CN113884059A - Single-datum plane shaft hole part gradient evaluation method based on rank analysis - Google Patents

Abstract

The invention belongs to the field of precision metering and computer application, and relates to a method for evaluating hole shaft parts by combining rank analysis and measurement data, in particular to a method for quickly evaluating the inclination of a single reference plane based on rank analysis, which comprises the following steps of: 1: acquiring a reference plane measuring point set and a measured element point set, and establishing a characteristic row vector set and a state element set: 2: obtaining an initial key sequence number set; 3: establishing an analysis matrix and an analysis column vector; 4: performing rank analysis; 5: determining an optimizing direction; 6: solving new key points and updating coordinates of the measuring point set; 7: judging whether the evaluation of the reference elements meets the qualification conditions; 8: pre-positioning the point set of the measured elements; 9: updating the set of real-time state elements: 10: updating the key sequence number set of the measured elements; 11: establishing an analysis matrix and an analysis column vector; 12: performing rank analysis; 13: determining an optimizing direction; 14: solving new key points and updating coordinates of the measuring point set; 15: and (5) judging the qualification.

Description

Single-datum plane shaft hole part gradient evaluation method based on rank analysis

Technical Field

The invention belongs to the field of precision measurement and computer application, and particularly relates to a single-datum plane shaft hole part gradient evaluation method which is stable, rapid and simple in form and based on rank analysis.

Background

The size error and the shape and position error (short for shape error and position error) directly influence the product quality, the assembly and the service life of the product, and the method has important significance for quickly and accurately calculating the part error. The inclination error of the single-datum-plane shaft part refers to the diameter of the minimum circumscribed cylinder which forms a theoretical correct angle with a datum plane and contains the axis of the measured shaft part.

First, a specialized geometric assessment method. The diameter of the minimum circumscribed cylinder which meets the definition and/or discrimination conditions of national standard and ISO standard is gradually searched by utilizing the geometric properties of the cylinder and according to the translation and deformation strategies of the circumscribed cylinder. The method has high speed, but the form of the mathematical model is complex and is not easy to popularize.

Second, convex hull or convex hull-like evaluation methods. And constructing a convex hull or a similar convex hull by using the properties of the convex hull, acquiring effective measurement data, reducing the scale of the data to be evaluated, and finally acquiring the diameter of the minimum circumscribed cylinder meeting the definition and/or judgment conditions of the national standard and the ISO standard by using an enumeration method. This type of approach has significant advantages when dealing with medium scale station data. Even when the data size is large, the data size can still be reduced by constructing the convex hull. However, the efficiency of such methods for direct assessment has been inadequate.

And in the third category, a linear or nonlinear target optimization function is constructed, optimization solution is carried out by adopting a common optimization method, and the optimization value of the target optimization function is taken as the diameter of the minimum circumscribed cylinder. The method is simple and easy to understand, and realizes a standard solution method in a plurality of software, so the method is easy to popularize. However, this type of method is generally inefficient because the geometric features of diameter assessment of the smallest circumscribing cylinder are not incorporated and the larger scale of data in the assessment task is not considered.

The fourth category, artificial intelligence/biological intelligence algorithms. The advantage of this type of method over the third type of method is to analyze the "objective function with complex gradient or no apparent analytic expression" and to find the "global optimum". The method also realizes standard solutions in a plurality of software at present, so the method is easy to popularize. Although these methods are relatively hot at present, they are not suitable for use in the diameter evaluation of the smallest circumscribed cylinder. This is because the gradient of the objective function for the diameter assessment of the minimum circumscribing cylinder is the sum of a large number of simple analytical expressions, and part errors are typically small. Therefore, the "local optimal value" of the objective function can be considered as the "global optimal value", and the fourth method has no obvious advantages over the third method.

The fifth category, active set methods. The active set method is a method specially used for processing large-scale planning problems and is characterized in that the processing of 'invalid constraint' is reduced as much as possible in the optimization process. When the method is applied to the diameter evaluation of the minimum circumscribed cylinder, the efficiency is equivalent to that of the first method, the algorithm maturity and the software integration are equivalent to that of the third method and the fourth method, and the method is a relatively quick and simple method for evaluating the diameter of the minimum inscribed cylinder at present. However, this method is very sensitive to initial values and does not always perform the geometric assessment task stably.

In summary, when the existing geometric evaluation method is applied to the inclination of the single-datum-plane axial hole type part, stability, quickness and simple form cannot be simultaneously considered.

Disclosure of Invention

The purpose of the invention is:

aiming at the problems in the prior art, the invention provides a single-datum plane axis hole part gradient error assessment method which is stable, quick and simple in form and is based on rank analysis of a hole axis part, and the assessment result can also provide guidance for improvement of a machining process.

The method can be used for evaluating the inclination of the gas jet hole on the pre-combustion chamber of the diesel engine.

The scheme adopted by the invention is as follows:

the method is used for evaluating the inclination of the single-datum-plane axial hole type part based on rank analysis on the basis that the datum plane is evaluated and qualified.

The single-datum-plane axial hole part gradient evaluation method based on rank analysis is realized through the following steps:

step 1: firstly, measuring points of a measured axis are obtained and are used to form a measuring point set p’ _j }; obtaining measuring points of a reference plane, and using the measuring points to form a reference measuring point set p _i }; wherein:

i=1, 2, 3, …, N；ithe serial numbers of the measuring points are shown,Nthe total number of measuring points as a benchmark;

p _i ={x _i , y _i , z _i is the measurement pointiThe reference plane is close to the XOY plane of the coordinate system;

j=1, 2, 3, …, M；ithe serial numbers of the measuring points are shown,Mthe total number of the measured points of the measured axis;

p’ _j ={x’ _j , y’ _j , z’ _j is the fitted axis measurement pointjThe axis of the space rectangular coordinate is close to form a theoretical correct angle theta with the XOY plane of the coordinate system;

then, obtain the initial key sequence numberl ₁Andl ₂will bel ₁Andl ₂adding key serial number setl}；

l ₁Is composed ofp _i Inz _j Point of maximum valuep _l1 The serial number of (a) is included,l ₂is composed ofp _i Inz _i Point of minimum valuep _l2 The serial number of (2);

then, the boundary position is setUAndB；

U=z _l1 ，z _l1 is composed ofp _l1 Z-coordinate value of (a);Uthe upper boundary position, which is the crossing point [0,U]and parallel to the XOY plane;

B=z _l2 ，z _l2 is composed ofp _l2 Z-coordinate value of (a);Bthe lower boundary position, the lower boundary being the crossing point [0,B]and parallel to the XOY plane;

then, obtaining a boundary middle position aver; aver = (a =)U+B)/2；

Finally, according to p _i Establishing a feature line vector set{A _i }; wherein:

for allz _i >Point of aver, whichA _i =[-1, -y _i , x _i ]; A _i Is a feature row vector, all feature row vectorsA _i Is a set of characteristic line vectors A _i }；

After step 1, step 2 is performed.

Step 2: according to p _i Establishing a reference state element setu _i And _i }；

u _i = U – z _i ；u _i The distance from the reference measuring point to the upper boundary;

d _i =z _i - B；d _i the distance from the reference measuring point to the lower boundary;

step 3 is carried out after step 2 is finished;

and step 3: according to the key sequence numberlEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:

A=[…, A _p ^T, …, A _q ^T, …]^Tis aeA matrix of rows and 4 columns,eis a critical sequence number setlThe number of the elements in the (C),p, qis a critical sequence number setlThe elements in (1);

b=[…, b _p , …, b _q , …]^Tis aeA column vector of rows;

after step 3, step 4 is performed.

And 4, step 4: for analysis matrixAAnd an augmented analysis matrixA, b]Performing rank analysis;

computing an analysis matrixARank ofr _A =rank(A) Extended analysis matrix [ alpha ], [ beta ] anA, b]Rank ofr _Ab =rank（[A, b]) And comparer _A Andr _Ab there are only two cases:

the first condition is as follows: if it is notr _A =r _Ab Then, the optimization should be continued, jumping to step 5;

case two: if it is notr _A < r _Ab Then, initializing the calculatorr=1, and step 4.1 is performed;

step 4.1: making key serial number collect lastlGet rid of the firstrAn elementl _r Then obtain l _s According to l _s Establishment of a reduction matrixA _s And reducing the column vectorb _s Wherein:

iis 1;

A _s =[…, A _p ^T, …, A _q ^T, …]^Tis a matrix of S rows and 4 columns, and S is a l _s The number of the elements in the (C),p, qis al _s The elements in (1);

b=[…, b _p , …, b _q , …]^Tis a column vector of S rows;

step 4.2: solving linear equationsA _s v _s = b _s Solution of (2)v _s =v _s0 Then calculateb _i =A _s v _s (ii) a If it is notb _i >b _s Then the matrix will be reducedA _s And reducing the column vectorb _s Respectively asAMatrix and analysis column vectorbAn element k _i Movable key serial number setkAnd jumping to the step 5; if it is notb _i <=b _s Then step 4.3 is performed;

step 4.3: judgment ofiWhether the number is equal to S +1, ifiThe number is less thanS+1, jumping to step 4; if it is notiThe number is equal toS+1, should finish the optimization, jump to step 7;

and 5: motion vector of measuring point is solvedv ₀I.e. linear equationsAv= bA solution ofv=v ₀Wherein, in the step (A),v=[v ₁, v ₂, v ₃]^T，v ₀=[v _0,1, v _0,2, v _0,3]^T；

after step 5, step 6 is performed.

Step 6: finding new key point by tracing problemp’ _j Anp _i Updating is carried out;

first, a relative velocity of each reference point and a boundary is calculatedv _i }：v _i = A _i v ₀ ；

Then, the time of pursuit is calculatedτ _i ；

τ _{i 1}= u _i / v _i | _{i N=1, 2, …}；τ’ _i Catch up points for upper boundariesp _i The time of (d);

τ _{i 2}= d _i / v _i | _{i N=1, 2, …}；τ’’ _i catch up a point for the lower boundaryp _i The time of (d);

τ _i getτ _i1、τ _i2The smaller of these;

then, the decision key point: to catch up timeτ _i Minimum value in the part of greater than zeroτ _minThe corresponding measuring points are key pointsp _l3The serial number corresponding to the pointl ₂Adding key serial number setl}；

Then, according top _i =τ _min∙ v ₁ ∙p _i +τ _min∙v ₂Updating reference measuring point setp _i }，

，v ₂=[0, 0, v _0,1]^T；

Then, according top ^, _j =τ _min∙ v ₁ ∙ p ^, _j +τ _min∙ v ₂Updating measured axis point set p ^, _j }；

Finally, according toU= U-τ _min∙bUpdating upper boundary positionsU(ii) a According toB= B+τ _min∙bUpdating upper boundary positionsB；

And 6, finishing one-time optimization after the step 6 is finished, and performing the step 2.

And 7: the effective size of the reference plane isU-BIf, ifU-B<t₁Then the reference plane meets the flatness requirements. Wherein, t₁Is a flatness tolerance value;

step 7 is over, ifU-B<t₁Then step 8 is performed to evaluate the inclination of the measured axis.

And 8: first, the corresponding measured axis measuring point set is evaluated by the fitting standard p’ _j }={x’ _j , y’ _j , z’ _j Determining the position w and direction vector of the fitted straight lineL(ii) a Wherein:

then calculating the position coordinate w of the minimum circumscribed cylindrical axis; wherein:

w=[ x _w , y _w , 0]^T，wfitting the intersection point of the straight line and the XOY plane for the measured point set by a least square method;

the direction vector isL=[x _L ,y _L ,z _L ]^T, x _L 、y _L 、z _L Satisfy the requirement of

；

Then, establishing a parameter describing the position of the minimum circumscribed cylinder axisa _wj And direction parametera _LWherein:

a _wj =L ^T（p’ _j -w），a _L,=L ^T L；

then according to p’ _j Anda _wj 、a _Lestablishing a feature line vector setA’ _j Great Chinese character and state element sett’ _j }; wherein:

all state elementst’ _j Is a set of state elements t’ _j }; catching pocket for state elementt’ _j Maximum value of }t’ _jmax =D’，D' is the distance dimension from the minimum circumscribed cylinder boundary to the minimum circumscribed cylinder axis;

establishingA’ _j A feature row vector, wherein

All feature row vectorsA’ _j Set as a set of feature line vectors{ A’ _j }；

After step 8, step 9 is performed.

And step 9: not performing step 14, taking a set of state elementst’ _j Maximum value of }t’ _jmax Corresponding measuring pointp’ _j Is a key point, and adds the measuring point serial number j to a key point set l' in, a set of key points l’}={j}；

If step 14 is performed, a keypoint is generatedp’ _l2 Then, the key pointp’ _l2 Will replace the measuring pointp’ _j Number of its measuring pointl’₂Last page added to key serial number set l' } in;

after step 9, performing step 10;

step 10: according to the key sequence number l' } establishing analysis matrixA' sum analysis column vectorb', wherein:

A’=[…, A’ _p ^T, …, A’ _q ^T, …]^Tis a matrix with f rows and 6 columns, and f is a key sequence number set lThe number of the elements in the' },p, qis a critical sequence number set l' } elements;

b’=[…, b’ _p , …, b’ _q , …]^Tis a column vector of f rows;

after step 10, step 11 is performed.

Step 11: for analysis matrixA' and extended analysis matrixA’, b’]Performing rank analysis;

computing an analysis matrixARank of `r _A =rank(A ^，) Extended analysis matrix [ alpha ], [ beta ] anA’, b’]Rank ofr _Ab =rank（[A’,b’]) And comparer _A Andr _Ab there are only two cases:

the first condition is as follows: if it is notr _A =r _Ab Then, the optimization should be continued, jumping to step 12;

case two: if it is notr _A < r _Ab Then, initializing the calculatorr=1, perform step 11.1;

step 11.1: making key serial number collect last l' take turns to remove the elements in the key sequence number setl’ _r Then obtain l’ _s According to l’ _s Establishment of a reduction matrixA’ _s And reducing the column vectorb’ _s Wherein:

jis 1;

A’ _s =[…, A’ _p ^T, …, A’ _q ^T, …]^Tis a matrix of S rows and 6 columns, and S is a l’ _s The number of the elements in the (C),p, qis a l’ _s The elements in (1);

b’=[…, b’ _p , …, b’ _q , …]^Tthis is the column vector for S rows, and step 11.2 is performed.

Step 11.2: solving linear equationsA’ _s v’ _s =b’ _s Solution of (2)v’ _s = v’ _s0 Then calculateb’ _j = A’ _s v’ _s ；

If it is notb’ _j > b’ _s Then the matrix will be reducedA’ _s And reducing the column vectorb’ _s Respectively asA' matrix and analysis column vectorb', will elementl’ _j Movable key serial number set l' }, and jump to step 11; if it is notb’ _j <= b’ _s Then step 11.3 is performed.

Step 11.3: judgment ofjWhether or not the number ofEqual to S +1, ifjIs not equal toS+1, jumping to step 11; if it is notjIs equal toS+1, the seek should be ended, jumping to step 15.

Step 12: motion vector of measuring point and boundary is solvedv’₀I.e. linear equationsA’v’= bA solution ofv’= v’₀Wherein, in the step (A),v’=[v’₁, v’₂, v’₃, v’₄, v’₅, v’₆]^T， v’₀=[ v’_0,1, v’ _0,2, v’ _0,3, v’ _0,4, v’ _0,5, v’_0,6]^T；

after step 12, step 13 is performed.

Step 13: finding new key point by tracing problemt’ _j }、D’，{A’ _j Updating is carried out;

first, calculating the relative speed between each measuring point and the boundaryv’ _i }：v’ _i = A’ _j v’ ₀ ；

Then, the time of pursuit of each measurement point is calculatedτ’ _j ，τ’ _j =(D’–t’ _j )÷(b’ _i – v’ _i ) | _{i N=1, 2, …}；

Then, the decision key point: to catch up timeτ’ _i Minimum value in the part of greater than zeroτ ^， _minCorresponding measuring pointp’ _j Is a key point;

then, according top’ _j = p’ _j +τ’_min∙v’ _m Updating measuring point setp’ _j }, wherein:

；

finally, according to w = w +τ’_min∙v’ _g Updating w, wherein:

；

at updated measuring point setp’ _i Updating said leaf on the basis oft’ _j }、D’，{A’ _j }；

And finishing one optimization after the step 14 is finished, and performing the step 9.

Step 15: at this time, the effective size of the measured axis isD', ifD’<t', the measured axis meets the requirement of gradient, and the measured axis is qualified; otherwise, the product is not qualified. Wherein t' is a gradient tolerance value.

Conveniently obtaining the measuring point set in step 1p’ _j A general measurement data can be preparedp _j A set of measuring points whose axes meet at a theoretically correct angle θ to the XOY plane of the coordinate system and whose intersection points are close to the origin of the coordinate system, is obtained by processingp _j }: firstly, moving according to the average value of coordinates; moving according to the extreme value of the coordinate; thirdly, moving according to the root-mean-square minimum principle of coordinates; and fourthly, obtaining data after the first measured element is evaluated as the data obtained after pre-positioning.

In step 14, ifτ’_min∙ v’ _i Single order value ofτ’_min∙ v’ _i Or accumulated value sigma of past iterationsτ’_min∙ v’ _i Greater than a given thresholdQThen, measuring point of the measured segmentp’ _j Is updated top’ _j | _{j N= 1, 2, …} +∑τ _min∙v’ _m And reassessed from step 9.

To facilitate numerical calculation, can makebAndb' takes a specific value greater than 0, and may be, but is not limited to, 1.

The invention has the beneficial effects that:

1. the geometrical characteristics of the inclination of the single-datum-plane shaft hole type part are fully considered, and the evaluation form is simplified, so that the method is easier to popularize than the first type of evaluation method. 2. The geometric characteristics of the inclination of the single-datum plane shaft hole type part are fully considered, a better value is obtained through mature linear operation in each iteration, and the minimum limit equivalent size can be finally obtained, so that the algorithm is stable, and the problem of initial value sensitivity of the fifth method does not exist. 3. The fact that most of the measuring points are invalid measuring points in the evaluation of the inclination of the single-datum-plane axial hole type part is implied, and the invalid measuring points are not added with iteration, so that the iteration times of the method are fewer and are equivalent to the first type evaluation method and the fifth type evaluation method. 4. Calculating the optimizing direction by considering only the keypoint setlAnd (4) corresponding measuring points, so that the operation amount of each iteration is small, and the method is equivalent to the fifth type evaluation method. 5. Because the iteration times are less and the operation amount of each iteration is less, the total operation speed is equivalent to the first type evaluation method and the fifth type evaluation method.

The invention provides a single datum plane shaft hole part gradient evaluation method based on rank analysis, which is stable, rapid and simple in form, can be used for evaluating a shaft hole part with a single datum plane gradient, and provides guidance for improvement of a machining process of the shaft hole part, so that the method has industrial possibility.

Drawings

FIG. 1 is a benchmarking flowchart A of the present invention.

FIG. 2 is a measured axis evaluation flow chart B of the present invention.

FIG. 3 is a tolerance layout for parts in an exemplary embodiment.

Detailed Description

The following are specific embodiments of the present invention, and the scheme of the present invention will be further described with reference to fig. 1 and 2, but the present invention is not limited to these examples.

The inclination of a hole shaft part based on a single datum plane is evaluated, and the tolerance design specification is shown in figure 2.

Step 1: measuring point set for obtaining reference planep _i Great square and measuring point set for obtaining measured axisp’ _j The method comprises the following steps:

the initial key serial numbers at this time are 2 and 4;

upper boundary position at this timeUIs z₂=0.01617, lower boundBIs z₄=-0.02328；

Obtaining a boundary middle position aver = -0.0036;

establishing a feature line vector setA _i The method comprises the following steps:

after step 1, step 2 is performed.

Step 2: according top _i Establishing a reference state element setu _i }：

According top _i Establishing a reference state element setd _i }：

After step 2, step 3 is performed.

And step 3:

，b=[1,1] ^T；

after step 3, step 4 is performed.

And 4, step 4:r _A =rank(A) =2，r _Ab =rank（[A, b]）=2，r _A =r _Ab and jumping to the step 5.

And 5: linear equation of equationsAv= bIs thatv=v ₀ =[0, -0.1449, -0.0110]^T；

After step 5, step 6 is performed.

Step 6: firstly, calculating the normal linear velocity of the measuring pointv _i ，v _i =A _i v ₀The results are as follows:

then, the minimum tracking time of each measuring point is calculatedτ _i And deciding a key point: to catch up timeτ _i Minimum value in the part of greater than zeroτ _minMeasured point corresponding to =0.000368 as key pointp ₁；

Finally, updating measuring point set p _i Anp’ _j As follows:

updating upper boundary positionsU= 0.0158, update lower bound locationB=0.0229。

And 6, finishing the first optimization of the benchmark evaluation after the step 6 is finished, and performing the step 2.

By analogy, after the sixth optimization of benchmark evaluation is completed according to the invention, the critical sequence number set is a final pagel} = {2, 1,14, 6}, step 6 gets the new key point asp’ ₆。

Measuring point set updated after sixth optimization p _i Anp’ _j As follows:

starting to perform 7 th optimization and updating the upper boundary positionU= 0.0148, updating the lower boundary positionB=-0.0219；

Step 6, ending and carrying out step 2;

step 2: according top _i Establishing a reference state element setu _i }：

According top _i Establishing a reference state element setd _i }：

After step 2, step 3 is performed.

And step 3:

，b=[1, 1, 1, 1] ^T；

after step 3, step 4 is performed.

And 4, step 4:r _A =rank(A) =3，r _Ab =rank（[A, b]）=4，r _A ≠r _Ab step 4.1 is performed.

Step 4.1: the key sequence number set {2, 1,14, 6} is made to get {2, 1,14, 6} after the 1 st element 2 is removed, and a reduced matrix is established according to {1, 14,6}A ₃ And reducing the column vectorb ₃ Respectively is as follows:

A ₃=[ A ₁ ^T, A ₁₄ ^T, A ₆ ^T]^T =

，b ₃=[1,1,1] ^T。

step 4.2: linear equation of equationsA ₃ v ₃ = b ₃ Solution of (2)v ₃ =[-0.6916，-0.3378，-0.1283]Then calculateb ₂ =A ₂ v ₃ = -2.1001<1；

Then, the 2 nd element 1 is removed to obtain {2, 14,6}, and a reduced matrix is built according to {2, 14,6}A _s And reducing the column vectorb _s Respectively is as follows:

A _s=[ A ₂ ^T, A ₁₄ ^T, A ₆ ^T]^T =

，b _s=[1,1,1] ^T。

step 4.2: linear equation of equationsA ₃ v ₃ = b _s Solution of (2)v ₃ =[-0.2094，-0.0824，-0.2203]Then calculateb ₁ =A ₁ v ₃ = -1.4573<1；

Then, the 3 rd element 14 is removed to obtain {2, 1,6}, and a reduced matrix is built according to {2, 1,6}A ₃ And reducing the column vectorb ₃ Respectively is as follows:

A ₃=[ A ₂ ^T, A ₁ ^T, A ₆ ^T]^T =

，b ₃=[1,1,1] ^T。

step 4.2: linear equation of equationsA ₃ v ₃ = b ₃ Solution of (2)v ₃ =[-0.2094，-0.0824，-0.2203]Then calculateb ₁₄ =A ₁₄ v ₃ = -9.7465<1；

Then, the 4 th element 6 is removed to obtain {2, 1,14}, and a reduced matrix is built according to {2, 1,14}A ₃ And reducing the column vectorb ₃ Respectively is as follows:

A ₃=[ A ₂ ^T, A ₁ ^T, A ₁₄ ^T]^T =

，b ₃=[1,1,1] ^T。

step 4.2: linear equation of equationsA _s v _s = b _s Solution of (2)v _s =[-0.2094，-0.0824，-0.2203]Then calculateb ₁₄ =A ₁₄ v ₃ = -4.6362<1；

And 4.2, ending the step and carrying out a step 4.3.

Step 4.3:b _i <the number of i in 1 is 4= S +1=3+1, and the optimization end jumps to step 7.

And 7: the effective size of the reference plane isU-B=0.0367< t₁And (5) the flatness requirement is met by = 0.05.

After step 7, step 8 is performed.

And 8:

primary evaluated measured element p _j And after pre-positioning:

the direction vector is L = [0,1 ]]^T, w=[0.0074,-0.0152, 0]^TInitial state collectiont’ _j The method comprises the following steps:

D’=0.0314；

establishing a feature line vector setA _j The method comprises the following steps:

after step 8, step 9 is performed.

And step 9: not performing step 14, taking a set of state elementst _j Maximum value of }t’ _jmax =0.0314 corresponding measuring pointp’₅Is a key point, and adds the measuring point serial number 5 to the key point set l' in, a set of key points l’}={5}；

After step 9, step 10 is performed.

Step 10: according to the key sequence number l' } establishing analysis matrixA' sum analysis column vectorb', wherein:

A’==[ A’₅ ^T]^T =[-0.06251,-0.2535,2.5136,0.6251, 0.2535, -2.5136], b’=[1];

after step 10, step 11 is performed.

Step 11:r _A =rank(A’) =1，r _Ab =rank（[A’, b’]）=1，r _A =r _Ab and a jump is made to step 12.

Step 12: linear equation of equationsA’v’= bOne solution to' isv’=v’₀ =[-0.0461，-0.0187，0.1856，0.0461，0.0187，-0.1856]^T；

After step 12, step 13 is performed.

Step 13: finding new key point by tracing problemt’ _j }、D’，{A’ _j Updating is carried out;

first, each measurement is calculatedRelative velocity between a point and a boundaryv’ _i }：v’ _i

Then, calculateτ’ _j =(D’–t’ _j )÷(b’ _i – v’ _i ) = (0.0314–t _j )÷(1– v _j ) | _{j=1, 2, …15}；

Then, the decision key point: to catch time τ'_iMinimum value τ in the portion of greater than zero^， _minCorresponding measurement point p'₁₁Is a key point; after that, there are no conditions to change the key points:

then, all oft’ _j The updating is as follows:

Dupdate to 0.0276;

updating leafA’ _j The method is as follows:

and finishing the first optimization after the step 14 is finished, and performing the step 9.

And step 9: after the first optimization is completed according to the invention, the key point setl' } = {5,11}, step 10 is performed.

Step 10:

A’=[ A’₅ ^T, A’₁₁ ^T]^T=

，

b=[1,1] ^T；

after step 10, step 11 is performed.

Step 11:r _A =rank(A’) =2，r _Ab =rank（[A’, b’]）=2，r _A =r _Ab and a jump is made to step 12.

Step 12: linear equation of equationsA’v’= bOne solution to' isv’=v’₀ =[-0.6035，-1.3086，-0.0783，0.6035，1.3086，-0.0783]^T；

After step 12, step 13 is performed.

Step 13: updating the last page by finding new key pointst’ _j }、D’，{A’ _j }；

Firstly, calculating the normal linear velocity of the measuring pointv’ _j ：

Then, calculateτ’ _j =(D’–t’ _j )÷(b’ _i – v’ _i )= (0.0276––t’ _j )÷(1– v’ _i ) | _{j=1, 2, …15}；

Then, the decision key point: to catch up timeτ’ _i Minimum value in the part of greater than zeroτ ^， _minCorresponding measuring pointp’ ₃ Is a key point;

finally, all thet’ _j The updating is as follows:

Dupdate to 0.0271;

{A’ _j the' update is:

and finishing one optimization after the step 14 is finished, and performing the step 9.

And step 9: after the third optimization is completed according to the invention, the key point setl' } = {5,11,3}, step 10 is performed.

Step 10:

A’=[ A’₅ ^T, A’₁₁ ^T,A’₃ ^T]^T=

，b=[1,1,1] ^T；

after step 10, step 11 is performed.

Step 11:r _A =rank(A) =3，r _Ab =rank（[A, b]）=3，r _A =r _Ab and a jump is made to step 12.

Step 12: linear equation of equationsA’v’= bThe solution of isv’=v’₀ =[-1.0968，-1.0439，-0.1698，1.0968，1.0439，0.1698]^T；

After step 12, step 13 is performed.

Step 13: finding new key point by tracing problemt’ _j }、D’，{A’ _j Updating is carried out;

firstly, calculating the normal linear velocity of the measuring pointv’ _j ：

Then, calculateτ’ _j =(D’–t’ _j )÷(b’ _i – v’ _i )= (0.0271–t’ _j )÷(b’ _i – v’ _i ) | _{j=1, 2, …15}；

Then, the decision key point: time of optional pursuitτ _j Minimum value in the part of greater than zeroτ _miCorresponding measuring pointp ₆Is a key point;

finally, all thet’ _j The updating is as follows:

D' update to 0.0248;

{A’ _j the update is:

and finishing the third optimization after the step 14 is finished, and performing the step 9.

And step 9: after the third optimization is completed according to the invention, the key point set l' } = {5,11,3,6 }; step 10 is performed.

Step 10:

A’=[A’₅ ^T, A’₁₁ ^T, A’₃ ^T, A’₆ ^T]^T

，b’=[1,1,1,1] ^T；

after step 10, step 11 is performed.

Step 11:r _A =rank(A’) =3，r _Ab =rank（[A’, b’]）=4，r _A <r _Ab jump to step 11.1.

Step 11.1: the key sequence number set {5,11,3,6} is obtained by removing the elements 5,11,3,6 in the key sequence number set in turnTol’ _s According to l’ _s Establishment of a reduction matrixA’ ₃ And reducing the column vectorb’ ₃ ；

Remove 5 to get the reduced matrixA’ ₃ And reducing the column vectorb’ ₃ The following were used:

A’₃=[ A’₁₁ ^T, A’₃ ^T, A’₆ ^T]^T

，b’₃=[1,1,1] ^Tand (6) performing step 11.2;

step 11.2: solving linear equationsA’₃ v’₃=b’₃Solution of (2)v’₃=

Then calculateb’₅= A’₅ v’₃=-2.5174<1;

Removing 11 yields a reduced matrixA’ ₃ And reducing the column vectorb’ ₃ The following were used:

A’₃=[ A’₅ ^T, A’₃ ^T, A’₆ ^T]^T=

，b’₃=[1,1,1] ^Tand (6) performing step 11.2;

step 11.2: solving linear equationsA’₃ v’₃=b’₃Solution of (2)v’ ₃ =

Then calculateb’₁₁= A’₁₁ v’₃=-6.2648<1;

Remove 3 to get the reduced matrixA’ ₃ And reducing the column vectorb’ ₃ The following were used:

A’₃=[ A’₅ ^T, A’₁₁ ^T, A’₆ ^T]^T=

，b’₃=[1,1,1] ^Tand (6) performing step 11.2;

step 11.2: solving linear equationsA’₃ v’₃=b’₃Solution of (2)v’ ₃ =

Then calculateb’₁₁= A’₁₁ v’₃=-2.1085<1;

Remove 6 to get the reduced matrixA’ ₃ And reducing the column vectorb’ ₃ The following were used:

A’₃=[ A’₅ ^T, A’₁₁ ^T, A’₃ ^T]^T=

，b’₃=[1,1,1] ^Tand (6) performing step 11.2;

step 11.2: solving linear equationsA’₃ v’₃=b’₃Solution of (2)v’ ₃ =

Then calculateb’₁₁= A’₁₁ v’₃=0.0470<1;

Step 11.3: satisfy the requirement ofb’ _j | _j=5,11,3,6<= b’ ₃ The number of j is 4= s +1=3+1, jump to step 15.

Step 15: at this time, the effective size of the measured axis isD’=0.0248，D’=0.0248<t' =0.03, the measured axis meets the inclination requirement, and the measured axis is qualified.

Claims (5)

1. A rank analysis-based fast and steady simple gradient assessment method is characterized by comprising the following steps of:

the method comprises the steps of evaluating the inclination of an axis on the basis of the evaluation of a reference plane and the qualification;

step 1: firstly, measuring points of a measured axis are obtained and are used to form a measuring point set p’ _j }; obtaining measuring points of a reference plane, and using the measuring points to form a reference measuring point set p _i }; wherein:

i=1, 2, 3, …, N；ithe serial numbers of the measuring points are shown,Nthe total number of measuring points as a benchmark;

p _i ={x _i , y _i , z _i is the measurement pointiThe reference plane is close to the XOY plane of the coordinate system;

j=1, 2, 3, …, M；ithe serial numbers of the measuring points are shown,Mthe total number of the measured points of the measured axis;

p’ _j ={x’ _j , y’ _j , z’ _j is the fitted axis measurement pointjThe axis of the space rectangular coordinate is close to form a theoretical correct angle theta with the XOY plane of the coordinate system;

then, obtain the initial key sequence numberl ₁Andl ₂will bel ₁Andl ₂adding key serial number setl}；

l ₁Is composed ofp _i Inz _j Point of maximum valuep _l1 The serial number of (a) is included,l ₂is composed ofp _i Inz _i Point of minimum valuep _l2 The serial number of (2);

then, the boundary position is setUAndB；

U=z _l1 ，z _l1 is composed ofp _l1 Z-coordinate value of (a);Uthe upper boundary position, which is the crossing point [0,U]and parallel to the XOY plane;

B=z _l2 ，z _l2 is composed ofp _l2 Z-coordinate value of (a);Bthe lower boundary position, the lower boundary being the crossing point [0,B]and parallel to the XOY plane;

then, obtaining a boundary middle position aver; aver = (a =)U+B)/2；

Finally, according top _i Establishing a characteristic line vector setA _i }; wherein:

for allz _i >Point of aver, whichA _i =[-1, -y _i , x _i ]For allz _i <Point of aver, whichA _i =[1, y _i , -x _i ]；A _i Is a feature row vector, all feature row vectorsA _i Is a set of characteristic line vectors A _i }；

After the step 1 is finished, performing a step 2;

step 2: according top _i Establishing a reference state element setu _i And _i }；

u _i = U – z _i ；u _i The distance from the reference measuring point to the upper boundary;

d _i =z _i - B；d _i the distance from the reference measuring point to the lower boundary;

step 3 is carried out after step 2 is finished;

and step 3: according to the key sequence numberlEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:

A=[…, A _p ^T, …, A _q ^T, …]^Tis aeA matrix of rows and 4 columns,eis a critical sequence number setlThe number of the elements in the (C),p, qis a critical sequence number setlThe elements in (1);

b=[…, b _p , …, b _q , …]^Tis aeA column vector of rows;

step 4 is carried out after step 3 is finished;

and 4, step 4: for analysis matrixAAnd an augmented analysis matrixA, b]Performing rank analysis;

computing an analysis matrixARank ofr _A =rank(A) Extended analysis matrix [ alpha ], [ beta ] anA, b]Rank ofr _Ab =rank（[A, b]) And comparer _A Andr _Ab there are only two cases:

the first condition is as follows: if it is notr _A =r _Ab Then, the optimization should be continued, jumping to step 5;

case two: if it is notr _A < r _Ab Then, initializing the calculatorr=1, and step 4.1 is performed;

step 4.1: making key serial number collect lastlGet rid of the firstrAn elementl _r Then obtain l _s According to l _s Establishment of a reduction matrixA _s And reducing the column vectorb _s Wherein:

iis 1;

A _s =[…, A _p ^T, …, A _q ^T, …]^Tis a matrix of S rows and 4 columns, and S is a l _s The number of the elements in the (C),p, qis al _s The elements in (1);

b=[…, b _p , …, b _q , …]^Tis a column vector of S rows;

step 4.2: solving linear equationsA _s v _s = b _s Solution of (2)v _s =v _s0 Then calculateb _i =A _s v _s (ii) a If it is notb _i >b _s Then the matrix will be reducedA _s And reducing the column vectorb _s Respectively asAMatrix and analysis column vectorbAn element k _i Movable key serial number setkAnd jumping to the step 5; if it is notb _i <=b _s Then step 4.3 is performed;

step 4.3: judgment ofiWhether the number is equal to S +1, ifiThe number is less thanS+1, jumping to step 4; if it is notiThe number is equal toS+1, should finish the optimization, jump to step 7;

and 5: motion vector of measuring point is solvedv ₀I.e. linear equationsAv= bA solution ofv=v ₀Wherein, in the step (A),v=[v ₁, v ₂, v ₃]^T，v ₀=[v _0,1, v _0,2, v _0,3]^T；

step 6 is carried out after step 5 is finished;

step 6: finding new key point by tracing problemp’ _j Anp _i Updating is carried out;

first, each reference point and edge are calculatedRelative speed of boundv _i }：v _i = A _i v ₀ ；

Then, the time of pursuit is calculatedτ _i ；

τ _{i 1}= u _i / v _i | _{i N=1, 2, …}；τ’ _i Catch up points for upper boundariesp _i The time of (d);

τ _{i 2}= d _i / v _i | _{i N=1, 2, …}；τ’’ _i catch up a point for the lower boundaryp _i The time of (d);

τ _i getτ _i1、τ _i2The smaller of these;

then, the decision key point: to catch up timeτ _i Minimum value in the part of greater than zeroτ _minThe corresponding measuring points are key pointsp _l3The serial number corresponding to the pointl ₂Adding key serial number setl}；

Then, according top _i =τ _min∙ v ₁ ∙p _i +τ _min∙v ₂Updating reference measuring point setp _i Therein of

，v ₂=[0, 0, v _0,1]^T；

Then, according top ^, _j =τ _min∙ v ₁ ∙ p ^, _j +τ _min∙ v ₂Updating measured axis point set p ^, _j }；

Finally, according toU= U-τ _min ∙bUpdating upper boundary positionsU(ii) a According toB= B+τ _min ∙bUpdating upper boundary positionsB；

Finishing one-time optimization after the step 6 is finished, and performing the step 2;

and 7: the effective size of the reference plane isU-BIf, ifU-B<t₁Then the reference plane meets the flatness requirement;

wherein, t₁Is a flatness tolerance value;

step 7 is over, ifU-B<t₁Then go to step 8;

and 8: first, the corresponding measured axis measuring point set is evaluated by the fitting standard p’ _j }={x’ _j , y’ _j , z’ _j Determining the position w and direction vector of the fitted straight lineL(ii) a Wherein:

then calculating the position coordinate w of the minimum circumscribed cylindrical axis; wherein:

w=[ x _w , y _w , 0]^T，wfitting the intersection point of the straight line and the XOY plane for the measured point set by a least square method;

the direction vector isL=[x _L ,y _L ,z _L ]^T, x _L 、y _L 、z _L Satisfy the requirement of

;

Then, establishing a parameter describing the position of the minimum circumscribed cylinder axisa _swj And direction parametera _LWherein:

a _wj =L ^T（p’ _j -w），a _L,=L ^T L；

then according to p’ _j Anda _wj 、a _Lestablishing a feature line vector setA’ _j Great Chinese character and state element sett’ _j }; wherein:

all state elementst’ _j Is a set of state elements t’ _j }; catching pocket for state elementt’ _j Maximum value of }t’ _jmax =D’，D' is the distance dimension from the minimum circumscribed cylinder boundary to the minimum circumscribed cylinder axis;

establishingA’ _j A feature row vector, wherein

All feature row vectorsA’ _j Set as characteristic line vector set A’ _j }；

Step 9 is performed after step 8 is completed;

and step 9: not performing step 14, taking a set of state elementst’ _j Maximum value of }t’ _jmax Corresponding measuring pointp’ _j Is a key point, and adds the measuring point serial number j to a key point set l' in, a set of key points l’}={j}；

If step 14 is performed, a keypoint is generatedp’ _l2 Then, the key pointp’ _l2 Will replace the measuring pointp’ _j Number of its measuring pointl’₂Last page added to key serial number set l' } in;

after step 9, performing step 10;

step 10: root of herbaceous plantAccording to the key sequence number set l' } establishing analysis matrixA' sum analysis column vectorb', wherein:

A’=[…, A’ _p ^T, …, A’ _q ^T, …]^Tis a matrix with f rows and 6 columns, and f is a key sequence number set lThe number of the elements in the' },p, qis a critical sequence number set l' } elements;

b’=[…, b’ _p , …, b’ _q , …]^Tis a column vector of f rows;

after step 10, step 11 is performed;

step 11: for analysis matrixA' and extended analysis matrixA’, b’]Performing rank analysis;

computing an analysis matrixARank of `r _A =rank(A ^，) Extended analysis matrix [ alpha ], [ beta ] anA’, b’]Rank ofr _Ab =rank（[A’,b’]) And comparer _A Andr _Ab there are only two cases:

the first condition is as follows: if it is notr _A =r _Ab Then, the optimization should be continued, jumping to step 12;

case two: if it is notr _A < r _Ab Then, initializing the calculatorr=1, perform step 11.1;

step 11.1: making key serial number collect last l' take turns to remove the elements in the key sequence number setl’ _r Then obtain l’ _s According tol’ _s Establishment of a reduction matrixA’ _s And reducing the column vectorb’ _s Wherein:

jis 1;

A’ _s =[…, A’ _p ^T, …, A’ _q ^T, …]^Tis a matrix of S rows and 6 columns, and S is a l’ _s The number of the elements in the (C),p, qis a l’ _s The elements in (1);

b’=[…, b’ _p , …, b’ _q , …]^Tif it is a column vector of S rows, go to step 11.2;

step 11.2: solving linear equationsA’ _s v’ _s =b’ _s Solution of (2)v’ _s = v’ _s0 Then calculateb’ _j = A’ _s v’ _s ；

If it is notb’ _j > b’ _s Then the matrix will be reducedA’ _s And reducing the column vectorb’ _s Respectively asA' matrix and analysis column vectorb', will elementl’ _j Movable key serial number set l' }, and jump to step 11; if it is notb’ _j <= b’ _s Then step 11.3 is performed;

step 11.3: judgment ofjIs equal to S +1, ifjIs not equal toS+1, jumping to step 11; if it is notjIs equal toS+1, should finish the optimization, jump to step 15;

step 12: motion vector of measuring point and boundary is solvedv’₀I.e. linear equationsA’v’= bA solution ofv’= v’₀Wherein, in the step (A),v’=[v’₁, v’₂, v’₃, v’₄, v’₅, v’₆]^T， v’₀=[ v’_0,1, v’ _0,2, v’ _0,3, v’ _0,4, v’ _0,5, v’_0,6]^T；

step 12, after the end, step 13 is performed;

step 13: finding new key point by tracing problemt’ _j }、D’，{A’ _j Updating is carried out;

first, calculating the relative speed between each measuring point and the boundaryv’ _i }：v’ _i = A’ _j v’ ₀ ；

Then, the time of pursuit of each measurement point is calculatedτ’ _j ，τ’ _j =(D’–t’ _j )÷(b’ _i – v’ _i ) | _{i N=1, 2, …}；

Then, the decision key point: to catch up timeτ’ _i Minimum value in the part of greater than zeroτ ^， _minCorresponding measuring pointp’ _j Is a key point

Then, according top’ _j = p’ _j +τ’ _min ∙v’ _m Updating measuring point setp’ _j }, wherein:

；

finally, according to w = w +τ’_min∙v’ _g Updating w, wherein:

；

at updated measuring point setp’ _i Updating said leaf on the basis oft’ _j }、D’，{A’ _j }；

Finishing one-time optimization after the step 14 is finished, and performing the step 9;

step 15: at this timeThe effective size of the measured axis isD', ifD’<t', the measured axis meets the requirement of gradient, and the measured axis is qualified; otherwise, the product is unqualified; wherein t' is a gradient tolerance value.

2. The rank analysis-based method for assessing the inclination of a single-datum-plane axial hole type part as claimed in claim 1, wherein the measurement data of a general segment to be measured is mapped p _j Great moment through coordinate transformation to obtain a measuring point set with axis approaching the theoretical correct angle theta to the XOY plane of the coordinate system and the intersection point of the cylinder axis and the plane approaching the origin of the coordinate system p’ _j }。

3. The method for evaluating the inclination of a single-datum-plane axial hole part according to claim 2, wherein the coordinate transformation is one, moving according to the average value of the coordinates, or two, moving according to the extreme value of the coordinates, or three, moving according to the root-mean-square minimum principle of the coordinates, or four, obtaining data after the first evaluation of the measured element as data obtained after pre-positioning.

4. The method for assessing the inclination of a single-datum-plane axial hole part based on rank analysis as claimed in claim 1, wherein in step 13, if yes, the stepτ _min∙ v _i Single order value ofτ _min∙ v _i Or accumulated value sigma of past iterationsτ _min∙ v _i Greater than a given thresholdQThen, measuring point of the measured segmentp’ _j Is updated top’ _j +∑τ _min∙v’₀| _{j N= 1, 2, …}And re-rated from step 1.

5. The method for assessing the inclination of a single-datum-plane axial hole part based on rank analysis as claimed in claim 1,b=1 andb’=1。

Images