Form Errors in Precision Metrology: A Survey of Measurement Techniques

REFERENCES

• American National Standards Institute. ( 1995a ). Mathematical Definitions of Dimensioning and Tolerancing Principles . New York : American Society of Mechanical Engineers .
   Google Scholar
• American National Standards Institute. ( 1995b ). Dimensioning and Tolerancing . New York : American Society of Mechanical Engineers .
   Google Scholar
• Badar , M. A. , Raman , S. , Pulat , P. S. ( 2003 ). Intelligent search-based selection of sample points for straightness and flatness estimation . Journal of Manufacturing Science and Engineering , 125 : 263 – 271 .
   Web of Science ®Google Scholar
• Bazaraa , M. , Sherali , H. , Shetty , C. ( 1993 ). Non-linear Programming: Theory and Algorithms, , 2nd ed. New York : John Wiley & Sons .
   Google Scholar
• Berrado , A. , Hubele , N. F. , Gel , E. S. ( 2006 ). An empricial investigation into the distribution of flatness measurements . Quality Engineering , 18 : 351 – 357 .
   Google Scholar
• Cardou , A. , Boullion , G. , Tremblay , G. ( 1972 ). Some considerations on the flatness of surface plates . Microtecnic , 26 ( 7 ): 367 – 368 .
   Google Scholar
• Carr , K. , Ferreira , P. ( 1995 ). Verification of form tolerances, Part I: Basic issues, flatness, and straightness . Precision Engineering , 17 ( 2 ): 131 – 143 .
   Web of Science ®Google Scholar
• Chatterjee , G. , Roth , B. ( 1997 ). On Chebyshev fits for pairs of lines and polygons with specified internal angles . Precision Engineering , 21 : 43 – 56 .
   Google Scholar
• Chaudhuri , B. , Kundu , P. ( 1993 ). Optimum circular fit to weighted data in multi-dimensional space . Pattern Recognition Letters , 14 : 1 – 6 .
   Web of Science ®Google Scholar
• Cheraghi , S. , Lim , H. , Motavalli , S. ( 1996 ). Straightness and flatness tolerance evaluation: An optimization approach . Precision Engineering , 18 : 30 – 37 .
   Google Scholar
• Cheraghi , S. H. , Jiang , G. , Ahmad , J. S. ( 2003 ). Evaluating the geometric characteristics of cylindrical features . Precision Engineering , 27 : 195 – 204 .
   Web of Science ®Google Scholar
• Chetwynd , D. ( 1979 ). Roundness measurement using limacons . Precision Engineering , 1 : 137 – 141 .
   Google Scholar
• Chetwynd , D. ( 1985 ). Applications of linear programming to engineering metrology . Proceedings of the Institution of Mechanical Engineers , 199 ( B2 ): 93 – 100 .
   Google Scholar
• Chung , S. , Raman , S. ( 1999 ). Linear methods for determination of conicity tolerance . CIRP Journal of Manufacturing Systems , 29 ( 4 ): 323 – 327 .
   Google Scholar
• Cooper , I. ( 1993 ). Circle fitting by linear and non-linear least squares . Journal of Optimization Theory and Applications , 76 : 381 – 388 .
   Web of Science ®Google Scholar
• Damodarasamy , S. , Anand , S. ( 1999 ). Evaluation of minimum zone for flatness by normal plane method and simplex search . IIE Transactions , 31 : 617 – 626 .
   Web of Science ®Google Scholar
• Dhanish , P. , Shunmugam , M. ( 1991 ). An algorithm for form error evaluation—Using the theory of discrete and linear Chebyshev approximation . Computer Methods in Applied Mechanics and Engineering , 92 : 309 – 324 .
   Web of Science ®Google Scholar
• Dowling , M. , Griffin , P. , Tsui , K. , Zhou , C. ( 1995 ). A comparison of the orthogonal least squares and minimum enclosing zone methods for form error estimation . Manufacturing Review , 8 : 120 – 138 .
   Google Scholar
• Dowling , M. , Griffin , P. , Tsui , K. , Zhou , C. ( 1997 ). Statistical issues in geometric feature inspection using coordinate measuring machines . Technometrics , 39 ( 1 ): 3 – 17 .
   Web of Science ®Google Scholar
• Elmaraghy , W. , Elmaraghy , H. , Wu , Z. ( 1990 ). Determination of actual geometric deviations using coordiante measuring machine data . Manufacturing Review , 3 ( 1 ): 32 – 39 .
   Google Scholar
• Elzinga , J. , Hearn , D. ( 1971 ). Geometrical solutions for some minimax problems . Transportation Science , 6 : 379 – 394 .
   Google Scholar
• Etesami , F. , Qiao , H. (1990). Analysis of two-dimensional measurement data for automated inspection. Precision Engineering , 9(1):21–34.
   Google Scholar
• Forbes , A. ( 1989 ). Least-squares best-fit geometric elements . NPL Report DITC 140/89 . London : National Physical Laboratories .
   Google Scholar
• Fukuda , M. , Shimokohbe , A. ( 1984 ). Algorithms for form-error evaluation—Methods of the minimum zone and the least squares. Paper read at the International Symposium on Metrology for Quality Control in Production, Tokyo.
   Google Scholar
• Gass , S. , Witzgall , C. , Harary , H. ( 1998 ). Fitting circles and spheres to coordinate measuring machine data . The International Journal of Flexible Manufacturing Systems , 10 : 5 – 25 .
   Google Scholar
• Gilbert , R. C. , Raman , S. , Trafalis , T. B. , Obeidat , S. M. , Aguirre-Cruz , J. A. ( 2009 ). Mathematical foundations for form inspection and adaptive sampling . Journal of Manufacturing Science and Engineering , 131 : 1 – 7 .
   Google Scholar
• Gosavi , A. ( 1995 ). Algorithm Development and Minimum Sample Size in Form Measurement . M.Tech Report . Madras , India : Mechanical Engineering, Indian Institute of Technology .
   Google Scholar
• Gosavi , A. , Phatakwala , S. ( 2006 ). A finite-differences derivative descent-approach for estimating form error in precision-manufactured parts . Journal of Manufacturing Science and Engineering , 128 ( 1 ): 355 – 359 .
   Web of Science ®Google Scholar
• Gota , M. , Lizuka , K. ( 1977 ). An analysis of the relationship between minimum zone deviation and least squares deviation in circularity and cylindricity. Paper read at the International Conference of Production Engineering, New Delhi.
   Google Scholar
• Griffith , G. K. ( 2002 ). Geometric Dimensioning and Tolerancing, , 2nd ed. Upper Saddle River , NJ : Prentice Hall .
   Google Scholar
• Grinde , R. , Ventura , J. ( 1994 ). Minimax center estimation for inspection of spherical parts . International Journal of Production Research , 32 ( 9 ): 2031 – 2047 .
   Web of Science ®Google Scholar
• Guu , S. , Tsai , D. ( 1999 ). Measurement of roundness: A nonlinear approach . Proceedings of National Science Council, ROC (A) , 23 ( 3 ): 348 – 352 .
   Google Scholar
• Hooke , R. , Jeeves , T. ( 1961 ). Direct search solution of numerical and statistical problems . Journal of the ACM , 8 : 212 – 229 .
   Google Scholar
• Huang , J. ( 1999 ). An exact minimum zone solution for three-dimensional straightness evaluation problems . Precision Engineering , 23 : 204 – 208 .
   Google Scholar
• Huang , S. , Fan , K. , Wu , J. ( 1993 ). A new minimum zone method for evaluating straightness errors . Precision Engineering , 15 ( 3 ): 158 – 165 .
   Google Scholar
• International Organization for Standardization . ( 1983 ). Technical Drawings: Tolerancing of Form, Orientation, Location, and Runout—Generalities, Definitions, Symbols, Indications on Drawing, ISO: 1101-983(E) . Geneva , Switzerland : International Standards Organization .
   Google Scholar
• Kanada , T. ( 1995 ). Evaluation of spherical form errors—Computation of sphericity by means of minimum zone method and some examinations with using simulated data . Precision Engineering , 17 : 281 – 289 .
   Google Scholar
• Kanada , T. , Suzuki , S. ( 1993 ). Evaluation of minimum zone flatness by means of non-linear optimization techniques . Precision Engineering , 15 : 274 – 280 .
   Google Scholar
• Kim , K. , Lee , S. , Jung , H. ( 2000 ). Assesing roundness errors using discrte Voronoi diagrams . International Journal of Advanced Manufacturing Technology , 16 ( 8 ): 559 – 563 .
   Google Scholar
• Kim , W. , Raman , S. ( 2000 ). On selection of flatness measurement points using coordinate measuring machines . International Jounral of Machine Tools Manufacturing , 40 : 427 – 443 .
   Web of Science ®Google Scholar
• Kurfess , T. , Banks , D. ( 1995 ). Statistical verification of conformance to geometric tolerance . Computer Aided Design , 27 ( 5 ): 353 – 361 .
   Web of Science ®Google Scholar
• Lai , H. , Jywe , W. , Chen , C. , Liu , C. ( 2000 ). Precision modeling of form errors for cylindricity evaluation using genetic algorithms . Precision Engineering , 24 : 310 – 319 .
   Web of Science ®Google Scholar
• Lai , J.-Y. , Chen , I.-H. ( 1996 ). Minimum zone evaluation of circles and cylinders . International Journal of Machine Tools Design Research , 36 : 435 – 451 .
   Web of Science ®Google Scholar
• Lai , K. , Wang , J. ( 1988 ). A computational geometry approach to geometric tolerancing. Transactions of the 16th North American Manufacturing Research Conference, 376–379. Urbana, IL: Society for Manufacturing Engineers.
   Google Scholar
• Landau , U. ( 1987 ). Estimation of a circular arc center and its radius . Computer Vision, Graphics, and Image Processing , 38 : 317 – 326 .
   Google Scholar
• Le , V. , Lee , D. ( 1991 ). Out-of-roundness problem revisited . IEEE Transactions on Pattern Analysis and Machine Intelligence , 13 : 217 – 223 .
   Web of Science ®Google Scholar
• Lin , S. S. , Varghese , P. , Zhang , C. , Wang , H. ( 1995 ). A comparative analysis of CMM form-fitting algorithms . Manufacturing Review , 8 : 47 – 58 .
   Google Scholar
• Loebritz , D. ( 1993 ). CMM software: The key issue . Quality Today , s1 – s6 .
   Google Scholar
• Marshall , D. , Lukas , G. , Martin , R. ( 2001 ). Robust segmentation of primitives from range data in the presence of geometric degeneracy . IEEE Transactions on Pattern Analysis and Machine Intelligence , 23 ( 3 ): 304 – 314 .
   Web of Science ®Google Scholar
• Miller , L. ( 1962 ). Engineering Dimensional Metrology . London : Edward Arnold .
   Google Scholar
• Murthy , T. ( 1982 ). A comparison of different algorithms for cylindricity evaluation . International Journal of Machine Tool Design Research , 22 : 283 – 292 .
   Web of Science ®Google Scholar
• Murthy , T. ( 1986 ). A comparison of different algorithms for circularity evaluation . Precision Engineering , 8 ( 1 ): 19 – 23 .
   Web of Science ®Google Scholar
• Murthy , T. , Abdin , S. ( 1980 ). Minimum zone evaluation of surfaces . International Journal of Machine Tool Design Research , 20 : 123 – 136 .
   Web of Science ®Google Scholar
• Namboothiri , V. , Shunmugam , M. ( 1999 ). On determination of sample size in form error evaluation using coordinate metrology . International Journal of Production Research , 37 : 793 – 804 .
   Web of Science ®Google Scholar
• Nelder , J. A. , Mead , R. ( 1965 ). A simplex method for function minimization . Computer Journal , 7 : 308 – 313 .
   Web of Science ®Google Scholar
• Obeidat , S. M. ( 2008 ). Adaptive methods for form error determination in discrete point metrology. Unpublished Ph.D. dissertation, University of Oklahoma, Norman, OK.
   Google Scholar
• Prakasvudhisarn , C. , Trafalis , T. , Raman , S. ( 2003 ). Support vector regression for determination of minimum zone . Transactions of the ASME, Journal of Manufacturing Science and Engineering , 125 ( 4 ): 736 – 739 .
   Web of Science ®Google Scholar
• Preparata , F. , Shamos , M. ( 1985 ). Computational Geometry . New York : Springer-Verlag .
   Google Scholar
• Press , W. H. , Tuekolsky , S. A. , Vetterling , W. T. , Flannery , B. P. ( 1992 ). Numerical Recipes in C: The Art of Scientific Computing . Cambridge : Cambridge University Press .
   Google Scholar
• Raja , J. , Muralikrishnan , B. , Fu , S. ( 2002 ). Recent advances in separation of roughness, waviness, and form . Precision Engineering , 26 : 222 – 235 .
   Web of Science ®Google Scholar
• Rajagopal , K. , Anand , S. ( 1999 ). Assessment of circularity error using a selective data partition approach . International Journal of Production Research , 37 : 3959 – 3979 .
   Web of Science ®Google Scholar
• Ralston , A. , Rabinowitz , P. ( 2001 ). A First Course in Numerical Analysis, , 2nd ed. New York : Dover Publishers .
   Google Scholar
• Roy , U. , Xu , Y. ( 1995 ). Form and orientation tolerance analysis for cylindrical surfaces in computer-adied inspection . Computers in Industry , 26 : 127 – 134 .
   Web of Science ®Google Scholar
• Roy , U. , Zhang , X. ( 1992 ). Establishment of a pair of concentric circles with minimum radial separation for assessing roundness error . Computer Aided Design , 24 : 161 – 168 .
   Web of Science ®Google Scholar
• Shakarji , C. ( 1998 ). Least squares fitting algorithms of the NIST algorithm testing system . Journal of Research of the National Institute of Standards and Technology , 103 ( 6 ): 633 – 641 .
   PubMed Web of Science ®Google Scholar
• Shunmugam , M. ( 1986 ). On assessment of geometric errors . International Journal of Production Research , 24 : 413 – 425 .
   Web of Science ®Google Scholar
• Shunmugam , M. ( 1987a ). Comparison of linear and normal deviations of forms of engineering surfaces . Precision Engineering , 9 ( 2 ): 96 – 102 .
   Google Scholar
• Shunmugam , M. S. ( 1987b ). New approach for evaluating form errors of engineering surfaces . Computer Aided Design , 19 : 368 – 374 .
   Web of Science ®Google Scholar
• Takiyama , R. , Ono , N. ( 1989 ). A least square error estimation of the center and radii of concentric arcs . Pattern Recognition Letters , 10 : 237 – 242 .
   Web of Science ®Google Scholar
• Traband , M. , Mederios , D. , Chandra , M. ( 2004 ). A statistical approach to tolerance evaluation for circles and cylinders . IIE Transactions , 36 ( 8 ): 777 – 785 .
   Web of Science ®Google Scholar
• Traband , M. T. , Joshi , S. , Wysk , R. A. , Cavalier , T. M. ( 1989 ). Evaluation of straightness and flatness tolerances using the minimum zone . Manufacturing Review , 2 : 189 – 195 .
   Google Scholar
• Ventura , J. , Yerelan , S. (1989). The minimax center estimation problem for automated roundness inspection. European Journal of Operational Research , 41:64–72.
   Web of Science ®Google Scholar
• Wang , M. , Cheraghi , S. H. , Masud , A. S. M. ( 1999 ). Circularity error evaluation: Theory and algorithm . Precision Engineering , 23 : 164 – 176 .
   Google Scholar
• Wang , M. , Cheraghi , S. H. , Masud , A. S. M. ( 2001 ). Sphericity error evaluation: Theoretical derivation and algorithm development . IIE Transactions , 33 : 281 – 292 .
   Web of Science ®Google Scholar
• Wang , Y. ( 1992 ). Minimum zone evaluation of form tolerances . Manufacturing Review , 5 : 213 – 220 .
   Google Scholar
• Weber , T. , Motavalli , S. , Fallahi , B. , Cheraghi , S. H. ( 2002 ). A unified approach to form error evaluation . Precision Engineering , 26 : 269 – 278 .
   Web of Science ®Google Scholar
• Whitehouse , D. ( 2002 ). Surfaces and Their Measurement . New York : Taylor & Francis .
   Google Scholar
• Yang , P. , Qian , X. ( 2008 ). Adaptive slicing of moving least squares surfaces: Toward direct manufacturing of point set surfaces . ASME Journal of Computing and Information Science in Engineering , 8 : 1 – 11 .
   Google Scholar
• Yerelan , S. , Ventura , J. ( 1988 ). Computerized roundness inspection . International Journal of Production Research , 26 ( 12 ): 1921 – 1935 .
   Web of Science ®Google Scholar
• Zhu , L. , Ding , H. , Xiong , Y. ( 2003 ). A steepest descent algorithm for circularity evaluation . Computer Aided Design , 35 ( 3 ): 255 – 265 .
   Web of Science ®Google Scholar