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Contact Area and its Relation to Friction?
Ok, I've searched around and have found many posts on CD dealing with this question... but no one has given a concrete answer.
As many of you know... a normal force * coefficient of friction = friction force... at least in everybody's text book. Obviously more contact area increases traction, or else race cars would have little skinny tires, not big fat wide tires. So... where does contact area factor in to friction force? I think it might have something to do with the non-homogeneous nature of tires and carpet or tires and asphalt or whatever the contact situation may be in most real world tire/track/other land propulsion applications... but I don't have an equation to give me friction force with non-homogeneous surfaces in that case. I'm hoping i don't have to break down and dervie a formula from empirical data, but if thats what has to happen so be it. Does anyone have a concrete (preferrably mathematical) answer to this vexing (or first-ing ;) ) problem? Thanks CD'ers/FIRST'ers, -q |
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Q,
Andy Baker or Raul Olivera will have a good handle on this question. You may want to PM them or use the email option directly in case they haven't seen this thread. |
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This isn't exactly a mathematical answer, but a quick search on google gives this link:
http://www.physlink.com/Education/As...TOKEN=72229625 Remember that most physics books deal in an ideal world where most things are point masses and all surfaces are completely uniform and flat. Consider too that since Force=Pressure*Area, that as area goes up, pressure can go down resulting in tires that can be made of softer materials or in the case of pnuematic tires, thinner walls because they need to contain lower air pressure. (but I'm a Computer Engineer not a Mechanical one, and could be completely wrong too) |
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Dragster tires are extremely wide because dynamic friction does depend on contact area, and they want to maximize the acceleration even when the tires slip. |
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We found that there is a very, very slight (under 5%) advantage to having a larger surface area on the plastic. This could have been due to a number of things... but each time we pulled on a larger area sample, it took a bit more force to move our object. We also found this same slight advantage (about 5%) when comparing treads to wheels on carpet. A treaded robot was a bit harder to move.* In both cases, there is not an ideal flat-to-flat surface interaction. I believe that the mechanical interaction between one surface and the other creates this slight advantage for larger surfaces. It's easy to see between wheels and carpet, and it's at a smaller scale between rubber and HDPE. * - This test was enough to prove to me that treads on a FIRST robot were NOT worth the effort. We did treads in 99, 01, 02, 03, but not ever since. We were very surprised at the results and did not see the 5% advantage justify the effort to do treads. Even though there is this 5% increase in the friction coefficient, a track system has more efficiency losses (maybe as high as 5% more, to offset the friction advantages) and uses more hardware to make the system weigh more. I'll contend that a wheeled FRC robot will push with as much force (within 3%) as a tank tread robot, as long as some conditions are met: 1. The robots weigh the same 2. The robots have similar Cg locations 3. The tread material for the wheels and treads are the same 4. There is a PID control system for the wheels (and the treads, to make it fair) so they don't slip All of these friction comparisons above were between STATIC situations. During a static comparison (when the wheels or treads are not spinning or moving), then the friction is very close. I believe that in FIRST, a wheeled robot with good treads on the wheels will hold it's ground very well until the wheels start spinning and DYNAMIC traction starts to come into play. Possibly the reason why treaded robots push around wheeled robots at times in FIRST is because wheeled robots get into dynamic friction situations by not having a traction limiting program, like PID control. This is definitely an area where more testing is needed. I am sure that others out there have opinions on this, and I am eager to see what people say. Andy B. |
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An example of friction being weird: Most material interfaces have a higher coefficient of static friction, than of dynamic friction. But aluminum to aluminum has a higher coefficient of dynamic friction than static friction. And when you consider automobile tires, think about what might be happening when the situation in my avatar occurs.... Good luck! |
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Another impact of contact area is in turning itself. We all know that the bots turn different on a hard floor like concrete than on the competition carpet.
<speculation>The carpet under the wheel locally acts like a spring. We know that things sitting on carpet sink in some amount (especially obvious when moving furnature) and the the area of carpet engaged affects how far into the carpet the item sinks. Therefore by increasing the size of the wheels contact patch (relative to the other wheels) we can affect the amount the wheel sinks into the carpet. <edit> ...by making the larger carpet patch behave like a stiffer spring</edit></speculation> How does this impact the friction? By moving changing the normal forces. It won't change the overall pushing capacity of the bot, but it will allow us to change which wheels have the majority of the traction. This is really what we are doing when we drop the center wheel of a 6x6 after all isn't it. So by widening the center wheel we can move the normal forces to the center axle which lessens the normal loads at the corners... reducing skidding forces... making it easier to turn... with less wheel drop (and rock)... without giving up pushing force. Attached is a crude spreadsheet attempting to explain my point. p.s. I am working on getting hard data to back-up my point, but until then feel free to roast me. |
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Jesse, there are some ways. One way is to have a passive wheel on an independent axis in the center of your robot, and encode it. It will only move if the robot is moving. You could also use mouse sensors or trackballs to accomplish similar things, I think. |
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This thread is pretty well covered. However, the math and actually what happens on the FIRST field regarding friction are two different things. Mark I like the spreadsheet some interesting data there nice work. My suggestion regarding this is test,test and test. In addition to that remember the basics for instance you want to be heavy as possible without being overweight especially with a game like 07's. watch your CG and keep it as low as possible and finally keep your tread in keep in good condition at all times. Besides this experiment with different materials and tread widths, design is an on going process. Finally, you don't want to spin your wheels in a pushing match, thats how you get pushed. The easiest way too figure this out is to put the bot pushing against the wall and record the numbers from dashboard when the wheels slip then set them up in programming as limits. Obviously do this while the bot is on a practice field were real carpet or as close to real carpet is present to get the most accurate results. Just a few things my team is doing regarding this issue
my two cents, Drew |
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Now, I'm not sure our available loop rates are really adequate for good stable control of this current, but you could certainly easily implement a simple controller to back-off on commanded PWM signals to keep the current in an acceptable bound that you know won't slip. Quote:
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I apologize for continuing off on a tangent, but I feel we're on a roll with the tangent and it's pertinent to the original topic to an extent. The biggest advantage I see for traction control is the ability to climb rough terrain (ramps) without too much driver input.
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Hmm, after a bit more thinking the mouse sensors seem easy enough to do if you have 1 mouse sensor on each side -- even though the PID control, for perfection and theory, would slightly change during a turn (higher I value) than in a straight (higher P value). I'll have to bring this up to the drive train design team tonight to see if we can focus a bit of time experimenting with it. Quote:
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Grippy non-linear materials like natural rubber, when on relatively smooth surfaces, can have a higher effective coefficient of friction at lower pressures--so for a fixed robot weight, larger contact patches can give higher friction becuase the rubber of the contact patch is under less pressure.
For an experiment showing the non-linear coefficient of friction of rubber (higher coefficient with lower load on the interface) see http://www.tuftl.tufts.edu/files/asu..._Testing.2.doc particularly graph 1 and graph 3. See also http://www.robotbooks.com/robot-materials.htm toward the bottom of the page, where you find the statement: "The confusion here comes from the fact that rubber has a very unusual property. The more lightly it is loaded, the higher its apparent coefficient of friction." Of course carpet can change everything, so you need to experiment for yourself. |
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So... the consensus is that contact area has little or nothing to do with friction? :confused: But it does? :confused: :confused:
Ok... i'll go get empirical data sometime... -q |
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QBranch (aka Alex) wants a definitive answer and he will get it right now.
Static friction force does not depend upon surface area. Static friction force does not depend upon surface area. Static friction force does not depend upon surface area. This assumes one major thing: The surface pressure between the two items is low enough to not cause material failure at either surface (wheel/tread or carpet). You must make your wheel width wide enough to not rip up the carpet and not yield your rubber (at least, too much). You should design your wheel width to not fail either material. Once you have done that, the width doesn't mean squat. Alan is correct about dynamic friction: surface area plays a bigger role. I have posted numerous times on this and the width does not matter. I will not argue with any of you about this. I am as certain as can be on this issue ... believe me. |
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Static friction force depends only on the coefficient of friction and the "normal force" (weight, for horizontal surfaces). There are boundary conditions for some combinations of materials where the coefficient of friction can change based on pressure, and since pressure depends on area and force, changing the area can affect the friction force, but the static friction force still depends only on the coefficient of friction and the normal force. |
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So if width doesnt mean squat quick question. in st louis us (1625) had to face 217 and 148 at times 217 had 6 wheel drive with im guessing 1inch wide tires and 148 had 6 wheel drive with 2 inch wide ifi traction wheels. both with what i believe to be identical tread. yet we could push 217 easily and 148 we tied head on. we had a 3 speed 4 wheel swerve drive with 1.75" wheels covered in lower cof blue nitrile roughtop from mcmaster. any explanation? my next years plans already inclue 2.5"wide wheels at the moment
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Gear ratios maybe? If you had a three-speed transmission, there's a good chance your lower gear was lower than theirs. That would result in more torque being delivered to your wheels, and hence a greater pushing power.
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Head on, 1625 did not push 217 easily. I can show you the video evidence. However, we were easily pushed sie to side for reasons completely separate from surface area and frictional force. Our side bumpers were located such that we (inadvertantly) were giving our opponents the ability to transfer our weight to them in a side pushing match, which lowered our normal force and increased our opponents normal force.
Besides, who says our robot was optimized for max pushing force last year? We had a single speed transmission that was not optimized for pushing. The fact that your team could push the T-Chickens last year has nothing to do with the fact that surface area has nothing to do with static friction. |
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Please keep in mind that what is written into fomulae is often NOT directly transferrable to robot drive systems in a way that can be accurately and completely calculated.
Yes, you can make general assumptions regarding friction and the effects of one material vs. another, etc. - but, some arguements relative to traction, best drive system configuration, best wheel type and material, treads vs wheels, and other drive system decisions - are best left to experimenting and lessons learned in the real world. Therefore, overly concerning yourself about static friction will only address one element of the problem. Robots are usually not designed for static friction. Something I learned a long time ago relative to contact area and friction. This applies more to mechanisms that are designed to slide, not grip. If the opposing materials are too smooth (maximizing the contact area) they will react opposite of what you would expect and want them to do. They have more difficulty sliding over each other. Sliding is accomplished easier when the contact surface is a little rough, giving up a little contact surface is productive in some cases. As to my own experiences in drive systems relative to this question, I would have to say that our robots with more contact area produced better traction against the carpet. When comparing the robots using wheel chair wheel (smooth) vs. treaded pnumatic tires - the treaded pnuematic tires won hands down. The differences could be attributed to a combination of both different material and more surface contact as the pnuematic tire actually increases in contact area as they are pushed against due to the forces subjected to. Will you get to a point where increasing contact area no longer makes a significant difference? Yes and No - it all depends on what you are attempting to do with it. Andy explained it well in his response. But at the same time, would the Beatty Beast have been such an immovable object without all of those file cards?? Just my thoughts - good topic, Mike Aubry |
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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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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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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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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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I think for the upcoming season, I'm sold on tracks. I get this from watching an outback system push anything it came against across the field. There might not be an easy explanation, but I've seen tracks outpush wheels every time. |
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Meet team 1516:
![]() Builders of one of the most enigmatic drivetrains in FIRST. In the last few years this team has won: -Highest Rookie Seed 2005 -Cal Games Champion 2006 -5th Seed? Silicon Valley Champion 2007 -8th Seed Archimedes division 2007 Most of these years they have not scored any points, and have just played defense. Most people will tell you that a kit-bot running four skyway wheels off a couple banebots cannot play defense. But how can those people explain team 1516? They certainly didn't win all those competitions scoring points. So here’s my point: the age old question of "who pushed who" cannot be solved by merely looking at traction, gear reductions, or motors. Its a combination of infinitely many things. |
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Smart defense doesn't even require your robot to push another.
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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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Since friction for a given wheel is dependant upon the force of gravity exerted by the mass of your robot, a 2-driven-wheel system needs most, if not all, of its weight centered directly over the drive axle for maximum traction. Changing to a 4-driven-wheel system spreads out where in your system the center of mass can be and still practically contribute to all of the wheels' traction. Come to think of it, I think someone previously in this thread mentioned it, and most of the drive train guides I've come across have the underlying assumption Center of Mass rests somewhere in between 4 driven wheels. |
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I'd like to pose a different question related to contact area v. friction. What benefit is given by adding additional wheels to your drive train? In 2005, we ran a 16 wheel drive train. In 2006, we went to 8x8, and in 2007 did 6x6. However, according to the coefficient of friction*normal force, we should maintain the same amount of grip regardless of presenting additional surface area by adding extra wheels. In all our robots, our CG is usually towards the rear. So, once again, I present the question. Is it worth making massive drive trains (besides the fact that you add many more fail-points, reducing chances of a crippling blow), or should we just stick with 4 wheels?
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But for cars, the problem is much more challenging, because road conditions are always different. ABS systems allow fairly large deceleration on dry roads, but when the road is wet or icy, this is somehow compensated for and maximum deceleration is much smaller. Can anyone explain this? This concept seems like it would be extremely useful if it could be applied to a FIRST robot. |
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This used to be a good guide with an animated gif showing how the internal cyllinders work in the brake pump -- but it looks like they've changed it a bit in the couple of years since I've looked at it. I too had this question a few years ago:
http://auto.howstuffworks.com/anti-lock-brake.htm It's "sorta" how it works. Instead of a speed sensor, some cars used to use a "slip" sensor that was a combination of a shaft encoder and accelerometer. Since then it's been proven to be easier and faster to use speed differentials to control the brake fluid pressure. |
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Based on my experience with ABS, this "constant" is smaller when driving on ice, than when driving on a dry road. But how does the control system know this? Theoretically, this could be done with an accelerometer and encoders on the wheels. Is this the way it's done? The problem that might happen is that by the time the controller realizes the wheel speed is different than the car speed to start removing brake pressure, the wheels will already be slipping. Doesn't ABS prevent this situation completely? |
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Not to want to carry on the ABS thing too long, but the article is a bit misleading. (and this part is actually valueable in a FIRST situation)
The wheel sensors look at rotational speed at each axle (i.e. an encoder at each wheel) The system then can look at the realtive speed of each wheel. When you mash on the brakes, it monitors each wheel to see that they are moving (more or less) at the same speed. When one stops turning, (no changes at the wheel sensor), the system sees the difference and dumps the pressure to that brake line until it starts turning again, whn it's turning again, the dump valve is closed and pressure returns. now since the systems lost pressure, the pump pushes some extra back in so your foot does not hit the floor. (this is a very generic description here, so some license is taken with when the valve closes etc) Now looking at vehicle stability systems is where you find the big use of the acceleramoters. They know what is supposed to be happening (accel, brake, turn etc,) and look at the body response. If it's out of bounds (accel a direction not intended), they use the ability of the ABS to apply and release the brakes in combination with changes in engine timing to reduce power to try and get things back within a safe zone. (again, this doesn't describe everything and there's much variation in the specific systems) So how can you use this on a robot?....well, if you can look at each of your wheels independently (one channel per independently rotational wheel ) to see what they are doing, and you can look at the operator input to see wht you want to be happening, and you can look at the net affect on the body (2d acceleramoter) then you can use this info to do things like pulse the motors (to change from the dynamic friction during wheel rotation) or stop the wheels from turning, or trun away......of course, a really good driver just does this without even thinking about it. sort of a hardware vs software trade |
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Paul is right. It's not the surface area.
and since it's not what is it? (and this is just my thoughts here) The surface we are dealing with is not normal. It's complex, it has threads, and some of thes threads are in contact with the wheel. so looking at the thread to wheel interaction is a start. I would look at the shape of the thread under your wheel when they are in contact. How can you use the fact that the thread is glued to the carpet mat as an advantage? The carpet is 3 dimensional. can projecting into the carpet be an advantage, can there even be a "best shape" for these projections relative to the carpet fibers? Don't think at the 1 square inch level, think at the .1sq mm level. How do I get the fibers to do more for me than the other guy? How can I trap them, bend them and make them do my bidding? Don't think about pushing down, think about pulling across. Find the exact right combination of shape, projection and force direction and you will solve this puzzle. |
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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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Hmm....I think 114Klutz is on the right track, but slightly off in the explanation. Bot A (1 wheel per axle) ____________________________ |back---------x------------front| |___________________________| /---\---------|----------/---\ (----)--------|---------(caster) \ _ /---------|----------\ _ / --------------|----------------- /\----------|-----------/\ |----------|-----------| |----------\/----------| F1---------W----------F2 |<----L1---->|<----L2--->| Sum of forces = zero: F1+F2=W Sum of moments about point x = zero: F1*L1 = F2*L2 So, F1 = (W-F1)*L2/L1 = W*L2/L1 - F1*L2/L1 This simplifies to: F1 = W*L2/(L1+L2) The max tractional force can be calculated by using: Ff=mu*F1 Or, Ff = mu*W*L2/(L1+L2) Bot A (2 wheels per axle) __________________________ |back---x----------------front| |_________________________| /--\----|---------------/--\ (----)---|-------------(caster) \ _ /---|---------------\ _ / --------|--------------------- ---/\---|----------------/\ ---|----|----------------| ---|----\/---------------| --F1---W---------------F2 |<-L1->|<------L2----->| When the extra rear wheels are added, the center of mass (the W) shifts more towards the back (the picture is slightly exaggerated). So, looking at the formula for traction force again: Ff = mu*W*L2/(L1+L2) L1+L2 is still the same but L2 has gotten bigger, which increases the traction force (Ff). So, it makes sense that the robot with more wheels would push the robot with less wheels even though the weights are the same because the weight distributions aren't perfectly equal. 114ManualLabor - maybe you could try powering all of the wheels - that way the distribution of weight doesn't matter as long as it is somewhere in between the wheel axles. I'd be really curious to see if the 2/axle bot could still beat the 1/axle bot. Then this would mean that mu does in fact change with surface area (to a very slight degree). |
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Recently we did a tire traction experiment to try to answer some of these same questions. Attached you will find our results. I present these only for your enjoyment and not as an endorsement for any particular tire. Since these were tires we had on hand, some were well worn, some were new.
The results were not what I expected. I was surprised at the performance of the large knobby tire. Perhaps this could be attributed to oxidation on the surface of the tire that made it less sticky. We have not paid too much attention to the air pressure in our tires in the past. We will now. Jay |
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"Recently we did a tire traction experiment . . ."
Loolking at your results, which were for dynamic friction on carpet, the highest effective coefficients of friction were achieved by the IFI wheels, and with the IFI wheels, the highest coefficients of friction were achieved by the wheels with the most lightly loaded contact patches. In other words, in your tests, for the IFI wheels, for a given weight, more contact area gave more friction. This is a fairly common result for high-traction materials on smooth surfaces. Looks like it could apply on carpet too. |
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Since static friction is greater than dynamic friction, your results don't say anything about what wheels would win a pushing contest. A robot with the wheels not sliding on the carpet is generally going to beat out a robot that's spinning its wheels. |
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Those results . . . were dynamic friction, not static friction . . . .
Yes, but the two are often, though not always, correlated. The standard rule (or standard model) for both static and dynamic friction (Amonton's or Amonton/Coulomb laws) is that that friction is the product of the load and the appropriate static or dynamic coefficient for the materials in contact, and is independent of the contact area. See, for example, http://hyperphysics.phy-astr.gsu.edu...frict.html#fri (Article on friction at the Hyperphysics site of Georgia State). Thus an experiment showing that the dynamic coefficient of friction varies with contact area might lead one to at least adopt the hypothesis that the coefficient of static friction does the same. The truth is that the nice linear model for both static and dynamic friction taught in basic physics and engineering courses only works well for some materials under some conditions. Rubber is not one of those materials. See, for example, http://www.springerlink.com/content/n30715161g635138/ (abstract of a book chapter entitled "The Influence of Contact Pressure on the Dynamic Friction Coefficient in Cylindrical Rubber-Metal Contact Geometries") which states in part: As it is commonly know[n], classic Coulomb’s and Amonton’s friction laws, which mainly establish that the friction coefficient is independent of the area of contact, are proven to be not valid in the case of rubber-like materials. See also http://www3.interscience.wiley.com/c...69929/ABSTRACT (abstract of an article entitled "Analytical and experimental investigation of the static friction regime for rubber-rigid ball contact") which states in part: The parameters of the static friction regime in terms of static friction force . . . are investigated for a rubber ball/metal flat configuration. . . . The coefficient of static friction decreases significantly by increasing the normal load . . . . Smaller radii of the ball determine a smaller static friction force . . . . Where rubber is involved, increased contact area (wider tires, larger radius tires, or belts/treads) and lower contact loads often have the effect of increasing the available traction (friction), whether static or dynamic. |
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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. |
Re: Contact Area and its Relation to Friction?
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Also as an answer to the question mu the mathmatical ratio of the force of friction/normal force is unique not only for every material but for every object. Thus, the contact area is calculated in when stating mu. I couldn't give you a mu of rubber on asphalt, but i could give you a mu of a specific tire with a specific contact area and texture. just as an explination of your source, I take Honors Physics and got a 20/20 on my friction quiz (no tests in this class) =P |
Re: Contact Area and its Relation to Friction?
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