Question 13.5: Design of a Disk Clutch A disk clutch with a single friction...
Design of a Disk Clutch
A disk clutch with a single friction surface has an outer diameter D and inner diameter d (Figure 13.14).Determine the torque that can be transmitted and the actuating force required of the spring, on the basis of
a. Uniform wear
b. Uniform pressure
Given: D = 500 mm, d = 200 mm
Design Decisions: Molded friction material and a steel disk are used, having f = 0.35 and p_{max} = 1.5 MPa (see Table 13.11).
| Table 13.11 Properties of Common Brake and Clutch Friction Materials, Operating Dry |
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| Dynamic Coefficient of Friction, f |
Maximum Pressure p_{max} |
Maximum Drum Temperature |
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| Material^{a} | Mpa | psi | °C | °F | |
| Molded | 0.25–0.45 | 1.03–2.07 | 150–300 | 204–260 | 400–500 |
| Woven | 0.25–0.45 | 0.35–0.69 | 50–100 | 204–260 | 400–500 |
| Sintered metal | 0.15–0.45 | 1.03–2.07 | 150–300 | 232–677 | 450–1250 |
| Cork | 0.30–0.50 | 0.06–0.10 | 8–14 | 82 | 180 |
| Wood | 0.20–0.25 | 0.35–0.63 | 50–90 | 93 | 200 |
| Cast iron, hard steel | 0.15–0.25 | 0.70–0.17 | 100–250 | 260 | 500 |
| Sources: Based on Binder, R.C., Mechanics of Roller Chain Drive, Prentice Hall, Upper Saddle River, NJ, 1956. a When rubbing against smooth cast iron or steel. |
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a. Through the use of Equation 13.29, we have
T=\int_{d / 2}^{D / 2}\left(\pi p_{\max } d\right) f r d r=\frac{1}{8} \pi f p_{\max } d\left(D^2-d^2\right) (13.29)
T=\frac{1}{8} \pi(0.35)(1500)(0.2)\left(0.5^2-0.2^2\right)=8.659 kN \cdot m
From Equation 13.28,
F_a=\int_{d / 2}^{D / 2} \pi p_{\max } d d r=\frac{1}{2} \pi p_{\max } d(D-d) (13.28)
F_a=\frac{1}{2} \pi(1500)(0.2)(0.5-0.2)=141.4 kN
b. Applying Equation 13.33,
T=\int_{d / 2}^{D / 2}\left(2 \pi p_{\max } r\right) f r d r=\frac{1}{12} \pi f p_{\max }\left(D^3-d^3\right) (13.33)
T=\frac{1}{12} \pi(0.35)(1500)\left(0.5^3-0.2^3\right)=16.08 kN \cdot m
By Equation 13.32,
F_a=\int_{d / 2}^{D / 2} 2 \pi p_{\max } r d r=\frac{1}{4} \pi p_{\max }\left(D^2-d^2\right) (13.32)
F_a=\frac{1}{4} \pi(1500)\left(0.5^2-0.2^2\right)=247.4 kN
Comment: The preceding results indicate that the uniform wear condition yielded a smaller torque and actuating force; it is therefore the more conservative of the two assumptions in terms of clutch capacity.