ABSTRACT
Although the brake lining is more easily attached to the inner cone, with the torque acting at the inner surface of the outer cone, we shall derive formulas on the assumption that the torque acts on the outer surface of the inner cone because this will give a torque capacity that the brake can equal or exceed until the lining is destroyed. Thus
(1-4)
where the element of area on the outside of the inner cone is given by
(1-5)
and where we have used dℓ sin α=dr and the Pappus theorem for the area of a surface of revolution. Upon integration the expression for the torque becomes
(1-6)
Since this expression vanishes for ri=0 and for ri=r0 but not for intermediate values, we may set the derivative of T with respect to ri equal to zero to find that the maximum torque may be obtained when
(1-7)
for which the torque is given by
(1-8)
To find the activation force, we return to Figure 1 to discover that it is given by
(1-9)
When α=π/2, equations (1-6) and (1-9) reduce to the correct expressions for the torque and activation force for an annular contact disk brake with a single friction surface.
