CN107270858A - A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces - Google Patents
A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces Download PDFInfo
- Publication number
- CN107270858A CN107270858A CN201710454589.6A CN201710454589A CN107270858A CN 107270858 A CN107270858 A CN 107270858A CN 201710454589 A CN201710454589 A CN 201710454589A CN 107270858 A CN107270858 A CN 107270858A
- Authority
- CN
- China
- Prior art keywords
- sampling
- point
- error
- along
- sampled
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
Abstract
The invention discloses a kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces, comprise the following steps：(1) by curved surface along u to v to it is discrete be transversal to be approximately surface；(2) along v to being sampled so that the sampled point after sampling reflect v to feature, obtain a point set, the point set obtained into a suite line along u to connection；(3) n has been obtained along u to discrete sampling point on the curveu×nvSampling number；(4) adaptive factor is optimized using genetic algorithm, to improve the accuracy of measurement.The inventive method have adjusted adaptability and uniform property that sample is distributed using adaptive factor, and adaptive weighted factor is optimized by genetic algorithm the accuracy for improving measurement, meanwhile, it is compared by one free form surface with error of design and with dated method known to other three kinds the validity for demonstrating this method.
Description
Technical field
It is to be related to one kind based on three Coordinate-frees song specifically the present invention relates to the set fields of measurement of mismachining tolerance
The intelligent geometric sampling method in face.
Background technology
Free form surface is widely used in engineering, and the measurement of free-form surface designing is quality control and fault diagnosis mistake
The basis of journey[1].Sampling process includes setting sampled point quantity and chooses tactful two parts of layouting of sampled point[2].But, very
The distribution of many situation down-sampling points is a principal element for determining sampled point quantity.Therefore, it is main at present to study sampled point cloth
Point strategy.It is relatively common in the way of uniform pattern profile samples point in the method for sampling, because this method can have letter
Change algorithm, calculate rapidly and to advantages such as the enough representative abilities of curved surface.But this kind of method have ignored the surface of finished surface
Feature, and surface characteristics plays very big effect in machining process, it is different in processing by taking the curvature of free form surface as an example
Caused tool contact, which changes, during curvature curve can bring form error[3].It may be missed using homogenization process sampling on surface
Crucial mismachining tolerance point.According to a kind of standard of measuring method validity is evaluated, i.e. can this method be caught with limited sampled point
Grasp for the point with larger error, homogenization process should avoid this defect[4].In order to solve this problem, many articles
Research is expanded for this problem.The curvature on wherein surface is a factor being widely studied.In Elkott[5]Experiment
In, form error is distributed according to the Curvature varying of curved surface；Yu[6]Establish a form error based on curvature of curved surface
Model knows measurement；Obeidat[7]Exist in view of the form error at curved surface point is proportional to the curvature at the place that changes the time, and
Therefore a kind of adaptively sampled method based on free form surface curvature is proposed；In Li[8]Research in, center of gravity model for the first time
Apply in the distribution of sampled point；Method based on Li, He[9-10]To between adaptive factor and the accuracy of measuring method
Relation is studied, it is proposed that a kind of improved adaptively sampled strategy based on curvature of curved surface.
The reference being related to:
[1]Rajamohan G,Shunmugam M S,Samuel G L,Effect of probe size and
measurement strategies on assessment of freeform profile deviations using
coordinate measuring machine,Measurement,44(2011)832-841.
[2]Raghunandan R,Rao P V,Selection of sampling points for accurate
evaluation of flatness error using coordinate measuring machine,Journal of
Materials Processing Technology 202(1-3)(2008)240-245.
[3]Rajamohan G,Shunmugam M,Samuel G.Practical Measurement Strategies
for Verification of Freeform Surfaces Using Coordinate Measuring Machines,
Metrology&Measurement Systems 18(2).(2011)209-222.
[4]Poniatowska M,Deviation model based method of planning accuracy
inspection of free-form surfaces using CMMs,Measurement,.45(5)(2012)927-937.
[5]Elkott D F,Veldhuis S C,Isoparametric line sampling for the
inspection planning of sculptured surfaces,Computer-Aided Design,37(2)(2005)
189-200.
[6]Yu M,Zhang Y,Li Y,et al,Adaptive sampling method for inspection
planning on CMM for free-form surfaces,The International Journal of Advanced
Manufacturing Technology,67(9)(2013)1967-1975.
[7]Obeidat S M,Raman S,An intelligent sampling method for inspecting
free-form surfaces,The International Journal of Advanced Manufacturing
Technology,40(11)(2009)1125-1136.
[8]Li S Z,Adaptive sampling and mesh generation,Computer-Aided
Design,27(27)(1995)235–240.
[9]GY He,HY Jia,LZ Guo,PP Liu,Adaptive sampling strategy for free-
form surface based on CAD model,Journal of Electronic Measurement&Instrument,
26(10)(2013)835-840.
[10]He Gaiyun,JiCaixia,GuoLongzhen,Analysis of Measurement Method
Error in Freeform Surface Based on Equal Moment Strategy,Journal of Tianjin
University(Science And Technology),49(2),2016.
The content of the invention
The invention aims to overcome deficiency of the prior art, there is provided a kind of intelligence based on three Coordinate-free curved surfaces
Can geometric sampling method.This method have adjusted adaptability and uniform property that sample is distributed using adaptive factor, and by losing
Propagation algorithm adaptive weighted factor is optimized the accuracy for improving measurement, meanwhile, there is error by designing one
Free form surface and be compared with indicating method known to other three kinds and demonstrate the validity of this method.
The purpose of the present invention is achieved through the following technical solutions：
A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces, comprises the following steps：
(1) by curved surface along u to v to it is discrete be transversal to be approximately surface；
(2) along v to being sampled so that the sampled point after sampling reflect v to feature, a point set is obtained, by institute
State point set and obtain a suite line along u to connection；
(3) n has been obtained along u to discrete sampling point on the curveu×nvSampling number；
(4) adaptive factor is optimized using genetic algorithm, to improve the accuracy of measurement.
Compared with prior art, the beneficial effect that technical scheme is brought is：
The strategy of layouting of sampled point is measurement and a key factor for expressing surface, and the present invention is on based on heredity calculation
The strategy process of layouting of method, can improve the point self-adapted accuracy layouted of sampling, and this method has the larger error of seizure
Also by the comparison with other several typical algorithms to prove the validity of this method in the ability of deviation point, specific embodiment.
Brief description of the drawings
The simulation schematic diagram of Fig. 1 testing curved surfaces.
The error distribution of Fig. 2 testing curved surfaces.
Fig. 3 be using Isoparametric method and etc. the obtained distribution of sampled point of area surface area method.
Fig. 4 is the distribution for the sampled point that the method for sampling and the inventive method based on curvature are obtained.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
1. on nurbs surface
NURBS (non-uniform rational B-spline) is widely used in curved design and reconstruction field.Because NURBS is in CAD/
Widely using in CAM/CAE fields and in international standard (IGES, STEP, PHIGS and OpenGL), uses in the present embodiment
Nurbs surface represents free form surface.
One in u to for p ranks, v can be expressed as to the nurbs surface for q ranks：
Wherein, Pi,jFor control point, ωi,jFor the weight at each control point, u and v are the parameter between [0,1], i=0,1,
2,3 ... m, j=0,1,2,3 ... n, Ni,p(u),Nj,q(v) it is the basic function of non-uniform rational B-spline that is determined by a vector, can
Obtained with being calculated by De Boor-Cox recurrence formula, wherein uiIt is a vector；It is same v to basic function can equally obtain.
2. adaptively sampled method
In the evaluation of Free-Form Surface Profile error, according to minimum area method ISO1101, worst error is determined on surface
The size of minimally surrounded area.Therefore, the strategy of layouting of sampled point should can catch those key points with larger error.
That is, capturing the probability of larger error dot to increase, those regions for being possible to generate error should distribute more
Sampled point.
In machining process, the Curvature varying of finished surface be influence one of machined surface quality it is critically important because
Element, such case is especially apparent at processed complex surface.On the other hand, vibration can cause poor crudy, a lot
In the case of be also attributable to the discontinuity of finished surface.In addition, random error is very important in process and is not avoided that.
Therefore, it is necessary to consider factors above.The inventive method take into account the complexity of finished surface and adopts simultaneously
The uniformity of sampling point distribution, wherein, the complexity on surface represents that uniformity expresses curved surface by sampled point by the curvature of finished surface
Ability represent.
Free form surface can be expressed as：S=r (u, v) | (u, v) ∈ [0,1] }.The average curvature put on curved surface can be by
Below equation is calculated and obtained：
Wherein,
WithBe along u to v to first derivative,WithRespectively along u to v to second dervative,It is
Along v to derivative.
By a discretization of half-space surface be the collection comprising infinite cross section curve and, in free form surface u to section line can be with table
It is shown as li=l (u, v)=(x (u, v), y (u, v)), v=vi, u ∈ [0,1], wherein, i=1,2,3 ... n, n is the number of section line
Mesh, can similarly obtain v to section line.
The curvature measurement function of i-th of section line can be expressed as：
By ci(u) as density, then the gross mass of i-th section line can be obtained by arc-length integration formula：
WhereinquAnd puBe surface section line u to adaptive factor, same section line
V to adaptive factor be qvAnd pv。
It is assumed that curved surface S by it is discrete be N bars section line and wi,j(ui,j,vi,j) define the relevant parameter set of sampled point.
Wherein, i={ 1,2,3 ..., MjJ={ 1,2,3 ..., N }, MjRepresent the sample size on j-th strip section line.
Free form surface sampling flow based on CAD model is as follows：
(1) curved surface is carried out into approximation surface for enough transversals along u to v to discrete.N=2000 is set；Mj=
2000, j=1,2,3 ... N.
(2) along v to profile samples point so that the sampled point after sampling can reflect v to feature, transversal is upward in v
Gross massObtained by formula (5), search unit is defined as follows：
Unit=mi/nv (6)
Unit up-samples the search unit of point, wherein n for search in transversalvFor v to sampling transversal number, obtain one
Individual point set Pv.Curve Sk', k=1,2,3 ... n be by connect u to point set PvObtain, it reflects surface mean curvature H.
(3) the sampled point number on every transversal is set as nu.By sampled point in Sk', it is distributed on k=1,2,3 ... n.Along S '
The quality for obtaining curve is integrated to arc length
Search unit is defined as follows：
uniti'=m'i/nu (8)
Equally, as shown in step (2), the quantity of sampled point can be obtained by using search unit has so just obtained nu
×nvSampling number.
3. the optimization of adaptively sampled distribution
It is adaptively sampled to have been obtained for realizing by above step.But one side free form surface is in two sides of u and v
To surface characteristics be different under many circumstances, therefore the adaptively sampled factor in the two directions is also different；It is another
Aspect, although four adaptive factors improve the free degree of adaptivity, but use example demonstration or the method tested
Determining these factors can take considerable time and may not be accurate.So needing a kind of intelligent algorithm to optimize point of sampled point
Cloth.
Genetic algorithm (GA) is a kind of exploratory algorithm for being widely used in and solving mechanical engineering field nonlinear problem.Heredity
Algorithm carrys out optimum results with hereditary principle, the survival of the fittest.Genetic algorithm, which has good robustness and is adapted to solution optimization, asks
Topic.
Genetic algorithm is assessed including health, selection, and crossing operation compiles the several processes of computing.Proposed in this patent
In method, it is contemplated that the complexity on surface and the uniformity of distribution, the reconstructed error and curved surface for obtaining curved surface are reconstructed using NURBS
Average curvature average reciprocal is added to as in minor function：
Wherein, wherein, error for reconstruct rear curved surface and original surface worst error, siIt is through NURBS using sampled point
Point on the reconstructed surface that interpolation is obtained；r(u*,v*) it is apart from s on curved surface SiNearest point, can be by surface subdivision method
Obtain.Average is averaging function.
4. experimental verification
One is used to verify the method proposed by the NURBS curved surfaces expressed, and testing curved surface is illustrated in fig. 1 shown below：
For simulating cutting surface, mismachining tolerance and random error are added in test surfaces.Because on the one hand on surface
G2 regions curvature crudy is had a huge impact, on the other hand in the region of sequential change, vibration or pulse
Presence can cause poor crudy, so addition mismachining tolerance include the influence of curvature and changing for surface continuity
Become.
Error is given by caused by curvature：
Wherein H represents mean curvature of surface, fmaxIt is the maximum of the error caused by curvature, fmax=0.01.
In addition, the change of curvature also reflects successional change.By G2 definition, the discontinuous position of curvature is considered as
Successional to change, this just obtains the point set on the border in the different continuity regions of a connection, the shadow changed due to continuity
Sound is zonal, so border is homogenized,
Therefore, changing caused error by continuity can be defined as：
Wherein,ddHuAnd ddHvIt is in two sides of u and v
The standardization that upward average curvature second order is led；fdIt is max value of error caused by sequential change, fd=0.01.
Meanwhile, random error is generated by Gaussian Profile：
δr(u, v)~N (0,0.022) (12)
Therefore, the mismachining tolerance of curved surface can be expressed by following formula, and Fig. 2 is shown in the distribution of error：
δ=δc+δd+δr (13)
To verify the validity of this patent, the inventive method is compared with three kinds of wide variety of method of samplings,
These methods include wait parametric technique (uniform parameter), etc. area surface area method (uniform surface area)
With the method (based on curvature) based on curvature.
In confirmatory experiment, number of samples is set to two kinds of 9x9 and 12x12, sampling point distributions situation such as Fig. 3 of correlation method
With shown in Fig. 4.
In wherein Fig. 3：Isoparametric method is represented, the area surface area method such as × expression；
In Fig. 4：+ method based on curvature is represented, represent the inventive method.
Profile error is worth to by calculating the distance maximum of sampled point to tested curved surface, and distance can be by thin
Point method is obtained.
In machining process, the generation of error is also influenceed by randomness.Those there is a strong possibility property generation errors
Region should distribute more sampled points.That is, will be as far as possible the key position of sampling point distributions to sample.
Verify that strategy of layouting is that one side sampled point max value of error is a criterion, but due to the randomness in process,
Each workpiece has particularity, and only considers that curvature institute cloth sampled point completely can not be drawn during reacting processing
All errors entered, so on the other hand, the position that whether cloth sampled point samples in order to verify all is the larger position of error, i.e.,
With the larger key position for being likely to occur worst error, the concept of a mean error is introduced, it is as follows：
Wherein, eiIt is the error of ith sample point, n × m is sample size.
The comparative result of several distinct methods of table 1
As a result it is as listed in Table 1.Data in analytical table 1 are can be found that, on the one hand, these methods, which are obtained for, more closes
The result of reason, wherein the method that the method based on curvature and this patent are proposed obviously can preferably capture it is larger on surface
Error dot, although because uniform method can preferably express curved surface, but have ignored the feature of curved surface.The opposing party
Face, method proposed by the present invention substantially obtains larger average error value compared to other three kinds of methods, this explanation this method institute
Cloth measuring point is distributed in the larger position of error.
To sum up, the inventive method is optimized the distribution of sampled point using adaptive factor.Related experiment is carried out simultaneously
To verify the effect of this method and other three kinds of well-known methods.In addition, it is proposed that a mean error assessment parameters.It is real in checking
In testing, use genetic algorithm to consider the feature that machining error is distributed so that the method for proposition have very strong adaptivity and
Preferably catch the ability of key point.The validity of this method is confirmed by experiment.
The present invention is not limited to embodiments described above.The description to embodiment is intended to describe and said above
Bright technical scheme, above-mentioned embodiment is only schematical, is not restricted.This is not being departed from
In the case of invention objective and scope of the claimed protection, one of ordinary skill in the art may be used also under the enlightenment of the present invention
The specific conversion of many forms is made, these are belonged within protection scope of the present invention.
Claims (1)
1. a kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces, it is characterised in that comprise the following steps：
(1) by curved surface along u to v to it is discrete be transversal to be approximately surface；
(2) along v to being sampled so that the sampled point after sampling reflect v to feature, a point set is obtained, by the point
Collection obtains a suite line along u to connection；
(3) n has been obtained along u to discrete sampling point on the curveu×nvSampling number；
(4) adaptive factor is optimized using genetic algorithm, to improve the accuracy of measurement.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710454589.6A CN107270858A (en) | 2017-06-15 | 2017-06-15 | A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710454589.6A CN107270858A (en) | 2017-06-15 | 2017-06-15 | A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107270858A true CN107270858A (en) | 2017-10-20 |
Family
ID=60066350
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710454589.6A Pending CN107270858A (en) | 2017-06-15 | 2017-06-15 | A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107270858A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107991993A (en) * | 2017-12-20 | 2018-05-04 | 天津大学 | Adaptively sampled method based on mismachining tolerance model and Hammersley sequences |
| CN108107836A (en) * | 2017-12-20 | 2018-06-01 | 天津大学 | A kind of method for establishing the mismachining tolerance model M EM for free form surface |
| CN114861244A (en) * | 2022-04-14 | 2022-08-05 | 中国科学院空间应用工程与技术中心 | Optimization method and system for sampling and building direction of free-form surface and electronic equipment |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101149253A (en) * | 2007-10-16 | 2008-03-26 | 浙江大学 | Unknown free-form surface self-adaptive measuring method based on exploration method and measuring head device |
| CN101672637A (en) * | 2009-09-24 | 2010-03-17 | 华东理工大学 | Digitizing detection method of complicated curved face |
| CN201514207U (en) * | 2009-09-25 | 2010-06-23 | 华东理工大学 | Digitized detection system for complex curved surface |
| CN104157013A (en) * | 2014-08-06 | 2014-11-19 | 杭州新迪数字工程系统有限公司 | Reestablishing method for smooth curved surface on arbitrary quadrilateral grid |
-
2017
- 2017-06-15 CN CN201710454589.6A patent/CN107270858A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101149253A (en) * | 2007-10-16 | 2008-03-26 | 浙江大学 | Unknown free-form surface self-adaptive measuring method based on exploration method and measuring head device |
| CN101672637A (en) * | 2009-09-24 | 2010-03-17 | 华东理工大学 | Digitizing detection method of complicated curved face |
| CN201514207U (en) * | 2009-09-25 | 2010-06-23 | 华东理工大学 | Digitized detection system for complex curved surface |
| CN104157013A (en) * | 2014-08-06 | 2014-11-19 | 杭州新迪数字工程系统有限公司 | Reestablishing method for smooth curved surface on arbitrary quadrilateral grid |
Non-Patent Citations (1)
| Title |
|---|
| 贾红洋: "《复杂曲面测量采样策略与轮廓度误差评定方法研究》", 《中国优秀硕士学位论文全文数据库 工程科技Ⅰ辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107991993A (en) * | 2017-12-20 | 2018-05-04 | 天津大学 | Adaptively sampled method based on mismachining tolerance model and Hammersley sequences |
| CN108107836A (en) * | 2017-12-20 | 2018-06-01 | 天津大学 | A kind of method for establishing the mismachining tolerance model M EM for free form surface |
| CN114861244A (en) * | 2022-04-14 | 2022-08-05 | 中国科学院空间应用工程与技术中心 | Optimization method and system for sampling and building direction of free-form surface and electronic equipment |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Poniatowska | Deviation model based method of planning accuracy inspection of free-form surfaces using CMMs | |
| CN111274671B (en) | Precise repair method for complex product assembly process based on digital twin and operation system thereof | |
| Yu et al. | Adaptive sampling method for inspection planning on CMM for free-form surfaces | |
| Gohari et al. | A digital twin for integrated inspection system in digital manufacturing | |
| Ren et al. | A curve network sampling strategy for measurement of freeform surfaces on coordinate measuring machines | |
| CN107270858A (en) | A kind of intelligent geometric sampling method based on three Coordinate-free curved surfaces | |
| CN112926152B (en) | Digital twin-driven thin-wall part clamping force precise control and optimization method | |
| Magdziak | The influence of a number of points on results of measurements of a turbine blade | |
| Zhu et al. | An improved tolerance analysis method based on skin model shapes of planar parts | |
| CN110864671B (en) | Robot repeated positioning precision measuring method based on line structured light fitting plane | |
| Cheung et al. | Measuring ultra-precision freeform surfaces using a robust form characterization method | |
| Zhang et al. | Intelligent sampling strategy for freeform surfaces based on on-machine measurement through real-time interactive communication | |
| Zhou et al. | Automated inspection planning of freeform surfaces for manufacturing applications | |
| Poniatowska | Research on spatial interrelations of geometric deviations determined in coordinate measurements of free-form surfaces | |
| CN109725595A (en) | Compensation method, processing method and the workpiece of the machining path of workpiece | |
| CN107991993A (en) | Adaptively sampled method based on mismachining tolerance model and Hammersley sequences | |
| Shen et al. | An Approach of Assembly Deviation Analysis based on Jacobian Model and Skin Model Shapes | |
| Dichev et al. | Accuracy evaluation of flat surfaces measurements in conditions of external influences | |
| Ren et al. | Self-learning based highly efficient sampling strategy for complex surface reconstruction on contact measurements | |
| Zhongwei et al. | A methodology of sculptured surface fitting from CMM measurement data | |
| Shao et al. | Spatial modeling and monitoring considering long-range dependence | |
| Tu et al. | Ceramic Process Optimization and Automation Design Based on CAD and Reinforcement Learning | |
| Cerardi et al. | Advanced characterization of free-form surfaces in high precision machining | |
| Du et al. | RAPID MODELLING FOR FLEXIBLE CABLE BASED ON THE REVERSE ENGINEERING TECHNOLOGY. | |
| Prabuwono et al. | Surface defects classification using artificial neural networks in vision based polishing robot |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| CB02 | Change of applicant information | ||
| CB02 | Change of applicant information |
Address after: 300350 District, Jinnan District, Tianjin Haihe Education Park, 135 beautiful road, Beiyang campus of Tianjin University Applicant after: Tianjin University Address before: 300072 Tianjin City, Nankai District Wei Jin Road No. 92 Applicant before: Tianjin University |
|
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20171020 |