Development of a library of feature fitting algorithms for CMMs
Conformance of a manufactured feature to the applied geometric tolerances is done by analyzing the point cloud that is measured on the feature. To that end, a geometric feature is fitted to the point cloud and the results are assessed to see whether the fitted feature lies within the specified toler...
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| Published in | International journal of precision engineering and manufacturing Vol. 16; no. 10; pp. 2101 - 2113 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Seoul
Korean Society for Precision Engineering
01.09.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2234-7593 2005-4602 |
| DOI | 10.1007/s12541-015-0272-1 |
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| Abstract | Conformance of a manufactured feature to the applied geometric tolerances is done by analyzing the point cloud that is measured on the feature. To that end, a geometric feature is fitted to the point cloud and the results are assessed to see whether the fitted feature lies within the specified tolerance limits or not. Coordinate Measuring Machines (CMMs) use feature fitting algorithms that incorporate least square estimates as a basis for obtaining minimum, maximum, and zone fits. However, it is well known that results obtained from different vendors for the same data set often do not agree. This may be because of different interpretations of the GD&T standards, or the use of least squares algorithms as the basis for all fitting. Therefore, a reference or normative comprehensive library of algorithms addressing the fitting procedure (all datums, targets) for every tolerance class is needed. The library is specific to feature fitting for tolerance verification. This paper addresses linear, planar, circular, and cylindrical features only. This set of algorithms described conforms to the international Standards for GD&T. In order to reduce the number of points to be analyzed, and to identify the possible candidate points for linear, circular and planar features, 2D and 3D convex hulls are used. For minimum, maximum, and Chebyshev cylinders, geometric search algorithms are used. Algorithms are divided into three major categories: least square, unconstrained, and constrained fits. |
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| AbstractList | Conformance of a manufactured feature to the applied geometric tolerances is done by analyzing the point cloud that is measured on the feature. To that end, a geometric feature is fitted to the point cloud and the results are assessed to see whether the fitted feature lies within the specified tolerance limits or not. Coordinate Measuring Machines (CMMs) use feature fitting algorithms that incorporate least square estimates as a basis for obtaining minimum, maximum, and zone fits. However, it is well known that results obtained from different vendors for the same data set often do not agree. This may be because of different interpretations of the GD&T standards, or the use of least squares algorithms as the basis for all fitting. Therefore, a reference or normative comprehensive library of algorithms addressing the fitting procedure (all datums, targets) for every tolerance class is needed. The library is specific to feature fitting for tolerance verification. This paper addresses linear, planar, circular, and cylindrical features only. This set of algorithms described conforms to the international Standards for GD&T. In order to reduce the number of points to be analyzed, and to identify the possible candidate points for linear, circular and planar features, 2D and 3D convex hulls are used. For minimum, maximum, and Chebyshev cylinders, geometric search algorithms are used. Algorithms are divided into three major categories: least square, unconstrained, and constrained fits. |
| Author | Haghighi, Payam Shah, Jami J. Davidson, Joseph K. Mohan, Prashant |
| Author_xml | – sequence: 1 givenname: Prashant surname: Mohan fullname: Mohan, Prashant organization: Design Automation Lab, Department of Mechanical Engineering, Arizona State University – sequence: 2 givenname: Payam surname: Haghighi fullname: Haghighi, Payam email: phaghigh@asu.edu organization: Design Automation Lab, Department of Mechanical Engineering, Arizona State University – sequence: 3 givenname: Jami J. surname: Shah fullname: Shah, Jami J. organization: Design Automation Lab, Department of Mechanical Engineering, Arizona State University – sequence: 4 givenname: Joseph K. surname: Davidson fullname: Davidson, Joseph K. organization: Design Automation Lab, Department of Mechanical Engineering, Arizona State University |
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| Cites_doi | 10.1016/j.ijmachtools.2007.10.019 10.1016/j.cad.2009.06.011 10.1016/0925-7721(93)90009-U 10.1016/j.ijmachtools.2006.08.010 10.1016/j.measurement.2011.06.010 10.1007/s10845-008-0096-2 10.1016/0141-6359(94)00018-U 10.1016/S0007-8506(07)60734-3 10.1016/S0890-6955(00)00029-8 10.1016/S0141-6359(02)00221-0 10.6028/jres.103.043 10.1016/j.measurement.2012.01.020 |
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| References_xml | – reference: ForbesA. B.Least-Squares Best-Fit Geometric ElementsNational Physical Laboratory1991 – reference: ShakarjiC. M.ClementA.Reference Algorithms for Chebyshev and One-Sided Data Fitting for Coordinate MetrologyCIRP Annals-Manufacturing Technology200453143944210.1016/S0007-8506(07)60734-3 – reference: EndriasD. H.FengH.-Y.MaJ.WangL.TaherM. A.A Combinatorial Optimization Approach for Evaluating Minimum-Zone Spatial Straightness ErrorsMeasurement20124551170117910.1016/j.measurement.2012.01.020 – reference: CormenT. H.LeisersonC. E.RivestR. L.SteinC.Introduction to AlgorithmsMcGraw-Hill Science/Engineering/Math2001955956 – reference: The American Society of Mechanical Engineers, “GDTP (Y14.5) -Geometric Dimensioning and Tolerancing Professional Certification,” 1994. – reference: ShakarjiC. M.Least-Squares Fitting Algorithms of the Nist Algorithm Testing SystemJournal of Research-National Institute of Standards and Technology1998103663364110.6028/jres.103.043 – reference: HermannG.Robust Convex Hull-based Algorithm for Straightness and Flatness Determination in Coordinate MeasuringActa Polytechnica Hungarica2007441111202119618 – reference: ClarksonK. L.MehlhornK.SeidelR.Four Results on Randomized Incremental ConstructionsComputational Geometry199334185212123792110.1016/0925-7721(93)90009-U0781.68112 – reference: XiumingL.ZhaoyaoS.Application of Convex Hull in the Assessment of Roundness ErrorInternational Journal of Machine Tools and Manufacture200848671171410.1016/j.ijmachtools.2007.10.019 – reference: Focus Technology Co., Ltd., “Sino-America Joint Venture Qingdao Leader Metrology Instruments Co., Ltd.,” http://www.made-inchina. com/showroom/qingdaoleader/ (Accessed 16 JUL 2015) – reference: ShenZ.ShahJ. J.DavidsonJ. K.Analysis Neutral Data Structure for Gd&TJournal of Intelligent Manufacturing200819445547210.1007/s10845-008-0096-2 – reference: NIST, “Dimensional Metrology Group,” http://www.nist.gov/pml/div683/grp01/ (Accessed 6 AUG 2015) – reference: CarrK.FerreiraP.Verification of Form Tolerances Part Ii: Cylindricity and Straightness of a Median LinePrecision Engineering199517214415610.1016/0141-6359(94)00018-U – reference: CheraghiS. H.JiangG.AhmadJ. S.Evaluating the Geometric Characteristics of Cylindrical FeaturesPrecision Engineering200327219520410.1016/S0141-6359(02)00221-0 – reference: LeeM.-K.An Enhanced Convex-Hull Edge Method for Flatness Tolerance EvaluationComputer-Aided Design2009411293094110.1016/j.cad.2009.06.011 – reference: WelberR.CMM Form Tolerance Algorithm TestingGIDEP1988 – reference: BhatV.De MeterE. C.An Analysis of the Effect of Datum-Establishment Methods on the Geometric Errors of Machined FeaturesInternational Journal of Machine Tools and Manufacture200040131951197510.1016/S0890-6955(00)00029-8 – reference: Thomasnet, “Coordinate Measuring Machine has Portable Design,” http://news.thomasnet.com/fullstory/coordinate-measuring-machinehas-portable-design-455365 (Accessed 12 AUG 2015) – reference: LeiX.SongH.XueY.LiJ.ZhouJ.DuanM.Method for Cylindricity Error Evaluation using Geometry Optimization Searching AlgorithmMeasurement20114491556156310.1016/j.measurement.2011.06.010 – reference: VenkaiahN.ShunmugamM. S.Evaluation of Form Data using Computational Geometric Techniques—Part I: Circularity ErrorInternational Journal of Machine Tools and Manufacture20074771229123610.1016/j.ijmachtools.2006.08.010 – volume-title: GIDEP year: 1988 ident: 272_CR5 – volume-title: National Physical Laboratory year: 1991 ident: 272_CR7 – volume: 48 start-page: 711 issue: 6 year: 2008 ident: 272_CR12 publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/j.ijmachtools.2007.10.019 – volume: 41 start-page: 930 issue: 12 year: 2009 ident: 272_CR14 publication-title: Computer-Aided Design doi: 10.1016/j.cad.2009.06.011 – volume: 3 start-page: 185 issue: 4 year: 1993 ident: 272_CR18 publication-title: Computational Geometry doi: 10.1016/0925-7721(93)90009-U – volume: 47 start-page: 1229 issue: 7 year: 2007 ident: 272_CR19 publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/j.ijmachtools.2006.08.010 – volume: 44 start-page: 1556 issue: 9 year: 2011 ident: 272_CR15 publication-title: Measurement doi: 10.1016/j.measurement.2011.06.010 – ident: 272_CR6 – ident: 272_CR1 – volume: 19 start-page: 455 issue: 4 year: 2008 ident: 272_CR4 publication-title: Journal of Intelligent Manufacturing doi: 10.1007/s10845-008-0096-2 – ident: 272_CR2 – ident: 272_CR3 – volume: 17 start-page: 144 issue: 2 year: 1995 ident: 272_CR9 publication-title: Precision Engineering doi: 10.1016/0141-6359(94)00018-U – volume: 53 start-page: 439 issue: 1 year: 2004 ident: 272_CR11 publication-title: CIRP Annals-Manufacturing Technology doi: 10.1016/S0007-8506(07)60734-3 – volume: 40 start-page: 1951 issue: 13 year: 2000 ident: 272_CR16 publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/S0890-6955(00)00029-8 – volume: 27 start-page: 195 issue: 2 year: 2003 ident: 272_CR10 publication-title: Precision Engineering doi: 10.1016/S0141-6359(02)00221-0 – volume: 4 start-page: 111 issue: 4 year: 2007 ident: 272_CR20 publication-title: Acta Polytechnica Hungarica – volume: 103 start-page: 633 issue: 6 year: 1998 ident: 272_CR8 publication-title: Journal of Research-National Institute of Standards and Technology doi: 10.6028/jres.103.043 – volume: 45 start-page: 1170 issue: 5 year: 2012 ident: 272_CR13 publication-title: Measurement doi: 10.1016/j.measurement.2012.01.020 – start-page: 955 volume-title: McGraw-Hill Science/Engineering/Math year: 2001 ident: 272_CR17 |
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| Title | Development of a library of feature fitting algorithms for CMMs |
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