Saturday, May 28, 2005

Loads estimate proposal for Holcombe Chassis


I've given Brian Holcombe a proposal for a simple estimate of loads and stress on his chassis design, in which the chassis is treated as a planar beam, as seen in the diagram above.

Assumptions:
  1. Treat wheels as pinned joints, resisting translation in x- and y-directions.
  2. Treat load f (x) as not predefined, regardless of what it looks like in the diagram above. The actual values can be loaded into a spreadsheet.
  3. Shear and moment diagrams will follow rules for a simple beam: the only discontinuities in these diagrams occur at the wheels. Equations of statics will then yield the reaction forces at the wheels.
  4. Horizontal or axial forces are ignored for now.
  5. For stress calculations, the cross-section of the chassis will be assumed to be concentric rectangles, with appropriate area moment of inertia:

    Izz = (bo ho3 – bi hi3) / 12

    where bo, bi == base of outer, inner rectangle; ho, hi == height of outer, inner rectangle, respectively.
  6. The spreadsheet can then be used to calculate bending stress:

    sigma == M c / Izz

    and shear stress:

    tau == P / A

    where M = bending moment; c = distance from neutral axis; P = active force; A = cross-sectional area. The neutral axis will go through the center of the cross-section, so c == ho / 2.
  7. The spreadsheet will find the maximum values of these two stresses, and that of their resultant. This analysis will verify what’s been done experimentally to date.
Brian believes, and I have no reason not to agree, that he has overengineered the chassis design. But I think some simple calculations will give him conviction -- something more powerful than belief -- and will look good in the next generation of his business plan as well.

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posted by Ron @ 1:14 PM

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