A new mathematical model for representing the geometric variations of lines is extended to include form and accumulation (stackup) of tolerances in an assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map©, a hypothetical volume of points which corresponds to all possible locations and variations of a segment of a line (the axis) which can arise from tolerances on size, position, orientation, and form. Every Tolerance-Map is a convex set in a metric space. The new model makes stackup relations apparent in an assembly, and these can be used to allocate size and orientational tolerances; the same relations also can be used to identify sensitivities for these tolerances. All stackup relations can be met for 100% interchangeability or for a specified probability. Much of the detail in this paper would probably reside internally to software for designers, yet would not be included in the interface; its workings should be invisible to the user.
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ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 2–6, 2003
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-3700-9
PROCEEDINGS PAPER
A New Mathematical Model for Geometric Tolerances as Applied to Axes
J. K. Davidson,
J. K. Davidson
Arizona State University, Tempe, AZ
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J. J. Shah
J. J. Shah
Arizona State University, Tempe, AZ
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S. Bhide
Hewlett Packard Company, Vancouver, WA
J. K. Davidson
Arizona State University, Tempe, AZ
J. J. Shah
Arizona State University, Tempe, AZ
Paper No:
DETC2003/DAC-48736, pp. 329-337; 9 pages
Published Online:
June 23, 2008
Citation
Bhide, S, Davidson, JK, & Shah, JJ. "A New Mathematical Model for Geometric Tolerances as Applied to Axes." Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2: 29th Design Automation Conference, Parts A and B. Chicago, Illinois, USA. September 2–6, 2003. pp. 329-337. ASME. https://doi.org/10.1115/DETC2003/DAC-48736
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