CN103480534B - Control During Paint Spraying by Robot curve surface of workpiece formative method - Google Patents

Abstract

The invention discloses a kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, comprise the following steps: curve surface of workpiece triangulation; Set maximum normal vector threshold value; According to triangular facet connection method, triangular facet is connected into less planar chip; Set up planar chip connection layout; According to planar chip connection layout merge algorithm, each is merged into some larger planar chips newly compared with facet sheet.The present invention can be applicable to the surface modeling of various complexity spraying workpiece, especially the curve surface of workpiece moulding that Curvature varying is large is applied to, and computational speed is very fast, thus the spray robot path planning that can be below and track optimizing work ready, to meet spray robot requirements of one's work, the quality of spray robot operating efficiency and product can be improved.

Description

Control During Paint Spraying by Robot curve surface of workpiece formative method

Technical field

The present invention relates to a kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, particularly relate to the spraying curve surface of workpiece formative method used in a kind of spray robot off-line programing system.

Background technology

The structure of spray robot off-line programing system mainly comprises following six large modules: workpiece moulding module, parameter setting module, spray robot Track Pick-up module, robot motion's Track Pick-up module, analysis emulation module and robot program's generation module.In workpiece moulding module, for plane or ruled surface, can directly write out its expression formula; And for free form surface or complex-curved, then need to carry out moulding with specific process to curved surface, after moulding, in system CAD database, just house the cad data of object, for spray robot Track Pick-up module provides workpiece data information.

The moulding of spraying curve surface of workpiece is the first step of carrying out spray robot track optimizing, is also design coating robot coats path and the key optimizing spraying profile.Use a kind of suitable Applications of Surface Modeling Methods, to follow-up coating robot coats's path planning and track optimizing work particularly important.In prior art, for the spraying curve surface of workpiece formative method that can use in spray robot off-line programing system, mainly contain following three kinds: (1) is based on the formative method of parametric surface.(2) based on the Applications of Surface Modeling Methods of cad model.(3) based on the Applications of Surface Modeling Methods of workpiece scanning system.These three class methods have limitation: be not both suitable for the surface modeling that Curvature varying is larger, and the surface that not also being suitable for needs to carry out burst process is complex-curved workpiece moulding.Therefore, owing to spraying the diversity of workpiece and complexity, find complete set, practical and the Applications of Surface Modeling Methods that can be applicable on the larger spraying workpiece of surface curvature change is not an easy thing.Application number is the spray gun track planing method disclosing a kind of free curved surface spraying robot in the patent document of CN201210050434, proposes will to be directly divided into the region of several regular shape by sprayed surface in the method in 3D sculpting software.The process of this method to surface modeling is fairly simple, can only be applicable to, in the less free form surface of Curvature varying, can not be used for the spraying operation on the complex curved surface part surface with duplicate connected domain.The patent No. be propose in the patent document of ZL200810020500.6 a kind of complex-curved on optimizing method of spray coating robot spray gun track, burst after complex-curved triangulation is proposed to process in the method, but this processing mode precision is lower, the curved surface that Curvature varying is less can only be used for, and on the larger 3D solid of the normal vector angle that can not be applicable to each spray-coating surface.

In sum, owing to spraying diversity and the complexity of workpiece, the surface that is applicable to still not having a whole set of complete in prior art is complex-curved and the Applications of Surface Modeling Methods of the spraying workpiece that Curvature varying is larger.

Summary of the invention

The object of the present invention is to provide a kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, being applicable to surface is complex-curved and the surface modeling of the spraying workpiece that Curvature varying is larger.

Object of the present invention is achieved by the following technical programs:

A kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, comprises the following steps:

1) curve surface of workpiece triangulation; Be expressed as with mathematic(al) representation after curved surface carries out triangulation:

M=｛T _i:i=1,…,P｝

Wherein T _ibe i-th triangular facet in triangle gridding, P is total number in triangle gridding intermediate cam face;

2) maximum normal vector threshold value θ is set _th;

3) according to triangular facet connection method, triangular facet is connected into less planar chip; Described triangular facet connection method comprises the following steps:

(1) any one triangular facet is specified to be initial triangular facet;

(2) find with the triangular facet of initial triangular facet vicinity and be connected with initial triangular facet and be connected into a sheet;

(3) judge whether the sheet connected into meets the feature of planar chip;

The determination methods of the feature of planar chip is:

A. the method for average vector of sheet is calculated $\stackrel{\→}{n_a}=\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}/\left|\right|\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}\left|\right|$

Wherein, represent T _ithe normal vector of individual triangular facet, s _irepresent T _ithe area of individual triangular facet, P represents the quantity in this curved surface triangle division Vee formation face;

B. the normal vector of the maximum projection plane of sheet is calculated, i.e. sail angle normal vector the steps include:

Write out maximum projection plane's area expression formula of sheet order solving equation draws the normal vector of maximum projection plane

C. the method for average vector of sheet with its sail angle normal vector between angle be maximum normal vector bias angle theta _mDA,

If θ _mDA≤ θ _th, then meet the feature of planar chip, confirm to connect effectively;

If θ _mDA﹥ θ _th, then do not meet the feature of planar chip, it is invalid to connect, and abandons this connection;

(4) seek and being connected with this sheet all over all new triangular facets adjacent with this sheet, and the feature whether meeting planar chip is judged;

4) searching not yet connects triangular facet in blocks as new initial triangular facet, by described triangular facet connection method, triangular facet is connected into less planar chip, until all triangular facets all connect into planar chip;

5) planar chip connection layout is set up; Concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as a node, and with a nondirectional connection layout G=(V, E) topological structure of this curved surface is represented, then nondirectional connection layout G is the planar chip connection layout on this spraying curved surface, wherein, V represents the node in connection layout, and E represents the boundary line of the figure that this group node forms, and

(2) set the normal vector of the planar chip in planar chip connection layout represented by any i-th node vi as planar chip area is A _i, the maximum normal vector drift angle on planar chip is θ _mDAi, then can by node v _ibe expressed as

(3) e is established _ijfor node v _iwith node v _jlimit, ω (i, j) represents limit e _ijweights, the angle of the normal vector of weights and every two panels, then two sheets that normal vector angle is minimum are the limit that in planar chip connection layout, weights ω (i, j) is minimum;

Certain the planar chip connection layout demand fulfillment following characteristics set up:

A. a planar chip connection layout is a connected graph;

B. the new nondirectional connection layout obtained after any node in a planar chip connection layout merges an other node remains a planar chip connection layout;

C. merging process can only merge a node in planar chip connection layout each time;

6) according to planar chip connection layout merge algorithm, each is merged into new larger planar chip compared with facet sheet, concrete steps are:

(1) in planar chip connection layout, find two node (v that adjacent normal vector angle is minimum _i, v _j);

(2) limit e is calculated _ijweights ω (i, j), if BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, if set up, enter next step, otherwise merge stopping;

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, by this sheet v _ijbe expressed as with mathematic(al) representation:

$v_{\mathrm{ij}}=v_i\⊕v_j=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}\⊕\{\stackrel{\→}{n_{\mathrm{pj}}},A_j,{\mathrm{\θ}}_{\mathrm{MDAj}}\}=\{\frac{\stackrel{\→}{n_{\mathrm{pi}}}{A}_i+\stackrel{\→}{n_{\mathrm{pj}}}{A}_j}{A_i+A_j},A_i+A_j,{\mathrm{\θ}}_{\mathrm{MDAij}}\}$

In above formula, A _iwith A _jrepresent the area of i-th and a jth planar chip respectively, θ _mDAijrepresent new sheet v _ijmaximum normal vector drift angle;

(4) v is judged _ijwhether be planar chip, if so, enter (5) step, otherwise make BV be 2 initial θ _thto 3 θ _thbetween an artificial setting value, then proceed to (1) step;

(5) upgrade planar chip connection layout and recalculate according to (1)-(4) step;

(6) in Judge plane sheet connection layout, whether all nodes merge all, if then terminate, otherwise forward step (1) to.

Object of the present invention can also be realized further by following technical measures:

Aforementioned machines people sprays curve surface of workpiece formative method, wherein step 2) described maximum normal vector threshold value θ _thbe located between 15 ° ~ 20 °.

Compared with prior art, the invention has the beneficial effects as follows: propose a kind of based on planar chip connection layout (FlatPatchAdjacencyGraph on the basis of triangulation method, be called for short FPAG) spraying curve surface of workpiece formative method, the method can be applicable to various complex part curved surface, especially the curve surface of workpiece moulding that Curvature varying is large is applied to, and computational speed is very fast, thus the spray robot path planning that can be below and track optimizing work ready, to meet spray robot requirements of one's work, the quality of spray robot operating efficiency and product can be improved.

Accompanying drawing explanation

Fig. 1 sets up planar chip connection layout FPAG schematic diagram;

Fig. 2 is based on the planar chip merge algorithm flow chart of planar chip connection layout FPAG;

Fig. 3 is all the 3D solid of convex surface;

Fig. 4 has the 3D solid of concave surface.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

The invention process step connects into less planar chip primarily of triangular facet, sets up planar chip connection layout FPAG, merges into some larger planar chip three parts compositions newly compared with facet sheet, and detailed description of the invention is as follows:

1. triangular facet connects into less planar chip

In engineer applied software (as GID7.2) after input workpiece cad data, the triangular facet output function of software is used directly to carry out triangle division to workpiece.Curve surface of workpiece triangulation concrete steps are as follows:

1. according to the cad model of workpiece, triangulation is carried out to surface of the work;

2. obtain triangle mesh curved surface after completing with division to go to approach original surface of the work.

Can be expressed as with mathematic(al) representation after curved surface carries out triangulation:

M=｛T _i:i=1,…,P｝

Here T _ibe i-th triangular facet in triangle gridding, P is total number in triangle gridding intermediate cam face.Set maximum normal vector threshold value θ in systems in which _th, generally θ _thbetween 15 degree to 20 degree.According to triangular facet connection method, triangular facet is connected into less planar chip, concrete steps are:

(1) any one triangular facet is specified to be initial triangular facet.

(2) triangular facet that searching and initial triangular facet are close to is connected with initial triangular facet and is connected into a sheet.

(3) verify in (2) step whether the sheet connected into meets the feature of planar chip, and seek and being connected with this sheet all over all new triangular facets adjacent with this sheet.Here planar chip is defined as: curved surface carries out being connected in flakes by some adjacent triangular facets after triangulation, if this sheet is a part for curved surface and its method of average is vectorial with its sail angle normal vector between angle be less than maximum normal vector threshold value θ _th, then this sheet is claimed to be a planar chip.In this definition, the method for average vector on certain sheet computational methods are:

$\stackrel{\→}{n_a}=\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}/\left|\right|\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}\left|\right|$

Wherein, represent T _ithe normal vector of individual triangular facet, s _irepresent T _ithe area of individual triangular facet, P represents the quantity in this curved surface triangle division Vee formation face.In planar chip definition, the sail angle normal vector of planar chip refers to the normal vector of the maximum projection plane of a sheet, uses symbol represent, its calculation procedure is:

1. maximum projection plane's area expression formula of a sheet is write out

2. make $\frac{\mathrm{dS}}{d\stackrel{\→}{v_a}}=0;$

3. 2. solving equation can obtain the normal vector of maximum projection plane

If establish with the normal vector of its maximum projection plane between angle be θ _mDA, then θ is claimed _mDAfor maximum normal vector drift angle, then planar chip must have: θ _mDA≤ θ _th, what meet just can be called planar chip.

(4) searching not yet connects triangular facet in blocks as new initial triangular facet, repeats (2), (3) step, until all triangular facets all connect in flakes.

2. set up planar chip connection layout FPAG

In spraying curve surface of workpiece, all triangular facets all connect in flakes, and each first needs to set up planar chip connection layout FPAG before merging into some larger planar chips newly compared with facet sheet, and concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as a node, and with a nondirectional connection layout G=(V, E) topological structure of this curved surface is represented, then nondirectional connection layout G is the planar chip connection layout (FlatPatchAdjacencyGraph is called for short FPAG) on this spraying curved surface.Wherein, V represents the node in connection layout, and E represents the boundary line of the figure that this group node forms, and

(2) any i-th node v in planar chip connection layout FPAG is established _i, reset and with the normal vector of the planar chip represented by this node be planar chip area is A _i, the maximum normal vector bias angle theta on planar chip _mDAi, then can by node v _ibe expressed as $V_i=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}.$

(3) e is supposed _ijfor node v _iwith node v _jlimit, ω (i, j) represents limit e _ijweights (i.e. the angle of the normal vector of every two panels), then two sheets that normal vector angle is minimum are the limit that in FPAG, weights ω (i, j) is minimum.

As shown in example in accompanying drawing 1, after some curved surfaces are divided into 5 less planar chips, wherein A sheet and C sheet normal vector angle are θ, then this curved surface is converted to length ω (A, the C)=θ of FPAG back AC.Thus, as node v _iwith node v _jmerge into new sheet v _ijafter, then this sheet v _ijavailable mathematic(al) representation is expressed as:

$v_{\mathrm{ij}}=v_i\⊕v_j=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}\⊕\{\stackrel{\→}{n_{\mathrm{pj}}},A_j,{\mathrm{\θ}}_{\mathrm{MDAj}}\}=\{\frac{\stackrel{\→}{n_{\mathrm{pi}}}{A}_i+\stackrel{\→}{n_{\mathrm{pj}}}{A}_j}{A_i+A_j},A_i+A_j,{\mathrm{\θ}}_{\mathrm{MDAij}}\}$

In above formula, A _iwith A _jrepresent the area of i-th and a jth planar chip respectively, θ _mDAijrepresent the v of new sheet _ijmaximum normal vector drift angle.

Further, certain planar chip connection layout FPAG demand fulfillment following characteristics of foundation:

(1) planar chip connection layout FPAG is a connected graph;

(2) the new nondirectional connection layout obtained after any node in a planar chip connection layout FPAG merges an other node remains a FPAG;

(3) merging process can only merge a node in planar chip connection layout FPAG each time.

3. merge into some larger planar chips newly compared with facet sheet

After planar chip connection layout FPAG has set up, each can be merged into some larger planar chips newly compared with facet sheet, its flow chart as shown in Figure 2.The concrete steps that planar chip merges are:

(1) in FPAG, find two node (v that adjacent normal vector angle is minimum _i, v _j).

(2) limit e is calculated _ijweights ω (i, j), if BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, if set up, enter (3) step, otherwise merge stopping.

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, and by this sheet v _ijbe expressed as with mathematic(al) representation:

(4) v is judged _ijwhether be planar chip, if so, enter (5) step, otherwise make BV be 2 initial θ _thto 3 θ _thbetween an artificial setting value after proceed to (1) step again.

(5) upgrade FPAG and recalculate according to (1)-(4) step.

(6) judge in FPAG, whether all nodes merge all, if then terminate, otherwise forward step (1) to.

In actual industrial production, many spraying workpiece shapes all more complicated, multiple spray-coating surface can be run into and the normal vector angle of each spray-coating surface is larger when it is sprayed, such as all face is all the 3D solid of convex surface, as shown in Figure 3, the spraying curve surface of workpiece formative method based on planar chip connection layout of the present invention is used can to obtain good effect in this case.And for the 3D solid with concave surface as shown in Figure 4, because its face shaping is very complicated, and during automatic spraying, need robot to have extremely good flexibility, therefore need research further.

In addition to the implementation, the present invention can also have other embodiments, and all employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop in the protection domain of application claims.

Claims (2)

1. a Control During Paint Spraying by Robot curve surface of workpiece formative method, is characterized in that, comprises the following steps:

1) curve surface of workpiece triangulation; Be expressed as with mathematic(al) representation after curved surface carries out triangulation:

M＝{T _i:i＝1,…,P}

Wherein T _ibe i-th triangular facet in triangle gridding, P is total number in triangle gridding intermediate cam face;

2) maximum normal vector threshold value θ is set _th;

3) according to triangular facet connection method, triangular facet is connected into less planar chip; Described triangular facet connection method comprises the following steps:

(1) any one triangular facet is specified to be initial triangular facet;

(2) find with the triangular facet of initial triangular facet vicinity and be connected with initial triangular facet and be connected into a sheet;

(3) judge whether the sheet connected into meets the feature of planar chip;

The determination methods of the feature of planar chip is:

A. the method for average vector of sheet is calculated $\stackrel{\→}{n_a}=\frac{{\Σ}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\Σ}_{i=1}^p{s}_i}/\left|\right|\frac{{\Σ}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\Σ}_{i=1}^p{s}_i}\left|\right|$

Wherein, represent T _ithe normal vector of individual triangular facet, S _irepresent T _ithe area of individual triangular facet, P represents the quantity in this curved surface triangle division Vee formation face;

B. the normal vector of the maximum projection plane of sheet is calculated, i.e. sail angle normal vector the steps include:

Maximum projection plane's area expression formula of sheet order solving equation draws the normal vector of maximum projection plane

C. the method for average vector of sheet with its sail angle normal vector between angle be maximum normal vector bias angle theta _mDA,

If θ _mDA≤ θ _th, then meet the feature of planar chip, confirm to connect effectively;

If θ _mDA﹥ θ _th, then do not meet the feature of planar chip, it is invalid to connect, and abandons this connection;

(4) seek and being connected with this sheet all over all new triangular facets adjacent with this sheet, and the feature whether meeting planar chip is judged;

4) searching not yet connects triangular facet in blocks as new initial triangular facet, by described triangular facet connection method, triangular facet is connected into less planar chip, until all triangular facets all connect into planar chip;

5) set up planar chip connection layout, concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as a node, and with a nondirectional connection layout G=(V, E) topological structure of this curved surface is represented, then nondirectional connection layout G is the planar chip connection layout on this spraying curved surface, wherein, V represents the node in connection layout, and E represents the boundary line of the figure that node forms, and

(2) any i-th node v in planar chip connection layout is established _ithe normal vector of represented planar chip is planar chip area is A _i, the maximum normal vector drift angle on planar chip is θ _mDAi, then can by node v _ibe expressed as

(3) e is established _ijfor node v _iwith node v _jlimit, ω (i, j) represents limit e _ijweights, the angle of the normal vector of weights and every two panels, then two sheets that normal vector angle is minimum are the limit that in planar chip connection layout, weights ω (i, j) is minimum;

Certain the planar chip connection layout demand fulfillment following characteristics set up:

A. a planar chip connection layout is a connected graph;

B. the new nondirectional connection layout obtained after any node in a planar chip connection layout merges an other node remains a planar chip connection layout;

C. merging process can only merge a node in planar chip connection layout each time;

6) according to planar chip connection layout merge algorithm, each less planar chip is merged into new larger planar chip, concrete steps are:

(1) in planar chip connection layout, find two node (v that adjacent normal vector angle is minimum _i, v _j);

(2) limit e is calculated _ijweights ω (i, j), if BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, if set up, enter next step, otherwise merge stopping;

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, by this sheet v _ijbe expressed as with mathematic(al) representation:

In above formula, represent the normal vector of the planar chip represented by a jth node, A _iwith A _jrepresent the area of i-th and a jth planar chip respectively, θ _mDAijrepresent new sheet v _ijmaximum normal vector drift angle;

(4) v is judged _ijwhether be planar chip, if so, enter (5) step, otherwise make BV be 2 initial θ _thto 3 θ _thbetween an artificial setting value, then proceed to (1) step;

(5) upgrade planar chip connection layout and recalculate according to (1)-(4) step;

(6) in Judge plane sheet connection layout, whether all nodes merge all, if then terminate, otherwise forward step (1) to.

2. Control During Paint Spraying by Robot curve surface of workpiece formative method as claimed in claim 1, is characterized in that, described step 2) maximum normal vector threshold value θ _thbe located between 15 ° ~ 20 °.