Coefficient of friction for plain bearings 3

[TerryR1]

I derived this formula for calculating friction for round plain bearings:

f = pi/2 * ? * P

f = frictional force
? = Coefficient of sliding friction
P = Radial force on bearing

I would expect this formula to be published in engineering books, but I'm not finding it. Can someone provide a source? Or prove me wrong? Thanks!

 

[TerryR1]

Very nice find!

On page 123:
f'=1.57 * f = pi/2 * f

Where
f = CoF
f' = adjusted CoF for tight fit of shaft in bearing


How did you find this pdf may I ask?

 

[electricpete]

Here is a thought about where the pi/2 comes from. It is simply converting between applied force straight down and normal force which is normal to the bearing surface.

Assume Fapplied is straight down.

Fn = Fapplied * cos(theta)
where theta goes from -Pi/2 to +Pi/2 over half the bearing... theta is the angle from vertical

The average value of Fn is <Fn> where
<Fn> = (1/pi)*int[Fapplied * cos(theta)] dtheta integrated over the range theta =-Pi/2..Pi.2
[the 1/pi is the length of the averaging interval)

Integral of cos(theta) is -sin(theta)

<Fn> = (1/pi) * Fapplied*[-sin(-Pi/2)- - sin(Pi/2)]
<Fn> = (1/pi) * Fapplied*[--1- - 1]
<Fn> = (1/pi) * Fapplied*2
<Fn> = (2/pi) * Fapplied

Ffriction = <Fn> * f = (2/pi) Fapplied * f
Ffriction = (f*2/pi) * Fapplied
Ffriction = f’ * Fapplied where f’ = f*2/pi

Hmmm... seems to have come out inverted? I have to go back and look a little closer.

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[desertfox]

hi TerryR1

I have access to some online books at Knovel and I found it in this book:-

Tribology in Machine DesignSearch WithinSearch By: Stolarski, T.A. © 1990 Elsevier

All I did was save the chapter to my comp, printed the relevant pages and scanned them to post here.

regards

desertfox

 

[TerryR1]

Signing up for knovel soon... ty!

 

[desertfox]

Hi TerryR1

your welcome

 

[unclesyd]

Wouldn't Pi/2 be one half the area of the circle. Looking back at some very old calculations for determining the COG of a shaft and bearing where I used Pi/2 as !/2 the area of the shaft.
I think I'm missing a page in my notebook because it's not very self evident in my written approach.

 

[abdul]

Gentlemen,

So far, it seems that everyone is claculating the friction force, however, the formulas used are not mentioning the length of the circular sleeve bearing. Therefore, the bearing length in contact with the shaft must be multiplied by the friction force in your equations to acheive the true value of friction force or friction moment acting at each bearing.

A second factor is to recognize that all such equations assume a 100% geometrical alignment of bearing to shaft journal. Many real world machinary do not have such alignment, so you may want to include for a misalignement factor that adds to the bearing friction formula. Then you are close to modelling the real world of the shaft to bearing friction.

Thanks,

Abdul