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CLUTCHES AND BRAKES 8.38
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FIGURE 8.20 Cone clutch; A, cup; B, cone; C, shifting groove; D, spring; E, friction lining; = cone angle.
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FIGURE 8.21 Cone brake; = cone angle.
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CLUTCHES AND BRAKES 8.39
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CLUTCHES AND BRAKES
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FIGURE 8.22 Elementary quantities on conical surface.
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F = 2 T= 2 sin
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d/2 D/2
(8.50) (8.51)
fpr 2 dr
Before these integrations can be carried out, assumptions have to be made about the way in which contact pressure p and friction coefficient f vary across the active face of the cone. In what follows, the variations of f with pressure and rubbing velocity have been neglected. Only the variation in contact pressure p is used. Contact-Pressure Distribution. When the friction surfaces are new, the pressure is fairly uniform across the clutch face. But after an initial wear-in period, the pressure
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CLUTCHES AND BRAKES 8.40
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
accommodates itself to a uniform rate of wear. We assume that the wear rate is proportional to the frictional work per unit area, that is, to fpV. If the variations in f are neglected, then the wear rate is proportional simply to pV, the product of contact pressure and rubbing velocity. We can write pV = 2 r p = constant (8.52)
Thus across the face the product pr is constant, implying that pmax occurs at the inner radius d/2. In general, p= pmax d 2r (8.53)
A typical pressure distribution is shown in Fig. 8.23. Torque Capacity. By substituting for p from Eq. (8.53) in Eq. (8.51) and carrying out the integration, we find the torque capacity T: T= f pmaxd (D2 d2) 8 sin (8.54)
Actuating Force. Equation (8.50) can be integrated to yield F= pmaxd (D d) 2 (8.55)
The last two equations can be combined to produce the useful result T= Ff (D + d) 4 sin (8.56)
The last equation indicates that for the uniformwear assumption, the mean friction radius is simply the average radius. Moment Equation for Brake Lever. The axial actuating force for the cone brake shown in Fig. 8.21 can be found by summing moments on the lever about the pivot point O and solving for F. Thus F= Q a (8.57)
FIGURE 8.23 Contact-pressure distribution on face of cone after wear-in period (for constant f).
8.7 DISK CLUTCHES AND BRAKES
8.7.1 Multidisk Clutches and Brakes The multidisk clutch in Fig. 8.24 is intended for wet operation using an oil coolant. Similar clutches are built for dry operation. Disk brakes are similar in construction
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CLUTCHES AND BRAKES 8.41
CLUTCHES AND BRAKES
to the disk clutch. In either case, an axial force is applied to the flat surfaces of the elements to produce tangential frictional forces.Typically not more than the outer 40 percent of the radius is used. The ratio of inside to outside diameters may be as high as 0.80/1. Contact-Pressure Distribution. The reasoning used to establish pressure distribution on the annular clutch or brake plate is the same as that used for cone clutches and brakes. After an initial wear-in period, the pressure distribution accommodates itself to a constant rate of wear across the active portion of the disk (Fig. 8.25). Equations (8.52) and (8.53) apply here also. Axial Actuating Force. For a given set of dimensions and a permissible contact pressure, the corresponding actuating force is given by Eq. (8.55), which was developed for cone clutches and brakes. Torque Capacity. For this pressure distribution, the torque capacity is 1 T = [ fpmaxd(D2 d2)Np] 8 (8.58)
Although the torque equation could be derived independently, it can also be derived directly from Eq. (8.54) by setting the cone angle = 90 and inserting Np, the num-
FIGURE 8.24 An oil-actuated multiple-disk clutch for enclosed operation in an oil spray or bath. (Twin Disc, Inc.)
FIGURE 8.25 A friction member of a multiple-disk clutch or brake with the pressure distribution for uniform wear.
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