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This is related to my recent question Can I weaken a coil spring consisting of spring steel?. The answer here could create an additional answer there, but I do not expect that. The difference to that question is that this is about changes in the actual spring properties, so much that there could be a fully theoretical answer with no relation to empiric coil behaviour.

What changes in the properties of a coil spring if I stretch it so much that it causes plastic deformation, and cut it to restore the length?

For example, I take a steel coil spring with a length without load of 100 mm. I extend it so much that it plastically deforms, and has a new rest length of 150 mm. Now, I cut the spring to the length of 100 mm. If it had 20 windings before, it now has about 13 windings. It does not need to be a steel spring, if a more homogeneous material simplifies it. An answer could even use an abstract material that may or may not

What is different?
How have the spring properties changed?
The mass is reduced to 2/3, how does that change the resonance frequency? Is it influenced by other factors?

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Stiffness:

  1. If you cut the spring by 1/2, it will have double stiffness (spring rate). This means your 2/3 springs rate will be 3/2 of the original rate. This is independent of the length of the spring, it is onyl the number of coils, that cause the difference.
  2. If you deform a material into plastic deformation, depending on the material anything can happen.
  3. For significant elongations, also the diameter of the coil will be reduced significantly (you can easily try this with a ball pens spring). This will increase the stiffness by the factor of whicht the coild diameter is reduced. 1/2 coild diameter, 2/1 stiffness.

The eigenfrequencies of the spring itself (note plural) change. For two reasons: increased stiffness and reduced wheight. Both will increase the eigenfrequencies.

If you assemble the spring with other bodies, the eigenfrequencies of the system will also depend on the other bodies masses and how the're connected.

In any way, the spring will become stiffer, this is opposite of what you wanted in your other question.

But I have an idea for the other question, that I will put there.

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