CN103292654A - Method for calculating function size of cylindrical part - Google Patents

Method for calculating function size of cylindrical part Download PDF

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CN103292654A
CN103292654A CN2013102302548A CN201310230254A CN103292654A CN 103292654 A CN103292654 A CN 103292654A CN 2013102302548 A CN2013102302548 A CN 2013102302548A CN 201310230254 A CN201310230254 A CN 201310230254A CN 103292654 A CN103292654 A CN 103292654A
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contact point
point
contact
coordinate
calculate
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CN103292654B (en
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黄美发
陈磊磊
宫文峰
孙永厚
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Guilin University of Electronic Technology
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Abstract

A method for calculating function size of a cylindrical part comprises the steps of firstly measuring and obtaining coordinates of measured points on a measured cylindrical surface, then providing initial parameter of the cylinder, projecting the measured points onto a plane perpendicular to the axis, calculating the function size of a projection circle through translation change of a tolerance zone and accordingly searching three contact points in the tolerance zone, respectively searching a fourth contact point and a fifth contact point in contact with the tolerance zone through rotating change of the tolerance zone and change of cylinder radius, using four contact points to form one group when the number of the contact points is larger than 5, further changing the cylinder radius under the condition that the four contact points are in contact, then replacing one group and continuing to change the cylinder radius, sequentially performing iterative computation till criterions are met, and outputting the function size of the cylinder, a cylindricity error and an optimal value of a cylinder axis parameter. By means of the method, a cylindrical radius optimal value and the cylindricity error meeting function surface criterions can be accurately calculated.

Description

A kind of method of calculating cylindrical part effect size
Technical field
The present invention relates to a kind of method of calculating cylindrical part effect size, belong to delicate metering and computer application field, the qualification that can be used for cylindrical geometric product under the various situations detects, and provides guidance for the improvement of part processing process and processing technology.
Background technology
Cylinder is one of modal element in the mechanical component, and its precision is to quality, performance and the serviceable life of product having significant effects, and the important technological parameters that cylindrical effect size is cylindrical component.Maximum inscribed cylinder and minimum circumscribed circle post are referred to as cylindrical action face, and the radius of the radius of maximum inscribed cylinder and minimum circumscribed circle post is referred to as cylindrical effect size.
The computing method of maximum inscribed cylinder and minimum circumscribed circle post are based on the computing method that the detection principle of smooth cylinder ring gauge is set up.Maximum inscribed cylinder has embodied the maximum fitted shaft that measured hole can pass through, and thus obtained deviation from cylindrical form can be considered the maximal clearance between measured hole and the maximum fitted shaft; And the minimum circumscribed circle cylinder has showed the minimum mating holes that measured axis can pass through, and thus obtained deviation from cylindrical form can be considered the maximal clearance between measured axis and the minimum mating holes.
Right cylinder effect size calculation belongs to the non-differentiability complex optimization problem.At present, Chinese scholars mainly adopts traditional optimization, intelligent algorithm, computational geometry method etc.Computational stability is poor, counting yield is low, number of spots is restricted to adopting, result of calculation is difficult to reach defectives such as exact solution owing to existing for these methods, causes maximum inscribed cylinder method and minimum circumscribed circle post method to be difficult in the actual detected and uses.Generally all adopt ripe least square method to calculate the effect size of cylindrical part approx in the market.
Summary of the invention
In order to overcome above-mentioned technical disadvantages, the purpose of this invention is to provide a kind of method of calculating cylindrical part effect size.This method has not only improved the precision of surveying instrument measurement right cylinder effect size, and algorithm stability is good, counting yield is high, can be applied to its solid effect size calculation.
A kind of method of calculating cylindrical part effect size of the present invention be used for to be calculated cylindrical imperial palace and is connect size, mainly may further comprise the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery
Figure 517506DEST_PATH_IMAGE001
, =1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points Form the measuring point collection
Figure 871761DEST_PATH_IMAGE004
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector
Figure 874352DEST_PATH_IMAGE005
Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector After the coordinate transform, with measuring point
Figure 748953DEST_PATH_IMAGE007
Be projected in XoyIn the plane, obtain measuring point
Figure 990579DEST_PATH_IMAGE008
Coordinate
Figure 468965DEST_PATH_IMAGE009
All measuring points
Figure 846856DEST_PATH_IMAGE010
Form the measuring point collection
Step 3: at point set
Figure 97895DEST_PATH_IMAGE011
In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 442289DEST_PATH_IMAGE012
, as the center of circle
Figure 940266DEST_PATH_IMAGE013
The iteration initial value.
Step 4: calculate the measuring point collection successively
Figure 384017DEST_PATH_IMAGE011
In each measuring point to the center of circle
Figure 600235DEST_PATH_IMAGE013
Distance; And record measuring point collection
Figure 482740DEST_PATH_IMAGE011
In each measuring point to central coordinate of circle
Figure 835224DEST_PATH_IMAGE013
The corresponding measuring point of the minor increment of distance obtains the contact point set of error containment region inner boundary
Figure 702073DEST_PATH_IMAGE014
Step 5: the contact point set of error in judgement containment region inner boundary
Figure 140008DEST_PATH_IMAGE014
In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 826204DEST_PATH_IMAGE015
Equal central coordinate of circle Deduct the contact point coordinate, jump to step 8;
If contact point quantity greater than 1, then jumps to next step.
Step 6: the contact point set of error in judgement containment region inner boundary In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 9558DEST_PATH_IMAGE015
Equal central coordinate of circle
Figure 233866DEST_PATH_IMAGE013
Deduct the middle point coordinate of 2 contact point lines, jump to step 8;
If contact point quantity greater than 2, then jumps to next step.
Step 7: calculate each contact point
Figure 747893DEST_PATH_IMAGE016
The relative center of circle
Figure 32243DEST_PATH_IMAGE013
The phasing degree
Figure 179191DEST_PATH_IMAGE017
,
Figure 144873DEST_PATH_IMAGE018
The phasing degree that has point of contact
Figure 326456DEST_PATH_IMAGE017
Form set
Figure 781708DEST_PATH_IMAGE019
, right
Figure 681531DEST_PATH_IMAGE019
In element sort, obtain vector
Figure 434592DEST_PATH_IMAGE020
, compute vector
Figure 470681DEST_PATH_IMAGE020
In adjacent 2 phasing degree
Figure 96834DEST_PATH_IMAGE020
Poor,
Figure 218374DEST_PATH_IMAGE021
Figure 525859DEST_PATH_IMAGE022
Quantity for contact point; Calculate
Figure 682033DEST_PATH_IMAGE023
If, , then satisfy the oxygon criterion, jump to step 9; If
Figure 274875DEST_PATH_IMAGE025
, inquiry
Figure 182788DEST_PATH_IMAGE023
2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 193469DEST_PATH_IMAGE015
Equal central coordinate of circle
Figure 161425DEST_PATH_IMAGE013
Deduct the middle point coordinate of 2 effective contact point lines.
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 195240DEST_PATH_IMAGE008
Center of circle virtual location during contact
Figure 906844DEST_PATH_IMAGE026
Calculate each noncontact measuring point at first respectively
Figure 37611DEST_PATH_IMAGE008
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 360490DEST_PATH_IMAGE013
And direction vector is
Figure 678339DEST_PATH_IMAGE015
The intersection point of straight line, be containment region and vary to and this measuring point
Figure 193634DEST_PATH_IMAGE008
During contact, the virtual location in the center of circle
Figure 178907DEST_PATH_IMAGE026
, all noncontact measuring point correspondences
Figure 426349DEST_PATH_IMAGE026
Form set , calculate each noncontact measuring point correspondence
Figure 284900DEST_PATH_IMAGE026
To the center of circle
Figure 124680DEST_PATH_IMAGE013
Distance
Figure 792291DEST_PATH_IMAGE028
, all
Figure 350311DEST_PATH_IMAGE028
Constitute set
Figure 941830DEST_PATH_IMAGE029
, in set In, reject
Figure 490940DEST_PATH_IMAGE015
With
Figure 270677DEST_PATH_IMAGE030
Incorgruous corresponding element, query set then
Figure 852837DEST_PATH_IMAGE029
In minimum value, be the translation variation of containment region According to the containment region variation
Figure 489672DEST_PATH_IMAGE031
And moving direction vector
Figure 694388DEST_PATH_IMAGE032
, calculate the coordinate in the center of circle
Figure 893288DEST_PATH_IMAGE012
Forward step 4 to.
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 562167DEST_PATH_IMAGE013
Coordinate after the coordinate transform
Figure 555531DEST_PATH_IMAGE033
, be cylinder axis LOn a bit, cylinder axis LWith
Figure 499402DEST_PATH_IMAGE006
Be direction vector.
Step 10: calculate the measuring point collection successively In each measuring point to axis LDistance; And record measuring point collection
Figure 124735DEST_PATH_IMAGE004
In each measuring point to axis LMinimum value and value, record is gathered for the contact point of containment region inner boundary apart from the measuring point set of minimum value correspondence
Figure 366361DEST_PATH_IMAGE035
, the minimum value and value that records is the radius of cylinder R
Step 11: judge the contact point set of containment region inner boundary
Figure 907063DEST_PATH_IMAGE035
Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis
Figure 474836DEST_PATH_IMAGE036
Direction vector In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure 538924DEST_PATH_IMAGE038
,
Figure 883317DEST_PATH_IMAGE039
, zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment
Figure 825045DEST_PATH_IMAGE041
Equal axis
Figure 775684DEST_PATH_IMAGE036
Direction vector
Figure 845140DEST_PATH_IMAGE006
With
Figure 197624DEST_PATH_IMAGE042
Vector multiplication cross; Rotation change angle is set
Figure 140172DEST_PATH_IMAGE043
Initial value; Calculate
Figure 515790DEST_PATH_IMAGE006
With
Figure 201986DEST_PATH_IMAGE042
Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14.
Step 12: calculate Around Rotation
Figure 634607DEST_PATH_IMAGE043
Direction vector after the angle
Figure 858915DEST_PATH_IMAGE044
Then, 3 contact points are projected in perpendicular to
Figure 185991DEST_PATH_IMAGE044
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with
Figure 142446DEST_PATH_IMAGE044
Determine the axis of postrotational cylinder
Figure 554973DEST_PATH_IMAGE045
Step 13: calculate all noncontacts and put Distance
Figure 951505DEST_PATH_IMAGE046
If,
Figure 406757DEST_PATH_IMAGE047
Figure 41001DEST_PATH_IMAGE048
, then represent the variation deficiency, the anglec of rotation
Figure 607111DEST_PATH_IMAGE043
Become
Figure 846463DEST_PATH_IMAGE049
Otherwise, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation Become
Figure 594156DEST_PATH_IMAGE050
Judge Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 327591DEST_PATH_IMAGE043
Before and after twice the difference of iterative value less than setting
Figure 62329DEST_PATH_IMAGE043
The error permissible value, then the 4th contact point found in explanation, then will
Figure 671165DEST_PATH_IMAGE044
Assignment is given
Figure 579078DEST_PATH_IMAGE006
, jump to step 10; If
Figure 776710DEST_PATH_IMAGE043
The difference of the iterative value that front and back are twice is not less than setting
Figure 744666DEST_PATH_IMAGE043
The error permissible value then jumps to step 12.
Step 14: judge the contact point set of containment region inner boundary Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius recruitment
Figure 490085DEST_PATH_IMAGE051
Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17.
Step 15:
Figure 355273DEST_PATH_IMAGE051
Add current cylindrical radius
Figure 494130DEST_PATH_IMAGE048
Obtain
Figure 264509DEST_PATH_IMAGE052
, obtaining cylinder after the dimensional variations, its axis is
Figure 779804DEST_PATH_IMAGE053
, each contact point is to axis
Figure 499498DEST_PATH_IMAGE053
Distance equal
Figure 746940DEST_PATH_IMAGE052
Relation, obtain following calculating formula,
Wherein
Figure 871071DEST_PATH_IMAGE055
Be axis Direction vector,
Figure 378461DEST_PATH_IMAGE056
Be axis
Figure 936482DEST_PATH_IMAGE053
On a bit, with
Figure 528000DEST_PATH_IMAGE057
,
Figure 159970DEST_PATH_IMAGE058
Be unknown quantity, obtain 4 quaternary nonlinear equations respectively, can solve 4 unknown quantitys by Nonlinear System of Equations, obtain the axis of cylinder
Figure 77110DEST_PATH_IMAGE053
Step 16: calculate all noncontacts successively and put
Figure 856847DEST_PATH_IMAGE053
Distance
Figure 441937DEST_PATH_IMAGE059
, all noncontact measuring point correspondences
Figure 256309DEST_PATH_IMAGE059
Form set
Figure 78771DEST_PATH_IMAGE060
If,
Figure 345805DEST_PATH_IMAGE061
Figure 482388DEST_PATH_IMAGE051
+ , then represent the variation deficiency, Become
Figure 898960DEST_PATH_IMAGE062
If
Figure 822922DEST_PATH_IMAGE063
Figure 346308DEST_PATH_IMAGE051
+
Figure 776152DEST_PATH_IMAGE048
, then change excessively, all the other noncontact measuring points exceed containment region,
Figure 955461DEST_PATH_IMAGE051
Become
Judge Before and after 2 times the difference of iterative value whether less than setting The error permissible value; If Before and after 2 times the difference of iterative value less than setting
Figure 203908DEST_PATH_IMAGE051
The error permissible value illustrates and finds the 5th contact point, will
Figure 701886DEST_PATH_IMAGE055
,
Figure 411216DEST_PATH_IMAGE056
Assignment is given axis respectively LParameter
Figure 361854DEST_PATH_IMAGE006
,
Figure 244359DEST_PATH_IMAGE033
, and judge whether to satisfy criterion, and then jump to step 18 if satisfy, if do not satisfy criterion, jump to step 10; If
Figure 596843DEST_PATH_IMAGE051
The difference of the iterative value that front and back are 2 times is not less than setting
Figure 726342DEST_PATH_IMAGE051
The error permissible value then jumps to step 15.
Step 17: judge the contact point set of containment region inner boundary
Figure 164277DEST_PATH_IMAGE035
Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 584894DEST_PATH_IMAGE051
Judge Whether less than setting The error permissible value; If
Figure 33827DEST_PATH_IMAGE051
Less than what set The error permissible value judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates
Figure 503653DEST_PATH_IMAGE051
, judge that again iteration is gone down successively; If
Figure 788004DEST_PATH_IMAGE051
Greater than what set
Figure 200530DEST_PATH_IMAGE051
The error permissible value is with what calculate
Figure 166212DEST_PATH_IMAGE053
The parameter assignment give cylinder axis respectively LParameter
Figure 347795DEST_PATH_IMAGE006
,
Figure 537468DEST_PATH_IMAGE033
, jump to step 10 then.
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
In the said method, described step 3 may be used solely to calculate maximum inscribed circle degree and the effect size of revolving parts cross section circle to step 8.
The another kind of method of calculating cylindrical part effect size of the present invention, be used for calculating the external size of cylindrical minimum, be characterized in connecing size calculation process basically identical with imperial palace, difference is to inquire about the mode of contact point, the change direction of containment region, comprises the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery
Figure 437291DEST_PATH_IMAGE001
,
Figure 190352DEST_PATH_IMAGE002
=1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points Form the measuring point collection
Figure 852594DEST_PATH_IMAGE004
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector
Figure 177397DEST_PATH_IMAGE005
Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector
Figure 547198DEST_PATH_IMAGE006
After the coordinate transform, with measuring point Be projected in XoyIn the plane, obtain measuring point
Figure 234848DEST_PATH_IMAGE008
Coordinate All measuring points
Figure 204127DEST_PATH_IMAGE010
Form the measuring point collection
Figure 214809DEST_PATH_IMAGE011
Step 3: at point set
Figure 182765DEST_PATH_IMAGE011
In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 216580DEST_PATH_IMAGE012
, as the center of circle
Figure 928184DEST_PATH_IMAGE013
The iteration initial value.
Step 4: calculate the measuring point collection successively
Figure 793372DEST_PATH_IMAGE011
In each measuring point to the center of circle
Figure 119180DEST_PATH_IMAGE013
Distance; And record measuring point collection
Figure 702608DEST_PATH_IMAGE011
In each measuring point to central coordinate of circle
Figure 952323DEST_PATH_IMAGE013
The corresponding measuring point of the ultimate range of distance obtains the contact point set that error contains area outer
Figure 937597DEST_PATH_IMAGE014
Step 5: the contact point set of error in judgement containment region outer boundary
Figure 185039DEST_PATH_IMAGE014
In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 255763DEST_PATH_IMAGE015
Equal the contact point coordinate and deduct central coordinate of circle
Figure 309170DEST_PATH_IMAGE013
, jump to step 8;
If contact point quantity greater than 1, then jumps to next step.
Step 6: the contact point set of error in judgement containment region outer boundary
Figure 338830DEST_PATH_IMAGE014
In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 819490DEST_PATH_IMAGE015
The middle point coordinate that equals 2 contact point lines deducts central coordinate of circle
Figure 111931DEST_PATH_IMAGE013
, jump to step 8;
If contact point quantity greater than 2, then jumps to next step.
Step 7: calculate each contact point
Figure 969028DEST_PATH_IMAGE016
The relative center of circle
Figure 600998DEST_PATH_IMAGE013
The phasing degree
Figure 252559DEST_PATH_IMAGE017
,
Figure 297876DEST_PATH_IMAGE018
The phasing degree that has point of contact
Figure 880036DEST_PATH_IMAGE017
Form set
Figure 428829DEST_PATH_IMAGE019
, right
Figure 516870DEST_PATH_IMAGE019
In element sort, obtain vector
Figure 783904DEST_PATH_IMAGE020
, compute vector
Figure 920487DEST_PATH_IMAGE020
In adjacent 2 phasing degree
Figure 323786DEST_PATH_IMAGE020
Poor,
Figure 582729DEST_PATH_IMAGE021
Figure 337059DEST_PATH_IMAGE022
Quantity for contact point; Calculate
Figure 261021DEST_PATH_IMAGE023
If,
Figure 784407DEST_PATH_IMAGE065
, then satisfy oxygon criterion or diameter criterion, jump to step 9; If
Figure 214251DEST_PATH_IMAGE066
, inquiry 2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 668683DEST_PATH_IMAGE015
The middle point coordinate that equals 2 effective contact point lines deducts the center of circle
Figure 312154DEST_PATH_IMAGE013
Coordinate.
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 834271DEST_PATH_IMAGE008
Center of circle virtual location during contact
Figure 563193DEST_PATH_IMAGE026
Calculate each noncontact measuring point at first respectively
Figure 642007DEST_PATH_IMAGE008
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 139985DEST_PATH_IMAGE013
And direction vector is
Figure 583735DEST_PATH_IMAGE015
The intersection point of straight line, be containment region and vary to and this measuring point During contact, the virtual location in the center of circle
Figure 682458DEST_PATH_IMAGE026
, all noncontact measuring point correspondences
Figure 218963DEST_PATH_IMAGE026
Form set
Figure 161512DEST_PATH_IMAGE027
, calculate each noncontact measuring point correspondence
Figure 599446DEST_PATH_IMAGE026
To the center of circle
Figure 957746DEST_PATH_IMAGE013
Distance
Figure 430316DEST_PATH_IMAGE028
, all Constitute set , in set
Figure 614676DEST_PATH_IMAGE029
In, reject With
Figure 226102DEST_PATH_IMAGE030
Incorgruous corresponding element, query set then
Figure 576312DEST_PATH_IMAGE029
In minimum value, be the translation variation of containment region
Figure 338732DEST_PATH_IMAGE031
According to the containment region variation
Figure 520315DEST_PATH_IMAGE031
And moving direction vector
Figure 162517DEST_PATH_IMAGE032
, calculate the coordinate in the center of circle
Figure 23DEST_PATH_IMAGE012
Forward step 4 to.
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 566134DEST_PATH_IMAGE013
Coordinate after the coordinate transform
Figure 602223DEST_PATH_IMAGE033
Figure 415327DEST_PATH_IMAGE034
, be cylinder axis LOn a bit, cylinder axis LWith Be direction vector.
Step 10: calculate the measuring point collection successively In each measuring point to axis LDistance; And record measuring point collection In each measuring point to axis LThe maximal value of distance, record is gathered for the contact point of containment region outer boundary apart from the measuring point set of maximal value correspondence
Figure 797581DEST_PATH_IMAGE067
, the maximal value of the distance that records is the radius of cylinder R
Step 11: judge the contact point set of containment region outer boundary
Figure 406417DEST_PATH_IMAGE067
Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis Direction vector
Figure 780471DEST_PATH_IMAGE037
In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure 748427DEST_PATH_IMAGE068
,
Figure 782242DEST_PATH_IMAGE069
,
Figure 228267DEST_PATH_IMAGE070
zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment
Figure 359034DEST_PATH_IMAGE041
Equal axis
Figure 497891DEST_PATH_IMAGE036
Direction vector
Figure 205953DEST_PATH_IMAGE006
With
Figure 455669DEST_PATH_IMAGE071
Vector multiplication cross; Rotation change angle is set
Figure 440942DEST_PATH_IMAGE043
Initial value; Calculate
Figure 937652DEST_PATH_IMAGE006
With
Figure 8376DEST_PATH_IMAGE072
Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14.
Step 12: calculate
Figure 61783DEST_PATH_IMAGE006
Around
Figure 901563DEST_PATH_IMAGE041
Rotation Direction vector after the angle
Figure 612347DEST_PATH_IMAGE044
Then, 3 contact points are projected in perpendicular to
Figure 469444DEST_PATH_IMAGE044
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with Determine the axis of postrotational cylinder
Figure 2243DEST_PATH_IMAGE045
Step 13: calculate all noncontact measuring points and arrive
Figure 47559DEST_PATH_IMAGE045
Distance
Figure 380451DEST_PATH_IMAGE046
If,
Figure 929244DEST_PATH_IMAGE073
Figure 17286DEST_PATH_IMAGE048
, then represent the variation deficiency, the anglec of rotation Become
Figure 401661DEST_PATH_IMAGE049
If
Figure 70540DEST_PATH_IMAGE074
Figure 329483DEST_PATH_IMAGE048
, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation
Figure 755916DEST_PATH_IMAGE043
Become
Figure 758507DEST_PATH_IMAGE050
Judge Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 446158DEST_PATH_IMAGE043
Before and after twice the difference of iterative value less than setting
Figure 874734DEST_PATH_IMAGE043
The error permissible value, then the 4th contact point found in explanation, then will
Figure 415437DEST_PATH_IMAGE044
Assignment is given
Figure 793328DEST_PATH_IMAGE006
, jump to step 10; If
Figure 331757DEST_PATH_IMAGE043
The difference of the iterative value that front and back are twice is not less than setting The error permissible value then jumps to step 12.
Step 14: judge the contact point set of containment region outer boundary Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius decrease Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17.
Step 15: Deduct current cylindrical radius
Figure 546707DEST_PATH_IMAGE048
Obtain
Figure 429212DEST_PATH_IMAGE052
, obtaining cylinder after the dimensional variations, its axis is
Figure 781696DEST_PATH_IMAGE053
, each contact point is to axis
Figure 396348DEST_PATH_IMAGE053
Distance equal
Figure 834283DEST_PATH_IMAGE052
Relation, obtain following calculating formula,
Figure 520479DEST_PATH_IMAGE075
Wherein
Figure 914420DEST_PATH_IMAGE055
Be axis
Figure 27870DEST_PATH_IMAGE053
Direction vector,
Figure 953100DEST_PATH_IMAGE056
Be axis
Figure 177408DEST_PATH_IMAGE053
On a bit, with
Figure 442167DEST_PATH_IMAGE057
,
Figure 726518DEST_PATH_IMAGE058
Be unknown quantity, obtain 4 quaternary nonlinear equations respectively, can solve 4 unknown quantitys by Nonlinear System of Equations, obtain the axis of cylinder
Step 16: calculate all noncontacts successively and put
Figure 91345DEST_PATH_IMAGE053
Distance , all noncontact measuring point correspondences
Figure 728180DEST_PATH_IMAGE059
Form set
Figure 628003DEST_PATH_IMAGE060
If,
Figure 131796DEST_PATH_IMAGE076
Figure 167885DEST_PATH_IMAGE051
+
Figure 980990DEST_PATH_IMAGE048
, then represent the variation deficiency,
Figure 102529DEST_PATH_IMAGE051
Become
Figure 472331DEST_PATH_IMAGE062
If
Figure 628506DEST_PATH_IMAGE077
Figure 363243DEST_PATH_IMAGE051
+
Figure 972079DEST_PATH_IMAGE048
, then change excessively, all the other noncontact measuring points exceed containment region,
Figure 879992DEST_PATH_IMAGE051
Become
Figure 890674DEST_PATH_IMAGE064
Judge
Figure 45581DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value whether less than setting
Figure 141712DEST_PATH_IMAGE051
The error permissible value; If
Figure 853317DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value less than setting The error permissible value illustrates and finds the 5th contact point, will
Figure 60624DEST_PATH_IMAGE055
,
Figure 378473DEST_PATH_IMAGE056
Assignment is given axis respectively LParameter
Figure 893768DEST_PATH_IMAGE006
,
Figure 65992DEST_PATH_IMAGE033
, and judge whether to satisfy criterion, and then jump to step 18 if satisfy, if do not satisfy criterion, jump to step 10; If
Figure 375751DEST_PATH_IMAGE051
The difference of the iterative value that front and back are 2 times is not less than setting
Figure 180896DEST_PATH_IMAGE051
The error permissible value then jumps to step 15.
Step 17: judge the contact point set of containment region outer boundary
Figure 171985DEST_PATH_IMAGE067
Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 11765DEST_PATH_IMAGE051
Judge
Figure 492425DEST_PATH_IMAGE051
Whether less than setting
Figure 50446DEST_PATH_IMAGE051
The error permissible value; If
Figure 849422DEST_PATH_IMAGE051
Less than what set The error permissible value judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates , judge that again iteration is gone down successively; If
Figure 240587DEST_PATH_IMAGE051
Greater than what set
Figure 573479DEST_PATH_IMAGE051
The error permissible value is with what calculate The parameter assignment give cylinder axis respectively LParameter
Figure 210314DEST_PATH_IMAGE006
,
Figure 664298DEST_PATH_IMAGE033
, jump to step 10 then.
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
In the said method, described step 3 may be used solely to calculate minimum circumscribed circle degree and the effect size of revolving parts cross section circle to step 8.
In the said method, described technical scheme can computer memory any direction linearity.
In the said method, described step 3 can be calculated any direction Line To Line parallelism error to step 8.At first, carry out Rotating Transition of Coordinate, the direction vector of datum line is parallel to zJust, done corresponding rigid body rotation by the discrete point of survey line simultaneously, existed by the containing cylinder of survey line this moment XoyThe plane inner projection is circle.Can use the step 3 described in the said method then to step 8, to being carried out match by the discrete point projection of survey line.
In the said method, described step 3 can be calculated any direction line opposite error of perpendicularity to step 8.At first carry out Rotating Transition of Coordinate, the normal vector of reference field is parallel to zJust, done corresponding rigid body rotation by the discrete point of survey line simultaneously, existed by the containing cylinder of survey line this moment XoyThe plane inner projection is circle.Can use the step 3 described in the said method then to step 8, to being carried out match by the discrete point projection of survey line.
 
The present invention on the optimization direction of cylindrical radius, carries out corresponding translation change, rotation change or translation change to containment region according to the feature of cylinder self, finally calculates cylinder parameter optimal value and deviation from cylindrical form optimal value.
Beneficial effect of the present invention is:
The cylindrical radius that calculates is optimal value, and the relative position of contact point satisfies criterion, and computational stability is good, counting yield is high.
To those skilled in the art, according to use design disclosed by the invention, can easily carry out various distortion and change to the present invention program, should be noted in the discussion above that all these distortion and change all should belong to scope of the present invention.
Description of drawings
Fig. 1 connects the radius calculation process flow diagram for the imperial palace of cylinder of the present invention.
Fig. 2 connects the radius calculation design sketch for the imperial palace of cylinder of the present invention.
Fig. 3 is the minimum external radius calculation design sketch of cylinder of the present invention.
Embodiment
Embodiment 1:
A kind of method of calculating cylindrical part effect size be used for to be calculated cylindrical imperial palace and is connect size, as shown in Figure 1, comprises the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery
Figure 863198DEST_PATH_IMAGE001
,
Figure 532077DEST_PATH_IMAGE002
=1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points
Figure 463123DEST_PATH_IMAGE003
Form the measuring point collection
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector
Figure 220044DEST_PATH_IMAGE005
Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector
Figure 743429DEST_PATH_IMAGE006
After the coordinate transform, with measuring point
Figure 94645DEST_PATH_IMAGE007
Be projected in XoyIn the plane, obtain measuring point Coordinate
Figure 876973DEST_PATH_IMAGE009
All measuring points Form the measuring point collection
Figure 793294DEST_PATH_IMAGE011
Step 3: at point set
Figure 256636DEST_PATH_IMAGE011
In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 601030DEST_PATH_IMAGE012
, as the center of circle
Figure 20379DEST_PATH_IMAGE013
The iteration initial value.
Step 4: calculate the measuring point collection successively
Figure 792025DEST_PATH_IMAGE011
In each measuring point to the center of circle
Figure 742664DEST_PATH_IMAGE013
Distance; And record measuring point collection
Figure 562852DEST_PATH_IMAGE011
In each measuring point to central coordinate of circle
Figure 915336DEST_PATH_IMAGE013
The corresponding measuring point of the minor increment of distance obtains the contact point set of error containment region inner boundary
Figure 857885DEST_PATH_IMAGE014
Step 5: the contact point set of error in judgement containment region inner boundary
Figure 295819DEST_PATH_IMAGE014
In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 171896DEST_PATH_IMAGE015
Equal central coordinate of circle Deduct the contact point coordinate, jump to step 8;
If contact point quantity greater than 1, then jumps to next step.
Step 6: the contact point set of error in judgement containment region inner boundary
Figure 430019DEST_PATH_IMAGE014
In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 355249DEST_PATH_IMAGE015
Equal central coordinate of circle
Figure 579557DEST_PATH_IMAGE013
Deduct the middle point coordinate of 2 contact point lines, jump to step 8;
If contact point quantity greater than 2, then jumps to next step.
Step 7: calculate each contact point
Figure 906634DEST_PATH_IMAGE016
The relative center of circle
Figure 112356DEST_PATH_IMAGE013
The phasing degree
Figure 524883DEST_PATH_IMAGE017
,
Figure 552881DEST_PATH_IMAGE018
The phasing degree that has point of contact
Figure 672147DEST_PATH_IMAGE017
Form set
Figure 127399DEST_PATH_IMAGE019
, right
Figure 761643DEST_PATH_IMAGE019
In element sort, obtain vector
Figure 327754DEST_PATH_IMAGE020
, compute vector
Figure 816373DEST_PATH_IMAGE020
In adjacent 2 phasing degree
Figure 442526DEST_PATH_IMAGE020
Poor,
Figure 501749DEST_PATH_IMAGE021
Figure 871550DEST_PATH_IMAGE022
Quantity for contact point; Calculate
Figure 27725DEST_PATH_IMAGE023
If,
Figure 11731DEST_PATH_IMAGE024
, then satisfy the oxygon criterion, jump to step 9; If
Figure 620566DEST_PATH_IMAGE025
, inquiry
Figure 528480DEST_PATH_IMAGE023
2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 539161DEST_PATH_IMAGE015
Equal central coordinate of circle
Figure 444800DEST_PATH_IMAGE013
Deduct the middle point coordinate of 2 effective contact point lines.
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 540932DEST_PATH_IMAGE008
Center of circle virtual location during contact
Figure 252536DEST_PATH_IMAGE026
Calculate each noncontact measuring point at first respectively
Figure 301745DEST_PATH_IMAGE008
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 440602DEST_PATH_IMAGE013
And direction vector is The intersection point of straight line, be containment region and vary to and this measuring point
Figure 477008DEST_PATH_IMAGE008
During contact, the virtual location in the center of circle
Figure 196703DEST_PATH_IMAGE026
, all noncontact measuring point correspondences
Figure 506461DEST_PATH_IMAGE026
Form set , calculate each noncontact measuring point correspondence
Figure 817543DEST_PATH_IMAGE026
To the center of circle
Figure 657323DEST_PATH_IMAGE013
Distance
Figure 137983DEST_PATH_IMAGE028
, all
Figure 633686DEST_PATH_IMAGE028
Constitute set
Figure 225204DEST_PATH_IMAGE029
, in set In, reject
Figure 23582DEST_PATH_IMAGE015
With
Figure 803319DEST_PATH_IMAGE030
Incorgruous corresponding element, query set then
Figure 198529DEST_PATH_IMAGE029
In minimum value, be the translation variation of containment region According to the containment region variation
Figure 773046DEST_PATH_IMAGE031
And moving direction vector , calculate the coordinate in the center of circle
Figure 238980DEST_PATH_IMAGE012
Forward step 4 to.
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 94809DEST_PATH_IMAGE013
Coordinate after the coordinate transform
Figure 88173DEST_PATH_IMAGE033
Figure 842502DEST_PATH_IMAGE034
, be cylinder axis LOn a bit, cylinder axis LWith Be direction vector.
Step 10: calculate the measuring point collection successively
Figure 40583DEST_PATH_IMAGE004
In each measuring point to axis LDistance; And record measuring point collection
Figure 470427DEST_PATH_IMAGE004
In each measuring point to axis LMinimum value and value, record is gathered for the contact point of containment region inner boundary apart from the measuring point set of minimum value correspondence
Figure 712052DEST_PATH_IMAGE035
, the minimum value and value that records is the radius of cylinder R
Step 11: judge the contact point set of containment region inner boundary
Figure 177056DEST_PATH_IMAGE035
Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis
Figure 820527DEST_PATH_IMAGE036
Direction vector
Figure 155694DEST_PATH_IMAGE037
In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure 822298DEST_PATH_IMAGE038
,
Figure 901113DEST_PATH_IMAGE039
,
Figure 399090DEST_PATH_IMAGE040
zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment Equal axis
Figure 308326DEST_PATH_IMAGE036
Direction vector
Figure 190832DEST_PATH_IMAGE006
With
Figure 543316DEST_PATH_IMAGE042
Vector multiplication cross; Rotation change angle is set
Figure 423547DEST_PATH_IMAGE043
Initial value; Calculate
Figure 861481DEST_PATH_IMAGE006
With Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14.
Step 12: calculate
Figure 754668DEST_PATH_IMAGE006
Around
Figure 55068DEST_PATH_IMAGE041
Rotation
Figure 980299DEST_PATH_IMAGE043
Direction vector after the angle
Figure 204607DEST_PATH_IMAGE044
Then, 3 contact points are projected in perpendicular to
Figure 203787DEST_PATH_IMAGE044
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with
Figure 488138DEST_PATH_IMAGE044
Determine the axis of postrotational cylinder
Step 13: calculate all noncontacts and put
Figure 115614DEST_PATH_IMAGE045
Distance
Figure 297197DEST_PATH_IMAGE046
If, , then represent the variation deficiency, the anglec of rotation
Figure 890486DEST_PATH_IMAGE043
Become
Figure 192155DEST_PATH_IMAGE049
Otherwise, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation
Figure 552729DEST_PATH_IMAGE043
Become
Figure 123869DEST_PATH_IMAGE050
Judge
Figure 493670DEST_PATH_IMAGE043
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 384266DEST_PATH_IMAGE043
Before and after twice the difference of iterative value less than setting
Figure 119004DEST_PATH_IMAGE043
The error permissible value, then the 4th contact point found in explanation, then will
Figure 727840DEST_PATH_IMAGE044
Assignment is given
Figure 901332DEST_PATH_IMAGE006
, jump to step 10; If
Figure 912013DEST_PATH_IMAGE043
The difference of the iterative value that front and back are twice is not less than setting
Figure 66920DEST_PATH_IMAGE043
The error permissible value then jumps to step 12.
Step 14: judge the contact point set of containment region inner boundary
Figure 163052DEST_PATH_IMAGE035
Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius recruitment
Figure 874656DEST_PATH_IMAGE051
Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17.
Step 15:
Figure 739844DEST_PATH_IMAGE051
Add current cylindrical radius Obtain , obtaining cylinder after the dimensional variations, its axis is
Figure 649528DEST_PATH_IMAGE053
, each contact point is to axis
Figure 821752DEST_PATH_IMAGE053
Distance equal
Figure 131511DEST_PATH_IMAGE052
Relation, obtain following calculating formula,
Wherein
Figure 255642DEST_PATH_IMAGE055
Be axis Direction vector,
Figure 513765DEST_PATH_IMAGE056
Be axis
Figure 806206DEST_PATH_IMAGE053
On a bit, with
Figure 850254DEST_PATH_IMAGE057
,
Figure 544541DEST_PATH_IMAGE058
Be unknown quantity, obtain 4 quaternary nonlinear equations respectively, can solve 4 unknown quantitys by Nonlinear System of Equations, obtain the axis of cylinder
Figure 196102DEST_PATH_IMAGE053
Step 16: calculate all noncontacts successively and put
Figure 179101DEST_PATH_IMAGE053
Distance
Figure 574311DEST_PATH_IMAGE059
, all noncontact measuring point correspondences Form set If,
Figure 668059DEST_PATH_IMAGE061
Figure 866959DEST_PATH_IMAGE051
+
Figure 270259DEST_PATH_IMAGE048
, then represent the variation deficiency,
Figure 466885DEST_PATH_IMAGE051
Become
Figure 221214DEST_PATH_IMAGE062
If
Figure 958226DEST_PATH_IMAGE063
Figure 481611DEST_PATH_IMAGE051
+
Figure 98406DEST_PATH_IMAGE048
, then change excessively, all the other noncontact measuring points exceed containment region,
Figure 74452DEST_PATH_IMAGE051
Become
Figure 615155DEST_PATH_IMAGE064
Judge
Figure 196309DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value whether less than setting
Figure 531476DEST_PATH_IMAGE051
The error permissible value; If
Figure 260397DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value less than setting
Figure 339212DEST_PATH_IMAGE051
The error permissible value illustrates and finds the 5th contact point, will
Figure 961823DEST_PATH_IMAGE055
, Assignment is given axis respectively LParameter
Figure 684108DEST_PATH_IMAGE006
, , with each contact point difference substitution following formula,
Figure 43731DEST_PATH_IMAGE079
Wherein
Figure 986280DEST_PATH_IMAGE080
Be contact point
Figure 608235DEST_PATH_IMAGE007
The relative phasing degree of axis, thus each contact point correspondence obtained
Figure 28852DEST_PATH_IMAGE081
, construct following discriminant function,
Figure 501422DEST_PATH_IMAGE082
Be the feasible zone of being determined by following inequality group:
Figure 212206DEST_PATH_IMAGE084
In the following formula, first constraint is vector equation,
Figure 436514DEST_PATH_IMAGE085
The zero column vector of expression 4 dimensions, second and third is constrained to numerical value equation,
Figure 763590DEST_PATH_IMAGE086
Be the quantity of contact point, judgement is the optimum solution discriminant value
Figure 234892DEST_PATH_IMAGE087
Whether equal 0, if
Figure 647418DEST_PATH_IMAGE087
Equal 0 expression and satisfy criterion, jump to step 18, if Be not equal to 0 sufficient criterion with thumb down, jump to step 10; If The difference of the iterative value that front and back are 2 times is not less than setting
Figure 984356DEST_PATH_IMAGE051
The error permissible value then jumps to step 15.
Step 17: judge the contact point set of containment region inner boundary
Figure 884179DEST_PATH_IMAGE035
Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 450289DEST_PATH_IMAGE051
Judge
Figure 673329DEST_PATH_IMAGE051
Whether less than setting
Figure 299482DEST_PATH_IMAGE051
The error permissible value; If
Figure 686601DEST_PATH_IMAGE051
Less than what set
Figure 728507DEST_PATH_IMAGE051
The error permissible value, the method for applying step 16 judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates
Figure 884682DEST_PATH_IMAGE051
, judge that again iteration is gone down successively; If
Figure 681736DEST_PATH_IMAGE051
Greater than what set
Figure 290572DEST_PATH_IMAGE051
The error permissible value is with what calculate
Figure 651015DEST_PATH_IMAGE053
The parameter assignment give cylinder axis respectively LParameter
Figure 661697DEST_PATH_IMAGE006
,
Figure 629653DEST_PATH_IMAGE033
, jump to step 10 then.
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
Below example by experiment illustrates the validity that institute of the present invention publish method is calculated.
On measuring table, obtain 24 points on the cylindrical part surface, the measuring point coordinate is as shown in table 1.Use the method that the present invention announces, the radius of action that calculates maximum inscribed cylinder is 14.99985062mm, cylinder axis direction vector (0.000459923841223342,-0.000624025400837475,0.999999699531135), a point coordinate is (432.422127159553,137.332674827430 on the cylinder axis, 0.252514286852374), cylindricity is 0.03418mm.The effect of calculating is (among the figure, * is measuring point, and O is contact point) as shown in Figure 2, and the 5th, 10,14,16, No. 17 measuring point is contact point.Calculate each contact point respectively
Figure 663468DEST_PATH_IMAGE088
Mapping, and the discriminant value of calculating optimum solution J, as calculated J=1.1382e-014 satisfies criterion, and the cylinder radius of action that calculates and deviation from cylindrical form are optimum solution.
The measuring point coordinate of table 1 cylinder (unit: Mm)
The measuring point numbering xCoordinate yCoordinate zCoordinate The measuring point numbering xCoordinate yCoordinate zCoordinate
1 447.47556 137.3431 -92.99958 13 447.48749 137.37276 -85.66769
2 440.00617 150.36197 -93.05586 14 439.98814 150.36122 -85.7225
3 424.95893 150.38625 -93.05948 15 424.97535 150.38594 -85.72581
4 417.45656 137.3433 -93.00753 16 417.4618 137.37364 -85.67423
5 425.00292 124.3788 -92.95196 17 424.98576 124.38214 -85.61846
6 439.9693 124.38485 -92.9484 18 439.98586 124.38661 -85.61504
7 439.98027 124.38204 -89.28298 19 439.99686 124.38255 -81.94842
8 424.99233 124.37691 -89.28517 20 424.96931 124.37052 -81.95173
9 417.46167 137.3578 -89.34018 21 417.459 137.38801 -82.007
10 424.96768 150.38132 -89.3926 22 424.96877 150.40734 -82.05929
11 439.9954 150.36113 -89.38932 23 439.98606 150.37835 -82.05603
12 447.48307 137.35783 -89.33457 24 447.49399 137.38793 -82.0014
Embodiment 2:
A kind of method of calculating cylindrical part effect size when be used for calculating the external size of cylindrical minimum, comprises the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery ,
Figure 240260DEST_PATH_IMAGE002
=1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points Form the measuring point collection
Figure 152425DEST_PATH_IMAGE004
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector After the coordinate transform, with measuring point
Figure 821807DEST_PATH_IMAGE007
Be projected in XoyIn the plane, obtain measuring point Coordinate
Figure 945938DEST_PATH_IMAGE009
All measuring points
Figure 785718DEST_PATH_IMAGE010
Form the measuring point collection
Figure 204061DEST_PATH_IMAGE011
Step 3: at point set In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 353600DEST_PATH_IMAGE012
, as the center of circle
Figure 234837DEST_PATH_IMAGE013
The iteration initial value.
Step 4: calculate the measuring point collection successively
Figure 886398DEST_PATH_IMAGE011
In each measuring point to the center of circle Distance; And record measuring point collection
Figure 264607DEST_PATH_IMAGE011
In each measuring point to central coordinate of circle
Figure 813400DEST_PATH_IMAGE013
The corresponding measuring point of the ultimate range of distance obtains the contact point set that error contains area outer
Figure 901441DEST_PATH_IMAGE014
Step 5: the contact point set of error in judgement containment region outer boundary In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 288746DEST_PATH_IMAGE015
Equal the contact point coordinate and deduct central coordinate of circle
Figure 957625DEST_PATH_IMAGE013
, jump to step 8;
If contact point quantity greater than 1, then jumps to next step.
Step 6: the contact point set of error in judgement containment region outer boundary
Figure 216568DEST_PATH_IMAGE014
In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 643001DEST_PATH_IMAGE015
The middle point coordinate that equals 2 contact point lines deducts central coordinate of circle
Figure 645592DEST_PATH_IMAGE013
, jump to step 8;
If contact point quantity greater than 2, then jumps to next step.
Step 7: calculate each contact point
Figure 168978DEST_PATH_IMAGE016
The relative center of circle The phasing degree
Figure 782327DEST_PATH_IMAGE017
,
Figure 323030DEST_PATH_IMAGE018
The phasing degree that has point of contact
Figure 700921DEST_PATH_IMAGE017
Form set
Figure 239350DEST_PATH_IMAGE019
, right
Figure 702692DEST_PATH_IMAGE019
In element sort, obtain vector
Figure 47086DEST_PATH_IMAGE020
, compute vector
Figure 732014DEST_PATH_IMAGE020
In adjacent 2 phasing degree
Figure 238082DEST_PATH_IMAGE020
Poor,
Figure 454300DEST_PATH_IMAGE021
Figure 274488DEST_PATH_IMAGE022
Quantity for contact point; Calculate
Figure 626972DEST_PATH_IMAGE023
If,
Figure 303941DEST_PATH_IMAGE065
, then satisfy oxygon criterion or diameter criterion, jump to step 9; If
Figure 741875DEST_PATH_IMAGE066
, inquiry
Figure 615022DEST_PATH_IMAGE023
2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 822013DEST_PATH_IMAGE015
The middle point coordinate that equals 2 effective contact point lines deducts the center of circle
Figure 935462DEST_PATH_IMAGE013
Coordinate.
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 798376DEST_PATH_IMAGE008
Center of circle virtual location during contact
Figure 22684DEST_PATH_IMAGE026
Calculate each noncontact measuring point at first respectively
Figure 349760DEST_PATH_IMAGE008
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 821062DEST_PATH_IMAGE013
And direction vector is
Figure 968009DEST_PATH_IMAGE015
The intersection point of straight line, be containment region and vary to and this measuring point
Figure 996008DEST_PATH_IMAGE008
During contact, the virtual location in the center of circle
Figure 115274DEST_PATH_IMAGE026
, all noncontact measuring point correspondences Form set
Figure 470349DEST_PATH_IMAGE027
, calculate each noncontact measuring point correspondence
Figure 226340DEST_PATH_IMAGE026
To the center of circle
Figure 262429DEST_PATH_IMAGE013
Distance
Figure 888582DEST_PATH_IMAGE028
, all
Figure 10122DEST_PATH_IMAGE028
Constitute set
Figure 317607DEST_PATH_IMAGE029
, in set
Figure 473782DEST_PATH_IMAGE029
In, reject
Figure 270836DEST_PATH_IMAGE015
With
Figure 66623DEST_PATH_IMAGE030
Incorgruous corresponding element, query set then
Figure 974536DEST_PATH_IMAGE029
In minimum value, be the translation variation of containment region According to the containment region variation
Figure 953173DEST_PATH_IMAGE031
And moving direction vector
Figure 986988DEST_PATH_IMAGE032
, calculate the coordinate in the center of circle
Figure 698592DEST_PATH_IMAGE012
Forward step 4 to.
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 829359DEST_PATH_IMAGE013
Coordinate after the coordinate transform
Figure 155167DEST_PATH_IMAGE033
Figure 473016DEST_PATH_IMAGE034
, be cylinder axis LOn a bit, cylinder axis LWith Be direction vector.
Step 10: calculate the measuring point collection successively
Figure 911268DEST_PATH_IMAGE004
In each measuring point to axis LDistance; And record measuring point collection
Figure 221027DEST_PATH_IMAGE004
In each measuring point to axis LThe maximal value of distance, record is gathered for the contact point of containment region outer boundary apart from the measuring point set of maximal value correspondence
Figure 26172DEST_PATH_IMAGE067
, the maximal value of the distance that records is the radius of cylinder R
Step 11: judge the contact point set of containment region outer boundary
Figure 79578DEST_PATH_IMAGE067
Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis
Figure 106309DEST_PATH_IMAGE036
Direction vector
Figure 586969DEST_PATH_IMAGE037
In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure 144989DEST_PATH_IMAGE068
, ,
Figure 634056DEST_PATH_IMAGE070
zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment
Figure 285617DEST_PATH_IMAGE041
Equal axis
Figure 65355DEST_PATH_IMAGE036
Direction vector With
Figure 458957DEST_PATH_IMAGE071
Vector multiplication cross; Rotation change angle is set
Figure 281420DEST_PATH_IMAGE043
Initial value; Calculate
Figure 486136DEST_PATH_IMAGE006
With
Figure 685036DEST_PATH_IMAGE072
Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14.
Step 12: calculate Around Rotation
Figure 288559DEST_PATH_IMAGE043
Direction vector after the angle
Figure 291150DEST_PATH_IMAGE044
Then, 3 contact points are projected in perpendicular to
Figure 814535DEST_PATH_IMAGE044
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with
Figure 103434DEST_PATH_IMAGE044
Determine the axis of postrotational cylinder
Figure 282743DEST_PATH_IMAGE045
Step 13: calculate all noncontact measuring points and arrive
Figure 823445DEST_PATH_IMAGE045
Distance
Figure 388288DEST_PATH_IMAGE046
If,
Figure 989033DEST_PATH_IMAGE073
Figure 452376DEST_PATH_IMAGE048
, then represent the variation deficiency, the anglec of rotation
Figure 734452DEST_PATH_IMAGE043
Become
Figure 966851DEST_PATH_IMAGE049
If
Figure 738498DEST_PATH_IMAGE074
, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation
Figure 761522DEST_PATH_IMAGE043
Become
Judge
Figure 56554DEST_PATH_IMAGE043
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 432172DEST_PATH_IMAGE043
Before and after twice the difference of iterative value less than setting
Figure 118368DEST_PATH_IMAGE043
The error permissible value, then the 4th contact point found in explanation, then will
Figure 325358DEST_PATH_IMAGE044
Assignment is given
Figure 625759DEST_PATH_IMAGE006
, jump to step 10; If The difference of the iterative value that front and back are twice is not less than setting
Figure 775297DEST_PATH_IMAGE043
The error permissible value then jumps to step 12.
Step 14: judge the contact point set of containment region outer boundary
Figure 102373DEST_PATH_IMAGE067
Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius decrease
Figure 58828DEST_PATH_IMAGE051
Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17.
Step 15:
Figure 471355DEST_PATH_IMAGE051
Deduct current cylindrical radius
Figure 499354DEST_PATH_IMAGE048
Obtain
Figure 867887DEST_PATH_IMAGE052
, obtaining cylinder after the dimensional variations, its axis is
Figure 447773DEST_PATH_IMAGE053
, each contact point is to axis
Figure 82017DEST_PATH_IMAGE053
Distance equal
Figure 648127DEST_PATH_IMAGE052
Relation, obtain following calculating formula,
Figure 887479DEST_PATH_IMAGE089
Wherein
Figure 513632DEST_PATH_IMAGE055
Be axis
Figure 635172DEST_PATH_IMAGE053
Direction vector,
Figure 188994DEST_PATH_IMAGE056
Be axis
Figure 345169DEST_PATH_IMAGE053
On a bit, with
Figure 142224DEST_PATH_IMAGE057
, Be unknown quantity, obtain 4 quaternary nonlinear equations respectively, can solve 4 unknown quantitys by Nonlinear System of Equations, obtain the axis of cylinder
Figure 596656DEST_PATH_IMAGE053
Step 16: calculate all noncontacts successively and put
Figure 607337DEST_PATH_IMAGE053
Distance
Figure 762244DEST_PATH_IMAGE059
, all noncontact measuring point correspondences Form set If,
Figure 435168DEST_PATH_IMAGE076
Figure 511708DEST_PATH_IMAGE051
+
Figure 95136DEST_PATH_IMAGE048
, then represent the variation deficiency,
Figure 610431DEST_PATH_IMAGE051
Become If
Figure 826835DEST_PATH_IMAGE077
+
Figure 950966DEST_PATH_IMAGE048
, then change excessively, all the other noncontact measuring points exceed containment region,
Figure 728429DEST_PATH_IMAGE051
Become
Judge
Figure 767109DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value whether less than setting
Figure 545578DEST_PATH_IMAGE051
The error permissible value; If
Figure 239865DEST_PATH_IMAGE051
Before and after 2 times the difference of iterative value less than setting
Figure 157005DEST_PATH_IMAGE051
The error permissible value illustrates and finds the 5th contact point, will
Figure 936742DEST_PATH_IMAGE055
,
Figure 269634DEST_PATH_IMAGE056
Assignment is given axis respectively LParameter
Figure 84007DEST_PATH_IMAGE006
,
Figure 906469DEST_PATH_IMAGE033
, and the method for step 16 judges whether to satisfy criterion in the Application Example 1, then jumps to step 18 if satisfy, if do not satisfy criterion, jumps to step 10; If
Figure 363383DEST_PATH_IMAGE051
The difference of the iterative value that front and back are 2 times is not less than setting
Figure 562283DEST_PATH_IMAGE051
The error permissible value then jumps to step 15.
Step 17: judge the contact point set of containment region outer boundary
Figure 231162DEST_PATH_IMAGE067
Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 162209DEST_PATH_IMAGE051
Judge
Figure 916538DEST_PATH_IMAGE051
Whether less than setting
Figure 653550DEST_PATH_IMAGE051
The error permissible value; If
Figure 301569DEST_PATH_IMAGE051
Less than what set
Figure 731413DEST_PATH_IMAGE051
The error permissible value, the method for step 16 in the Application Example 1 judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates , judge that again iteration is gone down successively; If
Figure 248162DEST_PATH_IMAGE051
Greater than what set
Figure 78584DEST_PATH_IMAGE051
The error permissible value is with what calculate
Figure 413750DEST_PATH_IMAGE053
The parameter assignment give cylinder axis respectively LParameter
Figure 142672DEST_PATH_IMAGE006
,
Figure 159169DEST_PATH_IMAGE033
, jump to step 10 then.
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
Below example by experiment illustrates the validity that institute of the present invention publish method is calculated.
On measuring table, obtain 24 points on the cylindrical part surface, the measuring point coordinate is as shown in table 2.Use the method that the present invention announces, the radius of action that calculates maximum inscribed cylinder is 11.9990887mm, cylinder axis direction vector (0.00111825745503225,0.000306176357337651,0.999999327877925), a point coordinate is (404.550573605996,126.630909902755 on the cylinder axis, 0.0446863090043053), cylindricity is 0.01475mm.The effect of calculating is (among the figure, * is measuring point, and ☆ is contact point) as shown in Figure 3, and the 1st, 5,14,19, No. 20 measuring point is contact point.Calculate each contact point respectively
Figure 657147DEST_PATH_IMAGE088
Mapping, and the discriminant value of calculating optimum solution J, as calculated J=2.5931e-014 satisfies criterion, and the cylinder radius of action that calculates and deviation from cylindrical form are optimum solution.
The measuring point coordinate of table 2 cylinder (unit: Mm)
The measuring point numbering xCoordinate yCoordinate zCoordinate The measuring point numbering xCoordinate yCoordinate zCoordinate
1 416.50196 126.62207 -42.61907 13 416.50921 126.6223 -35.28499
2 410.49696 137.01158 -42.60984 14 410.50862 137.01277 -35.27656
3 398.50797 136.99947 -42.59217 15 398.51415 137.00824 -35.25898
4 392.51838 126.62312 -42.58308 16 392.51911 126.62285 -35.24976
5 398.49642 116.23034 -42.59151 17 398.50985 116.23174 -35.25818
6 410.49805 116.22964 -42.60937 18 410.50947 116.22875 -35.27604
7 410.50638 116.22778 -38.94272 19 410.51541 116.2301 -31.6094
8 398.50449 116.23247 -38.92521 20 398.51512 116.23001 -31.59186
9 392.52266 126.62223 -38.91647 21 392.51775 126.62182 -31.58326
10 398.50907 137.00335 -38.9252 22 398.51751 137.0105 -31.59181
11 410.50058 137.01238 -38.94329 23 410.51169 137.01117 -31.60976
12 416.50494 126.62223 -38.95278 24 416.51224 126.62176 -31.61957

Claims (2)

1. method of calculating cylindrical part effect size is used for calculating cylindrical imperial palace and connects size, it is characterized in that, comprises the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery
Figure 2013102302548100001DEST_PATH_IMAGE001
,
Figure 2013102302548100001DEST_PATH_IMAGE003
=1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points
Figure 201194DEST_PATH_IMAGE004
Form the measuring point collection
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector
Figure 89515DEST_PATH_IMAGE006
Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector After the coordinate transform, with measuring point
Figure 972021DEST_PATH_IMAGE008
Be projected in XoyIn the plane, obtain measuring point
Figure 2013102302548100001DEST_PATH_IMAGE009
Coordinate
Figure 514385DEST_PATH_IMAGE010
All measuring points
Figure 2013102302548100001DEST_PATH_IMAGE011
Form the measuring point collection
Step 3: at point set
Figure 832551DEST_PATH_IMAGE012
In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 2013102302548100001DEST_PATH_IMAGE013
, as the center of circle
Figure 253168DEST_PATH_IMAGE014
The iteration initial value;
Step 4: calculate the measuring point collection successively In each measuring point to the center of circle
Figure 26138DEST_PATH_IMAGE014
Distance; And record measuring point collection
Figure 951368DEST_PATH_IMAGE012
In each measuring point to central coordinate of circle
Figure 113359DEST_PATH_IMAGE014
The corresponding measuring point of the minor increment of distance obtains the contact point set of error containment region inner boundary
Figure DEST_PATH_IMAGE015
Step 5: the contact point set of error in judgement containment region inner boundary
Figure 174856DEST_PATH_IMAGE015
In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 646158DEST_PATH_IMAGE016
Equal central coordinate of circle
Figure 58685DEST_PATH_IMAGE014
Deduct the contact point coordinate, jump to step 8;
If contact point quantity greater than 1, then jumps to next step;
Step 6: the contact point set of error in judgement containment region inner boundary
Figure 86684DEST_PATH_IMAGE015
In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 205949DEST_PATH_IMAGE016
Equal central coordinate of circle
Figure 395622DEST_PATH_IMAGE014
Deduct the middle point coordinate of 2 contact point lines, jump to step 8;
If contact point quantity greater than 2, then jumps to next step;
Step 7: calculate each contact point
Figure DEST_PATH_IMAGE017
The relative center of circle
Figure 482396DEST_PATH_IMAGE014
The phasing degree
Figure 48506DEST_PATH_IMAGE018
,
Figure DEST_PATH_IMAGE019
The phasing degree that has point of contact
Figure 287858DEST_PATH_IMAGE018
Form set
Figure 648432DEST_PATH_IMAGE020
, right
Figure 243009DEST_PATH_IMAGE020
In element sort, obtain vector
Figure DEST_PATH_IMAGE021
, compute vector In adjacent 2 phasing degree
Figure 628040DEST_PATH_IMAGE021
Poor,
Figure 425095DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE023
Quantity for contact point; Calculate
Figure 971614DEST_PATH_IMAGE024
If,
Figure DEST_PATH_IMAGE025
, then satisfy the oxygon criterion, jump to step 9; If
Figure 145106DEST_PATH_IMAGE026
, inquiry
Figure 342738DEST_PATH_IMAGE024
2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 310694DEST_PATH_IMAGE016
Equal central coordinate of circle Deduct the middle point coordinate of 2 effective contact point lines;
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 118430DEST_PATH_IMAGE009
Center of circle virtual location during contact
Figure DEST_PATH_IMAGE027
Calculate each noncontact measuring point at first respectively
Figure 921301DEST_PATH_IMAGE009
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 60159DEST_PATH_IMAGE014
And direction vector is
Figure 643587DEST_PATH_IMAGE016
The intersection point of straight line, be containment region and vary to and this measuring point
Figure 80253DEST_PATH_IMAGE009
During contact, the virtual location in the center of circle
Figure 65527DEST_PATH_IMAGE027
, all noncontact measuring point correspondences
Figure 375285DEST_PATH_IMAGE027
Form set
Figure 383693DEST_PATH_IMAGE028
, calculate each noncontact measuring point correspondence
Figure 437099DEST_PATH_IMAGE027
To the center of circle
Figure 276879DEST_PATH_IMAGE014
Distance , all
Figure 947420DEST_PATH_IMAGE029
Constitute set
Figure 239861DEST_PATH_IMAGE030
, in set
Figure 96958DEST_PATH_IMAGE030
In, reject
Figure 728928DEST_PATH_IMAGE016
With
Figure DEST_PATH_IMAGE031
Incorgruous corresponding element, query set then
Figure 380489DEST_PATH_IMAGE030
In minimum value, be the translation variation of containment region
Figure 612756DEST_PATH_IMAGE032
According to the containment region variation And moving direction vector
Figure DEST_PATH_IMAGE033
, calculate the coordinate in the center of circle
Figure 556758DEST_PATH_IMAGE013
Forward step 4 to;
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 582483DEST_PATH_IMAGE014
Coordinate after the coordinate transform
Figure 849516DEST_PATH_IMAGE034
, be cylinder axis LOn a bit, cylinder axis LWith
Figure 48417DEST_PATH_IMAGE007
Be direction vector;
Step 10: calculate the measuring point collection successively
Figure 638667DEST_PATH_IMAGE005
In each measuring point to axis LDistance; And record measuring point collection
Figure 897610DEST_PATH_IMAGE005
In each measuring point to axis LMinimum value and value, record is gathered for the contact point of containment region inner boundary apart from the measuring point set of minimum value correspondence
Figure 651939DEST_PATH_IMAGE036
, the minimum value and value that records is the radius of cylinder R
Step 11: judge the contact point set of containment region inner boundary
Figure 326634DEST_PATH_IMAGE036
Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis
Figure DEST_PATH_IMAGE037
Direction vector In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure DEST_PATH_IMAGE039
, ,
Figure DEST_PATH_IMAGE041
zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment
Figure 564565DEST_PATH_IMAGE042
Equal axis Direction vector
Figure 686422DEST_PATH_IMAGE007
With
Figure DEST_PATH_IMAGE043
Vector multiplication cross; Rotation change angle is set
Figure 208539DEST_PATH_IMAGE044
Initial value; Calculate
Figure 937460DEST_PATH_IMAGE007
With Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14;
Step 12: calculate
Figure 514252DEST_PATH_IMAGE007
Around
Figure 958003DEST_PATH_IMAGE042
Rotation
Figure 174221DEST_PATH_IMAGE044
Direction vector after the angle
Figure DEST_PATH_IMAGE045
Then, 3 contact points are projected in perpendicular to
Figure 243677DEST_PATH_IMAGE045
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with
Figure 596161DEST_PATH_IMAGE045
Determine the axis of postrotational cylinder
Figure 476392DEST_PATH_IMAGE046
Step 13: calculate all noncontacts and put
Figure 914326DEST_PATH_IMAGE046
Distance
Figure DEST_PATH_IMAGE047
If,
Figure 334944DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE049
, then represent the variation deficiency, the anglec of rotation
Figure 994464DEST_PATH_IMAGE044
Become Otherwise, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation Become
Figure DEST_PATH_IMAGE051
Judge
Figure 929556DEST_PATH_IMAGE044
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 256632DEST_PATH_IMAGE044
Before and after twice the difference of iterative value less than setting
Figure 730863DEST_PATH_IMAGE044
The error permissible value, then the 4th contact point found in explanation, then will Assignment is given
Figure 905810DEST_PATH_IMAGE007
, jump to step 10; If
Figure 87392DEST_PATH_IMAGE044
The difference of the iterative value that front and back are twice is not less than setting
Figure 480327DEST_PATH_IMAGE044
The error permissible value then jumps to step 12;
Step 14: judge the contact point set of containment region inner boundary Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius recruitment
Figure 946261DEST_PATH_IMAGE052
Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17;
Step 15:
Figure 982350DEST_PATH_IMAGE052
Add current cylindrical radius
Figure 795454DEST_PATH_IMAGE049
Obtain
Figure DEST_PATH_IMAGE053
, obtaining cylinder after the dimensional variations, its axis is
Figure 182573DEST_PATH_IMAGE054
, according to 4 contact points to axis Distance equal
Figure 380653DEST_PATH_IMAGE053
Relation, with axis
Figure 177708DEST_PATH_IMAGE054
Direction vector, axis Going up a bit is unknown quantity, obtains 4 quaternary nonlinear equations respectively, can obtain the axis of cylinder by Nonlinear System of Equations
Figure 960036DEST_PATH_IMAGE054
Direction vector, axis
Figure 157668DEST_PATH_IMAGE054
On a bit;
Step 16: calculate all noncontacts successively and put Distance
Figure DEST_PATH_IMAGE055
, all noncontact measuring point correspondences
Figure 159439DEST_PATH_IMAGE055
Form set
Figure 605464DEST_PATH_IMAGE056
If,
Figure DEST_PATH_IMAGE057
Figure 736231DEST_PATH_IMAGE052
+
Figure 62039DEST_PATH_IMAGE049
, then represent the variation deficiency,
Figure 645467DEST_PATH_IMAGE052
Become
Figure 895183DEST_PATH_IMAGE058
If
Figure DEST_PATH_IMAGE059
Figure 818140DEST_PATH_IMAGE052
+
Figure 127898DEST_PATH_IMAGE049
, then change excessively, all the other noncontact measuring points exceed containment region,
Figure 198623DEST_PATH_IMAGE052
Become
Figure 252029DEST_PATH_IMAGE060
Judge
Figure 275830DEST_PATH_IMAGE052
Before and after 2 times the difference of iterative value whether less than setting The error permissible value; If
Figure 48931DEST_PATH_IMAGE052
Before and after 2 times the difference of iterative value less than setting
Figure 906029DEST_PATH_IMAGE052
The error permissible value illustrates and finds the 5th contact point, will Direction vector, axis
Figure 189560DEST_PATH_IMAGE054
Go up some difference assignment and give axis LParameter
Figure 234876DEST_PATH_IMAGE007
, , and judge whether to satisfy criterion, and then jump to step 18 if satisfy, if do not satisfy criterion, jump to step 10; If
Figure 365829DEST_PATH_IMAGE052
The difference of the iterative value that front and back are 2 times is not less than setting
Figure 453871DEST_PATH_IMAGE052
The error permissible value then jumps to step 15;
Step 17: judge the contact point set of containment region inner boundary
Figure 720904DEST_PATH_IMAGE036
Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 591908DEST_PATH_IMAGE052
Judge
Figure 260787DEST_PATH_IMAGE052
Whether less than setting
Figure 519730DEST_PATH_IMAGE052
The error permissible value; If
Figure 195431DEST_PATH_IMAGE052
Less than what set
Figure 198022DEST_PATH_IMAGE052
The error permissible value judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates
Figure 721407DEST_PATH_IMAGE052
, judge that again iteration is gone down successively; If Greater than what set
Figure 64981DEST_PATH_IMAGE052
The error permissible value is with what calculate
Figure 605683DEST_PATH_IMAGE054
The parameter assignment give cylinder axis respectively LParameter
Figure 983575DEST_PATH_IMAGE007
,
Figure 771271DEST_PATH_IMAGE034
, jump to step 10 then;
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
2. a method of calculating cylindrical part effect size is used for calculating the external size of cylindrical minimum, it is characterized in that, comprises the steps:
Step 1: tested cylinder is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the point on the periphery
Figure 234614DEST_PATH_IMAGE001
,
Figure 579007DEST_PATH_IMAGE003
=1,2 ..., nRepresent the measuring point number and nFor greater than 5 positive integer; All measuring points Form the measuring point collection
Step 2: provide the parameter of cylinder at random, i.e. the axis of cylinder LDirection vector
Figure 736953DEST_PATH_IMAGE006
Carry out the rotational transform of coordinate system, make coordinate system zAxle is parallel to cylinder axis LDirection vector
Figure 619459DEST_PATH_IMAGE007
After the coordinate transform, with measuring point
Figure 971943DEST_PATH_IMAGE008
Be projected in XoyIn the plane, obtain measuring point
Figure 838792DEST_PATH_IMAGE009
Coordinate
Figure 276727DEST_PATH_IMAGE010
All measuring points
Figure 962923DEST_PATH_IMAGE011
Form the measuring point collection
Step 3: at point set
Figure 221046DEST_PATH_IMAGE012
In, take out 3 measuring points arbitrarily, and calculate 3 measuring points and form leg-of-mutton circumcenter
Figure 146277DEST_PATH_IMAGE013
, as the center of circle
Figure 370584DEST_PATH_IMAGE014
The iteration initial value;
Step 4: calculate the measuring point collection successively
Figure 697661DEST_PATH_IMAGE012
In each measuring point to the center of circle
Figure 168962DEST_PATH_IMAGE014
Distance; And record measuring point collection In each measuring point to central coordinate of circle
Figure 343909DEST_PATH_IMAGE014
The corresponding measuring point of the ultimate range of distance obtains the contact point set that error contains area outer
Figure 525491DEST_PATH_IMAGE015
Step 5: the contact point set of error in judgement containment region outer boundary
Figure 918426DEST_PATH_IMAGE015
In whether have only 1 contact point;
If have only 1 contact point, then this contact point is effective contact point, the direction vector of containment region translation this moment
Figure 818249DEST_PATH_IMAGE016
Equal the contact point coordinate and deduct central coordinate of circle
Figure 384360DEST_PATH_IMAGE014
, jump to step 8;
If contact point quantity greater than 1, then jumps to next step;
Step 6: the contact point set of error in judgement containment region outer boundary
Figure 420449DEST_PATH_IMAGE015
In whether have only 2 contact points;
If have only 2 contact points, then these 2 contact points are effective contact point, the direction vector of containment region translation this moment
Figure 233553DEST_PATH_IMAGE016
The middle point coordinate that equals 2 contact point lines deducts central coordinate of circle , jump to step 8;
If contact point quantity greater than 2, then jumps to next step;
Step 7: calculate each contact point
Figure 724894DEST_PATH_IMAGE017
The relative center of circle
Figure 881069DEST_PATH_IMAGE014
The phasing degree
Figure 615807DEST_PATH_IMAGE018
,
Figure 224643DEST_PATH_IMAGE019
The phasing degree that has point of contact
Figure 132556DEST_PATH_IMAGE018
Form set
Figure 330188DEST_PATH_IMAGE020
, right In element sort, obtain vector , compute vector
Figure 105880DEST_PATH_IMAGE021
In adjacent 2 phasing degree
Figure 174330DEST_PATH_IMAGE021
Poor,
Figure 497208DEST_PATH_IMAGE022
Figure 752740DEST_PATH_IMAGE023
Quantity for contact point; Calculate
Figure 268035DEST_PATH_IMAGE024
If,
Figure DEST_PATH_IMAGE061
, then satisfy oxygon criterion or diameter criterion, jump to step 9; If
Figure 440260DEST_PATH_IMAGE062
, inquiry
Figure 687701DEST_PATH_IMAGE024
2 corresponding contact points, 2 effective contact points of contact point that inquire, all the other contact points are invalid contact point, the direction vector of containment region translation this moment
Figure 492846DEST_PATH_IMAGE016
The middle point coordinate that equals 2 effective contact point lines deducts the center of circle
Figure 546253DEST_PATH_IMAGE014
Coordinate;
Step 8: calculate containment region successively and vary to and each noncontact measuring point
Figure 386033DEST_PATH_IMAGE009
Center of circle virtual location during contact
Figure 53644DEST_PATH_IMAGE027
Calculate each noncontact measuring point at first respectively
Figure 611664DEST_PATH_IMAGE009
With the vertical centering control separated time of one of them effective contact point, calculate the vertical centering control separated time then and cross the center of circle
Figure 203182DEST_PATH_IMAGE014
And direction vector is
Figure 100731DEST_PATH_IMAGE016
The intersection point of straight line, be containment region and vary to and this measuring point
Figure 752292DEST_PATH_IMAGE009
During contact, the virtual location in the center of circle
Figure 532029DEST_PATH_IMAGE027
, all noncontact measuring point correspondences
Figure 927239DEST_PATH_IMAGE027
Form set
Figure 928562DEST_PATH_IMAGE028
, calculate each noncontact measuring point correspondence To the center of circle
Figure 18057DEST_PATH_IMAGE014
Distance
Figure 216958DEST_PATH_IMAGE029
, all
Figure 823519DEST_PATH_IMAGE029
Constitute set
Figure 816883DEST_PATH_IMAGE030
, in set
Figure 571213DEST_PATH_IMAGE030
In, reject With
Figure 287069DEST_PATH_IMAGE031
Incorgruous corresponding element, query set then
Figure 451334DEST_PATH_IMAGE030
In minimum value, be the translation variation of containment region
Figure 692960DEST_PATH_IMAGE032
According to the containment region variation
Figure 171346DEST_PATH_IMAGE032
And moving direction vector
Figure 549237DEST_PATH_IMAGE033
, calculate the coordinate in the center of circle Forward step 4 to;
Step 9: carry out with step 2 in the coordinate transform of contrary, the measuring point coordinate reverts to original value, calculates
Figure 800276DEST_PATH_IMAGE014
Coordinate after the coordinate transform
Figure 144670DEST_PATH_IMAGE034
Figure 377068DEST_PATH_IMAGE035
, be cylinder axis LOn a bit, cylinder axis LWith
Figure 148715DEST_PATH_IMAGE007
Be direction vector;
Step 10: calculate the measuring point collection successively
Figure 37036DEST_PATH_IMAGE005
In each measuring point to axis LDistance; And record measuring point collection
Figure 919542DEST_PATH_IMAGE005
In each measuring point to axis LThe maximal value of distance, record is gathered for the contact point of containment region outer boundary apart from the measuring point set of maximal value correspondence
Figure DEST_PATH_IMAGE063
, the maximal value of the distance that records is the radius of cylinder R
Step 11: judge the contact point set of containment region outer boundary Whether the quantity of middle contact point is 3;
If the quantity of contact point equals 3, then the butt contact coordinate conversion of carrying out makes coordinate system zAxle forward and cylinder axis
Figure 401525DEST_PATH_IMAGE037
Direction vector
Figure 839459DEST_PATH_IMAGE038
In the same way and parallel, butt contact carries out ascending ordering by its z axial coordinate, makes
Figure 525656DEST_PATH_IMAGE064
,
Figure DEST_PATH_IMAGE065
,
Figure 670329DEST_PATH_IMAGE066
zAxial coordinate increases progressively, the direction vector of error containment region rotation change this moment Equal axis
Figure 709009DEST_PATH_IMAGE037
Direction vector
Figure 120268DEST_PATH_IMAGE007
With
Figure DEST_PATH_IMAGE067
Vector multiplication cross; Rotation change angle is set
Figure 447344DEST_PATH_IMAGE044
Initial value; Calculate With Dot product, if the dot product result equals 0, jump to step 18, if the dot product result is not equal to 0, jump to next step;
If the quantity of contact point is not 3, jump to step 14;
Step 12: calculate
Figure 844324DEST_PATH_IMAGE007
Around
Figure 25907DEST_PATH_IMAGE042
Rotation
Figure 481159DEST_PATH_IMAGE044
Direction vector after the angle Then, 3 contact points are projected in perpendicular to
Figure 888972DEST_PATH_IMAGE045
The plane in, and the center of circle of calculating the circumscribed circle of 3 contact points, according to the circumcenter with
Figure 190640DEST_PATH_IMAGE045
Determine the axis of postrotational cylinder
Figure 754477DEST_PATH_IMAGE046
Step 13: calculate all noncontact measuring points and arrive
Figure 876016DEST_PATH_IMAGE046
Distance
Figure 245818DEST_PATH_IMAGE047
If, , then represent the variation deficiency, the anglec of rotation
Figure 385998DEST_PATH_IMAGE044
Become
Figure 994834DEST_PATH_IMAGE050
If
Figure 902747DEST_PATH_IMAGE070
Figure 851112DEST_PATH_IMAGE049
, change excessively, all the other noncontact measuring points exceed containment region, the anglec of rotation
Figure 819068DEST_PATH_IMAGE044
Become
Figure 915200DEST_PATH_IMAGE051
Judge
Figure 626804DEST_PATH_IMAGE044
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting; If
Figure 678942DEST_PATH_IMAGE044
Before and after twice the difference of iterative value less than setting
Figure 817799DEST_PATH_IMAGE044
The error permissible value, then the 4th contact point found in explanation, then will Assignment is given
Figure 916523DEST_PATH_IMAGE007
, jump to step 10; If
Figure 573900DEST_PATH_IMAGE044
The difference of the iterative value that front and back are twice is not less than setting
Figure 883659DEST_PATH_IMAGE044
The error permissible value then jumps to step 12;
Step 14: judge the contact point set of containment region outer boundary
Figure 954383DEST_PATH_IMAGE063
Whether the quantity of middle contact point is 4;
If the quantity of contact point equals 4, set the cylindrical radius decrease
Figure 194740DEST_PATH_IMAGE052
Initial value, jump to next step;
If the quantity of contact point is not equal to 4, then jump to step 17;
Step 15:
Figure 34520DEST_PATH_IMAGE052
Add current cylindrical radius
Figure 515180DEST_PATH_IMAGE049
Obtain
Figure 73200DEST_PATH_IMAGE053
, obtaining cylinder after the dimensional variations, its axis is
Figure 602402DEST_PATH_IMAGE054
, according to 4 contact points to axis
Figure 296688DEST_PATH_IMAGE054
Distance equal
Figure 213829DEST_PATH_IMAGE053
Relation, with axis
Figure 993566DEST_PATH_IMAGE054
Direction vector, axis
Figure 578655DEST_PATH_IMAGE054
Going up a bit is unknown quantity, obtains 4 quaternary nonlinear equations respectively, can obtain the axis of cylinder by Nonlinear System of Equations
Figure 393028DEST_PATH_IMAGE054
Direction vector, axis
Figure 215490DEST_PATH_IMAGE054
On a bit;
Step 16: calculate all noncontacts successively and put Distance
Figure 619107DEST_PATH_IMAGE055
, all noncontact measuring point correspondences
Figure 287986DEST_PATH_IMAGE055
Form set
Figure 281349DEST_PATH_IMAGE056
If,
Figure DEST_PATH_IMAGE071
Figure 222629DEST_PATH_IMAGE052
+
Figure 959641DEST_PATH_IMAGE049
, then represent the variation deficiency,
Figure 483026DEST_PATH_IMAGE052
Become
Figure 850554DEST_PATH_IMAGE058
If
Figure 92179DEST_PATH_IMAGE072
Figure 367303DEST_PATH_IMAGE052
+ , then change excessively, all the other noncontact measuring points exceed containment region, Become
Judge Before and after 2 times the difference of iterative value whether less than setting
Figure 838604DEST_PATH_IMAGE052
The error permissible value; If
Figure 547934DEST_PATH_IMAGE052
Before and after 2 times the difference of iterative value less than setting
Figure 498573DEST_PATH_IMAGE052
The error permissible value illustrates and finds the 5th contact point, will
Figure 381078DEST_PATH_IMAGE054
Direction vector, axis
Figure 733562DEST_PATH_IMAGE054
Go up some difference assignment and give axis LParameter ,
Figure 300996DEST_PATH_IMAGE034
, and judge whether to satisfy criterion, and then jump to step 18 if satisfy, if do not satisfy criterion, jump to step 10; If The difference of the iterative value that front and back are 2 times is not less than setting
Figure 194182DEST_PATH_IMAGE052
The error permissible value then jumps to step 15;
Step 17: judge the contact point set of containment region outer boundary Whether the quantity of middle contact point is more than or equal to 5;
If the quantity of contact point jumps to step 10 less than 5;
If the quantity of contact point is more than or equal to 5, with in the contact point set 4 be 1 combination, and with wherein 1 be combined as calculating object, determine according to the method that the exploratory trace in the step 15,16 is adjusted
Figure 170546DEST_PATH_IMAGE052
Judge
Figure 394854DEST_PATH_IMAGE052
Whether less than setting
Figure 456351DEST_PATH_IMAGE052
The error permissible value; If
Figure 924722DEST_PATH_IMAGE052
Less than what set
Figure 337249DEST_PATH_IMAGE052
The error permissible value judges whether to satisfy criterion, if satisfy then jump to step 18, if do not satisfy criterion, changes 1 combination, recomputates
Figure 365248DEST_PATH_IMAGE052
, judge that again iteration is gone down successively; If
Figure 546831DEST_PATH_IMAGE052
Greater than what set
Figure 674187DEST_PATH_IMAGE052
The error permissible value is with what calculate
Figure 574009DEST_PATH_IMAGE054
The parameter assignment give cylinder axis respectively LParameter
Figure 140120DEST_PATH_IMAGE007
,
Figure 628739DEST_PATH_IMAGE034
, jump to step 10 then;
Step 18: the optimal value of output deviation from cylindrical form, cylindrical radius RAnd cylinder axis LParameter.
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CN108253917A (en) * 2017-12-30 2018-07-06 唐哲敏 A kind of minimum circumscribed cylinder diameter assessment method of fast steady letter
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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106289145A (en) * 2016-10-27 2017-01-04 北京理工大学 A kind of cylindricity On-machine Test method
CN108121876A (en) * 2017-12-30 2018-06-05 唐哲敏 A kind of square groove interaction in vitro width assessment method of fast steady letter
CN108253917A (en) * 2017-12-30 2018-07-06 唐哲敏 A kind of minimum circumscribed cylinder diameter assessment method of fast steady letter
CN109029326A (en) * 2018-10-11 2018-12-18 唐哲敏 A kind of installation gap quick calculation method of two sections of axis
CN109029326B (en) * 2018-10-11 2020-06-23 合肥源康信息科技有限公司 Method for rapidly calculating installation clearance of two sections of shafts
CN113709167A (en) * 2021-08-30 2021-11-26 杭州百子尖科技股份有限公司 Compression transmission method of appearance detection data
CN113709167B (en) * 2021-08-30 2023-04-07 杭州百子尖科技股份有限公司 Compression transmission method of appearance detection data

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