Solid Pneumatic Tire Contact Area 1

[Parosh]

I am checking forklift tire load on a checkered steel plate. I have tire dimensions and I'm using one of Roarks equations for stress on a steel plate where I need the surface contact area. Typically, the tires are air filled and I can find this surface area quite easily by dividing the tire load by the tire pressure. However, in this case, the contact area will be dependent on the compression of the tire rubber on the plate and I am not sure how to go about calculating this.

Has anyone ever calculated something similar?

 

[JStephen]

Roark may have load cases for two elastic cylinders in touch, which would be similar to elastic cylinder on rigid plane.
Considering the tires don't form a full cylinder and you likely have no elastic properties for the tire, I don't know that you'd gain much by going down that route.
I'd suggest to either treat as a line load (rigid cylinder on rigid plane) or assume some high pressure and treat it as pneumatic.

 

[Parosh]

I found a comment in Portland Cement Associations "Concrete Floors on Ground" that mentioned contact area (in[sup]2[/sup]) of a solid or cushion tire can be approximated by multiplying tire width (in) by 3 or 4.

 

[RPMG]

I would create FEM shell and check deflection L/100 first, with the wheel size sloped 2.5k to the neutral axis, similar to bearing plates. Usually, deflection governs plates.

 

[Ron]

On concrete or soil the contact area would make a difference. On checkered steel plate, it is essentially a point load and the sheet reacts to it that way. If you did a von Mises stress distribution on the plate, the stress pattern would be larger with the actual area, but the point load would produce a similar but smaller stress distribution. You are not likely to shear the plate with your loads so don't worry too much about size. If you want a distributed load, I would suggest 2x the tire width for hard tires and 3-4x for tires with a "softer" surface. Use a Shore D durometer value to differentiate. In my opinion, a Shore D value less than 60 would use a 3-4x width for the contact area, while a Shore D value greater than 60 would use a 2x width for the contact area.

 

[JAE]

On some forklift tires I've looked at in the past with non-pneumatic tires, I've bent down and eyeballed the "flat" length on the floor...usually about 2 to 3 inches long.

 

[Parosh]

Thanks for all the input everyone!

I'm going to use 3" as the "flat" area. I realized that varying the width between 2-4 inches doesn't have a huge impact on the stress value when using Roarks method due to having to pick out values and interpolating from one of the tables.

 

[JLNJ]

I'm with JAE. For the contact patch, I use 2 or 3 in length x the tire width. This is small but realistically conservative, especially if your span is short relative to the tire size.

My guess is that the thicker the plate and the longer the span, the lesser the effect of the exact contact patch.

You comment that it is "checkered plate" makes me think something on the order of 1/4" or maybe 3/8" thick. If it's that thin, almost any decent sized fork truck will fail the plate. Even a small 2 ton truck will have a 5000# wheel load. You will need to overlay with something thicker. And if the plate fails, the beams which support the plate will probably fail as well (unless your original design load is very high).

 

[Parosh]

Hah, great guesses... Right in between at 5/16". The plate is definitely failing and so are some of the members. This check was primarily to figure out how thick of a plate I needed to overlay.

Thanks for your help.

 

[ACtrafficengr]

I was going to say jack it up, place a sheet of paper and carbon paper under the tire, set it down, jack it up again, and measure the area of the carbon transfer, but it sounds like you have your answer, and laser printers have probably killed off the carbon paper industry by now anyway.

My glass has a v/c ratio of 0.5

Maybe the tyranny of Murphy is the penalty for hubris. -

http://xkcd.com/319/

 

[rb1957]

I like the "arts and crafts" approach (as opposed to a mathematical solution). in no carbon paper (where these days !?) then maybe chalk ? maybe trace around the wheel then remove 1/2" or 1" around the traced perimeter ?

but how significant is this area in loading the plate ?? If 5/16" plate is NG then what do you need ? a total of 1" thick ?? 3/4" ?

how to reinforce the plate ? an overlay seems easy but heavy and awkward ? Attaching some stiffeners under the plate and some indication of this "safe" zone above the plate … either paint or maybe angles (to keep the truck wheels above the stiffeners) ?

another day in paradise, or is paradise one day closer ?

 

[BridgeSmith]

I was going to say...carbon paper...probably killed off the carbon paper industry by now anyway.

I think so, but unless someone thoroughly cleaned the tires recently, using just a white sheet of paper will show the contact area, although just eyeballing it closely will likely work just about as well. The contact area for it unloaded should be a significantly conservative estimate for the loaded condition.

One caution on the recommendations above - I would guess the contact length would be some percentage of the diameter of the tire, so if your tire size isn't what the other posters assumed, they may not be accurate.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Parosh]

If I had the access to the forklift, I probably could have tried to measure by hand or use a paper like you guys mentioned. However, this is all assuming you can fully load the forklift when you're measuring (which is most certainly not the case)... wouldn't that area will be larger under a greater load?

 

[BridgeSmith]

wouldn't that area will be larger under a greater load?

Most definitely it would be somewhat bigger, but maybe not a lot.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[UcfSE]

You can use Hertz contact stress equations to estimate the flat dimension. If you find a contact stress equation for line contact, usually for two cylinders touching along their height with different radii you can set the radius of one of them to a very large value to represent the flat floor. then you solve for contact length. You can estimate the rubber modulus from the durometer value.