆，其中椭圆的长轴a和短轴b分别为：When the spray gun sprays at a static inclination angle, the shape of the spray pattern formed on the plane is an ellipse, where the major axis a and the minor axis b of the ellipse are:
Figure FDA0002656945380000013
Figure FDA0002656945380000013
Figure FDA0002656945380000014
Figure FDA0002656945380000014
 其中，a1(H,α),a2(H,α)分别为：Among them, a 1 (H,α), a 2 (H,α) are:
Figure FDA0002656945380000015
Figure FDA0002656945380000015
Figure FDA0002656945380000016
Figure FDA0002656945380000016
 102、当喷枪沿圆弧路径轨迹动态喷涂时，设圆弧路径半径为r，圆弧的曲率中心为O′，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rS，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 FDA0002656945380000021
表示喷幅范围内点S被喷枪扫掠过的弧长，在同一段圆弧上喷枪在切线方向的喷涂速率是不变的，假设喷枪固定不动，喷涂过程可看作是椭圆形喷幅范围内任意点S绕O′点做的匀速圆周运动，因此任意点S通过椭圆形喷幅范围的时间为
Figure FDA0002656945380000022
通过对公式(1)进行积分，建立喷枪沿圆弧路径轨迹动态喷涂后喷幅范围内任意点S的涂膜厚度模型为102. When the spray gun is dynamically spraying along the arc path, set the radius of the arc path as r, the center of curvature of the arc as O', the speed direction of the spray gun as the tangent direction of the arc path, and the dynamics of the spray gun on the arc path. The spraying rate is v, the spraying rate at any point S within the spray width is v s , and the radius of curvature of the arc where the point S is located is r S . Cartesian coordinate system, where
Figure FDA0002656945380000021
Indicates the arc length swept by the spray gun at the point S within the spray width range. On the same arc, the spray rate of the spray gun in the tangential direction is constant. Assuming that the spray gun is fixed, the spraying process can be regarded as an elliptical spray pattern. The uniform circular motion of any point S in the range around the point O', so the time for any point S to pass through the elliptical spray width is
Figure FDA0002656945380000022
By integrating the formula (1), the film thickness model of any point S within the spray width range after the spray gun is dynamically sprayed along the arc path trajectory is established as follows:
Figure FDA0002656945380000023
Figure FDA0002656945380000023
 式(6)中，任意点S上的喷涂速率及其所在y轴坐标值分别为：In formula (6), the spraying rate at any point S and its y-axis coordinate value are:
Figure FDA0002656945380000024
Figure FDA0002656945380000024
Figure FDA0002656945380000025
Figure FDA0002656945380000025
 点S被喷枪扫掠过的弧长
Figure FDA0002656945380000026
为：The arc length of point S swept by the gun
Figure FDA0002656945380000026
for:
Figure FDA0002656945380000027
Figure FDA0002656945380000027
 式(7)、(8)和(9)中的rs、
Figure FDA0002656945380000028
和p分别为： rs in formulas (7), (8) and (9),
Figure FDA0002656945380000028
and p are: rS＝r-x (10)r S = rx (10)
Figure FDA0002656945380000029
Figure FDA0002656945380000029
Figure FDA00026569453800000210
Figure FDA00026569453800000210
 式(12)中的q和j分别为：q and j in formula (12) are respectively:
Figure FDA00026569453800000211
Figure FDA00026569453800000211
Figure FDA0002656945380000031
Figure FDA0002656945380000031
 将式(8)代入式(6)中，即可得到喷幅范围内任意点S的涂膜厚度的模型。Substituting Equation (8) into Equation (6), the model of the coating film thickness at any point S within the spray width range can be obtained. 3.根据权利要求1所述的一种边界约束喷涂轨迹规划边界约束距离值的设定方法，其特征在于，步骤2中以工件边界处满足允许的最低涂膜厚度为要求，对边界约束距离进行定义，并分别阐明边界曲线曲率半径、喷涂高度和喷涂倾角对边界约束距离的影响规律，包括如下步骤：3. the setting method of a kind of boundary constraint spraying trajectory planning boundary constraint distance value according to claim 1, it is characterized in that, in step 2, with workpiece boundary place meeting the minimum coating thickness that is allowed as a requirement, to boundary constraint distance Define and clarify the influence law of boundary curve curvature radius, spraying height and spraying inclination on boundary constraint distance, including the following steps: 201、设涂膜厚度目标值为Td，通过对式(6)中的x进行求导，获得涂膜厚度峰值所在X轴的坐标值x0，具体表示如下：201. Set the target value of the coating film thickness as T d , and obtain the coordinate value x 0 of the X-axis where the peak value of the coating film thickness is located by derivation of x in the formula (6), which is specifically expressed as follows:
Figure FDA0002656945380000032
Figure FDA0002656945380000032
 由公式(15)可知，喷涂速率v、喷涂倾角α和喷涂高度H满足特定函数关系，若已知其中一个参数，通过求解上述方程组即可求得其余两个参数；It can be seen from formula (15) that the spraying rate v, the spraying inclination angle α and the spraying height H satisfy a specific functional relationship. If one of the parameters is known, the remaining two parameters can be obtained by solving the above equations; 202、边界约束喷涂路径是基于工件边界曲线向工件表面内部内缩一定的边界约束距离值生成的，边界曲线比喷涂路径在曲率半径上大一个边界约束距离的值，其值的合理设定直接影响到边界处的涂膜厚度质量是否满足要求；202. The boundary constraint spraying path is generated based on the workpiece boundary curve shrinking a certain boundary constraint distance value to the inside of the workpiece surface. The boundary curve is larger than the spray path on the curvature radius by a value of the boundary constraint distance, and the reasonable setting of its value is directly Whether the thickness and quality of the coating film affecting the boundary meet the requirements; 设工件表面上任意一点的涂膜厚度要求满足TS∈[Tmin,Tmax]，在边界曲线曲率半径方向上，这里定义边界处喷涂路径点到刚好满足最小涂膜厚度(Tmin)要求的边界间的距离为边界约束距离，根据边界约束距离相对于喷涂路径的位置关系，其值受到喷枪位姿和边界曲线曲率半径的影响，采用正交实验法阐明其影响规律；根据正交实验原理，分别固定H、r和α三个参数中的两个，以第三个参数为自变量，边界约束距离为函数，分别分析喷枪位姿和喷涂路径曲率半径对边界约束距离的影响规律，喷涂路径曲率半径对边界约束距离的影响等同于边界曲线对边界约束距离的影响。Assume that the thickness of the coating film at any point on the workpiece surface meets T S ∈ [T min ,T max ], and in the direction of the curvature radius of the boundary curve, the spray path point at the boundary is defined to just meet the minimum coating film thickness (T min ) requirements The distance between the boundaries is the boundary constraint distance. According to the positional relationship between the boundary constraint distance and the spraying path, its value is affected by the spray gun pose and the curvature radius of the boundary curve. The orthogonal experiment method is used to clarify its influence law; according to the orthogonal experiment In principle, two of the three parameters H, r and α are fixed respectively, and the third parameter is used as the independent variable, and the boundary constraint distance is used as a function to analyze the influence of the spray gun pose and the radius of curvature of the spray path on the boundary constraint distance, respectively. The effect of the radius of curvature of the spray path on the boundary constraint distance is the same as the effect of the boundary curve on the boundary constraint distance. 4.根据权利要求3所述的一种边界约束喷涂轨迹规划边界约束距离值的设定方法，其特征在于，步骤202中所述的边界约束距离有左、右之分，分别令其为d1和d2。4. the setting method of a kind of boundary restraint spraying trajectory planning boundary restraint distance value according to claim 3, is characterized in that, the boundary restraint distance described in step 202 has the points of left and right, let it be respectively d 1 and d 2 .
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