CN101382409A - Method for precisely measuring points on space curved surface and space curved surface by using barycentric coordinate - Google Patents

Abstract

The invention relates to a method for precisely measuring points on a space curved surface by using barycentric coordinates, which comprises the following steps: (1) establishing a micro triangle with a regular triangle projection surface on the space curved surface, and enabling a projection point (M) of a measurement point (G) on the space curved surface to be positioned on the center of the regular triangle; (2) calculating the plane coordinates of three vertexes of the regular triangle on the projection plane according to the plane coordinates of the projection point (M); (3) and closing the radius compensation of the measuring needle, enabling the measuring needle to measure the z coordinates of three vertexes of the micro triangle along the vector direction vertical to the projection plane: (4) calculating the barycentric coordinates of the micro-triangle by using the space coordinates of three vertexes of the micro-triangle; (5) calculating the normal vector of the miniature triangle on the space curved surface; (6) starting the radius compensation of the measuring needle by taking the normal vector as the approaching and compensating direction of the measuring needle and the barycentric coordinate as a measuring target point to obtain an accurate measuring value of a measuring point (G); the whole measuring process is automatically completed by a measuring machine CNC control system. The invention can also be used for measuring complex space curve surfaces and has high measurement precision.

Description

Utilize on the barycentric coordinates precision measurement space curved surface method of point and space curved surface

Technical field

The present invention relates on the precision measurement space curved surface method of point and space curved surface.Relate in particular to and creating little triangle on the space curved surface arbitrarily, finish its direction cosine and calculate, use its normal vector on three coordinate measuring machine, any space curved surface to be implemented the method for precision measurement.Be applicable to that mechanical manufacturing field is to the test of space curved surface on measuring machine, as reverse-engineering; Also be applicable to the precision measurement technical research on measuring machine on any space curved surface simultaneously, comprise the research of measuring machine control system and software systems, the modular design of measuring machine function etc.

Background technology

Finish with three-dimensional coordinates measurement in the metrology and measurement of any space curve face, gordian technique is exactly how to compensate the chaining pin radius value, the key theory of compensation chaining pin radius is again the normal vector on the computer memory curved surface how, to any space curve face, there is not mathematical equation, can not use the direction cosine of the measured some normal vector of partial derivative calculating in the infinitesimal analysis, therefore, the measurement to any space curved surface on measuring machine is all difficult.

The application of space curved surface is very extensive, and modal is exactly blade face, three-D profile surface etc.In measurement, when the application that can't determine space curved surface, perhaps can't determine the design rule of space curved surface, we are seen as any space curve face to it.In the past, a lot of measuring machines do not have space curve planar survey function, if exist, are that measurement data is processed in corresponding software or mathematical model yet, directly obtain almost not having of profile measurement data from measuring technology; At present, be called as advanced measuring system such as PC-DMIS in the world, a small amount of measurement space curve function is arranged, but condition is: its space CAD/CAM model be imported PC-DMIS, in fact, be that the space law that measuring system has been finished institute's measuring point is calculated to vector, what finish is the measurement of Partial Feature point, so, if there is not the CAD/CAM model, to do precision measurement to any space curve face, will consider that still the space law of institute's measuring point is calculated to vector.If can not calculate the space normal vector of any space curve face measuring point, its precision measurement can not be finished on measuring machine, if measuring machine does not provide the design environment of program, or do not provide corresponding order, equally, the measurement of space curve face can not be finished on measuring machine arbitrarily, unless data processing software or other mathematical model compensation chaining pin radius are arranged.

If close the measurement radius compensation during measurement space curved surface, the coordinate data of obtaining so is not the coordinate data on the contoured surface, is the coordinate position at chaining pin center; If start measuring needle radius compensation, its measure theory requires chaining pin to make the convergence compensating measure along the normal vector of institute's measuring point, otherwise will produce measuring error, or the measurement result of mistake, but the normal vector that calculates institute's measuring point on the face of any space is very difficult.In the face of this class technical matters, the invention provides structure and the normal vector computing method thereof of a kind of miniature triangle on space curved surface, this method has been used the geometrical feature of equilateral triangle, application vector calculation theory, finish the calculating of measuring target point on the space curved surface, normal vector and direction cosine thereof, with this miniature leg-of-mutton center of gravity is that measuring target point is implemented precision measurement to any space curve face, and this method has high measuring accuracy by theoretical and experiment.

Summary of the invention

Finish the test of any space curved surface for making three coordinate measuring machine, as complex outline, 3D contoured surface and blade etc. in the cigarette machine fitting of tobacco business, the invention provides structure and the normal vector computing method thereof of a kind of miniature triangle on space curved surface, so that can adopt the vector compensation mensuration to finish any space curved surface precision measurement.In selecting suitable projecting plane, utilization is perpendicular to the vector on projecting plane, adopt 3 measurement points on the closing measuring needle radius compensation measurement space curved surface, utilize these 3 measurement points on space curved surface, to set up " the miniature triangle " of projecting plane for " equilateral triangle ", calculate this " miniature triangle " barycentric coordinates point, be its measuring target point with this point; Use vector calculation and be somebody's turn to do " miniature triangle " normal vector, use the DEAPPL language and design program, use this normal vector, start measuring needle radius compensation this space curved surface is done precision measurement.The precision of its measurement depends on this miniature leg-of-mutton microminiaturized degree, i.e. the high convergence " certain value " of this equilateral triangle, and then the precision of Ce Lianging is just high; Measure the outline line that produces and to generate the corresponding data file; Because therefore measuring target point-" barycentric coordinates " of this method have higher efficiency of measurement for obtaining by calculating, and are convenient to reverse-engineering; Change design if y=f (x) is pressed in the projection of measurement point, so, this theory can be used for measurement of complicated space curved surface, as Archimedes' helicoid; Owing to draw high measuring accuracy by experiment, therefore, can be used on measuring machine, doing the precision measurement technical research; Because almost do not have the scan function of any space curve face on the present three coordinate measuring machine, therefore, this invention can be used for the modular design and the research of measuring machine function.

The technical solution adopted in the present invention is as follows:

A kind of method of putting on the barycentric coordinates precision measurement space curved surface of utilizing is characterized in that, comprises the steps:

(1) on space curved surface, set up the miniature triangle that the projecting plane is an equilateral triangle, the subpoint (M) that makes measurement point on the space curved surface (G) in this equilateral triangle in the heart;

(2) according to the planimetric coordinates of this subpoint (M), calculate the planimetric coordinates on three summits of this equilateral triangle on the projecting plane;

(3) closing measuring needle radius compensation makes chaining pin along the direction vector perpendicular to the projecting plane, measures the z coordinate on these miniature leg-of-mutton three summits;

(4) utilize the volume coordinate on miniature leg-of-mutton three summits, calculate this miniature leg-of-mutton barycentric coordinates;

(5) this miniature leg-of-mutton normal vector on the computer memory curved surface;

(6) being chaining pin convergence and compensation direction with this normal vector, is measuring target point with these barycentric coordinates, starts measuring needle radius compensation, obtains the accurate measured value of measurement point (G).

Further, described step (5) further may further comprise the steps:

(5.1) to record these miniature leg-of-mutton three summits on the space curved surface, make the line vector in twos respectively, utilize the vector product of these two line vectors to obtain this miniature leg-of-mutton normal vector.

The present invention also provides a kind of method of utilizing chaining pin sphere centre coordinate precision measurement space curved surface, on the projecting plane of space curved surface, set up several measurement points successively, adopt step to require 1,2,3 or 4 described methods to obtain the accurate coordinates value of each measurement point respectively, thereby obtain the whole profile coordinate figure on the space curve face.

At first, measurement mechanism opinion: because in the three-dimensional coordinates measurement technology, the any geometric element of precision measurement, all must make measuring needle radius compensation, when measuring " point ", chaining pin must along the normal of measured point without barrier the convergence measurement point measure, and on this normal vector, do measuring needle radius compensation, otherwise, to produce error, state, be the some A synoptic diagram on the measurement space curved surface M as Fig. 1, P is A point section, N is an A point normal, except that any vector measurement A point along the vector V 1 of N, as V2, V3, all will produce the measuring needle radius compensation error, this error is a systematic error.Therefore, finish the calculating of normal vector.

Secondly, the space normal of curved surface and measurement space curved surface relation demonstration: two equidistant surfaces of following surface analysis are about the normal situation at point of contact, state as Fig. 2: M1 and M2 are equidistant surfaces, its distance is d, ball at a φ d of equidistant surface intercropping, the point of contact of this ball and M1 curved surface is the A point, cross this point of contact and make section P1, cross the A point and make this section P1 vertical line N1, then N1 is the M1 normal to a surface and the centre of sphere that passes through φ d, since be equidistant surface, so there are unique intersection points B in this ball and M2 curved surface, and on M1 normal to a surface N1, cross the B point and make two parallel lines P2 and the P3 of section P1, then the determined plane of P2 and P3 is the section of curved surface M2, and therefore, normal N 1 also is the M2 normal to a surface.

This conclusion is: the normal of space curved surface also is its isometric space normal to a surface.(inference 1)

Can demonstrate,prove with reason: a normal to a curve also is the normal of its equidistant curve.(inference 2)

In the measurement space curved surface profile, because during closing measuring needle radius compensation, the space curved surface at place, chaining pin center is the equidistant curved surface of this profile, according to " inference 1 " as can be known, if during the measuring wheel contour curved surface, can determine the coordinate and the normal thereof at chaining pin center, then available its normal vector, starting measuring needle radius compensation, is impact point with the coordinate at this chaining pin center, and the point coordinate on this curved surface profile is implemented precision measurement.

The 3rd, make up miniature triangle theory: state as Fig. 3, be the local space contour surface: in how much of space analysis, for arbitrary surface S, can on this curved surface, select set up one " miniature Δ abc " at 3, make it be projected as positive Δ ABC on XOY plane, the center M of this positive Δ ABC is the unifications of 4 hearts, and promptly its center of gravity, orthocenter, unfaithful intention and heart overlap.Because the intersection point of positive Δ ABC center line AE, BF and CD is M, " miniature Δ abc " summit a, b, c are projected as A, B, C point XOY plane, can demonstrate,prove by plane geometry, subpoint e, f, d that mid point E, F and D project to " miniature Δ abc " also are the mid points of its each limit ab, bc, ca, so getting " miniature Δ abc " center line intersection point is G, is focus point.As Fig. 3, in quadrilateral AEea, known by center of gravity character: AM/ME=aG/Ge=2, so as can be known, GM is parallel to eE, and the projection that the M point is ordered for G promptly can be described.This conclusion is that positive Δ ABC center M projects to curved surface S when going up once more, becomes the center of gravity G of " miniature Δ abc " at least.

Owing to constitute the point of space diagram, position is separately all arranged, constituting the mean place that space diagram is had a few, be called the center of gravity of this figure, and with its position as whole figure.Therefore, the position of this center of gravity G can be seen as the position of " miniature Δ abc ", utilizes its its normal N of determined plane computations, uses the direction vector of this normal, is measuring target point with this center of gravity G, can implement the precision measurement to space curved surface.When each limit of positive Δ ABC is tending towards infinitely small, then the normal of " miniature Δ abc " also levels off to this normal to a surface, focus point G promptly levels off to the point on this curved surface, promptly this space curved surface is subdivided into " miniature triangle " by " limit ", therefore, measure its focus point, can reflect the position of putting on this space curved surface.But, the degree that this method physical presence error, reason are " microminiaturization " how because it is not all right to make up triangle " too small ", because there is measuring error in measuring machine, main influence is measuring machine precision and performance, and it can make the composition error influence " extension " of measuring machine, therefore, leg-of-mutton " microminiaturization " should look concrete condition, or obtain by experiment, the height that generally makes positive Δ ABC with interior selection, can be finished the space curve planar survey of a lot of precisions in the 2mm scope.

The 4th, implement the measure theory of any space curved surface: on the feature locations of space curved surface arbitrarily such as hole upper thread, set up coordinate system, as Fig. 8, select suitable projecting plane, as YOZ or ZOX or XOY.Select XOY for use as Fig. 4 and Fig. 8, closing measuring needle radius compensation, application direction cosine V (0,0 ,-1) makes the chaining pin direction vector of cosine in the direction, measures first M1 on this any space curved surface _J+1, measure second M3 then _J+1And M3 _J+3Guarantee M1 _J+1, M3 _J+1And M3 _J+3The necessary condition of formation equilateral triangle such as following in projection XOY coordinate: as Fig. 4, this is projected as the high d of being of equilateral triangle, and the length of side is 2K, so, satisfy the d and the K value that form equilateral triangle and should meet following relationship:

d＝K×tg60°

Meet the above-mentioned relation formula, then the projection of " miniature Δ abc " then constitutes positive Δ ABC.

Equally, if provide the center of this equilateral triangle, i.e. x and y coordinate, so, the coordinate on this each summit of equilateral triangle all can calculate by the characteristic of equilateral triangle, as Fig. 4 and Fig. 6,

If establish volume coordinate is M1 _J+1(x _J+1, y _J+1, z _J+1), M3 _J+1(x _J+2, y _J+2, z _J+2), M3 _J+3(x _J+3, y _J+3, z _J+3), the center of gravity G coordinate of then miniature Δ abc can be made as:

$x_G=\frac{x_{j+1}+x_{j+2}+x_{j+3}}{3},$ $y_G=\frac{y_{j+1}+y_{j+2}+y_{j+3}}{3},$ $z_G=\frac{z_{j+1}+z_{j+2}+z_{j+3}}{3}$

As Fig. 4 is the projection of Fig. 3, should " miniature triangle " be equilateral triangle in the XOY projecting plane in space coordinates.

Use M1 _J+1With M3 _J+2And M3 _J+2With M3 _J+2Do the line vector respectively, use " right hand rule ", utilize " vector product " of these two vectors to calculate its normal vector, it is the approach direction of chaining pin, uses the direction cosine of this space law vector V1 that calculates to do measuring needle radius compensation, is measuring target point with focus point G, start measuring needle radius compensation, can do the measurement of any space curved surface profile S, state as Fig. 5, this method claims " barycentric coordinates mensuration " temporarily.In the time finishing a new equilateral triangle and make up, then measure its barycentric coordinates point, the rest may be inferred then, referring to Fig. 6, finishes up to needed point of any space curved surface contoured surface or curved measurement.

As Fig. 5 is sectional view in Fig. 3 coordinate system, measure the chaining pin sphere center position that a is ordered in a location tables diagrammatic sketch 3, e represents the position to make up the bc limit point midway of " miniature Δ abc ", and its projection in positive Δ ABC is respectively A and E point, d is positive Δ ABC height, and the G position is the center of gravity of " miniature Δ abc ".

The 5th, the measurement of space curved surface arbitrarily: if measuring a curve on the space curved surface arbitrarily, as this curve is function y=f (x) in the projection XOY plane, so, as long as the given x of this function and the coordinate points of y correspondence of meeting can be the center of gravity coordinate points with this point then, method by above-mentioned Fig. 4 and Fig. 6 constructs equilateral triangle, it is implemented precision measurement, and the meaning of this method is important, its energy measurement function face.

The invention has the beneficial effects as follows: this invention is compared the advantage and the good effect that are had and is with prior art: structure and the method vector meter algorithm thereof of miniature triangle on space curved surface, finish the test based theoretical of space profiles curved surface for measuring machine, owing to obtained high measuring accuracy,, this method sets up scientific evidence so being the process of measurement design of space rotating curve face and 3D profile etc. by standard ball experiment.Because the equilateral triangle that 3 measurement points form in the measurement coordinate system projecting plane is finished under the NC of measuring machine pattern easily, so this method helps the automatic measurement Study on Technology and uses, and can solve the measurement difficult problem of complex space curvilinear plane.Because measuring target point " barycentric coordinates " is for calculating by 3 measurement points, utilized miniature triangle to calculate its direction cosine, started the measuring needle radius compensation measurement, therefore, obtained the coordinate figure on the space profiles curved surface, the data file of its formation can directly import the measurement reverse-engineering that CAD/CAM implements space curved surface; Because the track of measurement point in projection can so this invention can be applied to measurement of complicated space curved surface, because measurement and data procedures are finished by computer control, therefore, have high efficiency of measurement by y=f (x) design.In addition, the selection of the high d of equilateral triangle has determined the precision of measuring, and is also determining efficiency of measurement.

Description of drawings

The chaining pin compensating error analysis synoptic diagram that Fig. 1 produces for measuring the A point;

Fig. 2 has the principle schematic of same normal for the equidistant curve face;

Fig. 3 is the normal of space curved surface, the formation synoptic diagram of miniature leg-of-mutton structure and equilateral triangle;

Fig. 4 is the synoptic diagram of the equilateral triangle geometrical property of structure;

Fig. 5 is for being the synoptic diagram of impact point measurement space curved surface S with barycentric coordinates G with V1;

Fig. 6 makes up synoptic diagram for the equilateral triangle of measuring y=f (x) curve;

Fig. 7 is for using equal indicative method measurement space surface of revolution and making up the synoptic diagram that equilateral triangle is measured center of gravity;

Fig. 8 is any space curved surface test synoptic diagram on the standard ball;

Fig. 9 is the track while scan perspective view of space curved surface test;

Figure 10 utilizes the method flow diagram of putting on the barycentric coordinates precision measurement space curved surface for the present invention;

Figure 11 utilizes the method flow diagram of barycentric coordinates precision measurement space curved surface for the present invention.

Embodiment

The present invention is further described below in conjunction with accompanying drawing.

Set up measurement coordinate system on measuring workpieces, analysis chart 3,4,5 is referring to instance graph 8 and 9.

Measure the theory of computation of vector: in how much of space analysis, represent respectively along the vector of unit length of x, y, z axle with I, j, k, and claim that they are basis vector.As Fig. 4 and 7, M1 on space curved surface _J+1And M3 _J+1Line vector if be defined as a, M3 _J+1And M3 _J+3The line vector be defined as b, the normal line vector on the plane that a and b two vectors are determined is defined as c, then can calculate c by " vector product ".If volume coordinate is M1 _J+1(x _J+1, y _J+1, z _J+1), volume coordinate is M3 _J+1(x _J+2, y _J+2, z _J+2), volume coordinate is M3 _J+3(x _J+3, y _J+3, z _J+3), then a and b two vectors are respectively calculated as follows:

$\left\{\begin{array}{c}{a}_x=x_{j+2}-x_{j+1}\\ a_y=y_{j+2}-y_{j+1}\\ a_z=z_{j+2}-z_{j+1}\end{array}\right.$

$\left\{\begin{array}{c}{b}_x=x_{j+3}-x_{j+2}\\ b_y=y_{j+3}-y_{j+2}\\ b_z=z_{j+3}-z_{j+2}\end{array}\right.$

Just: a=a _xI+a _yJ+a _zK, b=b _xI+b _yJ+b _zk

By vector product formula: c=a * b, and i * i=j * j=k * k=0, i * j=k, j * k=i, k * i=j, j * i=-k, k * j=-i, i * k=-j.

: a * b=(a _yb _z-a _zb _y) i+ (a _zb _x-a _xb _z) j+ (a _xb _y-a _yb _x) k

That is: $c=a\×b=\left|\begin{array}{ccc}i& j& k\\ a_x& a_y& a_z\\ b_x& b_y& b_z\end{array}\right|$

If order: c ₁=(a _yb _z-a _zb _y), c ₂=(a _zb _x-a _xb _z), c ₃=(a _xb _y-a _yb _x)

: c=a * b=c ₁I+c ₂J+c ₃k

So the vector of unit length of c is:

$(\frac{c_1}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}},\frac{c_2}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}},\frac{c_3}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}})$

Like this, the V1 vector just can be determined, uses approach direction and the compensation vector of this vector direction as chaining pin, is impact point with the barycentric coordinates G among Fig. 5, then can implement precision measurement to contour surface S.

Embodiment 1: the measurement and the Programming Methodology of any unique point on any space curved surface

The precision measurement of putting on the space curved surface arbitrarily, artificial mode can not be finished, and must design program and measure automatically under the NC pattern.

Referring to Fig. 4 and Fig. 5, establishing on the space curved surface arbitrarily, unique point in the projection coordinate of XOY is: (x0 y0), establishes it and is barycentric coordinates G, and then the apex coordinate of equilateral triangle is M1 _J+1(x0-2d/3, y0), M3 _J+1(x0+d/3, y0-k) and M3 _J+3(x0+d/3, y0+k).Like this, formation on the space curved surface is projected as the condition point of equilateral triangle and determines, uncertain is this z coordinate of 3, closing measuring needle radius compensation is measured this 3 point, obtains its three-dimensional coordinate, calculate the miniature triangle core coordinate and the normal thereof of these 3 compositions, with these barycentric coordinates is measuring target point, and its normal is convergence and compensation direction, then can test space curved surface on the arbitrary characteristics set point.

For given any space curved surface profile, measurement coordinate system generally builds on the feature locations of workpiece as hole line face etc., and selects suitable projecting plane, and this process can be by manually finishing.See also Fig. 8-9.

Measure the point on any space curved surface profile:, this partial content is elaborated below in conjunction with reference Figure 10:

(1) on space curved surface, set up the miniature triangle that the projecting plane is an equilateral triangle, the subpoint (M) that makes measurement point on the space curved surface (G) in this equilateral triangle in the heart;

(2) according to the planimetric coordinates of this subpoint (M), calculate the planimetric coordinates on three summits of this equilateral triangle on the projecting plane;

The projection coordinate of at first definite measurement point G (x0, y0) position is stated as Fig. 4, and d gets smaller value, and according to equilateral triangle character, then the apex coordinate of equilateral triangle is M1 _J+1(x0-2d/3, y0), M3 _J+1(x0+d/3, y0-k) and M3 _J+3(x0+d/3, y0+k);

(3) closing measuring needle radius compensation makes chaining pin along the direction vector perpendicular to the projecting plane, measures the z coordinate on these miniature leg-of-mutton three summits:

Predict the z coordinate figure of first measurement point, the error of itself and actual value can be in ± 6mm (generally be set at the measurement convergence distance of measuring machine, be the constant under the measuring machine NC pattern), and like this, the theoretical coordinate position of first measurement point is just determined.Then, closing measuring needle radius compensation, with vector V (0,0 ,-1), after measuring machine was measured this point coordinate automatically, measurement point M1 then won _J+1The accurate coordinates position; Then, measurement point M3 again _J+1(x0+d/3, y0-k), its z coordinate M1 _J+1The coordinate figure of z1 substitute i.e. z2=z1, M3 _J+1(x0+d/3, y0-k z2), so just can measure M3 _J+1The point; Same method can be measured M3 _J+3The point.

(4) utilize the volume coordinate on miniature leg-of-mutton three summits, calculate this miniature leg-of-mutton barycentric coordinates;

Use M1 _J+1, M3 _J+1And M3 _J+3Calculate the normal line vector on the spatial triangle plane of these 3 compositions, these 3 is the coordinate at chaining pin center, calculates this leg-of-mutton barycentric coordinates G;

(5) this miniature leg-of-mutton normal vector on the computer memory curved surface;

(6) being chaining pin convergence and compensation direction with this normal vector, is measuring target point with these barycentric coordinates, starts measuring needle radius compensation, obtains the accurate measured value of measurement point (G).

Starting measuring needle radius compensation, is chaining pin convergence and compensation direction with this normal vector, is measuring target point with barycentric coordinates G, and it is the G location point among Fig. 4 and Fig. 5, can implement the precision measurement to the space profiles face.So just obtained the coordinate figure of a point on any space curved surface.

Embodiment 2: the measurement of space curved surface

On the projecting plane of space curved surface, set up several measurement points successively, adopt said method to obtain the accurate coordinates value of each measurement point respectively, thereby obtain the whole profile coordinate figure on the space curved surface.

Fig. 7 is seen as the projection of Fig. 3, states as Fig. 7, sets up in the coordinate system at the rotation center of space curved surface, in projection XOY coordinate, with equal indicative measurement space surface of revolution.Guarantee M3 _J+1, M3 _J+3And M1 _J+2In projection XOY coordinate, form equilateral triangle.Do geometric analysis from Fig. 7: the high d of being of this equilateral triangle, the polar angle variable quantity on its each summit is identical θ, M1 _J+2, positive Δ ABC center and M3 _J+1The polar radius of point is respectively R1, R2, R3.So get the mathematical equation of R1, R2 and R3:

$\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">R</figure-callout>}2=\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">R</figure-callout>}1+\frac{2\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="A200810171918E00201.png,A200810171918E00211.png"\; state="\{\{state\}\}">d</figure-callout>}}{3}$

Meet aforesaid equation, then the projection of " miniature Δ abc " then constitutes positive Δ ABC.

Following formula shows, aligns Δ ABC, its center and three summits, as long as provide one of them polar radius value and polar angle value, all the other measuring positions all can calculate by aforesaid equation.

Polar coordinate system mathematical equation according to circular curve:

x＝Rcosα＝Rcos(Φ+kθ)

y＝Rsinα＝Rsin(Φ+kθ)

α represents polar angle in the following formula, and Φ represents initial polar angle, and θ represents angle, and k is an integer.

Measuring a curve on the surface of revolution of space, is function y=f (x) in the projection XOY plane as this curve, measures as stated above, and the x and the y coordinate points that then meet this function are circular curves, and y=f (x) is an equation of a circle.

In addition: can know that according to Fig. 6 analysis if miniature leg-of-mutton center of gravity G coordinate, its x coordinate is a constant, i.e. x=a, then said method can be finished the scanning of 3D linear profile face.

The space curved surface measurement finishes arbitrarily, can obtain the outline data on the curved surface, can save as data file and finish its reverse-engineering, also can do measurement verification etc.

Can also can solidify in measuring system by above Design Theory process of measurement, so that finish the unique point check of space curved surface by above-mentioned theory design module function.

If make up " positive Δ ABC " in XOZ, YOZ projecting plane, the direction cosine of measuring vector V can change into: (1,0,0), (1,0,0), (0,1,0), (0,-1,0), (0,0,1) reaches (0,0 ,-1), so, it can do the scanning of 6 kinds of modes at the space arbitrary surface in spatial dimension.

Embodiment 3: the space curved surface test on the standard ball:

Profile on the standard ball can be thought space curved surface, because standard ball has high-precision contour surface, it is measuring machine reference calibration ball, if when using the program of above-mentioned theory design and doing space curve face test on the standard ball, so, test result also can be used as the scientific evidence of estimating process of measurement and method.

The standard ball parameter is: diameter deviation is 0.00015mm, the about 15.875152mm of mean diameter.As Fig. 8, on ball, set up measurement coordinate system, its center is arranged at the centre of sphere, the space curved surface of test episphere:

The first step: make up the geometrical property of equilateral triangle according to Fig. 4, at first determine to make up the position on each summit of equilateral triangle: as Fig. 8 for setting up measurement coordinate system, the track projection of Fig. 9 for scanning.Make k=0.5774, so, high d=K * tg60 °=1 of equilateral triangle, according to equilateral triangle character, then each apex coordinate of equilateral triangle is M1 _J+1(x0, y0), M3 _J+1(x0+d, y0-k) and M3 _J+3(x0+d, y0+k).

Use y=f (x) function, as the projection among Fig. 9, the x coordinate is constant, then M1 _J+1The x coordinate be x=0, M3 _J+1And M3 _J+3The x coordinate be x=d, M1 _J+1The y coordinate begin to measure 6mm, variable quantity k=0.5774 from-6mm.

Predicting the z coordinate figure of first measuring point, is preset value as z=4, considers the reference field of z=0, should be with the actual point error less than in the 6mm (measuring the convergence distance), and like this, the coordinate position of first measurement point is just determined.Then, closing measuring needle radius compensation, after measuring machine was measured this point coordinate automatically, measurement point M1 then won _J+1Coordinate position; After this, measurement point M3 again _J+1, its z coordinate M1 _J+1The coordinate figure of z1 substitute, promptly z2=z1 so just can measure M3 _J+1The point; Same method can be measured M3 _J+3The point.

Second step: use M1 _J+1, M3 _J+1And M3 _J+3Calculate the normal line vector on the spatial triangle plane of these 3 compositions, these 3 is the coordinate at chaining pin center, method vector with it is chaining pin convergence and compensation direction, calculate this leg-of-mutton barycentric coordinates G, start measuring needle radius compensation, with barycentric coordinates G is measuring target point, and it is the G location point among Fig. 4 and Fig. 5, can implement the precision measurement of this standard ball space curved surface.So just obtained the coordinate figure of a point on the space curved surface.

The 3rd step: repeat similar step 1,2, finish up to needed some test.

The 4th step: design program and finish the data file generation, its form meets reading of professional software, or prints the data processing report.

State as table 1: the raw data test report of computer printout standard ball space curved surface is single, has provided the measurement of correlation parameter in this table 1, as the profile coordinate (x, y, z), standard ball facial contour orbital radius r and deviation thereof.Wherein chaining pin track and standard ball facial contour track are equidistant surface, and its equidistant value equals chaining pin radius value 0.9958mm in theory for R-r, and being calculated as by the chaining pin centre of sphere of R calculated, and its theoretical value is R=8.9333mm.In the table $r=\sqrt{x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A200810171918E00201.png"\; state="\{\{state\}\}">z</figure-callout>}}^2}.$

Table 1: space curved surface test data table-barycentric coordinates mensuration

The measuring machine model SCIROCCO RECORD that uses is because its measuring accuracy is: 1.9+3L/1000 μ m (L is in mm).From the tables of data analysis, " radius of a ball error of this standard sphere from scope 0.2-3.9 μ m, average 1.8 μ m ".Because standard ball is the calibration ball of measuring machine, is benchmark, its precision height, the sphere diameter error can be ignored, so the error that tests out in the tables of data can think that measuring machine precision and measuring method produce.Like this, illustrate that also the measuring accuracy that this method obtains is very high, the theory of the design and use of process of measurement is correct, is used to measure any space curved surface and can meets technical requirement.

Claims (7)

1, a kind of method of putting on the barycentric coordinates precision measurement space curved surface of utilizing is characterized in that, comprises the steps:

(1) on space curved surface, set up the miniature triangle that the projecting plane is an equilateral triangle, the subpoint (M) that makes measurement point on the space curved surface (G) in this equilateral triangle in the heart;

(2) according to the planimetric coordinates of this subpoint (M), calculate the planimetric coordinates on three summits of this equilateral triangle on the projecting plane;

(3) closing measuring needle radius compensation makes chaining pin along the direction vector perpendicular to the projecting plane, measures the z coordinate on these miniature leg-of-mutton three summits;

(4) utilize the volume coordinate on miniature leg-of-mutton three summits, calculate this miniature leg-of-mutton barycentric coordinates;

(5) this miniature leg-of-mutton normal vector on the computer memory curved surface;

(6) being chaining pin convergence and compensation direction with this normal vector, is measuring target point with these barycentric coordinates, starts measuring needle radius compensation, obtains the accurate measured value of measurement point (G).

2, method according to claim 1 is characterized in that, described step (5) further may further comprise the steps:

(5.1) to record these miniature leg-of-mutton three summits on the space curved surface, make the line vector in twos respectively, utilize the vector product of these two line vectors to obtain this miniature leg-of-mutton normal vector.

3, method according to claim 1 and 2 is characterized in that, the height of this equilateral triangle is in the 2mm on the projecting plane.

4, method according to claim 1 and 2 is characterized in that, measuring machine is determined the high optimum valuing range of equilateral triangle by the standard ball experiment.

5, a kind of method of utilizing chaining pin sphere centre coordinate precision measurement space curved surface, it is characterized in that, on the projecting plane of space curved surface, set up several measurement points successively, adopt claim 1,2,3 or 4 described methods to obtain the accurate coordinates value of each measurement point respectively, thereby obtain the whole profile coordinate figure on the space curve face.

6, method according to claim 5 is characterized in that, this space curved surface is the space surface of revolution, and use equal indicative method is set up the measurement point on the surface of revolution of space.

7, method according to claim 5 is characterized in that, the lopcus function of measurement point on the projecting plane is y=f (x) on this space curved surface.

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