×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Coil Spring exhibiting slightly different stiffness when compressing than when expanding

Coil Spring exhibiting slightly different stiffness when compressing than when expanding

Coil Spring exhibiting slightly different stiffness when compressing than when expanding

(OP)
Hi,

I came across to this problem for research and educational reasons.

Could someone suggest how to best describe the oscillation motion of a Coil Spring exhibiting slightly different stiffness when compressing than whn expanding?

Mathematically it consists in "just" solving the standard harmonic oscillator, but with the additional (maybe subtle) condition that the "K" constant of the spring changes across the equilibrium position
of the coil spring at x = 0. This can be done for example solving the associated differential equations using commercially available software. Before starting to work on that I would like to ask if someone is aware about work of this type already done in some engineering textbook or software tutorials (?)

thanks,

Best Regards,

F_C

RE: Coil Spring exhibiting slightly different stiffness when compressing than when expanding

I usually solve them numerically, to be honest. The extreme case is when the spring loses contact completely, as in the jounce bumper of a car, which has a non linear rate of its own. This introduces odd order harmonics to the vibration spectrum, as will your case, if you are driving with a pure sine wave of force, or vice versa if you are driving with a pure displacement sine wave.

If you are thinking about a spring mass system then I'm gently wondering in your case whether you can do SHM for each half of the cycle and then make sure the velocities and displacements are equal at x=0.

So for the shm, at maximum extension energy =1/2*k1*r1^2, and minimum 1/2*k2*r2^2, and obviously they are equal. The velocity at x=0 is 1/2*m*v^2, and again is equal to the max extension energy. In each half of the oscillation the angular frequency w=v/r, so it takes pi/w seconds to perform its half of the oscillation, add the times up and invert and there's your fundamental frequency. I think. If I've got the derivation right then w_combined=1/(pi*sqrt(m))*sqrt(k1*k2)/(sqrt(k1)+sqrt(k2)) which looks reasonable but needs checking. I am slightly mystified why SHM, a very linear analysis, is able to cope with a non linear spring.


<Note above has been edited>

A common way to get this effect in practice is to have two concentric springs of different lengths, so one only comes into play in compression. Oh, here we go

https://holooly.com/solutions/a-concentric-spring-...



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Design for Additive Manufacturing (DfAM)
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a part’s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close