FRICTION AND LUBRICATION 267 
_ Comparing the different cases for uniform pressure and uniform wear, 
it will be seen that the moment of friction for uniform pressure is 
? 4 1- Gti \ of the moment for uniform wear, and when r, = 0, this 
q “ratio becomes 
Footstep or Pivot bearings are frequently fitted with loose discs, as 
shown in Fig. 408. Under normal conditions these 
dises will all rotate in the same direction, but with 
different velocities, consequently the relative velocity 
between the pivot and the disc next it, or between two 
UN 
YE: 
dises, will be less than between the pivot and a fixed Wi Li 
bearing. The total moment of friction is, however. XSAN 
med not altered by the presence of the discs. If, VES 
wever, one of the discs should heat up and seize, the Ve 
next will act and give the first a better chance of cooling. 
A similar arrangement may be applied to collar bearings. ——- FIG. 408. 
234. Schiele’s Pivot.—The form of pivot known as Schiele’s pivot 
was designed to give uniform wear in the direction of the axis with 
uniform pressure, the coefficient of friction being assumed to be constant. 
Let A (Fig. 409) be a point on the surface of the pivot, 7 the radius, and 
AB the tangent at A, YY being the axis. Let AC be the amount of 
vertical wear taking place.at A ; then if CD be drawn parallel to and AD 
perpendicular to AB, AD will be the amount of wear normal to the 
surface of the pivot at A. Let p=the intensity of the pressure normal 
to the surface of the pivot, p being assumed to be constant. The wear 
AD is assumed to be proportional to p and to the velocity of rubbing at 
A, and therefore AD is proportional to pr. Let AD=kpr, where k is a 
constant, By similar triangles 
AC = 2 , therefore AC = a8 AB 
=Kp- AB. 
_ Hence if. AC is to be the same for every point on the pivot surface, AB 
must be constant. The curve which has the 
property that its tangent AB is of constant 
length is known as the tractriz, and also as the 
—anti-friction curve. 
It is evident that if a pivot wears equally in 
the direction of its axis it will preserve its shape, 
and there is a better chance of p, the intensity of 
the pressure, remaining uniform; also if p is 
uniform, the lubricant is more likely to remain 
between the rubbing surfaces. 
The curve EAF will never meet the axis YY, 
consequently this form of pivot cannot be brought Frq. 409. 
to a point and have its proper shape to the end. 
To find the moment of the friction of a Schiele pivot, consider a ring 
of the surface of radius r and width dr measured at right angles to the 
axis, The area of this ring is 277 oe a= 2rldr, where = AB. Moment 
of friction on ring = 24lyprdr. 
