CN103810348A - Automatic analytical algorithm for workpiece locating errors - Google Patents

Abstract

The invention provides an automatic analytical algorithm for workpiece locating errors. The automatic analytical algorithm is characterized by including the first step of searching for directed size paths starting from a locating point, passing through contact points and reaching cutter setting points according to the type of contact between a workpiece and a fixture, the second step of utilizing a contact point position tolerance mathematical model to solve a contact point position tolerance and then going to the fourth step if parameters of each vector ring in the directed size paths are known quantity, and if not, executing the third step, the third step of utilizing a closed dimension chain to solve the contact point position tolerance if unknown parametric variables exist in the vector rings in the directed size paths, and the fourth step of utilizing a locating error mathematical model to solve locating errors. The automatic analytical algorithm for the workpiece locating errors has the advantages that the calculation models and the calculation process are good in universality and strong in logicality, and the automatic analytical algorithm provides a basic theory for research and development of a practical computer-assisted fixture design system, and automation can be easily achieved.

Description

A kind of Workpiece's Tack Error automatic parsing algorithm

Technical field

The invention belongs to jig Design field, relate to a kind of Workpiece's Tack Error automatic parsing algorithm based on kinematics and oriented size path.

Background technology

Fixture Location Error is to evaluate the key index of fixture performance, and analysis of Positioning Error is a vital task in jig Design.Can clamp structure should position precision analysis and estimation after tentatively drafting, guarantee the accuracy requirement of workpiece machining surface to weigh clamp structure, thus the rationality of the judgement clamp structure of intending.But the analysis of Positioning Error method such as traditional extreme position method, the differential method, dimension chain method, has one-sidedness and limitation, or be exactly the difference along with workpiece and clamp structure, Model of locating error is different, does not have ubiquity; Be exactly extreme position, anchor point and the workpiece of anchor point, funtcional relationship of clamp structure etc., computing machine can not obtain, and is difficult to realize robotization.These problems cause Computer Aided Fixture Design (CAFD) system all seldom to relate to so far the analysis of size and tolerance.

For this reason, domestic and international many experts, scholar have poured into a large amount of painstaking effort to the analysis of positioning error, have obtained good effect.CAI etc., according to contact point this fact on surface of the work, are described as workpiece attitude the function of contacting points position, the mathematical relation of utilizing the differential method to derive between Workpiece's Tack Error and setting element alignment error.For " 3-2-1 " targeting scheme of workpiece planarization, KANG etc. utilize coordinate conversion technology, have set up the mathematical relation between Workpiece's Tack Error and setting element foozle.Liu Wenlin etc. are equal in the position vector of global coordinate system according to contact point in workpiece coordinate system, setting element coordinate system, and integrated use coordinate conversion technology and Taylor expansion principle have obtained the mapping model between Workpiece's Tack Error and setting element foozle.China of the state of Qin waits the impact of the foozle butt contact site error that has considered setting element manufacture, alignment error and workpiece locating surface, and the speed composition principle of utilization is set up the analytical model of Workpiece's Tack Error.These research work are that the universal computer model that builds Workpiece's Tack Error has been established solid foundation.But, but there is no further to discuss the acquisition methods of contacting points position error, cause Calculating Models of Location Errors poor practicability, be difficult to realize the robotization of computation process.

Wu Yu light etc. has proposed the linkage assembly model of analysis of Positioning Error, and the targeting scheme of workpiece is equivalent to three mechanisms such as finished surface and operation benchmark, operation benchmark and positioning datum, positioning datum and setting element.Attempt to obtain the relation between position and the relative dimensions of operation benchmark by linkage assembly, then utilize differential method calculation of position errors.But the method is had relatively high expectations to operating personnel's professional knowledge.

Summary of the invention

The object of this invention is to provide a kind of Workpiece's Tack Error automatic parsing algorithm, overcome existing algorithm and adopt computer automation to analyze poor practicability, shortcoming that error is large.

A kind of Workpiece's Tack Error automatic parsing algorithm, is characterized in that, comprises the steps:

(1) according to the contact type of workpiece and fixture, search out from anchor point, arrive the oriented size path of tool setting point through contact point;

In oriented size path, each vector ring, using size L and azimuth β thereof as parametric description, is designated as d=(L, β); The direction of vector ring is designated as n _l=[cos β, sin β] ^t;

If when workpiece and setting element are plane-plane contact, oriented size path is started by anchor point, arrive tool setting point and finish, and anchor point is distance contact point end points farthest on positioning datum surface, and now finite size path only comprises a vector ring

If workpiece and setting element are plane-curved surface while contacting, oriented size path is started by anchor point, after contact point, then finishes to tool setting point, now anchor point is distance contact point end points farthest on positioning datum surface, and finite size path comprises two vector rings like this

with

If when workpiece and setting element are curved surface-plane contact, oriented size path is started by anchor point, finish to tool setting point through contact point, and tool setting point is distance contact point end points farthest on setting element working surface, now finite size path comprises two vector rings again

with

If workpiece and setting element are curved surface-curved surface while contacting, oriented size path is started by anchor point, after contact point, finish to tool setting point, generally set up coordinate system take the anchor point on workpiece positioning datum as initial point, now finite size path only comprises a vector ring

(2) if the parameter of each vector ring of oriented size path is known quantity, utilize mathematical model δ r _c=| e| δ y solves contacting points position tolerance δ r _c, then proceed to step (4), otherwise execution step (3);

In mathematical model, δ y=[δ L ^t, δ β ^t] ^t, e=[n, R], wherein, $\mathrm{\δL}={[\mathrm{\δ}{L}_1^c,\mathrm{\δ}{L}_2^c,...,\mathrm{\δ}{L}_m^c]}^T$ For dimensional tolerence vector, $\mathrm{\δ\β}={[\mathrm{\δ}{\mathrm{\β}}_1^c,\mathrm{\δ}{\mathrm{\β}}_2^c,...,\mathrm{\δ}{\mathrm{\β}}_m^c]}^T$ For angle tolerance vector, $R=[R$ ${\mathrm{}}_1^c,R_2^c,...,R_m^c]$ For angle tolerance coefficient, $R_i^c={[-L_i^c\sin {\mathrm{\β}}_i^c,L_i^c\cos {\mathrm{\β}}_i^c]}^T$ (i=1,2 ..., m) be i angle tolerance coefficient.

(3), if vector ring exists unknown parameter in this oriented size path, utilize the dimension chain of sealing to solve contacting points position tolerance;

Specific algorithm flow process is as follows:

S01: connect two one of oriented size paths formations and comprise the dimension chain of unknown parameter vector ring in interior sealing;

S02: if unknown parameter number is less than 3 in this dimension chain, utilizes sciagraphy and differentiate to obtain respectively unknown parameter, and obtain matrix delta Y, E, δ y, e, P and p; Otherwise, return to step S01, reconstitute new dimension chain;

Wherein:

δ Y is the tolerance of known parameters in dimension chain, and E is its matrix of coefficients, and δ Y=[δ l ₁..., δ l _i, δ α ₁..., δ α _n] ^t, E=[n ₁..., n _i, R ₁..., R _n];

δ y is the tolerance of known parameters in oriented size path, and e is its matrix of coefficients, and δ y=[δ l _u..., δ l _s, δ α _u..., δ α _y] ^t, e=[n _u, n _v, R _u..., R _v];

P and p are respectively the matrix of coefficients of unknown parameter tolerance in dimension chain and oriented size path, and if unknown parameter be only angle, P=[R _i, R _j], p=[R _s, R _t]; If unknown parameter is only size, P=[n _i, n _j], p=[n _s, n _t]; If unknown parameter contains angle and size, P=[n _i, R _j], p=[n _s, R _t];

S03: if in dimension chain or its oriented size path comprising, have known parameters and unknown parameter to have identical tolerance, the tolerance step S02 being obtained and matrix of coefficients carry out the duplicate removal processing of zero-suppressing; Otherwise proceed to step S04;

S04: utilize schedule method to obtain the transition matrix H of δ y to δ Y conversion;

S05: utilize mathematical model δ r _c=| eH-pPE| δ Y obtains the position of related features of contact point;

(4) utilize positioning error mathematical model to solve positioning error;

In above-mentioned positioning error automatic parsing algorithm design cycle, described positioning error mathematical model is set up according to the speed composition principle of particle movement, and mathematical model is J δ q _w=-N δ r, wherein

for the positioning error of workpiece,

and

(c=1,2 ..., k).

Computation model involved in the present invention and process versatility are good, logicality is strong, easily are automated, for practical Computer Aided Fixture Design System is researched and developed the theory that provides the foundation.

Accompanying drawing explanation

Fig. 1 is the bicylindrical targeting scheme instance graph of algorithm disk cover parts end face machining hole of the present invention;

Fig. 2 is the oriented size path profile going out by algorithm search rule searching of the present invention;

Fig. 3 is the oriented size path profile going out by algorithm search rule searching of the present invention;

Fig. 4 is first the dimension link going out by algorithm search of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail:

Fig. 1 is the bicylindrical targeting scheme of disk cover parts end face machining hole, diameter of work

two positioning cylinder diameters are respectively

with

centre distance is

be symmetric deviations form φ D=69.989 ± 0.011 by each Size Conversion, φ d ₁=49.9905 ± 0.0095, φ d ₂behind=49.9905 ± 0.0095, B=63.336 ± 0.0095, Workpiece's Tack Error to resolve process as follows.

Referring to Fig. 1, the implementation process of this algorithm is as follows:

Step 1: search oriented size path

In bicylindrical targeting scheme, there are two oriented size paths, respectively by (R, α ₁), (r ₁, α ₁) and (R, α ₂), (r ₂, α ₂) composition, as shown in Figure 2.

Step 2: selected Article 1 finite size path

Article 1, it is angle [alpha] that oriented size path exists unknown parameter ₁, need utilize dimension chain to solve contacting points position error.

Step 3: search for first dimension chain

Connect the 1st article of oriented size path and the 2nd article of finite size path, form the dimension chain (Fig. 3) of a sealing.Like this, in the oriented size of dimension chain and Article 1 path each parameter as table (1,2) shown in.

Parameter, tolerance and the coefficient thereof of table 1 dimension chain

Parameter and the coefficient thereof in the oriented size of table 2 Article 1 path

Then the processing of zero-suppressing of parameter duplicate removal is carried out in dimension chain and oriented size path, guarantee the independence of parameter, after duplicate removal, each parameter is shown in table (3,4).Due to known θ ₃=0, there is θ in dimension chain ₁, θ ₂two unknown parameters.Like this, the known parameters tolerance of dimension chain is δ Y ₂=[δ R, δ r ₁, δ B, δ r ₂, δ θ ₃] ^t, the matrix of coefficients of known parameters tolerance is $E_2=\left[\begin{array}{cccccc}\cos {\mathrm{\θ}}_1& +\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_3& \cos {\mathrm{\θ}}_2& -B\sin {\mathrm{\θ}}_3\\ \sin {\mathrm{\θ}}_1& +\sin {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_3& \sin {\mathrm{\θ}}_2& B\cos {\mathrm{\θ}}_3\end{array}\right];$ And in the 1st article of oriented size path, known parameters tolerance and matrix of coefficients thereof are δ y ₂=[δ R, δ r ₁] ^t, $e_2=\left[\begin{array}{cc}\cos {\mathrm{\θ}}_1& \cos {\mathrm{\θ}}_1\\ \sin {\mathrm{\θ}}_1& \sin {\mathrm{\θ}}_1\end{array}\right];$ The matrix of coefficients of unknown parameter tolerance in dimension chain $P_2=\left[\begin{array}{cc}-(R+r_1)\sin {\mathrm{\θ}}_1& -(R+r_2\sin {\mathrm{\θ}}_2)\\ (R+r_1)\cos {\mathrm{\θ}}_1& (R+r_2)\cos {\mathrm{\θ}}_2\end{array}\right],$ The matrix of coefficients of oriented size path unknown parameter tolerance $p_2=\left[\begin{array}{cc}-(R+r_1)\sin {\mathrm{\θ}}_1& 0\\ (R+r_1)\cos {\mathrm{\θ}}_1& 0\end{array}\right].$

Table 3 is looked into the dimension chain parameter after weighing

Table 4 is looked into the Article 1 path parameter after weighing

Again according to δ y after duplicate removal ₂with δ Y ₂in the relation of each element, as shown in table 5, easily determine δ y ₂to δ Y ₂the transition matrix H of conversion ₂, $H_2=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\\ 0& 1& 0& 0& 0\end{array}\right].$

Obtaining of table 5 transition matrix

H2	δR	δr1	δB	δr2	δθ3
						δR	1	0	0	0	0
δr1	0	1	0	0	0

Finally, obtain θ 1=238.1413 °, θ 2=121.8569 ° according to sciagraphy and derived function; According to formula δ r _c=| the site error that eH-pP|E δ Y can be calculated contact point in the oriented size of Article 1 path is δ r1=[0.01375,0.01502] and T.

Step 4: selected next finite size path

It is angle [alpha] that the oriented size of Article 2 path exists unknown parameter ₂, still need to solve contacting points position error by dimension chain.

Step 5: search for next dimension chain

Article 1, oriented size path and the 2nd article of finite size path can only form the dimension chain of a sealing, therefore this dimension chain and parameter thereof are all identical with first dimension chain.Equally, the parameter after the duplicate removal of the oriented size of Article 2 path is as shown in table 1.

Table 6 is looked into the Article 2 path parameter after weighing

From table (1), in the 2nd article of oriented size path, known parameters tolerance and matrix of coefficients thereof are respectively δ y ₂=[δ R, δ r ₂] ^t, $e_2=\left[\begin{array}{cc}\cos {\mathrm{\θ}}_2& \cos {\mathrm{\θ}}_2\\ \sin {\mathrm{\θ}}_2& \sin {\mathrm{\θ}}_2\end{array}\right];$ The matrix of coefficients of unknown parameter tolerance in dimension chain $P_2=\left[\begin{array}{cc}-(R+r_1)\sin {\mathrm{\θ}}_1& -(R+r_2)\sin {\mathrm{\θ}}_2\\ (R+r_1)\cos {\mathrm{\θ}}_1& (R+r_2)\cos {\mathrm{\θ}}_2\end{array}\right],$ The matrix of coefficients of oriented size path unknown parameter tolerance $p_2=\left[\begin{array}{cc}0& -(R+r_2)\sin {\mathrm{\θ}}_2\\ 0& (R+r_2)\cos {\mathrm{\θ}}_2\end{array}\right].$

Subsequently according to δ y after duplicate removal ₂with δ Y ₂in the relation of each element, as shown in table 7, easily determine δ y ₂to δ Y ₂the transition matrix of conversion.

Obtaining of table 7 transition matrix

H 2	δR	δr 1	δB	δr 2	δθ 3
						δR	1	0	0	0	0
δr 2	0	0	0	1	0

Finally, the site error that can be calculated contact point in the oriented size of Article 2 path is δ r ₂=[0.01375,0.01502] ^t.

Step 6: calculation of position errors

The site error of contact point is $\mathrm{\δr}={[\mathrm{\δ}{r}_1^T,\mathrm{\δ}{r}_2^T]}^T.$ Due to $J=\left[\begin{array}{ccc}0.5279& 0.8493& 0\\ -0.5279& 0.8493& 0\end{array}\right],$ $N=\left[\begin{array}{cc}-0.5279& 0\\ -0.8493& 0\\ 0& 0.5279\\ 0& -0.8493\end{array}\right],$ According to J δ q _w=-N δ r can be calculated positioning error and is ${\mathrm{\δq}}_w=\left[\begin{array}{c}0.01375\\ 0.0150\\ 0\end{array}\right].$

Above content is in conjunction with concrete preferred implementation further description made for the present invention, can not assert that specific embodiment of the invention is confined to these explanations.For general technical staff of the technical field of the invention; make without departing from the inventive concept of the premise some alternative or obvious modification that are equal to; and performance or purposes identical, should be considered as belonging to the definite protection domain of claims that the present invention submits to.

Claims (1)

1. a Workpiece's Tack Error automatic parsing algorithm, is characterized in that, comprises the steps:

(1) according to the contact type of workpiece and fixture, search out from anchor point, arrive the oriented size path of tool setting point through contact point;

In oriented size path, each vector ring, using size L and azimuth β thereof as parametric description, is designated as d=(L, β); The direction of vector ring is designated as n _l=[cos β, sin β] ^t;

If when workpiece and setting element are plane-plane contact, oriented size path is started by anchor point, arrive tool setting point and finish, and anchor point is distance contact point end points farthest on positioning datum surface, and now finite size path only comprises a vector ring

If workpiece and setting element are plane-curved surface while contacting, oriented size path is started by anchor point, after contact point, then finishes to tool setting point, now anchor point is distance contact point end points farthest on positioning datum surface, and finite size path comprises two vector rings like this

with

If when workpiece and setting element are curved surface-plane contact, oriented size path is started by anchor point, finish to tool setting point through contact point, and tool setting point is distance contact point end points farthest on setting element working surface, now finite size path comprises two vector rings again

with

If workpiece and setting element are curved surface-curved surface while contacting, oriented size path is started by anchor point, after contact point, finish to tool setting point, generally set up coordinate system take the anchor point on workpiece positioning datum as initial point, now finite size path only comprises a vector ring

(2) if the parameter of each vector ring of oriented size path is known quantity, utilize mathematical model δ r _c=| e| δ y solves contacting points position tolerance δ r _c, then proceed to step (4), otherwise execution step (3);

In mathematical model, δ y=[δ L ^t, δ β ^t] ^t, e=[n, R], wherein,

for dimensional tolerence vector, $\mathrm{\δ\β}={[\mathrm{\δ}{\mathrm{\β}}_1^c,\mathrm{\δ}{\mathrm{\β}}_2^c,...,\mathrm{\δ}{\mathrm{\β}}_m^c]}^T$ For angle tolerance vector, $R$ $=[R_1^c,R_2^c,...,R_m^c]$ For angle tolerance coefficient, $R_i^c={[-L_i^c\sin {\mathrm{\β}}_i^c,L_i^c\cos {\mathrm{\β}}_i^s]}^T$ (i=1,2 ..., m) be i angle tolerance coefficient.

(3), if vector ring exists unknown parameter in this oriented size path, utilize the dimension chain of sealing to solve contacting points position tolerance;

Specific algorithm flow process is as follows:

S01: connect two one of oriented size paths formations and comprise the dimension chain of unknown parameter vector ring in interior sealing;

S02: if unknown parameter number is less than 3 in this dimension chain, utilizes sciagraphy and differentiate to obtain respectively unknown parameter, and obtain matrix delta Y, E, δ y, e, P and p; Otherwise, return to step S01, reconstitute new dimension chain;

Wherein: δ Y is the tolerance of known parameters in dimension chain, E is its matrix of coefficients, and δ Y=[δ l ₁..., δ l _i, δ α ₁..., δ α _n] ^t, E=[n ₁..., n _i, R ₁..., R _n];

δ y is the tolerance of known parameters in oriented size path, and e is its matrix of coefficients, and δ y=[δ l _u..., δ l _s, δ α _u..., δ α _y] ^t, e=[n _u, n _v, R _u..., R _v];

P and p are respectively the matrix of coefficients of unknown parameter tolerance in dimension chain and oriented size path, and if unknown parameter be only angle, P=[R _i, R _j], p=[R _s, R _t]; If unknown parameter is only size, P=[n _i, n _j], p=[n _s, n _t]; If unknown parameter contains angle and size, P=[n _i, R _j], p=[n _s, R _t];

S03: if in dimension chain or its oriented size path comprising, have known parameters and unknown parameter to have identical tolerance, the tolerance step S02 being obtained and matrix of coefficients carry out the duplicate removal processing of zero-suppressing; Otherwise proceed to step S04;

S04: utilize schedule method to obtain the transition matrix H of δ y to δ Y conversion;

S05: utilize mathematical model δ r _c=| eH-pPE| δ Y obtains the position of related features of contact point;

(4) utilize positioning error mathematical model to solve positioning error.

Images