Guide Wheel Forces in Circular Motion - Loads on Guide Wheels

[George Zucas]

Dear friends,

I have an application where a cart of some sort travels on a circular path. The circular direction is assured by guide wheels on the structure. Please see the attached photo which is pretty much the same as in my case.

My problem is the forces on these guide wheels during circular motion.

First, I thought this is simply a case of circular motion. The force that holds a swinging rock connected to a rope on the path is the centripetal force which is the tension in the rope. In my case this is the force applied by the guide wheels.

Calculating this results a pretty much infinitesimal force with respect to the other forces involved.

mV^2/R= (100000kg)(0.5m/s)^2/25m= 1000 N

Which I think cannot be true. For carts along a linear path, the skewing force is generally taken as 10-15% of the gravitational force which would be in this case (100000 kg)* (9.81m/s^2)*0.1=981000 N. IF the above were true, then this would be a huge overestimation. The force in this case should be even higher since on a linear path the force only makes a correction to ensure linearity, while this force rotates the cart completely.

My second thought is simply drawing a free body diagram, there is no force on the tangential direction since it is a constant speed motion. The net force is the centripetal force which is 1000 N, then the forces on the guide wheels should also be 1000 N. Same result since I did the same thing I have realized.

Any guidance? I think I'm looking at it completely wrong but cannot think of any other solution.

 

[BvU]

I see no error in your 1000 N calculation. (I do see (100000 kg)* (9.81m/s^2)*0.1=98100 N, not 981000).
Apparently this is a slow turn: 5 minutes per revolution isn't like a centrifuge (fortunately in your case).

 

[CWatters]

Are the turns flat? Banked?

 

[George Zucas]

Thanks BVU, though in that case I'm going to ask why the standard advises to take skewing forces on linear path as 10% of the vertical wheel load. Though I'll need to find the exact phrase, I'll take a look when I get home.

 

[George Zucas]

Are the turns flat? Banked?

Not banked. Flat turns.

 

[BvU]

cart of some sort travels on a circular path

Sloshing liquids ? High center of mass ? Overhang ? Tourists all leaning to one side ? Gun turret ? We really can't give a general answer, so more context is indicated !

 

[George Zucas]

Sloshing liquids ? High center of mass ? Overhang ? Tourists all leaning to one side ? Gun turret ? We really can't give a general answer, so more context is indicated !

It is pretty much the same as this one:

http://www.rail-cart.com/d/pic/aluminium-coil-car.jpg

Though all 4 wheels can rotate like the front wheels of a regular car and are directed by the guide wheels.

I cannot find the standard text which mentions the 10% rule but I am pretty sure I have seen it. Maybe somewhere else.

 

[BvU]

Do you know how much 100000 kg of Aluminum is ? A bit more than three rolls ! Still, a mere 1000 N to make the described turn at 0.5 m/s ...

 

[George Zucas]

Do you know how much 100000 kg of Aluminum is ? A bit more than three rolls ! Still, a mere 1000 N to make the described turn at 0.5 m/s ...

It is not aluminum but steel so not that big. I have designed carts with 300T capacity though they were on flat tracks.

Yeah I guess the speed being only 0.5 m/s helps a lot. If it was traveling at 2m/s the force would be 16 times higher, though still it would not be a big problem.

I hesitate to put this in a calculation report now, it is a miniscule amount. I also think that guide wheels designs seem overengineered what with double bearings and all...

 

[CWatters]

As I recall wheels and track are usually profiled so the carriage centers itself reducing the rubbing between flange and track. I think this profile cause outward pressure on the rails although if anything I think it would reduce the load on the guide wheels.