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Chapter 14: Problem 28

Given the following data for a helical compression spring loaded in fatigue, design the spring for infinite life. State all assumptions and sources of empirical data used. \(C=8.5, d=8 \mathrm{~mm}, 625 \mathrm{rpm}\), working deflection \(=20 \mathrm{~mm}, 15 \%\) clash allowance, unpeened music wire, squared ends, preset, \(F_{\max }=450 \mathrm{~N}, F_{\min }=225 \mathrm{~N}\).

Short Answer

Expert verified
With the calculated stress amplitude, mean stress, and using the Goodman Criterion, the design can be deemed satisfactory if the final value is less than or equal to one. If any of these steps show that the spring is outside of acceptable parameters, adjustments need to be made to the spring's size, material, or both to ensure it is designed for infinite life.

Step by step solution

01

Compute the Spring Rate

The spring rate (k) is calculated by the formula \(k=\frac{{F_{\max} - F_{\min}}}{{\text{{deflection}}}} = \frac{{450 \mathrm{~N} - 225 \mathrm{~N}}}{{20 \mathrm{~mm}}} = 11.25 \mathrm{~N/mm}\).
02

Calculate the Mean Coil Diameter

The mean coil diameter (D) can be derived from the spring index (C) and wire diameter (d) using the formula \(D = C \cdot d = 8.5 \cdot 8 \mathrm{~mm} = 68 \mathrm{~mm}\).
03

Compute the Stress Correction Factor

Utilize the formula for the stress correction factor (Ks) which is \(Ks = \left(1 + \frac{{0.615}}{{C}}\right)\), where C is the spring index. Substituting C = 8.5, the stress correction factor is \(Ks = 1 + \frac{{0.615}}{{8.5}} = 1.072\).
04

Determine Stress Amplitude and Mean Stress

The stress amplitude (\(\Delta \sigma\)) and the mean stress (\(\sigma_m\)) can be calculated by the formulas \(\Delta \sigma = \frac{{Ks \cdot d \cdot k}}{{4 \cdot D}} = \frac{{1.072 \cdot 8 \mathrm{~mm} \cdot 11.25 \mathrm{~N/mm}}}{{4 \cdot 68 \mathrm{~mm}}}\), and \(\sigma_m = \frac{{Ks \cdot d \cdot F_{\max}}}{{8 \cdot D^3}} = \frac{{1.072 \cdot 8 \mathrm{~mm} \cdot 450 \mathrm{~N}}}{{8 \cdot (68 \mathrm{~mm})^3}}\).
05

Validate for Infinite Life

Check for the Goodman relation for infinite life which is \(\frac{{\sigma_m}}{{S_{e}}} + \frac{{\Delta \sigma}}{{S_{u}}} 鈮� 1\), where \(S_e\) and \(S_u\) are the endurance limit and ultimate strength of the material, respectively. These can be obtained from tables depending on the nature of the material used, in this case, unpeened music wire. If the equation is satisfied, then the spring is designed for infinite life.

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Most popular questions from this chapter

Design a straight-ended helical torsion spring for a static load of \(50 \mathrm{~N}-\mathrm{m}\) at a deflection of \(60^{\circ}\) with a safety factor of 2 . Specify all parameters necessary to manufacture the spring. State all assumptions.

Given the following data for a helical torsion spring, loaded in fatigue, find the spring index, unloaded coil diameter, minimum loaded coil diameter, and safety factor in fatigue. State all assumptions and sources of empirical data used. Deflection at assembly \(=0.15 \mathrm{rev}\), working deflection \(=0.35 \mathrm{rev}, k=10 \mathrm{~N}-\mathrm{m} / \mathrm{rev}, N_{a}=25\), \(4.50 \mathrm{~mm}\) oil-tempered wire, unpeened.

Design a helical compression spring to handle a dynamic load that varies from 780 \(\mathrm{N}\) to \(1000 \mathrm{~N}\) over a 22 -mm working deflection. Use squared and ground, unpeened music wire and a \(10 \%\) clash allowance. The forcing frequency is \(500 \mathrm{rpm}\). Infinite life is desired. Minimize the package size. Choose appropriate safety factors against fatigue, yielding, and surging.

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 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.
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