CN105868496A - Method for determining assembly-oriented rectangular plane shape error evaluation parameters - Google Patents

Abstract

The invention relates to a method for determining assembly-oriented rectangular plane shape error evaluation parameters and belongs to the field of error evaluation. The method comprises: generating a cutting surface by non-Gaussian plane simulation method, acquiring a shape error surface via wavelet filtering, and extracting characterization parameters of surface shape error distribution; subjecting the shape error surface to simulation assembly through contact algorithm, calculating assembly precision of spatial orientation changes of a second part after assembly, determining a relation between surface characterization parameters and post-assembly part assembly precision through correlation analysis, thereby determining shape error evaluation parameters and enabling quantitative description for the relation between the surface distribution characterization parameters and assembly precision. Plane characteristic parameters having important impact on assembly precision are obtained, and scientific basis is provided for improving machining quality of mating planes and optimizing assembly process to improve assembly precision.

Description

A kind of rectangular planar shape error assessment parameter determination method towards assembling

Technical field

The present invention relates to a kind of rectangular planar shape error assessment parameter determination method towards assembling, belong to error assessment Field.

Background technology

During the assembling of China's precision mechanical system, parts form error be impact assembling after parts at complete machine One of key factor of middle relative positional accuracy.In Modern Manufacturing Industry, assembly work amount averagely accounts for and manufactures amount of work 45%, assembly fee accounts for the 20-30% or higher manufacturing total cost.Processing, assembling link various factors (i.e. manufacturing characteristics) right After assembling, the Influencing Mechanism of systematic function, the research of coupled relation are increasingly becoming the focus studied both at home and abroad, are also to manufacture A Main way in urgent need of strengthening in technical research.

Existing form error evaluating, is to be evaluated from mismachining tolerance angle mostly, and the most usually makes Such phenomenon can occur, and i.e. in the case of whole parts machinings are up-to-standard, assembling yield rate is the lowest, produces after assembling Moral character can cannot meet design requirement, and very difficult batch comes into operation.Main cause is to precision mechanical system assembly precision shadow From the point of view of sound, there is the fitting plane of same shape error, due to the form error distribution that they are different, assembly precision will be produced Raw diverse impact.As depicted in figs. 1 and 2.The most how to reflect that the impact of assembly precision is exactly by surface shape error One important research contents.Yet with the complexity of three-dimensional surface, its characterization parameter has a lot, how to obtain and to assemble essence Spend relevant parameter relatively difficult.

Summary of the invention

It is an object of the invention to provide a kind of rectangular planar shape error assessment parameter determination method towards assembling, the party Method obtains the plane characteristic parameter having a major impact assembly precision, for improving the crudy coordinating plane, improves assembling essence Degree provides foundation.

It is an object of the invention to be achieved through the following technical solutions.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, specifically comprises the following steps that

Step one, the form error of piece surface are obtained by following method: generate with non-gaussian plane simulation method Machining surface, wavelet filtering obtains form error surface afterwards；Utilize orthogonal experiment design method, arranged by orthogonal arrage Multiple influence factors, thus obtain many group form error surfaces.

The characterization parameter of the form error surface shape error distribution that step 2, extraction step one obtain；

Step 3, form error surface step one obtained all are simulated assembling with ideal surfaced；

(1) search peak, as first make contact；

(2) first make contact and four summits of rectangle are connected to form four planar deltas；

(3) calculate rectangle plane point in each planar delta drop shadow spread and first make contact is wired to corresponding three The angle of angle plane, in taking corresponding planar delta drop shadow spread, point is minimum with the angle being wired to planar delta of first make contact Point, as the second contact point, i.e. rotate to four direction around peak, the point touched at first is the point that angle is minimum.Four Individual planar delta i.e. can get four the second contact points；

(4) planar delta is forwarded to the second contact point around peak, form median surface；

(5) with the line of peak and the second contact point as axle, rotate and find the 3rd contact point.In search rectangular plane 3rd contact point, made the 3rd contact point and by peak and the vertical line of the line of the second contact point；Calculate the 3rd contact point Vertical line and by the angle of median surface, the point corresponding to angle minimum is the 3rd contact point, and same four triangular facets can find Four the 3rd contact points；

(6) connect first make contact, the second contact point and the 3rd contact point and obtain the equation of four contact surfaces；

(7) other constraintss are considered, such as the position relationship of assembly force position Yu contact point, thus from four contact surfaces Equation screens an optimum.

The assembly precision of the dimensional orientation change of part it is assembled after step 4, calculating assembling；Assembly precision is characterized as dress Being assembled the part plane locus relative to Norm part plane after joining, assembly precision is with after assembling six of part space The free degree is weighed:

Γ=[d_x,d_y,d_z,δ_x,δ_y,δ_z] (1)

Wherein d_x,d_y,d_zFor X, the skew in tri-directions of Y, Z；δ_x,δ_y,δ_zFor the rotation amount around three axles.

Step 5, determined the characterization parameter of step 2 and the relation of the assembly precision of step 4 by correlation analysis, thus Determine form error evaluating, it is achieved surface distributed characterization parameter and the quantitative description of assembly precision relation.

Described in step one with the method on non-gaussian plane simulation method generation machining surface it is: by given plane Auto-correlation function R and power spectral density G_z(ω_x,ω_y), obtain system transter H (ω_x,ω_y), utilize Johnson to change System obtains the random column η ' with the non-gaussian distribution of certain deflection and kurtosis, utilizes computer coarse flat to generate non-gaussian Face.

Described in step one with the method on wavelet filtering acquisition form error surface it is: use wavelet analysis, use basic function Bior6.8, as the wavelet basis function decomposed, carries out multiple dimensioned separation to the characteristic information of part plane pattern, isolates shape Error plane.

The method of Orthogonal Experiment and Design described in step one is: use orthogonal experiment, six influence factors of orthogonal test Be respectively mean height of surface mu, standard deviation sd of apparent height, auto-correlation length bx in x direction, surface, y direction, surface from Correlation length by, degree of skewness skew on surface, kurtosis kurt on surface, select typical Orthogonal table to be analyzed, determine test time Number.Establishment orthogonal test scheme table, and then form error surface can be organized much.

Characterization parameter described in step 2 is: range parameter, spatial parameter, functional parameter and hybrid parameter；

Described in step 3, other constraintss are: be assembled part center of gravity all with in the position relationship of contact point and plane The position relationship of z is put in value zi of point and ideal plane.

It is assembled the position relationship of part center of gravity and contact point to meet and be assembled part center of gravity in the middle of three contact points. In plane put the position relationship of z on value zi a little and ideal plane and should meet all z values respectively less than zi, see formula 3, then say Bright three contact points now are one group of potential contact point.Three contact points are determined by constraints.Three contact points obtained For P (x₁,y₁,z₁),Q(x₂,y₂,z₂),R(x₃,y₃,z₃) then equation be:

$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0---\left(2\right)$

That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, are derived from.

$z\left(i\right)=\frac{D-{\mathrm{Ax}}_i-{\mathrm{By}}_i}{C}\≤z_i---\left(3\right)$

The assembly precision of the dimensional orientation change of part it is assembled: after contact condition determines after calculating assembling described in step 4 The differential motion change being assembled part relative to Norm part can be calculated, three contact points can obtain ideal plane Equation Ax+By+Cz+D=0, i.e. can obtain the change of normal vector (A, B, C), and then can obtain three rotation (δ_x,δ_y,δ_z), Plane equation has been had to compare the skew (d that i.e. can obtain tri-directions of X, Y, Z with ideal plane_x,d_y,d_z), the most small rotation amount With small translational movement.Three skews are that the changes in coordinates at two coordinate system centers represents；Three rotation amounts are by plane equation Normal vector n=(A, B, C) asks for, and formula 4 is shown in three rotations.

$\begin{array}{c}{\mathrm{\δ}}_x=\arccos \left(\right(n\×e_x)/(\left|n\right|\·{|e}_x\left|\right))\\ {\mathrm{\δ}}_y=\arccos \left(\right(n\×e_y)/(\left|n\right|\·\left|e_y\right|\left)\right)\\ {\mathrm{\δ}}_z=\arccos \left(\right(n\×e_z)/(\left|n\right|\·\left|e_z\right|\left)\right)\end{array}---\left(4\right)$

Wherein n=(A, B, C) is planar process vector；e_x,e_y,e_zFor X, the unit vector in tri-directions of Y, Z.

Correlation analysis method described in step 5 is:

(1) correlation analysis process of the test

Change input parameter by orthogonal test, obtain organizing the data of characterization parameter and assembly precision more；Data are carried out Correlation analysis.By the height correlation during relatively each coefficient obtains coefficient correlation as evaluating.

(2) characterization parameter and the correlation analysis of precision

The correlation of each component and characterization parameter is set up based on each component calculating characterization parameter and the assembly precision obtained Analytical formula, correlation analysis computing formula is

$A=\frac{\mathrm{cov}(V,\mathrm{\Γ})}{\sqrt{D\left(V\right)}\·\sqrt{D\left(\mathrm{\Γ}\right)}},V=\[v_1,v_{2,}...,v_l\],\mathrm{\Γ}=\[d_x,d_y,d_z,{\mathrm{\δ}}_x,{\mathrm{\δ}}_y,{\mathrm{\δ}}_z\]---\left(5\right)$

Wherein V is expressed as representing characterization parameter, and l is characterization parameter number, and Γ represents assembly precision.Each by com-parison and analysis Height correlation in coefficient is as evaluating, i.e.

$\begin{array}{cc}{d}_x\∝\[S_1,S_2,\mathrm{...},S_i\]& {\mathrm{\δ}}_x\∝\[S_1,S_2,\mathrm{...},S_m\]\\ d_y\∝\[S_1,S_2,\mathrm{...},S_j\],& {\mathrm{\δ}}_y\∝\[S_1,S_2,\mathrm{...},S_n\]\\ d_z\∝\[S_1,S_1,\mathrm{...},S_k\]& {\mathrm{\δ}}_z\∝\[S_1,S_1,\mathrm{...},S_p\]\end{array}---\left(6\right)$

In formula, S is corresponding evaluating, and i, j, k, m, n, p are the number of each component correspondence evaluating.

The one group of parameter inputted by change, generation has the Rough Horizontal Plane of certain plane pattern and can change, after reconstructing The parameter extracted of plane also just corresponding change, therefore can arbitrarily be organized data；Data are carried out correlation analysis.From table Levying according to correlation analysis in parameter, the size of coefficient correlation has reacted degree of correlation between variable, is obtained by relatively each coefficient Height correlation in coefficient correlation (| ρ | " 0.6) as evaluating.

Beneficial effect

By considering that assembling is evaluated in the distribution of form error, determine the evaluation ginseng of the flat form error towards assembling Number, it is achieved the characterization parameter of surface shape error distribution and the quantitative description of assembly precision relation, i.e. obtains and has assembly precision The plane characteristic parameter of material impact, for improving the crudy coordinating plane, optimizes assembly technology thus improves assembly precision Scientific basis is provided.

Accompanying drawing explanation

Fig. 1 is the different distributions of same shape error delta；

Fig. 2 is the rigging error caused by the distribution of difformity error；

Fig. 3 is general frame figure；

Fig. 4 is assembly simulation flow chart；

Fig. 5 is the contact condition of plane.

Detailed description of the invention

The invention will be further described with embodiment below in conjunction with the accompanying drawings.

Embodiment 1

A kind of rectangular planar shape error assessment parameter determination method towards assembling, as it is shown on figure 3, concrete steps are such as Under:

Step one, the form error of piece surface are obtained by following method, generate with non-gaussian plane simulation method Machining surface, by the auto-correlation function R or power spectral density function G of given plane_z(ω_x,ω_y), obtain the biography of system Delivery function H (ω_x,ω_y), utilize Johnson converting system to obtain the random column with the non-gaussian distribution of certain deflection and kurtosis η ', utilizes computer to generate non-gaussian Rough Horizontal Plane.Wavelet filtering obtains form error surface afterwards；Use wavelet analysis, Use basic function Bior6.8 as the wavelet basis function decomposed, the characteristic information of part plane pattern carried out multiple dimensioned separation, Isolate form error plane.Input parameter is shown in Table 1, utilizes orthogonal experiment design method, arranges multiple impact by orthogonal arrage Factor, is shown in Table 2, and six influence factors of orthogonal test are respectively mean height of surface mu, standard deviation sd of apparent height, surface Auto-correlation length bx in x direction, auto-correlation length by y direction, surface, degree of skewness skew on surface, kurtosis kurt on surface, Select typical Orthogonal table to be analyzed, be shown in Table 3.Determining test number (TN) 25, work out orthogonal test scheme table, often group carries out 50 examinations Test, and then 1250 groups of form error surfaces can be obtained.

Table 1 inputs parameter

Table 2 orthogonal test factor level table

Table 3 orthogonal test scheme table

The characterization parameter of the form error surface shape error distribution that step 2, extraction step one obtain；Described sign is joined Number is: range parameter, spatial parameter, functional parameter and hybrid parameter；

The following parameter of initial option calculates, and see table 4:

Table 4 characterization parameter table

Step 3, form error surface step one obtained all are simulated assembling with ideal surfaced；As shown in Figure 4.

(1) search peak, as first make contact；

(2) first make contact and four summits of rectangle are connected to form four planar deltas；

(3) calculate rectangle plane point in each planar delta drop shadow spread and first make contact is wired to corresponding three The angle of angle plane, in taking corresponding planar delta drop shadow spread, point is minimum with the angle being wired to planar delta of first make contact Point, as the second contact point, i.e. rotate to four direction around peak, the point touched at first is the point that angle is minimum.Four Individual planar delta i.e. can get four the second contact points；

(4) planar delta is forwarded to the second contact point around peak, form median surface；

(5) with the line of peak and the second contact point as axle, rotate and find the 3rd contact point.In search rectangular plane 3rd contact point, made the 3rd contact point and by peak and the vertical line of the line of the second contact point；Calculate the 3rd contact point Vertical line and by the angle of median surface, the point corresponding to angle minimum is the 3rd contact point, and same four triangular facets can find Four the 3rd contact points；

(6) connect first make contact, the second contact point and the 3rd contact point and obtain the equation of four contact surfaces；

(7) other constraintss are considered, such as the position relationship of assembly force position Yu contact point, thus from four contact surfaces Equation screens an optimum.

Described in step 3: other constraintss described are: be assembled part center of gravity and the position relationship of contact point and plane The position relationship of z is put on upper value zi a little and ideal plane.

It is assembled the position relationship of part center of gravity and contact point to meet and be assembled part center of gravity in the middle of three contact points. In plane put the position relationship of z on value zi a little and ideal plane and should meet all z values respectively less than zi, see formula 3, then say Bright three contact points now are one group of potential contact point.Three contact points are determined by constraints.Three contact points obtained For P (x₁,y₁,z₁),Q(x₂,y₂,z₂),R(x₃,y₃,z₃) then equation be:

$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0---\left(2\right)$

That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, are derived from.

$z\left(i\right)=\frac{D-{\mathrm{Ax}}_i-{\mathrm{By}}_i}{C}\≤z_i---\left(3\right)$

The assembly precision of the dimensional orientation change of part it is assembled after step 4, calculating assembling；Assembly precision is characterized as dress Being assembled the part plane locus relative to Norm part plane after joining, assembly precision is with after assembling six of part space The free degree is weighed.

Γ=[d_x,d_y,d_z,δ_x,δ_y,δ_z] (1)

Wherein d_x,d_y,d_zFor X, the skew in tri-directions of Y, Z；δ_x,δ_y,δ_zFor the rotation amount around three axles.

Described in step 4: only consider the six-freedom degree of local, can calculate after determining based on above-mentioned contact condition and treat Assembly part changes relative to the differential motion of Norm part, three contact points can obtain ideal plane equation Ax+By+Cz + D=0, i.e. can obtain the change of normal vector (A, B, C), and then can obtain three rotation (δ_x,δ_y,δ_z), there is plane equation Skew (the d that i.e. can obtain tri-directions of X, Y, Z is compared with ideal plane_x,d_y,d_z), the most small rotation amount and small translation Amount.Three skews are that the changes in coordinates at two coordinate system centers represents；Three rotation amounts are by the normal vector n=of plane equation (A, B, C) asks for, and formula 4 is shown in three rotations.

$\begin{array}{c}{\mathrm{\δ}}_x=\arccos \left(\right(n\×e_x)/(\left|n\right|\·{|e}_x\left|\right))\\ {\mathrm{\δ}}_y=\arccos \left(\right(n\×e_y)/(\left|n\right|\·\left|e_y\right|\left)\right)\\ {\mathrm{\δ}}_z=\arccos \left(\right(n\×e_z)/(\left|n\right|\·\left|e_z\right|\left)\right)\end{array}---\left(4\right)$

Wherein n=(A, B, C) is planar process vector；e_x,e_y,e_zFor X, the unit vector in tri-directions of Y, Z.

Step 5, determined the characterization parameter of step 2 and the relation of the assembly precision of step 4 by correlation analysis, to obtaining The 1250 groups of data taken carry out correlation analysis, computational representation parameter and the coefficient correlation of assembly precision, obtain big the commenting of correlation Valency parameter, so that it is determined that form error evaluating, it is achieved surface distributed characterization parameter and the quantitative description of assembly precision relation.

Correlation analysis method described in step 5 is:

(1) correlation analysis process of the test

Change input parameter by orthogonal test, obtain organizing the data of characterization parameter and assembly precision more；Data are carried out Correlation analysis.By the height correlation during relatively each coefficient obtains coefficient correlation as evaluating.

(2) characterization parameter and the correlation analysis of precision

The correlation of each component and characterization parameter is set up based on each component calculating characterization parameter and the assembly precision obtained Analytical formula, correlation analysis computing formula is

${\mathrm{\ρ}}_i=\frac{\mathrm{cov}(V,\mathrm{\Γ})}{\sqrt{D\left(V\right)}\·\sqrt{D\left(\mathrm{\Γ}\right)}},V=\[v_1,v_{2,}...,v_l\]\mathrm{\Γ}=\[d_x,d_y,d_z,{\mathrm{\δ}}_x,{\mathrm{\δ}}_y,{\mathrm{\δ}}_z\]---\left(5\right)$

Wherein V is expressed as representing characterization parameter, and l is characterization parameter number, and Γ represents assembly precision.Each by com-parison and analysis Height correlation in coefficient is as evaluating, i.e.

$\begin{array}{cc}{d}_x\∝\[S_1,S_2,\mathrm{...},S_i\]& {\mathrm{\δ}}_x\∝\[S_1,S_2,\mathrm{...},S_m\]\\ d_y\∝\[S_1,S_2,\mathrm{...},S_j\],& {\mathrm{\δ}}_y\∝\[S_1,S_2,\mathrm{...},S_n\]\\ d_z\∝\[S_1,S_1,\mathrm{...},S_k\]& {\mathrm{\δ}}_z\∝\[S_1,S_1,\mathrm{...},S_p\]\end{array}---\left(6\right)$

In formula, S is corresponding evaluating, and i, j, k, m, n, p are the number of each component correspondence evaluating.

The one group of parameter inputted by change, generation has the Rough Horizontal Plane of certain plane pattern and can change, after reconstructing The parameter extracted of plane also just corresponding change, therefore can arbitrarily be organized data；Data are carried out correlation analysis.From table Levying according to correlation analysis in parameter, the size of coefficient correlation has reacted degree of correlation between variable, is obtained by relatively each coefficient Height correlation in coefficient correlation (| ρ | " 0.6) as evaluating.

Characterization parameter is shown in Table 5 with the coefficient correlation of assembly precision

Table 5 correlation coefficient charts

From table it follows that in ten given parameters, summit density S_dsRotation δ with assembly precision x, y direction_xWith δ_yRelevant；Surface Root Mean Square deviation Sq, surface arithmetic average deviation Sa, 10, surface height Sz, surface maximum height S_p, surface Mean μ and surface variances sigma²With assembly precision z direction offset d_zHighly dependent.That is:

$\begin{array}{c}{\mathrm{\δ}}_x\∝\left[S_{\mathrm{ds}}\right]\\ {\mathrm{\δ}}_y\∝\left[S_{\mathrm{ds}}\right]\\ d_z\∝[S_q,S_a,S_z,\mathrm{\μ},{\mathrm{\σ}}^2]\end{array}---\left(7\right)$

Claims (8)

1. the rectangular planar shape error assessment parameter determination method towards assembling, it is characterised in that: specifically comprise the following steps that

Step one, the form error of piece surface are obtained by following method: generate cutting with non-gaussian plane simulation method Finished surface, wavelet filtering obtains form error surface afterwards；Utilize orthogonal experiment design method, arranged by orthogonal arrage multiple Influence factor, thus obtains many group form error surfaces；

The characterization parameter of the form error surface shape error distribution that step 2, extraction step one obtain；

Step 3, form error surface step one obtained all are simulated assembling with ideal surfaced；

(1) search peak, as first make contact；

(2) first make contact and four summits of rectangle are connected to form four planar deltas；

(3) calculate rectangle plane point in each planar delta drop shadow spread to put down to the corresponding triangle that is wired to of first make contact The angle in face, takes point in corresponding planar delta drop shadow spread minimum with the angle being wired to planar delta of first make contact Point, as the second contact point, i.e. rotates to four direction around peak, and the point touched at first is the point that angle is minimum；Four Planar delta i.e. can get four the second contact points；

(4) planar delta is forwarded to the second contact point around peak, form median surface；

(5) with the line of peak and the second contact point as axle, rotate and find the 3rd contact point；In search rectangular plane the 3rd Contact point, made the 3rd contact point and by peak and the vertical line of the line of the second contact point；Calculate the 3rd contact point vertical Line and by the angle of median surface, the point corresponding to angle minimum is the 3rd contact point, and same four triangular facets can find four 3rd contact point；

(6) connect first make contact, the second contact point and the 3rd contact point and obtain the equation of four contact surfaces；

(7) other constraintss are considered, such as the position relationship of assembly force position Yu contact point, thus from four contact surface equations One optimum of middle screening；

The assembly precision of the dimensional orientation change of part it is assembled after step 4, calculating assembling；After assembly precision is characterized as assembling Being assembled the part plane locus relative to Norm part plane, assembly precision is with six freedom in part space after assembling Degree is weighed:

Γ=[d_x,d_y,d_z,δ_x,δ_y,δ_z] (1)

Wherein d_x,d_y,d_zFor X, the skew in tri-directions of Y, Z；δ_x,δ_y,δ_zFor the rotation amount around three axles；

Step 5, determined the characterization parameter of step 2 and the relation of the assembly precision of step 4 by correlation analysis, so that it is determined that Form error evaluating, it is achieved surface distributed characterization parameter is quantitatively retouched with assembly precision relation.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature Be: described in step one with non-gaussian plane simulation method generate machining surface method be: by given plane from Correlation function R and power spectral density G_z(ω_x,ω_y), obtain system transter H (ω_x,ω_y), utilize Johnson to change system System obtains the random column η ' with the non-gaussian distribution of certain deflection and kurtosis, utilizes computer coarse flat to generate non-gaussian Face.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature It is: described in step one with the method on wavelet filtering acquisition form error surface be: use wavelet analysis, use basic function Bior6.8, as the wavelet basis function decomposed, carries out multiple dimensioned separation to the characteristic information of part plane pattern, isolates shape Error plane.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature Being: the method for Orthogonal Experiment and Design described in step one is: use orthogonal experiment, six influence factors of orthogonal test are respectively For mean height of surface mu, standard deviation sd of apparent height, auto-correlation length bx in x direction, surface, the auto-correlation in y direction, surface Length by, degree of skewness skew on surface, kurtosis kurt on surface, select typical Orthogonal table to be analyzed, determine test number (TN)；Compile Orthogonal test scheme table processed, and then form error surface can be organized much.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature It is: characterization parameter described in step 2 is: range parameter, spatial parameter, functional parameter and hybrid parameter.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature It is: described in step 3, other constraintss are: be assembled in the position relationship of part center of gravity and contact point and plane institute a little Value zi and ideal plane on put the position relationship of z；

It is assembled the position relationship of part center of gravity and contact point to meet and be assembled part center of gravity in the middle of three contact points；Plane The position relationship putting z on upper value zi a little and ideal plane should meet all z values respectively less than zi, sees formula 3, then this is described Time three contact points be one group of potential contact point；Three contact points are determined by constraints；Three contact points obtained are P (x₁,y₁,z₁),Q(x₂,y₂,z₂),R(x₃,y₃,z₃) then equation be:

$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0---\left(2\right)$

That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, are derived from；

$z\left(i\right)=\frac{D-{\mathrm{Ax}}_i-{\mathrm{By}}_i}{C}\≤z_i---\left(3\right)$

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature It is: be assembled the assembly precision of the dimensional orientation change of part after calculating assembling described in step 4: contact condition after determining is The differential motion change being assembled part relative to Norm part can be calculated, three contact points can obtain ideal plane side Journey Ax+B y+Cz+D=0, i.e. can obtain the change of normal vector (A, B, C), and then can obtain three rotation (δ_x,δ_y,δ_z), have Plane equation compares the skew (d that i.e. can obtain tri-directions of X, Y, Z with ideal plane_x,d_y,d_z), the most small rotation amount with Small translational movement；Three skews are that the changes in coordinates at two coordinate system centers represents；Three rotation amounts are by the method for plane equation Vector n=(A, B, C) asks for, and formula 4 is shown in three rotations；

δ_x=arccos ((n × e_x)/(|n|·|e_x|))

δ_y=arccos ((n × e_y)/(|n|·|e_y|)) (4)

δ_z=arccos ((n × e_z)/(|n|·|e_z|))

Wherein n=(A, B, C) is planar process vector；e_x,e_y,e_zFor X, the unit vector in tri-directions of Y, Z.

A kind of rectangular planar shape error assessment parameter determination method towards assembling, its feature It is: the correlation analysis method described in step 5 is:

(1) correlation analysis process of the test

Change input parameter by orthogonal test, obtain organizing the data of characterization parameter and assembly precision more；Data are correlated with Property analyze；By the height correlation during relatively each coefficient obtains coefficient correlation as evaluating；

(2) characterization parameter and the correlation analysis of precision

The correlation analysis of each component and characterization parameter is set up based on each component calculating characterization parameter and the assembly precision obtained Formula, correlation analysis computing formula is

${\mathrm{\ρ}}_i=\frac{\mathrm{cov}(V,\mathrm{\Γ})}{\sqrt{D\left(V\right)}\·\sqrt{D\left(\mathrm{\Γ}\right)}},V=\[v_1,v_{2,}...,v_l\],\mathrm{\Γ}=\[d_x,d_y,d_z,{\mathrm{\δ}}_x,{\mathrm{\δ}}_y,{\mathrm{\δ}}_z\]---\left(5\right)$

Wherein V is expressed as representing characterization parameter, and l is characterization parameter number, and Γ represents assembly precision；By each coefficient of com-parison and analysis In height correlation as evaluating, i.e.

d_x∝[S₁,S₂,…,S_i] δ_x∝[S₁,S₂,…,S_m]

d_y∝[S₁,S₂,…,S_j], δ_y∝[S₁,S₂,…,S_n] (6)

d_z∝[S₁,S₁,…,S_k] δ_z∝[S₁,S₁,…,S_p]

In formula, S is corresponding evaluating, and i, j, k, m, n, p are the number of each component correspondence evaluating；

The one group of parameter inputted by change, generation has the Rough Horizontal Plane of certain plane pattern and can change, by putting down after reconstructing The parameter that face is extracted is also the most corresponding to be changed, and therefore can arbitrarily be organized data；Data are carried out correlation analysis；From characterizing ginseng According to correlation analysis in number, the size of coefficient correlation has reacted degree of correlation between variable, obtains relevant by relatively each coefficient Height correlation in coefficient (| ρ | " 0.6) as evaluating.