266 APPLIED MECHANICS 
Case II. Flat Collar or Re- 
cessed Footstep (Fig. 405).—(a)z 
SMA vy 
Y ——— 
Uniform pressure. Proceeding as 
. for a flat pivot. 
Moment of friction on ring 
= 2pprr-dr, 
M=2upe | mdr = duane rae. ’ 
oe Pt ee 
2pP(ri - 72) 
therefore M = “307 — 7)” Fia. 405. 
(>) Uniform wear. Let pr=c. Load on ring=2arprdr=2redr. 
1 P 
Total load = P= 2 dr = 2re(r, — 1), therefore ¢ = Saito : 
—19) 
Moment of friction on ring = 2meprdr =" ~~ ; 
| ee 
Ya ide! p iit, tha 
‘ Mone [rir te 9 1 5 2 = duP(r, +1). 
To increase the amount of rubbing surface, and so diminish the 
intensity of the pressure, it is better to use two or more collars, as shown 
at (c), Fig. 405, rather than have one large collar. 
Case IIL. Conical Pivot (Fig. 406).—(a) Uniform 
pressure. Area of surface of cone = - 6: 
sin 
P=p sin gan =prrj, therefore p= noe as for a 
sin 0 wre 
flat pivot. The normal pressure on the surface of the cone 
is therefore independent of the angle at the vertex of the 
cone. 
Load on ring = esd a2 
sin 6 
2 
Moment of friction on ring = oh Bh 
sin 0 
_ 2ppt | "L 2dp = 2hP™ i _ 2pPry 
0 
: Fie. 406. 
sin sin 0° 3 3 sin 0” 
(>) Uniform wear. From the above and Case I. it follows that 
pPr, 
2 sin 0° 
Case IV. Clea Collar (Fig. 
407).—It is obvious from the pre- 
ceding cases that in this case 
— 2hP(r = 13) 
=sa00 a for uniform 
pressure, and 
M=" Syaet +r) for uniform wear. 
sin 
Fig. 407. 
