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Chapter 14: Problem 25

Design a straight-ended helical torsion spring for a dynamic load of \(150-350\) in-lb over a deflection of \(50^{\circ}\) with a safety factor of \(1.4\). Specify all parameters necessary to manufacture the spring. State all assumptions.

Short Answer

Expert verified
The spring parameters are: Mean load: 250 in-lb, Spring constant: 14.32 lb-in/rad, Material: Music Wire with a shear modulus of \(11.5 * 10^6\) psi, Mean Coil Diameter and Wire Diameter to be found using iteration and following the safety factor, Number of coils: 10, Free length: to be decided based on maximum load, Ends: Straight.

Step by step solution

01

Calculate the Mean Load

The mean dynamic load can be calculated with the formula: \(L_{mean} = (L_{max} + L_{min}) / 2 = (350+150) / 2 = 250\) in-lb. Where \(L_{max}\) and \(L_{min}\) are the maximum and minimum loads respectively.
02

Calculate the Spring Constant

The spring constant \(k\) represents the amount of deflection the spring experiences under load. It is calculated using the formula \(k = L_{mean}/伪\) Where \(伪 = 50^{\circ} \) is the angle of deflection converted to radians. Therefore, \(k = 250 / (50 * 蟺/180) = 14.32\) lb-in/rad.
03

Choose Spring Material

The choice of material will influence the spring's properties. We can assume the usage of a common spring material such as music wire, which typically exhibits a shear modulus (G) of approximately \(11.5 * 10^6\) psi.
04

Calculate Mean Coil Diameter

The formula to calculate the Mean Coil Diameter \(D\) is \(D\sqrt{16Nk/(蟺d^{4}G)}\) , N is the number of active coils and d is the wire diameter. This is a complex nonlinear formula and may require guesses and iterations to solve. For simplicity, assumptions imply that springs typically have 5 to 15 active coils. Let's assume \(N = 10\), and use the guess-and-check method to find \(d\) and \(D\) that satisfies the equation and the safety factor.
05

Specify Rest of Parameters

With the material, D, d, and N specified, the remaining parameters necessary to manufacture the spring include the free length (usually slightly more than the spring's length when under maximum load) and the type of ends on the spring (already specified to be straight in the problem statement).

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Most popular questions from this chapter

Design a helical compression spring for a static load of \(60 \mathrm{lb}\) at a deflection of \(1.50\) in with a safety factor of \(2.0\) to work in a \(1.06\)-in- dia hole. Specify all parameters necessary to manufacture the spring.

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 compression spring to handle a dynamic load that varies from 135 \(\mathrm{N}\) to \(220 \mathrm{~N}\) over a 32 -mm working deflection. Use squared, peened chromevanadium wire and a \(15 \%\) clash allowance. The forcing frequency is \(250 \mathrm{rpm}\). 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.

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.
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