As in the case of the arms, centrifugal force does not play much part in the design of the hub of a pulley. The hub is designed principally to carry the key, and through it transmit the turning moment to the shaft. Considered thus, the hub may tear along the line of the key or crush in front of the key.
For example, in Fig. 22, if the connection with the lower arms be neglected, and the upper arms be held fast while a turning force P1 at the surface of the shaft, is transmitted to the hub through the key, then the metal of the hub directly in front of the key is under crushing stress; and the metal along the line eb, from the corner to the outside, is under tensile stress. This condition is the worst that could possibly happen, because the bracing effect of the lower arms has been neglected, and the key is located between.
Makiug moments about the center of the shaft, the value of the Give at the shaft circumference, or the "key pull," is:
P1 = PR. / r (26)
Now- P1 / P3 = k/r, k being the distance from the center of shaft to center of eb, and the area of metal which is subjected to the tearing action P3 is l X eb. Equating the external force to the internal resistance, and assuming that the stress is equally distributed over the area l X eb, we have:
P3 = r/k p1 = r/k x PR/r = s x l x eb; or, S = PR / k x l x eb (27)
The intensity of crushing on the metal in front of the key, due to force P1 depends upon the thickness of the key, and is properly discussed later under "Keys".