/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 A torque of \(14.0 \mathrm{~N} \... [FREE SOLUTION] | 91影视

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Chapter 18: Problem 1

A torque of \(14.0 \mathrm{~N} \cdot \mathrm{m}\) is to be transmitted through a basic disk clutch. The outer ring diameter is to be \(120 \mathrm{~mm}\). Design values for the steel disk and the molded friction material to be used are \(p_{\max }=1.55 \mathrm{MPa}\) and \(f=0.28\). Determine appropriate values for the ring inside diameter and the clamping force.

Short Answer

Expert verified
The clutch's inside diameter, \(R_1\), and the clamping force, \(F_c\), can be calculated by plugging in known parameters into the torque equation, rearranging it for the desired variable, and solving for that variable. Exact numeric values will depend on the specific inputs.

Step by step solution

01

Determine the outside radius

Given that the outside diameter is \(120 \mathrm{~mm}\), we can calculate the outside radius \(R_2\) since the radius is half the diameter. Hence, \(R_2\) is \(60 \mathrm{~mm}\) or \(0.06 \mathrm{~m}\).
02

Formulate the torque equation

We know that the transmitted torque \(T\) is given by \(T = \mu \cdot p_{\max} \cdot \pi \cdot (R_2^4 - R_1^4) \cdot F_c\), where \(\mu\) is the material friction factor, \(p_{\max}\) is the peak stress, \(R_2\) is the outside radius, \(R_1\) is the inside radius and \(F_c\) is the clamping force. To calculate \(R_1\) and \(F_c\) we rearrange the equation and we have to use the given values of \(T\) and \(\mu\) and \(p_{\max}\).
03

Determine the inside radius from the torque equation

We know the value of the torque, friction factor and peak stress. We can solve the equation \(R_2^4 - R_1^4 = T/(\mu \cdot p_{\max} \cdot \pi \cdot F_c)\) as a function of \(R_1\) to calculate the inside radius.
04

Determine the clamping force from the torque equation

After we have the value for \(R_1\), we can determine the clamping force \(F_c\). We plug \(R_1\) and the known values for \(T\), \(\mu\) and \(p_{\max}\) in to the equation \(T = \mu \cdot p_{\max} \cdot \pi \cdot (R_2^4 - R_1^4) \cdot F_c\) and solve for \(F_c\).

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Most popular questions from this chapter

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.)

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 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?

The wheels of a standard adult bicycle have a rolling radius of approximately \(13.5\) in. and a radius to the center of the caliper disk brake pads of \(12.5\) in. The combined weight of bike plus rider is \(225 \mathrm{lb}\), equally distributed between the two wheels. If the coefficient of friction between the tires and road surface is twice that between the brake pads and the metal wheel rim, what clamping force must be exerted at the caliper in order to slide the wheels?

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 \(0.60 \mathrm{~s}\) ?
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