Spring Design

Greetings,

I need some help on a leaf spring that will be 3/8” wide by whatever thickness I need. I’m looking for 50 pound of force at approximately .110” deflection.

I would like it to be about 1.15 inches long. I can go slightly longer, or shorter. It will be a cantilever with a single point load at one end of the spring.

When I calculate a beam deflection for O-1, for example, I come up with a beam that is .061” thick, and will deflect .115” at 50 pounds of force.

At RC 50 O-1 has a modulus of elasticity of 31,000,000 and a yield of 218,000 psi. I’m looking at the stress due to bending at about 246,000 psi which would exceed the elastic limits.

This doesn’t “seem” right that a .115 deflection on a 1.15 inch long beam will exceed the elastic limits. Am I overlooking something, or doing some calculations wrong?

I have an office supply paper clip with the blue steel and chrome handles. I assume this is 1095. It is .015 thick and 1.25” wide, with each leg at .65 inches and .60 across the back (1.90 inches long total). When I open it .60 inches it produces about 20 lbs. of force.

Using a beam deflection of FL^3/3EI I come up with 4.19” deflection, and 810,000 psi stress from bending.

Any advice as to where I’m going wrong would be greatly appreciated.

This is an unusual application so I will need to cut it from bar stock and therefore need the material to be available in 3/8” thick bar stock. I was unable to find any 1095 in 3/8” thick bar stock, so I’m probably looking at O-1, or something. Any suggestions of a material that would work well for spring applications, that is readily available, would be appreciated.

Thanks in advance for any help.

OK, some miscellaneous thoughts.
(1) Your high stress is coming from your thickness. Beam stress is mc/I. "c" is the distance from the surface to the neutral axis. A thicker beam has a greater "c".
(2) "O-1" is tool steel, right? Not known for its flexibility. I wouldn't expect to find springs made from O-1.
(3) Have you contacted a spring manufacturer? There are several that could be of great assistance.

Well, not thinking too hard on my part see the following link to see if it helps [url]http://www.engineersedge.com/material_science/leaf-spring-design.htm[/url]

[url]http://www.engineersedge.com/beam_bending/beam_bending9.htm[/url]

This link is more appropriate, however, my results didn't seem correct. It seems that with less than .11" deflection on a beam that is about 1.25" long, and say .060" thick, that the elastic limits shouldn't be exceeded.

Also, when I tested the office supply paper clip, it should have exceed the elastic limits, but didn't. The deflection force/distance and the stress don't work out.

Could be material properties?

>> force/distance and the stress don't work out.
>> Could be material properties?

WJ, you are kidding right? :) Unless you know the material properties of the paper clip, a guess would be as accurate as the calculator.

Dave
Generally, I will not give you the answer to your question, but I *will* guide you into discovering how to solve this yourself.

PinkertonD, my point was that with the most likely candidates for material on the paper clip, 1095 or 1075, my numbers were not close. Obviously it does work because I have one sitting right in front of me.

With that in mind, it just "seemed" that the leaf spring I am trying to make should not bend with only .11" deflection. And I get that "seems like it shouldn't" isn't any way to engineer something. The paper clip/spring clip is way more elastic than it "should" be.

Just trying to figure out if my calculations are wrong on my leaf spring, or if I am overlooking something.

Thanks again for all your help and suggestions

Pardon my flippant remark, but I was trying to point out that the material properties of the paper clip are unknown as guessing the material, in which you may be correct, the actual "spring" properties could be vastly changed by the degrees (pun intended) of heat treatment.

I am with JB, maybe contact a spring company. I have always found Century Spring to be very helpful.

Dave
Generally, I will not give you the answer to your question, but I *will* guide you into discovering how to solve this yourself.

"have an office supply paper clip with the blue steel and chrome handles. I assume this is 1095. It is .015 thick and 1.25” wide, with each leg at .65 inches and .60 across the back (1.90 inches long total). When I open it .60 inches it produces about 20 lbs. of force.

Using a beam deflection of FL^3/3EI I come up with 4.19” deflection, and 810,000 psi stress from bending."

You have 2 basic equations for this
1)F=deltaEbt^3/4L^3
2)s=6FL/bt^2 where s< yield stress
delta defflection
F force
b width
t thickness
L length
s stress

You can't specify F,L, and b and delta
and hope to satisfy 2)

Finally your analogy with that paper clip is flawed. If you look at it,you don't add those lengths to get 1.90 inch for L; it is closer to .65 " and from 1) would reduce your stress result by a factor of 3.

I believe my material properties are in error, as Dave suggested.

However, the only material property in the bending equation is the modulus of elasticity.

To the best of my knowledge the modulus stays the same (at approx. 30 million) regardless of hardness.

So that would mean that if I take two identical leaf springs such as the one we are talking about here, leave one fully annealed, (lets just say as an example it’s 1075 at 17 RC) and harden one to 50 RC, that under the same conditions they would both deflect the same amount under the same load.

Is this correct?

The reason a spring returns to its original shape is that the deflection has not taken it beyond its ultimate yield point. As long as you don't exceed the ultimate yield stress any material can act as a spring. All the bending formulas on this site assume you stay under the ultimate yield stress of the material. Once you exceed the yield point you are in the plastic region, which is a whole different ball game. Ultimate yield stress and modulus of elasticity are two different things. Did you ever contact a spring manufacturer as we suggested earlier?

Yes, I contacted several spring manufacturers and none of them were very helpful with any information. One did mention that they use about 50 Rockwell for their springs when finished, however.

I understand that I don't want to exceed the yield stress of the material. I also understand that the modulus of elasticity is a different thing than the yield stress. I was merely asking if anyone here could verify that Rockwell hardness has no affect on the modulus of elasticity.

It just seemed that if I took two leaf springs, as I stated above, that were otherwise identical, and that the one that was at a higher Rockwell hardness, that the harder one would have a greater resistance to bending, and thus a greater "spring" effect.

If this is true, then it would make sense that it should be reflected in the modulus of elasticity.

So does the modulus of elasticity remain constant regardless of material condition (Rockwell hardness)?

[QUOTE=
So does the modulus of elasticity remain constant regardless of material condition (Rockwell hardness)?[/QUOTE]

Yes..................

zeke, thanks that's what I was wondering.

That would imply that the Rockwell hardness will affect the yield strength allowing the spring to bend farther and still be within the elastic range, but not affect the "spring" properties.

So, just use these - [url]http://www.engineersedge.com/beam_bending/beam_bending9.htm[/url] and use the yield stress of the material at the hardness I'll be using. Thanks.

yes it would work like that...






_________________
(Edit: Removed commercial link)