Design of a Nine-Leaf Cantilever Spring A steel 0.9 m long cantilever spring has 80 mm wide nine leaves. The spring is subjected to a concentrated load P at its free end. Find: The depth of the leaves and the largest bending stress. Given: b=80 mm, L=0.9 m, P=2.5 kN, n=9 E=200 GPa, ν=0.3.

Question

Design of a Nine-Leaf Cantilever Spring

A steel 0.9 m long cantilever spring has 80 mm wide nine leaves. The spring is subjected to a concentrated load [latex] P [/latex] at its free end.

Find: The depth of the leaves and the largest bending stress.

Given: [latex] b [/latex]=80 mm, [latex] L [/latex]=0.9 m, [latex] P [/latex]=2.5 kN, [latex] n=9 E [/latex]=200 GPa, [latex] u [/latex]=0.3.

Assumption: Maximum vertical deflection caused by the load will be limited to 50 mm.

Accepted Answer

Equation (14.43) may be rearranged into the form

[latex] \delta=\left(1- u ^2 ight) \frac{6 P L}{E n b}\left(\frac{L}{h} ight)^3 [/latex] (14.43)

[latex] h^3=\left(1- u ^2 ight) \frac{6 P L}{E n \delta} [/latex] (d)

Inserting the given data, we have

[latex] h^3=\left(1-0.3^2 ight) \frac{6(2500)(0.9)^3}{\left(200 imes 10^9 ight)(9)(0.08)(0.05)}=1.382\left(10^{-6} ight) [/latex]

or

[latex] h=0.0111 m =11.1 mm [/latex]

Equation (14.42) results in the maximum stress as

[latex] \sigma=\frac{6 P L}{n b h^2} [/latex] (14.42)

[latex] \sigma_{\max }=\frac{6 P L}{n b h^2}=\frac{6(2500)(0.9)}{9(0.08)(0.0111)^2}=152.2 MPa [/latex]

The Goodman criterion may be used in the design of leaf springs subject to cyclic loading, as illustrated in the solution of the following numerical problem

Chapter 14

Q. 14.8

Q. 14.8

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