[+] Author and Article Information
Aniket N. Chitale

Design Automation Laboratory Department of Mechanical and Aerospace Engineering Tempe, AZ 85287-6106 achitale@asu.edu

Joseph K. Davidson

Mechanical Engineering Tempe, AZ 85287-6106 J.Davidson@asu.edu

Jami Shah

201 W 19th Ave Columbus, OH 43210 shah.493@osu.edu

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received August 7, 2018; final manuscript received January 31, 2019; published online xx xx, xxxx. Assoc. Editor: Kristina Wärmefjord.

ASME doi:10.1115/1.4042838 History: Received August 07, 2018; Accepted February 01, 2019


Math models aid designers in assessing relationships between tolerances that contribute to variations of a dependent dimension which must be controlled to achieve some design function at a target feature. The T-Maps model that represents limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each contributing tolerance of the relationship. For every contributing feature and tolerances specified on it, the appropriate T-Map is chosen from a library of T-Maps, each represented in its own respective local reference frame. Each chosen T-Map is then transformed to the coordinate frame at the target feature, and the accumulation T-Map of these is formed with the Minkowski sum. The shape of a functional T-Map/deviation space is circumscribed (fitted) to this accumulation map. Since fitting is accomplished numerically by intersecting geometric shapes, T-Maps/deviation spaces are constructed with linear half-spaces. The sensitivity for each tolerance-feature combination is determined by perturbing the tolerance, refitting the functional shape to the modified accumulation map, and forming a ratio of the increment of functional tolerance to the perturbation. Taking tolerance-feature combinations one-by-one, sensitivities for an entire stack can be built. For certain loop equations, the same sensitivities result by fitting the functional shape to the T-Map for each feature, without a Minkowski sum, and forming the overall result as a scalar sum. Sensitivities are used to identify tolerances that most influence the dependent dimension at the target feature.

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