A form tolerancing theory using fractals and wavelets

Journal of Mechanical Design, Transactions of the ASME

Volumn 119, Issue 2, 1997, Pages 185-193

  Srinivasan, R S ^a,b   Wood, K L ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b APPLIED MATERIALS INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BALL BEARINGS; DESIGN; FRACTALS; MECHANICAL ENGINEERING; WAVELET TRANSFORMS;

FORM TOLERANCING THEORY;

FITS AND TOLERANCES;

EID: 0031169481     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2826234     Document Type: Article

References (41)

1. Anton, H., 1984, Elementary Linear Algebra (4th edition). John Wiley & Sons, New York.
2. Arneodo, A., Argoul, F., Muzy, J. F., Pouligny, B., and Freysz, E., 1992, “The Optical Wavelet Transform,” Wavelets and Their Applications, Ruskai, M. B., ed., pp. 241-273, Jones and Bartlett Publishers, Boston.
3. Bendat, J. S., and Piersol, A. G., 1966, Measurement and Analysis of Random Data, John W’iley & Sons, Inc., New York.
4. Cliui, C. K., 1992, An Introduction to Wavelets, Wavelet Analysis and its Applications, Academic Press, Boston.
5. Daubechies, I., 1988, “Orthonormal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, Vol. XLI, No. 7, pp. 909-996.
6. Farge, M., Hunt, J. C. R., and Vassilicos, J. G, eds., 1993, Wavelets, Fractals, and Fourier Transforms, Oxford University Press, New York.
7. Flandrin, P., 1992, “Wavelet Analysis and Synthesis of Fractional Brownian Motion,” IEEE Transactions on Information Theory, Vol. 38, No. 2, pp. 910-917.
8. Gc, Q., Chen, B., Smith, P., and Menq, C. H., 1992, “Tolerance Specification and Comparative Analysis lor Computer-Integrated Dimensional Inspection,” International Journal of Production Research, Vol. 30, No. 9, pp. 2173-2197.
9. Jayaraman, R., and Srinivasan, V., 1989, “Geometric Tolerancing: Parts I and II,” IBM Journal of Research and Development. Vol. 33, No. 2, pp. 90-124.
10. Li, J. K., and Zhang, C., 1989, “Operational Dimensional and Tolerances Calculation in CAPP System for Precision Manufacturing,” Annals of the CIRP, Vol. 38, No. 1, pp. 403-406.
11. Mallat, S. G., 1989, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674-693.
12. Mallat, S. G., and Zhong, S., 1992, “Characterization of Signals from Multiscale Edges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 7, pp. 710-732.
13. Mandelbrot, B. B., 1983, The Fractal Geometry of Nature (2nd edition), W. H. Freeman and Co., San Francisco.
14. McKeown, P., 1987, “The Role of Precision Engineering in Manufacturing of the Future,” Annals of the CIRP, Vol. 36, No. 2, pp. 495-501.
15. Meyer, Y., 1987, “Orthonormal Wavelets,” Wavelets: Time-Frequency Methods and Phase Space, Combes, J. M., ed., pp. 21-37, Berlin, Springer Verlag.
16. Muzy, J. F., Bacry, E., and Arneodo, A., 1994, “The Multifractal Formalism Revisited with Wavelets,” International Journal of Bifurcation and Chaos, Vol. 4, No. 2, pp. 245-302.
17. Oppenheim, A. V., and Schafer, R. W., 1989, Discrete-Time Signal Processing. Prentice Hall, New Jersey.
18. Priestley, M. B., 1981, Spectral Analysis and Time Series, Vol. I, Academic Press, Inc., London.
19. Radhakrishnan, V., 1971, “On an Appropriate Radius for the Enveloping Circle for Roughness Measurement in the E-System,” Annals of the CIRP, Vol. 20, No. I, pp. 109-110.
20. Requicha, A. A., 1983, “Toward a Theory of Geometric Tolerancing,” The huernational Journal of Robotics Research, Vol. 2, No. 4, pp. 45-60.
21. Resnikoff, H. L., 1992, “Wavelets and Adaptive Signal Processing,” Optical Engineering, Vol. 31, No. 6, pp. 1229-1234.
22. Rioul, O., and Vetterli, M., 1991, “Wavelets and Signal Processing,” IEEE Signal Processing Magazine, pp. 14-38.
23. Sen, A., and Srivastava, M., 1990, Regression Analysis: Theory, Methods, and Applications Springer-Verlag, New York.
24. Shah, J., and Miller, D., 1989, “A Structure for Supporting Geometric Tolerances for Computer Integrated Manufacturing,” Proceedings of the ASM E Annual Meeting, pp. 344-351.
25. Srinivasan, R. S., 1994, “A Theoretical Framework for Functional Form Tolerances in Design for Manufacturing,” Ph.D. thesis, The University of Texas, Austin, TX.
26. Srinivasan, R. S., and Wood, K. L., 1992a, “A Computational Investigation into the Structure of Form and Size Errors Based 011 Machining Mechanics,” Advances in Design Automation 1992, Vol. I, pp. 161-171, Phoenix, AZ, ASME.
27. Srinivasan, R. S., and Wood, K. L., 1992b, “Fractal-Based Geometric Toleranc-ing in Mechanical Design,” Proceedings of the 1992 ASME DTM Conference. pp. 107-115 Phoenix, AZ.
28. Srinivasan, R. S., and Wood, K. L., 1995, “Geometric Tolerancing in Mechanical Design Using Fractal-Based Parameters,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 117, No. 1, pp. 203-205.
29. Srinivasan, R. S., Wood, K. L., and McAdams, D., 1996, “A Methodology for Functional Tolerancing in Design for Manufacture.” Journal of Research in Engineering Design, Vol. 8, No. 2, pp. 99-115.
30. Stupak, P. R., Syu, C. Y., and Donovan, J. A., 1992, “The Effect of Filtering Proiilometer Data on Fractal Parameters,” Wear, Vol. 154, No. I, pp. 109-114.
31. Tipnis, V. A., ed., 1992, Tolerance and Deviation Information, New York, ASME CRTD-15-1.
32. Turner, I. Y., Srinivasan, R. S., and Wood, K. L., 1995, “Investigation of Characteristic Measures for the Analysis and Synthesis of Precision-Machined Surfaces,” SME Journal of Manufacturing Systems, Vol. 14, No. 5, pp. 378-392.
33. Turner, J. U., and Wozny, M. J., 1990, “The M-Space Theory of Tolerances,” Advances in Design Automation, 1990. Vol 1., Ravani, B. ed., pp. 217-225. ASME.
34. Vasseur, FI., Kurless, T., andCagan, J., 1993, “Optimal Tolerance Allocation for Improved Productivity,” Proceedings of the 1993 NSE Design and Manufacturing Systems Conference, pp. 715-719 Charlotte, NC. NSF, SME.
35. Walker, R. K., and Srinivasan, V., 1993, “Creating a Standard: YI4.5.1,” Quality, Vol. 32, pp. 24-28.
36. Wardle, F. P., 1988, “Vibration Forces Produced by the Waviness of the Rolling Surfaces of Thrust Loaded Ball Bearings-Parts 1 and 2,” Proceedings of the Institution of Mechanical Engineers, Vol. 202, No. C5, pp. 305-319.
37. Whitehouse, D. J., 1978, “Surfaces-A Link between Manufacture and Design,” Proceedings of the Institution of Mechanical Engineers, Vol. 192, pp. 179-188.
38. Whitehouse, D. J., and Vanherck, P., 1972, “Survey of Reference Lines in the Assessment of Surface Texture,” Annals of the CIRP, Vol. 21, No. 2, pp. 267-273.
39. Wick, C., ed., 1987, Measurement of Circularity (4th edition), Vol. IV of Tool and Manufacturing Engineers Handbook, Chap. 4, pp. 427-432, Society of Manufacturing Engineers, Dearborn, Michigan.
40. Worncll, G. W., 1991, “Synthesis, Analysis, and Processing of Fractal Signals,” Tech. rep. 566, Massachusetts Institute of Technology, Cambridge, MA.
41. Zhang, H. C., and Huq, M. E., 1992, “Tolerancing Techniques: The State-of-thc-Art,” International Journal of Production Research, Vol. 30, No. 9, pp. 2111-2135.