CN105091748B - Rail vehicle tolerance dimension measuring system - Google Patents
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Abstract
The invention discloses a kind of rail vehicle tolerance dimension measuring system, including hand-held measurement device and three-dimensional data processing unit;Hand-held measuring apparatus, including DLP projector, two CCD cameras, SECO plate, image pick-up card and data processor;Three-dimensional data processing unit interface, including a cloud viewing area, the point cloud information area, commard editor area and camera viewing area.SECO plate is connected with data processor, two CCD cameras, DLP projectors respectively, and DLP projector is connected with data processor, and two ccd video cameras are connected by image pick-up card with data processor.The present invention is stable, efficiently, can be perfectly suitable for the size detection of rail vehicle inside gadget, avoid conventional method obtain interior trim tolerance dimension precision is low, the shortcomings of speed is slow, artificial influence factors are big, meet the requirement of modern railway vehicle production.
Description
Technical field
The present invention relates to a kind of rail vehicle tolerance dimension measuring system, by introducing advanced measuring method and repair hand
Section, packing quality in rail vehicle is improved, belongs to rail vehicle three-dimensional measurement technical field.
Background technology
The assembling of rail vehicle inside gadget is that the important quality of rail vehicle production controls corner, its controlled level concentrated expression
Rail vehicle product development and quality control level, therefore turn into rail traffic vehicles manufacturing enterprise focus of attention.Track
In the vehicle manufacture cycle, product design, process exploitation, production phase can produce considerable influence to interior trim fitted position.
With flourishing for track transportation industry, the manufacture of each bound pair rail vehicle requires also more and more higher.Abroad,
Italy Spanesi companies, the Caroliner companies of Sweden develop body of a motor car electronic measurement system measurement accuracy,
Operational aspect has certain advantage, and the measurement to vehicle body three-dimensional dimension can be realized using laser, noctovisor scan technology, full
Foot new demand of the Modern Vehicle Repair industry to detection technique.But at home, intelligent scanning measuring system is in vehicle body of railway vehicle
The application of production is also fewer.And traditional rail vehicle interior trim measuring method be by manually measuring, measurement result by
Human factor influences more, and the efficiency and precision etc. that measure all are difficult to the requirement for meeting the modern production cycle.
The content of the invention
Purpose:In order to overcome the deficiencies in the prior art, the present invention provides a kind of rail vehicle tolerance dimension measurement
System, it can quickly and efficiently measure rail vehicle interior trim tolerance dimension.System possesses bulk test technique automatic,
Can simultaneously multimetering, can be rapidly and efficiently acquisition be measured automobile interior three-dimensional data, it is right so as to improve efficiency of assembling
The assembling of whole rail traffic vehicles is significant.
Technical scheme:In order to solve the above technical problems, the technical solution adopted by the present invention is:
A kind of rail vehicle tolerance dimension measuring system, it is characterised in that:Including hand-held measurement device and three-dimensional data
Processing unit;
Hand-held measuring apparatus, including at DLP projector, two CCD cameras, SECO plate, image pick-up card and data
Manage device;
Three-dimensional data processing unit interface, including a cloud viewing area, the point cloud information area, commard editor area and camera are shown
Area.
Described rail vehicle tolerance dimension measuring system, it is characterised in that:SECO plate respectively with data processor,
Two CCD cameras, DLP projectors are connected, and DLP projector is connected with data processor, and two ccd video cameras are adopted by image
Truck is connected with data processor;
Described rail vehicle tolerance dimension measuring system, it is characterised in that:The photocentre axle of two CCD cameras with
The angle of DLP projector photocentre axle keeps DLP projector and two CCD cameras between 20 degree to 60 degree, and when measuring
Relative position is constant.
Described rail vehicle tolerance dimension measuring system, it is characterised in that:The rail vehicle tolerance dimension measurement system
System is provided with the USB interface for being connected with computer.
A kind of rail vehicle tolerance dimension measuring method, using described rail vehicle tolerance dimension measuring system, including
Following steps:
(1) before measuring, hand-held measuring apparatus is attached with computer using USB interface, the processing of supporting three-dimensional data
Unit is installed in a computer;During measurement, it is in the grating that dextrorotation is distributed to project one group of light intensity to testee using DLP projector
Image, and shoot the raster image deformed through testee surface modulation simultaneously using two CCD cameras;
(2) absolute phase values of raster image are obtained according to phase shift algorithm and multifrequency heterodyne solution phase method;According to advance demarcation
Systematic parameter or phase height mapping relation, the three dimensional point cloud on testee surface is calculated from absolute phase values;
(3) after the cloud data for obtaining testee, the menu item on corresponding software is selected, automobile interior public affairs needed for calculating
Difference size, measurement result is shown in the form of message box.
Described rail vehicle tolerance dimension measuring method, it is characterised in that:Automobile interior tolerance dimension includes:Plane
Degree, angle, length, cylinder circularity.
Beneficial effect:Rail vehicle tolerance dimension measuring system provided by the invention, projected using to measured target object
One group of light intensity is in the raster image of Sine distribution, the three dimensional point cloud on testee surface is obtained by correlation computations, to three
Tie up cloud data and carry out related algorithm processing, the data needed, be directed to the angle of object, flatness, length, circle
Degree, also relates to three-dimensional values of miniature parts etc..Compared with the method for existing measurement automobile interior tolerance, advantages of the present invention
It is:(1) it is affected by human factors small, has simplified the operating procedure of rail wheel dimension tolerance measurement significantly, easy to operate, inspection
Surveying result can be visually displayed on computer screen;(2) can collect traditional measurement method measurement local time can not collect
Data, gathered data efficiency high;(3) it is high, reproducible to measure dimensional accuracy.
Brief description of the drawings
Fig. 1 is the schematic diagram of hand-held measurement device in the present invention;
Fig. 2 is three-dimensional data processing unit interface schematic diagram in the present invention;
Fig. 3 is the measuring method of the present invention;
Fig. 4 is phase measurement consistency profiles angular surveying schematic diagram;
Fig. 5 is that corner detection approach surveys object length schematic diagram;
Fig. 6 is observation station and axis geometrical relationship figure.
In figure:DLP projector 1, CCD camera 2,3, SECO plate 4, image pick-up card 5, data processor 6, tested rail
Road vehicle 7.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of rail vehicle tolerance dimension measuring system, measuring system is divided into two parts, and hand-held is surveyed
Measure equipment and three-dimensional data processing generation unit.
Hand-held measurement device includes:DLP projector 1, left and right CCD camera 2,3, SECO plate 4, data processor 5
With image pick-up card 6.Wherein, the angle of the photocentre axle of two CCD cameras 2,3 and the photocentre axle of DLP projector 1 is at 20 degree to 60
Between degree, and it need to strictly keep DLP projector 1 and the relative position of two CCD cameras constant in measurement.In Fig. 1,7 tables
Show tested rail vehicle.
SECO plate 4 is connected with DLP projector 1, two CCD cameras 2,3, data processor 5 respectively, two CCD phases
Machine 2,3 is connected by image pick-up card 6 with data processor 5.
Wherein DLP projector 1 projects the raster image that one group of light intensity is in Sine distribution, two CCD cameras to testee
2nd, 3 synchronizing signals transmitted according to SECO plate 6 carry out IMAQ, and the view data of collection is passed by image pick-up card 6
It is sent on data processor 5 and stores.
The system architecture for holding measuring apparatus shown in Fig. 1 solves the problems, such as the acquisition of destination object three-dimensional data, measuring apparatus
It is attached with computer using USB interface, in a computer, computer carries figure for supporting three-dimensional data processing unit installation
Video card.Accompanying drawing 2 represents three-dimensional data processing unit interface schematic diagram.
As shown in figure 3, rail vehicle tolerance dimension measuring method, is comprised the following steps that:
(1) it is tested rail vehicle 7 to testee using DLP projector 1 when measuring and projects one group of light intensity in dextrorotation distribution
Raster image, and shoot the raster image deformed through testee surface modulation simultaneously using CCD camera 2,3;
(2) absolute phase values of raster image are obtained according to phase shift algorithm and multifrequency heterodyne solution phase method;According to advance demarcation
Systematic parameter or phase height mapping relation, the three dimensional point cloud on testee surface is calculated from absolute phase values;
(specific implementation step referring to:Structural light three-dimensional e measurement technologies of the big based on digital fringe projection and system research [D] in Lee
[D] Wuhan:The Central China University of Science and Technology, 2009).
(3) after the cloud data for obtaining testee, the menu item on corresponding software is selected, required automobile interior can be calculated
Tolerance dimension, such as flatness, angle, length, cylinder circularity, show measurement result in the form of message box.Wherein mutually inside the Pass
It is as follows to adorn size calculation step:
3.1 flatnesses calculate
Flatness refers to variation of the tested actual surface to its ideal plane.Flatness error is by tested actual surface
Compared with ideal plane, line value distance as flatness error value between the two.Ignore measurement error, by plane to be measured
Cloud data be considered as the True Data of tested actual surface, the plane fitted is considered as ideal plane.
3.11st step determines the initial parameter values of fit Plane using the characteristic vector estimation technique (EVE);If treat fit Plane
Equation is:Ax+by+cz=d;Wherein:A, b, c are the unit normal vector of plane, i.e.,:a2+b2+c2=1, wherein:D is that coordinate is former
Put to the distance of plane, d >=0;
3.12nd step is set to be scanned to a certain plane, has obtained n data point, then the three-dimensional coordinate of any one data point
(xi,yi,zi) to the distance of the plane be:
dI=|axi+byi+czi-d| (1)
Obtain best-fitting plane, then should a under conditions2+b2+c2=1, meet:
3.4th step obtains object function by lagrange's method of multipliers:
Wherein λ is Lagrange's multiplier;
Ask d, a, b, c local derviation final respectively formula (3):
Wherein: It is cloud data three-dimensional coordinate
Average value.
3.14th step solves to above-mentioned matrix, obtains initial value a, b, c of plane parameter.
3.15th step calculates the standard deviation δ for the distance for arriving fit Plane a little, and is rejected using 2 δ as threshold value to plan
Close the excessive interference noise point of plan range;
31.6th step recalculates parameter a, b, c of fit Plane using remaining significant figure strong point;Repeat above step
Until arriving fit Plane your distance a little is both less than the threshold value that this time calculates, optimal fit Plane is finally given, work
On the basis of ideal plane;
3.17th step brings the coordinate of each available point in plane equation into, judges that the point is located at plane upper side or downside;
Calculate each point in plane to be measured and, to the distance d (computational methods are referring to formula (1)) of ideal plane, try to achieve the maximum for a little arriving plan range
Value dmax, the flatness of plane as to be measured.
3.2 angular surveying
Angular surveying, that is, measure the angle between two planes.Phase measurement consistency profiles measurement angle principle, as shown in Figure 4.
3.21st step carries out plane fitting to obtained three dimensional point cloud, plane fitting process referring to step 3.1 to
3.6, fit two planes of P1, P2;
Plane equations of the 3.22nd step Calculation Plane P1 and plane P2 under world coordinate system, and obtain P1 and P2 intersection
L;
3.23rd step, which is appointed, takes a point O on L, calculated on plane P1 O points and on L straight line L1 and P2 O
The equation in coordinates formula of point and straight line L2 perpendicular to L;
The angle theta that 3.24th step calculates L1 and L2 is the angle between the plane of necessary requirement two.
3.3 linear measure longimetry
The method of measurement length mainly has following two:
Corner detection approach
It is generally acknowledged that angle point is the violent point of two dimensional image brightness change, the maximum point of curvature on the curve of image border,
Or two, the point that intersects at an angle of two or more linear edge.Corner detection approach principle is as shown in Figure 5.
3.31st step uses Harris Corner Detection Algorithms, detects to shoot angle point and mark on picture, as icon is remembered
For 1,2,3,4;
After a local window in Harris Corner Detection Algorithm research images carries out a small amount of skew in different directions,
The average of image brightness values in window.Harris corner detection operators can be briefly described for:Some in angle point is adjacent
In domain, the change of brightness is all very big on any one straight line by the point.Window is taken to each pixel to be detected,
The non-regularization autocorrelation value of this pixel is calculated from all directions, and selects angle point of the minimum value as this pixel
Receptance function.
3.32nd step calculates the distance L between angle point, is the length of required object.
(2) edge extracting method
The edge of image refers to the part that image local area brightness is changed significantly, i.e., from a gray value in the slow of very little
Region is rushed to have to go to the toilet the acute gray value for changing to another gray scale and differing larger.The rim detection of image is realized, is sought to discrete
Change the gray scale transition position that gradient approximating function finds gradation of image matrix according to two dimensional gray matrix gradient vector, Ran Hou
The point of these positions is linked up in image and just constitutes so-called image border.
The step of rim detection:
1) common filtering method mainly has gaussian filtering, i.e., normalized using one group of the Gaussian function generation of discretization
Gaussian kernel, it is then based on gaussian kernel function and summation is weighted to the every bit of gradation of image matrix.
2) strengthen:The basis at enhancing edge is to determine the changing value of each vertex neighborhood intensity of image.Enhancing algorithm will can scheme
As the point that gray scale vertex neighborhood intensity level has significant change highlights.
3) detect:By the image of enhancing, often there is that the Grad much put is bigger in neighborhood, and specifically applying
In, these points are not intended to the marginal point looked for, so should be accepted or rejected using some way to these points.Conventional method
It is to be detected by thresholding method.
3.33rd step carries out edge extracting to the image of shooting, extracts the profile for the object to be measured;
3.34th step fitting edge contour point obtains equation of the edge line under world coordinate system;
The distance between straight line of 3.35th step digital simulation, it is required.
3.4 cylinder roundness calculations
Cylinder circularity refers to point on the face of cylinder to the distance between cylindrical center's axis and the difference of cylindrical radius.Cylinder
Face may be considered the set of the point equal to a constant R to the distance of a central axis, be understood by this feature by 7 ginsengs
Number can uniquely determines a cylinder, and this 7 parameters are the direction vector (a of this central axis respectively1,b1,c1) and straight line
On certain a starting point coordinate (x0,y0,z0), and the radius R of cylinder.Observation station and axis geometrical relationship figure, observation station with
Axis geometrical relationship figure, as shown in Figure 6.
3.41st step sets any observation point coordinates as Pi(xi,yi,zi), then PiVertical range on to axis is to measure
Real radius R ', α PiP0With the angle of central axis.
Wherein:
Error equation can be classified as:
υ=R '-R
Wherein υ is obserred coordinate value residual error.
3.42nd step introduces least square constraint vTP υ=min are (referring specifically to document:Wang Sui brightness error theories and measurement
Adjustment [M] Shanghai:Publishing house of Tongji University, 2010.), resolve equation group (7);In addition for ensure starting point coordinate and axis to
The uniqueness of amount, introduce two conditional equations:
x0=average (X), y0=average (Y), z0=average (Z) (9)
Wherein x0、y0、z0Respectively x a littlei、yi、ziThe average value of coordinate.
3.43rd step calculates a1, b1, c1, x0, y0, z0And R.
3.44th step calculates cylinder circularity, i.e. υ in error equation, as a mark for weighing face of cylinder fitting quality
It is accurate.
Described above is only the preferred embodiment of the present invention, it should be pointed out that:For the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (4)
- A kind of 1. rail vehicle tolerance dimension measuring system, it is characterised in that:At hand-held measurement device and three-dimensional data Manage unit;Hand-held measuring apparatus, including DLP projector, two CCD cameras, SECO plate, image pick-up card and data processor;Three-dimensional data processing unit interface, including a cloud viewing area, the point cloud information area, commard editor area and camera viewing area;Survey Before amount, hand-held measuring apparatus is attached with computer using USB interface, and supporting three-dimensional data processing unit, which is arranged on, to be calculated In machine;(1) when measuring, it is in the raster image that dextrorotation is distributed to project one group of light intensity to testee using DLP projector, and is used Two CCD cameras shoot the raster image deformed through testee surface modulation simultaneously;(2) absolute phase values of raster image are obtained according to phase shift algorithm and multifrequency heterodyne solution phase method;It is according to what is demarcated in advance Parameter of uniting or phase height mapping relation, the three dimensional point cloud on testee surface is calculated from absolute phase values;(3) after the cloud data for obtaining testee, the menu item on corresponding software, automobile interior tolerance chi needed for calculating are selected It is very little, measurement result is shown in the form of message box;The automobile interior tolerance dimension includes:Flatness, angle, length, cylinder Circularity;Wherein flatness calculation procedure is as follows:3.11st step:The initial parameter values of fit Plane are determined using the characteristic vector estimation technique;If the equation for treating fit Plane is:ax + by+cz=d;Wherein:(a, b, c) is the unit normal vector of plane, i.e.,:a2+b2+c2=1, (x, y, z) is three-dimensional coordinate, its In:D is the origin of coordinates to the distance of plane, d >=0;3.12nd step:If being scanned to a certain plane, n data point is obtained, then three-dimensional coordinate (the x of any one data pointi, yi,zi) to the distance of the plane be:di=| axi+byi+czi-d| (1)Obtain best-fitting plane, then should a under conditions2+b2+c2=1, meet:<mrow> <msubsup> <mi>&Sigma;id</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mi>&Sigma;</mi> <mi>i</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>ax</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>by</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>cz</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>d</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&RightArrow;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>3.13rd step:Object function is obtained by lagrange's method of multipliers:<mrow> <mi>f</mi> <mo>=</mo> <msubsup> <mi>&Sigma;id</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Wherein λ is Lagrange's multiplier;Ask d, a, b, c local derviation final respectively formula (3):<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;x</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;z</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>&lambda;</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Wherein: It is the flat of cloud data three-dimensional coordinate Average;3.14th step:Above-mentioned matrix is solved, obtains initial value a, b, c of plane parameter;3.15th step:The standard deviation δ for the distance for arriving fit Plane a little is calculated, and is rejected to fitting and put down using 2 δ as threshold value Identity distance is from excessive interference noise point;3.16th step:Parameter a, b, c of fit Plane are recalculated using remaining significant figure strong point;Repeat above step until The distance for arriving fit Plane a little is both less than the threshold value that this time calculates, and optimal fit Plane is finally given, as benchmark Ideal plane;3.17th step:The coordinate of each available point is brought into plane equation, judges that the point is located at plane upper side or downside;Calculate For each point to the distance d of ideal plane, computational methods try to achieve the maximum for a little arriving plan range referring to formula (1) in plane to be measured dmax, the flatness of plane as to be measured;Wherein angular surveying step is as follows:Angular surveying, that is, the angle between two planes is measured, using phase measurement consistency profiles measurement angle principle,3.21st step:Carry out plane fitting to obtained three dimensional point cloud, plane fitting process referring to step 3.11 to 3.16, Two planes of P1, P2 are fitted, the ideal plane on the basis of one of them, another is plane to be measured;3.22nd step:The plane equation of Calculation Plane P1 and plane P2 under world coordinate system, and obtain P1 and P2 intersection L;3.23rd step:Appoint and take a point O on L, calculated on plane P1 O points and on L straight line L1 and P2 O points and Perpendicular to L straight line L2 equation in coordinates formula;3.24th step:The angle theta for calculating L1 and L2 is the angle between required two planes;Wherein linear measure longimetry step is as follows:The method of measurement length has following two:(1) corner detection approach3.31st step:Using Harris Corner Detection Algorithms, detect to shoot the angle point and mark on picture;After a local window in Harris Corner Detection Algorithm research images carries out a small amount of skew in different directions, The average of image brightness values in window;Harris corner detection operators can be briefly described for:Some in angle point is adjacent In domain, the change of brightness is all very big on any one straight line by the point;Window is taken to each pixel to be detected, The non-regularization autocorrelation value of this pixel is calculated from all directions, and selects angle point of the minimum value as this pixel Receptance function;3.32nd step:The distance L between angle point is calculated, is the length of required object;(2) edge extracting methodThe edge of image refers to the part that image local area brightness is changed significantly, i.e., from a gray value very little buffering area Domain is had to go to the toilet the acute gray value for changing to another gray scale and differing larger;The rim detection of image is realized, is sought to discretization ladder Degree approximating function finds the gray scale transition position of gradation of image matrix according to two dimensional gray matrix gradient vector, then in image Middle link up the point of these positions just constitutes so-called image border;The step of rim detection:1) filtering method has gaussian filtering, i.e., produces one group of normalized Gaussian kernel, Ran Houji using the Gaussian function of discretization Summation is weighted to the every bit of gradation of image matrix in gaussian kernel function;2) strengthen:The basis at enhancing edge is to determine the changing value of each vertex neighborhood intensity of image;Strengthening algorithm can be by image ash The point that degree vertex neighborhood intensity level has significant change highlights;3) detect:By the image of enhancing, often there is that the Grad much put is bigger in neighborhood, and in specific applications, These points are not intended to the marginal point looked for, and these points are accepted or rejected using thresholding method;3.33rd step:Edge extracting is carried out to the image of shooting, extracts the profile for the object to be measured;3.34th step:Fitting edge contour point obtains equation of the edge line under world coordinate system;3.35th step:The distance between straight line of digital simulation, it is the length of required object;Wherein cylinder roundness calculation step is as follows:Cylinder circularity refers to point on the face of cylinder to the distance between cylindrical center's axis and the difference of cylindrical radius;The face of cylinder can be with It is considered that the distance of a central axis is equal to the set of constant R point, understands to be determined by 7 parameters by this feature One cylinder, this 7 parameters are the direction vector coordinate (a of this central axis respectively1,b1,c1) and straight line on a certain starting Coordinate (the x of point0,y0,z0), and the radius R of cylinder;Establish observation station PiWith central axis P0P geometrical relationship figure;3.41st step:If any observation station PiCoordinate be (xi,yi,zi), then PiVertical range on to central axis is Real radius R ', the α P measurediP0With the angle of central axis;<mrow> <msup> <mi>R</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <msub> <mi>P</mi> <mi>i</mi> </msub> <msub> <mi>P</mi> <mn>0</mn> </msub> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein:<mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&alpha;</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>Error equation can be classified as:υ=R '-R<mrow> <mtable> <mtr> <mtd> <msub> <mi>v</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>R</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Wherein υ is obserred coordinate value residual error;υiFor any observation station PiResidual error;3.42nd step:Introduce least square constraint vTP υ=min, resolve equation group (7);In addition it is to ensure starting point coordinate with The uniqueness of mandrel line vector, introduces two conditional equations:<mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>b</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>c</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>x0=average (X), y0=average (Y), z0=average (Z) (9)Wherein x0、y0、z0Respectively x a littlei、yi、ziCoordinate is averaged Value;3.43rd step:Calculate a1, b1, c1, x0, y0, z0And R;3.44th step:Calculate cylinder circularity, i.e. υ in error equation, as a standard for weighing face of cylinder fitting quality.
- 2. rail vehicle tolerance dimension measuring system according to claim 1, it is characterised in that:SECO plate respectively with Data processor, two CCD cameras, DLP projectors are connected, and DLP projector is connected with data processor, two ccd video cameras It is connected by image pick-up card with data processor.
- 3. rail vehicle tolerance dimension measuring system according to claim 1, it is characterised in that:Two CCD cameras Photocentre axle and DLP projector photocentre axle angle between 20 degree to 60 degree, and keep DLP projector and Liang Tai when measuring The relative position of CCD camera is constant.
- A kind of 4. rail vehicle tolerance dimension measuring method, using the rail vehicle tolerance chi described in claim any one of 1-3 Very little measuring system, comprises the following steps:(1) before measuring, hand-held measuring apparatus is attached with computer using USB interface, supporting three-dimensional data processing unit Installation is in a computer;During measurement, it is in the raster pattern that dextrorotation is distributed to project one group of light intensity to testee using DLP projector Picture, and shoot the raster image deformed through testee surface modulation simultaneously using two CCD cameras;(2) absolute phase values of raster image are obtained according to phase shift algorithm and multifrequency heterodyne solution phase method;It is according to what is demarcated in advance Parameter of uniting or phase height mapping relation, the three dimensional point cloud on testee surface is calculated from absolute phase values;(3) after the cloud data for obtaining testee, the menu item on corresponding software, automobile interior tolerance chi needed for calculating are selected It is very little, measurement result is shown in the form of message box;The automobile interior tolerance dimension includes:Flatness, angle, length, cylinder Circularity;Wherein flatness calculation procedure is as follows:3.11st step:The initial parameter values of fit Plane are determined using the characteristic vector estimation technique;If the equation for treating fit Plane is:ax + by+cz=d;Wherein:(a, b, c) is the unit normal vector of plane, i.e.,:a2+b2+c2=1, (x, y, z) is three-dimensional coordinate, its In:D is the origin of coordinates to the distance of plane, d >=0;3.12nd step:If being scanned to a certain plane, n data point is obtained, then three-dimensional coordinate (the x of any one data pointi, yi,zi) to the distance of the plane be:di=| axi+byi+czi-d| (1)Obtain best-fitting plane, then should a under conditions2+b2+c2=1, meet:<mrow> <msubsup> <mi>&Sigma;id</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mi>&Sigma;</mi> <mi>i</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>ax</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>by</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>cz</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>d</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&RightArrow;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>3.13rd step:Object function is obtained by lagrange's method of multipliers:<mrow> <mi>f</mi> <mo>=</mo> <msubsup> <mi>&Sigma;id</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Wherein λ is Lagrange's multiplier;Ask d, a, b, c local derviation final respectively formula (3):<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;x</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;y</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;y</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&Sigma;</mo> <msub> <mi>i&Delta;z</mi> <mi>i</mi> </msub> <msub> <mi>&Delta;z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>&lambda;</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Wherein: It is the flat of cloud data three-dimensional coordinate Average;3.14th step:Above-mentioned matrix is solved, obtains initial value a, b, c of plane parameter;3.15th step:The standard deviation δ for the distance for arriving fit Plane a little is calculated, and is rejected to fitting and put down using 2 δ as threshold value Identity distance is from excessive interference noise point;3.16th step:Parameter a, b, c of fit Plane are recalculated using remaining significant figure strong point;Repeat above step until The distance for arriving fit Plane a little is both less than the threshold value that this time calculates, and optimal fit Plane is finally given, as benchmark Ideal plane;3.17th step:The coordinate of each available point is brought into plane equation, judges that the point is located at plane upper side or downside;Calculate For each point to the distance d of ideal plane, computational methods try to achieve the maximum for a little arriving plan range referring to formula (1) in plane to be measured dmax, the flatness of plane as to be measured;Wherein angular surveying step is as follows:Angular surveying, that is, the angle between two planes is measured, using phase measurement consistency profiles measurement angle principle,3.21st step:Carry out plane fitting to obtained three dimensional point cloud, plane fitting process referring to step 3.11 to 3.16, Two planes of P1, P2 are fitted, the ideal plane on the basis of one of them, another is plane to be measured;3.22nd step:The plane equation of Calculation Plane P1 and plane P2 under world coordinate system, and obtain P1 and P2 intersection L;3.23rd step:Appoint and take a point O on L, calculated on plane P1 O points and on L straight line L1 and P2 O points and Perpendicular to L straight line L2 equation in coordinates formula;3.24th step:The angle theta for calculating L1 and L2 is the angle between required two planes;Wherein linear measure longimetry step is as follows:The method of measurement length has following two:(1) corner detection approach3.31st step:Using Harris Corner Detection Algorithms, detect to shoot the angle point and mark on picture;After a local window in Harris Corner Detection Algorithm research images carries out a small amount of skew in different directions, The average of image brightness values in window;Harris corner detection operators can be briefly described for:Some in angle point is adjacent In domain, the change of brightness is all very big on any one straight line by the point;Window is taken to each pixel to be detected, The non-regularization autocorrelation value of this pixel is calculated from all directions, and selects angle point of the minimum value as this pixel Receptance function;3.32nd step:The distance L between angle point is calculated, is the length of required object;(2) edge extracting methodThe edge of image refers to the part that image local area brightness is changed significantly, i.e., from a gray value very little buffering area Domain is had to go to the toilet the acute gray value for changing to another gray scale and differing larger;The rim detection of image is realized, is sought to discretization ladder Degree approximating function finds the gray scale transition position of gradation of image matrix according to two dimensional gray matrix gradient vector, then in image Middle link up the point of these positions just constitutes so-called image border;The step of rim detection:1) filtering method has gaussian filtering, i.e., produces one group of normalized Gaussian kernel, Ran Houji using the Gaussian function of discretization Summation is weighted to the every bit of gradation of image matrix in gaussian kernel function;2) strengthen:The basis at enhancing edge is to determine the changing value of each vertex neighborhood intensity of image;Strengthening algorithm can be by image ash The point that degree vertex neighborhood intensity level has significant change highlights;3) detect:By the image of enhancing, often there is that the Grad much put is bigger in neighborhood, and in specific applications, These points are not intended to the marginal point looked for, and these points are accepted or rejected using thresholding method;3.33rd step:Edge extracting is carried out to the image of shooting, extracts the profile for the object to be measured;3.34th step:Fitting edge contour point obtains equation of the edge line under world coordinate system;3.35th step:The distance between straight line of digital simulation, it is the length of required object;Wherein cylinder roundness calculation step is as follows:Cylinder circularity refers to point on the face of cylinder to the distance between cylindrical center's axis and the difference of cylindrical radius;The face of cylinder can be with It is considered that the distance of a central axis is equal to the set of constant R point, understands to be determined by 7 parameters by this feature One cylinder, this 7 parameters are the direction vector coordinate (a of this central axis respectively1,b1,c1) and straight line on a certain starting Coordinate (the x of point0,y0,z0), and the radius R of cylinder;Establish observation station PiWith central axis P0P geometrical relationship figure;3.41st step:If any observation station PiCoordinate be (xi,yi,zi), then PiVertical range on to central axis is Real radius R ', the α P measurediP0With the angle of central axis;<mrow> <msup> <mi>R</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <msub> <mi>P</mi> <mi>i</mi> </msub> <msub> <mi>P</mi> <mn>0</mn> </msub> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein:<mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&alpha;</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>Error equation can be classified as:υ=R '-R<mrow> <mtable> <mtr> <mtd> <msub> <mi>v</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>R</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Wherein υ is obserred coordinate value residual error;υiFor any observation station PiResidual error;3.42nd step:Introduce least square constraint vTP υ=min, resolve equation group (7);In addition it is to ensure starting point coordinate with The uniqueness of mandrel line vector, introduces two conditional equations:<mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>b</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>c</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>x0=average (X), y0=average (Y), z0=average (Z) (9)Wherein x0、y0、z0Respectively x a littlei、yi、ziCoordinate is averaged Value;3.43rd step:Calculate a1, b1, c1, x0, y0, z0And R;3.44th step:Calculate cylinder circularity, i.e. υ in error equation, as a standard for weighing face of cylinder fitting quality.
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