Page 159 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 145

number of wooden blocks or other friction material, each of which is in
contact with the rim of the brake wheel. Each block, as seen in the elevation,
subtends an angle 2\l/ at the centre of the wheel. When the brake is in action
the greatest and least tensions in the brake strap are T t and T 2, respectively,
and the blocks are numbered from the point of least tension, T 2.
Let kT 2 denote the band tension between blocks 1 and 2. The resultant
force R\ exerted by the rim on the block must pass through the point of
intersection of T 2 and kT 2. Again, since 2i// is small, the line of action of/?i
will cut the resultant normal reaction R at the point C closely adjacent to
1
the rim, so that the angle between R and R\ is 0=tan~ f.
Suppose that the angle between R and the line of symmetry OS is /?, then,
from the triangle of forces xyz, we have

If this process is repeated for each block in turn, the tension between blocks
2 and 3 is k. Hence, if the maximum tension is 7\, and the number of blocks
is n, we can write

Figure 4.45

If the blocks are thin the angle (3 may be regarded as small, so that

or

so that

4.12. The role of The maximum possible acceleration or retardation of a vehicle depends
friction in the propulsion upon the limiting coefficient of friction between the wheels and the track.
Tnus
and the braking of if
vehicles R=the total normal reaction between the track and the driving
wheels, or between the track and the coupled wheels in the case
of a locomotive,