Maximum bending moment and maximum deflection of the spring?

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SUMMARY

The discussion focuses on determining the maximum bending moment and maximum deflection of a coil spring under compression. It clarifies that a compression coil spring does not experience bending moments as typically understood in structural mechanics; instead, it is analyzed for torsion. The maximum deflection occurs when the clearance between the coils reaches zero. Key references for the relevant formulas include "Shigley’s Mechanical Engineering Design" and "Roark’s Formulas for Stress and Strain."

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  • Access to "Shigley’s Mechanical Engineering Design" and "Roark’s Formulas for Stress and Strain"
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  • Study the torsion formulas applicable to helical springs
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Mechanical engineers, students studying mechanical design, and professionals involved in spring analysis and design will benefit from this discussion.

metalsunsuccess1
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TL;DR
How do I find the maximum bending moment and maximum deflection of the spring?
How can I find the maximum bending moment and maximum deflection for a spring?

It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner.

that's all, thank you very much.
 
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What kind of spring is this?
 
Thank you for your reply.

This assumed mechanical spring is a coil spring, and the lower part is placed on a table (not fixed), and a concentrated load is applied from above in the compression direction.

Thank you.
 
metalsunsuccess1 said:
Thank you for your reply.

This assumed mechanical spring is a coil spring, and the lower part is placed on a table (not fixed), and a concentrated load is applied from above in the compression direction.

Thank you.

So how is there a "bending moment"? The loading you described wouldn't produce one.

The "maximum deflection" of a compression coil is when the clearance between the coils is zero.
 
Helical springs subjected to compression are calculated for torsion. You can find the formulas for example in "Shigley’s Mechanical Engineering Design" or in "Roark’s Formulas for Stress and Strain".
 
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It looks like you saw the units [N.m] or [lbf.ft] somewhere and thought it was bending moment, but springs are usually loaded in pure torsion, which uses the same units, but the meaning is completely different.
 

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