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These brakes have the advantage of greater torque for a smaller axial force than either type of disk brake discussed in Chapter 5. The magnitude of the improvement is limited, however, by the observation that for small cone angles a disengagement force may be required, depending on the friction coefficient, because the inner and outer cones may tend to wedge together. This is because on engagement the inner cone is radially compressed and the outer cone is radially enlarged as the brake is engaged. For small cone angles the induced friction force dominates the normal force, which tends to expel. | 6 Cone Brakes and Clutches These brakes have the advantage of greater torque for a smaller axial force than either type of disk brake discussed in Chapter 5. The magnitude of the improvement is limited however by the observation that for small cone angles a disengagement force may be required depending on the friction coefficient because the inner and outer cones may tend to wedge together. This is because on engagement the inner cone is radially compressed and the outer cone is radially enlarged as the brake is engaged. For small cone angles the induced friction force dominates the normal force which tends to expel the inner cone so that an external force is required for separation. This characteristic however may be useful in those applications where a brake is to remain engaged in the presence of disengagement forces. I. TORQUE AND ACTIVATION FORCE The pertinent geometry of the cone brake is shown in Figure 1. If the inner and outer cones are concentric and rigid the amount worn from the lining during engagement will be given by 8 kpr 1-1 where p denotes the pressure and r is the radius to the point where p acts. Proportionality constant k may be evaluated by observing that the form of relation 1-1 demands that the maximum pressure occur at the minimum radius. Hence 8 kpmaxri 1-2 Copyright 2004 Marcel Dekker Inc. Figure 1 Cone brake and its geometry partially worn lining . Upon equating equations 1-1 and 1-2 we find that ri P Pmax r 1-3 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 T A prda APmax ri A da A 2fikpmaxri sin a r rdr ri 1-4 Copyright 2004 Marcel Dekker Inc. where the element of area on the outside of the inner cone is given by da 2krd 2 -- 1-5 sin a and .
