CN110595424A - Method for evaluating straightness in any direction based on digital gauge - Google Patents
Method for evaluating straightness in any direction based on digital gauge Download PDFInfo
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Abstract
The invention belongs to the field of precision measurement and computer application, and relates to a method for evaluating the straightness of an entity gauge in any direction, which is rapid, stable, simple in form and digitalized, wherein the method comprises the following steps: 1: acquiring a measuring point set, and establishing a boundary element set and a state element set according to the measuring point set; 2: establishing a characteristic line vector set according to the measuring point set and the corresponding normal vector; 3: adding a key point; 4: establishing an analysis matrix and an analysis column vector; 5: performing rank analysis on the analysis matrix and the augmented analysis matrix to determine whether to continue optimizing, eliminating key points or terminating the program; 6: calculating an optimizing direction; 7: solving new key points by using the pursuit problem, calculating the optimization step, updating according to the formula in the step 1, and entering the next cycle, or entering the next cycle according to the step 4; 8: the procedure is terminated and the optimum value is obtained.
Description
Technical Field
The invention belongs to the field of precision metering and computer application, and relates to a rapid, stable, simple-form and digital method for evaluating straightness in any direction, which can be used for detecting and evaluating the axial straightness qualification of a stepped shaft of a winch device and provides guidance for the improvement of a machining process of the stepped shaft.
Background
The shaft and hole parts are common geometric elements in mechanical parts, the precision of the shaft and hole parts has important influence on the quality, performance and service life of products, and the straightness is a main technical index of the shaft and hole parts. According to the definition and the judgment method of the straightness in any direction given in the national standard GB/T11336-2004 and ISO standard, the straightness error evaluation of the part in any direction needs to meet the minimum region condition to obtain a better evaluation verification result. In view of the widespread application of computer digitization technology and the rapid development of digital measurement in current social production, the way of combining the physical gauge with measurement data to process parts in a mathematical model is undoubtedly superior to the traditional physical gauge detection. The loss of the gauge caused by use is avoided, and the geometric parameters of the gauge can be changed according to the detection requirements of different parts due to the fact that the gauge exists in a virtual model mode. Only the limitation of qualification can be detected relative to a physical gauge, and a digital gauge can also give an exact error value in detection.
At present, the evaluation of straightness errors of a digital gauge used in a given plane is a research hotspot of academia, and two main problems exist in the realization of the evaluation. One of the methods is how to establish an evaluation method model to optimally match the spatial position of the measuring point with an ideal straight line, so that the measuring point is in a minimum area taking the ideal straight line as an axis. At present, scholars at home and abroad propose corresponding optimization evaluation methods, such as: and carrying out minimum region search by using algorithms such as a genetic algorithm, a particle swarm algorithm, a containment region iterative search algorithm, a longicorn algorithm and the like. The models of the methods are complex in form and random in the calculation process, the stability of the result is ensured by the corresponding methods, and when the number of the measuring points is large, the calculation efficiency is not high so that the production requirement cannot be met.
In summary, a method for evaluating the straightness in any direction, which is rapid, stable, simple in form and digital, is still lacking at present.
Disclosure of Invention
The purpose of the invention is:
aiming at the problems in the prior art, the invention provides a quick, stable, simple-form and digital method for evaluating the straightness in any direction, which can be used for detecting and evaluating the axial straightness qualification of the stepped shaft of the winch equipment and provides guidance for the improvement of the processing technology of the stepped shaft.
The scheme adopted by the invention is as follows:
a method for evaluating the straightness in any direction based on a digital gauge is realized by the following steps:
step 1: placing the part to be measured on a measuring platform, measuring in a coordinate system of a measuring machine and obtaining a measuring pointQ i * ={X i , Y i ,Z i Great, collect the measurementQ i * And obtaining a z axis with the position of the measuring point as the minimum area line and close to the coordinate system through conventional coordinate transformation, wherein the central planes at two ends of the measuring point are close to the xoy plane of the coordinate system. Calculating according to a conventional fitting circle to obtain the center of each circle and obtain the coordinate value of a center measuring point passing through prepositioningQ i ={x i , y i , z i GreatQ i }. According to a set of measuring pointsQ i Establishing a boundary element setb i Great Chinese character and state element sett i }; wherein:i=1, 2, 3, …, N;ithe serial numbers of the measuring points are shown,Nthe total number of the measuring points is;
all state elementst i Is a set of state elementst i };
b i =bIs a real number greater than 0, all boundary elementsb i Is a set of boundary elementsb i };
After the step 1 is finished, performing a step 2;
step 2:Q i ={x i , y i , z i is the measurement pointiIs expressed in a space rectangular coordinate of (a), the envelope boundary is expressed with the Z-axis as an axis,t maxForming a cylindrical surface for an initial radius, the collection of all measuring pointsQ i The envelope boundary is positioned in the envelope boundary, and the envelope boundary contracts towards the Z axis at an assumed speed to enable the measuring point to adjust the position until the measuring point is in the minimum area;
measuring point setQ i The method is regarded as a rigid body, the measuring point set is pushed to slightly translate and rotate when the envelope boundary shrinks, and the normal vector of each measuring point isN i =[x i , y i ]TAnd projecting the motion speed of the measuring point to the normal vector. According to each measuring pointQ i And establishing characteristic row vectors by using corresponding normal vectorsA i Namely: A i =([-x i , -y i , y i z i , -x i z i ])/t i all characteristic line vectorsA i Is a set of characteristic line vectorsA i };
Step 3 is carried out after step 2 is finished;
and step 3: gett i Maximum valuet maxCorresponding measuring pointQ m Is a key point and the serial number of the measuring point ismJoined to a set of key pointsmIn (1) };
step 4 is carried out after step 3 is finished;
and 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
A=[…, A j T, …, A k T, …]Tis aLA matrix of rows and 4 columns,Lis a set of key pointsmThe number of the elements in the (C),j, kis a set of key pointsmThe elements in (1);
b=[…, b, …]Tis aLA column vector of rows;
step 5 is carried out after step 4 is finished;
and 5: for analysis matrixAAnd an augmented analysis matrixA, b]Performing rank analysis;
computingr A =rank(A),r Ab =rank([A, b]) And comparer A Andr Ab there are only two cases:
the first condition is as follows: if the judgment criterion is:r A =r Ab then, the optimization should be continued, jumping to step 6;
case two: if the judgment criterion is:r A < r Ab then, an attempt is made to determine from the analysis matrixAAnd analyzing the column vectorsbMiddle deleted key point setmOne of the elementsmCorresponding rows, obtaining a reduced matrixA m- And reducing the column vectorb m- Calculating a matrixA m- The rank of (c) is determined,r Am_ =rank(A m_ ) Extension matrix [ alpha ]A m_ , b m_ ]Rank ofr Am_bm_ =rank([A m_ , b m_ ]) Judgment ofr Am_ Andr Am_bm_ whether they are equal; in thatr Am_ Andr Am_bm_ if they are equal, then solve the linear equationA m- v m- = b l- Solution of (2)v m- =v m-0 Then calculateb m- =A m v m-0 (ii) a If the key point set is triedlElements in (b) }lWhen it is obtainedb m- >bThen, the matrix will be reducedA m- And reducing the column vectorb m- Are respectively updated toAMatrix and analysis column vectorbWill elementmMoving out key point setmAnd jumps to step 6, where,v m- =[v m-,1, v m-,2, v m-,3, v m-,4]T,v m-0 =[v m-0,1, v m-0,2, v m-0,3, v m-0,4]T. Key point setmEach of themmThe elements have tried, eachmElement is inr Am_ Andr Am_bm_ in case of inequality, that is to say none is obtainedb m- >bThen, the optimization should be ended, jumping to step 8;
step 6: solving linear equationsAv= bSolution of (2)v=v 0 Wherein, in the step (A),v=[v 1, v 2, v 3, v 4]T,v 0 =[v 0,1, v 0,2, v 0,3, v 0,4]T;
step 7 is carried out after step 6 is finished;
and 7: computingv i =A i v 0 Then calculateτ i =(t max– t i )÷(b - v i ). Getτ i Minimum value in the part of greater than zeroτ minCorresponding measuring pointQ m Is a new key point and the measured point is numberedmJoined to a set of key pointsmAll will bet i Is updated tot i –τ min∙ v i ,t maxIs updated tot i And updating the feature row vector set according to the formulas in step 1 and step 2A i Great, boundary element setb i Great Chinese character and state element sett i };
Finishing one-time optimization after the step 7 is finished, and performing the step 4;
and 8: computingt=2 t max The straightness error value in any direction is obtained;
to facilitate numerical calculation, can makebTaking a specific value greater than 0, but not limited to 1.
To facilitate numerical calculations, the measurement set is pre-positioned as: firstly, moving according to the average value of the coordinates, or secondly, moving according to the extreme value of the coordinates, or thirdly, moving according to the root mean square minimum principle of the coordinates.
To get a more accurate solution, the following optimization can be done: in step 7, a threshold value is assumed for controlling the amount of movement of the measurement point setqIf, ifτ min∙ v i Single order value ofτ min∙v i Or accumulated values sigma of several iterationsτ min∙v i Greater than a given thresholdqThen, willτ min∙ v i Single value of (S) or accumulated value (sigma) of past iterationsτ min∙ v i Is equal to a threshold valueqCollecting measuring pointsQ i Is updated toQ i + τ min∙vOrQ i +∑τ min∙v。
A method for quickly and stably evaluating the linearity in any direction in a simple and digitalized manner features that the measuring points are used for measuringQ i * ={X i , Y i ,Z i Obtained from the step shaft of the winch equipment.
The invention has the beneficial effects that:
1. the geometric characteristics of straightness in any direction are fully considered, the evaluation form is simplified, and the evaluation method is easier to popularize. 2. The geometric characteristics of straightness in any direction are fully considered, and a better value is obtained through mature linear operation in each iterationAnd finally the minimum straightness error is obtained, the motion displacement of the measuring point set is controlled, and a threshold value is assumedqTherefore, the algorithm is stable. 3. The fact that most measuring points are invalid measuring points in the straightness evaluation in any direction is implicit, the invalid measuring points are not added into iteration, and therefore the iteration number is small. And only the keypoint set is considered for the last page in the calculation of the optimizing directionmThe corresponding measuring points are calculated, so that the calculation amount of each iteration is small, and the algorithm is quick;
the invention provides a quick, stable, simple-form and digital method for evaluating the straightness in any direction, which can be used for detecting and evaluating the straightness errors of the axes of shaft and hole parts and provides guidance for the improvement of the processing technology of the shaft and hole parts, thereby having industrial possibility.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a tolerance layout of parts in an exemplary embodiment.
Detailed Description
The following are specific embodiments 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 embodiments;
evaluation test setQ i Straightness error in any direction.
Step 1: calculating to obtain measuring point setQ i The method comprises the following steps:
establishing a set of state elementst i The method comprises the following steps:
establishing a set of boundary elementsb i The method comprises the following steps:
{b i }=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]T。
after step 1, step 2 is performed.
Step 2: establishing a feature line vector setA i The method comprises the following steps:
after step 2, step 3 is performed.
And step 3: gett 16 =0.0531 maximum valuet maxCorresponding measuring pointQ 16Is a key point, and adds the measuring point serial number 16 to a key point setmIn is made-m}={16}。
After step 3, step 4 is performed.
And 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
A=[ A 16 T]T=[-0.68572 -0.72787 116.4585 -109.71516]is a matrix with 1 row and 4 columns;
b=[1]Tand is a column vector of 1 row.
After step 4, step 5 is performed.
And 5: for analysis matrixAAnd an augmented analysis matrixA, b]Rank analysis was performed. Computingr A =rank(A) =1,r Ab =rank([A, b]) =1, and comparingr A Andr Ab . Because of the fact thatr A =r Ab Then, the optimization should be continued, jumping to step 6;
step 6: solving linear equationsAv= bSolution of (2)v=v 0 Wherein, in the step (A),v 0 =[0,0,0.0045,-0.0043]T。
after step 6, step 7 is performed.
And 7: byv i =A i v 0 Calculating the measured point andrelative speed of its corresponding point on the gaugeb - v i The following are:
then calculateτ i =(t max – t i )÷(b - v i ). Getτ i Minimum value in the part of greater than zeroτ minThe corresponding measuring point 6 is a new key point, and the measuring point serial number 6 is added into the key point setmIn is made-m} = {6,16 }; and updating the boundary element set according to the formula in step 1b i Great Chinese character and state element sett i };
Establishing a set of boundary elementsb i The method comprises the following steps:
{b i }=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]T;
establishing a set of state elementst i The method comprises the following steps:
updating characteristic line vector set according to formula in step 2A i As follows:
and (4) jumping to the step 4 after the step 2 is finished.
And 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
is a matrix with 2 rows and 4 columns;
b=[1 1]Tand is a 2-row column vector.
After step 4, step 5 is performed.
And 5: for analysis matrixAAnd an augmented analysis matrixA, b]Rank analysis was performed. Computingr A =rank(A) =2,r Ab =rank([A, b]) =2, and comparingr A Andr Ab . Because of the fact thatr A =r Ab Then, the optimization should be continued, jumping to step 6;
step 6: solving linear equationsAv= bSolution of (2)v=v 0 Wherein, in the step (A),v 0 =[0.0001,0.0002,0.0153,-0.0071]T。
after step 6, step 7 is performed.
And 7: byv i =A i v 0 Calculating the relative speed of the measuring point and the corresponding point on the gaugeb - v i The following are:
then calculateτ i =(t max – t i )÷(b - v i ). Getτ i Minimum value in the part of greater than zeroτ minThe corresponding measuring point 6 is a new key point, and the measuring point serial number 6 is added into the key point setmIn is made-m} = {6,16 }; and updating the boundary element set according to the formulas in step 1 and step 2b i Great Chinese character and state element sett i Great, a feature line vector setA i };
And so on, iterating for the 16 th time to make the lastm} = {1,10,11,12,16 }; and updating the boundary element set according to the formula in step 1b i Great Chinese character and state element sett i }:
Establishing a set of boundary elementsb i The method comprises the following steps:
{b i }=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]T;
establishing a set of state elementst i The method comprises the following steps:
jumping to the step 4 after the step 1 is finished;
and 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
is a matrix with 2 rows and 4 columns;
b=[1 1]Tand is a 2-row column vector.
After step 4, step 5 is performed.
And 5: for analysis matrixAAnd an augmented analysis matrixA, b]Rank analysis was performed. Computingr A =rank(A) =2,r Ab =rank([A, b]) =2, and comparingr A Andr Ab . Because of the fact thatr A =r Ab Then, the optimization should be continued, jumping to step 6;
and (4) jumping to the step 4 after the step 2 is finished.
And 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
is a matrix with 5 rows and 4 columns;
b=[1 1 1 1 1]Tis 5 linesA column vector.
After step 4, step 5 is performed.
And 5: for analysis matrixAAnd an augmented analysis matrixA, b]Rank analysis was performed. Computingr A =rank(A) =4,r Ab =rank([A, b]) =5, and comparingr A Andr Ab . Because of the fact thatr A <r Ab Attempting to derive a secondary analysis matrixAAnd analyzing the column vectorsbMiddle deleted key point setmA row corresponding to one element 1,10,11,12 or 16 in (i);
firstly, deleting the row corresponding to the 1 st element in the key point to obtain a reduced matrixA 1And reducing the column vectorb 1Calculating a matrixA 1The rank of (c) is determined, r A1=rank(A 1) =4, augmentation matrix [, ]A 1, b 1]Rank ofr A1b1=rank([A 1, b 1]) =4 becauser A1=r A1b1 ,Then solve the linear equationA 1 v 1= b 1Solution of (2)v 1=v 10Then calculateb 1=A 1 v 20= -10.095 becauseb 1<bSo key point 1 is not a virtual contact;
then, deleting the row corresponding to the 10 th element in the key point to obtain a reduced matrixA 10And reducing the column vectorb 10Calculating a matrixA 10The rank of (c) is determined, r A10=rank(A 10) =4, augmentation matrix [, ]A 10, b 10]Rank ofr A10b10=rank([A 10, b 10]) =4 becauser A10=r A10b10 ,Then solve the linear equationA 10 v 4= b 10Solution of (2)v 10=v 100Then calculateb 10=A 10 v 100= -1.5445 becauseb 10<bSo the key point 10 is not a virtual contact;
then, deleting the row corresponding to the 11 th element in the key point to obtain a reduced matrixA 11And reducing the column vectorb 11Calculating a matrixA 11The rank of (c) is determined, r A11=rank(A 11) =4, augmentation matrix [, ]A 11, b 11]Rank r ofA11b11=rank([A 11, b 11]) =4 becauser A11=r A11b11 ,Then solve the linear equationA 11 v 11= b 11Solution of (2)v 11=v 110Then calculateb 11=A 11 v 110= -24.6985 becauseb 11<bSo the key point 11 is not a virtual contact point;
then, deleting the row corresponding to the 12 th element in the key point to obtain a reduced matrixA 12And reducing the column vectorb 12Calculating a matrixA 12The rank of (c) is determined, r A12=rank(A 12) =4, augmentation matrix [, ]A 12, b 12]Rank r ofA12b12=rank([A 12, b 12]) =4 becauser A12=r A12b12 ,Then solve the linear equationA 12 v 12= b 12Solution of (2)v 12=v 120Then calculateb 12=A 12 v 120= -1.3294 becauseb 12<bSo the keypoint 112 is not a virtual contact;
then, deleting the row corresponding to the 16 th element in the key point to obtain a reduced matrixA 16And reducing the column vectorb 16Calculating a matrixA 16The rank of (c) is determined, r A16=rank(A 16) =4, augmentation matrix [, ]A 16, b 16]Rank r ofA16b16=rank([A 16, b 16]) =4 becauser A16=r A16b16 ,Then solve the linear equationA 16 v 16= b 16Solution of (2)v 16=v 160Then calculateb 16=A 16 v 160= -19.5520 becauseb 16<bSo the keypoint 16 is not a virtual contact and the optimization is finished.
And jumping to the step 8 after the step 5 is finished.
And 8: computingt=2*0.0457=0.0914 is the straightness error value in any direction;
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 in the spirit and scope of the invention without departing from the scope of the claims;
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.
Claims (5)
1. A method for evaluating the straightness in any direction based on a digital gauge is realized by the following steps:
step 1: placing the part to be measured on a measuring platform, measuring in a coordinate system of a measuring machine and obtaining a measuring pointQ i * ={X i , Y i ,Z i Great, collect the measurementQ i * And obtaining a z axis with the position of the measuring point as the minimum area line and close to the coordinate system through conventional coordinate transformation, wherein the central planes at two ends of the measuring point are close to the xoy plane of the coordinate system. Calculating according to a conventional fitting circle to obtain the center of each circle and obtain the coordinate value of a center measuring point passing through prepositioningQ i ={x i , y i , z i GreatQ i }. According toMeasuring point setQ i Establishing a boundary element setb i Great Chinese character and state element sett i }; wherein:i=1, 2, 3, …, N;ithe serial numbers of the measuring points are shown,Nthe total number of the measuring points is;
all state elementst i Is a set of state elementst i };
b i =bIs a real number greater than 0, all boundary elementsb i Is a set of boundary elementsb i };
After the step 1 is finished, performing a step 2;
step 2:Q i ={x i , y i , z i is the measurement pointiIs expressed in a space rectangular coordinate of (a), the envelope boundary is expressed with the Z-axis as an axis,t maxForming a cylindrical surface for an initial radius, the collection of all measuring pointsQ i The envelope boundary is positioned in the envelope boundary, and the envelope boundary contracts towards the Z axis at an assumed speed to enable the measuring point to adjust the position until the measuring point is in the minimum area;
measuring point setQ i The method is regarded as a rigid body, the measuring point set is pushed to slightly translate and rotate when the envelope boundary shrinks, and the normal vector of each measuring point isN i =[x i , y i ]TAnd projecting the motion speed of the measuring point to the normal vector. According to each measuring pointQ i And establishing characteristic row vectors by using corresponding normal vectorsA i Namely: A i =([-x i , -y i , y i z i , -x i z i ])/t i all characteristic line vectorsA i Is a set of characteristic line vectorsA i };
Step 3 is carried out after step 2 is finished;
and step 3: gett i Maximum valuet maxCorresponding measuring pointQ m Is a key point and the serial number of the measuring point ismJoined to a set of key pointsmIn (1) };
step 4 is carried out after step 3 is finished;
and 4, step 4: according to the set of key pointsmEstablishment of an analysis matrixAAnd analyzing the column vectorsbWherein:
A=[…, A j T, …, A k T, …]Tis aLA matrix of rows and 4 columns,Lis a set of key pointsmThe number of the elements in the (C),j, kis a set of key pointsmThe elements in (1);
b=[…, b, …]Tis aLA column vector of rows;
step 5 is carried out after step 4 is finished;
and 5: for analysis matrixAAnd an augmented analysis matrixA, b]Performing rank analysis;
computingr A =rank(A),r Ab =rank([A, b]) And comparer A Andr Ab there are only two cases:
the first condition is as follows: if the judgment criterion is:r A =r Ab then, the optimization should be continued, jumping to step 6;
case two: if the judgment criterion is:r A < r Ab then, an attempt is made to determine from the analysis matrixAAnd analyzing the column vectorsbMiddle deleted key point setmOne of the elementsmCorresponding rows, obtaining a reduced matrixA m- And reducing the column vectorb m- Calculating a matrixA m- The rank of (c) is determined,r Am_ =rank(A m_ ) Extension matrix [ alpha ]A m_ , b m_ ]Rank ofr Am_bm_ =rank([A m_ , b m_ ]) Judgment ofr Am_ Andr Am_bm_ whether they are equal; in thatr Am_ Andr Am_bm_ if they are equal, then solve the linear equationA m- v m- = b l- Solution of (2)v m- =v m-0 Then calculateb m- =A m v m-0 (ii) a If the key point set is triedlElements in (b) }lWhen it is obtainedb m- >bThen, the matrix will be reducedA m- And reducing the column vectorb m- Are respectively updated toAMatrix and analysis column vectorbWill elementmMoving out key point setmAnd jumps to step 6, where,v m- =[v m-,1, v m-,2, v m-,3, v m-,4]T,v m-0 =[v m-0,1, v m-0,2, v m-0,3, v m-0,4]T. Key point setmEach of themmThe elements have tried, eachmElement is inr Am_ Andr Am_bm_ in case of inequality, that is to say none is obtainedb m- >bThen, the optimization should be ended, jumping to step 8;
step 6: solving linear equationsAv= bSolution of (2)v=v 0 Wherein, in the step (A),v=[v 1, v 2, v 3, v 4]T,v 0 =[v 0,1, v 0,2, v 0,3, v 0,4]T;
step 7 is carried out after step 6 is finished;
and 7: computingv i =A i v 0 Then calculateτ i =(t max– t i )÷(b - v i ). Getτ i Minimum value in the part of greater than zeroτ minCorresponding measuring pointQ m Is a new key point and the measured point is numberedmJoined to a set of key pointsmAll will bet i Is updated tot i –τ min∙ v i ,t maxIs updated tot i And updating the feature row vector set according to the formulas in step 1 and step 2A i Great, boundary element setb i Great Chinese character and state element sett i };
Finishing one-time optimization after the step 7 is finished, and performing the step 4;
and 8: computingt=2 t max Is the error value of straightness in any direction.
2. The method of claim 1, wherein the linear degree in any direction is evaluated based on a digital gauge, wherein the linear degree is assumed to be linearb=1。
3. A method for assessing straightness in any direction based on a digitized gauge as claimed in claim 1, wherein for ease of numerical calculations the measurement set is pre-positioned by: firstly, moving according to the average value of the coordinates, or secondly, moving according to the extreme value of the coordinates, or thirdly, moving according to the root mean square minimum principle of the coordinates.
4. A method for assessing the linearity of any direction based on a digital gauge as claimed in claim 1, wherein the following optimization is performed for obtaining a more accurate solution: in step 7, in order to control the amount of movement displacement of the measuring point set,assume a threshold valueqIf, ifτ min∙ v i Single order value ofτ min∙v i Or accumulated values sigma of several iterationsτ min∙v i Greater than a given thresholdqThen, willτ min∙v i Single value of (S) or accumulated value (sigma) of past iterationsτ min∙ v i Is equal to a threshold valueqCollecting measuring pointsQ i Is updated toQ i + τ min∙vOrQ i +∑τ min∙v。
5. The method for assessing the linearity of any direction based on the digital gauge as claimed in claim 1, wherein the method can be used for detecting and assessing the qualification of the linearity of the axis of the stepped shaft of the winding machine equipment.
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