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Chapter 14: Problem 1

A linear spring is to give \(200 \mathrm{~N}\) at its maximum deflection of \(150 \mathrm{~mm}\) and \(40 \mathrm{~N}\) at its minimum deflection of \(50 \mathrm{~mm}\). What is its spring rate?

Short Answer

Expert verified
The spring rate of the linear spring is \(1600 N/m\).

Step by step solution

01

Understand the given values

The problem provides two pairs of forces \(F_1, F_2\) and their corresponding deflections \(x_1, x_2\). Here \(F_1 = 200N, x_1 = 150mm = 0.15m\) (converted from mm to m for consistency of units) and \(F_2 = 40N, x_2 = 50mm = 0.05m\)
02

Formulate the equation for spring rate

The spring rate formula with regards to the provided pairs (values) is given by: \(k = \frac{F_1 - F_2}{x_1 - x_2}\)
03

Substitute the real values into the equation

Now we substitute the values into the spring rate formula: \(k = \frac{200N - 40N}{0.15m - 0.05m}\)
04

Perform the computation

Solving the equation gives: \(k = \frac{160N}{0.1m} = 1600 N/m\)

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Most popular questions from this chapter

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.

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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.

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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