CN105868496B - A kind of rectangular planar shape error assessment parameter determination method towards assembly - Google Patents
A kind of rectangular planar shape error assessment parameter determination method towards assembly Download PDFInfo
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Abstract
The rectangular planar shape error assessment parameter determination method towards assembly that the present invention relates to a kind of, belongs to error assessment field.Machining surface is generated in non-gaussian plane simulation method first, form error surface is obtained with wavelet filtering, and extract the characterization parameter of surface shape error distribution；Form error surface is simulated by Contact Algorithm and is assembled, and calculate the assembly precision of the dimensional orientation variation of second part after assembly, the relationship of component assembly precision after Surface Characterization parameter and assembly is determined by correlation analysis, so that it is determined that form error evaluation parameter, realizes the quantitative description of surface distribution characterization parameter and assembly precision relationship.The plane characteristic parameter having a major impact to assembly precision is obtained, for the processing quality for improving cooperation plane, optimization assembly technology provides scientific basis to improve assembly precision.
Description
Technical field
The rectangular planar shape error assessment parameter determination method towards assembly that the present invention relates to a kind of, belongs to error assessment
Field.
Background technique
In the assembling process of China's precision mechanical system, components form error be influence assembly after components in complete machine
One of an important factor for middle relative positional accuracy.In Modern Manufacturing Industry, assembly work amount averagely accounts for manufacture amount of work
45%, assembly costs account for the 20-30% or higher of manufacture total cost.Processing, assembling link various factors (i.e. manufacturing characteristics) are right
The research of the Influencing Mechanism, coupled relation of system performance is increasingly becoming the hot spot studied both at home and abroad, and manufacture after assembly
A Main way in urgent need of strengthening in technical research.
Existing form error evaluation parameter is to be evaluated from mismachining tolerance angle mostly, and in this way usually
Can be there is a phenomenon where such, i.e., in the case where whole parts machinings are up-to-standard, assembly yield rate is but very low, produces after assembly
Moral character can be unable to satisfy design requirement, be difficult batch and come into operation.Main cause is to precision mechanical system assembly precision shadow
From the point of view of sound, the fitting plane with same shape error will produce assembly precision due to its different form error distribution
Raw entirely different influence.As depicted in figs. 1 and 2.Therefore how to reflect that influence of the surface shape error to assembly precision is exactly
One important research contents.However due to the complexity of three-dimensional surface, characterization parameter has very much, how to obtain and assemble essence
It is relatively difficult to spend related parameter.
Summary of the invention
The object of the present invention is to provide a kind of rectangular planar shape error assessment parameter determination method towards assembly, the party
Method obtains the plane characteristic parameter having a major impact to assembly precision, for the processing quality for improving cooperation plane, improves assembly essence
Degree provides foundation.
The purpose of the present invention is what is be achieved through the following technical solutions.
A kind of rectangular planar shape error assessment parameter determination method towards assembly, the specific steps are as follows:
Step 1: the form error of piece surface is obtained by following methods: with the generation of non-gaussian plane simulation method
Machining surface, wavelet filtering obtains form error surface later；Using orthogonal experiment design method, pass through orthogonal arrage arrangement
Thus multiple influence factors obtain multiple groups form error surface.
Step 2: the characterization parameter for the form error surface shape error distribution that extraction step one obtains；
Step 3: the form error surface that step 1 obtains is carried out simulation assembly with ideal surfaced；
(1) highest point is searched for, as first contact point；
(2) four vertex in first contact point and rectangle are connected to form four planar deltas；
(3) calculate point of the rectangle plane in each planar delta drop shadow spread and first contact point is wired to corresponding three
The angle of angle plane takes the angle minimum for being wired to planar delta put in corresponding planar delta drop shadow spread with first contact point
Point, as the second contact point, i.e., around highest point to four direction rotate, the point touched at first be the smallest point of angle.Four
Four the second contact points can be obtained in a planar delta；
(4) planar delta is gone to the second contact point around highest point, forms median surface；
(5) using the line of highest point and the second contact point as axis, third contact point is found in rotation.In search rectangular plane
The vertical line of third contact point and the line by highest point and the second contact point was made in third contact point；Calculate third contact point
Vertical line and angle by median surface, point corresponding to angle minimum is third contact point, and same four triangular facets can be found
Four third contact points；
(6) first contact point, the second contact point and third contact point are connected and obtains the equation of four contact surfaces；
(7) consider other constraint conditions, the positional relationship of line of force and contact point is such as assembled, thus from four contact surfaces
Screening one is optimal in equation.
Step 4: being assembled the assembly precision of the dimensional orientation variation of part after calculating assembly；Assembly precision is characterized as filling
It is assembled spatial position of the part plane relative to Norm part plane after matching, assembly precision is with six of part space after assembling
Freedom degree is measured:
Γ=[dx,dy,dz,δx,δy,δz] (1)
Wherein dx,dy,dzFor X, the offset in tri- directions Y, Z；δx,δy,δzFor around the rotation amount of three axis.
Step 5: the relationship of the characterization parameter of step 2 and the assembly precision of step 4 is determined by correlation analysis, thus
It determines form error evaluation parameter, realizes the quantitative description of surface distribution characterization parameter and assembly precision relationship.
The method for generating machining surface described in step 1 in non-gaussian plane simulation method are as follows: by giving plane
Auto-correlation function R and power spectral density Gz(ωx,ωy), obtain system transter H (ωx,ωy), it is converted using Johnson
System obtains the random column η ' with the non-gaussian distribution of certain deflection and kurtosis, and it is coarse flat that non-gaussian is generated using computer
Face.
The method that form error surface is obtained with wavelet filtering described in step 1 are as follows: wavelet analysis is used, using basic function
Bior6.8 carries out multiple dimensioned separation as the wavelet basis function decomposed, to the characteristic information of part plane pattern, isolates shape
Error plane.
The method of Orthogonal Experiment and Design described in step 1 are as follows: use orthogonal experiment, six influence factors of orthogonal test
Respectively mean height of surface mu, the standard deviation sd of apparent height, the auto-correlation length bx in the surface direction x, the surface direction y from
Correlation length by, the degree of skewness skew on surface, surface kurtosis kurt, select typical Orthogonal table analyzed, determine test time
Number.Orthogonal test scheme table is worked out, and then multiple groups form error surface can be obtained.
Characterization parameter described in step 2 are as follows: range parameter, spatial parameter, functional parameter and hybrid parameter；
Other constraint conditions described in step 3 are as follows: be assembled in part center of gravity and the positional relationship and plane of contact point and own
The positional relationship of the value zi of point and point z on ideal plane.
The positional relationship for being assembled part center of gravity and contact point, which should meet, is assembled part center of gravity among three contact points.
The positional relationship of point z should meet all z values and be respectively less than zi on the value zi of all the points and ideal plane in plane, see formula 3, then say
Bright three at this time contact point is one group of potential contact point.Three contact points are determined by constraint condition.Three obtained contact point
For P (x1,y1,z1),Q(x2,y2,z2),R(x3,y3,z3) then equation are as follows:
That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, thus to obtain.
The assembly precision of the dimensional orientation variation of part is assembled after calculating assembly described in step 4: after contact condition determines
The differential motion variation for being assembled part relative to Norm part can be calculated, by the available ideal plane in three contact points
Equation Ax+By+Cz+D=0, it can obtain the variation of normal vector (A, B, C), and then three rotation (δ can be found outx,δy,δz),
There is plane equation that can find out the offset (d in tri- directions X, Y, Z compared with ideal planex,dy,dz), i.e., small rotation amount
With small translational movement.Three offsets are the changes in coordinates at two coordinate system centers to indicate；Three rotation amounts are by plane equation
Normal vector n=(A, B, C) is sought, and three rotations are shown in formula 4.
Wherein n=(A, B, C) is plane normal vector；ex,ey,ezFor X, the unit vector in tri- directions Y, Z.
Correlation analysis method described in step 5 are as follows:
(1) process is tested in correlation analysis
Change input parameter by orthogonal test, obtains the data of multiple groups characterization parameter and assembly precision；Data are carried out
Correlation analysis.It is obtained by comparing each coefficient highly relevant as evaluation parameter in related coefficient.
(2) correlation analysis of characterization parameter and precision
Characterization parameter based on calculating acquisition establishes the correlation of each component with characterization parameter with each component of assembly precision
Analytical formula, correlation analysis calculation formula are
Wherein V is expressed as indicating that characterization parameter, l are characterization parameter number, and Γ indicates assembly precision.It is more each by analyzing
It is highly relevant as evaluation parameter in coefficient, i.e.,
S is corresponding evaluation parameter in formula, and i, j, k, m, n, p are the number that each component corresponds to evaluation parameter.
By changing one group of parameter of input, generating, there is the Rough Horizontal Plane of certain plane pattern can change, after reconstructing
The parameter extracted of plane it is also just corresponding change, therefore available any group of data；Correlation analysis is carried out to data.From table
It levies in parameter according to correlation analysis, the size of related coefficient has reacted degree of correlation between variable, obtains by comparing each coefficient
Highly relevant (| ρ | " 0.6) in related coefficient is used as evaluation parameter.
Beneficial effect
Assembly is evaluated by considering the distribution of form error, determines the evaluation ginseng of the flat form error towards assembly
Number realizes the characterization parameter of surface shape error distribution and the quantitative description of assembly precision relationship, that is, obtaining has assembly precision
The plane characteristic parameter of great influence, for the processing quality for improving cooperation plane, optimization assembly technology is to improve assembly precision
Scientific basis is provided.
Detailed description of the invention
Fig. 1 is the different distributions of same shape error delta；
Fig. 2 is the caused rigging error of different shape error distribution；
Fig. 3 is general frame figure；
Fig. 4 is assembly simulation flow chart；
Fig. 5 is the contact condition of plane.
Specific embodiment
The invention will be further described with embodiment with reference to the accompanying drawing.
Embodiment 1
A kind of rectangular planar shape error assessment parameter determination method towards assembly, as shown in figure 3, specific steps are such as
Under:
Step 1: the form error of piece surface is obtained by following methods, with the generation of non-gaussian plane simulation method
Machining surface, by the auto-correlation function R or power spectral density function G that give planez(ωx,ωy), obtain the biography of system
Delivery function H (ωx,ωy), the random column of the non-gaussian distribution with certain deflection and kurtosis is obtained using Johnson converting system
η ' generates non-gaussian Rough Horizontal Plane using computer.Wavelet filtering obtains form error surface later；Using wavelet analysis,
Using basic function Bior6.8 as the wavelet basis function decomposed, multiple dimensioned separation is carried out to the characteristic information of part plane pattern,
Isolate form error plane.Input parameter is shown in Table 1, using orthogonal experiment design method, arranges multiple influences by orthogonal arrage
Factor is shown in Table 2, and six influence factors of orthogonal test are respectively mean height of surface mu, the standard deviation sd of apparent height, surface
The auto-correlation length bx in the direction x, the auto-correlation length by the surface direction y, the degree of skewness skew on surface, surface kurtosis kurt,
Selection typical Orthogonal table is analyzed, and is shown in Table 3.It determines test number (TN) 25, works out orthogonal test scheme table, every group of carry out 50 times examination
It tests, and then 1250 groups of form error surfaces can be obtained.
Table 1 inputs parameter
2 orthogonal test factor level table of table
3 orthogonal test scheme table of table
Step 2: the characterization parameter for the form error surface shape error distribution that extraction step one obtains；The characterization ginseng
Number are as follows: range parameter, spatial parameter, functional parameter and hybrid parameter；
The following parameter of initial option is calculated, and see the table below 4:
4 characterization parameter table of table
Step 3: the form error surface that step 1 obtains is carried out simulation assembly with ideal surfaced；As shown in Figure 4.
(1) highest point is searched for, as first contact point；
(2) four vertex in first contact point and rectangle are connected to form four planar deltas；
(3) calculate point of the rectangle plane in each planar delta drop shadow spread and first contact point is wired to corresponding three
The angle of angle plane takes the angle minimum for being wired to planar delta put in corresponding planar delta drop shadow spread with first contact point
Point, as the second contact point, i.e., around highest point to four direction rotate, the point touched at first be the smallest point of angle.Four
Four the second contact points can be obtained in a planar delta；
(4) planar delta is gone to the second contact point around highest point, forms median surface；
(5) using the line of highest point and the second contact point as axis, third contact point is found in rotation.In search rectangular plane
The vertical line of third contact point and the line by highest point and the second contact point was made in third contact point；Calculate third contact point
Vertical line and angle by median surface, point corresponding to angle minimum is third contact point, and same four triangular facets can be found
Four third contact points；
(6) first contact point, the second contact point and third contact point are connected and obtains the equation of four contact surfaces；
(7) consider other constraint conditions, the positional relationship of line of force and contact point is such as assembled, thus from four contact surfaces
Screening one is optimal in equation.
Described in step 3: other described constraint conditions are as follows: be assembled the positional relationship and plane of part center of gravity and contact point
The positional relationship of the value zi of upper all the points and point z on ideal plane.
The positional relationship for being assembled part center of gravity and contact point, which should meet, is assembled part center of gravity among three contact points.
The positional relationship of point z should meet all z values and be respectively less than zi on the value zi of all the points and ideal plane in plane, see formula 3, then say
Bright three at this time contact point is one group of potential contact point.Three contact points are determined by constraint condition.Three obtained contact point
For P (x1,y1,z1),Q(x2,y2,z2),R(x3,y3,z3) then equation are as follows:
That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, thus to obtain.
Step 4: being assembled the assembly precision of the dimensional orientation variation of part after calculating assembly；Assembly precision is characterized as filling
It is assembled spatial position of the part plane relative to Norm part plane after matching, assembly precision is with six of part space after assembling
Freedom degree is measured.
Γ=[dx,dy,dz,δx,δy,δz] (1)
Wherein dx,dy,dzFor X, the offset in tri- directions Y, Z；δx,δy,δzFor around the rotation amount of three axis.
Described in step 4: only consider part six-freedom degree, based on above-mentioned contact condition determine after can calculate to
Assembly part changes relative to the differential motion of Norm part, by the available ideal plane equation Ax+By+Cz in three contact points
+ D=0, it can obtain the variation of normal vector (A, B, C), and then three rotation (δ can be found outx,δy,δz), there is plane equation
Offset (the d in tri- directions X, Y, Z can be found out compared with ideal planex,dy,dz), i.e., small rotation amount and small translation
Amount.Three offsets are the changes in coordinates at two coordinate system centers to indicate；Three rotation amounts by plane equation normal vector n=
(A, B, C) is sought, and three rotations are shown in formula 4.
Wherein n=(A, B, C) is plane normal vector；ex,ey,ezFor X, the unit vector in tri- directions Y, Z.
Step 5: determine the relationship of the characterization parameter of step 2 and the assembly precision of step 4 by correlation analysis, to obtaining
1250 groups of data taking carry out correlation analysis, the related coefficient of computational representation parameter and assembly precision, find out that correlation is big to be commented
Valence parameter, so that it is determined that form error evaluation parameter, realizes the quantitative description of surface distribution characterization parameter and assembly precision relationship.
Correlation analysis method described in step 5 are as follows:
(1) process is tested in correlation analysis
Change input parameter by orthogonal test, obtains the data of multiple groups characterization parameter and assembly precision；Data are carried out
Correlation analysis.It is obtained by comparing each coefficient highly relevant as evaluation parameter in related coefficient.
(2) correlation analysis of characterization parameter and precision
Characterization parameter based on calculating acquisition establishes the correlation of each component with characterization parameter with each component of assembly precision
Analytical formula, correlation analysis calculation formula are
Wherein V is expressed as indicating that characterization parameter, l are characterization parameter number, and Γ indicates assembly precision.It is more each by analyzing
It is highly relevant as evaluation parameter in coefficient, i.e.,
S is corresponding evaluation parameter in formula, and i, j, k, m, n, p are the number that each component corresponds to evaluation parameter.
By changing one group of parameter of input, generating, there is the Rough Horizontal Plane of certain plane pattern can change, after reconstructing
The parameter extracted of plane it is also just corresponding change, therefore available any group of data；Correlation analysis is carried out to data.From table
It levies in parameter according to correlation analysis, the size of related coefficient has reacted degree of correlation between variable, obtains by comparing each coefficient
Highly relevant (| ρ | " 0.6) in related coefficient is used as evaluation parameter.
The related coefficient of characterization parameter and assembly precision is shown in Table 5
5 correlation coefficient charts of table
From in table it follows that in ten given parameters, summit density SdsWith the rotation δ in the direction assembly precision x, yxWith
δyIt is related；Surface Root Mean Square deviation Sq, surface arithmetic average deviation Sa, ten point height Sz of surface, surface maximum height Sp, surface
Mean μ and surface variances sigma2With the direction assembly precision z offset dzIt is highly dependent.That is:
Claims (6)
1. a kind of rectangular planar shape error assessment parameter determination method towards assembly, it is characterised in that: specific step is as follows:
Step 1: the form error of piece surface is obtained by following methods: generating and cut in non-gaussian plane simulation method
Finished surface, wavelet filtering obtains form error surface later；Using orthogonal experiment design method, arranged by orthogonal arrage multiple
Thus influence factor obtains multiple groups form error surface；
Step 2: the characterization parameter for the form error surface shape error distribution that extraction step one obtains；
Step 3: the form error surface that step 1 obtains is carried out simulation assembly with ideal surfaced；
(1) highest point is searched for, as first contact point；
(2) four vertex in first contact point and rectangle are connected to form four planar deltas；
(3) point of the rectangle plane in each planar delta drop shadow spread is calculated to put down to the corresponding triangle that is wired to of first contact point
The angle in face takes point in corresponding planar delta drop shadow spread the smallest with the angle for being wired to planar delta of first contact point
Point is rotated around highest point to four direction as the second contact point, the point touched at first is the smallest point of angle；Four
Four the second contact points can be obtained in planar delta；
(4) planar delta is gone to the second contact point around highest point, forms median surface；
(5) using the line of highest point and the second contact point as axis, third contact point is found in rotation；Third in search rectangular plane
The vertical line of third contact point and the line by highest point and the second contact point was made in contact point；It is vertical to calculate third contact point
Line and angle by median surface, point corresponding to angle minimum is third contact point, and same four triangular facets can find four
Third contact point；
(6) first contact point, the second contact point and third contact point are connected and obtains the equation of four contact surfaces；
(7) consider the positional relationship of assembly line of force and contact point, that is, be assembled the positional relationship of part center of gravity and contact point
With the positional relationship of point z on the value zi of all the points in plane and ideal plane；To screen one from four contact surface equations
It is optimal；
The positional relationship for being assembled part center of gravity and contact point, which should meet, is assembled part center of gravity among three contact points；Plane
The positional relationship of the value zi of upper all the points and point z on ideal plane should meet all z values and be respectively less than zi, see formula 3, then illustrate this
When three contact points be one group of potential contact point；Three contact points are determined by constraint condition；Three obtained contact point is P
(x1,y1,z1),Q(x2,y2,z2),R(x3,y3,z3) then equation are as follows:
That is: Ax+By+Cz+D=0, A, B, C, D are equation coefficient, thus to obtain；
Wherein, x, y are the coordinate value of any point x-axis and y-axis in three-coordinate in space；xi,、yi, and ziIt is any one for space
The coordinate of point, i indicate at i-th point, and i takes natural number, as any point；
Step 4: being assembled the assembly precision of the dimensional orientation variation of part after calculating assembly；After assembly precision is characterized as assembly
It is assembled spatial position of the part plane relative to Norm part plane, assembly precision is with six freedom in part space after assembling
Degree is to measure:
Γ=[dx,dy,dz,δx,δy,δz] (1)
Wherein dx,dy,dzFor X, the offset in tri- directions Y, Z；δx,δy,δzFor around the rotation amount of three axis；
Step 5: the relationship of the characterization parameter of step 2 and the assembly precision of step 4 is determined by correlation analysis, so that it is determined that
Form error evaluation parameter realizes that surface distribution characterization parameter is retouched with quantifying for assembly precision relationship；
Correlation analysis method described in step 5 are as follows:
(1) process is tested in correlation analysis
Change input parameter by orthogonal test, obtains the data of multiple groups characterization parameter and assembly precision；Data are carried out related
Property analysis；It is obtained by comparing each coefficient highly relevant as evaluation parameter in related coefficient；
(2) correlation analysis of characterization parameter and precision
The correlation analysis of each component and characterization parameter is established based on each component for calculating the characterization parameter and assembly precision that obtain
Formula, correlation analysis calculation formula are
Wherein V is expressed as indicating characterization parameter, v1,v2,…,viI characterization parameter, v are arrived for 1iIndicate that i-th of characterization parameter, i take
It is not 0 natural number；L is characterization parameter number, and Γ indicates assembly precision；By analyzing the highly relevant work in more each coefficient
For evaluation parameter, i.e.,
S is corresponding evaluation parameter in formula, and i, j, k, m, n, p are the number that each component corresponds to evaluation parameter；
By changing one group of parameter of input, generating, there is the Rough Horizontal Plane of certain plane pattern can change, by flat after reconstructing
The parameter that face is extracted is also just corresponding to be changed, therefore available any group of data；Correlation analysis is carried out to data；Join from characterization
According to correlation analysis in number, the size of related coefficient has reacted degree of correlation between variable, obtains by comparing each coefficient related
It is highly relevant in coefficient, | ρ | " 0.6, as evaluation parameter；ρ, ρiIndicate that characterization parameter is related to each component of assembly precision
Coefficient.
2. a kind of rectangular planar shape error assessment parameter determination method towards assembly as described in claim 1, feature
Be: described in step 1 with non-gaussian plane simulation method generate machining surface method are as follows: by give plane from
Correlation function R and power spectral density Gz(ωx,ωy), obtain system transter H (ωx,ωy), system is converted using Johnson
System obtains having the random column η ' of the non-gaussian distribution of certain deflection and kurtosis, and it is coarse flat that non-gaussian is generated using computer
Face.
3. a kind of rectangular planar shape error assessment parameter determination method towards assembly as described in claim 1, feature
It is: the method that form error surface is obtained with wavelet filtering described in step 1 are as follows: wavelet analysis is used, using basic function
Bior6.8 carries out multiple dimensioned separation as the wavelet basis function decomposed, to the characteristic information of part plane pattern, isolates shape
Error plane.
4. a kind of rectangular planar shape error assessment parameter determination method towards assembly as described in claim 1, feature
It is: the method for Orthogonal Experiment and Design described in step 1 are as follows: use orthogonal experiment, six influence factors of orthogonal test are distinguished
For mean height of surface mu, the standard deviation sd of apparent height, the auto-correlation length bx in the surface direction x, the surface direction y auto-correlation
Length by, the degree of skewness skew on surface, surface kurtosis kurt, select typical Orthogonal table analyzed, determine test number (TN)；It compiles
Orthogonal test scheme table processed, and then multiple groups form error surface can be obtained.
5. a kind of rectangular planar shape error assessment parameter determination method towards assembly as described in claim 1, feature
It is: characterization parameter described in step 2 are as follows: range parameter, spatial parameter, functional parameter and hybrid parameter.
6. a kind of rectangular planar shape error assessment parameter determination method towards assembly as described in claim 1, feature
It is: is assembled the assembly precision of the dimensional orientation variation of part after calculating assembly described in step 4: after contact condition is determining i.e.
The differential motion variation for being assembled part relative to Norm part can be calculated, by the available ideal plane side in three contact points
Journey Ax+By+Cz+D=0, it can obtain the variation of normal vector (A, B, C), and then three rotation (δ can be found outx,δy,δz), have
Plane equation can find out the offset (d in X, Y, Z tri- directions compared with ideal planex,dy,dz), i.e., small rotation amount with
Small translational movement；Three offsets are the changes in coordinates at two coordinate system centers to indicate；Three rotation amounts by plane equation method
Vector n=(A, B, C) is sought, and three rotations are shown in formula 4；
Wherein n=(A, B, C) is plane normal vector；ex,ey,ezFor X, the unit vector in tri- directions Y, Z；
X, y, z are any point x-axis in three-coordinate in space, the coordinate value of y-axis and z-axis；A, B, C, D are equation coefficient.
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| CN109117460B (en) * | 2018-09-12 | 2021-05-07 | 大连理工大学 | Method for calculating rotor assembly axis deflection based on end jump measurement |
| CN110853134B (en) * | 2019-10-25 | 2022-02-11 | 西安交通大学 | Method for calculating contact state of assembly matching surface containing geometric errors |
| CN112179236B (en) * | 2020-09-24 | 2022-06-24 | 青岛科技大学 | Assembly-oriented plane assembly performance evaluation method based on minimum potential energy |
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