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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| Maximum Pressure p_{max} | Maximum Drum Temperature | ||||
| Material ^a |
Dynamic Coefficient of Friction, f | 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 |
| {} ^ {a} When rubbing against smooth cast iron or steel. | |||||
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}{2} \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.