How Quickly Can a Conical Spring Expand from Compressed to Free Length?

[mhalc]

TL;DR Summary

How to determine the coil speed of a conical telescopic spring from its fully compressed height i.e. its spring wire dia to its free length.

I require a small conical spring to open from its compressed pancake height of its wire diameter to a free length of 11mm > 0.2 seconds (20 milliseconds)

The large end outer diameter = 7.80mm.
The small end inner diameter must be greater than or equal to 2.75mm.
The conical's spring's will be stored at a height = 5.5mm.
The conical spring will be subject to a set back force of at least 106N for 0.0005 seconds, which will cause the concial spring to pancake.
After pancaking the conical spring must achieve a working free length of 11.20mm.
The conical spring will need to move a mass of 5gms to get to its working free length.
Wire diameter and wire material are to be determined.

I require the conical spring to open from its solid height (wire diameter) to its free length of 11.20 mm in 0.20 seconds or longer.

Can anybody help with the maths please as this is way beyond my knowledge base?

I have attached a draft drawing of a potential conical spring design, which has spring material and wire diameter.

Please note that a similar request was made by a member in 2014 - see post - https://www.physicsforums.com/threads/how-fast-coil-springs-are-greatest-mystery-today.752813/

 

[berkeman]

Summary:: How to determine the coil speed of a conical telescopic spring from its fully compressed height i.e. its spring wire dia to its free length.

to a free length of 11mm > 0.2 seconds (20 milliseconds)

0.2s = 200ms.

And you want it to take longer than that? (>)

 

[mhalc]

0.2s = 200ms.

And you want it to take longer than that? (>)

Anything that is greater than 200ms would work.

 

[mhalc]

0.2s = 200ms.

And you want it to take longer than that? (>)

I am really sorry but I put the decimal place incorrectly in my first post.
Should be 0.02 seconds = 20 milliseconds

 

[berkeman]

Summary:: How to determine the coil speed of a conical telescopic spring from its fully compressed height i.e. its spring wire dia to its free length.

After pancaking the conical spring must achieve a working free length of 11.20mm.
The conical spring will need to move a mass of 5gms to get to its working free length.

Should be 0.02 seconds = 20 milliseconds

So you are worried that the extension time will be too quick? 20ms is a pretty short time...

Can you say what the application is? Does the 5g mass get launched by the helical spring, or is it attached to the end of the spring, or is it constrained to stop at the 11mm distance?

Here is a useful paper about springs, where they show an equation that you can use for the spring force as a function of extension for a conical spring:

http://www.faculty.fairfield.edu/wdornfeld/ME311/AssocSpringBarnes-SpringDesignHandbook.pdf

I also found that there are Conical Spring Force Calculators with a Google search:

https://www.google.com/search?q=con...mg&ei=KIm5Xve6PNO0-gSsh7qQCQ&bih=540&biw=1110

 

[mhalc]

Thank you for your reply and the links provided.

The extension time of the conical spring is critical to the application that the spring is working in.

The conical spring's large OD sits in a spring tube. When the spring is released the spring enables the spring tube to rotate and move a 5 gm component. The 5 gm component is not launched - it is just rotated 45 degrees.
The spring tube that the conical spring sits in only allows a max 11.20 free length - so the conical spring is constrained so that it can only achieve an 11.20 free length.
In its storage position the conical spring length is 5.50mm; under 106N set back force the conical spring pancakes to its solid height i.e. wire diameter, and then expands to 11.20 mm.

 

[Baluncore]

The traditional solution to this problem would be to use a “dashpot”.
https://en.wikipedia.org/wiki/Dashpot
https://en.wikipedia.org/wiki/Dashpot_timer

 

[mhalc]

Thank you for your help

 

[Chestermiller]

What do you estimate the mass of the spring to be?

 

[mhalc]

The mass of the spring is estimated at 0.169 gms

 

[Chestermiller]

The mass of the spring is estimated at 0.169 gms

This means that the mass of the spring is negligible compared to the 5 gm mass that is being accelerated. So the spring can be treated as massless. That makes things much easier.

You need to determine the force-displacement equation for your conical spring. That may be available analytically from the references @berkeman provided or from a more detailed (fairly complicated, in my judgment) stress/strain analysis requiring an expert consultant. Have you made a prototype and measured its force-displacement relationship?

 

[mhalc]

We have made 20 prototypes

See attached spec sheet from the manufacturer of the 20 prototypes

Does this help you?

 

[BvU]

Yes. The 0.12 N/mm will accelerate your 0.005 kg like crazy. You need damping.

 

[mhalc]

Thank you

 

[Chestermiller]

Yes. The 0.12 N/mm will accelerate your 0.005 kg like crazy. You need damping.

Or use a flimsier spring.

 

[Baluncore]

Will the spring always be operated with axis vertical?
Will the base be steady with only low amplitude vibration?

 

[Chestermiller]

Will the spring always be operated with axis vertical?
Will the base be steady with only low amplitude vibration?

My understanding was that there is not going to be vibration. I thought it was just that the 5 gm mass was being launched.

 

[mhalc]

Will the spring always be operated with axis vertical?
Will the base be steady with only low amplitude vibration?

Yes and Yes

 

[Baluncore]

I thought it was just that the 5 gm mass was being launched.

11 mm in 0.2 seconds will lift, but not launch. Does the mass remain attached to, or in contact with the spring?

The spring will need to be submerged in a viscous oil to delay the response.

 

[berkeman]

We have made 20 prototypes

Cool. Can you post your test data with your prototypes? That will probably save everybody a lot of time...

 

[mhalc]

Thank you for your reply. I have already posted the prototype spring test data in an earlier post
I have not been able to find any company that is able to measure the time that the conical spring takes to open from its solid height to its free length.

 

[mhalc]

11 mm in 0.2 seconds will lift, but not launch. Does the mass remain attached to, or in contact with the spring?

The spring will need to be submerged in a viscous oil to delay the response.

The 5gm mass remains in contact with a spring tube that encloses the conical spring
I will not be able to use viscous oil as this would contaminate other components in the assembled product

 

[jrmichler]

I require a small conical spring to open from its compressed pancake height of its wire diameter to a free length of 11mm > 0.2 seconds (20 milliseconds)

I have not been able to find any company that is able to measure the time that the conical spring takes to open from its solid height to its free length.

Most modern cell phones have "sport mode" video, which is 120 frames per second. That's 8 milliseconds per frame. Take a video, download the video to your computer, then step through the video frame by frame. That's for a move on the order of 20 msec. If you need 200 msec, then normal 30 frames / sec video will do the job.