CN101403611A - Method for measuring space rotating curved surface with microdelta barycentric coordinates as objective point - Google Patents

Abstract

The invention discloses a space rotation surface measurement method by using a micro triangle gravity coordinate as an object point. The method comprises the steps of: constructing a coordinate system according to the space rotation surface; determining the measurement range of the space rotation surface; and selecting a plurality of polar radii Rs in the range; aiming at each polar radius R, constructing a plurality of micro triangles to calculate the plane normal vector, and calculating the gravity coordinates, and the gravity is regarded as an object point, using sub-degree method to measure each curve in the space rotation surface; generating datum file consistent with the professional software to read; and analyzing the value range of the equilateral triangle height d through the standard ball experiment. Adopting the method that the gravity coordinates are regarded as the object point can measure the space rotation surface, and the measuring precision is high.

Description

A kind of method that is impact point measurement space surface of revolution with little triangle core coordinate

Technical field

The present invention relates to the automatic measurement field of space curved surface, refer to the measuring method of a kind of space surface of revolution especially.The present invention is applicable to measurement and the reverse-engineering that contains the space surface of revolution in tobacco machine such as the parts such as space cam, blade; The fields such as China's Aero-Space, automobile making and machine-building that also are applicable to simultaneously are to the measurement of impeller, blade profile face and reverse-engineering thereof etc.

Background technology

Finish the precision measurement of space curved surface profile on three coordinate measuring machine with touch trigger probe, the manual measurement pattern is difficult to finish, and must design process of measurement, and reason is that the normal of institute's measuring point on its contoured surface is difficult definite, and chaining pin is difficult to do compensating measure along its normal.

In the productive life of reality, the applied range of space surface of revolution in tobacco machine equipment, typically is exactly those space cam faces, blade face, various complicated cam and the surfaces of revolution of finishing various high-speed motion functions etc.; In machinery manufacturing industry, can finish the blade face of aerodynamic function, the cylindrical space cam of machine-tool industry etc. as aerospace field; In navigation, as finish the impeller contoured surface of fluid mechanics function, they require very high to the manufacturing of contoured surface.In the three-dimensional coordinates measurement field, measuring software system all is an external product generally, mainly contains PC-DMIS (U.S.), TUTOR (Italy), QUINDOS (Germany) etc., the not open process of measurement design that has, what have provides curvilinear plane scan function such as PC-DMIS CAD, but range of application is narrow.In fact, measuring machine manufacturer is difficult to design the general commodity software that meets the surface of revolution scanning requirement of any space.The advanced measuring machine of part has the curvilinear plane measurement function, but generally will be by means of cad model, as PC-DMIS, do not have cad model, generally will handle measurement data, or use corresponding process software to finish with mathematical method, therefore, the measurement difficulty to the space surface of revolution is bigger.In present scientific and technical information, also be difficult to inquire the direct measuring method of finishing the space surface of revolution with three coordinate measuring machine.

In reverse-engineering, the measurement of two-dimensional curve can be adopted the measuring method of closing measuring needle radius compensation, to reduce test specification, wait with application software such as Prof, CAD/CAM again and finish equidistant curve and look unfamiliar, but it is also complicated to obtain the data file of this profile; For the three dimensions surface of revolution, if the closing measuring needle radius is done measurement, the difficulty of then finishing its equidistant surface generation in CAD/CAM is big, to the space surface of revolution too.So ask in the processes such as design and measurement verification the counter of implementation space surface of revolution, difficulty strengthens, and for example, study or room for improvement surface of revolution performance, not only will obtain its profile coordinate graphic, also will obtain outline data file etc.

And in the three-dimensional coordinates measurement technology, if start measuring needle radius compensation, its measure theory requires chaining pin to measure along the normal vector convergence of institute's measuring point, otherwise will produce measuring error, or wrong measurement result.

In sum, to the measurement of space surface of revolution in the three-dimensional coordinates measurement field than difficult, be called as one of gordian technique in the geometry test, as three-dimensional coordinates measurement commodity software, also not have to find the application or the report of being correlated with at present at home.

Summary of the invention

The problem to be solved in the present invention provide a kind of accurately measurement space surface of revolution with little triangle core coordinate method that is impact point measurement space surface of revolution.

In order to address the above problem, of the present invention is that the method for impact point measurement space surface of revolution comprises the steps: with little triangle core coordinate

0) sets up coordinate system according to described space surface of revolution;

1) determine the measurement range of space surface of revolution, the span of the polar radius R of the subpoint of point on coordinate plane on the surface of revolution of promptly described space, and in described scope, choose a plurality of polar radius R;

2) at each polar radius R, make up a plurality of little triangles and calculate the normal vector on its determined plane, with its barycentric coordinates is impact point, utilization equal indicative method is measured a curve on the surface of revolution of space, described little triangle is projected as an equilateral triangle on coordinate plane, the polar radius of one of them summit or the subpoint of this leg-of-mutton center of gravity on coordinate plane is R.

3) generate data file, form meets the reading format of professional software;

4) span by the high d of this equilateral triangle of standard ball experimental analysis.

Compared with prior art, of the present invention is that the beneficial effect of the method for impact point measurement space surface of revolution is with little triangle core coordinate:

Make measuring machine finish the measurement of space surface of revolution such as contoured surfaces such as space cam, arc surfaced indexing cam, blade and impeller, worked out measuring method and designed program.This invention is applied to the measurement reverse-engineering and the measurement verification of space surface of revolution, it and CAD/CAM combination, can enlarge the manufacturing scope of cigarette accessory and improve workmanship, can be directly in the face of the import core component on the cigarette machine, if be attached to multidimensional NC lathe and ERP again, then this program design can promote the Informatization Development of manufacturing technology.Because the precision of its measurement depends on this miniature leg-of-mutton microminiaturized degree, therefore, the high size that described miniature triangle is projected in " equilateral triangle " on the coordinate surface is determining measuring accuracy and efficient; Owing to adopted the equal indicative mensuration, make the theoretical position of measuring determine, so, be beneficial to and do reverse-engineering and measurement verification; Because adopted full automatic process of measurement design, measuring process, data processing and data file generate and be robotization, therefore, this method and program have high efficiency of measurement; Owing to directly obtained the data file of profile, therefore, can finish its modeling and manufacturing in CAD/CAM fast, and the data available file done the anti-analysis of asking; Because the equal indicative mensuration has high five equilibrium accuracy, so the entire data files that is generated is beneficial to measurement verification.Program is used simple and convenient, only needs the initial value of input measurement, can automatically perform measurement.Again because measuring target point for by drawing by " miniature triangle " calculating barycentric coordinates point, not by the measuring machine collection, so efficiency of measurement is compared for impact point with " chaining pin sphere centre coordinate ", improves 25%.

Description of drawings

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

Fig. 2 is the formation synoptic diagram of the normal of space curved surface, miniature leg-of-mutton structure and equilateral triangle;

Fig. 3 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. 4 is for to use normal vector V1 to be impact point with little triangle core, and measurement space curved surface S goes up the synoptic diagram of a bit;

Fig. 5 is a standard ball experimental analysis synoptic diagram;

Fig. 6 is the projected footprint synoptic diagram of the chaining pin centre of sphere on XOY plane in the standard ball experiment;

Fig. 7 is applied to the synoptic diagram that the space cam in the tobacco machine is measured for the present invention;

Fig. 8 imports the space curve synoptic diagram that CAD/CAM forms for the outline data file that produces;

Fig. 9 is to be that the present invention is the process flow diagram of the method for impact point measurement space surface of revolution with little triangle core coordinate;

Figure 10 is the described step 2 among Fig. 9 of the present invention) further decomposition step process flow diagram;

Figure 11 is the described step 25 of Figure 10 of the present invention) further decomposition step process flow diagram;

Figure 12 is the described step 26 of Figure 10 of the present invention) further decomposition step process flow diagram;

Figure 13 is the described step 22 of Figure 10 of the present invention) further decomposition step process flow diagram.

Embodiment

The present invention is that the applied principle of method of impact point measurement space surface of revolution is as follows with little triangle core coordinate:

The measurement mechanism opinionBecause in the three-dimensional coordinates measurement technology, any geometric element of precision measurement all must be made measuring needle radius compensation, chaining pin must be along contoured surface to be measured normal convergence measurement point measurement without barrier at this measurement point, and on this normal vector, do measuring needle radius compensation, otherwise, error will be produced.State as Fig. 1, be the some A synoptic diagram on the measurement space curved surface M, P is described space curved surface M in the section that A is ordered, N is the normal that described space curved surface M is ordered at A, along any vector measurement A point except that 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.

Make up miniature triangle theoryState as Fig. 2, 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 on XOY plane, be projected as positive Δ ABC, 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 positive Δ ABC center line AE, the intersection point of BF and CD is M, " miniature Δ abc " summit a, b, c is A at the subpoint of XOY plane, B, C, can demonstrate,prove by plane geometry, AB, the mid point E on BC and CA limit, F and D are respectively the some e on " miniature Δ abc ", f, the subpoint of d on XOY plane, and described some e, f, it also is its each limit ab that d is respectively, bc, the mid point of ca, so getting " miniature Δ abc " center line intersection point is G, be focus point, as Fig. 2, in quadrilateral AEea, know 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, that is to say that Δ ABC is an equilateral triangle, but " miniature Δ abc " equilateral triangle not necessarily.

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 described " miniature Δ abc " its normal N of determined plane computations, uses the direction vector of this normal, with this center of gravity G is measuring target point, 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 is 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, it can make the composition error influence " extension " of measuring machine, and main influence is measuring machine precision and performance.Therefore, leg-of-mutton " microminiaturization " should look concrete condition, or by the standard ball experimental analysis, the height that generally makes positive Δ ABC in the 2mm scope with interior selection, can finish the space curve planar survey of a lot of precisions, can the coincidence measurement accuracy requirement to the vital part on the cigarette machine.

The enforcement of equal indicative mensurationThe space surface of revolution is measured and can just be finished with the equal indicative mensuration.Fig. 3 has projection on the XOY coordinate surface for Fig. 2, at this moment, should " miniature triangle " be equilateral triangle in the XOY projecting plane in space coordinates.

(1) sets up coordinate system at the rotation center of space curved surface, in projection XOY coordinate, with equal indicative measurement space surface of revolution.Closing measuring needle radius compensation, application direction cosine V (0,0 ,-1) makes the chaining pin direction vector of cosine in the direction, the some M1 on difference measurement space curved surface on the circumference that with R1 and R3 is polar radius _J+1And M2 _J+1, the polar angle value α of these points is all identical, can be set at the preliminary survey polar angle, usually

In preferred embodiment of the present invention, establish α=0; Again respectively with

With

For polar angle is to put M1 on the measurement space curved surface on the circumference of polar radius at R1 and R3 respectively _J+2And M2 _J+2Point and M1 _J+3And M2 _J+3Point, the rest may be inferred then.Wherein, referring to Fig. 2, Fig. 3, M1 _J+2, M2 _J+1And M2 _J+3Projection is respectively A, B and C point.

Guarantee M1 _J+2, M2 _J+1And M2 _J+3In projection XOY coordinate, form equilateral triangle.Do geometric analysis from Fig. 3: 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, M2 _J+1And M2 _J+3The polar radius of point is respectively R1, R2, R3 and R3.So get the mathematical equation of R1, R2 and R3:

$R2=R1+\frac{2d}{3}---\left(2\right)$

Meet aforesaid equation, then " miniature Δ M1 _J+2M2 _J+1M2 _J+3" projection on the XOY coordinate plane then constitutes positive Δ ABC.

If establish volume coordinate is M1 _J+2(x1 _J+2, y1 _J+2, z1 _J+2), M2 _J+3(x2 _J+3, y2 _J+3, z2 _J+3), M2 _J+1(x2 _J+1, y2 _J+1, z2 _J+1), then miniature Δ M1 _J+2M2 _J+1M2 _J+3Center of gravity G coordinate can be made as:

$x_G=\frac{x{2}_{j+1}+x{1}_{j+2}+x{2}_{j+3}}{3},$ $y_G=\frac{y{2}_{j+1}+y{1}_{j+2}+y{2}_{j+3}}{3},$ $z_G=\frac{z{2}_{j+1}+z{1}_{j+2}+z{2}_{j+3}}{3}$

(2), use M1 _J+2With M2 _J+3And M2 _J+3With M2 _J+1Do 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, using this space law to do measuring needle radius compensation to the direction cosine of vector V 1, is measuring target point with focus point G, does the measurement of space surface of revolution profile S, state as Fig. 4, this method is called " barycentric coordinates mensuration ".With the equal indicative variable quantity, in the time finishing a new equilateral triangle and make up, then measure its barycentric coordinates point, the rest may be inferred then, finishes up to the surface of revolution contoured surface measurement of whole space.As Fig. 4 is sectional view in Fig. 3 coordinate system, measures the chaining pin sphere center position that a order in a location tables diagrammatic sketch 2, and e represents the position structure " miniature Δ M1 _J+2M2 _J+1M2 _J+3" M2 _J+1M2 _J+3Limit point midway, its subpoint at coordinate plane XOY are respectively an A and put E, and d is positive Δ ABC height, and the G position is " miniature Δ M1 _J+2M2 _J+1M2 _J+3" center of gravity.

In addition, during the measurement space surface of revolution, using the chaining pin position may be a plurality of locus sometimes, and as the measurement space cylindrical cam, therefore, chaining pin number and position need to want when designing program corresponding its measurement range to elect.

After space surface of revolution measurement finishes, obtain the data file of 3 curves, wherein 1 curve is on the surface of revolution of space, other 2 is chaining pin track data file, if they are imported CAD/CAM when finishing reverse-engineering, the curved surface of its formation and real space contour surface be equidistant surface each other, and distance is a chaining pin radius value.The space curved surface of complexity is selected different R1, d and the combination of θ value, can record the data file of many real profile curved surface upper curves.Because the equal indicative mensuration has higher equal indicative accuracy, so chaining pin track data file is in its reverse product processing quality control and quantize in the check important application is arranged.

Finish the generation of space surface of revolution profile traces data file, the analysis of data etc.

By design processs of measurement such as above theoretical employing DEAPPL language.

The present invention reaches by the following method.

At first, on measuring workpieces, set up measurement coordinate system, analysis chart 2-3, referring to lab diagram 5, instance graph 7.

Secondly, measure the calculating 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.M1 on space curved surface _J+2And M2 _J+3Line vector if be defined as a, M2 _J+3And M2 _J+1The line vector be defined as b, the normal 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+2(x1 _J+2, y1 _J+2, z1 _J+2), volume coordinate is M2 _J+1(x2 _J+1, y2 _J+1, z2 _J+1), volume coordinate is M2 _J+3(x2 _J+3, y2 _J+3, z2 _J+3), then a and b two vectors are respectively calculated as follows:

$\left\{\begin{array}{c}{a}_x=x{2}_{j+3}-x{1}_{j+2}\\ a_y=y{2}_{j+3}-y{1}_{j+2}\\ a_z=z{2}_{j+3}-z{1}_{j+2}\end{array}\right.$

$\left\{\begin{array}{c}{b}_x=x{2}_{j+1}-x{2}_{j+s}\\ b_y=y{2}_{j+1}-y{2}_{j+s}\\ b_z=z{2}_{j+1}-z{2}_{j+s}\end{array}\right.$

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:

$(\frac{c_1}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20081018122300191.png,A20081018122300231.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}},\frac{c_2}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20081018122300191.png,A20081018122300231.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}},\frac{c_3}{\sqrt{{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20081018122300191.png,A20081018122300231.png"\; state="\{\{state\}\}">c</figure-callout>}}_1}^2+{{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_2}^2+{{\mathrm{<figure-callout\; id="3"\; label="c"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">c</figure-callout>}}_3}^2}})$

Using approach direction and the compensation vector of this vector direction as chaining pin, is impact point with the barycentric coordinates G among Fig. 4, then can implement precision measurement to profile S.

Show that as Fig. 9 the present invention is that a preferred embodiment of the method for impact point measurement space surface of revolution comprises the steps: with miniature triangle core coordinate

0) sets up coordinate system according to described space surface of revolution, the rotary middle spindle of surface of revolution to be measured is set at the z axle;

1) determine the measurement range of space surface of revolution, the span of the polar radius R of the subpoint of point on coordinate plane XOY on the surface of revolution of promptly described space, and in described scope, choose N polar radius R ₁, R ₂..., R _N, described R ₁, R ₂..., R _NBe an arithmetic progression, wherein, R _i=R _I-1(2≤i≤N) and Δ r are measurement variable quantity default in the measuring machine to+Δ r;

2) at each polar radius R _iIt calculates the normal vector on its determined plane to make up a plurality of little triangles, with its barycentric coordinates is impact point, utilization equal indicative method is measured a contour curve to be measured on the surface of revolution of space, described little triangle is projected as an equilateral triangle on coordinate plane, the polar radius of the subpoint of one of them summit on coordinate plane is R _i, in the present embodiment, some M1 _J-1The polar radius R1 of the subpoint on XOY plane _iEqual R _i, R1 _i=R _i

Further, in this step 2) in, the measurement of a curve on the surface of revolution of space is comprised the steps:

20) measure the starting point of described curve and the coordinate parameters of terminal point by measuring machine, promptly

And Wherein

For measuring the polar angle of the subpoint of starting point on the XOY coordinate plane, preferably,

Be to measure the polar angle of the subpoint of terminal point on the XOY coordinate plane, in other embodiments of the invention, if all be in identical polar angle scope, to carry out for the measurement of each bar curve on the surface of revolution, i.e. required measurement for each bar curve

With

All be identical, can at the beginning of measuring, preset so that then this moment is described to described two extreme values With

Be constant;

21) determine the appropriate equal indicative variable quantity θ and the high d of described " equilateral triangle ";

22) number M of measurement point on the calculating curve to be measured;

23) definition counting variable j, j=0;

24) closing measuring needle is closed the footpath compensation, selected direction cosine (0,0 ,-1) perpendicular to the projecting plane;

25) measure N _jThe point M1 of position _J+1

26) measure N _jThe point M2 of position _J+1

27)j＝j+1；

28) whether judge j greater than 2, if j be not more than 2 return step 25) continue to carry out;

29) start measuring needle radius compensation;

2A) calculate by M1 _J-1, M2 _jAnd M2 _J-23 miniature leg-of-mutton barycentric coordinates G that constituted are with the normal vector on its determined plane;

2B) with center of gravity G be the j-2 point of a curve on the impact point measurement space surface of revolution;

2C) whether judge j, if j less than M, then returns step 24 more than or equal to M) continue to carry out.

3) generate data file, form meets the reading format of professional software;

4) span by the high d of this equilateral triangle of standard ball experimental analysis.

Wherein, be described step 21) at given polar radius R1 _iAnd the high d of equilateral triangle as described in trying to achieve by method as described below under the situation of equal indicative variable quantity θ (as θ=1 °), wherein said equal indicative variable quantity θ can be for being set in advance in the measuring machine: at first, and by formula

Calculate the high d of described equilateral triangle; Judge whether coincidence measurement requirement of d then, in this embodiment, the high d of positive Δ ABC in the 2mm scope with interior selection, if d is less than the scope of measurement requirement, then increase the value of equal indicative variable quantity θ and recomputate, if d, then reduces the value of equal indicative variable quantity θ greater than the scope of measurement requirement and recomputates; Write down the high d and the equal indicative variable quantity θ of the described equilateral triangle of coincidence measurement requirement at last.

In addition, described step 21) can also be at definite polar radius R1 _iAnd under the situation of the high d (as d=2mm) of given described equilateral triangle, by above-mentioned formula

Directly try to achieve equal indicative variable quantity θ.

The measuring machine of different performance, the optimum valuing range of d can be done standard ball experiment by the program of design and determine, in this embodiment, the high d of positive Δ ABC in the 2mm scope with interior selection.

In addition, as shown in figure 11, described step 25) further comprise following steps:

250) by formula

Calculation level M1 _J+1Be projected in the polar angle of the point on the XOY plane

251) according to a M1 _J+1Be projected in the polar angle of the point on the XOY plane

With polar radius R1 _iCalculation level M1 _J+1X coordinate and Y coordinate;

252) judge whether j equals 0, if j be not equal to 0 skip to step 253 ');

253) bigness scale point M1 _J+1Z coordinate z1 _J+1, the reference field of consideration z=0 should skip to step 254 less than in the 6mm (measuring the convergence distance) with the actual point error);

253 ') some M1 _J+1Z coordinate z1 _J+1=z1 _j

254) according to a M1 _J+1Coordinate adjust the target location of measuring machine chaining pin;

255) measure a M1 by measuring machine _J+1Accurate coordinates position M1 _J+1(x1 _J+1, y1 _J+1, z1 _J+1).

As shown in figure 12, described step 26) further comprise following steps:

260) calculation level M2 _J+1Be projected in the polar radius R3 of the point on the XOY plane _i, R3 _i=d * tg30/sin θ;

261) according to a M2 _J+1Be projected in the polar angle of the point on the XOY plane

With polar radius R3 _iCalculation level M2 _J+1X coordinate and Y coordinate;

262) some M2 _J+1Z coordinate z2 _J+1=z1 _J+1

263) according to a M2 _J+1Coordinate adjust the target location of measuring machine chaining pin;

264) measure a M2 by measuring machine _J+1Accurate coordinates position M2 _J+1(x2 _J+1, y2 _J+1, z2 _J+1).

As shown in figure 13, described step 22) further comprise the steps:

220) read the starting point of curve to be measured and the polar angle parameter of terminal point, both

And

221) according to formula

Calculate the number M of measurement point on the curve to be measured.

After the measuring task of space to be measured surface of revolution is finished, can design on demand and generate the data file of finishing, its form meets read (as described in the step 3)) of professional software.

Described data file is pressed different file storage with the x, the y that measure the contoured surface track with the z coordinate figure with the chaining pin centrode respectively, and is as shown in table 1.

Table 1: the measurement data file group generates type

	The mea type	The ISO-G type
			Chaining pin curve m1	mcurve1.mea	mcurve1
Chaining pin curve m2	mcurve2.mea	mcurve2
			Contour curve s	Profm.mea	Profm
Contour curve s	Profl.mea

Mea type and ISO-G type file can be changed mutually, also can the designing treatment program be converted to the data file of any needs, are beneficial to reading in the specialized softwares such as CAD/CAM, Master CAM.Wherein the Profl.mea file of contour curve s is a polar angle

With the data file of z changes in coordinates, it is at the cylindrical cam design, uses it can generate polar angle in AutoCAD With the two-dimensional curve figure of z changes in coordinates, its data file can be studied the measurement verification in cylindrical cam rule, curve improvement and the processing.The generation of above-mentioned 7 files is the design of " covering " type, i.e. the last file measured of the file of measuring for the second time automatic " covering ".

In addition, as described in step 4), in this program design, should contain the standard ball experiment, so that determine that used measuring machine uses this theory to do the best d value scope of precision measurement, the measuring machine of different performance may d value scope difference.

Further, in other embodiments of the invention, described N polar radius R ₁, R ₂..., R _NAlso can be for having one group of ordered series of numbers of other funtcional relationship, as Geometric Sequence etc.

In another embodiment of the present invention, some M2 _J+1The polar radius R3 of the subpoint on XOY plane _iEqual R _i, R3 _i=R _i, then described step 21) and can determine polar radius R3 _iAnd the high d of equilateral triangle as described in trying to achieve by method as described below under the situation of equal indicative variable quantity θ (as θ=1 °): at first, by formula

Calculate the high d of described equilateral triangle; Judge whether coincidence measurement requirement of d then, if d, then increases the value of equal indicative variable quantity θ less than the scope of measurement requirement and recomputates, if d, then reduces the value of equal indicative variable quantity θ greater than the scope of measurement requirement and recomputates; Write down the high d and the equal indicative variable quantity θ of the described equilateral triangle of coincidence measurement requirement at last, wherein said equal indicative variable quantity θ can be for being set in advance in the measuring machine.

In addition, described step 21) polar radius R3 can also determined _iAnd under the situation of the high d (as d=2mm) of given described equilateral triangle, then can be by above-mentioned formula Directly try to achieve equal indicative variable quantity θ.

Further, in the present embodiment, described step 25) also comprise the steps:

250) by formula

Calculation level M1 _J+1The polar angle of the subpoint on XOY plane

251 ') calculation level M1 _J+1The polar radius R1 of the subpoint on XOY plane _i, and by the polar angle of this subpoint

With polar radius R1 _i, calculation level M1 _J+1X coordinate and Y coordinate;

252) judge whether j equals 0, if j be not equal to 0 skip to step 253 ');

253) estimation point M1 _J+1Z coordinate z1 _J+1, skip to step 254);

253 ') some M1 _J+1Z coordinate z1 _J+1=z1 _j

254) according to a M1 _J+1Coordinate adjust the target location of measuring machine chaining pin;

255) measure a M1 by measuring machine _J+1Accurate coordinates position M1 _J+1(x1 _J+1, y1 _J+1, z1 _J+1).And described step 26) further comprise following steps:

260 ') according to a M2 _J+1The polar angle of the subpoint on XOY plane With polar radius R3 _iCalculation level M2 _J+1X coordinate and Y coordinate;

261 ') some M2 _J+1Z coordinate z2 _J+1=z1 _J+1

262 ') according to a M2 _J+1Coordinate adjust the target location of measuring machine chaining pin;

263 ') measure a M2 by measuring machine _J+1Accurate coordinates position M2 _J+1(x2 _J+1, y2 _J+1, z2 _J+1).

In another embodiment of the present invention, the polar radius R2 of the subpoint of described little leg-of-mutton center of gravity on XOY plane _iEqual R _i, R2 _i=R _i, then in described step 21) in, formula passed through ${R2}_i={R1}_i+\frac{2\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">d</figure-callout>}}{3},$

Determine the high d of equal indicative variable quantity θ and described " equilateral triangle ", and application of formula

And

Obtain a M1 respectively _J+1And M2 _J+1The polar radius R1 of the subpoint on XOY plane _iAnd R3 _i, finish described step 25 again) and 26) and from measuring N _jThe point M1 of position _J+1And some M2 _J+1

The standard ball experiment

Profile on the standard ball is the space surface of revolution, uses said method and does the standard ball experiment, analyzes its measuring accuracy.The standard ball parameter is: diameter deviation is+0.000006Inch (about 0.00015mm) mean diameter 0.625006Inch (about 15.875152mm).As Fig. 5, on ball, set up measurement coordinate system, its center is arranged at the centre of sphere, on episphere, do experiment, select R1, d and θ combination, get combination R1=2.2743mm, d=1mm and θ=10 ° according to formula 1-3, R2=2.941mm then, the curve to be measured of this on the contoured surface have 36 measurement points (

And

Application of formula

Calculate M=36), the direction cosine of measuring during closing measuring needle radius compensation are: V (0,0 ,-1), use this program to do the space spherical scanning, track projection such as Fig. 6 of its scanning state.

As described in Table 2, the raw data inspection report of computer printout has provided the measurement of correlation parameter in this table, as the chaining pin centre coordinate (x, y, z), chaining pin track r1, standard ball facial contour track r and r1-r.Wherein chaining pin track and standard ball facial contour track are equidistant surface, and its equidistant value equals the chaining pin radius value in theory for r1-r; R1 in theory can determine measuring ball, in the table when selecting R, d and θ combination $r$ $1=\sqrt{x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">y</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="A20081018122300191.png"\; state="\{\{state\}\}">z</figure-callout>}}^2},$ X, y and z represent the coordinate at chaining pin center respectively.

Table 2 standard ball experimental data table-barycentric coordinates mensuration

The measuring machine model SCIROCCO RECORD that uses, because its measuring accuracy is: 1.9+3L/1000 μ m (L is in mm), therefore, it is very high obtaining such experimental precision, the theory that the design and use of process of measurement are described is correct, be used for the measurement space surface of revolution and can meet technical requirement, in the experiment, R1, d and the θ combination of the mathematical equation that does not meet R1 and R3 have also been adopted, the precision of finding experiment will descend, therefore, R1, d and θ combination will meet the pacing items that this mathematical equation is the accurate precision of raising measurement.

About the experimental analysis of equilateral triangle d value, by the experiment of different d values, d=0.7mm-3.0mm to above-mentioned employed measuring machine, all has high accuracy of measurement.

Embodiment: the surface of revolution of space cam is measured

Program is used tobacco business.In the cigarette machine equipment, the space surface of revolution is used a lot, being more common in mica wrappingmachine GDX2000 and GDX1, as piece number: 0X9674,0X9196,0X7400,0X7531,2XKDA4, OX6126 and OAS947 etc., is the duplex cylindrical cam as Fig. 7, Fig. 8 measures the contour curve figure that obtains for it, being does not have treated primary curve, and 3 contour curves are arranged respectively on each curved surface, and every all has data file, generate with 12 data files, measure dot number about 3200 is arranged.At cigarette enterprise, use Fig. 8, can directly import the measurement reverse-engineering of this accessory of enforcement in the CAD/CAM system and the quality control in the manufacturing; In Cigarette Machine Company,, can also implement the anti-design of asking to it except that doing the measurement verification.Making up equilateral triangle R, d and θ combination is respectively: R1=61, d=1.9016, θ=1; R1=64.1527, d=2, θ=1 etc.

In other preferred embodiment of the present invention, direction cosine can be set at (0,0,1); Also the rotary middle spindle of surface of revolution to be measured can be set at the x axle, then described polar radius R1 is the polar radius of the subpoint of point on the YOZ plane on the volume coordinate, answers direction initialization cosine to be (1,0,0) or (1,0,0) accordingly; The rotary middle spindle of surface of revolution to be measured can also be set at the y axle, then described polar radius R1 is the polar radius of the subpoint of point on the XOZ plane on the volume coordinate, answering direction initialization cosine accordingly is (0,-1,0) or (0,1,0), can design 6 general standard scan programs altogether by above-mentioned variation, it can do the complex-curved scanning of 6 kinds of modes at part in spatial dimension, can finish the measurement that has a plurality of spaces surface of revolution on the part under a coordinate system.

Claims (9)

1, a kind of method that is impact point measurement space surface of revolution with little triangle core coordinate is characterized in that described method comprises the steps:

1) determine the measurement range of space surface of revolution, the span of the polar radius R of the subpoint of point on coordinate plane on the surface of revolution of promptly described space, and in described scope, choose a plurality of polar radius R;

2) at each polar radius R, make up a plurality of little triangles and calculate the normal vector on its determined plane, with its barycentric coordinates is impact point, utilization equal indicative method is measured a curve on the surface of revolution of space, described little triangle is projected as an equilateral triangle on coordinate plane, and the polar radius of one of them summit or the subpoint of this leg-of-mutton center of gravity on coordinate plane is R.

2, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 1 is characterized in that, described method also comprised step before the measurement range of determining the space surface of revolution:

0) sets up coordinate system according to described space surface of revolution.

3, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 2 is characterized in that described method also comprises:

3) generate data file, form meets the reading format of professional software;

4) span by the high d of this equilateral triangle of standard ball experimental analysis.

4, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 3, it is characterized in that, described step 0) in, if the Z axle is the rotation center of space surface of revolution to be measured, described polar radius R is the polar radius of the subpoint of point on XOY plane on the surface of revolution of space.

5, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 4, it is characterized in that, in described step 1), described a plurality of polar radius R are one group of arithmetic progression, and the tolerance of this ordered series of numbers is a measurement variable quantity default in the measuring machine.

6, as claim 4 or the 5 described methods that are impact point measurement space surface of revolution with little triangle core coordinate, it is characterized in that described step 2) in, the measurement of a curve on the surface of revolution of space is further comprised the steps:

20) set or measure the starting point of described curve and the coordinate parameters of terminal point;

21) determine the high d of equal indicative variable quantity θ and described " equilateral triangle ";

22) number M of measurement point on the calculating curve to be measured;

23) definition counting variable j, j=0;

24) closing measuring needle is closed the footpath compensation, selected direction cosine perpendicular to the projecting plane;

25) measure N _jThe point M1 of position _J+1

26) measure N _jThe point M2 of position _J+1

27) counting variable j=j+1;

28) whether judge j greater than 2, if j be not more than 2 return step 25) continue to carry out;

29) start chaining pin and close the footpath compensation;

2A) calculate by M1 _J-1, M2 _jAnd M2 _J-23 miniature leg-of-mutton barycentric coordinates G that constituted are with the normal vector on its determined plane;

2B) with center of gravity G be the j-2 point of a curve on the impact point measurement space surface of revolution;

2C) whether judge j, if j less than M, then returns step 24 more than or equal to M) continue to carry out.

7, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 6 is characterized in that, described some M1 _J+1The polar radius R of the subpoint on XOY plane equals R1, described step 25) further comprise following steps:

250) by formula

Calculation level M1 _J+1The polar angle of the subpoint on XOY plane

251) according to the polar angle of this spot projection point

With polar radius R1, calculation level M1 _J+1X coordinate and Y coordinate;

252) judge whether j equals 0, if j be not equal to 0 skip to step 253 ');

253) determine M1 _J+1Z coordinate z1 _J+1, skip to step 254);

253 ') some M1 _J+1Z coordinate z1 _J+1=z1 _j

254) according to a M1 _J+1Coordinate adjust the target location of measuring machine chaining pin;

255) measure a M1 by measuring machine _J+1Accurate coordinates position M1 _J+1(x1 _J+1, y1 _J+1, z1 _J+1).

8, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 7 is characterized in that described step 26) further comprise following steps:

260) calculation level M2 _J+1The polar radius R3 of the subpoint on XOY plane;

261) according to a M2 _J+1The polar angle of the subpoint on XOY plane

With polar radius R3 calculation level M2 _J+1X coordinate and Y coordinate;

262) some M2 _J+1Z coordinate z2 _J+1=z1 _J+1

263) according to a M2 _J+1Coordinate adjust the target location of measuring machine chaining pin;

264) measure a M2 by measuring machine _J+1Accurate coordinates position M2 _J+1(x2 _J+1, y2 _J+1, z2 _J+1).

9, the method that is impact point measurement space surface of revolution with little triangle core coordinate as claimed in claim 8 is characterized in that described step 22) further comprise the steps:

220) read the starting point of curve to be measured and the polar angle parameter of terminal point, both And

221) according to formula

Calculate the number M of measurement point on the curve to be measured.

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