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Chapter 18: Problem 6

A multiple-disk clutch is to operate in oil and be able to transmit a design overload torque of \(800 \mathrm{~N} \cdot \mathrm{m}\). The disks are alternately high-carbon steel and molded asbestos, with inside and outside diameters of 90 and \(150 \mathrm{~mm}\), respectively. Design values based on test experience for this application are \(p_{\max }=1000 \mathrm{kPa}\) and \(f=0.10\). What total number of disks is required?

Short Answer

Expert verified
The total number of disks required is approximately 851.

Step by step solution

01

Compute radii in meters.

Convert the given diameters into radii and then into meters. \nWe have a diameter of \(150mm\) for the outer disc, hence the radius \(r_2\) is \(r_2 = \frac{150}{2} = 75mm = 0.075m\).\nThe inside diameter is \(90 mm\), hence, the inner radius \(r_1\) is \(r_1 = \frac{90}{2} = 45mm = 0.045m\).
02

Calculate the Torque for one disc pair.

The expression for maximum torque \(T\) of one disc pair is given by the formula \(T_{one} = 2p_{max} \cdot f \cdot (r_2^2 - r_1^2)\). Substitute the given values into the formula we get \(T_{one} = 2 \cdot 1000kPa \cdot 0.1 \cdot (0.075^2 -0.045^2)\)N.m. Remember that 1kPa = \(10^3\)N/m虏. So, \(T_{one} = 2 \cdot 10^3 N/m^2 \cdot 0.1 \cdot (0.075^2 - 0.045^2)\) = \( T_{one} = 2 \cdot 0.47 N.m \) = \(0.94 N.m.\)
03

Calculate total number of discs.

Total torque requirement is \(800 N.m\). The total number of discs can be obtained by the formula: Number of discs \(= \frac{Total Torque}{Torque for one disc}\) Substitute the given values into the formula we get Number of discs \(= \frac{800}{0.94}\)

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Most popular questions from this chapter

Figure P18.16 shows a 1000-kg mass being lowered by a cable at a uniform rate of \(4 \mathrm{~m} / \mathrm{s}\) from a drum of \(550-\mathrm{mm}\) diameter weighing \(2.5 \mathrm{kN}\) and having a 250 -mm-radius of gyration. (a) What is the kinetic energy in the system? (b) The uniform rate of descent is maintained by a brake on the drum which applies a torque of \(2698 \mathrm{~N} \cdot \mathrm{m}\). What additional brake torque is required to bring the system to rest in \(0.60 \mathrm{~s}\) ?

A basic disk clutch is to be designed to transmit a torque of \(100 \mathrm{lb} \cdot\) in. The outer ring diameter is to be 4 in. Design values for the steel disk and the molded friction material to be used are \(p_{\max }=200 \mathrm{psi}\) and \(f=0.25\). Determine appropriate values for the ring inside diameter and the clamping force.

A multiple-disk dry clutch for an industrial application must transmit \(6 \mathrm{hp}\) at \(200 \mathrm{rpm}\). Based on space limitations, inside and outside disk diameters have been set at 5 and 7 in., respectively. Materials are hardened steel and sintered bronze. Tests have indicated that design values of \(p_{\max }=225 \mathrm{psi}\) and \(f=0.20\) are appropriate. (a) For a safety factor of \(2.0\) with respect to clutch slippage, what total number of disks is needed? (b) Using this number of disks, what is the least clamping force that will provide the desired torque capacity? (c) Using this clamping force, what is the interface pressure at the inside and outside contact radii? (Assume that "initial wear" has taken place.)

An industrial diesel engine is attached to a \(4: 1\) ratio gear reducer, the output of which is coupled by means of a friction clutch to a machine having a mass moment of inertia of \(15 \mathrm{~N} \cdot \mathrm{m} \cdot \mathrm{s}^{2}\). Assume that the clutch is controlled so that during its engagement the engine operates continuously at \(2800 \mathrm{rpm}\), delivering a torque of \(127.5 \mathrm{~N} \cdot \mathrm{m}\) : (a) What is the approximate time required for the clutch to accelerate the driven machine from rest to \(700 \mathrm{rpm}\) ? (b) How much energy is delivered to the driven machine in increasing the speed to \(700 \mathrm{rpm}\) ? (c) How much heat energy is generated in the clutch during this engagement?

A multiple-disk wet clutch is to be designed to transmit a torque of \(700 \mathrm{lb} \cdot\) in. The outer disk diameter is to be 4 in. Design values for the steel disks and the molded friction material to be used are \(p_{\max }=200 \mathrm{psi}\) and \(f=0.06\) (wet). Determine appropriate values for the disk inside diameter, total number of disks, and clamping force.
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