A flat spiral spring is required to provide a maximum torque of 1200 N-mm. The spring is made of a steel strip and the maximum bending stress should not exceed 800 N/mm^2. When the stress in the spring decreases from 800 to 0 N/mm^2, the arbor turns through three complete revolutions with respect

Question

A flat spiral spring is required to provide a maximum torque of 1200 N-mm. The spring is made of a steel strip and the maximum bending stress should not exceed 800 N/mm². When the stress in the spring decreases from 800 to 0 N/mm², the arbor turns through three complete revolutions with respect to the retaining drum. The thickness of the steel strip is 1.25 mm and the modulus of elasticity is 207 000 N/mm². Calculate the width and length of the steel strip.

Accepted Answer

[latex] ext { Given } M=1200 N - mm \quad \sigma_{b}=800 N / mm ^{2} [/latex].

[latex] E=207000 N / mm ^{2} \quad t=1.25 mm [/latex].

Step I Width of strip
From Eq. (10.32),

[latex] \sigma_{b}=\frac{12 M}{b t^{2}} [/latex] (10.32).

[latex] \sigma_{b}=\frac{12 M}{b t^{2}} \quad ext { or } \quad 800=\frac{12(1200)}{b(1.25)^{2}} [/latex].

∴ b = 11.52 or 12 mm
Step II Length of strip

[latex] heta=3 ext { revolutions }=3(2 \pi)=6 \pi ext { radians } [/latex].

From Eq. (10.33),

[latex] heta=\frac{12 M l}{E b t^{3}} [/latex] (10.33).

[latex] heta=\frac{12 M l}{E b t^{3}} [/latex].

or [latex] 6 \pi=\frac{12(1200) l}{(207000)(12)(1.25)^{3}} [/latex].

∴ l = 6350.68 mm or 6.35 m.

Question 10.22: A flat spiral spring is required to provide a maximum torque...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions