CN113624192B - 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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Abstract
The invention discloses a method for measuring 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 section as circle fitting points, and recording space coordinates of the points as circle fitting points(ii) a 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 epsilon ji (ii) a Defining an allowable error value mu, counting the number of circle fitting points meeting the requirement, and taking the number of points meeting the error requirement as a sequencing index to obtain 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 gamma k According to the distance gamma k The 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 n circle fitting points are obtained by one group of r circle fitting points
Combining the circle fitting point sets;
(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 circle ji As the error between the jth circle fitting point and the verified ith least square 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 circle ji The 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 following equation is satisfied ji Taking the average value of the errors less than or equal to mu as the optimal basis for secondary sorting, and taking the center of the circle with the minimum error average value as the center of the cross-section circle of the hole to be measured;
(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 gamma k According to the distance gamma k The 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-x i ) 2 +(y-y i ) 2 ＝R i 2
wherein (x) i ,y i ) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, R i Is the radius value corresponding to the ith least square circle,
preferably, the error ε in said step (4) ji Can be expressed as:
wherein (x) j ,y j ) J =1,2,3, \8230;, n, the projected coordinates on the XOY plane of the circle fitting point.
Further, the reference axis of the hole measured in the step (6) is expressed as:
(x-x s )/(x m -x s )＝(y-y s )/(y m -y s )＝(z-z s )/(z m -z s )
wherein (x) s ,y s ,z s ) Is the center coordinate of the first section circle of the hole, (x) m ,y m ,z m ) 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 { γ 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 holes 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 fig. 2, a method for measuring coaxiality based on multiple preferred large diesel engine hole systems 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 the 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 for each least squares circle can be expressed as:
(x-x i ) 2 +(y-y i ) 2 ＝R i 2
wherein (x) i ,y i ) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, R i Is the radius value corresponding to the ith least square circle,
(4) Sequentially calculating the homologies of the selected n circle fitting pointsObtained by synthesis
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 circle ji As the error between the jth circle fitting point and the verified ith least square circle; error epsilon ji Can be expressed as:
wherein (x) j ,y j ) J =1,2,3, \ 8230;, 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 circle ji The number of the circle fitting points which are required to be less than or equal to mu is used as a sequencing index, and the circle center corresponding to the least square circle with the largest number of the points which meet the error requirement is used as the circle center of the section circle of the measured hole;
if the number is the same, then the following equation is satisfied ji Taking 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 a circle center connecting line of the first cross-section circle and the last cross-section circle of the measured hole as a reference axis of the measured hole, wherein the reference axis of the measured hole is expressed as follows:
(x-x s )/(x m -x s )＝(y-y s )/(y m -y s )＝(z-z s )/(z m -z s )
wherein (x) s ,y s ,z s ) Is the center coordinate of the first section circle of the hole, (x) m ,y m ,z m ) 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 gamma k According to the distance gamma k The coaxiality of the crankshaft holes and the coaxiality of the crankshaft holes are obtainedCan be expressed as: f =2max { γ 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 the diesel engine body to be measured on an XOY plane is (0, 0), the corresponding hole radius is 313mm, taking the section as an object, setting a certain number of deviation points on the section, 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 sequence 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 were divided into 20 groups in 3 random combinations, and the grouping is shown in table 2:
TABLE 2
(3) Obtaining 20 groups of circle center coordinates (x) based on least square fitting i ,y i ) And the corresponding radius value R i The resulting circular curve equation can be written as:
(x-x i ) 2 +(y-y i ) 2 ＝R i 2
wherein (x) i ,y i ) To the centre coordinates obtained by fitting, R i I =1,2,3, \ 8230;, 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 circle ji As the error between the jth circle fitting point and the verified ith least squares circle, ε ji Can be expressed as:
wherein (x) j ,y j ) J =1,2,3, \ 8230;, 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 points ji The 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 numbers of the groups 5, 6, 7, 8, 9, 17, 18, 19 and 20 which meet the requirements are all 5 so as to meet the requirement of epsilon ji The 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 |
| 18 th itemGroup of | 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 313mm;
if the method is not based on the method provided by the invention, the circle center fitting is directly carried out based on the selected 6 points and the least square method, the obtained circle center coordinates are (-0.000036765, -0.1472, 50), and the corresponding radius value is 313.099mm.
Compared with the assumed true circle center (0, 50) and the radius value 313mm of the cross 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 fitting is influenced by deviation points, and the longitudinal 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-x s )/(x m -x s )＝(y-y s )/(y m -y s )＝(z-z s )/(z m -z s )
wherein (x) s ,y s ,z s ) Is the center coordinate of the initial section circle, (x) m ,y m ,z m ) The coordinates of the center of the last section circle are shown;
calculating the distance between the centers of the other hole cross sections and the reference axis, and assuming the center of a measured crankshaft hole cross section circleThe coordinates are (x) k ,y k ,z k ) The distance between the reference axis and the reference axis is calculated as follows:
[x,y,z]*[x m -x s ,y m -y s ,z m -z s ] T ＝[x k ,y k ,z k ]*[x m -x s ,y m -y s ,z m -z s ] T
let x m -x s ＝a,y m -y s ＝b,z m -z s ＝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 coaxiality of the crankshaft holes is expressed as follows:
f＝2max{γ k }。
Claims (5)
1. a measurement method based on multiple optimized large diesel engine hole coaxiality 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 n circle fitting points are obtained by one group of r circle fitting 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 circle ji As the error between the jth circle fitting point and the verified ith least square 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 circle ji The 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 satisfied ji Taking 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 section circles as the reference axis of the measured hole, and calculating the distance between the centers of the other section circles and the reference axis as gamma k According to the distance gamma k The 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-x i ) 2 +(y-y i ) 2 ＝R i 2
wherein (x) i ,y i ) For the projection coordinates of the fitted i-th least squares circle center on the XOY plane, R i Is 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) is ji Can be expressed as:
wherein (x) j ,y j ) J =1,2,3, \ 8230;, n, the projected coordinates on the XOY plane for a circle fitting point.
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-x s )/(x m -x s )＝(y-y s )/(y m -y s )＝(z-z s )/(z m -z s )
wherein (x) s ,y s ,z s ) Is the center coordinate of the first section circle of the hole, (x) m ,y m ,z m ) 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 { γ 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 |