Page 149 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 135

giving greater resistance to slipping. If the drive is fitted with a guide pulley,
or a tensioning device similar to the belt jockey or idler pulley, the rope rests
on the bottom of the groove as shown in Fig. 4.38, case (b). To avoid
excessive loss of energy due to bending of the rope as it passes over the
pulley, the diameter of the pulley should be greater than 30d, where d is the
diameter of the rope.
For wire ropes the groove is as shown in Fig. 4.38, case (c). In this case
also, the rope rests on the bottom of the groove, since no jamming action is
permissible if increased wear and breakage of the wires is to be avoided. The
wedge-shaped recess at the bottom of the groove is packed with a relatively
soft material, such as wood or leather. In addition to diminishing-the wear
Figure 4.38
on the rope this gives a greater coefficient of friction.
Figure 4.38, case (d), shows the groove for a high speed V-belt machine
drive. The belt is of rubber, reinforced with cotton fibre. It consists of a load-
carrying core of rubber-impregnated fabric and the surrounding layers are
carefully designed to withstand a repeated bending action during driving.
The sides of the groove must be prepared to a fine finish and the pulleys
placed carefully in alignment if wear of the belt is to be reduced to an
acceptable level. The diameter of the smaller pulley should be greater than
Id to 16J, where d is the depth of the V-belt section. The angle of the groove
varies from 30 to 40 degrees.
An important feature of rope or V-belt drives is the virtual coefficient of
friction. Referring to Fig. 4.39, let
2\(/ = the total angle of the groove,
R = the resultant radial force exerted by the pulley on an element
of length rd© of the rope, where r and 0 have the same
meaning as discussed previously in connection with the flat
Figure 4.39 belt action.
The force R is the resultant of the side reactions RI where the rope makes
contact with the surface of the groove. It is usual to neglect the friction due
to wedge action, in which case R^ is normal to the contact surface.

Again, as previously shown, the increment of tension in the length r<50 is

where

To take account of the V-groove we must therefore replace/by the virtual
coefficient of friction /' in the ordinary belt formulae. Thus, eqn (4.79)
becomes