CN100354868C - Layout planing method for positioning unit of precise clamp - Google Patents

Abstract

A precision fixture positioning element layout planning method, according to the manufacturing task to select the feature points and direction vectors on the workpiece to define the positioning error measurement index, and deduce the positioning error control index as the objective function of the optimal design, the discretized workpiece reference plane The obtained dense data point cloud is used as the fixture location element candidate set, and the initial location element solution set is an empty set, and the floating search method is used to select a point from the location element candidate set to add to the location element solution set, and conditionally delete the existing The selected disadvantages are circulated in this way until six positioning element points are screened out, so as to plan the best positioning element layout. The positioning error measurement index in the present invention has a geometric meaning related to the manufacturing task, and it and the positioning error control index induced by it have nothing to do with the selection of the reference coordinate system. The present invention can reduce the Accuracy requirements for fixture positioning elements and workpiece reference planes, thus saving manufacturing costs.

Description

Layout Planning Method of Positioning Elements for Precision Fixtures

technical field

The invention relates to a precision fixture positioning element layout planning method, which can be used for precision fixture design in manufacturing engineering and belongs to the technical field of mechanical manufacturing.

Background technique

In the manufacturing process, the fixture plays the role of positioning and supporting the workpiece. Correctly designing the fixture according to the precision requirements of the workpiece is one of the key factors to ensure product quality. The fixture is composed of two parts, the positioning element and the clamping element. The positioning accuracy of the fixture is determined by the manufacturing and assembly accuracy of the positioning element, the manufacturing accuracy of the workpiece reference surface, and the spatial layout of the positioning element. The first two are related to the manufacturing Technology and equipment are related, and improving manufacturing accuracy often leads to a sharp increase in manufacturing costs, and the positioning accuracy can also be effectively improved by rationally planning the spatial layout of positioning elements, so this work has attracted widespread attention in the industry in recent years. The optimal placement of localization elements involves three aspects of work: (1) localization error metric, (2) optimization objective function, and (3) optimization algorithm, where the optimization objective function is derived from the localization error metric. At present, the positioning error measurement index is usually taken as the Euclidean norm of the motion screw, and a series of optimization objective functions have been developed, but this definition has the following disadvantages: (1) It involves the addition of values of different dimensions (2) It is not related to the manufacturing task and has no physical meaning; (3) It is related to the specific machine tool coordinate system and workpiece coordinate system, and has no coordinate transformation invariance. The existing optimization schemes can be divided into two categories, one is to use continuous surfaces to describe the datum plane, express the optimal layout problem of positioning elements as a constrained optimization problem, and then apply conventional nonlinear programming methods to solve it; the other is to use The datum plane is described by the data point cloud, and the optimal layout problem of positioning elements is expressed as a combinatorial optimization problem, and then heuristic algorithm is applied to solve it. The former has a large amount of calculation, and it is not easy to deal with additional geometric constraints and the transition between surfaces; the displacement algorithm in the latter has too much calculation, and the incremental algorithm does not have the ability to backtrack.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the prior art, and propose a new method for layout planning of fixture positioning elements to reduce the manufacturing and assembly errors of positioning elements, and the influence of manufacturing errors on workpiece reference planes on subsequent manufacturing tasks. Under the premise of reducing the precision requirements, the precision requirements for the fixture positioning element and the workpiece datum surface are reduced, thereby saving manufacturing costs.

The technical solution of the present invention: first, according to the manufacturing task, select a group of feature points and a group of direction vectors on the workpiece to define the positioning error measurement index, and deduce the positioning error control index as the objective function of the optimal design. The dense data point cloud obtained by discretizing the workpiece reference plane is used as the candidate set of fixture positioning elements, and the initial positioning element solution set is an empty set, and then the floating search method is used to select one point from the positioning element candidate set to add to the positioning element solution set , and conditionally delete the selected disadvantages, and so on until six positioning element points are selected, so that the optimal design objective function value reaches a minimum, and thus the best positioning element layout is planned.

The inventive method mainly comprises following two steps:

1. Define the positioning error measurement index and derive the positioning error control index: first, select a set of feature points and a set of direction vectors on the workpiece according to the manufacturing task, and define two positioning error measurement indexes e ₁ and e ₂ . e ₁ represents the sum of the squares of the deviation of the key point on the workpiece from the ideal position due to the positioning error, and e ₂ represents the sum of the squares of the projection of the deviation of the key point on the workpiece from the ideal position due to the positioning error in a given direction . Then the positioning error control index e _c is deduced according to the positioning error measurement index, which is used as the objective function of the optimal layout of the fixture positioning element.

2. Positioning element optimization layout: use the dense data point cloud obtained from the discretized workpiece reference plane as the fixture positioning element candidate set, and make the initial positioning element solution set an empty set, and then use the fixture positioning element optimal layout algorithm to find the six most Excellent positioning element. The optimal layout algorithm of fixture positioning elements is composed of two parts: "supplementing positioning elements" and "conditionally deleting positioning elements". In the process of "supplementing positioning element points", a point is selected from the positioning element candidate set to be added into the positioning element solution set each time, so that the value of the positioning error control objective function decreases the fastest after adding this point; in the "conditional deletion of positioning element In the process of "point", select a point from the solution set of positioning elements each time, so that the value of the positioning error control objective function rises the slowest after deleting the point. If the value of the positioning error control objective function is smaller than the previously obtained If the target function value corresponding to the meta-solution set is found, delete the point from the positioning meta-solution set, and continue to execute "conditionally delete positioning meta-points", otherwise execute "additional positioning meta-points". Repeat the above two steps of "supplementation" and "deletion" until the positioning element solution set contains six elements, that is, six positioning element points are screened out, so that the value of the positioning error control objective function is minimized, and the optimal Good positioning meta layout.

The positioning error measurement indexes _e1 and _e2 in the present invention have geometric meanings related to the manufacturing task, and have nothing to do with the selection of the reference coordinate system, and the positioning error control index _e induced by them has nothing to do with the selection of the reference coordinate system , the positioning element layout planning algorithm based on index e _c has the advantages of simple form and high calculation efficiency. The optimal positioning element layout obtained by the method of the present invention can reduce the manufacturing and assembly errors of the positioning element, reduce the influence of the manufacturing error of the workpiece reference plane on the subsequent manufacturing tasks, and reduce the positioning of the fixture on the premise of meeting the manufacturing accuracy requirements of the workpiece. The accuracy requirements of the element and workpiece reference plane, thus saving manufacturing costs. The invention is especially suitable for fixture design in precision machining, assembly and measurement.

Detailed ways

In order to better understand the technical solution of the present invention, the implementation steps of the precision fixture positioning element layout planning method are described in detail below.

(1) Define the positioning error measurement index and derive the positioning error control objective function: due to the influence of manufacturing errors, the actual pose of the workpiece fixed by the fixture will deviate from the ideal pose, and this deviation can be calculated by the differential motion vector ξ relative to the workpiece coordinate system =[v ^T , ω ^T ] ^T ∈ R ⁶ , where v ∈ R ³ and ω ∈ R ³ are differential translation and differential rotation vectors, respectively. Select a set of feature points on the workpiece according to the manufacturing task $\{{\mathrm{the\; s}}_i={[{\mathrm{the\; s}}_i^1,{\mathrm{the\; s}}_i^2,{\mathrm{the\; s}}_i^3]}^T\∈R^3,i=1,...,\mathrm{no}\},$ And determine a set of direction vectors {m _i ∈ R ³ , i=1,...,n}, define two positioning error metrics:

e ₁ =ξ ^T M ₁ ξ

e ₂ =ξ ^T M ₂ ξ

in $m_1=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left[\begin{array}{c}I\\ {\widehat{\mathrm{the\; s}}}_i\end{array}\right]\left[\begin{array}{cc}I& {-\widehat{\mathrm{the\; s}}}_i\end{array}\right],$ $m_2=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left[\begin{array}{c}I\\ {\widehat{\mathrm{the\; s}}}_i\end{array}\right]m_i{m_i}^T\left[\begin{array}{cc}I& -{\widehat{\mathrm{the\; s}}}_i\end{array}\right],$ ${\widehat{\mathrm{the\; s}}}_i=\left[\begin{array}{ccc}0,& -{\mathrm{the\; s}}_i^3,& {\mathrm{the\; s}}_i^2\\ {\mathrm{the\; s}}_i^3,& 0& -{\mathrm{the\; s}}_i^1\\ -{\mathrm{the\; s}}_i^2,& {\mathrm{the\; s}}_i^1& 0\end{array}\right].$

e ₁ represents the sum of the squares of the deviation of the key point on the workpiece from the ideal position due to the positioning error, and e ₂ represents the sum of the squares of the projection of the deviation of the key point on the workpiece from the ideal position due to the positioning error in a given direction , which have nothing to do with the selection of the reference coordinate system.

Assuming that the i-th positioning element of the fixture is in contact with the workpiece surface q _i under ideal conditions, record n ^qi as the unit external normal vector of the workpiece surface at q _i point, let $l_i={[{\left({\mathrm{no}}^{q_i}\right)}^T,{(q_i\×{\mathrm{no}}^{q_i})}^T]}^T,$ L=[I ₁ ,..., _In ] ^T , select M=M ₁ or M ₂ according to the requirements of the manufacturing task, and define the following positioning error control objective function:

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span>$

where _λXi ^represents the ith eigenvalue of matrix X. e _c quantitatively describes the manufacturing and assembly errors of the fixture positioning element, and the influence of the manufacturing error of the workpiece reference surface on the positioning error measurement index e ₁ or e ₂ (depending on whether M is taken as M ₁ or M ₂ ), the smaller the value The better, it also has nothing to do with the choice of reference coordinate system.

(2) Optimal layout of positioning elements: use dense discrete data point cloud H={h _i ∈ R ³ , 1≤i≤N} to represent the workpiece reference plane, and reduce the layout planning problem of fixture positioning elements to six points selected from H For the combinatorial optimization problem that makes the corresponding e _c value extremely small, the optimal position of the six positioning elements is determined by applying the following fixture positioning element optimization layout algorithm:

Input: positioning element candidate set H={h _i R ³ , 1≤i≤N}, positioning error control objective function e _c

Output: positioning element solution set P _k = {p _i ∈ H, 1≤i≤k}, k=1,...,6

Initialization: P ₀ =_, k = 0

Termination condition: k=6

Step 1 (Supplementary positioning element):

${\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \backslash </span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; min</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; )</span>$

P _k+1 = P _k ∪{p ⁺ }, k=k+1

Step 2 (Conditionally delete the positioning element point):

${\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \backslash </span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; )</span>$

If e _c (P _k \{p ^- })＜e _c (P _k-1 )then

P _k-1 ＝P _k \{p ^- }，k＝k-1

go to step 2

otherwise

go to step 1

Note: When calculating e _c value, replace L ^T L with L ^T L + εI, ε is a very small positive real number, usually 10 ^-6 .

Claims (1)

1, a kind of layout planing method for positioning unit of precise clamp is characterized in that comprising the steps:

1) definition positioning error metric and derive the positioning error controlling index: at first select a group of feature point on the workpiece and a prescription to vector, define two positioning error metric e according to manufacturing operation ₁And e ₂, e ₁Expression is because the key point on the workpiece that positioning error causes departs from the quadratic sum of the deviation of ideal position, e ₂Expression is derived positioning error controlling index e according to the positioning error metric then because the key point on the workpiece that positioning error causes departs from the quadratic sum of the projection of deviation on assigned direction of ideal position _c, as the first objective function of optimizing distribution in anchor clamps location; e _cExpression formula be

$e_c=\underset{1\&le;i\&le;6}{\max }\left\{{\mathrm{\&lambda;}}_{M{\left(L^{T}L\right)}^{-1}}^i\right\}$

Sign of lambda wherein _X ⁱI the eigenwert of representing matrix X;

Matrix L=[I ₁..., I ₆] ^T, wherein $I_i={[{\left(n^{q_i}\right)}^T,{(q_i\&times;n^{q_i})}^T]}^T,$ q _iThe contact point of i location unit of expression surface of the work and anchor clamps, n ^QiExpression surface of the work q _iMethod is vowed outside the unit at some place; Matrix M is taken as M according to the requirement of manufacturing operation ₁Or M ₂

$M_1=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\left[\begin{array}{c}I\\ {\hat{s}}_i\end{array}\right]\left[\begin{array}{cc}I& -{\hat{s}}_i\end{array}\right],$

$M_2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\left[\begin{array}{c}I\\ {\hat{s}}_i\end{array}\right]m_i{m}_i^T\left[\begin{array}{cc}I& -{\hat{s}}_i\end{array}\right],$

Wherein ${\hat{s}}_i=\left[\begin{array}{ccc}0,& -s_i^3,& s_i^2\\ s_i^3,& 0& -s_i^1\\ -s_i^2,& s_i^1& 0\end{array}\right],$

Be one group on the workpiece

Unique point,

For a corresponding prescription to vector;

2) location unit optimizes distribution: the density data point cloud that discretize workpiece reference field obtains is located first Candidate Set as anchor clamps, and make that to locate first disaggregation when initial be empty set, adopt the optimize distribution location unit of six optimums of algorithm searching of anchor clamps location unit then; The anchor clamps location unit algorithm of optimizing distribution partly is made up of " augmenting the first point in location " and " have ready conditions and delete the first point in location " two, in " augmenting the first point in location " process, from locate first Candidate Set, select a bit to augment at every turn location unit separate concentrated, make increase this point afterwards positioning error control target function value descend the most soon; In " have ready conditions and delete the first point in location " process, separate concentrated the selection a bit from locating unit at every turn, making it to satisfy this some back positioning error control target function value of deletion rises the most slowly, if this moment, positioning error control target function value was less than the identical pairing target function value of location unit's disaggregation of the radix that obtains before, then should separate concentrated deletion from locating unit by point, and continue to carry out " have ready conditions and delete the first point in location ", otherwise carry out " augmenting the first point in location "; Repeat above-mentioned " augmenting " and " deleting " two steps, until location unit separate concentrate comprise six elements till, promptly filter out six first points in location, make positioning error control target function value reach minimum, cook up best location unit layout thus.