CN1153901A - Curved surface shape measuring method - Google Patents
Curved surface shape measuring method Download PDFInfo
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- CN1153901A CN1153901A CN 96101004 CN96101004A CN1153901A CN 1153901 A CN1153901 A CN 1153901A CN 96101004 CN96101004 CN 96101004 CN 96101004 A CN96101004 A CN 96101004A CN 1153901 A CN1153901 A CN 1153901A
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Abstract
The principle of measuring surface shape is that through the measurement of curvature functions of surface cross sections, the surface shape is measured. The said method is suitable for various workpieces of different shapes. The present invention solves the problem of shape measurement and the said technology may be used in reforming and simplifying available surface shape measuring instruments.
Description
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, complex structure, bulky not only, the positioning accuracy request height, 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
i(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
i(s), any given starting point (x
0, y
0), and one on any one direction vowed T
0=icos φ
0+ jsin φ
0(ij is 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(s)＝x(s)i+y(s)j S
0≤s≤S
1 (1)
In the formula
φ wherein is the function about s that satisfies the following relationship formula:
(i=1,2,3 ... the cross section sequence number) (3)
Therefore, if can measure the curvature function K of each cross section curve
i(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) can to go out another characteristics of the present invention be 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 Δ z) as axis, obtains one group of cross section curve C on the curved surface S
i(i=1,2,3 ... n), curve C as shown in fig. 1
1To 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
1To C
nThe cutting plane P at place
i(i=1,2,3 ... n) move in, measure cross section curve C respectively
1To C
nCurvature function K
i(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
i(s) (i=1,2,3 ... n) difference principle of substitution formula (3) calculates corresponding φ
i(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
w' shape;
4. at an optional three-dimensional cartesian coordinate system { 0; Along the Z axle,, arrange each measured bar equally spacedly and measure curve C among the XYZ} with separation delta z
i' (i=1,2,3 ... the three-dimension curved surface shape that n), can obtain to measure.
Claims (3)
1. the measuring method of a curve form is characterized in that: measure the shape of three-dimension curved surface by the curvature function of measuring some cross section curves (two-dimensional curve) 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, it is levied the spy and is: 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
φ wherein is the function about s that satisfies the following relationship formula:
(i=1,2,3 ... the cross section sequence number)
3. measuring method according to claim 1 is characterized in that: can carry out the shape measure of two-dimensional curve.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 96101004 CN1065047C (en) | 1996-01-06 | 1996-01-06 | Curved surface shape measuring method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 96101004 CN1065047C (en) | 1996-01-06 | 1996-01-06 | Curved surface shape measuring method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN1153901A true CN1153901A (en) | 1997-07-09 |
| CN1065047C CN1065047C (en) | 2001-04-25 |
Family
ID=5116865
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 96101004 Expired - Fee Related CN1065047C (en) | 1996-01-06 | 1996-01-06 | Curved surface shape measuring method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN1065047C (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1296676C (en) * | 2005-03-17 | 2007-01-24 | 上海交通大学 | Bending sensor capable of simultaneously measuring bending curvature and bending direction |
| CN104316014A (en) * | 2014-10-21 | 2015-01-28 | 西安交通大学 | Rapid measurement route planning method of sections of blades of aviation engine |
| CN114985300A (en) * | 2022-04-27 | 2022-09-02 | 佛山科学技术学院 | Method and system for classifying outlet paperboards of corrugated paperboard production line |
-
1996
- 1996-01-06 CN CN 96101004 patent/CN1065047C/en not_active Expired - Fee Related
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1296676C (en) * | 2005-03-17 | 2007-01-24 | 上海交通大学 | Bending sensor capable of simultaneously measuring bending curvature and bending direction |
| CN104316014A (en) * | 2014-10-21 | 2015-01-28 | 西安交通大学 | Rapid measurement route planning method of sections of blades of aviation engine |
| CN104316014B (en) * | 2014-10-21 | 2017-04-19 | 西安交通大学 | Rapid measurement route planning method of sections of blades of aviation engine |
| CN114985300A (en) * | 2022-04-27 | 2022-09-02 | 佛山科学技术学院 | Method and system for classifying outlet paperboards of corrugated paperboard production line |
| CN114985300B (en) * | 2022-04-27 | 2024-03-01 | 佛山科学技术学院 | Method and system for classifying outlet paperboards of corrugated board production line |
Also Published As
| Publication number | Publication date |
|---|---|
| CN1065047C (en) | 2001-04-25 |
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