The submacrogeometric (tolerance) variations of mechanical components have an important impact on product function. The problem of combining tolerance assignment in engineering design with tolerance control in manufacturing and quality assurance presents a continuing challenge to researchers. This paper illustrates the feasibility of using fractal-based methods for the problem of tolerance specification in engineering design. Error data are generated as a function of the fractal dimension using the fractional Brownian motion model and are superposed on an ideal profile of a slider bearing. The consequent changes in performance parameters are studied and the detrimental effect of large variations perceived. This simple case study indicates the potential of the method to be extended for more complex problems.
Issue Section:
Technical Briefs
1.
ANSI-Y14.5M, 1982, “Geometric Dimensioning and Tolerancing,” ANSI Standard Y14.5M-82.
2.
Bjorke, O., 1989, Computer-Aided Tolerancing, ASME Press, New York.
3.
Chase, K. W., and Greenwood, W. H., 1987, “Design Issues in Mechanical Tolerance Analysis,” Advanced Topics in Manufacturing Technology, pp. 11–26, ASME Winter Annual Meeting, Boston, MA.
4.
Christensen
H.
1969
, “Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces
,” Proc. of the Instn. of Mech. Engrs.
, Vol. 184
, Pt. 1, No. 55
, pp. 1013
–1026
.5.
Finger
S.
Dixon
J. R.
1989
, “A Review of Research in Mechanical Design. Part II: Representations, Analysis and Design for the Life Cycle
,” Research in Engineering Design
, Vol. 1
, No. 2
, pp. 121
–137
.6.
Hargreaves
D. J.
1991
, “Surface Waviness Effects on the Load-Carrying Capacity of Rectangular Slider Bearings
,” Wear
, Vol. 145
, No. 1
, pp. 137
–151
.7.
Jaggard
D. L.
Kim
Y.
1987
, “Diffraction by Band-Limited Fractal Screens
,” Journal of the Optical Society of America A
, Vol. 4
, No. 6
, pp. 1055
–1062
.8.
Jayaraman
R.
Srinivasan
V.
1989
, “Geometric Tolerancing: Parts I and II
,” IBM Journal of Research and Development
, Vol. 33
, No. 2
, pp. 90
–124
.9.
Lin
B. C.
Gossard
D. C.
Light
R. A.
1981
, “Variational Geometry in Computer-Aided Design
,” Computer Graphics
, Vol. 15
, No. 3
, pp. 171
–177
.10.
Mandelbrot, B. B., 1983, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco.
11.
Martino, P. M., and Gabriele, G. A., 1989, “Application of Variational Geometry to the Analysis of Mechanical Tolerances,” ASME Advances in Design Automation, Ravani, B., ed., pp. 19–27.
12.
Ostwald
P. F.
Huang
J.
1977
, “A Method for Optimal Tolerance Selection
,” ASME Journal of Engineering for Industry
, Series B, Vol. 99
, No. 3
, pp. 558
–565
.13.
Peitgen, H. O., and Saupe, D., 1988, The Science of Fractal Images, Springer Verlag, New York.
14.
Peklenik
J.
Jerele
A.
1992
, “Some Basic Relationships for Identification of the Machining Processes
,” Annals of the CIRP
, Vol. 41
, No. 1
, pp. 155
–159
.15.
Requicha
A. A.
1983
, “Toward a Theory of Geometric Tolerancing
,” The International Journal of Robotics Research
, Vol. 2
, No. 4
, pp. 45
–60
.16.
Siddall, J. N., 1983, Probabilistic Engineering Design, Marcel Dekker Inc., New York.
17.
Srinivasan, R. S., and Wood, K. L., 1992a, “A Computational Investigation into the Structure of Form and Size Errors Based on Machining Mechanics,” ASME Advances in Design Automation 1992, Vol. 1, pp. 161–171, Phoenix, AZ.
18.
Srinivasan, R. S., and Wood, K. L., 1992b, “Fractal-Based Geometric Tolerancing in Mechanical Design,” ASME Proceedings of the 1992 ASME DTM Conference, pp. 107–115, Phoenix, AZ.
19.
Srinivasan, R. S., and Wood, K. L., 1993, “Wavelet Transforms in Fractal-Based Form Tolerancing,” ASME Design Theory and Methodology-DTM ’93, Hight, T. K., ed., pp. 51–63, Albuquerque, NM.
20.
Taguchi, G., 1986, Introduction to Quality Engineering, Asian Productivity Organization, Unipub, White Plains, NY.
21.
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.
22.
Vasseur, H., Kurfess, T., and Cagan, J., 1993, “Optimal Tolerance Allocation for Improved Productivity,” Proceedings of the 1993 NSF Design and Manufacturing Systems Conference, pp. 715–719, Charlotte, NC. NSF, SME.
This content is only available via PDF.
Copyright © 1995
by The American Society of Mechanical Engineers
You do not currently have access to this content.
