TY - GEN

T1 - Using tolerance-maps to generate frequency distributions of clearance for pin-hole assemblies

AU - Ameta, Gaurav

AU - Davidson, Joseph K.

AU - Shah, Jami J.

PY - 2006

Y1 - 2006

N2 - A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of 1-D clearance which arise from multi-dimensional variations of an axis, a hole and a pin-hole assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map1 (T-Map), a hypothetical volume of points that models the 3-D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increase in yield that occurs when maximum material condition (MMC) is specified. The frequency distribution of 1-D clearance is decomposed into manufacturing bias, i.e. toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is focused on geometric bias and manufacturing bias is presumed to be uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole.

AB - A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of 1-D clearance which arise from multi-dimensional variations of an axis, a hole and a pin-hole assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map1 (T-Map), a hypothetical volume of points that models the 3-D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increase in yield that occurs when maximum material condition (MMC) is specified. The frequency distribution of 1-D clearance is decomposed into manufacturing bias, i.e. toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is focused on geometric bias and manufacturing bias is presumed to be uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole.

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U2 - 10.1115/detc2006-99585

DO - 10.1115/detc2006-99585

M3 - Conference contribution

AN - SCOPUS:33751337380

SN - 079183784X

SN - 9780791837849

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - Proceedings of 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006

PB - American Society of Mechanical Engineers (ASME)

T2 - 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006

Y2 - 10 September 2006 through 13 September 2006

ER -