Shape sensitivity analysis and design studies for CAD flume sections |
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Authors: | Kuang-Hua Chang |
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Affiliation: | (1) Concurrent Design and Manufacturing Research Laboratory and School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA |
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Abstract: | This paper presents shape design sensitivity analysis (DSA) and design studies for recreational waterslides represented in
computer-aided design (CAD) environment. The mathematical representations of a number of commonly used flume sections that
serve as the building blocks for waterslide configurations are created in CAD tools. Geometric dimensions of the individual
sections that affect not only their geometric shape but also the overall configurations are identified as design variables.
These design variables can be varied to search for better design alternatives, for example, safer waterslides. A set of coupled
differential equations based on Lagrange’s equations of motion that describe the motion of the riding object are derived.
The equations of motion incorporate friction forces between the riding object and the surface of the flume sections. These
second-order differential equations are then solved using Mathematica. Based on the equations of motion and design variables
identified, a set of differential equations are derived for calculating shape DSA coefficients. These equations are solved
numerically again using Mathematica. The major contribution of the paper are (1) extending waterslide design parameterization
and shape DSA computation to true CAD-based flume sections, which greatly alleviates the design for manufacturing issues previously
encountered, (2) incorporating friction forces into shape DSA computation, and (3) developing a design scenario that includes
sensitivity display and what-if studies for a compromised design that is safer and with a larger acceleration, therefore,
higher excitement levels. Incorporating friction forces into the computation supports design for rider’s excitement levels,
which are related to accelerations. Waterslide design will not be realistic without including friction forces. |
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Keywords: | Computer-aided design Design study Design sensitivity analysis Waterslides |
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