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Chapter 14: Problem 23

Design a straight-ended helical torsion spring for a static load of 300 in-lb at a deflection of \(75^{\circ}\) with a safety factor of 2 . Specify all parameters necessary to manufacture the spring. State all assumptions.

Short Answer

Expert verified
Wire diameter \(d\) can be calculated from step 1. Step 2 showed that Mean coil diameter \(D = 10d\). Steps 3, 4, 5 give us the spring constant \(k\), number of active coils \(n\), and spring rate \(K\), respectively. Refer to each step for the calculation process.

Step by step solution

01

Determine Wire Diameter

Use the formula: \[d = \sqrt{\frac{16T_s}{\pi\tau_{max}}}\]where \(T_s\) is the torque with the safety factor considered, \(\tau_{max}\) is the maximum allowable shear stress of the material (~0.4 times the Ultimate Strength). For stainless steel, \(\tau_{max}\) is approximately 70,000 psi. Compute \(T_s=2*300\) in-lb and convert to psi, then plug values into formula to find \(d\).
02

Find Mean Coil Diameter

The mean coil diameter \(D\) is preferably 10 times the wire diameter \(d\). Make the assumption that \(D = 10d\).
03

Spring Constant Calculation

Next, calculate the spring constant \(k\) using the formula: \[k = \frac{T_d}{\theta_d}\]Where: \(T_d\) is the deflection torque (300 in-lb) and \(\theta_d\) is the deflection (convert \(75^{\circ}\) to radians).
04

Active Coils Calculation

Then, to find the number of active coils \(n\), the formula is: \[n = \frac{Gd^4}{8D^3k}\]Where \(G\) is the shear modulus of the spring material (For stainless steel, typically \(G = 11.5*10^6 psi\)).
05

Spring Rate Calculation

Finally, compute the spring rate \(K\) by the formula \[K = \frac{1}{k}\]

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Most popular questions from this chapter

A helical extension spring, loaded in fatigue, has been designed for infinite life with the following data. \(C=9, d=8 \mathrm{~mm}\), working deflection \(=50 \mathrm{~mm}\), unpeened chrome-silicon wire, \(F_{\max }=935 \mathrm{~N}, F_{\min }=665 \mathrm{~N}, F_{\text {init }}=235 \mathrm{~N}, 13.75\) active coils. Find the safety factors for failure in the standard hooks. State all assumptions and sources of empirical data used.

Design a helical extension spring to handle a dynamic load that varies from 60 lb to 75 lb over \(0.5\)-in working deflection. Use music wire and standard hooks. The forcing frequency is \(1200 \mathrm{rpm}\). Infinite life is desired. Minimize the package size. Choose appropriate safety factors against fatigue, yielding, and surging.

Design a helical extension spring to handle a dynamic load that varies from \(175 \mathrm{~N}\) to \(225 \mathrm{~N}\) over a \(0.85\)-cm working deflection. Use music wire and standard hooks. The forcing frequency is \(1500 \mathrm{rpm}\). Infinite life is desired. Minimize the package size. Choose appropriate safety factors against fatigue, yielding, and surging.

Given \(d=0.312\) in, \(y_{\text {working }}=0.75\) in, \(15 \%\) clash allowance, unpeened chromevanadium wire, squared ends, \(F_{\max }=250 \mathrm{lb}\), and \(F_{\min }=50 \mathrm{lb}\), find \(N_{a}, D, L_{f}, L_{s h u t}\), \(k, y_{\text {initial }}\), and the minimum hole diameter for the spring. Infinite life is desired with a safety factor of 1.4. Choose an acceptable spring index. Setting will be done.

Design a straight-ended helical torsion spring for a dynamic load of \(50-105 \mathrm{~N}-\mathrm{m}\) over a deflection of \(80^{\circ}\) with a safety factor of \(2.5\). Specify all parameters necessary to manufacture the spring. State all assumptions.
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