Linearity of Helical Springs

[thadman]

For the design of a cantilever, assuming a Hookean material is used below its proportionality limit, stress will be proportional to strain. From this we can conclude that its behavior will be linear.

However, how can we apply this knowledge towards helical springs? Is it possible to design a helical spring whose linearity approaches or equals the cantilever?

Thanks,
Thadman

[noah katz]

Depends on how close you want to approach it.

I think the only significant linearity in a helical spring is change in the helix angle with displacement, but I suspect it's minor for any realistic spring.

What's the application?

[thadman]

Originally Posted by noah katz

Depends on how close you want to approach it.

I think the only significant linearity in a helical spring is change in the helix angle with displacement, but I suspect it's minor for any realistic spring.

Assuming a cylindrical, uniform, helical spring, whose coils have not started to close, which supports a surface. Would the spring force be linear across the contact surface?

[noah katz]

Depends on the surface shape; if it matches that of the undeflected spring, I'd think not, and the force would be concentrated at the latest point of contact.

If it's flat maybe, but it may need to be some other shape.

[thadman]

I picked up the seventh edition of Roark's formulas for Stress and Strain. It appears to be rather trivial to calculate the fundamental resonance for a helical spring (f(n)=1/2sqrt(k/m), where k=spring constant and m=mass). However, calculating the mass normalized modes does not appear to be trivial.

How should we approach solving this problem?

[noah katz]

The engineering section on a spring company's (try Associated Spring) site should have formula for res freq.

Again, what's the application?

You could really step out of the box and try google.

[thadman]

Originally Posted by noah katz

You could really step out of the box and try google.

I've searched google and have purchased several engineering texts (>$300! academia is EXPENSIVE!). I have been trying to schedule meetings with a few of the professors in the engineering department, however they are very busy with research and have limited time to answer my questions. However, I do have a meeting tomorrow, we'll see if I'm able to reach any resolution.

Let me be more explicit,

Assuming a cantilever (left end fixed, right end free), an equation exists which defines all of the natural frequencies.

F(x)=(K(n)/2pi)*sqrt(EIg/wl^4)

Where K(n) = 3.52 for the 1st mode (n=1), 22 for the second mode (n=2), 61.7 for the third mode (n=3), 121 for the fourth mode (n=4), 200 for the fifth mode (n=5), etc.

Nodal position wrt length = .783 for the 2nd mode (n=2), .504/.868 for the third mode (n=3), .358/.644/.905 for the fourth mode (n=4), .279/.5/.723/.926 for the fifth mode (n=5), etc

How can we define a similar equation for a helical spring?

[noah katz]

"Again, what's the application?"

You won't answer that question, so let me ask you this - why are you posting this here?

[thadman]

Originally Posted by noah katz

"Again, what's the application?"

You won't answer that question, so let me ask you this - why are you posting this here?

The application is abstract, purely inquisitive (ie personal interest). I'm sorry if I offended you. I'm simply trying to gain a more complete understanding of the behavior of systems. I take great pride in being able to visualize and understand systems that I am interested in. Loudspeakers use a variety of springs in their construction. My interest in the helical spring simply arose as a tangent off of my interest in the springs in loudspeakers (surround, suspension, etc).

If we acquire a complete understanding of the system, qualitative logic can be exploited.

For example, the electric field within a uniformly charged sphere is 0 due to symmetry.

However, if we were to observe a charged rod of uniform cross section with an arbitrary length, it can only approach infinite linearity (with regards to the field), it will never achieve it.

I find (as demonstrated in example 1) systems which equal a value (rather than approach it) deeply fascinating.

Why do I post on this forum? I feel this community is highly educated, open-minded, and mature. Intelligent discussion benefits the community, ideas/concepts become more accessible to those with an incomplete understanding and those ideas/concepts reach a higher resolution through debate.

[noah katz]

Yes, I was a bit annoyed by the one-wayness of your inquiry.