Ensuring a Roller Rolls ?

[4059dcb]

Help - does anyone know the formula, or ratio that will ensure that a round roller will roll on a flat surface - what is the maximum round axel shaft dia. ?? that will allow rolling and not sliding.
is there a ratio that is a guideline ??

Thanks a lot
Dave B.

 

[MintJulep]

FRA > T

Where:

F is the normal force against the surface that the roller is intended to roll on.

R is the roller radius.

A is the coeficient of adhesion between the roller and whatever it is supposed to roll on. This is not the same a the coeficient of friction, although it may be close.

T is the torque required to overcome the roller's bearing resistance.

 

[diamondjim]

I find it strange that there is
no length as a factor in the
given equation.

What is the length of travel of
the roller that you are disigning
for?

 

[zekeman]

Figure it this way. Assume that the bearing is locked. Then the static coefficient of friction, fstatic times Fn, the normal force, times the roller radius,r will be the initial moment on the bearing.However,if the restraining bearing moment, Bf due to friction is less than this, the roller will roll; if greater it will slide or skid. Then we may write.
condition for initial rolling:
Fn*fstatic*r>Bf=bearing frictional moment
condition for steady rolling:
Fn*fdynamic*r>Bf
Changing the inequality from > to < then gives the conditions for skidding or sliding.

 

[Cockroach]

MintJulep has correctly answered the problem. This is commonly found in elementry static textbooks as "Rolling Resistance".

If the coefficient of rolling resistance is given, "a", then a roller of radius "r" and weight "W" will need a horizontal force of "F" such that:

F = Wa/r

Typical rolling resistances are 0.003 in for steel on steel to 4 inches for steel on soft ground. I have used 0.05 inches for steel on level pavement and got very close horizontal forces, i.e. realistic nominal values.

I guess the big question is to determine your resistance on a medium other than these listed.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[MikeHalloran]

For a roller that's driven solely by friction with the surface on which it rolls, from that perspective, the ideal axle radius is zero. Somewhat larger axles are used in practice in order to provide bending strength and bearing area. Break apart an audiotape cassette and look at the rollers and axles where the tape turns a corner inside.





Mike Halloran
Pembroke Pines, FL, USA