CN102508979A - Optional layout robust design and optimization method for two-dimensional assembly fixture - Google Patents

Abstract

The invention discloses an optional layout robust design and optimization method for a two-dimensional assembly fixture. The optional layout robust design and optimization method comprises the following steps of: (1) establishing an optional layout and location deviation model of a two-dimensional part assembly fixture a fixture locating parameter of which has influence on a part deviation; (2) solving the part deviation model in the step (1) to obtain an optional layout robust design model of the two-dimensional part assembly fixture with a minimum mean square error of part deviation as a target; and (3) analyzing the robust design model in the step (2), and carrying out single parameter optimization and multiple-parameter comprehensive optimization of fixture layout and fixture location by using an analysis method and a genetic algorithm respectively. According to the invention, a universal two-dimensional part assembly scheme for optional layout and location of the fixture is adopted; and through the optional layout robust design and optimization of the fixture, transmission, coupling and accumulation of deviation sources are reduced, the part assembly deviation is decreased and the assembly quality of a product is improved.

Description

Two dimension assembling jig arbitrary placement's based Robust Design and optimization method

Technical field

The present invention relates to a kind of two-dimentional assembling jig layout based Robust Design and optimization method.

Background technology

In the multiple operation assembling process, the part that is assembled generally adopts N-2-1 (N >=3) Fixture Layout to locate the limit feature skew.How to carry out the N-2-1 Fixture Layout and effectively design, propagate in deviation farthest reduced in size source, and the robustness that improves product assembly quality is the problem that advanced manufacture process field demands urgently studying.Through the prior art searching document is found; To Fixture Layout research aspect; W.Cai has shown " N-2-1 " positioning principle that " Deformable SheetMetal Fixturing:Principles, Algorithms, and Simulations " proposed the thin plate location in " Journal of Manufacturing Scienceand Engineering " (manufacturing science and engineering magazine) 118 curly hair in 1996; Based on " N-2-1 " positioning principle; Utilization finite element analysis and Nonlinear Programming Method are minimised as target with workpiece deformation, and Fixture Layout is optimized; W.Cai " InternationalJournal of Advanced Manufacturing Technology " (advanced manufacturing technology international magazine) 28 curly hair in 2006 shown " Robust pin layout design for sheet-panel locating " utilization analytical method to the thin plate assembling process in Fixture Layout carried out based Robust Design, make the assembling deviation minimum of critical product or technology characteristics point.But above research about Fixture Layout all limits the pose of anchor clamps register pin, and promptly the four-way register pin is parallel with the X axle to the line at register pin center with two, and this does not always conform to actual assembled condition.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides a kind of transmission, coupling and accumulation that can reduce the deviation source, the part assembling deviation be can reduce, and then the two-dimentional assembling jig arbitrary placement's based Robust Design and the optimization method of the assembly quality of product improved.

The technical scheme that the present invention solves above-mentioned technical matters is: a kind of two-dimentional assembling jig arbitrary placement's based Robust Design and optimization method may further comprise the steps:

1) sets up the part two dimension assembling jig arbitrary placement deviations model of anchor clamps positional parameter to the part effects;

2) solution procedure 1) described in part buggy model, obtain the part two dimension assembling jig arbitrary placement based Robust Design model that mean square deviation with the part deviation is minimised as target;

3) analytical procedure 2) described in the based Robust Design model, utilization analytical method and genetic algorithm are carried out single parameter optimization and a plurality of parametric synthesis optimization that Fixture Layout and anchor clamps are located respectively.

Further; The concrete grammar of setting up part two dimension assembling jig arbitrary placement deviations model in the described step 1) does; According to the Fixture Layout principle, analyze the anchor clamps positional parameter to the part effects, be reference frame with the three coordinate measuring machine coordinate system; Comprise four-way register pin coordinate, two to the register pin coordinate, two to location cotter way slope, two to the layout location slope of four-way register pin line, wherein the anchor clamps positional parameter has six.

Further; Described step 2) concrete grammar that makes up part two dimension assembling jig arbitrary placement based Robust Design model in does; The given anchor clamps positional parameter deviation source vector that satisfies normal distribution; Mean square deviation with the part deviation is minimised as target; Making up part two dimension assembling jig arbitrary placement based Robust Design model, is reference frame with the three coordinate measuring machine coordinate system, and wherein the mean square deviation of part deviation comprises the part deviation mean square deviation of part deviation mean square deviation, X and Z compound direction of part deviation mean square deviation, the corner φ of part deviation mean square deviation, the Z direction of directions X.

Further; The concrete grammar of parameter optimization does in the described step 3); Analyze in the said based Robust Design model influence degree of six parametric variables to part assembling deviation robustness; Obtain the variable that single parameter optimization and a plurality of parametric synthesis are optimized, wherein the variable of single parameter optimization is two to location cotter way slope, the variable of a plurality of parameter optimizations be two to register pin coordinate and two to register pin flute length axle slope.

Owing to adopt technique scheme; The invention has the beneficial effects as follows: the present invention adopts the part two dimension assembling scheme of the anchor clamps arbitrary placement location that has more versatility; Transmission, coupling and the accumulation in deviation source have been reduced through anchor clamps arbitrary placement based Robust Design and optimization; Reduce the part assembling deviation, improved the assembly quality of product.

Description of drawings

Fig. 1 is the process flow diagram of the present invention's two dimension assembling jig arbitrary placement's based Robust Design and optimization method.

Fig. 2 is the part two dimension assembling reference coordinate synoptic diagram of the arbitrarily angled Fixture Layout of the present invention location.

Fig. 3 is wheel cover inner panel Fixture Layout figure among the embodiment.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is done further detailed explanation.

As shown in Figure 1, a kind of two-dimentional assembling jig arbitrary placement's based Robust Design and optimization method may further comprise the steps:

1) sets up the part two dimension assembling jig arbitrary placement deviations model of anchor clamps positional parameter to the part effects;

2) solution procedure 1) described in part buggy model, obtain the part two dimension assembling jig arbitrary placement based Robust Design model that mean square deviation with the part deviation is minimised as target;

3) analytical procedure 2) described in the based Robust Design model, utilization analytical method and genetic algorithm are carried out single parameter optimization and a plurality of parametric synthesis optimization that Fixture Layout and anchor clamps are located respectively.

Particularly, said step (1) comprising:

Shown in accompanying drawing 2, for part two dimension assembling jig arbitrary placement, set up the coordinate system O-XYZ that invests part, definition anchor point section equation is following:

L ₁Anchor point section equation F ₁:

ax+bz+c＝0 (1)

L ₂Anchor point section equation F ₂:

y-z ²＝0 (2)

L ₃Anchor point section equation F ₃:

x-x ₂＝0 (3)

By formula (1)-Shi (3), must locate Jacobian matrix and be:

$J=\left[\begin{array}{ccc}-a& -b& {\mathrm{bx}}_1-{\mathrm{az}}_1\\ 0& -1& x_2\\ -1& 0& -z_2\end{array}\right]---\left(4\right)$

Then

|J|＝b(x ₂-x ₁)-a(z ₂-z ₁) (5)

And

$\left\{\begin{array}{c}{x}_1\&NotEqual;x_2,{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\&NotEqual;z_2\\ b(x_2-x_1)\&NotEqual;a(z_2-z_1)\end{array}\right.---\left(6\right)$

Adjoint matrix J then ^*For:

$J^{*}=\left[\begin{array}{ccc}{z}_2& -{\mathrm{bz}}_2& b(x_2-x_1)-{\mathrm{az}}_1\\ x_2& {\mathrm{bx}}_1-a(z_1-z_2)& {\mathrm{ax}}_2\\ -1& b& a\end{array}\right]---\left(7\right)$

Composite type (4) and formula (7) can get:

$J^{-1}=\frac{J^{*}}{\left|J\right|}=\frac{\left[\begin{array}{ccc}{z}_2& -{\mathrm{bz}}_2& b(x_2-x_1)-{\mathrm{az}}_1\\ x_2& {\mathrm{bx}}_1-a(z_1-z_2)& {\mathrm{ax}}_2\\ -1& b& a\end{array}\right]}{b(x_2-x_1)-a(z_2-z_1)}---\left(8\right)$

And

${\mathrm{\&Phi;}}_R=\left[\begin{array}{cccccc}a& \mathrm{<figure-callout\; id="0"\; label="b"\; filenames="111119094705.png"\; state="\{\{state\}\}">b</figure-callout>}& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\end{array}\right]---\left(9\right)$

Order

$\left\{\begin{array}{c}\tan \mathrm{\&alpha;}=-\frac{a}{b}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\\ \tan \mathrm{\&beta;}=\frac{z_2-z_1}{x_2-x_1}=k_2\end{array}\right.---\left(10\right)$

In the formula, k ₁Be two to location cotter way slope, k ₂Four-way register pin and two abbreviates layout location slope as to register pin line of centres slope.

According to formula (8), (9) and formula (10), part bias vector δ q ₀Can be expressed as

Particularly, step (2) comprising:

Suppose contact anchor point deviation δ x ₁, δ z ₁, δ x ₂, δ z ₂, δ x ₃, δ z ₃Equal Normal Distribution

Then part X axis, Z axially and corner φ to two-dimentional assembling jig arbitrary placement based Robust Design model do

minσ(q ₀)

s.t.0≤|x _i-x _j|≤B

0≤|z _i-z _j|≤H i，j＝1，2，3

(12)

In the formula, σ (q ₀) expression deviation q ₀Mean square deviation, B, H are part overall dimensions (like length and width etc.).

Part at the two-dimentional assembling jig arbitrary placement based Robust Design model of X axle and Z axle compound direction is:

min?σ _∑(q ₀)

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}\left(q_0\right)=\frac{\sqrt{{\mathrm{\&sigma;}}^2\left({\mathrm{\&delta;x}}_0\right)+{\mathrm{\&sigma;}}^2\left({\mathrm{\&delta;z}}_0\right)}}{\sqrt{2}}$

$=\frac{{\mathrm{\&sigma;}}_0}{\left|(x_2-x_1)(1+k_1{k}_2)\right|}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2(x_2^2+z_1^2-z_1{z}_2+z_2^2)+(z_2^2+x_1^2-x_1{x}_2+x_2^2)}$

s.t.0≤|x _i-x _j|≤B

0≤|z _i-z _j|≤H i，j＝1，2，3 (13)

In the formula, σ _∑(q ₀) expression X axle and Z axle compound direction deviation q ₀Mean square deviation, B, H meaning are the same.

To above-mentioned based Robust Design modular form (12) and formula (13), can do following analysis

(1) works as x ₂-x ₁=0, z ₂-z ₁=0 is x ₂=x ₁, z ₂=z ₁The time, promptly one of them disconnected take off or lost efficacy in two register pins, at this moment, and the part assembling deviation fluctuation maximum that causes because of register pin, i.e. σ (δ x ₀), σ (δ z ₀),

And σ _∑(q ₀) all trending towards infinity, the part assembling is least sane.This also is consistent with the practical set situation.

(2) work as 1+k ₁k ₂=0, promptly The time, promptly the four-way register pin is vertical each other with part locating slot major axis to the line of centres of register pin with two, σ (δ x ₀), σ (δ z ₀),

And σ _∑(q ₀) all being tending towards infinitely great, the part assembling deviation fluctuation that the expression register pin causes is maximum, i.e. and part assembling is also least sane, makes every effort to avoid this kind situation when this requires practical set.

(3) work as k ₁→ ∞, promptly the part locating slot is vertically arranged, can try to achieve σ (δ x by formula (12) and formula (13) so ₀), σ (δ y ₀),

And σ _∑(q ₀) be respectively:

$\mathrm{\&sigma;}\left(q_0\right)=\left[\begin{array}{c}\mathrm{\&sigma;}\left(\mathrm{\&delta;}{x}_0\right)\\ \mathrm{\&sigma;}\left({\mathrm{\&delta;z}}_0\right)\\ \mathrm{\&sigma;}\left(\mathrm{\&delta;}{\mathrm{\&phi;}}_0\right)\end{array}\right]=\left[\begin{array}{c}\frac{\sqrt{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+z_2^2}}{\left|k_2(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0\\ \frac{\sqrt{{2x}_2^2+{(z_1-z_2)}^2}}{\left|k_2(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0\\ \frac{\sqrt{2}{\mathrm{\&sigma;}}_0}{\left|k_2(x_2-x_1)\right|}\end{array}\right]---\left(14\right)$

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}\left(q_0\right)=\frac{\sqrt{x_2^2+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2-z_1{z}_2+z_2^2}}{\left|k_2(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0---\left(15\right)$

(4) work as k ₁=0, promptly part locating slot horizontal arrangement can get σ (δ x by formula (12) and formula (13) so equally ₀), σ (δ z ₀),

And σ _∑(q ₀) be respectively:

$\mathrm{\&sigma;}\left(q_0\right)=\left[\begin{array}{c}\mathrm{\&sigma;}\left({\mathrm{\&delta;x}}_0\right)\\ \mathrm{\&sigma;}\left(\mathrm{\&delta;}{z}_0\right)\\ \mathrm{\&sigma;}\left({\mathrm{\&delta;\&phi;}}_0\right)\end{array}\right]=\left[\begin{array}{c}\frac{\sqrt{{(x_1-x_2)}^2+{2z}_2^2}}{|x_2-x_1|}{\mathrm{\&sigma;}}_0\\ \frac{\sqrt{x_1^2+x_2^2}}{|x_2-x_1|}{\mathrm{\&sigma;}}_0\\ \frac{\sqrt{2}{\mathrm{\&sigma;}}_0}{|x_2-x_1|}\end{array}\right]---\left(16\right)$

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}\left(q_0\right)=\frac{\sqrt{z_2^2+x_1^2-x_1{x}_2+x_2^2}}{\left|(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0$

Particularly, step (3) comprising:

Can be known by formula (12) and formula (13), comprise six parametric variables in the based Robust Design model, the parameter optimization of this model can be divided into single parameter optimization and a plurality of parametric synthesis optimization.Can be known that by the front model analysis two is one of most important factor that influences part assembling deviation robustness to location cotter way slope, therefore, this paper chooses this location cotter way slope and carries out single parameter robust optimized.

(1) location cotter way slope one-parameter based Robust Design is optimized

Work as k ₁During for other arbitrary values, make the part assembling deviation fluctuation that causes by the register pin deviation minimum, must find the solution the part feature point so respectively at directions X, the lowest mean square difference of the deviation of Y direction, corner direction and X and Y compound direction, i.e. σ (δ x ₀) _Min, σ (δ z ₀) _Min,

And σ _∑(q ₀) _Min

(1) find the solution since the part that causes of register pin deviation at the Minimum Mean Square Error σ of x direction assembling deviation (δ x ₀) _Min, can get by formula (12)

$\mathrm{\&sigma;}\left({\mathrm{\&delta;x}}_0\right)=\frac{{\mathrm{\&sigma;}}_0}{\left|(x_2-x_1)(1+k_1{k}_2)\right|}\sqrt{{(x_2-x_1)}^2+({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2+2)z_2^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}---\left(17\right)$

By following two kinds of situation to following formula (17) differentiate:

1) as (x ₂-x ₁) (1+k ₁k ₂)＞0 o'clock,

$\frac{\mathrm{d\&sigma;}\left(\mathrm{\&delta;}{x}_0\right)}{\mathrm{<figure-callout\; id="1"\; label="d\; k"\; filenames="111119094705.png"\; state="\{\{state\}\}">d</figure-callout>}{k}_{}{}_1}=\frac{{\mathrm{\&sigma;}}_0}{(x_2-x_1)}\frac{({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+z_2^2)k_1-[{(x_2-x_1)}^2+{2z}_2^2]k_2}{{(1+k_1{k}_2)}^2\sqrt{{(x_2-x_1)}^2+({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2+2)z_2^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}}---\left(18\right)$

Order $\frac{\mathrm{D\&sigma;}\left({\mathrm{\&delta;\; x}}_0\right)}{\mathrm{<figure-callout\; id="1"\; label="d\; k"\; filenames="111119094705.png"\; state="\{\{state\}\}">d</figure-callout>}{k}_{}{}_1}=0,$ So, when ${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1=\frac{{(x_2-x_1)}^2+{2z}_2^2}{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+z_2^2}{k}_2$ The time, σ (δ x ₀) obtain minimal value.

2) as (x ₂-x ₁) (1+k ₁k ₂)＜0 o'clock,

$\frac{\mathrm{d\&sigma;}\left(\mathrm{\&delta;}{x}_0\right)}{\mathrm{<figure-callout\; id="1"\; label="d\; k"\; filenames="111119094705.png"\; state="\{\{state\}\}">d</figure-callout>}{k}_{}{}_1}=-\frac{{\mathrm{\&sigma;}}_0}{(x_2-x_1)}\frac{({\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+z_2^2)k_1-[{(x_2-x_1)}^2+{2z}_2^2]k_2}{{(1+k_1{k}_2)}^2\sqrt{{(x_2-x_1)}^2+({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2+2)z_2^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}}---\left(19\right)$

Order

So, when

The time, σ (δ x ₀) obtain minimal value.The result is consistent under two kinds of situation.In like manner can get

(2) find the solution since the part that causes of register pin deviation at the Minimum Mean Square Error σ of z direction assembling deviation (δ z ₀) _MinIn time, can get, when The time, σ (δ z ₀) obtain minimal value.

(3) finding the solution because the part that the register pin deviation causes rotates the lowest mean square difference of assembling deviation

In time, can get, and works as k ₁=k ₂The time,

Obtain minimal value.

(4) find the solution since the part that causes of register pin deviation at the assembling deviation δ of X and Z compound direction q ₀Minimum Mean Square Error σ _∑(δ q ₀) _MinIn time, can get, when ${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1=\frac{n}{m}{k}_2=\frac{z_2^2+x_1^2-x_1{x}_2+x_2^2}{x_2^2+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2-z_1{z}_2+z_2^2}{k}_2$ The time, σ (δ z ₀) obtain minimal value.

(2) a plurality of parametric synthesis based Robust Design are optimized

A plurality of parametric synthesis optimizations comprise four-way register pin coordinate (x in the based Robust Design model ₂, z ₂), two to register pin coordinate (x ₁, z ₁), the cotter way slope k ₁With the layout slope k ₂Because parameter is many, finds the solution the optimum point parameter through objective function (12) or formula (13), will be the process of a more complicated.This paper intends and adopts genetic algorithm to carry out part assembling deviation multiparameter Robust Optimal Design.

Implement the basic step of genetic algorithm:

(1) selects the binary coding strategy, convert relevant parameter sets into the bit string structure space;

(2) definition adaptive value function f (t);

(3) select the population size, confirm selection, intersection, variation method, and the probability that intersects, makes a variation;

(4) in given range, generate initial population at random, population quantity is 40, establishes gen=0;

(5) calculate the decoded adaptive value of individual bit string in the population, choose minimum adaptive value, note is made c _Min

(6) utilization selection, intersection and mutation operator act on colony, form colony of future generation;

(7) recomputate the decoded adaptive value of individual bit string in the population, choose minimum adaptive value, note is made c _tIf c _t＜c _Max, c then _Min=c _t

(8) establish gen=gen+1, if gen＜600 (600 is maximum genetic algebra) forwards step 6) to; Otherwise, stop genetic algorithm;

(9) output c _Min, and c _MinTwo the coordinate (x that corresponding genetic coding is represented to register pin ₁, z ₁) and two slope k to register pin flute length axle ₁Be Optimization result.

Embodiment: with the wheel cover inner panel is example, according to accompanying drawing 3, with hole in piece part or four-way register pin P ₁The center be true origin, i.e. (x ₂, z ₂)=(0,0), set up part rectangular coordinate system OXYZ, known two to register pin P ₂Coordinate (x ₁, z ₁)=(-595,315), so, four-way register pin and two slopes to the register pin line

(1) works as k ₁→ ∞, when promptly locating groove angle α=± 90 °, the wheel cover inner panel is respectively in the part deviation mean square deviation of X axle, Z axle, rotation and X and Y compound direction

$\mathrm{\&sigma;}\left({\mathrm{\&delta;x}}_0\right)=\frac{\sqrt{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+z_2^2}}{\left|k_2(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0=\frac{\sqrt{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}}{\left|k_2{x}_1\right|}={\mathrm{\&sigma;}}_0$

$\mathrm{\&sigma;}\left({\mathrm{\&delta;z}}_0\right)=\frac{\sqrt{2x_2^2+{(z_1-z_2)}^2}}{\left|k_2(x_2-x_1)\right|}{\mathrm{\&sigma;}}_0=\frac{\sqrt{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}}{\left|k_2{x}_1\right|}={\mathrm{\&sigma;}}_0$

${\mathrm{\&delta;}}_{\mathrm{\&Sigma;}}\left(q_0\right)=\frac{\sqrt{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}}{\left|k_2{x}_1\right|}{\mathrm{\&sigma;}}_0={\mathrm{\&sigma;}}_0$

It is thus clear that, identical along the wheel cover inner panel deviation fluctuation size of X axle, Z axle and compound direction thereof when groove tilt angle α=± 90 ° with register pin, be a constant.And the Z between fluctuation of part rotation direction deviation and two register pins is inversely proportional to distance, and distance is far away, and part rotation direction deviation is more sane.

(2) find the solution wheel cover inner panel assembling two to location cotter way slope k ₁The based Robust Design analytic solution

1), can get wheel cover inner panel assembling deviation by formula (12) and obtain along the X-direction Minimum Mean Square Error and be as

promptly when

:

$\mathrm{\&sigma;}{\left({\mathrm{\&delta;x}}_0\right)}_{\min }=\frac{{\mathrm{\&sigma;}}_0}{\left|(x_2-x_1)(1+k_1{k}_2)\right|}\sqrt{{(x_2-x_1)}^2+({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2+2)z_2^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}=\frac{\sqrt{{2x}_1^2}}{\left|{2x}_1\right|}=\frac{\sqrt{2}}{2}{\mathrm{\&sigma;}}_0$

2), can get wheel cover inner panel assembling deviation by formula (12) and obtain along the Z-direction Minimum Mean Square Error and be as promptly when

:

$\mathrm{\&sigma;}{\left({\mathrm{\&delta;z}}_0\right)}_{\min }=\frac{{\mathrm{\&sigma;}}_0}{\left|(x_2-x_1)(1+k_1{k}_2)\right|}\sqrt{({2\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2+1)x_2^2+x_1^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{(z_1-z_2)}^2}=\frac{\sqrt{{2x}_1^2}}{\left|{2x}_1\right|}=\frac{\sqrt{2}}{2}{\mathrm{\&sigma;}}_0$

3) work as k ₁=k ₂=0.529 o'clock, can get wheel cover inner panel assembling deviation by formula (12) and obtain and rotate Minimum Mean Square Error around the Y axle and be:

4), can get wheel cover inner panel assembling deviation by formula (13) and obtain along X and Z axle compound direction Minimum Mean Square Error and be as promptly when

:

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}{\left({\mathrm{\&delta;q}}_0\right)}_{\min }=\frac{{\mathrm{\&sigma;}}_0}{(x_2-x_1)(1+k_1{k}_2)}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2(x_2^2+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2-z_1{z}_2+z_2^2)+(z_2^2+x_1^2-x_1{x}_2+x_2^2)}$

$=\frac{{\mathrm{\&sigma;}}_0}{2\left|x_1\right|}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2+x_1^2}=\frac{\sqrt{2}}{2}{\mathrm{\&sigma;}}_0$

(3) the wheel cover inner panel assembles a plurality of parametric synthesis based Robust Design and optimization

Know by formula (12) and formula (13); And

wheel cover inner panel totally is size B=660, H=400.

Center with hole in piece part or four-way register pin is initial point, i.e. (x ₂, z ₂)=(0,0).According to known conditions, wheel cover inner panel assembling based Robust Design and Optimization Model can be reduced to:

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}\left({\mathrm{\&delta;q}}_0\right)=\frac{{\mathrm{\&sigma;}}_0}{|x_1+k_1{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1|}\sqrt{x_1^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}$

Optimum parameters is in the model: the two coordinate (x to register pin ₁, z ₁) and two to location cotter way slope k ₁

1) parameter setting

Individual quantity NIND is 40; Maximum genetic algebra MAXGEN is 600; The variable dimension is that NVAR is 3; Each variable representes that with 20 binary code promptly PRECI is 20; Interleaved mode is got the single-point intersection, and crossover probability is 0.7; The variation probability is 0.017.

2) fitness function

The objective function of genetic algorithm optimization is from the above:

${\mathrm{\&sigma;}}_{\mathrm{\&Sigma;}}\left({\mathrm{\&delta;q}}_0\right)=\frac{{\mathrm{\&sigma;}}_0}{|x_1+k_1{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1|}\sqrt{x_1^2+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="111119094705.png"\; state="\{\{state\}\}">z</figure-callout>}}_1^2}$

Make x ₁=t ₁, z ₁=t ₂, k ₁=t ₃Then objective function can turn to:

$g({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="111119094705.png"\; state="\{\{state\}\}">t</figure-callout>}}_1,t_2,t_3)=\frac{{\mathrm{\&sigma;}}_0}{|{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="111119094705.png"\; state="\{\{state\}\}">t</figure-callout>}}_1+t_2{t}_3|}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="111119094705.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2+t_2^2{t}_3^2}$

Then adapting to function does

In the formula, c _MaxBe the maximal value of current all generations or nearest K g (t) in generation, c at this moment _MaxAlong with algebraically can change.

From the above mentioned basic step is implemented genetic algorithm optimization, and with two to location cotter way slope k ₁, four-way register pin and two is to the layout of register pin line location slope k ₂Be converted into two to register pin groove tilt angle α and layout orientation angle β by following formula respectively.

$\left\{\begin{array}{c}\tan \mathrm{\&alpha;}=-\frac{a}{b}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="111119094705.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\\ \tan \mathrm{\&beta;}=\frac{z_2-z_1}{x_2-x_1}=k_2\end{array}\right.$

The complex optimum result is as shown in table 1.

For multi-variable function, often there are a plurality of locally optimal solutions.When utilizing genetic algorithm that multi-variable function is optimized, its result is near the local optimum value of globally optimal solution in a plurality of locally optimal solutions.In addition, the genetic manipulation of genetic algorithm is a randomness in whole evolutionary process, so in general each Search Results is different.Therefore, carry out repeatedly genetic algorithm usually and calculate, get the optimization solution of wherein suitable value as genetic algorithm.

The present invention chooses two groups of Genetic Algorithm optimized design results and compares; As shown in table 1; As a result 1 with optimize before compare, X to, Z to X and Z compound direction part deviation mean square deviation all reduce 11.71%, and rotation φ to the deviation mean square deviation increased 61.9%; As a result 2 with optimize before compare, X all reduces 11.25% to, Z to the deviation mean square deviation with X and Z compound direction, and rotation φ to the deviation mean square deviation only increased 14.29%.Contrasting above-mentioned two groups of Optimization result can know, X has all obtained optimization to, Z to the deviation mean square deviation with X and Z compound direction, and Optimization result differs and have only 0.52%, but rotate φ to the deviation mean square deviation 29.41% variation is but arranged.Take all factors into consideration the actual conditions of part erecting yard and anchor clamps location, choose Optimization result 2 as model Robust Optimal Design numerical solution.

Result's contrast before and after table 1 based Robust Design is optimized

Claims (4)

1. two-dimentional assembling jig arbitrary placement's based Robust Design and optimization method is characterized in that: may further comprise the steps:

1) sets up the part two dimension assembling jig arbitrary placement deviations model of anchor clamps positional parameter to the part effects;

2) solution procedure 1) described in part buggy model, obtain the part two dimension assembling jig arbitrary placement based Robust Design model that mean square deviation with the part deviation is minimised as target;

3) analytical procedure 2) described in the based Robust Design model, utilization analytical method and genetic algorithm are carried out single parameter optimization and a plurality of parametric synthesis optimization that Fixture Layout and anchor clamps are located respectively.

2. two-dimentional assembling jig arbitrary placement's based Robust Design according to claim 1 and optimization method; It is characterized in that: the concrete grammar of setting up part two dimension assembling jig arbitrary placement deviations model in the described step 1) does; According to the Fixture Layout principle; Analyze the anchor clamps positional parameter to the part effects; With the three coordinate measuring machine coordinate system is reference frame, comprise four-way register pin coordinate, two to the register pin coordinate, two to location cotter way slope, two to the layout location slope of four-way register pin line, wherein the anchor clamps positional parameter has six.

3. two-dimentional assembling jig arbitrary placement's based Robust Design according to claim 1 and optimization method; It is characterized in that: the concrete grammar that makes up part two dimension assembling jig arbitrary placement based Robust Design model described step 2) does; The given anchor clamps positional parameter deviation source vector that satisfies normal distribution; Mean square deviation with the part deviation is minimised as target; Making up part two dimension assembling jig arbitrary placement based Robust Design model, is reference frame with the three coordinate measuring machine coordinate system, and wherein the mean square deviation of part deviation comprises XThe part deviation mean square deviation of direction, ZThe part deviation mean square deviation of direction, corner φPart deviation mean square deviation, XWith ZThe part deviation mean square deviation of compound direction.

4. two-dimentional assembling jig arbitrary placement's based Robust Design according to claim 1 and optimization method; It is characterized in that: the concrete grammar of parameter optimization does in the described step 3); Analyze in the said based Robust Design model influence degree of six parametric variables to part assembling deviation robustness; Obtain the variable that single parameter optimization and a plurality of parametric synthesis are optimized; Wherein the variable of single parameter optimization is two to location cotter way slope, the variable of a plurality of parameter optimizations be two to register pin coordinate and two to register pin flute length axle slope.

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