4" vs. 6" + 8" Diameter Wheels
 

I've noticed a lot of the veteran teams used the 4" diameter wheels in their 6WD or 8WD drive systems.

Is there any significant advantage to using them over the larger 6" or 8" diameter wheels?

And is there any significant advantage to implementing a 8WD instead of a 6WD?

Re: 4" vs. 6" + 8" Diameter Wheels
 

4" wheels allow you to create a longer wheelbase, since the smaller wheel allows the axles to be spaced apart further.

Additionally, 4" wheels reduce the reduction required from a CIM motor to achieve a reasonable speed. Smaller reductions mean less frictional loss.

They arguably produce faster acceleration, since the wheels have less rotational inertia.

Re: 4" vs. 6" + 8" Diameter Wheels
 

In addition to what Joe posted above they are also lighter and tend to result in a chassis with a slightly lower Center of Gravity.

Re: 4" vs. 6" + 8" Diameter Wheels
 

i really like small wheels, but i like 5 or 6 inch wheels the best. they are large enough to raise the ground clearance above what a 4 inch wheel set would give.

Re: 4" vs. 6" + 8" Diameter Wheels
 

What for? Is there any reason you needed more than ~5." of ground clearance this year?

Re: 4" vs. 6" + 8" Diameter Wheels
 

Check out this nearly identical thread. If you search around a bit on CD I'm sure you can find multiple threads with this information.

If you are careful when designing your drive for 4" wheels, you shouldn't have a ground clearance problem.

Re: 4" vs. 6" + 8" Diameter Wheels
 

See this post I made in another thread for why we like small wheels.

http://www.chiefdelphi.com/forums/sh...6&postcount=74


In 2010 we climbed the bump with 4" wheels.

Re: 4" vs. 6" + 8" Diameter Wheels
 

i would prefer 5 inch wheels, but settle for 6 inch wheels for several reasons. most of the omni wheels from andymark smaller than 6 inches are very bumpy, also 4 inch mechanums don't exist for FRC. i think 6 inch wheels are the most versatile, and that the tiny benefit of going to 4 inch wheels is not worth the flexibility trade-off.

Re: 4" vs. 6" + 8" Diameter Wheels
 

When do you ever design a drivetrain for both mecanum and regular wheels? There's flexibility, and then there's being a jack-of-all-trades, master of none.

Re: 4" vs. 6" + 8" Diameter Wheels
 

This thread is useful too.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Even when two are paired together?

You can get a smooth ride with omnis...

Re: 4" vs. 6" + 8" Diameter Wheels
 

one reason is nonadrive or octomanium or any other number of names for the same basic mechanical idea, the drives usually use 6 inch mechs and 6 inch traction wheels. i prefer to use a very standard, modular design strategy, with multiple options. there are many more options for 6 inch wheels than any other wheel set. closon, andymark, pneumatic, good omni wheels, mechanum. with 4 inch wheels many of these types of wheels must be custom made. the 6 inch wheel size is the most versatile. and while it is true that some sacrifice is made in order to gain this flexibility, it is such a small advantage that it doesn't really impact performance too much.

I already designed a frame that will accommodate any drive-train. one of the sacrifices of that frame, was giving up 4 inch wheels of any type.

Re: 4" vs. 6" + 8" Diameter Wheels
 

The 4" dualie omnis on 2175's robot this year gave a smoother ride than 6" omnis we have used in the past IMO. Admittedly they are a bit heavier and are more expensive than a single 6" omni, but the weight and cost both typically are gained back by knocking out a stage of reduction.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Smaller wheels in octocanums make desired reductions easier to produce.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Does anybody have mass and moment of inertia data for comparable 4", 6", and 8" wheels?

Re: 4" vs. 6" + 8" Diameter Wheels
 

Wouldn't this vary somewhat significantly based on the material of the wheel as well as any lightening? I'm sure we could calculate worst case scenarios (solid wheel of aluminum billet) but I'm not sure it would actually be terribly useful. Perhaps assign real materials to the AM plaction/performance wheels and use your CAD program of choice to computer the moments?

Re: 4" vs. 6" + 8" Diameter Wheels
 

Roughly speaking, it will increase with the square of the radius. (I say roughly, because the different sizes aren't scaled versions of each other; some things, like hub size and rim thickness, tend to be driven to a large degree by other design constraints.)

Re: 4" vs. 6" + 8" Diameter Wheels
 

Yes, of course. That's why I said "comparable" in my post. Compare a 6" wheel that you would make for your robot to a 4" wheel that you would make for the same robot.


Exactly. That's why I said "comparable" :-)

Re: 4" vs. 6" + 8" Diameter Wheels
 

The major reasons have been stated, but the biggest for me is the redundancy in gear ratio of having a big wheel. Gearing down then using a big wheel is redundant. The wheel size is part of your gear ratio. If you have a 2 stage reduction gearing down 12:1 with an 8 inch wheel, you could achieve the same ratio with one stage 6:1 and a 4 inch wheel. The weight savings add up, lighter wheel, less reduction, therefore fewer gears etc...You will also get better acceleration (relative to the gear ratio) with a smaller wheel because, in a general comparison, smaller wheels have a smaller moment of inertia.

(Big wheels do have some advantages in tackling rough terrain, but we don't see that too much in FIRST).

Re: 4" vs. 6" + 8" Diameter Wheels
 

Worst case scenario, solid wheel made of 6061 Aluminum 1 inch thick. (I picked a type of Aluminum)

I used (m*r^2)2 for the moment of inertia.

Once you start lightening it could get different since the amount of material you have to leave on the edge of the wheel doesn't scale with size so we would start treating it as a tick walled tube + however many support spokes you have. This starts getting a little more complicated but it is still doable. I am attaching an excel spreadsheet that (unless I did something stupid) should compute a rough estimate of the rim and spoke style wheels.

Edit: I had originally forgotten the width of the spoke so I was finding the area instead of volume, this has been fixed.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Less reduction != easier to produce.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Yes, useful exercise for students.

The numbers above can't be used, of course, to answer the original engineering question, to wit: all other things being equal, how much acceleration advantage does a 4" wheel vehicle have over a 6" wheel vehicle (where both the 4" and 6" wheels have been reasonably individually optimized for the vehicle).

Does anybody have CAD models (from this or past years) of 4" vs 6" drive train options which included enough detail to calc the mass and moment of the wheels?

Re: 4" vs. 6" + 8" Diameter Wheels
 

We don't need a CAD model to do a rough estimate. We could assume 140 pounds (close to full size robot + battery + bumpers). We could assume a somewhat reasonable gear ratio (4 CIMS geared down 18:1 with 6 inch wheels and 12:1 with 4 inch wheels). Theoretically these are geared to move at the same speed, the problem is we don't have estimates on the exact weight savings with a smaller gear ratio and smaller wheels (someone else might be able to help estimate the weight savings).

Re: 4" vs. 6" + 8" Diameter Wheels
 

For us we use the smallest practical wheel we can get away with. Why?

1. Less gear ratio required for same pushing force at the wheel.

2. Move the wheels out further front and back.

3. Less linear feet of tread to deal with (less chance of losing tread)


This really adds up to less weight overall. Smaller wheels = less weight. Less gear ratio usually = less weight.

For us, 4" seems to be the sweet spot.

Re: 4" vs. 6" + 8" Diameter Wheels
 

The rotational inertia is of the form

K*M*R*R.

In the limit, a small wheel is a solid object and K = 1/2. Large wheels put more mass at the rim and begin to approximate a hoop, K = 1.0. Not only does the mass get larger, but the ratio of mass at a distance tends to do this too (K goes up).

The wheel must also get heavier because the stresses to perform similar maneuvers are higher.

Interestingly, radius has nothing to do with this discussion of acceleration and drops out of the equation.

T = I * alpha

The gear ratio must change to keep the same ground force and free speed, so force is constant not torque.

F * R = I * alpha

Pluggin in the inertia

F * R = K*M*R*R * alpha

Then relating rotational acceleration to linear acceleration

F * R = K*M*R*R * A / R

Then dividing through by radius gives

F = K*M * A

If M goes up faster (proportionally speaking) than K, then acceleration must go down. Per prior logic, K and M generally move upwards together when scaling the same "spoke" type design.

These effects should be in the noise compared to the reflected inertia of the motor (through all of those gears) and the associated losses. Also keep in mind that most teams use chain drives to keep the wheels on each side moving together. The inertia of the chain is more signifficant? And it has the oposite effect, causing large wheel drive trains to have a lower effective rotational inertia. I expect all of this to be in the noise... now I'm just waiting to be surprised by the results Ether's calculations. :ahh:

Re: 4" vs. 6" + 8" Diameter Wheels
 

Of course.

Yes, that is the problem.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Well I wouldn't want to disappoint :-)

Looking at the wheel without the vehicle (as you did):

I*alpha is equal to the net torque on the wheel. If "tau" is the driving torque on the wheel and F is the floor reaction force responsible for the linear acceleration of the wheel, then a free-body analysis of the torques and forces on the wheel gives:

tau - F*R = I*alpha

tau - (M*A)*R = (K*M*R*R)*(A/R)

tau = = M*A*R*K + M*A*R

A = tau/(M*R*(K+1))



For the analysis of wheel plus vehicle, see attached PDF.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Sorry Ether, I'm just not being clear. :(

The torque available "at the motor" and "by the motor" is the same for all wheel sizes. However, keeping the same top speed and low end torque requires a different gear box (this is a common assertion by others in this thread). So the torque applied TO THE WHEEL must go through a different gearbox, and will then be a different torque. Having so designed all gearbox-wheel combinations, at stall the force at the exterior rim of any wheel will actually be the same (no losses). So the applied torque as indicated is actually F_stall * R which was used correctly.

Then I'm spinning the wheel under no load... I don't mean to set a bad example, but there is no need for a free body diagram, just the applied load (analytical dynamics). My "linear acceleration" term is also somewhat abusive, but it relates to the same setup (e.g. rad/ss converted to ft/ss). Clearly if the vehicle weighs more it will also accelerate slower. That doesn't help prove the assertion that "the vehicle accelerates slower BECAUSE the moment of inertia is higher for larger wheels." This statement was one of several independent reasons to use smaller wheels. This simple setup really lets you isolate everything.

I've shown that radius drops out of the equation entirely and that only mass and mass distribution ratio "k" contribute. In the strictest sense, I've actually disproved this assertion. YAY ME!!! :( If the mass and mass distribution ratio "k" of the wheel remain constant (e.g. use a lighter material as the wheel gets larger) then the moment of inertia will actually go up (as it MUST with R squared) but there is absolutely no performance penalty!!! In fact the inertia can go up and you can increase performance using a lower mass or k value.

None of this is practical, the product of mass and k REALLY should go up in any reasonable manufacturing process. So I did not bother to argue the causality bit.

I worked out the equation because I suspected that something neat would happen to the radius, and it did.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Our 4x2" wheels this season are .8 lb-in^2 and our 1" ones are .467 lb-in^2.

Modifying the 1" wide wheel to a 6" diameter and changing no other factors (face thickness, spoke width, etc...) results in 1.999 lb-in^2. The design appears to weak for such a diameter though, and would likely need more material, increasing that number. These are both very light compared to the available COTS wheels.

Re: 4" vs. 6" + 8" Diameter Wheels
 

No, you were quite clear.


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If a wheel of mass M_w and moment I and radius R is sitting on the floor and is free to accelerate, then the force F that it exerts on the floor when a torque tau is applied is not equal to tau/R.

It is equal to tau*M_w*R / (M_w*R² + I). That approximately equals tau/R only if I is negligible compared to M_w*R².

That wasn't made clear in your post.


If four of the above wheels are on a vehicle of mass M_v which is free to accelerate, then the force F with which each wheel pushes against the floor is given by

F = tau*R*(4*M_w+M_v) / (R²*(4*M_w+M_v)+4*I)

The above approximately equals tau/R only if I is negligible compared to R²*(M_w+M_v/4).


...


The acceleration is given by a = 4*tau*R / (R²*(4*M_w+M_v) + 4*I)

Letting I=K*M*R² this becomes:

a = 4*(tau/R) / (M_v+4*M_w*(K+1))

Compare the acceleration of two vehicles, one with wheels of mass M_w1, K= K₁, radius R₁, applied torque tau₁, and vehicle weight M_v1, and the other with wheels of mass M_w2, K= K₂, radius R₂=2*R₁, applied torque tau₂=2*tau₁, and vehicle weight M_v2. Then

a1/a2 = (M_v2+4*M_w2*(K₂+1)) / (M_v1+4*M_w1*(K₁+1))

... and R does not appear in the ratio, as you said.

Re: 4" vs. 6" + 8" Diameter Wheels
 

There is a difference in the contact patch. Also the carpeting is 3 dimensional. The wheels sink into the carpet. So how do the different size wheels affect the contact patch for traction and the ability to turn?

Re: 4" vs. 6" + 8" Diameter Wheels
 

Various teams have done experiments to measure CoF with different wheel configurations. The data that I've seen (it was given to me by another team, so I will let them post it if they choose to) was quite surprising - wheel diameters and widths can make a big difference! Definitely worth experimenting with.

Re: 4" vs. 6" + 8" Diameter Wheels
 

Still not clear.

No load means no load. The robot is on jack stands. If radius drops out here, then it's not coming back as the model becomes more complicated.

The bottom line is that an increase in rotational inertia of large wheels alone is not a valid reason to choose smaller wheels. It is an increase in total mass of the robot or (EDIT) increase in rotational inertia attributed to (END EDIT) mass distribution (EDIT) and mass (END EDIT) of the wheels that contributes to any performance degradation. These and all of the other excellent reasons cited in this thread push for smaller wheels.

Re: 4" vs. 6" + 8" Diameter Wheels
 

YMMV, but I think it's clearer to explain it the following way:

The equation for vehicle acceleration in the PDF file attached to this post can be re-arranged as follows:

a = (tau/r) / (I/r² + (1/4)*(M_v+4*M_w))

or, substituting K*M_w for I/r²

a = (tau/r) / (K*M_w + (1/4)*(M_v+4*M_w))


Since tau/r remains unchanged when you change the wheel radius (if you change the gearing accordingly), what remains is

a) the total vehicle mass M_v+4*M_w, and

b) the mass of the wheel times the mass distribution factor of the wheel (K*M_w)

Since neither (a) nor (b) is likely to remain the same when you change wheel size, there will be a change in vehicle acceleration.

The equation also gives a way to estimate the change.

Re: 4" vs. 6" + 8" Diameter Wheels
 

All,

While the calculations in this thread appear correct (I haven't checked them against mine thoroughly, since mine are done a little differently), they really aren't the main reason for going to small wheels on our team.

It is all about the huge constraint placed on us in FRC for max robot weight. While the wheel weight effect on overall robot acceleration is low (if you do the math you will see), it is significant to help meet the weight restriction in FRC. The max weight restriction is really the driving force for us to go to smaller wheels. Second is the smaller packaging. Robot acceleration is not on our list of reasons.

Paul