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Unread 03-07-2008, 15:59
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AKA: Mark Kramarczyk
FRC #3096 (Highlanders)
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Re: 6WD Chassis Stiffness vs. Maneuverability

Quote:
Originally Posted by kramarczyk View Post
A low CG certainly does help you withstand higher turning moments, but it does not help you generate them.

For those that have read Chris Hibner's whitepaper on turning (http://www.chiefdelphi.com/media/papers/1443), which is everybody I hope, it looks at the individual contribution of each wheel to the turning moment, so I suggest we start here. The moment is generated at each wheel by the coefficient of friction (CoF) and normal force (Fn) at each wheel. I think that the CoF is largely understood as demonstrated by the unusual wheel choices cited above. So what changes the Fn at each wheel? Simplifying the frame as a series of beams for discussion we can reference some stock solutions for the beams with 3 supports; based upon a uniform load the 3 moment equations show that the center axle would support 62.5% of the load with 18.75% for the outer axles. A snapshot of this eqn is in a previous post here.
Apparently that got submitted early... whoops. To finish my point...

<theory>
When driving on concrete (or a similar surface) my observations have been that the chassis drives very similarly to how this distribution suggests, however, when we put them on carpet it can be very different. Many attribute this to the CoF change on the carpet, but I think that the Fn also changes as the carpet compresses under the bot like a spring. (See attached spreadsheet.) This is why lowering the center wheels improves the turning of a chassis. Yes, the center wheels can be lowered to the point of rocking, but my 3+ minutes of bot driving time suggest that rocking between 4x4 cg aft and 4x4 forward is not a pleasant experience. A lot of folk do manage it though and they are amazing.

So how does the stiffness of the frame play into this...

Assuming the carpet is spring 'like', the deflection of the frame limits the difference in deflection of the 'springs' under each wheel which eats into the wheel drop. The stiffer the frame, the less wheel drop lost.

In working terms, a stiffer frame requires less wheel drop to move the weight to the center than a less stiff frame. Consequentially a stiffer frame is also more greatly influenced by a change in wheel drop than a less stiff frame. i.e. a more flexible frame is more robust to wheel drop.

</theory>

Unfortunately, the situation is statically indeterminate so I don't have a set of equations to conduct an optimization study with.
Attached Files
File Type: xls 20080703 - Carpet Compression.xls (26.5 KB, 92 views)
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Brick walls are for other people. - Randy Pausch