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#1
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Re: Contact Area and its Relation to Friction?
The rule that static friction does not depend upon contact area is a first-order approximation only. If a first-order rule is good enough, go ahead and use it.
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#2
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Re: Contact Area and its Relation to Friction?
Contact area has no significant impact on static friction in the FIRST world. As mentioned earlier, Normal Force can be defined as Pressure multiplied by Area, but in this scenario Pressure is equal to Normal Force/Area. So your pressure will decrease at the same rate your area increases, resulting in your Normal Force remaining the same. As such, your traction will remain the same. Granted you want to have large enough wheel that the tread won't fail (nor the carpet).
As for the debate on PID traction systems, couldn't it be accomplished by comparing the data from the encoders in the drive to an accelerometer? If the acceleration of the wheels is greater than the acceleration of the robot, wouldn't it determine that they are spinning out? I speak purely out of speculation, and I don't have any real experience developing PID systems, but it seems like that solution could be possible to me. |
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#3
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Re: Contact Area and its Relation to Friction?
This is an interesting thread.
Short disclaimer: I have yet to take physics, so anything I write is a result of observation. Anywhoo. I think I understand what people here are talking about, yet I'm still confused. If everyone says that the contact area doesn't matter, then can someone explain how this makes sense: I built two robots. Both were with the kitbot chassis. Both were driven off of Banebots transmissions. Both had two driven wheels, and two casters. One bot had two andymark kit wheels per axle for driving, and the other had only one per axle. I added extra weight on each in order to make the weight exactly equal. I wired both motors to a single battery and switch. Then I put the two drive bases head to head, set so they would drive directly into each other, on an area of FIRST carpet. When turned on, the base with 2 wheels per axle could overcome and outpush the other base every time. We did this 12 times, each time changing to a new, fresh battery. Anyone care to help me out here? I guess that physics and math and stuff say this shouldn't work, but it did. So I'm confused. |
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#4
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Re: Contact Area and its Relation to Friction?
Quote:
Thursday night another 1885 mentor was under the impression that traction control isn't needed at all. I see the greatest advantage during climbing ramps; he says our "drive straight" code takes care of that since it uses the gyro & encoders to keep us going in a straight line. Not sure how to argue it with him that it's hard to not over-compensate with the gyro technique, but perhaps he's correct and it's enough for the time being. No student is advanced enough in programming yet to be able to take interest in it, but maybe we can throw it in there late in the season. Low-gear + high-torque situations are the next advantageous place to use it. |
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#5
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Re: Contact Area and its Relation to Friction?
Where did you put the weights to equalize the mass of the two 'bots? I ask because if there was more weight directly over the double-wheel's driven wheels it would behave as you describe.
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#6
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Re: Contact Area and its Relation to Friction?
Friction, as taught in introductory physics courses, is a macroscopic empirical model. The model does surprisingly well, much better than an empirical model should do, but one should be careful in how far one takes it. One should not assume that the dogma of the empirical model is true for every possible situation.
Your approach of actually measuring the effect of doubling up on the wheel surface area for your given situation is the right one to take. Don't be surprised when the data shows that the empirical model is a little out of step with reality. There will be those that say that there is a lot more going on than the simple friction when a wedgetop, or roughtop, tread is forced to slide across an industrial carpet, and this is true. There is also something much more complicated than the simple macroscopic empirical friction model going on when two "hard surfaces" are sliding across each other, when you actually look at the microscopic details of what is happening at the atomic level, which you must do to understand the physical process in a predictive manner. Eugene Quote:
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#7
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Re: Contact Area and its Relation to Friction?
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Lets take bot A and bot B, both bots have X amount of weight. The coefficient of friction between the wheels and the ground is Us Bot A has 6 wheels, 4 of which are powered, so, 2/3rdsX * Us is the max tractional force provided. Bot B has 4 wheels, 2 of which are powered, so 1/2X*Us is the max tractional force. This is, assuming, of course, that the distribution of weight and the wheel spacing is perfectly even. |
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#8
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Re: Contact Area and its Relation to Friction?
Alrighty. This is where being a gearhead my entire life pays off.
FACT 1: As a vehicle turns, the contact patch (and weight) move to the outside of the tires. re: if a vehicle makes a right turn, the contact patch moves to the left sides of the tires. That's why you see road racing cars with lots of negative camber (wheels angled inward towards the top). This keeps the contact patch closer to the insides of a tire, and when the car makes a corner, the outside tire keeps more contact with the ground. FACT 2: As a vehicle accelerates, weight tranfers to the rear, making the rear contact patch wider, and the front contact patch thinner. That's why FWD cars STINK at drag racing. FACT 3: The faster a vehicle is moving, the more it's weight tranfers in a corner. That's why cars get "body lean", or leans towards the outside of the corner. Some cars (especially Volkswagen Corrados) even lift the inside rear tire when braking and turning hard. FACT 4: THE MORE CONTACT THE BETTER, unless on a soft, malleable surface, such as snow. FACT 5: The stiffer the chassis, the more contact all tires will have with the ground at all times. Hence, a flimbsy chassis will handle MUCH worse than one that stays stiff and keeps all tires in contact with the ground. FACT 6: The lower the center of gravity, the better. That's why cars lowered on a good suspension setup (stiff) always handle better than stock. The higher the center of gravity the vehicle has, the more the weight will transfer. Say a vehicle is making another right-hand turn. A high center of gravity will lead to very thin contact patches on the outsides of the right-side tires, and a contact patch that may even shrink towards the outsides of the left-side tires. These are simple terms. I am taking my first physics class, and I source all of this information from my vehicluar knowledge. PLEASE CORRECT ME IF THESE FACT SEEM INNACURATE. I see no need to break the traction of a 10 ft/s robot down into static or dyanic friction. You simply need to know where that friction is and how to maximize it. Last edited by cobrawanabe1699 : 16-01-2008 at 21:29. |
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