This paper examines the scaling of an energetic system to meet new design requirements while satisfying dynamic similitude. The literature defines such similitude discretely, in terms of whether the scaled design satisfies monomial scaling laws derived via the Pi Theorem (or its group-theoretic extensions). Previous work adds flexibility to this approach by using activity analysis to (i) assess the relative importance of scaling laws and (ii) neglect less important ones. Difficulties still arise when scaling laws deemed important cannot be followed exactly (e.g., due to design constraints), thus precluding exact similitude. To address these difficulties, this paper proposes the first continuous measure of approximate similitude, namely, the activity-weighted deviation of a system design from exact similitude. The paper then presents a multiobjective scaling framework that trades approximate similitude off versus other scaling requirements and constraints. Two examples, pertaining to quarter-car and fuel cell air supply scaling, demonstrate the proposed approach.
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ASME 2007 International Mechanical Engineering Congress and Exposition
November 11–15, 2007
Seattle, Washington, USA
Conference Sponsors:
- ASME
ISBN:
0-7918-4303-3
PROCEEDINGS PAPER
Approximate Dynamic Similitude in Energetic Multi-Domain Systems: Quantification and Use in Multiobjective Scaling
Burit Kittirungsi,
Burit Kittirungsi
University of Michigan, Ann Arbor, MI
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Hosam K. Fathy,
Hosam K. Fathy
University of Michigan, Ann Arbor, MI
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Jeffrey L. Stein
Jeffrey L. Stein
University of Michigan, Ann Arbor, MI
Search for other works by this author on:
Burit Kittirungsi
University of Michigan, Ann Arbor, MI
Hosam K. Fathy
University of Michigan, Ann Arbor, MI
Jeffrey L. Stein
University of Michigan, Ann Arbor, MI
Paper No:
IMECE2007-42045, pp. 853-864; 12 pages
Published Online:
May 22, 2009
Citation
Kittirungsi, B, Fathy, HK, & Stein, JL. "Approximate Dynamic Similitude in Energetic Multi-Domain Systems: Quantification and Use in Multiobjective Scaling." Proceedings of the ASME 2007 International Mechanical Engineering Congress and Exposition. Volume 9: Mechanical Systems and Control, Parts A, B, and C. Seattle, Washington, USA. November 11–15, 2007. pp. 853-864. ASME. https://doi.org/10.1115/IMECE2007-42045
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