Free Body Diagram of a Tire in Steady state motion

[ckguru]

Along the lines of discussion thread108-192670 ...

I have been puzzled by the question of how a single tire on a moving vehicle maintains steady state motion. Both the torque acting on the center, and the resistive moment of the ground (weak assumption I know) seem to cause an unbalanced force sum.

What other force, ie. compression of the rubber material, am I missing to complete the free-body diagram? If this was kept a 2D problem, that would be appreciated.

Thanks,

 

[GregLocock]

Presumably you want to push the body of the car forwards.

Cheers

Greg Locock

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[Compositepro]

The important thing to realize is that the wheel is hanging from the top half of the tire due to tension in the tire cords that run through the sidewall (like spokes in a bicycle wheel). The bead of the tire that fits the wheel contains significant cord reinforcement in the hoop direction. Air pressure keeps the top of the tire from being pulled toward the ground.
Of course, torque is transfered through the sidewalls of the tire as well. It gets pretty complicated and there are several different ways you can analyze the loads which are all correct.

 

[ivymike]

no need to complicate the question - Greg has pointed in the right direction. Take a stone wheel for simplicity. There are both forces and moments present at the hub.

 

[Compositepro]

I guess I didn't think the question was quite so basic, but it seems Greg is correct.

 

[hydtools]

The weight on the axle acts through the center of the axle. The ground reaction acts on the same line through the tire at the tire-ground contact. The rolling friction * the ground reaction is the friction force. The torque around the axle equals the ground friction torque/moment, friction force * tire radius. Assumes constant speed, no acceleration.

Ted

 

[GregLocock]

...same problem as the 'guru'. Your free body diagram is not in equilibrium.







Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[ckguru]

Thanks for the thoughts. After writing my post, I convinced myself about the forward acting friction force, which I had trouble accepting earlier.

Can the friction force be considered of the static type, since relative motion of tire contact patch and road is null? I think that was the hurdle there, trying to classify the type of friction force.

 

[Compositepro]

There is no "forward acting friction force". I you are wondering how to depict the rolling resistance of a tire, I think there is an upward force at the front of the ground contact patch that is slightly higher than the upward force at the back of the contact patch. These create torques about the axle. The reason for the different forces is the energy lost in hysteresis of the rubber.

 

[btrueblood]

"There is no "forward acting friction force"."

Well, I think he means the static friction force between tire and road, from which traction is derived.

 

[ckguru]

So in other words, there is no horizontal component of force between the rubber and the road? Now that would describe an icy road no? Can we define or take apart the term "rolling resistance" better as I think it has meaning that has been lost in over-use.

 

[btrueblood]

the following link provides at least one view of rolling resistance, and it's how I learnt it:

http://images.google.com/imgres?img...stance+free+body+diagram&gbv=2&hl=en&safe=off

 

[Compositepro]

Sorry, ckguru, I see what you meant now. These discussions are hard to do in words. Drawings and vectors would be much more clear.

 

[patprimmer]

Maybe inertia and aero drag need to be considered to balance drive at the tyre inerface.

Regards
Pat
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[hydtools]

There is a horizontal component at the tire-surface contact. The contact is not friction free.

I inadvertantly left out the horizontal force acting through the axle. That force is the driving torque divided by the tire radius. The flatting of the tire contact patch adds a complication. It reduces the effective tire radius and adds a rolling resistance term.

Ted