CN113932754A - Method for quickly evaluating verticality of error measurement workpiece based on single reference plane - Google Patents

Abstract

The invention belongs to the field of precision measurement and computer application, and relates to a method for evaluating hole shaft parts by combining a virtual gauge with measurement data in a mathematical model mode, in particular to a method for evaluating the perpendicularity of an L-shaped error measurement workpiece based on a single reference plane, which comprises the following steps: 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: updating the point set of the measured elements; 9: updating the real-time state element set; 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

Method for quickly evaluating verticality of error measurement workpiece based on single reference plane

Technical Field

The invention belongs to the field of precision metering and computer application, and particularly relates to a method for evaluating the verticality of an error measurement workpiece based on a single reference plane, which is stable, rapid and simple in form, can be used for the qualification detection and error evaluation of the verticality of an L-shaped measurement workpiece of the single reference plane, and the evaluation result can provide useful guidance for the improvement of a machining process.

Background

The invention takes an L-shaped error measurement workpiece as an example, and verifies a single-datum-plane-based quick evaluation method for perpendicularity of the L-shaped error measurement workpiece. The specific placing position of the workpiece is that the bottom surface of the L-shaped workpiece is attached to a horizontal plane, and the side surface of the L-shaped workpiece is vertical to the bottom surface. The bottom surface of the L-shaped workpiece is used as a reference surface, and the vertical surface is a measured plane.

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 perpendicularity error of the angle iron part based on the single reference plane refers to the fact that a theoretical correct angle is formed between the angle iron part and the reference plane, and an extraction (actual) surface is limited between two parallel planes which are perpendicular to the reference plane and have a tolerance value h. However, the four types of currently popular evaluation methods are difficult to directly apply to the quick evaluation of the perpendicularity of the angle iron parts with a single reference plane.

The first, the optical gap method. By comparing the right-angle measuring tool with the measured element, whether the part meets the verticality error requirement can be directly measured through the optical gap (or the feeler gauge). During detection, one surface of the square is placed on a reference surface, so that the two surfaces are tightly attached, and the square can be adjusted to a position meeting the minimum condition when necessary. And then, the vertical edge of the square is contacted with the measured actual surface, and the maximum gap f is formed between the vertical edge of the square and the measured actual surface, namely the perpendicularity error of the part. The gap value can be measured directly by the optical gap method or with a feeler gauge. The variation between the measured actual element and the square can be measured by using the measuring blocks, namely two groups of measuring blocks with different sizes are respectively padded at the maximum and minimum gaps between the measured actual surface and the square. And adjusting the thicknesses of the two groups of gauge blocks until the gaps at the gauge blocks are eliminated, wherein the size difference of the two groups of gauge blocks is the perpendicularity error of the part. The measurement method mainly depends on manual measurement, has low measurement efficiency and is not suitable for measurement in mass part production.

The second category, indicator methods. And (3) taking two adjacent vertical surfaces of the square box as ideal simulation elements, and comparing the ideal simulation elements with the measured elements through an indicator to measure the verticality error. According to the perpendicularity tolerance of the upper surface to the left side surface of the given part. During detection, the reference surface of the detected part is fixed on the right-angle seat, and the difference of the indicating and measuring values close to the reference detected surface is adjusted to be minimum. And then sliding the whole surface for measurement, and taking the difference between the maximum and minimum indication values in each measurement point as the verticality error of the part. If necessary, the verticality error can be evaluated by the minimum directional area. The indicator used in the method has errors and has no obvious advantage compared with the first method.

And in the third category, the horizontal plane is used as a reference, two adjacent vertical surfaces of the frame type level meter are used as ideal simulation elements, and the perpendicularity error is measured. According to the perpendicularity tolerance of the vertical guide rail to the plane of the workbench. During detection, a frame type level meter is used for roughly adjusting the reference surface to a horizontal position, then the frame type level meter is used for sequentially measuring the reference actual surface according to a certain point distribution distance, the vertical side surface of the frame type level meter is used for measuring the measured actual surface, and indication values of all measuring points are recorded. And converting the measured angle value into a line value, thereby solving the perpendicularity error of the measured part. The method can not solve the problem of low measurement efficiency, is not simple and convenient to operate, has no obvious advantages compared with the first two methods, and is mainly suitable for measuring large parts.

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.

And a fifth category, specialized geometric assessment methods. And gradually searching for perpendicularity errors meeting the definition according to the geometric properties between the reference elements and the measured elements and the national standard and ISO standard of the angle iron parts. In the method, the form of a mathematical model is complex, the speed change is uneven, and the method is not easy to be popularized to various tolerance evaluations, and certainly, the method is also difficult to be popularized to the verticality evaluation of the angle iron parts based on the single reference plane.

In conclusion, when the existing geometric evaluation method is applied to the perpendicularity of the angle iron parts with a single reference plane, 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 stable, quick and simple-form quick evaluation method for L-shaped measurement workpiece perpendicularity errors based on a single reference plane, and the evaluation result can also provide useful guidance for subsequent improved machining processes.

The scheme adopted by the invention is as follows:

according to the method, on the basis that the evaluation of the reference plane is completed and qualified, the verticality error of the angle iron part based on the single reference plane is evaluated.

A method for quickly evaluating the verticality of a measured workpiece based on a single reference plane is mainly realized by the following steps:

step 1: firstly, measuring points of a reference surface A are obtained and are used to form a reference measuring point setu _j ^，And according to au _j ^，Establishing a characteristic line vector setW _j ^，Greatb _j ^，}; obtaining initial measuring point of measured element and using it to form measuring point setu _i }; wherein:

j=1, 2, 3, …, M；jthe serial number of the reference measuring point is,Mthe total number of the measuring points of the reference plane is;

i=1, 2, 3, …, N；ithe serial number of the measuring point of the measured segment,Nthe total number of the measuring points of the measured plane is;

u _j ^，={x _j , y _j , z _j is the measurement pointjAnd the Z-axis of the coordinate system is perpendicular to the reference plane, the XOY plane of the coordinate systemClose to the ideal reference plane;

t _j =z _j all state elementst _j Is a set of state elementst _j }；

When z is _j >At the time of 0, the number of the first,W _j ^，=([-1, -y _j , x _j ]) (ii) a When z is _j <At the time of 0, the number of the first,W _j ^，=([1, y _j ,- x _j ])；W _j ^，is a feature row vector, all feature row vectorsW _j ^，Is a set of characteristic line vectorsW _j ^，}；

b _j =bIs a real number greater than 0, all boundary elementsb _j Is a set of boundary elementsb _j }；

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

step 2: gett _j Maximum valuet _max Corresponding serial numberr ₂ Is numbered for the key point and willr ₂ Last page added to key serial number setrIn (c) } the reaction solution is,t _max the distance from the reference measuring point to the upper boundary; gett _j Minimum valuet _min Corresponding serial numberr ₁ Is numbered for the key point and willr ₁ Last page added to key serial number setrIn (c) } the reaction solution is,t _min is the distance from the reference point to the lower boundary.

Step 3 is carried out after step 2 is finished;

and step 3: according to the key sequence numberrEstablishment of an analysis matrixWAnd analyzing the column vectorsbWherein:

W=[…, A _p ^T, …, A _q ^T, …]^Tis aFA matrix of rows and 4 columns,Fis a set of key pointsrThe number of the elements in the (C),p, qis a set of key pointsrThe elements in (1);

b=[…, b _p , …, b _q , …]^Tis aFA column vector of rows.

Step 4 is carried out after step 3 is finished;

and 4, step 4: for analysis matrixWAnd an augmented analysis matrixW, b]Performing rank analysis;

computing an analysis matrixWRank ofR _W =rank(W) Extended analysis matrix [ alpha ], [ beta ] anW, b]Rank ofR _Wb =rank（[W, b]) And compareR _W AndR _Wb there are only two cases:

the first condition is as follows: if it is notR _W =R _Wb Then, the optimization should be continued, jumping to step 5;

case two: if it is notR _W <R _Wb Then, the counter C =1 is initialized and step 4.1 is performed;

step 4.1: attempting to slave an analysis matrixWAnd analyzing the column vectorsbMiddle removed key point setrGet the line corresponding to one element in the matrix to get the reduced matrixW _{r -} And reducing the column vectorb _{r -} (ii) a WhereinW _{r -} Is oneJA matrix of rows and 4 columns,b _{r -} is oneJA column vector of rows.

Step 4.2: solving linear equationsW _{r -} ∙ v _{r -} = b _{r -} Solution of (2)v _{r -} =v _r-0 Then calculateb _r =W _r ∙ v _r-0 (ii) a If it is notb _{r -} > b _r Then, the matrix will be reducedW _{r -} And reducing the column vectorb _{r -} Respectively asWMatrix and scoreDisjunctive column vectorbWill elementrMoving out key point setrAnd jumping to the step 5; if it is notb _{r -} <= b _r Then step 4.3 is performed;

step 4.3: judging counterCWhether or not equal toJIf, ifC≠JJumping to step 4.1; if it is notC=JIf the optimization should be ended, jump to step 7

And 5: calculating motion vector of measuring pointv ₀I.e. linear equationsW ∙ v= 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: solving a new key point by the tracing problem, and updating the state of the measuring point of the reference segment;

firstly, calculating the linear velocity of the measuring pointv _j =W _j ∙ v ₀；

Then, calculating the dynamic tracking time of each measuring point of the reference segmentτ _j ：τ _j,down =(t _j -t _min )÷(b _j - v _j ) | _{j 1,2, … M=}；τ _j,up =(t _max-t _j )÷(b _j - v _j ) | _{j 1,2, … M=}(ii) a Whereinτ _j ={τ _j,down ，τ _j,up }。τ _j,down Is the dynamic tracking time from the reference measuring point to the lower boundary,τ _j,up is the dynamic time of tracing from the reference point to the upper boundary.

Then, the decision key point: dynamic tracking time of each measuring point of reference segmentτ _j Minimum value ofτ _j,min Corresponding measurementThe point is the next key pointr ₃ And adding the corresponding serial number to the key serial number setrIn (c) }.

Then, updating a reference segment measuring point state set, wherein the measuring point state element set below the XOY plane is updated as follows:

t _j =τ _j,min ∙ v _j -t _min (ii) a The measuring point state element set of the measuring point positioned above the XOY surface of the coordinate is updated intot _j =t _max -τ _j,min ∙ v _i 。

Finally, according tou _j ^，= u _j ^，+τ _min ∙ v _j Updating reference segment measuring point setu _j ^，}; and simultaneously, updating the coordinates of the measurement point sets of all the measured segments in the same way.

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

and 7: determine whether the reference section meets the flatness error requirement, i.e.t _max -t _min ≦TAnd T is the tolerance value of the reference plane. If yes, jumping to step 8; if not, the evaluation is finished, and the part is not qualified.

And 8: obtainingu _i ={x _i , y _i , z _i I.e. measured plane fitting pointiAnd fitting the measured surface to the XOZ plane of the rectangular spatial coordinate system, i.e. the Z-axis of the coordinate system is perpendicular to the reference surface, in order to make the center plane of the measured surface close to the XOZ plane of the coordinate system. At the same time, the XOY plane of the coordinate system is close to the ideal reference plane. First, for measurement convenience, all the measurement points of the measured surface are projected to the XOY plane. Secondly, two contraction planes of the virtual gauge are established by points of the measuring points which are farthest away from the Y axis and the negative Y axis of the central plane of the virtual gauge respectively. Then, obtaining the initial key of the tested sectionSerial numberl ₁ Andl ₂ will bel ₁ Andl ₂ adding key serial number setlIn (1) };

l ₁ is defined asu _i Iny _i Point of maximum valueu _{l, 1}The serial number of (a) is included,l ₂ is defined asu _i Iny _i Point of minimum valueu _{l, 2}The serial number of (2);

then, setting boundary positions H and G;

H=y _l,1，y _{l, 1}is composed ofu _{l, 1}Is/are as followsyCoordinate values; h is the left boundary position, the left boundary is the crossing point [0, H, 0 ]]And parallel to the XOZ plane;

G=y _l,2，y _{l, 2}is composed ofu _{l, 2}Is/are as followsyCoordinate values; g is the right boundary position, the right boundary is the crossing point [0, G, 0 ]]And parallel to the XOZ plane;

obtaining the middle position midle of the left and right boundaries according to the above; midle = (H + G)/2;

finally, according to the measured point setu _i Establishing state element set of measuring pointsc _i Great Chinese character and feature line vector setW _i }; wherein:

c _i= y _i status elements of all stationsc _i Is a set of state elementsc _i }；

When y is _i >At the time of the middle of the message,W _i =([1, x _i ,-1, -x _i ])/y _i ；y _i <at the time of the middle of the message,W _i =([-1, -x _i ,1, x _i ,])/y _i ；W _i is a special oneSyndrome row vector, characteristic row vector of all measurement pointsW _i Is a set of characteristic line vectorsW _i }；

Step 9 is performed after step 8 is completed;

and step 9: according tou _i Establishing a state element set (R) of a measured plane measuring point _i And { E } and _i }；

R _i = H - y _i ；R _i the distance from a measuring point of the measured plane to the left boundary;

E _i =y _i - G；E _i the distance from a measuring point of the measured plane to the right boundary is obtained;

after step 9, performing step 10;

step 10: adding the measuring point serial number of a key point into a key serial number setlIn (1) }; if step 14 has not been performed, then a set of real-time state elements is takenc _i Maximum value ofc _max Corresponding measuring pointu _{l, 3}Is a key point and the serial number of the measuring point isl ₃Last page added to key serial number setlIn (1) }; at this time D/2 =c _max D is the distance size from the boundary to the center; if step 14 generates a keypointu _l,4Then, the key pointu _l,4Will replace the measuring pointu _{l, 3}Number of its measuring pointl ₄Last page added to key serial number setlIn (1) };

step 11: according to the above-mentioned key point setlEstablishment of an analysis matrixWAnd analyzing the column vectorsbWherein:bis a number greater than zero, and:

W=[…, W _u ^T, …, W _v ^T, …]^Tis a matrix with L rows and 4 columns, and L is a key point setlThe number of the elements in the (C),u, vis a set of key pointslThe elements in (1);

b=[…, b _u , …, b _v , …]^Tis a column vector of L rows;

step 12 is performed after step 11 is completed;

step 12: for the above-mentioned established analysis matrixWAnd an augmented analysis matrixW, b]Analyzing the rank;

first computing analysis matrixWRank ofr _W =rank(W) Extended analysis matrix [ alpha ], [ beta ] anW, b]Rank ofr _Wb =rank（[W, b]) And further compare the rankr _W Sum rankr _Wb By verification, there are only two cases:

the first situation is as follows: if it is notr _W = r _Wb If yes, the optimization should be continued, and the step 13 is skipped;

case two: if it is notr _W < r _Wb Then go to step 12.1;

step 12.1: let the key point collectlGet rid of the firstkAn elementl _k Then obtainl _q According tol _q Establishment of a reduction matrixW _q And reducing the column vectorb _q Wherein:kis 1;

W _q =[…, W _u ^T, …, W _v ^T, …]^Tis aQA matrix of rows and 4 columns,Qis a setl _q The number of the elements in the (C),uv isl _q The elements in (1);

b _q =[…, b _u , …, b _v , …]^Tis aQA column vector of rows;

step 12.2: solving linear equationsW _q f _q = b _q Solution of (2)f _q =f _o Then calculateb _k =W _q f _o (ii) a If it is notb _k > b _q Then the matrix will be reducedW _q And reducing the column vectorb _q Respectively asWMatrix and analysis column vectorbWill elementl _k Moving out key point setlAnd jumping to the step 13; if it is notb _k <=b _q Then step 12.3 is performed;

step 12.3: judgment ofkWhether or not equal toQIf, ifkIs not equal toQThen jump to step 11.1; if it is notkIs equal toQIf the optimization should be finished, jump to step 15; wherein the content of the first and second substances,f _q =[f _q,1 , f _q,2 , f _q,3 , f _q,4 ]^T，f _o =[f _q0,1, f _q0,2, f _q0,3, f _q0,4]^T；

step 13: motion vector of measuring point and virtual gauge is solvedf _o I.e. linear equationsWf = bA solution off=f _o Wherein:

f=[f ₁, f ₂, f ₃, f ₄]^T，f _o =[f _o,1, f _o,2, f _o,3, f _o,4]^T；

step 14 is performed after step 13 is completed;

step 14: finding new key point by tracing problemu _i Updating is carried out;

first, calculating the relative speed between each measuring point and the virtual gaugef _i }：f _i =W _i ∙ f _o ；

Then, the time of pursuit of each measurement point is calculatedt _i ^，Andt _i ^，，；

t _i ^，=R _i / f _i | _{i=1, 2,} ..._M；t _i ^，trace the left boundary with the measuring pointu _i The time of (d);

t _i ^，，=E _i / f _i | _{i=1, 2,} ..._M；t _i ^，，trace the right border with the measuring pointu _i The time of (d);

t _i gett _i ^，Andt _i ^，，the smaller of these;

then, the decision key point: to catch up timet _i Minimum value in the part of greater than zerot _minThe corresponding measuring points are key pointsu _{l ,3}And corresponding the serial number to the pointl ₃Adding key serial number setl}；

Then, according tou _i =u _i + t _min ∙ f _i Updating measuring point setu _i }；

Finally, according toH= H - t _min ∙ bUpdating the position of the left boundaryH(ii) a According toG= G + t _min ∙ bUpdating right boundary positionG；

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

step 15: the actual size of the measured plane isH - GIf (a), (b) isH - G）< dIf the measured plane meets the verticality requirement, the measured plane is qualified; otherwise, the product is not qualified. Wherein the content of the first and second substances,dis the tolerance value of verticality.

To facilitate numerical calculations, the following optimizations may be performed:

order tobTaking a value greater than 0, may be, but is not limited to, 1.

The measured elements are side surface measuring point sets of the measured workpiece.

The invention has the beneficial effects that:

1. the geometrical characteristics of the L-shaped measurement workpiece verticality based on the single reference plane are fully considered, the computer is used for replacing the considered manual evaluation, and the evaluation mode is simple and convenient, so that the method has higher efficiency and is easier to popularize compared with the first type of evaluation method. 2. The geometrical characteristics of the perpendicularity of the L-shaped measuring workpiece based on the single datum plane 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 that the evaluation indicator of the second method has errors is solved. 3. The fact that most of measuring points are invalid measuring points in the evaluation of the perpendicularity of the shaft hole type part based on the single datum plane is implied, and the invalid measuring points are not added with iteration, so that the iteration times are less, and the method is more suitable for evaluating large-sized workpieces compared with a third evaluation method. 4. Calculating the optimizing direction by considering only the keypoint setkAnd (4) corresponding measuring points, so that the operation amount of each iteration is small, the mathematical model is established simply, and compared with the fourth type of evaluation method, the method has the advantages of equivalent total operation speed, lower mathematical modeling complexity and worth popularizing.

The invention provides a method for quickly evaluating the perpendicularity of an L-shaped measuring workpiece based on a single reference plane, which is stable, quick and simple in form, can be used for evaluating the error of the L-shaped measuring workpiece based on the perpendicularity of the single reference plane, and provides guidance for the improvement of the machining process, so that the method has industrial possibility.

Drawings

FIG. 1 is a baseline assessment summary flow chart A of the present invention.

FIG. 2 is a flowchart B of the measured element evaluation method of the present invention.

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

Detailed Description

The following are specific examples of the present invention, and the aspects of the present invention will be further described with reference to the drawings, but the present invention is not limited to these examples.

And evaluating the verticality error of the L-shaped measuring workpiece based on the single datum plane, wherein the tolerance design specification is shown in figure 3.

Step 1: measuring point set for obtaining reference segmentu _j ^，Great moment and measuring point set of the segment to be measuredu _i The method comprises the following steps:

the initial key serial numbers at this time are 6 and 8;

at this time, the upper boundary position of the reference plane is z'₆=0.0514 and lower boundary is z'₈=0.0014；

Obtaining a middle position of the boundary as midle = 0.0264;

establishing a characteristic line vector set of reference plane measuring pointsW _j ^，The method comprises the following steps:

after step 1, step 2 is performed.

Step 2: according tou _j ^，Establishing a reference state element sett _j Ant' _j }：

After step 2, step 3 is performed.

And step 3: establishing an analysis matrix according to the key sequence numberWAnd analyzing the column vectorsb：

W= [ W ₆ ^T , W ₈ ^T ]^T =

，b=[1, 1]^T。

After step 3, step 4 is performed.

And 4, step 4:R _W =rank(W) =2，R _{W b} =rank（[W, b]）=2，R _W =R _{W b} and jumping to the step 5.

After step 4, step 5 is performed.

And 5: linear equation of equationsW ∙ v = bIs thatv = v ₀ =[ 0, 0.1000, 0.2000]^T。

Step 5 ends and proceeds to step 6.

Step 6: calculating the normal linear velocity of the measuring pointv _j ，v _j =W _j ∙ v ₀The results are as follows:

then, the minimum tracking time of each measuring point is calculatedτ _j And deciding a key point: to catch up timeτ _j Of greater than zero

Minimum value ofτ _j,min The measured point corresponding to the value of =0.00033 is a key pointu ₁₃ ^，

Finally, updating the reference measuring point setu _j ^，Greatu _j The method comprises the following steps:

updating the upper and lower boundary positions of the reference, wherein the upper boundary is z'₆=0.0511, lower boundary z'₈=0.0018。

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

After the benchmark evaluation optimization is completed according to the invention, all the key sequence number sets are obtained as a great facer}={6，8，13，15}；

Step 6 obtains a new key point ofu ₁₅ ^，

Step 6, after finishing step 2;

step 2: according tou _j ^，Establishing a reference state element sett _j Ant' _j }；

And step 2 is finished and step 3 is carried out.

And step 3:W = [ W ₆ ^T , W ₈ ^T , W ₁₃ ^T ,W ₁₅ ^T ]^T=

，b= [1，1，1，1]^T 。

after step 3, step 4 is performed.

And 4, step 4:R _W = rank(W) = 3，R _Wb =rank（[W, b]）= 4，R _W ≠ R _Wb step 4.1 is performed.

Step 4.1: making key serial number collect lastrRemoving the 1 st element 6 to obtain {8, 13, 15} = {6, 8, 13, 15}, and establishing a reduction matrix according to {8, 13, 15}W _r- And reducing the column vectorb _r- Respectively is as follows:

W _r- =[ W ₈ ^T , W ₁₃ ^T ,W ₁₅ ^T ]^T=

，b= [1，1，1]^T 。

step 4.2: linear equation of equationsW _r- ∙ v _r- = b _r- Solution of (2)v _r- =[5.5000，-0.1000，0.1500]Calculatingbr=W _r- ∙ v _r- = -3<1。

Step 4.3 is performed.

Step 4.3: counter C =1<4, jump to step 4.1.

Step 4.1: making key serial number collect lastrRemoval of the 2 nd element 8 yields a retaining openingr} = {6, 13, 15}, and a reduction matrix is established according to {6, 13, 15}W _r- And reducing the column vectorb _r- Respectively is as follows:

W _r- =[ W ₆ ^T , W ₁₃ ^T ,W ₁₅ ^T ]^T=

，b= [1，1，1]^T 。

step 4.2: linear equation of equationsW _r- ∙ v _r- = b _r- Solution of (2)v _r- =[-0.5000，-0.1000，-0.0500]Calculatingbr=W _r- ∙ v _r- = -3.1862<1。

Step 4.3 is performed.

Step 4.3: counter C =2<4, jump to step 4.1.

Step 4.1: making key serial number collect lastrRemoving the 3 rd element 13 to obtain a retaining openingr} = {6, 8, 15}, and a reduction matrix is established according to {6, 8, 15}W _r- And reducing the column vectorb _r- Respectively is as follows:

W _r- =[ W ₆ ^T , W ₈ ^T ,W ₁₅ ^T ]^T=

，b= [1，1，1]^T 。

step 4.2: linear equation of equationsW _r- ∙ v _r- = b _r- Solution of (2)v _r- =[-1.5000，0.1000，0.0500]Calculatingbr=W _r- ∙ v _r- = -3.2954<1。

Step 4.3 is performed.

Step 4.3: counter C =3<4, jump to step 4.1.

Step 4.1: making key serial number collect lastrRemoval of the 4 th element 15 yields a retaining openingr} = {6, 8, 13}, and a reduction matrix is established according to {6, 8, 13}W _r- And reducing the column vectorb _r- Respectively is as follows:

W _r- =[ W ₆ ^T , W ₈ ^T ,W ₁₃ ^T ]^T=

，b= [1，1，1]^T 。

step 4.2: linear equation of equationsW _r- ∙ v _r- = b _r- Solution of (2)v _r- =[-1.5000，0.1000，0.0500]Calculatingbr=W _r- ∙ v _r- = -1.3495<1. Step 4.3 is performed.

Step 4.3: counter C =4, jump to step 7.

And 7: judging whether the reference section meets the requirement of flatness error:t _max -t _min =0.0501- 0.0028=0.0473≦0.05=Tthe reference plane meets the flatness requirement, wherein T is the tolerance value of the reference plane,t _max the distance from the measuring point to the upper boundary z,t _min is the distance from the measured point to the lower boundary z. Step 8 is performed.

And 8: measured plane measuring point set after benchmark evaluation is completed{u _i The method comprises the following steps:

the initial key serial numbers at this time are 7 and 15;

the left boundary of the reference plane is H =0.0449 and the right boundary is G = -0.0036 at this time;

obtaining a boundary middle position as midle = 0.0207;

establishing a set of state elementsc _i Anc' _i The method comprises the following steps:

establishing a feature line vector setWiThe method comprises the following steps:

step 8 ends and step 9 is performed.

And step 9: updating a real-time state element set { R } _i And { E } and _i therein ofy _i<At the time of the middle of the message,c _{i =} R _i ；y _i>at the time of the middle of the message,c _{i =} E _i 。

step 9 ends and proceeds to step 10.

Step 10: if step 14 has not been performed, a set of real-time state elements is takenc _i Maximum value y of }_max =0.0485 corresponding measuring pointu ₁₅The measuring point serial number 15 of the key point is listed as a set of key points during the initialization processlIn (1) }; at this time D =0.0485, D being the virtual gauge size.

Step 10 ends and proceeds to step 11.

Step 11:W _q = [ W ₇ ^T , W ₁₅ ^T ]^T =

，b _q =[1, 1]^T。

step 11 ends and proceeds to step 12.

Step 12:r _W =rank(W) =2，r _Wb =rank([W, b])=2，r _W = r _Wb and a jump is made to step 13.

Step 13: linear equation of equationsWq ∙ f _q = b _q Is thatf _q = f _o =[0.0656 , -0.0021 , 0 , 0]^T。

Step 13 ends and step 14.

Step 14: first, according tof _i =W _i ∙ f _o Calculating the relative speed between each measuring point and the virtual gaugef _i The method comprises the following steps:

secondly, a new key point is found by tracing the problem,t _i ^，=R _i / f _i | _{i=1, 2,} ..._M；

then, the decision key point: to catch up timet _i ^，Minimum value in the part of greater than zerot _i ^， _minThe measured point corresponding to the value of =0.00083 is a key pointu ₅And adding the serial number of the key measuring point into the key point setlIn (1) };

then, according tou _i =u _i + t _min ∙ f _i Updating measuring point setu _i As follows:

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

And step 9: updating a set of real-time state elementsc _i }

After step 9, step 10 is performed.

Step 10: according to the invention, new key points are searched in the tracking time, and after all the optimizations are completed, a key sequence number set is obtainedl} = {7, 15, 5}, when D =c _max =0.0485 distance size of left and right boundaries of gauge;

after step 10, step 11 is performed.

Step 11:W=[W ₇ ^T，W ₁₅ ^T，W ₅ ^T]^T=

，

b=[1，1，1]^T。

step 11 ends and proceeds to step 12.

Step 12:r _W = rank(W) =2，r _Wb = rank（[W , b]）=3，r _W ≠r _Wb step 12.1 is performed.

Step 12.1: the key sequence number set {7, 15, 5} gets {15, 5} after the first element 7 is removed, and a reduced matrix is built according to {15, 5}W _q And reducing the column vectorb _q Respectively is as follows:

W _q =[W ₁₅ ^T，W ₅ ^T]^T=

，b _q =[1，1]^T。

after step 12.1 is finished, step 12.2 is performed.

Step 12.2: solving linear equationsW _q ∙ f _q = b _q Is solved byf _q = f _o =[-0.0046，0.00027，0，0]Then calculateb _k =W _q ∙ f _o =-2.5<1; namely, it isb _k <=b _q Then step 12.3 is performed.

Step 12.3: counter with a memoryk =1<3, jumping to step 12.1.

Step 12.1: the second element 15 of the key sequence number set {7, 15, 5} is removed to obtain {7, 5}, and a reduced matrix is established according to {7, 5}W _q And reducing the column vectorb _q Respectively is as follows:

W _q =[W ₇ ^T，W ₅ ^T]^T=

，b _q =[1，1]^T。

after step 12.1 is finished, step 12.2 is performed.

Step 12.2: solving linear equationsW _q ∙ f _q = b _q Is solved byf _q = f _o =[114.9624，-11.4964，0，0]Then calculateb _k =W _q ∙ f _o =-6.8074<1; namely, it isb _k <=b _q Then step 12.3 is performed.

Step 12.3: counter with a memoryk =2<3, jumping to step 12.1.

Step 12.1: order keyThe sequence number set {7, 15, 5} gets {7, 15} after the third element 5 is removed, and a reduced matrix is built according to {7, 15}W _q And reducing the column vectorb _q Respectively is as follows:

W _q =[W ₇ ^T，W ₁₅ ^T]^T=

，b _q =[1，1]^T。

after step 12.1 is finished, step 12.2 is performed.

Step 12.2: solving linear equationsW _q ∙ f _q = b _q Is solved byf _q = f _o =[0.0656，-0.0021，0，0]Then calculateb _k =W _q ∙ f _o =-24.1818<1; namely, it isb _k <=b _q Then step 12.3 is performed.

Step 12.3: counter with a memoryk =3, jump to step 15

Step 15: at the moment, the effective size D =0.0485 between the left plane and the right plane of the measured plane is less than 0.05, the measured plane meets the verticality requirement, and the measured plane is qualified.

To conclude: the tested L-shaped error measurement workpiece based on single reference meets the verticality requirement given by the figure 3

In the above description, the present invention has been described by way of specific embodiments, but those skilled in the art will appreciate that various modifications and variations can be made within the spirit and scope of the invention as hereinafter claimed.

The verticality measurement result of the L-shaped error measurement workpiece meets the definition and requirement of the verticality in GB/T1182-2018.

The measurement result of the invention shows that the L-shaped error measurement workpiece can be used for measuring the verticality error of the part with the precision requirement.

Claims (6)

1. The invention takes an L-shaped error measurement workpiece as an example, and verifies a single-datum-plane-based quick evaluation method for perpendicularity of the L-shaped error measurement workpiece; the specific placing position of the workpiece is that the bottom surface of the L-shaped workpiece is attached to a horizontal plane, and the side surface of the L-shaped workpiece is vertical to the bottom surface;

the bottom surface of the L-shaped workpiece is used as a reference surface, and the vertical surface is a measured plane.

2. A single datum plane based method for quickly evaluating the verticality of an error measurement workpiece is characterized by comprising the following steps of:

step 1: firstly, measuring points of a reference surface A are obtained and are used to form a reference measuring point setu _j ^，And according to au _j ^，Establishing a characteristic line vector setW _j ^，Greatb _j ^，}; obtaining initial measuring point of measured element and using it to form measuring point setu _i }; wherein:

j=1, 2, 3, …, M；jthe serial number of the reference measuring point is,Mthe total number of the measuring points of the reference plane is;

i=1, 2, 3, …, N；ithe serial number of the measuring point of the measured segment,Nthe total number of the measuring points of the measured plane is;

u _j ^，={x _j , y _j , z _j is the measurement pointjAnd the Z-axis of the coordinate system is perpendicular to the reference plane, the XOY plane of the coordinate system is close to the ideal reference plane;

t _j =z _j all state elementst _j Is a set of state elementst _j }；

When z is _j >At the time of 0, the number of the first,W _j ^，=([-1, -y _j , x _j ]) (ii) a When z is _j <At the time of 0, the number of the first,W _j ^，=([1, y _j ,- x _j ])；W _j ^，is a feature row vector, all feature row vectorsW _j ^，Is a set of characteristic line vectorsW _j ^，}；

b _j =bIs a real number greater than 0, all boundary elementsb _j Is a set of boundary elementsb _j }；

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

step 2: gett _j Maximum valuet _max Corresponding serial numberr ₂ Is numbered for the key point and willr ₂ Last page added to key serial number setrIn (c) } the reaction solution is,t _max the distance from the reference measuring point to the upper boundary; gett _j Minimum valuet _min Corresponding serial numberr ₁ Is numbered for the key point and willr ₁ Last page added to key serial number setrIn (c) } the reaction solution is,t _min 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 numberrEstablishment of an analysis matrixWAnd analyzing the column vectorsbWherein:

W=[…, A _p ^T, …, A _q ^T, …]^Tis aFA matrix of rows and 4 columns,Fis a set of key pointsrThe number of the elements in the (C),p, qis a set of key pointsrThe elements in (1);

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

step 4 is carried out after step 3 is finished;

and 4, step 4: for analysis matrixWAnd an augmented analysis matrixW, b]Performing rank analysis;

computing an analysis matrixWRank ofR _W =rank(W) Extended analysis matrix [ alpha ], [ beta ] anW, b]Rank ofR _Wb =rank（[W, b]) And compareR _W AndR _Wb there are only two cases:

the first condition is as follows: if it is notR _W =R _Wb Then, the optimization should be continued, jumping to step 5;

case two: if it is notR _W <R _Wb Then, the calculator C =1 is initialized and step 4.1 is performed;

step 4.1: attempting to slave an analysis matrixWAnd analyzing the column vectorsbMiddle removed key point setrGet the line corresponding to one element in the matrix to get the reduced matrixW _r- And reducing the column vectorb _r- (ii) a WhereinW _r- Is oneJA matrix of rows and 4 columns,br-is oneJA column vector of rows;

step 4.2: solving linear equationsW _r- ∙ v _r- = b _r- Solution of (2)v _r- =v _r-0 Then calculateb _r =W _r ∙ v _r-0 (ii) a If it is notb _r- > b _r Then, the matrix will be reducedW _r- And reducing the column vectorb _r- Respectively asWMatrix and analysis column vectorbWill elementrMoving out key point setrAnd jumping to the step 5; if it is notb _r- <= b _r Then step 4.3 is performed;

step 4.3: judging counterCWhether or not equal toJIf, ifC≠JJumping to step 4.1; if it is notC=JShould end the optimization and jump to stepStep 7

And 5: calculating motion vector of measuring pointv ₀I.e. linear equationsW ∙ v= 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: solving a new key point by the tracing problem, and updating the state of the measuring point of the reference segment;

firstly, calculating the linear velocity of the measuring pointv _j =W _j ∙ v ₀(ii) a Then, calculating the dynamic tracking time of each measuring point of the reference segmentτ _j ：

τ _j,down =(t _j -t _min )÷(b _j - v _j ) | _{j 1,2, … M=}；τ _j,up =(t _max-t _j )÷(b _j - v _j ) | _{j 1,2,… M=}(ii) a Whereinτ _j ={τ _j,down ，τ _j,up }；τ _j,down Is the dynamic tracking time from the reference measuring point to the lower boundary,τ _j,up is the dynamic time of tracing from the reference measuring point to the upper boundary;

secondly, the decision key points are: dynamic tracking time of each measuring point of reference segmentτ _j Minimum value ofτ _j,min The corresponding measuring point is the next key pointr ₃ And adding the corresponding serial number to the key serial number setrIn (1) }; then, updating a reference segment measuring point state set, wherein the measuring point state element set below the XOY plane is updated as follows:t _j =τ _j,min ∙ v _j -t _min (ii) a The measuring point state element set of the measuring point positioned above the XOY surface of the coordinate is updated intot _j =t _max -τ _j,min ∙ v _i ；

Finally, according tou _j ^，= u _j ^，+τ _min∙ v _j Updating reference segment measuring point setu _j ^，}; simultaneously, updating the coordinates of the measured point sets of all the measured sections in the same way;

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

and 7: determine whether the reference section meets the flatness error requirement, i.e.t _max -t _min ≦TWherein T is a tolerance value of the reference plane; if yes, jumping to step 8; if not, finishing the evaluation, and enabling the part not to meet the requirements;

and 8: obtainingu _i ={x _i , y _i , z _i I.e. measured plane fitting pointiFitting the measured surface on an XOZ plane of a space rectangular coordinate system, namely, the Z axis of the coordinate system is vertical to a reference surface, so that the central plane of the measured surface is close to the XOZ plane of the coordinate system; meanwhile, the XOY plane of the coordinate system is close to an ideal reference plane; firstly, projecting all measuring points of a measured surface to an XOY plane for convenient measurement; secondly, establishing two contraction planes of the virtual gauge by using points at which the measuring points are farthest away from the Y axis and the negative Y axis of the central plane of the virtual gauge respectively; then, obtaining the initial key sequence number of the segment to be testedl ₁ Andl ₂ will bel ₁ Andl ₂ adding key serial number setlIn (1) };

l ₁ is defined asu _i Iny _i Point of maximum valueu _{l, 1}The serial number of (a) is included,l ₂ is defined asu _i Iny _i Point of minimum valueu _l,2The serial number of (2);

then, setting boundary positions H and G;

H=y _l,1，y _{l, 1}is composed ofu _l,1Is/are as followsyCoordinate values; h is the left boundary position, the left boundary is the crossing point [0, H, 0 ]]And parallel to the XOZ plane;

G=y _l,2，y _{l, 2}is composed ofu _l,2Is/are as followsyCoordinate values; g is the right boundary position, the right boundary is the crossing point [0, G, 0 ]]And parallel to the XOZ plane;

obtaining the middle position midle of the left and right boundaries according to the above; midle = (H + G)/2;

finally, according to the measured point setu _i Establishing state element set of measuring pointsc _i Great Chinese character and feature line vector setW _i }; wherein:

c _i= y _i status elements of all stationsc _i Is a set of state elementsc _i }；

When y is _i >At the time of the middle of the message,W _i =([1, x _i ,-1, -x _i ])/y _i ；y _i <at the time of the middle of the message,W _i =([-1, -x _i ,1, x _i ,])/y _i ；W _i is a characteristic line vector, the characteristic line vectors of all measuring pointsW _i Is a set of characteristic line vectorsW _i }；

Step 9 is performed after step 8 is completed;

and step 9: according tou _i Establishing a state element set (R) of a measured plane measuring point _i And { E } and _i }；

R _i = H - y _i ；R _i the distance from a measuring point of the measured plane to the left boundary;

E _i =y _i - G；E _i the distance from a measuring point of the measured plane to the right boundary is obtained;

after step 9, performing step 10;

step 10: adding the measuring point serial number of a key point into a key serial number setlIn (1) }; if step 14 has not been performed, then a set of real-time state elements is takenc _i Maximum value ofc _max Corresponding measuring pointu _l,3Is a key point and the serial number of the measuring point isl ₃Last page added to key serial number setlIn (1) }; at this time D/2 =c _max D is the distance size from the boundary to the center; if step 14 generates a keypointu _l,4Then, the key pointu _l,4Will replace the measuring pointu _l,3Number of its measuring pointl ₄Last page added to key serial number setlIn (1) };

step 11: according to the above-mentioned key point setlEstablishment of an analysis matrixWAnd analyzing the column vectorsbWherein:bis a number greater than zero, and:

W=[…, W _u ^T, …, W _v ^T, …]^Tis a matrix with L rows and 4 columns, and L is a key point setlThe number of the elements in the (C),u, vis a set of key pointslThe elements in (1);

b=[…, b _u , …, b _v , …]^Tis a column vector of L rows;

step 12 is performed after step 11 is completed;

step 12: for the above-mentioned established analysis matrixWAnd an augmented analysis matrixW, b]Analyzing the rank;

first computing analysis matrixWRank ofr _W =rank(W) Enhanced analysis matrix[W, b]Rank ofr _Wb =rank（[W, b]) And further compare the rankr _W Sum rankr _Wb By verification, there are only two cases:

the first situation is as follows: if it is notr _W = r _Wb If yes, the optimization should be continued, and the step 13 is skipped;

case two: if it is notr _W < r _Wb Then go to step 12.1;

step 12.1: let the key point collectlGet rid of the firstkAn elementl _k Then obtainl _q According tol _q Establishment of a reduction matrixW _q And reducing the column vectorb _q Wherein:kis 1;

W _q =[…, W _u ^T, …, W _v ^T, …]^Tis aQA matrix of rows and 4 columns,Qis a setl _q The number of the elements in the (C),uv isl _q The elements in (1);

b _q =[…, b _u , …, b _v , …]^Tis aQA column vector of rows;

step 12.2: solving linear equationsW _q f _q = b _q Solution of (2)f _q =f _o Then calculateb _k =W _q f _o (ii) a If it is notb _k > b _q Then the matrix will be reducedW _q And reducing the column vectorb _q Respectively asWMatrix and analysis column vectorbWill elementl _k Moving out key point setlAnd jumping to the step 13; if it is notb _k <=b _q Then step 12.3 is performed;

step 12.3: judgment ofkWhether or not equal toQIf, ifkIs not equal toQThen jump to step 11.1; if it is notkIs equal toQIf the optimization should be finished, jump to step 15; wherein the content of the first and second substances,f _q =[f _q,1 , f _q,2 , f _q,3 , f _q,4 ]^T，f _o =[f _q0,1, f _q0,2, f _q0,3, f _q0,4]^T；

step 13: motion vector of measuring point and virtual gauge is solvedf _o I.e. linear equationsWf= bA solution off=f _o Wherein:

f=[f ₁, f ₂, f ₃, f ₄]^T，f _o =[f _o,1, f _o,2, f _o,3, f _o,4]^T；

step 14 is performed after step 13 is completed;

step 14: finding new key point by tracing problemu _i Updating is carried out;

first, calculating the relative speed between each measuring point and the virtual gaugef _i }：f _i =W _i ∙ f _o ；

Then, the time of pursuit of each measurement point is calculatedt _i ^，Andt _i ^，，；

t _i ^，=R _i / f _i | _{i=1, 2,} ..._M；t _i ^，trace the left boundary with the measuring pointu _i The time of (d);

t _i ^，，=E _i / f _i | _{i=1, 2,} ..._M；t _i ^，，trace the right border with the measuring pointu _i The time of (d);

t _i gett _i ^，Andt _i ^，，the smaller of these;

then, the decision key point: to catch up timet _i Minimum value in the part of greater than zerot _minThe corresponding measuring points are key pointsu _{l, 3}And corresponding the serial number to the pointl ₃Adding key serial number setl}；

Then, according tou _i =u _i + t _min∙ f _i Updating measuring point setu _i }；

Finally, according toH= H - t _min ∙ bUpdating the position of the left boundaryH(ii) a According toG= G + t _min ∙ bUpdating right boundary positionG；

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

step 15: the actual size of the measured plane isH - GIf (a), (b) isH - G）< dIf the measured plane meets the verticality requirement, the measured plane is qualified; otherwise, the product is unqualified; wherein the content of the first and second substances,dis the tolerance value of verticality.

3. The single reference plane-based error measurement workpiece perpendicularity rapid assessment method according to claim 1, wherein the measurement data of the general reference plane and the measured plane fitting data are subjected to coordinate transformation to obtain the XOZ plane of the measured plane three-dimensional center plane close to the coordinate system, the reference plane close to the XOY plane of the coordinate systemMeasuring point set of faceu _i }。

4. The method for rapidly evaluating the verticality of a single-datum-plane-based error measurement workpiece according to claim 2, wherein the coordinate transformation is as follows: moving according to the average value of the coordinates; or two: moving according to the extreme value of the coordinate; or three: and moving according to the root-mean-square minimum principle of coordinates.

5. The method for rapidly evaluating the verticality of a workpiece based on single reference plane error measurement according to claim 1, wherein the method comprises the steps ofb =1。

6. The single-datum-plane-based error measurement workpiece perpendicularity rapid assessment method according to claim 1, wherein the measured plane is a vertical plane perpendicular to the measured plane, and the datum plane is a vertical plane;

the verticality measurement result of the L-shaped error measurement workpiece meets the definition and requirement of verticality in GB/T1182-2018; the measurement result of the invention shows that the L-shaped error measurement workpiece can be used for measuring the verticality error of the part with the precision requirement.

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