CN114427839B - Method and system for measuring diameter of cylinder and height of protrusion based on line structured light - Google Patents
Method and system for measuring diameter of cylinder and height of protrusion based on line structured light 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
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/08—Measuring arrangements characterised by the use of optical techniques for measuring diameters
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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
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
- G01B11/0608—Height gauges
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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
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
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Abstract
The invention discloses a method and a system for measuring the diameter of a cylinder and the height of a bulge of line structured light, comprising the following steps: fixing a cylindrical workpiece, starting a line laser, and adjusting line structure light to be perpendicular to the central line of the cylinder; acquiring arc profile data of a plurality of positions of a cylindrical workpiece; determining the height of the surface bulge by adopting a secondary circle fitting processing method for removing bulge noise based on the arc profile data of the current position; repeating the steps to obtain secondary circle fitting data of a plurality of positions and corresponding surface protrusion heights, and obtaining the diameter of a minimum bounding circle as the diameter of a cylinder based on the secondary circle fitting data of the plurality of positions; and (5) turning off the line laser after the measurement is finished. The invention can rapidly realize synchronous measurement of the diameter of the cylinder and the height of the bulge, and improves the measurement precision.
Description
Technical Field
The invention relates to a method for measuring the diameter of a cylinder, in particular to a method and a system for measuring the diameter of the cylinder and the height of a bulge in line structured light.
Background
In the field of industrial production, it is necessary to measure the diameter of cylindrical workpieces to determine whether the workpieces meet the production process requirements. At present, the diameter of the cylinder is basically measured by adopting a vernier caliper, the cylinder is required to be measured for multiple times in different sections, and when a detector adopts the vernier caliper to measure, the detector is easily interfered by human factors, such as the proficiency of the detector, a measuring operation method and the like, so that the accuracy of a measuring result is low, the deviation is large, the vernier caliper is required to be adjusted for each measurement, and the detection efficiency is low. Meanwhile, the measurement of the height of the bulge on the surface of the cylinder also depends on a vernier caliper, and the same human factor interference is encountered.
In laser triangulation, a laser emits a beam of laser light to irradiate the surface of a measured object, diffuse reflection occurs, and part of the reflected light is converged in an imaging system. When the surface of the object to be measured is shifted in the laser axis direction (namely, the height is changed), the angle of the reflected light is changed, and the light spot is correspondingly moved in the imaging of the imaging system. And further the function of measuring the depth information of the surface of the measured object can be realized.
Disclosure of Invention
The invention aims to provide a method and a system for measuring the diameter of a cylinder and the height of a bulge in line structured light, which can rapidly realize synchronous measurement of the diameter of the cylinder and the height of the bulge and improve the detection efficiency and the detection precision.
The technical scheme for realizing the purpose of the invention is as follows:
a measuring method of cylinder diameter and surface bulge based on line structured light comprises the following steps:
step 1, fixing a cylindrical workpiece, starting a line laser, and adjusting line structure light to be perpendicular to the central line of the cylinder;
step 2, acquiring arc profile data of a plurality of positions of a cylindrical workpiece;
step 3, determining the height of the surface bulge by adopting a secondary circle fitting processing method for removing bulge noise based on the arc profile data of the current position;
step 4, repeating the step 2-3 to obtain secondary circle fitting data of a plurality of positions and corresponding surface protrusion heights, and obtaining the diameter of the minimum bounding circle as the diameter of the cylinder based on the secondary circle fitting data of the plurality of positions;
and 5, turning off the line laser after the measurement is finished.
Further, the step 3 specifically includes the following steps:
performing filtering treatment on the arc profile data by adopting a median filtering method;
performing primary circle fitting on the arc profile data subjected to the filtering treatment;
removing the interference of the raised noise to perform secondary circle fitting;
the cylinder surface protrusion height is determined based on the secondary circle.
Further, the filtering processing of the arc profile data by adopting the median filtering method specifically comprises the following steps:
the filter window length l=2×n+1, and the samples in the filter window are:
{(x i-N ,y i-N ),...,(x i ,y i ),...,(x i+N ,y i+N )}
wherein x and y are point coordinates, the L coordinate point data are sequentially arranged from large to small, and a median value is defined as an output value of median filtering:
y i =Med{y s(i-N) ,...,y si ,...,y s(i+N) }
and repeating the steps to sequentially perform median filtering treatment on each point in the arc profile data, wherein the obtained arc profile data after the filtering treatment is as follows:
Profile={(x 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 )...(x n ,y n )}
further, the median filtering method is a 7-point median filtering method, and n=3.
Further, the performing a circle fitting on the arc profile data after the filtering process specifically includes:
the other circular curve equation is:
x 2 -y 2 +ax+by+c=0
the relationship among the circle center coordinates, the circle radius and a, b and c is as follows:
the distance from the other point to the circle center is d i Setting the error as the distance from the point to the center of the circle minus the radius, and establishing an objective function as follows:
since the objective function S does not resolve the solution, the approximate objective function S' is:
and respectively solving partial derivatives of the objective function S' on a, b and c to obtain a matrix:
performing matrix operation to determine values of a, b and c, and further solving primary Center coordinates Center 0 (x o ,y o ) Sum circle diameter D 0 。
Further, the removing the noise interference of the protrusion to perform the second circle fitting specifically includes:
fitting the Center coordinates Center once 0 (x o ,y o ) Diameter D of circle 0 Setting the maximum iteration times and a deviation threshold as initial conditions and finishing the operation; fitting a circle by adopting an average absolute error circle fitting method and iterating, and obtaining a secondary fitting circle Center position coordinate Center (x) for eliminating the interference of raised noise when the condition operation ending condition is met c ,y c ) And diameter D, the second fit circle is:
Circle={(x i ,y i )|(x i -x c ) 2 +(y i -y c ) 2 =(D/2) 2 }
further, the determining the height of the protrusion on the surface of the cylinder based on the secondary circle specifically comprises the following steps: according to the Center position coordinates Center (x c ,y c ) Traversing all coordinate points on the arc Profile, calculating the distance between each coordinate point and the circle center, and respectively making difference with the radius of the secondarily fitted circle to obtain a group of deviation valuesMaximum deviation value d max =Max{d 1 ,d 2 ,...,d n And the value of the protrusion height of the outer surface of the cylinder is shown.
Further, in the step 4, the diameter of the smallest bounding circle obtained based on the quadratic circle fitting data is specifically: the sequence of the quadratic circle fitting data of a plurality of positions is disordered and recombined into a group of data Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) -a }; determining Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) The smallest circumscribed circle diameter of all points is the cylinder diameter.
Further, the determining Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) The minimum circumscribed circle diameter of all points is specifically:
step 4-1, selecting the first three points to calculate the minimum circumcircle D 1 If the three points are collinear, discarding the third coordinate pointAt the same time, continuing to newly add one coordinate point downwards until three non-collinear coordinate points P are found 1 、P 2 、P k Obtaining a first minimum circumscribing circle D 1 Another circle D t =D 1 ,P i =P 1 ;
Step 4-2, traversing whether all points are located in circle D t Inside, if all points are located in circle D t Inside, another minimum circumscribing circle D out =D t Executing the step 4-6; otherwise, obtain the first position in circle D t Outer point P j Executing the step 4-3;
step 4-3, at P i P j Resetting circle D for diameter t Traversing whether all points lie in circle D t In the case that all points are located in circle D t Inside, another minimum circumscribing circle D out =D t Executing the step 4-6; otherwise, the first position in circle D is obtained t Outer point P m Executing the step 4-4;
step 4-4, at P m P j Resetting circle D for diameter t Traversing whether all points lie in circle D t In the case that all points are located in circle D t Inside, another minimum circumscribing circle D out =D t Executing the step 4-6; otherwise, the first position in circle D is obtained t Outer point P n Executing the step 4-5;
step 4-5, obtaining P j 、P m 、P n Minimum circumcircle D of three points t Another P i =P j Repeating the step 4-2;
step 4-6, obtaining the minimum circumcircle D of all points out 。
A measuring system based on the diameter of a cylinder and the surface bulge of line structured light comprises an acquisition module, a secondary circle fitting module, a bulge height calculating module and a cylinder diameter calculating module; wherein:
the acquisition module acquires arc profile data of a plurality of positions of the cylindrical workpiece through the sensor based on line structured light;
the secondary circle fitting module acquires secondary arc profile data of each position by adopting a secondary circle fitting processing method for eliminating raised noise;
the protrusion height calculation module is used for obtaining the surface protrusion height of each position of the cylinder;
the cylinder diameter calculation module obtains the diameter of the smallest surrounding circle, namely the cylinder diameter, based on the quadratic circle fitting data of a plurality of positions.
Compared with the prior art, the invention has the remarkable effects that:
(1) According to the invention, the interference of the convex part on the outer surface of the cylinder on the circle fitting is eliminated through the filtering treatment and the secondary circle fitting for eliminating the convex noise interference, so that the synchronous measurement of the diameter of the cylinder and the height of the convex can be rapidly realized, and the measurement precision is improved;
(2) According to the invention, the diameter of the smallest surrounding circle of the secondary circles at a plurality of positions is used as the diameter of the cylinder, so that the measurement at the plurality of positions of the cylinder is not needed, the measurement workload is greatly reduced, and the detection efficiency is improved.
Drawings
FIG. 1 is a flow chart of a method for measuring cylinder diameter and surface protrusions based on line structured light.
Fig. 2 is a graph of an original arc profile of a cylindrical workpiece taken by a line laser at a location.
Fig. 3 is a graph of a fitted circle profile after a general circle fitting process.
Fig. 4 is a graph of a fitted circle profile after a circle fitting process with noise interference removed.
Fig. 5 is a graph of the measurement result of the height of the protrusion of the cylinder surface.
Fig. 6 is a graph of a fitted circle profile for a minimum bounding circle.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In combination with fig. 1, a method for measuring the diameter of a cylinder and the surface bulge based on line structured light comprises the following steps:
firstly, adjusting line structure light to be perpendicular to the center line of a cylinder, wherein a line laser can freely move along the direction of the center line of a workpiece to collect data, and the method comprises the following steps:
step a, fixing a cylindrical workpiece;
step b, starting a line laser to acquire sensor data in real time;
step c, acquiring arc profiles of a plurality of positions of the cylindrical workpiece;
step d, calculating the diameter of the cylinder and the height of the surface bulge, and outputting a calculation result;
and e, turning off the line laser.
The calculation method of the diameter of the cylinder and the height of the surface bulge comprises the following steps:
step 1: and (3) carrying out median filtering treatment on the contour of the outer surface of the cylinder:
the invention adopts 7-point median filtering, namely the filtering window length L=2×N+1, N=3, and at a certain position of the outline, the samples in the window are { (x) i-N ,y i-N ),...,(x i ,y i ),...,(x i+N ,y i+N ) }. After the L coordinate point data are sequentially arranged from large to small, the median value is defined as the output value of median filtering:
y i =Med{y s(i-N) ,...,y si ,...,y s(i+N) }
each point in the original contour source_profile is sequentially subjected to median filtering processing to obtain:
Profile={(x 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 )...(x n ,y n )}
the processed arc profile curve is shown in figure 2.
Step 2: general circle fitting:
circular curve equation:
x 2 +y 2 +ax+by+c=0
the relationship between the center coordinates, the radius of the circle and a, b and c is as follows:
existing sample set Profile = { (x) 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 )...(x n ,y n ) Adopting an objective function S' to solve the circle center coordinates and the circle radius:
and respectively solving partial derivatives of the objective function S' on a, b and c to obtain a matrix:
the matrix operation is performed to obtain values of a, b and c, and then the Center coordinates Center (x o ,y o ) Sum circle diameter D 0 The outline of the fitting circle obtained by the general circle fitting process is shown in figure 3.
Step 3: circle fitting process for eliminating bump noise interference
From the diameter D of the cylindrical workpiece obtained in S2 0 Center position coordinates Center (x) of the contour o ,y o ) Profile = { (x) 1 ,y 1 ),(x 2 ,y 2 ),...,(x n ,y n ) And performing secondary circle contour fitting.
Wherein the diameter D of the cylindrical workpiece 0 Center position coordinates Center (x) of the contour o ,y o ) As initial conditions. The maximum number of operations 100 and the deviation threshold value 0.01 are set as operation end conditions. When the maximum operation times or deviation threshold value are satisfied<At 0.01, the operation ends.
After the calculation is finished, the diameter D of the cylindrical workpiece with the interference of the convex noise removed and the Center position coordinate Center (x) of the current position are obtained c ,y c ) And fitting a circular profile:
Circle={(x i ,y i )|(x i -x c ) 2 +(y i -y c ) 2 =(D/2) 2 }
the round outline obtained after the round fitting process of eliminating the interference of the convex noise is shown in figure 4
Step 4: calculation of the height of the protrusion of the surface of the cylinder
Center position coordinates Center (x) of a fitting circle according to the current position of the cylindrical workpiece c ,y c ) Fitting the diameter D of the circle and the source_profile of the original Profile data, traversing all coordinate points on the original Profile, calculating the distance between each coordinate point and the circle center, and respectively making differences with the radius of the cylinder to obtain a group of deviation values:
wherein the maximum deviation value d max =Max{d 1 ,d 2 ,...,d n And the value of the protrusion height of the outer surface of the cylinder is shown. The measurement result of the height of the bump is shown in figure 5
Step 5: multiple arc profile processing
And (3) repeating the steps 1-4 for 3 original contours obtained by the line laser, and calculating the diameter of the cylinder, the center coordinates of the fitting circle and the contour data of the fitting circle corresponding to each original contour.
Step 6: least squares circle fitting process
The sequence of all the fitting circle outline data is disordered and recombined into oneGroup data { (x) 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m )}。
Firstly, selecting the first three points to calculate the minimum circumcircle D 1 . If the three points are collinear, the third coordinate point is discarded. Meanwhile, continuing to newly add one coordinate point downwards until three non-collinear coordinate points are found, thereby obtaining a minimum circumcircle D 1 The method comprises the steps of carrying out a first treatment on the surface of the Next, the coordinate points P are added one by one j =(x j ,y j ) If P j Located at circle D i I=1, 2,..k internal, execute downward. If there is no point outside the circle, the algorithm ends. Otherwise, the minimum circumscribed circle is recalculated:
1) Setting circle D t : with P 1 P j As diameter, search for the first position in circle D t Outer point P m If no result is found, end, D outer =D t ;
2) Find the point P m Then set a circle D t2 : with P m P j For diameter, continue searching for the position in circle D t2 Outer point P n If no result is found, end, D outer =D t2 。
3) Find the point P n P is then j 、P m 、P n Three points are in common circle, and the minimum circumcircle D can be calculated outer . Finally, the diameter D of the minimum bounding circle is calculated by traversing all coordinate points outer 。
The result of the fitting process of the minimum bounding circles is shown in figure 6.
Aiming at the problem that the traditional circle fitting method is easily influenced by the protruding parts to cause larger measuring error of the diameter of the cylinder, the invention designs a secondary circle fitting processing method for eliminating the influence of protruding noise, removes the influence of surface protrusions on circle fitting and cylinder diameter measurement, and measures the height of the surface protrusions on the basis of secondary circle fitting; and then, according to the diameter of a plurality of positions of the cylindrical workpiece, the circle center coordinate measurement result and the circular arc profile data of the cylindrical workpiece, the minimum bounding circle of the cylindrical workpiece is measured, so that the measurement accuracy is improved, the measurement workload is greatly reduced, and the detection efficiency is improved.
Claims (4)
1. A measuring method of cylinder diameter and surface bulge based on line structured light is characterized in that: the method comprises the following steps:
step 1, fixing a cylindrical workpiece, starting a line laser, and adjusting line structure light to be perpendicular to the central line of the cylinder;
step 2, acquiring arc profile data of a plurality of positions of a cylindrical workpiece;
step 3, determining the height of the surface bulge by adopting a secondary circle fitting processing method for removing bulge noise based on the arc profile data of the current position;
step 4, repeating the steps 2-3 to obtain secondary circle fitting data of a plurality of positions and corresponding surface protrusion heights, and obtaining the diameter of the minimum bounding circle as the diameter of the cylinder based on the secondary circle fitting data of the plurality of positions;
step 5, closing the line laser after the measurement is finished;
the step 3 specifically comprises the following steps:
performing filtering treatment on the arc profile data by adopting a median filtering method;
performing primary circle fitting on the arc profile data subjected to the filtering treatment;
removing the interference of the raised noise to perform secondary circle fitting;
determining the height of the protrusion on the surface of the cylinder based on the quadratic fit circle;
the filtering processing of the arc profile data by adopting the median filtering method specifically comprises the following steps:
let filtering window length l=2×n+1, the samples in the acquisition window are:
{(x i-N ,y i-N ),...,(x i ,y i ),...,(x i+N ,y i+N )}
wherein x and y are point coordinates, the L coordinate point data are sequentially arranged from large to small, and a median value is defined as an output value of median filtering:
y i =Med{y s(i-N) ,...,y si ,...,y s(i+N) }
and repeating the steps to sequentially perform median filtering treatment on each point in the arc profile data, wherein the obtained arc profile data after the filtering treatment is as follows:
Profile={(x 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 )...(x n ,y n )}
the circular fitting of the circular arc outline data after the filtering treatment is specifically as follows:
let the circular curve equation be:
x 2 +y 2 +ax+by+c=0
the relationship among the circle center coordinates, the circle radius and a, b and c is as follows:
let the distance from the point to the center of the circle be d i Setting the error as the distance from the point to the center of the circle minus the radius, and establishing an objective function as follows:
since the objective function S does not resolve the solution, the approximate objective function S' is:
and respectively solving partial derivatives of the objective function S' on a, b and c to obtain a matrix:
performing matrix operation to determine values of a, b and c, and further solving a fitting Center coordinate Center 0 (x o ,y o ) Sum circle diameter D 0 ;
The removing of the convex noise interference for the secondary circle fitting specifically comprises the following steps:
fitting the Center coordinates Center once 0 (x o ,y o ) Diameter D of circle 0 Setting the maximum iteration times and a deviation threshold as initial conditions and finishing the operation; fitting a circle by adopting an average absolute error circle fitting method and iterating, and obtaining a secondary fitting circle Center position coordinate Center (x) for eliminating the interference of raised noise when the condition operation ending condition is met c ,y c ) And diameter D, the second fit circle is:
Circle={(x i ,y i )|(x i -x c ) 2 +(y i -y c ) 2 =(D/2) 2 };
in the step 4, the diameter of the minimum bounding circle obtained based on the quadratic circle fitting data is taken as the diameter of the cylinder, and the diameter is specifically as follows: the sequence of the quadratic circle fitting data of a plurality of positions is disordered and recombined into a group of data Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) -a }; determining Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) The smallest circumscribed circle diameter of all points is the cylinder diameter;
the determination Profile C ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x m ,y m ) The minimum circumscribed circle diameter of all points is specifically:
step 4-1, selecting the first three points to calculate the minimum circumcircle D 1 If the three points are collinear, discarding the third coordinate point, and continuing to increase the coordinate point downwardsOne coordinate point until three non-collinear coordinate points P are found 1 、P 2 、P k Obtaining a first minimum circumscribing circle D 1 Circle D t =D 1 ,P i =P 1 ;
Step 4-2, traversing whether all points are located in circle D t Inside, if all points are located in circle D t Inside, make the minimum circumcircle D out =D t Executing the step 4-6; otherwise, obtain the first position in circle D t Outer point P j Executing the step 4-3;
step 4-3, at P i P j Resetting circle D for diameter t Traversing whether all points lie in circle D t In the case that all points are located in circle D t Inside, make the minimum circumcircle D out =D t Executing the step 4-6; otherwise, the first position in circle D is obtained t Outer point P m Executing the step 4-4;
step 4-4, at P m P j Resetting circle D for diameter t Traversing whether all points lie in circle D t In the case that all points are located in circle D t Inside, make the minimum circumcircle D out =D t Executing the step 4-6; otherwise, the first position in circle D is obtained t Outer point P n Executing the step 4-5;
step 4-5, obtaining P j 、P m 、P n Minimum circumcircle D of three points t Let P i =P j Repeating the step 4-2;
step 4-6, obtaining the minimum circumcircle D of all points out 。
2. The method for measuring the diameter of a cylinder and the surface bulge based on line structured light according to claim 1, wherein the method comprises the following steps: the median filtering method is a 7-point median filtering method, and n=3.
3. The method for measuring the diameter of a cylinder and the surface bulge based on line structured light according to claim 1, wherein the method comprises the following steps: the circle based on quadratic fitThe determination of the height of the protrusion on the surface of the cylinder is specifically as follows: according to the Center position coordinates Center (x c ,y c ) Traversing all coordinate points on the arc Profile, calculating the distance between each coordinate point and the circle center, and respectively making difference with the radius of the secondarily fitted circle to obtain a group of deviation valuesMaximum deviation value d max =Max{d 1 ,d 2 ,...,d n And the value of the protrusion height of the outer surface of the cylinder is shown.
4. A system for measuring cylinder diameter and surface protrusions based on line structured light using the method of any one of claims 1 to 3, characterized in that: the device comprises an acquisition module, a secondary circle fitting module, a protrusion height calculation module and a cylinder diameter calculation module; wherein:
the acquisition module acquires arc profile data of a plurality of positions of the cylindrical workpiece through the sensor based on line structured light;
the secondary circle fitting module acquires secondary arc profile data of each position by adopting a secondary circle fitting processing method for eliminating raised noise;
the protrusion height calculation module is used for obtaining the surface protrusion height of each position of the cylinder;
the cylinder diameter calculation module obtains the diameter of the smallest surrounding circle, namely the cylinder diameter, based on the quadratic circle fitting data of a plurality of positions.
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CN109997202A (en) * | 2016-11-11 | 2019-07-09 | 法马通股份有限公司 | For detecting and/or checking the device and method of the abrasion on cylindrical parts surface |
CN108627841A (en) * | 2018-01-24 | 2018-10-09 | 天津大学 | A kind of circle center locating method in shoal buried pipes supersonic sounding |
CN111322950A (en) * | 2020-04-17 | 2020-06-23 | 易思维(杭州)科技有限公司 | Method for positioning cylinder position by line structured light sensor and its use |
CN112629424A (en) * | 2020-11-24 | 2021-04-09 | 江南大学 | High-precision sandwich valve outer diameter dynamic vision measurement system and method |
CN113446952A (en) * | 2021-08-17 | 2021-09-28 | 华北科技学院(中国煤矿安全技术培训中心) | Online non-contact shaft diameter measuring method |
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