CN1065047C - Curved surface shape measuring method - Google Patents

Abstract

The present invention provides a universal curved surface shape measuring method. The present invention has the principle that the shape of a curved surface is measured through the measurement of a curvature function of a set of cross section curves on the curved surface. The present invention is suitable for shape measurement of the curved surface of various workpieces. The present invention not only can solve the problem of shape measurement which is not solved at present, but also can be used for reforming the existing curved surface shape measurement device according to the present invention. Thus, the structure is greatly simplified.

Description

A kind of measuring method of curve form

The present invention proposes a kind of general little range sensors that utilizes and realizes the measuring method of large-sized curve form, is mainly used in the shape measure of three-dimension curved surface and two-dimensional curve.

The shape measure of curve surface work pieces is a complexity and difficult measuring technique problem always.General shape measure instrument all designs at a certain concrete measurand at present, not only complex structure, bulky, positioning accuracy request is high, more inconvenient is: 1, owing to be a kind of specialized apparatus and the curve form that can't be suitable for various moulding workpiece is measured; 2, measurement range is limited; 3, the range to sensor requires bigger.Existing curve form measuring method for measuring all is to measure the shape of curved surface by the coordinate of measuring workpieces curved surface in a fixing coordinate system, as three-dimensional mark machine is present unique a kind of general curve form measuring equipment, but it is low also to exist efficiency of measurement; Measurement range is limited; Require the volume and weight of tested curved surface place workpiece all can not be too big etc. shortcoming.

The objective of the invention is: propose a kind of general curve form measuring method, calculate the shape of reorganization curved surface by the curvature function of measuring some curves on the curved surface.Specifically can utilize little range sensors to realize large-sized curve form measurement, solve the geometric shape measuring of various curve surface work pieces.

To achieve the above object of the invention, elaborate principle of the present invention below, according to Riemannian and differential geometric knowledge, " the curvature of space characteristic " of space curved surface is that shape can be described by the curve in any one the parametric line net on the curved surface.Curve surface work pieces for an arbitrary shape, always can find a suitable straight line as axis in the space at tested curved surface place, remove to cut tested curved surface along axis with one group of plane with axis normal, to obtain one group of cross section curve (seal or do not seal) on curved surface, obviously each bar cross section curve all is a plane curve.If can measure the shape of each bar cross section curve, also just can obtain the shape of tested curved surface.

If cross section curve has or segmentation has Second Order Continuous partial derivative (can prove that general workpiece all satisfies this condition), can derive the curvature function K of cross section curve _l(s) (there is certain relation in x between y) with the coordinate of cross section curve in any selected rectangular coordinate system.That is: in a selected arbitrarily rectangular coordinate system, if a known closed interval [S ₀, S ₁] the curvature function K of interior continuous curve _l(s) any given starting point (x ₀, y ₀), and one on any one direction vowed T ₀=icos φ ₀+ jsin φ ₀(i, j are the axial vector of unit length of coordinate system) then should have and have only a plane directing curve to make it satisfy given curvature function in the curvature of each point in given interval as starting condition. $r=r\left(s\right)=x\left(s\right)i+y\left(s\right)j---{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="9610100400072.png"\; state="\{\{state\}\}">S</figure-callout>}}_0\&le;s\&le;S_1---\left(1\right)$ In the formula $x\left(s\right)={\&Integral;}_{s_0}^s\cos \mathrm{\&phi;ds}+x_0$ $y\left(s\right)={\&Integral;}_{s_0}^s\sin \mathrm{\&phi;ds}+y_0----\left(2\right)$ φ wherein is the function about s that satisfies the following relationship formula:

Therefore, if can measure the curvature function K of each cross section curve _l(s), can under selected arbitrarily coordinate system, complex-curved geometric configuration be described so.

Because the curvature function of each bar cross section curve is the intrinsic geometry characteristic of this cross section curve, from ultimate principle formula (1)～when (3) adopt the curve form of the inventive method measuring workpieces as can be seen, measurement result can be described in selected arbitrarily coordinate system, the selection that is measurement result and coordinate system is irrelevant, so need not accurately locate measured workpiece.

The main points and the step of the inventive method are:

1, on space curved surface, selects one group of cross section curve arbitrarily;

2, measure the curvature function of each cross section curve;

3, calculate the shape of each bar cross section curve according to formula (1)～(3);

4, by the shape of every the cross section curve shape reorganization space three-dimensional curved surface that records.The present invention compares with existing other curve form measuring method and has the following advantages:

1, because the measurement of pair cross-section curvature of curve only need be measured the relative position of the interior point of a minimum neighborhood of measured point on the curve, little to the measuring amount range request of sensor, can use the shape measure of the sensor realization large-size workpiece of little range.This is that traditional curve form measuring method is irrealizable;

2, the measuring accuracy of this measuring method depends mainly on the measuring accuracy of sensor, and is irrelevant with bearing accuracy;

3, because the curvature of each bar cross section curve is the intrinsic geometry characteristic of this cross section curve, from ultimate principle formula (1)～(3) another characteristics of the present invention as can be seen is that measurement result can be described optional coordinate system, i.e. the selection of measurement result and coordinate system is irrelevant;

4. be applicable to the general curve form measuring method of on-line measurement.

The present invention is suitable for the curve form of various moulding workpiece and measures, as: the measurement of the shape of aerospace equipment part, the shape measure of turbine blade blade profile, the nemaline measurement of cam contour, the shape measure of large-size spherical tank container, the shape measure of irregular curve surface container etc.Therefore have very big application scope and promotion prospect.

Fig. 1 is that tested curved surface reaches the method synoptic diagram of selecting one group of cross section curve on measured curved surface in the embodiment of the invention

Fig. 2 is the actual measurement curvature function figure of a cross section curve wherein on the tested curved surface in the embodiment of the invention

Fig. 3 in the embodiment of the invention according to the curvature function of Fig. 2 by the curve shape that principle formula (1)～calculates (3)

Embodiment: with the shape of method measurement of the present invention three-dimension curved surface S as shown in Figure 1, the step of its realization is:

1. the straight line L that selects space, tested curved surface S place arbitrarily goes to cut a tested curved surface S with one group of parallel plane with this axis normal and equidistant (spacing is △ z) as axis, obtains one group of cross section curve C on the curved surface S _t(i=1,2,3 ... n), curve C as shown in fig. 1 _lTo C _nN is a selected cross section sum;

2. with combining the sensing head of curvature sensing function and arc length sensing function respectively at cross section curve C _lTo C _nThe cutting plane P at place _l(i=1,2,3 ... n) move in, measure cross section curve C respectively _lTo C _nCurvature function K _l(i=1,2,3 ... n), Fig. 2 is the curvature function K of the actual w bar cross section curve that records _w(s) figure;

3. the curvature function K that just records _l(s) (i=1,2,3 ... n) difference principle of substitution formula (3) calculates corresponding φ _l(s), distinguish principle of substitution formula (2) again, obtain respectively to measure the parametric equation of curve.Be designated as C if respectively measure curve _i(i=1,2,3 ... n), Fig. 3 is by the actual measurement curvature function K among Fig. 2 _w(s) the w bar that calculates is measured the described curve C of parametric equation of curve _wShape;

4. at an optional three-dimensional cartesian coordinate system { O; Along the Z axle,, arrange each measured bar equally spacedly and measure curve C among the XYZ} with spacing △ z _i(i=1,2,3 ... the three-dimension curved surface shape that n), can obtain to measure.

Claims (2)

1, a kind of measuring method of curve form is characterized in that: measure the shape of three-dimension curved surface by the curvature function of measuring some cross section two-dimensional curves on the curved surface, its concrete steps are:

1. on space curved surface, select one group of cross section curve arbitrarily;

2. measure the curvature function of each cross section curve;

3. calculate the shape of each bar cross section curve;

4. by the shape of every the cross section curve shape reorganization space three-dimensional curved surface that records.

2, measuring method according to claim 1 is characterized in that: the shape of cross section curve is by following vector description

r=r(s)=x(s)i+y(s)j S ₀≤S≤S ₁

In the formula $x\left(s\right)={\&Integral;}_{s_0}^s\cos \mathrm{\&phi;ds}+x_0$ $y\left(s\right)={\&Integral;}_{s_0}^s\sin \mathrm{\&phi;ds}+y_0$ φ wherein is the function about s that satisfies the following relationship formula:

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