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MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
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ber of pairs of contacting disk faces. Torque capacity can also be expressed in terms of the actuating force F: T= 8.7.2 Caliper Disk Brakes The automotive caliper disk brake shown in Fig. 8.9 is hydraulically operated. Two pads are pressed against opposite sides of the brake disk to provide a braking torque. The principle of operation is shown schematically in Fig. 8.26a. Usually each pad is nearly the annular shape, illustrated in Fig. 8.26b, but occasionally a circular pad ( puck or button ) is used (Fig. 8.26c). Ff Np (D + d) 4 (8.59)
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FIGURE 8.26 Caliper disk brake. (a) Principle of operation; (b) annular pad; (c) circular pad.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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Torque Capacity. The torque capacity per pad is T = fFRe (8.60)
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If two pads are used, then the torque capacity is double the value calculated by Eq. (8.60). This torque equation is quite simple. A friction force fF acting at an effective friction radius Re produces a braking torque T. The practical issues are (1) the value to use for the effective friction radius Re and (2) the maximum contact pressure pmax developed. Actuating Force for Annular Pad. Brake designers often assume that the contact pressure does not vary very much over the annular pad. But you may prefer to use the uniform-wear approach as more realistic. Both approaches are given here. The following two equations are used to calculate the actuating force for the constant-contact-pressure and the uniform-wear approaches, respectively: F = pav
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2 R o R2 i 2
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(8.61) (8.62)
F = pmax Ri (Ro Ri)
The notation is shown in Fig. 8.26a and b. The relation between average and maximum contact pressures for the uniformwear approach is pav 2Ri /Ro = pmax 1 + Ri /Ro (8.63)
In the limit, the average and maximum pressures become equal as the inner radius approaches the outer one. For Ri/Ro = 0.60, pav = 0.75pmax; but for Ri/Ro = 0.80, pav = 0.89pmax. The uniform-wear assumption is the more conservative approach. For a given actuating force, it implies a smaller torque capacity. Effective Friction Radius for Annular Pad. If the contact pressure is assumed to be constant over the pad, the effective friction radius is Re =
3 2 R o R3 l 2 3 R o R2 l
(8.64)
When the uniform-wear assumption is made, the effective friction radius is simply Re = R i + Ro 2 (8.65)
Circular Pads. Fazekas [8.3] has derived the basic equations for circular pads. The effective friction radius is Re = e (8.66)
where e = radius from the center of the disk to the center of the pad and = multiplier found in Table 8.9. Also tabulated in Table 8.9 is the ratio of maximum to average contact pressure.
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CLUTCHES AND BRAKES 8.44
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TABLE 8.9 Design Factors for Caliper Disk Brakes with Circular Pads
The actuating force on each pad is F = R2pav (8.67)
The torque capacity per pad is found by using Eq. (8.60) after F and Re have been calculated. Example 9. A sports car requires disk brakes for the front wheels. It has been decided to use two annular pads per wheel with Ri = 3.875 in, Ro = 5.5 in, and = 108 . The friction material supplier guarantees a coefficient of friction of at least f = 0.37. Each pad is actuated by two hydraulic cylinders, each 1.5 in in diameter. Each frontwheel brake provides a braking torque capacity of 13 103 lb in. What hydraulic pressure is needed at the wheel cylinders What are the average and the maximum contact pressures Assume uniform wear. Solution 1. The torque capacity per pad has to be (13 103)/2 = 6500 lb in. Given uniform wear, the effective friction radius is, by Eq. (8.65), Re = R i + Ro 3.875 + 5.5 = = 4.69 in 2 2
The corresponding actuating force is, by Eq. (8.60), T= or F = 1875 lb per wheel cylinder The hydraulic pressure at the wheel cylinder has to be ph = 4(1875) F 4F = = = 1060 psi A p d 2 (1.5)2 p T 6500 = = 3750 lb per pad f Re 0.37(4.69)
2. Equation (8.62) can be used to find the maximum contact pressure: pmax = 3750 F = = 316 psi Ri (R o Ri ) (108 /57.296)(3.875)(5.5 3.875)
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