Full Text:
<4029>
Summary: 
<2166>
CLC number: TH161
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2015-04-15
Cited: 3
Clicked: 7897
Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments
| ||||||||||||||
Yifei He, Joseph K. Davidson, Jami J. Shah. Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments[J]. Journal of Zhejiang University Science A, 2015, 16(5): 341-352.
@article{title="Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments",
author="Yifei He, Joseph K. Davidson, Jami J. Shah",
journal="Journal of Zhejiang University Science A",
volume="16",
number="5",
pages="341-352",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1400239"
}
%0 Journal Article
%T Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments
%A Yifei He
%A Joseph K. Davidson
%A Jami J. Shah
%J Journal of Zhejiang University SCIENCE A
%V 16
%N 5
%P 341-352
%@ 1673-565X
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1400239
TY - JOUR
T1 - Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments
A1 - Yifei He
A1 - Joseph K. Davidson
A1 - Jami J. Shah
J0 - Journal of Zhejiang University Science A
VL - 16
IS - 5
SP - 341
EP - 352
%@ 1673-565X
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1400239
Abstract: For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to describe a new method of construction, using computer-aided geometric design, which can produce the T-Map for any line-profile. The new method requires decomposing a profile into segments, creating a solid-model T-Map primitive for each, and then combining these by boolean intersection to generate the T-Map for a complete line profile of any shape. To economize on length, the scope of this paper is limited to line-profiles formed from circular arc-segments. The parts containing the line-profile features are considered to be rigid.
T-maps have been the key concept of tolerancing modeling literature for the last two decades. Its creators have developed and documented it through many papers, each providing an extension to new types of tolerances and insights for possible applications in tolerance analysis. The submitted paper may have little incremental value but contributes to the whole body of work, which I hope to see in a dedicated book before long.
[1]ASME (American Society of Mechanical Engineers), 2009. Dimensioning and Tolerancing, ASME Y14.5. ASME, New York.
[2]Ameta, G., Samper, S., Giordano, M., 2011. Comparison of spatial math models for tolerance analysis: Tolerance-Maps, deviation domain, and TTRS. ASME Journal of Computing and Information Science in Engineering, 11(2):021004.
[3]Apostol, T.M., Mnatsakanian, M.A., 2012. New Horizons in Geometry. Mathematical Association of America, Washington, DC.
[4]Davidson, J.K., Shah, J.J., 2012. Modeling of geometric variations for line-profiles. ASME Journal of Computing and Information Science in Engineering, 12(4):041004.
[5]Davidson, J.K., Mujezinović, A., Shah, J.J., 2002. A new mathematical model for geometric tolerances as applied to round faces. ASME Journal of Mechanical Design, 124(4):609-622.
[6]Davidson, J.K., Shah, J.J., Mujezinović, A., 2005. Method and Apparatus for Geometric Variations to Integrate Parametric Computer-aided Design with Tolerance Analysis and Optimization. US Patent No. 6963824, Washington, DC.
[7]Giordano, M., Duret, D., 1993. Clearance space and deviation space: application to three-dimensional chains of dimensions and positions. In: Bourdet, P., Mathieu, L. (Eds.), Proc. 3rd CIRP Seminar on Computer-aided Tolerancing, Eyrolles, Paris, p.179-196.
[8]Giordano, M., Pairel, E., Samper, S., 1999. Mathematical representation of tolerance zones. In: van Houten, F., Kals, H. (Eds.), Global Consistency of Tolerances. Springer, Amsterdam, p.177-186.
[9]Hain, K., 1967. Applied Kinematics, 2nd Edition. McGraw-Hill, New York.
[10]He, Y., Davidson, J.K., Shah, J.J., 2013. Tolerance-Maps for line-profiles constructed from Boolean operations on primitive T-Map elements. 33rd ASME Computers and Information in Engineering Conference, Portland, OR. ASME, New York, USA, p.V02AT02A003.
[11]ISO (International Organization for Standardization), 1987. Technical Drawings—Dimensioning and Tolerancing of Profiles, ISO 1660. ISO, Geneva.
[12]Mujezinović, A., Davidson, J.K., Shah, J.J., 2004. A new mathematical model for geometric tolerances as applied to polygonal faces. ASME Journal of Mechanical Design, 126(3):504-518.
[13]Pasupathy, T.M.K., Morse, E.P., Wilhelm, R.G., 2003. A survey of mathematical methods for the construction of geometric tolerance zones. ASME Journal of Computing and Information Science in Engineering, 3(1):64-75.
[14]Roy, U., Li, B., 1999. Representation and interpretation of geometric tolerances for polyhedral objects. II: size, orientation and position tolerances. Computer-Aided Design, 31(4):273-285.
[15]Spatial Co., 2012. ACIS, Release: R23. Available from http://doc.spatial.com/index.php/Portal:ACIS [Accessed on Nov. 12, 2014]
[16]Uicker, J.J., Pennock, G.R., Shigley, J.E., 2010. Theory of Machines and Mechanisms, 4th Edition. Oxford University Press, Oxford.
Open peer comments: Debate/Discuss/Question/Opinion
<1>