CN113624192A - Large diesel engine hole coaxiality measuring method based on multiple optimization - Google Patents
Large diesel engine hole coaxiality measuring method based on multiple optimization Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
- G01B21/24—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes
Abstract
The invention discloses a method for measuring the coaxiality of a large diesel engine hole system based on multiple optimization, which comprises the following steps of selecting hole sections on a measured diesel engine hole system at equal intervals, uniformly selecting n points on the selected sections as circle fitting points, and recording the space coordinates of the points; based on permutation and combination method
Combining a set of circle fitting points; fitting to obtain
A least squares circle; obtaining a fitted point sum
The distance between the centers of the least square circles is obtained to obtain an error epsilonji(ii) a Defining an allowable error value as mu, counting the number of circle fitting points meeting the requirement, and using the number of points meeting the error requirement as a sequenceThe index is used for obtaining the center of a circle of the section of the measured hole; obtaining the reference axis of the measured hole, and calculating the distance between the centers of the cross-sectional circles of the centers of the rest holes and the reference axis as gammakAccording to the distance gammakThe coaxiality of the crankshaft hole is obtained. The method avoids the problem that the least square method is easily influenced by interference points when fitting the circle center, and improves the accuracy of hole coaxiality measurement.
Description
Technical Field
The invention relates to an off-line measuring method of hole coaxiality, in particular to a measuring method of hole system coaxiality of a large diesel engine based on multiple optimization.
Background
The large diesel engine is used as a main power device of various large machines, the large diesel engine is expensive in manufacturing cost and complex in structure, and once a fault occurs, the construction period is delayed and even an accident can occur, so that huge loss is caused to enterprises. The number of holes on the diesel engine is large, and if the measured value of the hole coaxiality has large deviation to cause misjudgment, the performance and the reliability of the diesel engine in the use process can be influenced.
The hole coaxiality measurement accuracy is directly influenced by the hole circle center fitting accuracy, in the prior art, the hole circle center fitting is mostly carried out by a least square method, but the hole circle center fitting is easily influenced by interference points when the least square method is used, so that the fitted circle center has large deviation, and a large error exists between the measured hole coaxiality and the actual coaxiality.
Therefore, it is desired to solve the above problems.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a measuring method based on multiple optimized hole system coaxiality of a large diesel engine, which solves the problem that the circle center is easy to be influenced by interference points when the least square method is used for fitting the circle center, obtains the high-precision circle center of the hole section and improves the hole coaxiality measuring precision.
The invention discloses a method for measuring coaxiality of large diesel engine hole systems based on multiple optimization, which comprises the following steps:
(1) selecting the cross section of each hole at equal intervals on the diesel engine hole system to be tested, uniformly selecting n points on the selected cross section as circle fitting points, and recording the space coordinates of the points;
(2) based on the permutation and combination method, the obtained n circle fitting points are obtained in a group of r points
Combining a set of circle fitting points;
(3) based on the least square method and the obtained
Combining the circle fitting point set to obtain a fitting result
A least squares circle;
(4) sequentially calculating and fitting the selected n circle fitting points
The distance between the centers of the least square circles and the difference epsilon between the distance and the corresponding radius of the least square circlejiAs the error between the jth circle fitting point and the verified ith least squares circle;
(5) defining an allowable error value as mu, and counting the satisfied error epsilon between the n circle fitting points and the verified least square circlejiThe number of the circle fitting points required to be less than or equal to mu is taken as a sequencing index, and the circle center corresponding to the least square circle with the largest number of the points meeting the error requirement is taken as the circle center of the cross-section circle of the measured hole;
if the number is the same, then the condition of epsilon is satisfiedjiError less than or equal to mu requirementTaking the magnitude of the average difference value as a preferred basis to perform secondary sorting, and taking the circle center with the minimum error average value as the circle center of the section circle of the measured hole;
(6) using the connection line of the centers of the first and last cross-sectional circles of the hole as the reference axis of the hole, and calculating the distance between the centers of the cross-sectional circles of the other holes and the reference axis as gammakAccording to the distance gammakThe coaxiality of the crankshaft hole is obtained.
Wherein in the step (3)
The circular curve equation corresponding to the least squares circle can be expressed as:
(x-xi)2+(y-yi)2＝Ri 2
wherein (x)i,yi) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, RiIs the radius value corresponding to the ith least square circle,
preferably, the error ε in said step (4)jiCan be expressed as:
wherein (x)j,yj) The projection coordinates on the XOY plane, j, which are the circle fitting points, are 1,2,3, …, n.
Further, the reference axis of the hole measured in the step (6) is expressed as:
(x-xs)/(xm-xs)＝(y-ys)/(ym-ys)＝(z-zs)/(zm-zs)
wherein (x)s,ys,zs) Is the center coordinate of the first section circle of the hole, (x)m,ym,zm) Is the center coordinate of the cross section circle at the end of the hole.
Further, the coaxiality of the crankshaft holes in the step (6) can be expressed as: f 2max [ gamma ]k}。
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention randomly combines selected circle fitting points on the hole section, obtains a series of discrete circle centers as circle center candidates through least square fitting based on the obtained circle fitting point combination, judges the precision of multiple circle center candidate points according to the selected circle fitting points and uses the circle center candidate point with the highest precision as the real circle center of the hole section, converts the single selected circle center obtained by the traditional method into multiple selected circle centers, avoids the problem that the circle centers are easily influenced by interference points when the circle centers are fitted by the least square method, obtains the high-precision circle center of the hole section and improves the precision of hole coaxiality measurement.
Drawings
FIG. 1 is a schematic illustration of a marine diesel engine block of the present invention;
FIG. 2 is a schematic diagram of the circle center of the least square fitting in the present invention;
FIG. 3 is a schematic view of the coaxiality of the bore of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1 and 2, a method for measuring coaxiality of a hole system based on multiple optimized large diesel engines comprises the following steps:
1. a method for measuring coaxiality of large diesel engine hole systems based on multiple optimization comprises the following steps:
(1) selecting the cross section of each hole at equal intervals on the diesel engine hole system to be tested, uniformly selecting n points on the selected cross section as circle fitting points, and recording the space coordinates of the points;
(2) based on the permutation and combination method, the obtained n circle fitting points are obtained in a group of r points
Combining a set of circle fitting points;
(3)、based on least square method and the obtained
Combining the circle fitting point set to obtain a fitting result
A least squares circle;
the circular curve equation corresponding to the least squares circle can be expressed as:
(x-xi)2+(y-yi)2＝Ri 2
wherein (x)i,yi) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, RiIs the radius value corresponding to the ith least square circle,
(4) sequentially calculating and fitting the selected n circle fitting points
The distance between the centers of the least square circles and the difference epsilon between the distance and the corresponding radius of the least square circlejiAs the error between the jth circle fitting point and the verified ith least squares circle; error epsilonjiCan be expressed as:
wherein (x)j,yj) The projection coordinates on the XOY plane, j being the circle fitting point, 1,2,3, …, n;
(5) defining an allowable error value as mu, and counting the satisfied error epsilon between the n circle fitting points and the verified least square circlejiThe number of circle fitting points with the requirement of less than or equal to mu, and the number of points meeting the error requirement as a sequencing indexThe circle center corresponding to the least square circle with the largest number of the error required points is used as the circle center of the measured hole section circle;
if the number is the same, then the condition of epsilon is satisfiedjiTaking the average value of the errors less than or equal to mu as a preferred basis to carry out secondary sorting, and taking the circle center with the minimum error average value as the circle center of the section circle of the measured hole;
(6) and taking the circle center connecting line of the first and the last section circles of the measured hole as the reference axis of the measured hole, wherein the reference axis of the measured hole is expressed as:
(x-xs)/(xm-xs)＝(y-ys)/(ym-ys)＝(z-zs)/(zm-zs)
wherein (x)s,ys,zs) Is the center coordinate of the first section circle of the hole, (x)m,ym,zm) The center coordinates of the cross section circle at the end of the hole;
calculating the distance between the centers of the cross-sectional circles of the other holes and the reference axis as gammakAccording to the distance gammakThe coaxiality of the crankshaft holes is obtained, and can be expressed as: f 2max [ gamma ]k}。
Example 1
Taking the coaxiality measurement of the crankshaft holes of a certain marine diesel engine body as an example, the marine diesel engine body is schematically shown in figure 1.
As shown in fig. 2 and 3, a method for measuring coaxiality of hole systems of a large diesel engine based on multiple optimization comprises the following steps:
(1) assuming that the projection of the real circle center of a section of a crankshaft hole of a diesel engine body to be measured on an XOY plane is (0,0), the corresponding hole radius is 313mm, setting a certain number of deviation points on the section by taking the section as an object, and fitting the circle center of the section;
uniformly extracting 6 points on the measured hole section, and recording the space coordinates of the points as shown in table 1:
TABLE 1
| Dot number | Spatial coordinates |
| 1 | (0,313,50) |
| 2 | (-10,313.1,50) |
| 3 | (-250,188.33215,50) |
| 4 | (-265,166.5653,50) |
| 5 | (260,174.26,50) |
| 6 | (255,181.5048,50) |
Wherein point 2 is the assumed deviation point;
(2) randomly combining the point coordinates of the extracted crankshaft hole section circle based on a permutation and combination method, and fitting by a least square method according to the coordinate points obtained by random combination to obtain a plurality of circles
The selected 6 points are divided into 20 groups in 3 random combinations, and the grouping conditions are shown in table 2:
TABLE 2
(3) Obtaining 20 groups of circle center coordinates (x) based on least square fittingi,yi) And the corresponding radius value RiThe resulting circular curve equation can be written as:
(x-xi)2+(y-yi)2＝Ri 2
wherein (x)i,yi) For the centre coordinates obtained by fitting, RiThe corresponding circle radius value, i is 1,2,3, …, 20;
(4) sequentially calculating the distance between the selected 6 circle fitting points and the center of the 20 least square circles obtained by fitting, and calculating the difference epsilon between the distance and the corresponding radius of the least square circlejiAs the error between the jth circle fitting point and the verified ith least squares circle, εjiCan be expressed as:
wherein (x)j,yj) The projection coordinates on the XOY plane, j being the circle fitting point, 1,2,3, …, 6;
(5) defining allowable error value mu as 0.003, and making statistics on the satisfied error epsilon between the verified least square circle and 6 circle fitting pointsjiThe number of the circle fitting points required to be less than or equal to 0.003 is taken as a sequencing index, the circle center corresponding to the least square circle with the largest number of the points meeting the error requirement is taken as the circle center of the section circle of the crankshaft hole to be measured, and the statistical result is shown in table 3;
TABLE 3
| Group number | Number meeting error requirement |
| Group 1 | 3 |
| Group 2 | 3 |
| Group 3 | 4 |
| Group 4 | 4 |
| Group 5 | 5 |
| Group 6 | 5 |
| Group 7 | 5 |
| Group 8 | 5 |
| Group 9 | 5 |
| Group 10 | 5 |
| Group 11 | 3 |
| Group 12 | 3 |
| Group 13 | 3 |
| Group 14 | 3 |
| Group 15 | 3 |
| Group 16 | 3 |
| Group 17 | 5 |
| Group 18 | 5 |
| Group 19 | 5 |
| Group 20 | 5 |
Table 3 shows that the number of the groups 5, 6, 7, 8, 9, 17, 18, 19 and 20 meeting the requirements is 5 so as to meet the requirement of epsilonjiThe average value of the errors less than or equal to mu is used as the preferred basis to carry out secondary sorting, the circle center with the minimum error average value is used as the circle center of the section circle of the crankshaft hole to be measured, and the average result is shown in table 4;
TABLE 4
| Group number | Mean value of error |
| Group 5 | 1.3416e-5 |
| Group 6 | 1.8897e-06 |
| Group 7 | 1.8636e-06 |
| Group 8 | 1.8544e-06 |
| Group 9 | 1.8353e-06 |
| Group 17 | 4.0111e-06 |
| Group 18 | 3.5228e-06 |
| Group 19 | 3.2578e-05 |
| Group 20 | 3.3854e-05 |
The average error value of the 9 th group of fitting points is minimum, the error value is taken as the center of a circle of the section of the measured hole, the coordinates are (-0.0000069238, -0.000015384, 50), and the corresponding radius value is 313 mm;
if the method is not based on the method provided by the invention, circle center fitting is directly carried out on the basis of the selected 6 points and a least square method, the obtained circle center coordinate is (-0.000036765, -0.1472, 50), and the corresponding radius value is 313.099 mm.
Compared with the assumed true circle center (0,0, 50) and radius value 313mm of the section, the circle center value obtained by the method is closer to the true circle center, while the circle center obtained by the traditional least square method is influenced by deviation points, and the vertical coordinate of the circle center is greatly deviated compared with the true circle center.
(6) Selecting the cross sections of the crankshaft hole at equal intervals, calculating the circle centers of all the cross sections according to the method, and taking the circle center connecting line of the first cross section circle and the last cross section circle of the measured crankshaft hole as the reference axis of the measured hole, wherein the reference axis is expressed as follows:
(x-xs)/(xm-xs)＝(y-ys)/(ym-ys)＝(z-zs)/(zm-zs)
wherein (x)s,ys,zs) Is the center coordinate of the initial section circle, (x)m,ym,zm) The coordinates of the center of the last section circle are shown;
calculating the distance between the centers of the other hole sections and the reference axis, and assuming the center coordinate of a measured crankshaft hole section circle as (x)k,yk,zk) The distance between the reference axis and the reference axis is calculated as follows:
[x,y,z]*[xm-xs,ym-ys,zm-zs]T＝[xk,yk,zk]*[xm-xs,ym-ys,zm-zs]T
let xm-xs＝a,ym-ys＝b,zm-zs＝c，
The distance between the center of the measured cross-section circle of the crankshaft hole and the reference axis is as follows:
the measured crankshaft bore coaxiality is then expressed as:
f＝2max{γk}。
Claims (5)
1. a method for measuring coaxiality of large diesel engine hole systems based on multiple optimization is characterized by comprising the following steps:
(1) selecting the cross section of each hole at equal intervals on the diesel engine hole system to be tested, uniformly selecting n points on the selected cross section as circle fitting points, and recording the space coordinates of the points;
(2) based on the permutation and combination method, the obtained n circle fitting points are obtained in a group of r points
Combining a set of circle fitting points;
(3) based on the least square method and the obtained
Combining the circle fitting point set to obtain a fitting result
A least squares circle;
(4) sequentially calculating and fitting the selected n circle fitting points
The distance between the centers of the least square circles and the difference epsilon between the distance and the corresponding radius of the least square circlejiAs the error between the jth circle fitting point and the verified ith least squares circle;
(5) defining an allowable error value as mu, and counting the satisfied error epsilon between the n circle fitting points and the verified least square circlejiThe number of the circle fitting points required to be less than or equal to mu is taken as a sequencing index, and the circle center corresponding to the least square circle with the largest number of the points meeting the error requirement is taken as the circle center of the cross-section circle of the measured hole;
if the number is the same, then the condition of epsilon is satisfiedjiTaking the average value of the errors less than or equal to mu as a preferred basis to carry out secondary sorting, and taking the circle center with the minimum error average value as the circle center of the section circle of the measured hole;
(6) using the connection line of the centers of the first and last cross-sectional circles of the hole as the reference axis of the hole, and calculating the distance between the centers of the cross-sectional circles of the other holes and the reference axis as gammakAccording to the distance gammakThe coaxiality of the crankshaft hole is obtained.
2. The method for measuring the coaxiality of the hole series of the large diesel engine based on multiple optimization in the step (3) as claimed in claim 1, wherein
The circular curve equation corresponding to the least squares circle can be expressed as:
(x-xi)2+(y-yi)2＝Ri 2
wherein (x)i,yi) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, RiIs the radius value corresponding to the ith least square circle,
3. the method for measuring the coaxiality of the hole series of the large diesel engine based on multiple optimization in the step (4) as claimed in claim 2, wherein the error epsilon in the step (4) isjiCan be expressed as:
wherein (x)j,yj) The projection coordinates on the XOY plane, j, which are the circle fitting points, are 1,2,3, …, n.
4. The method for measuring the coaxiality of the hole series of the large diesel engine based on multiple optimization in the step (6) is characterized in that the reference axis of the hole measured in the step (6) is represented as follows:
(x-xs)/(xm-xs)＝(y-ys)/(ym-ys)＝(z-zs)/(zm-zs)
wherein (x)s,ys,zs) Is the center coordinate of the first section circle of the hole, (x)m,ym,zm) Is the center coordinate of the cross section circle at the end of the hole.
5. The method for measuring the coaxiality of the hole series of the large diesel engine based on multiple optimization in the step (6) is characterized in that the coaxiality of the crankshaft holes in the step (6) can be expressed as follows: f 2max [ gamma ]k}。
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Application publication date: 20211109 Assignee: BEIJING DACHENG YONGSHENG TECHNOLOGY Co.,Ltd. Assignor: JIANGSU University OF SCIENCE AND TECHNOLOGY Contract record no.: X2023980034168 Denomination of invention: A Measurement Method for Coaxiality of Large Diesel Engine Bore System Based on Multiple Optimization Granted publication date: 20221014 License type: Common License Record date: 20230328 |
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