Band brake surface pressure

[Sco79]

Hi All,

I have a problem concerning band brake surface (contact) pressure. Formulas and examples are given in textbooks and they look simple, but direction of the forces is difficult to understand. I think the basic equation is called capstan equation and it's used often in rope and belt friction calculations. There's usually a proof of the equation including integration.

I know the method for calculating forces, or tensions, on both ends of the brake band, P1 and P2. Also max. surface pressure which is in the tight/fixed end of the band where contact area begins. Question is, how do I calculate the surface pressure on a specific point of the brake band?

For example:
Brake band with friction lining, tightened around a brake drum/rim. Tight end (force P1) of the band fixed to foundation, other end is the "slack" end with smaller pulling force (P2). Total friction force which the brake has to hold (=P1-P2) is 500kN, wrap angle 270 degrees, friction coefficient 0.4, brake band width 150mm, diameter 1000mm.

What's the pressure between brake lining and brake rim in 200 degrees, measured from the slack end (70 degrees from fixed end) and how big are the tangential forces P1 and P2 in that point?

Any help which would make the issue more clear is appreciated.

 

[Compositepro]

First you have to convince us that we are not doing your homework for you. Hint: pressure will be proportional to radius of curvature of the drum and to tension at that point.

 

[Sco79]

You have my word for it I haven't seen this kind of example in any book - it's always the p(max) which is calculated. I actually got this problem at work with real brakes. Nobody had ever thougt about how the surface pressure changes over the whole lining area.

There's also a more difficult problem, but it may require testing instead of just trying to calculate the values. What if the contact surface is not 100%? I mean that the band is not touching the drum at all points. Just like there would be a piece/pieces of lining cut off somewhere from the contact area. How much bigger pulling force P2 there has to be then - not so easy to estimate.

 

[IRstuff]

Contact force problems are always constructed as average force problems, since there's no other method for doing the problem. The degree of contact is embedded in the friction coefficient term already. This is true, even for flat contacts.

TTFN

FAQ731-376

 

[zekeman]

From equilibrium

Mormal force
prd@=Td@
Therefrore
(1) T=pr

Tangential force
(2) dT=-mu*prd@

Dividing (2) by (1)
dT/T=-mud@
T=T0*exp^-mu@

From (1)
p=T/r
Substituting
p=T0/r*exp^-mu@