CN110285781B - Rapid assessment method for plane parallelism relative to reference plane - Google Patents
Rapid assessment method for plane parallelism relative to reference plane Download PDFInfo
- Publication number
- CN110285781B CN110285781B CN201910620598.7A CN201910620598A CN110285781B CN 110285781 B CN110285781 B CN 110285781B CN 201910620598 A CN201910620598 A CN 201910620598A CN 110285781 B CN110285781 B CN 110285781B
- Authority
- CN
- China
- Prior art keywords
- plane
- measuring point
- reference plane
- measured
- key
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims description 53
- 239000011159 matrix material Substances 0.000 claims abstract description 36
- 239000013598 vector Substances 0.000 claims abstract description 32
- 238000004458 analytical method Methods 0.000 claims abstract description 27
- 238000005457 optimization Methods 0.000 claims description 10
- 238000004364 calculation method Methods 0.000 claims description 5
- 230000009191 jumping Effects 0.000 claims description 3
- 230000003416 augmentation Effects 0.000 claims description 2
- 238000012360 testing method Methods 0.000 claims description 2
- 238000005259 measurement Methods 0.000 abstract description 12
- 238000011156 evaluation Methods 0.000 abstract description 11
- 238000004883 computer application Methods 0.000 abstract description 3
- 239000000243 solution Substances 0.000 description 5
- 238000012545 processing Methods 0.000 description 4
- 238000013459 approach Methods 0.000 description 3
- 238000004422 calculation algorithm Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 238000012797 qualification Methods 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 239000012086 standard solution Substances 0.000 description 2
- 241001394244 Planea Species 0.000 description 1
- 238000013473 artificial intelligence Methods 0.000 description 1
- 230000003190 augmentative effect Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 210000000988 bone and bone Anatomy 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000014509 gene expression Effects 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Bridges Or Land Bridges (AREA)
- Length Measuring Devices With Unspecified Measuring Means (AREA)
Abstract
The invention belongs to the fields of precision measurement and computer application, and relates to a quick and simple plane parallelism evaluation method relative to a reference plane, which comprises the following steps: step 1: acquiring a measuring point set, constructing a state element set, a characteristic line vector set, a boundary element set and determining the position of a gauge according to the measuring point set; step 2: acquiring two key points; step 3: constructing an analysis matrix by using the key point set; step 4: performing rank analysis, determining whether to continue optimizing, and determining an optimizing strategy; step 5: solving an analysis matrix and analyzing column vectors to obtain an optimizing direction; step 6, solving new key points, updating the coordinate set of the measuring point and the position of the gauge, and entering the next circulation step; step 7, calculating the flatness of the reference plane; step 8: comparing flatness errorstWith a given tolerance valueT D Judging whether the product is qualified or not; step 9: if the flatness is qualified, calculating a parallelism error value of the measured plane; step 10: comparing parallelism errorst' with a given tolerance valueT’ D And (5) judging whether the line is qualified or not.
Description
Technical Field
The invention belongs to the field of precision measurement and computer application, and relates to a quick and simple method for evaluating the parallelism of a side surface to a reference plane, which can be used for detecting and evaluating the error qualification of the parallelism of the plane relative to the reference plane and provides reasonable guidance for the improvement of a processing technology.
Background
The shape and position errors (short for shape errors and position errors) have direct influence on the assembly precision, working precision, service life and other performances of machines and instruments, and have important significance for controlling the shape and position errors of machine parts, improving the precision of the machines, prolonging the service life, ensuring interchangeability and carrying out quick and accurate part error calculation.
The national standard GB/1182-2018 specifies a plane parallelism tolerance with respect to a reference plane, the surface to be measured being defined between two parallel planes parallel to the reference plane, with a spacing equal to the tolerance value. The invention refers to the parallelism as follows: parallelism of the plane with respect to the reference plane.
For face-to-face parallelism error measurement, the traditional method is to place the part to be tested on a flat plate, and use the working surface of the flat plate to simulate the reference plane of the part to be tested as a measurement reference, and measure each point on the actual surface, wherein the difference between the maximum reading and the minimum reading of the indicating surface is the parallelism error of the actual surface to the reference plane. However, this method is complicated to operate, takes a long time, and the measurement result is greatly affected by the measuring instrument and human factors.
In the fields of precision measurement and computer application, the parallelism of a measured plane relative to a reference plane can be calculated by measuring points on the measured plane and the reference plane through a three-coordinate measuring machine, and whether the parallelism of the measured plane is qualified or not is judged. However, the five currently popular assessment methods are difficult to directly apply to the error assessment of the plane parallelism with respect to the reference plane.
The first category, specialized geometric assessment methods. By utilizing the geometrical properties of the plane, gradually searching the minimum area meeting the definition and/or discrimination conditions of the national standard and the ISO standard according to the translation and deformation strategies of the plane. The method has high speed, but the mathematical model is complex, and the method is not easy to popularize in various tolerance assessment. Of course, this method is also difficult to generalize to planar parallelism assessment with respect to a reference plane.
And a second kind of convex hull or a method for evaluating the convex hull. And constructing a convex hull or a quasi-convex hull by utilizing the property of the convex hull, obtaining effective measurement data, reducing the scale of the data to be assessed, and finally obtaining a minimum area meeting the definition and/or discrimination conditions of the national standard and the ISO standard by an enumeration method. This type of method has significant advantages when dealing with mid-scale survey point data. In the case of larger data size, the data size can still be reduced by constructing convex hulls. However, the efficiency of such methods for direct assessment has been inadequate.
And thirdly, constructing a linear or nonlinear target optimization function, and carrying out optimization solution by adopting a common optimization method, wherein an optimization value of the target optimization function is used as a minimum area. The method is simple and easy to understand, and a standard solution method is realized in a plurality of software, so that the method is easy to popularize. However, such methods are generally inefficient because no geometric features are added to the assessment and the large data size in the assessment task is not considered.
Fourth, artificial intelligence/biological intelligence algorithms. The advantage of this type of approach over the third type of approach is to analyze the objective function with complex gradient resolution or no obvious resolution and find a "global optimum". The method realizes the standard solution in a plurality of software at present, and is easy to popularize. Although such methods are presently relatively hot, they are not well suited for use in error assessment of planar parallelism relative to a reference plane. This is because the gradient of the objective function of the assessment is the sum of a large number of simple analytical expressions and the part error is typically small. Thus, the "local optimum" of the objective function can be considered to be the "global optimum", and the fourth class of methods does not have significant advantages over the third class of methods.
And fifth, effective collection method. The active set method is a method for specially treating the large-scale planning problem, and is characterized in that the treatment of invalid constraint is reduced as much as possible in the optimizing process. When the method is applied to error assessment of the plane parallelism relative to the reference plane, the efficiency is equivalent to that of the first class of methods, the algorithm maturity and the software integration level are equivalent to those of the third class of methods and the fourth class of methods, and the method is a fast and simple error assessment method of the plane parallelism relative to the reference plane at present. However, this approach is very sensitive to initial values and does not always perform the geometric assessment task stably.
In summary, when the present geometric assessment method is applied to the plane parallelism relative to the reference plane, the characteristics of stability, rapidness and simple form cannot be simultaneously considered.
Disclosure of Invention
The purpose of the invention is that:
the invention provides a stable, quick and simple plane parallelism evaluation method relative to a reference plane, which aims at the problems in the prior art and can be used for detecting and evaluating the parallelism error qualification of a side plane relative to the reference plane. The results of parallelism qualification detection and evaluation of the mechanical parts can be used as the basis of part acceptance, and reasonable guidance can be provided for improvement of the processing technology.
The invention adopts the scheme that:
the method for rapidly evaluating the plane parallelism relative to the reference plane is realized by the following steps:
step 1: the measuring points of the reference plane are obtained and used for forming a measuring point set {p i And according to {p i Set of set-up feature row vectors {A i { boundary element set }b i { and state element set }T i }，G i,up For the position of the plane on the virtual gauge,G i,down is the position of the virtual gauge lower plane; the measuring points of the measured plane are obtained and used for forming a measured point set {p’ j And according to {p’ j Establishing a set of state elements under test {T’ j }，G’ j,up To determine the position of the plane on the virtual gauge of the plane to be measured,G’ j,down is the position of the virtual gauge lower plane, wherein:
i=1, 2, 3, …, N，iis the measuring point serial number of the reference plane,Nthe total number of measuring points is the reference plane;
p i ={x i , y i , z i the } is the measuring pointiIs close to the XOY plane of the coordinate system;
obtaining initial position of reference plane gaugeG i,up =z i,max ，G i,down =z i,min ；
Obtaining the position of the gauge mid-planeG mid =(G up +G down )÷2；
Measuring pointiDistance to plane on virtual gaugeT i,up = G i,up - z i,up Measuring pointiDistance to virtual gauge lower planeT i,down = z i,down - G i,down ；
A i =[1,/> y i ,/> x i ]Is a characteristic line vector, all characteristic line vectorsA i Is a feature row vector set {A i }；
b i =bIs a real number greater than 0, all boundary elementsb i Is a set of boundary elements {b i }；
j=1, 2, 3, …, N，jFor the measuring point serial number of the measured plane,Nthe total number of the measuring points is the measured plane;
p’ j ={x' j , y' j , z' j the } is the measuring pointjIs a space rectangular coordinate of (2);
obtaining initial position of measured plane gaugeG’ j,up = z' j,max ，G’ j,down = z' j,min ；
Obtaining the position of the gauge mid-planeG’ mid = (G’ up +G’ down ) ÷ 2；
Measuring pointjDistance to plane on virtual gaugeT’ j,up = G’ j,up -z' j,up Measuring pointjDistance to virtual gauge lower planeT’ j,down = G’ j,down - z' j,down All state elementsT’ j Is a set of state elements {T’ j }。
And (3) after the step (1) is finished, performing a step (2).
Step 2: taking outT i,up Corresponding measuring point with value of zerop l1 Is the key point and its measuring point sequence number l 1 Adding the key points into a key point set { l }; taking outT i,down Corresponding measuring point with value of zerop l2 Is the key point and its measuring point sequence number l 2 Added to the set of key points { l }.
And (3) after the step (2) is finished, performing a step (3).
Step 3: establishing an analysis matrix according to the key point set { l }, andAand analyzing column vectorsb, wherein ：
A=[…, A p T , …, A q T , …] T is one ofLA matrix of rows and columns 3,Lfor the number of elements in the set of key points l,p, qis an element in the set of key points { l };
b=[…, b p , …, b q , …] T is one ofLColumn vector of rows.
And step 4 is carried out after the step 3 is finished.
Step 4: pair analysis matrixAAugmentation analysis matrixA, b]Rank analysis was performed as follows:
computing an analysis matrixARank ofr A =rank(A) Augmentation of analysis matrixA, b]Rank ofr Ab =rank([A, b]) And comparer A Andr Ab there are only two cases:
case one: if it isr A =r Ab Then the optimization should be continued and the process jumps to step 5;
and a second case: if it isr A < r Ab Then, an attempt is made to analyze the matrix fromAAnd analyzing column vectorsbThe row corresponding to one element l in the key point set { l } is deleted to obtain a reduced matrixA l- And shrinkingColumn vectorb l- Solving a linear equationA l- v l- = b l- Solution of (2)v l- =v l-0 Then calculateb l- =A l v l-0 The method comprises the steps of carrying out a first treatment on the surface of the If all elements in the set of key points { l } are tried and none are obtainedb l- >b l Then, the optimization should be ended and the process jumps to step 7; if element l in the set of key points { l } is tried, we getb l- >b l Then the matrix will be scaled downA l- And narrowing the column vectorb l- Respectively asAMatrix and analytical column vectorsbShifting the element l out of the key point set { l }, and jumping to the step 5; wherein,v l- =[v l-,1 , v l-,2 , v l-,3 ] T ，v l-0 =[v l-0,1 , v l-0,2 , v l-0,3 ] T 。
step 5: measuring point motion vectorv 0 I.e. linear equationAv= bIs a solution of (1)v=v 0, wherein ,v=[ v 1 , v 2 , v 3 ] T ，v 0 =[ v 0,1 , v 0,2 , v 0,3 ] T 。
and (5) after the step (5) is finished, performing a step (6).
Step 6: calculation ofv i =A i v 0 ；
And then calculating: when (when)v i In the case of 1, the number of the times of the process is reduced,τ i =nan (NaN is equal to zero or negative); when (when)v i <In the case of 1, the number of the times of the process is reduced,τ i,up = T i,up ÷ (1- v i )，τ i,down = T i,down ÷ (1- v i ) Taking outτ i Minimum value in that part of the system that is greater than zeroτ min Corresponding serial number l 3 Is a new key sequence number and will l 3 Adding to the key point set { l };
{ all coordinate sets of the reference planep i Updates to [x i , y i , z i ] T + τ min ∙ v i All coordinate sets of the plane to be measured { simultaneouslyp’ j The motion rule according to the reference plane is updated as [ [x' j , y' j , z' j ] T + τ min ∙ v i ；
Updating gauge position of reference planeG i,up =z i,max ，G i,down =z i,min Gauge position updating of a measured planeG’ j,up = z' j,max ，G’ j,down = z' j,min 。
And (6) after the step (6) is finished, optimizing once, and performing the step (3).
Step 7: calculating flatness error of the reference plane:t = G i,up - G i,down 。
and step 8 is performed after the step 7 is finished.
Step 8: error in flatness of reference planetWith a given tolerance valueT D For comparison, there are two cases:
case one: when (when)t<T D When the flatness of the reference plane is qualified, performing a step 9;
and a second case: when (when)t>T D When the flatness of the reference plane is unqualified;
step 9: calculating parallelism error of the measured plane:t’= G’ j,up - G’ j,down ；
after the end of step 9, step 10 is performed.
Step 10: parallelism error of plane to be measuredt' with a given tolerance valueT’ D For comparison, there are two cases:
case one: when (when)t’<T’ D When the parallelism of the measured plane is qualified;
and a second case: when (when)t’>T’ D And when the parallelism of the measured plane is unqualified.
In order to conveniently obtain the measuring point set { in the step 1p i { and the measured point set }p’ j Measurement data of a general reference plane { may be used }p i Measurement data { of } and measured plane }p’ j Processing to obtain an axis approaching a coordinate system by, but not limited tozMeasuring point set { of plane center plane of shaft and measured two planes approaching to coordinate system XOY planep i { and the measured point set }p’ j }: 1. moving according to the average value of the coordinates; 2. moving according to the extreme value of the coordinates; 3. and moving according to the root mean square minimum principle of the coordinates.
To facilitate the numerical calculation, the method can be used to makebTake a specific value greater than 0 and may be, but is not limited to, 1.
The beneficial effects of the invention are as follows:
1. the geometrical characteristics of the plane parallelism relative to the reference plane are fully considered, and the evaluation form is simplified, so that the method is easier to popularize than the first-class evaluation method. 2. The geometrical characteristics of plane parallelism relative to a reference plane are fully considered, a better value is obtained through mature linear operation in each iteration, and the size of a minimum area is finally obtained, so that the algorithm is stable, and the initial value sensitivity problem of a fifth type of method does not exist. 3. The fact that most measuring points are invalid measuring points in the evaluation of plane parallelism errors relative to a reference plane is implied, and the invalid measuring points do not add iteration, so that the iteration number of the invention is less and is equivalent to the first-class evaluation method and the fifth-class evaluation method. 4. When calculating the optimizing direction, only the measuring points corresponding to the key point set { l } are considered, so the calculation amount of each iteration is small and is equivalent to a fifth type of evaluation method. 5. The total operation speed is equivalent to that of the first type evaluation method and the fifth type evaluation method because the iteration times are less and the operation amount of each iteration is smaller.
The invention provides a method for evaluating the plane parallelism relative to the reference plane, which is stable, quick and simple in form, can be used for evaluating the plane parallelism error relative to the reference plane, provides guidance for improving the processing technology of the plane parallelism error relative to the reference plane, and has industrial possibility.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a diagram of a tolerance design for a part in an embodiment.
Detailed Description
The following are specific embodiments of the present invention, and the embodiments of the present invention will be further described with reference to the accompanying drawings, but the present invention is not limited to these embodiments.
The parallelism of the parts of an inner ring of a tapered roller bearing was evaluated, and the tolerance design specifications thereof are shown in FIG. 2.
Step 1: obtain the reference plane measurement point set {p i And the measured plane measuring point set {p’ j Under }:
obtaining the size of the reference plane initial gaugeG up =0.0143，G down =5.1669e-04；
Obtaining gauge mid-plane positionG mid =0.0074；
Obtaining the size of the initial gauge of the measured planeG’ j,up = 60.0048，G’ j,down = 60.0007；
Obtaining gauge mid-plane positionG’ mid = 60.0027；
Set up reference plane state element set {T i And the measured plane state element set {T’ j The following are noted:
set up the characteristic line vector set { of the measured planeA i The following are noted:
and (3) after the step (1) is finished, performing a step (2).
Step 2: taking outT up Corresponding measuring point with value of zerop l7 The method comprises the steps that a key point is obtained, and a measuring point serial number 7 of the key point is added into a key point set { l }; taking outT down Corresponding measuring point with value of zerop l8 Is a key point and its measurement point sequence number 8 is added to the set of key points { l }, { l = {7,8}.
And (3) after the step (2) is finished, performing a step (3).
Step 3: establishing an analysis matrix according to the key point set { l }, andAand analyzing column vectorsb, wherein ：
，
is a matrix with two rows and three columns, the number of elements in the key point set { l } = {7,8} is 2, the elements are 7 and 8,
b=[1,1] T is a column vector of 2 rows.
And step 4 is carried out after the step 3 is finished.
Step 4: pair analysis matrixAAugmentation analysis matrixA, b]Rank analysis was performed as follows:
computing an analysis matrixARank ofr A =rank(A) =2, increaseBroad analysis matrix [A, b]Rank ofr Ab =rank([A,b]) =2, so the optimizing should be continued to step 5.
Step 5: linear equationAv=bOne solution of (2) isv=v 0 =[0, 0.0317, -0.0050] T 。
And (5) after the step (5) is finished, performing a step (6).
Step 6: calculating measuring pointiSpeed of (2)v i =A i v 0 The following are provided:
then calculate the tracking timeτ i The results were recorded as follows, with greater than 0:
wherein τ i，down = 7.5870e-05 is the minimum, corresponding stationp l2 For the new key sequence number, its measurement sequence number 2 is added to the key set { l }, { l = {7,8,2}.
And (6) after the step (6) is finished, optimizing once, and performing the step (3).
Similarly, after the third optimization is completed, the set of key points { l } = {7,8,2,3}.
At this time, all coordinates of the reference plane are collectedp i And all coordinate sets of the measured planep’ j The update results are as follows:
updating the gauge position of the reference plane toG i,up =0.0139，G i,down =8.8251e-04, updating the gauge position of the plane to be measured toG’ j,up =60.0055，G’ j,down =60.0011。
And (3) performing the following steps: establishing an analysis matrix according to the key point set { l } = {7,8,2,3}AAnd analyzing column vectorsb, wherein ：
，
is a matrix with four rows and three columns, the number of elements in the key point set { l } = {7,8,2,3} is 4, the elements are 7,8,2,3,
b=[1,1,1,1] T is a column vector of 4 rows.
And step 4 is carried out after the step 3 is finished.
Step 4: pair analysis matrixAAugmentation analysis matrixA, b]Rank analysis was performed as follows:
computing an analysis matrixARank ofr A =rank(A) =3, augmented analysis matrix [A, b]Rank ofr Ab =rank([A, b])=4。
Attempting to analyze the matrix fromAAnd analyzing column vectorsbThe row of element 7 in the key point set {7,8,2,3} is deleted to obtain a reduced matrixA -7 And narrowing the column vectorb -7 The method comprises the following steps of:
，
b -7 column vectorb=[1,1,1] T 。
Linear equationA -7 v -7 =b -7 Solution of (2)v -7 =v -70 =[1, 0.0368,0.0267] T 。
And then calculating:b -7 =A 7 v -70 = 1。
similarly, the corresponding one of {7,8,2,3} can be calculatedb -8 =1=b、b -2 =1= b、b -3 = -1.6364<1= b。
And (7) finishing optimizing and jumping to the step (7).
Step 7: calculating flatness error of reference planet = 0.0139 - 8.8251e-04 = 0.0130。
And step 8 is performed after the step 7 is finished.
Step 8: error in flatness of reference planetWith a given tolerance valueT D A comparison is made with respect to the number of the cells,t = 0.0130 < T D =and (9) performing step 9, wherein the flatness of the reference plane is qualified.
Step 9: calculating parallelism error of the measured plane:t’=60.0055-60.0011=0.0044。
after the end of step 9, step 10 is performed.
Step 10: parallelism error of plane to be measuredt' with a given tolerance valueT’ D A comparison is made with respect to the number of the cells,t’=0.0044<T’ D =0.005，
and the parallelism of the measured plane is qualified.
And (3) giving a conclusion: the part being inspected meets the parallelism requirements given in fig. 2.
In the above description, the present invention has been described by way of specific embodiments, but it will be understood by those skilled in the art that various modifications and variations can be made without departing from the spirit and scope of the invention within the scope of the claims.
Claims (1)
1. The method for rapidly evaluating the plane parallelism relative to the reference plane is characterized by comprising the following steps of:
step 1: the measuring points of the reference plane are obtained and used for forming a measuring point set {p i And according to {p i Set of set-up feature row vectors {A i { boundary element set }b i { and state element set }T i }，G i,up For the position of the plane on the virtual gauge,G i,down is the position of the virtual gauge lower plane; the measuring points of the measured plane are obtained and used for forming a measured point set {p’ j And according to {p’ j Establishing a set of state elements under test {T’ j }，G’ j,up To determine the position of the plane on the virtual gauge of the plane to be measured,G’ j,down is the position of the virtual gauge lower plane, wherein:
i=1, 2, 3, …, N，iis the measuring point serial number of the reference plane,Nthe total number of measuring points is the reference plane;
p i ={x i , y i , z i the } is the measuring pointiIs close to the XOY plane of the coordinate system;
obtaining initial position of reference plane gaugeG i,up =z i,max ，G i,down =z i,min ；
Obtaining the position of the mid-planeG mid =(G up +G down )÷2；
Measuring pointiDistance to plane on virtual gaugeT i,up = G i,up - z i,up Measuring pointiDistance to virtual gauge lower planeT i,down = z i,down - G i,down ；
A i =[ 1,/> y i ,/> x i ]Is a characteristic line vector, all characteristic line vectorsA i Is a feature row vector set {A i }；
b i =bIs a real number greater than 0, all boundary elementsb i Is a set of boundary elements {b i }；
j=1, 2, 3, …, N，jFor the measuring point serial number of the measured plane,Nthe total number of the measuring points is the measured plane;
p’ j ={x' j , y' j , z' j the } is the measuring pointjIs a space rectangular coordinate of (2);
obtaining initial position of measured plane gaugeG’ j,up = z' j,max ，G’ j,down = z' j,min ；
Obtaining the position of the mid-planeG’ mid = (G’ up +G’ down ) ÷ 2；
Measuring pointjDistance to plane on virtual gaugeT’ j,up = G’ j,up -z' j,up Measuring pointjDistance to virtual gauge lower planeT’ j,down = G’ j,down - z' j,down All state elementsT’ j Is a set of state elements {T’ j };
Step 2 is carried out after the step 1 is finished;
step 2: taking outT i,up Corresponding measuring point with value of zerop l1 Is the key point and its measuring point sequence number l 1 Adding the key points into a key point set { l }; taking outT i,down Has a value of zeroCorresponding measuring pointp l2 Is the key point and its measuring point sequence number l 2 Adding the key points into a key point set { l };
step 3 is carried out after the step 2 is finished;
step 3: establishing an analysis matrix according to the key sequence number set { l }AAnd analyzing column vectorsbWherein:
A=[…, A p T , …, A q T , …] T is one ofLA matrix of rows and columns 3,Lfor the number of elements in the set of key points l,p, qis an element in the set of key points { l };
b=[…, b p , …, b q , …] T is one ofLColumn vectors of rows;
step 3, after finishing the step 4;
step 4: pair analysis matrixAAugmentation analysis matrixA, b]Rank analysis was performed as follows:
computing an analysis matrixARank ofr A =rank(A) Augmentation of analysis matrixA, b]Rank ofr Ab =rank([A, b]) And comparer A Andr Ab there are only two cases:
case one: if it isr A =r Ab Then the optimization should be continued and the process jumps to step 5;
and a second case: if it isr A < r Ab Then, an attempt is made to analyze the matrix fromAAnd analyzing column vectorsbThe row corresponding to one element l in the key point set { l } is deleted to obtain a reduced matrixA l- And narrowing the column vectorb l- Solving a linear equationA l- v l- = b l- Solution of (2)v l- =v l-0 Then calculateb l- =A l v l-0 The method comprises the steps of carrying out a first treatment on the surface of the If all elements in the set of key points { l } are tried and none are obtainedb l- >b l Then, the optimization should be ended and the process jumps to step 7; if element l in the set of key points { l } is tried, we getb l- >b l Then the matrix will be scaled downA l- And narrowing the column vectorb l- Respectively asAMatrix and analytical column vectorsbShifting the element l out of the key point set { l }, and jumping to the step 5; wherein,v l- =[v l-,1 , v l-,2 , v l-,3 ] T ，v l-0 =[v l-0,1 , v l-0,2 , v l-0,3 ] T ;
step 5: measuring point motion vectorv 0 I.e. linear equationAv= bIs a solution of (1)v=v 0 Wherein, the method comprises the steps of, wherein,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 the step 5 is finished;
step 6: calculation ofv i =A i v 0 ；
And then calculating: when (when)v i In the case of 1, the number of the times of the process is reduced,τ i =nan (NaN is equal to zero or negative); when (when)v i <In the case of 1, the number of the times of the process is reduced,τ i,up = T i,up ÷ (1-v i )，τ i,down = T i,down ÷ (1- v i ) Taking outτ i Minimum value in that part of the system that is greater than zeroτ min Corresponding serial number l 3 Is a new key sequence number and will l 3 Adding to the key point set { l };
integrating all coordinates of a reference planep i Updated to [x i , y i , z i ] T + τ min ∙ v i All coordinate sets of the plane to be measured simultaneouslyp’ j Updated according to the motion law of the reference planex' j , y' j , z' j ] T + τ min ∙ v i ；
Updating gauge position of reference planeG i,up =z i,max ，G i,down =z i,min Gauge position updating of a measured planeG’ j,up = z' j,max ，G’ j,down = z' j,min ;
Step 6, optimizing once after finishing the step 3;
step 7: calculating flatness error of the reference plane:t = G i,up - G i,down ;
step 8 is carried out after the step 7 is finished;
step 8: error in flatness of reference planetWith a given tolerance valueT D For comparison, there are two cases:
case one: when (when)t<T D When the flatness of the reference plane is qualified, performing a step 9;
and a second case: when (when)t>T D When the flatness of the reference plane is unqualified;
step 9: calculating parallelism error of the measured plane:t’= G’ j,up - G’ j,down ；
step 10 is carried out after the step 9 is finished;
step 10: parallelism error of plane to be measuredt' with a given tolerance valueT’ D For comparison, there are two cases:
case one: when (when)t’<T’ D When the parallelism of the measured plane is qualified;
and a second case: when (when)t’>T’ D And when the parallelism of the measured plane is unqualified.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910620598.7A CN110285781B (en) | 2019-07-10 | 2019-07-10 | Rapid assessment method for plane parallelism relative to reference plane |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910620598.7A CN110285781B (en) | 2019-07-10 | 2019-07-10 | Rapid assessment method for plane parallelism relative to reference plane |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110285781A CN110285781A (en) | 2019-09-27 |
| CN110285781B true CN110285781B (en) | 2023-09-29 |
Family
ID=68021117
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910620598.7A Active CN110285781B (en) | 2019-07-10 | 2019-07-10 | Rapid assessment method for plane parallelism relative to reference plane |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110285781B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112747698A (en) * | 2019-10-29 | 2021-05-04 | 复盛应用科技股份有限公司 | Golf club head measuring method |
| CN111177645B (en) * | 2019-12-26 | 2023-08-29 | 哈尔滨工业大学 | Large-scale high-speed rotation equipment error hybrid assessment method based on large-scale point cloud data |
| CN112902880A (en) * | 2021-01-22 | 2021-06-04 | 大连理工大学 | Method and device for measuring parallelism of planar member |
| CN112902900A (en) * | 2021-01-22 | 2021-06-04 | 大连理工大学 | Parallelism measuring method of weak-rigidity plane member |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103292769A (en) * | 2013-06-19 | 2013-09-11 | 陈磊磊 | Plane inclination error evaluation method based on minimum zone |
| CN105841640A (en) * | 2016-04-29 | 2016-08-10 | 北京航空航天大学 | Planeness error evaluation method and device |
| CN108267106A (en) * | 2017-12-30 | 2018-07-10 | 唐哲敏 | A kind of Cylindricity error evaluation of fast steady letter |
| CN108286957A (en) * | 2017-12-30 | 2018-07-17 | 唐哲敏 | A kind of Flatness error evaluation method of fast steady letter |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE602004017513D1 (en) * | 2003-09-09 | 2008-12-11 | Mitutoyo Corp | Apparatus and method for shape measurement |
| JP2006119839A (en) * | 2004-10-20 | 2006-05-11 | Hitachi Cable Ltd | Science and engineering simulator using numerical value analysis method for simultaneous linear equations |
-
2019
- 2019-07-10 CN CN201910620598.7A patent/CN110285781B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103292769A (en) * | 2013-06-19 | 2013-09-11 | 陈磊磊 | Plane inclination error evaluation method based on minimum zone |
| CN105841640A (en) * | 2016-04-29 | 2016-08-10 | 北京航空航天大学 | Planeness error evaluation method and device |
| CN108267106A (en) * | 2017-12-30 | 2018-07-10 | 唐哲敏 | A kind of Cylindricity error evaluation of fast steady letter |
| CN108286957A (en) * | 2017-12-30 | 2018-07-17 | 唐哲敏 | A kind of Flatness error evaluation method of fast steady letter |
Non-Patent Citations (1)
| Title |
|---|
| 基于Matlab的平面度误差最小区域法评定;史立新, 朱思洪;组合机床与自动化加工技术(第09期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110285781A (en) | 2019-09-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110285781B (en) | Rapid assessment method for plane parallelism relative to reference plane | |
| CN111414658A (en) | Rock mass mechanics parameter inverse analysis method | |
| CN109948207A (en) | A kind of aircraft engine high pressure rotor rigging error prediction technique | |
| CN113609749B (en) | Current calculation method applicable to multiple scenes and based on magnetic field signals | |
| CN102445174A (en) | Multipoint flatness assessment method based on support vector regression | |
| Pathak et al. | Form error evaluation of noncontact scan data using constriction factor particle swarm optimization | |
| CN109931903A (en) | A kind of cylindricity assessment method based on improvement whale optimization algorithm | |
| CN109284574B (en) | Non-probability reliability analysis method for series truss structure system | |
| CN108846200B (en) | Quasi-static bridge influence line identification method based on iteration method | |
| Song et al. | Evaluation of axis straightness error of shaft and hole parts based on improved grey wolf optimization algorithm | |
| CN108267106B (en) | Quick, stable and simple cylindricity error evaluation method | |
| CN108286957A (en) | A kind of Flatness error evaluation method of fast steady letter | |
| CN107103129A (en) | The Forecasting Methodology of workpiece surface residual stress in a kind of machining | |
| CN109614758A (en) | The monitoring method of circular shape error with spatial coherence | |
| CN108680129A (en) | A kind of assessment method of the concentricity based on dual Tolerance Principle | |
| CN108592852A (en) | A kind of assessment method of the fast steady letter of the concentricity based on dual Tolerance Principle | |
| CN109858699B (en) | Water quality quantitative simulation method and device, electronic equipment and storage medium | |
| CN109063399A (en) | A kind of concentricity assessment method of the dual maximum material requirement of hole axle part | |
| CN108629127B (en) | Semi-analytic calculation method for eddy current detection magnetic field with circumferential asymmetric defects | |
| CN109214063A (en) | A kind of concentricity assessment method of the dual minimum material requirement of hole axle part | |
| CN110619139A (en) | Rapid position degree evaluation method based on single-datum hole shaft part | |
| CN108253917A (en) | A kind of minimum circumscribed cylinder diameter assessment method of fast steady letter | |
| CN113483721A (en) | Method for rapidly evaluating straightness in any direction by applying maximum entity requirement | |
| CN112212758A (en) | Method for evaluating digitalized common reference radial total run-out error | |
| CN108562258A (en) | A kind of maximum inscribed circle column diameter assessment method of fast steady letter |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |