Jump to content
Geoff Keyes

Spring rate

Recommended Posts

I have heard, but not verified, that the spring rate of heat treated and tempered steel is the same as mild steel, for a given size, shape, and taper. The difference is the yield point of the spring (the point where it bends and does not return to shape).

Does anyone have hard information on this?

If this were true, then a prod for a crossbow, or the limbs of a steel bow, could be made of mild steel. This would be safer and a lot easier than try to do the same thing in, say 5160.

Just watched MaA, and questions occur

 

Geoff

Share this post


Link to post
Share on other sites

Safer, yes. But I believe it would considerably reduce the possible stroke before the steel bends so it would require much larger prods and limbs to compensate. I may use the wrong nomenclature, but I believe hardened steel can accumulate a lot more kinetic energy per given weight than mild steel.

Edited by Joël Mercier

Share this post


Link to post
Share on other sites

Geoff ; the rate may be the same, but spring steel alloy makes for repetitive flexing without structural damage at the molecular level

whereas mild steel doesn't, and will fail after time.......

In my humble opinion 5160 is the logical choice...............................

Share this post


Link to post
Share on other sites

Up to the point where elastic deformation takes place there is no difference in the spring action.  

Does

4 hours ago, Joël Mercier said:

 but I believe hardened steel can accumulate a lot more kinetic energy per given weight than mild steel.

Can you demonstrate this or give a reference to support your belief?  I'm not saying you're wrong, but some hard evidence would go a long way.

 

3 hours ago, Clifford Brewer said:

Geoff ; the rate may be the same, but spring steel alloy makes for repetitive flexing without structural damage at the molecular level

whereas mild steel doesn't, and will fail after time.......

See above.  If you don't exceed the deformation point, no structural damage is taking place and so the failure rate should be the same.  This is the question of course, would it be the same in the real world.

There is another question buried in all of this (in fact there are many questions buried in this idea) .  How many cycles would you expect to get out of a spring arm, like a crossbow, before you would replace it?  Most of the historical crossbows that I have seen are designed to have the prod remounted pretty easily.  Is this because you just didn't get that many fires before failure?

 

p-6383-bow3.jpg

You can see that the prod was held in place with rope lashing and two opposite side steel (?) wedges.  Knock the wedges out and the prod is loose.

Geoff

 

Share this post


Link to post
Share on other sites

well there is a lot of head scratching that goes along with crossbows and steel prods, some of it is counterintuative all of it is potentialy dangerous if you get it wrong.

I have made hundreds of crossbow prods over the years from 150lb to 1400 lb..... and hardening and indeed temper temperature does not effect the rate of energy return (we tested it! with a crono and prods multiply tempered to reduce hardness in steps)  it is so counter intuative.

 however

it is very easy to make crossbow prods that will bend under use (if  they are unherdned or high tempered) and the tillering is incredibly important  (bot in thickness and width) so as to share the bend over the whole limb.

steel crossbow prods are by thier nature not great at returning energy , a lot of the return energy harnessed in the spring is needed to overcome the inertia in the mass of the material. a hardned and tempered prod can be lighter and give a greater draw than an unhardned or mild steel prod.

 having measured quite a few origional prods I would guess they are hardned steel as they would deform if wrought or low carbon . that is if you take origional dimentions, short prods and a short draw. If you go outside of this with thinner bigger prods and a much longer draw its totaly possable you could use mild steel...but to what end, as this is not what was done.

I would not think that origioanl crossbows had a huge rate  of failure, failure could be catastrophic or fatal, but i do understand the relative diferences in risk adversity as we go back in time...life being cheap and all. I see the means of securing as a way to allow flex through the center of the prod (where the most leverage is occuring).

I will add that the risk is certainly there though.

historic crossbows are interesting and can be disapointing unless you view them from a materials and physics POV a 900lb crossbow will be easily out performed by a 150 longbow ..however with the rite mechanism it can be cocked by anyone., certainly not the case with a war bow.....Wood is much more eficient at returning stored energy into kinetic energy its lighter for one.. crossbows seem to do well at delivering heavy projectiles but by their nature are not that fast.

the big advantage of a steel prod over seemingly more eficient wooden prods is that it needs relativly little care , grease it up and leave it in your dingy damp castle keep for a decade and when you get attacked all you need is fresh strings and its to the ramparts...your wooden prod would certainly be ruined if not cared for.

If you are used to modern fiberglass crossbows a steel prod is very disapointing...

Take care , look into spring temper temperatures for the material you chose ( not getting it to blue but real temperatures that real modern springs are tempered to, often much higher)

and I reemphasise these things would easily take your face off if you get it wrong.

 

 

  • Like 2

Share this post


Link to post
Share on other sites

Thanks Owen, some of that needs thinking about and all of it makes sense.  It's good to hear from someone with considerable practical experience, since in other fora I am getting a lot of opinion backed up by nothing.

For the general info flow I  borrowed this from another source and it also has good information well presented

"I am posting this because it has come up a few times in different groups that I am part of, this group being one of them:

Heat treating does not change how a material bends. Neither its rigidity to bending, nor the shape that it takes while bending, so long as you don’t apply so much force that your material yields and takes a permanent set. The shape of bending is purely a function of the material you are working with and the shape of that material, nothing more.

Straight flat pointy objects, like knives and swords, the engineering of how much the object will flex is easy to understand, as it can be represented by a simple cantilevered beam under a point load, for which the deflection at any point along the beam (sword/knife) is defined by the following equation:

deflection @ x= [(Wx^2)/6EI] * (3L-x)

For the above:
x is the distance along said beam where we want to know the deflection
L is the overall length of the beam
W is the applied force

The interesting part of the above is the term E*I, which is termed the flexural rigidity. One term, E is the Modulus of Elasticity for the material you are looking at, which is an intrinsic property of the steel that DOES NOT CHANGE with heat treat. The second term, I, is the area moment of inertia, which is a measure of shape rigidity and how it resists movement (think I- beam vs round stock), and is a function of the size of the material, meaning the larger the shape, the larger the moment of inertia. Nowhere in the measure of flexural rigidity is a term that is affected by heat treatment or any other measure of yield strength.

For more complex shapes, like springs, the deflection of them is still defined by this concept of flexural rigidity. Redoing Heat treating your spring (which is already heat treated), will not make it stiffer. It can’t because the physics don’t allow it.

Heat treating only affects yield strength, which is a measure of how far you can bend an object before it takes a permanent set." 

Author

Geoff

Share this post


Link to post
Share on other sites

The maths for a crossbow is quite complicated...very complicated. I was discussing it once with my good Friend Leo Todescini ( a cropssbow maker) and a professor of engineering ( whos name escapes me)  , what could we do to try and model the optimal shape of prod  (thickness and width at any point)  for a given poundage or draw length ...the conclusion after a page or two of Math was that it would be a great summer project for one of his PHD students....if we were interested in funding it!

lots of changing vectors involved in the way an arrow or bolt is accelerated...not simple at all.

Share this post


Link to post
Share on other sites

Just wanted to add a little more information (stress-strain diagrams stolen form a quick Google search):

image.png

Here we see the relationship with Modulus of Elasticity (E), also called Young's Modulus as it relates to yield strength and such.  Stress is load/area (typically measures as psi, ksi, or MPa).  Strain is unitless, but is a measure of displacement (inches per inch, thus unitless).  

In actual practice, the slope is much steeper, like this:  

Image result for stress strain curve for steel

Every steel will have their own modulus, but they are generally all pretty close to each other.  

Hardening steel moves the yield stress (and ultimate tensile) further up the chart, along the straight line that defines the modulus.  It will also cause the metal to break more abruptly once the ultimate tensile strength is passed.  

Share this post


Link to post
Share on other sites
On 12/16/2018 at 1:43 AM, Geoff Keyes said:

 If you don't exceed the deformation point, no structural damage is taking place and so the failure rate should be the same. 

That isn't exactly right.  Cyclical loading below the yield point will eventually cause a failure.  I'm an EE, so don't take my word for it, but if I remember right, for something to be considered strong enough to take an infinite number of cycles, the peak load has to be something like no more than 5% or 10% of the yield strength.  Anything above that, and you can calculate the number of cycles before failure.

Share this post


Link to post
Share on other sites

It's that combo of a finite number of cycles and the abrupt failure Jerrod mention that led Owen to casually mention they can take your face off.    Or even your head.  

That actually factored into a medieval mystery I read once.  Someone attempted to assassinate a nobleman by putting a nick in his crossbow prod right at the tiller (or stock), then sending him out hunting on a sub-zero day.  Hilarity failed to ensue.

Share this post


Link to post
Share on other sites
7 minutes ago, Alan Longmire said:

Hilarity failed to ensue.

LOL!  

Cyclical loading leading to failure is a fatigue failure.  Some materials have a definitely fatigue limit, where any movement (strain) will eventually lead to failure, with larger strains leading to failure in fewer cycles.  Steel is pretty neat in that it has a endurance limit such that if you don't over strain it then it will not fail from fatigue.  Of course, outside factors like damage and corrosion can alter service life, but a spring that is not over-loaded could indeed last "forever"*.   

Image result for fatigue limit of steel

 

*Limitations apply.  Null and void during supernovae and other cataclysmic events.  No refunds.  

Share this post


Link to post
Share on other sites
44 minutes ago, Jerrod Miller said:

Steel is pretty neat in that it has a endurance limit such that if you don't over strain it then it will not fail from fatigue. 

I stand happily corrected.  I am also reminded that stuff that seems very clear in my memory from 30 years ago needs to be treated as suspect :lol:

Share this post


Link to post
Share on other sites
43 minutes ago, Jerrod Miller said:

LOL!  

Cyclical loading leading to failure is a fatigue failure.  Some materials have a definitely fatigue limit, where any movement (strain) will eventually lead to failure, with larger strains leading to failure in fewer cycles.  Steel is pretty neat in that it has a endurance limit such that if you don't over strain it then it will not fail from fatigue.  Of course, outside factors like damage and corrosion can alter service life, but a spring that is not over-loaded could indeed last "forever"*.   

Image result for fatigue limit of steel

 

*Limitations apply.  Null and void during supernovae and other cataclysmic events.  No refunds.  

Thank you Jerrod, your chart searches explain my comment, I took a working metallurgy class in college but did not pursue it more than that.

I know just enough about it to be dangerous I guess.......................:rolleyes:

Share this post


Link to post
Share on other sites

In case it isn't clear, I'll also add this (which is just a summary of things already mentioned):

Hardening the steel means the yield strength goes up.  Since it goes up, you can now bend the spring further before it breaks/permanently bends.  Since you can bend it further, it can store more potential energy, which can then be translated to kinetic energy into the bolt's flight.  A heavier steel prod can store more energy than a lighter one of the same material (including HT), but it then has the problems of being heavier to lug around as well as slower to release that energy, thus less speed (energy) in the arrow.  

Share this post


Link to post
Share on other sites

The failure issues are one thing. Owen mentioned issues of steel actually being a fairly poor transmitters of energy

On 12/16/2018 at 2:27 AM, owen bush said:

historic crossbows are interesting and can be disappointing unless you view them from a materials and physics POV a 900lb crossbow will be easily out performed by a 150 longbow ..however with the rite mechanism it can be cocked by anyone., certainly not the case with a war bow.....Wood is much more efficient at returning stored energy into kinetic energy its lighter for one.. crossbows seem to do well at delivering heavy projectiles but by their nature are not that fast.

Limb speed and tip speeds are issues for bow makers that I don't understand very well.

When I posted this question I was  primarily interested in the nature of springs and spring materials, which drifted through the realm of crossbows as a specific example.  I have learned a a ton of new stuff this week and I'd like to thank all of the people who have contributed.  Please don't take this as an attempt to choke this thread off, just an acknowledgment of the information base we have here.

But back to springs in application.  I think we are agreed (to an extent) that non-hardened steels can be used as springs, given that you don't exceed the yield point of the material.  Take a rocking spring hammer like this

Spring hammer.jpg 

That top spring could be made of mild steel, I think.  These are the sort of things that float around in my head while polishing.

Geoff

BTW this is the hammer that I thought we were going to build back in 2000, but I found a drive unit all built (from a pump, I think) and we went another way entirely, see below.

Abiyoyo.jpeg

Which leads me to wonder if that spring pack could not have been built out of mild, or as forged 5160, and still worked.  The ends of the long spring were heated and rolled around the wrist pins and then left as forged (we didn't have a way to quench and temper that much steel).  The ends have not moved a bit since we set the preload in 2000.

Geoff

Share this post


Link to post
Share on other sites

My understanding is that yes, mild would have worked in that application just fine as long as the yield strength didn't get exceeded.  

Share this post


Link to post
Share on other sites

Given that a failing hammer can also take parts of the operator off, I'd feel happier with: yes, mild would have worked in that application just fine as long as the fatigue limit didn't get exceeded.

Share this post


Link to post
Share on other sites

welllll.....I would try an not reinvent the wheel...especialy when it can take your face off!. I have had 3 of the spring hammers I have owned break springs so obviously these machines take the material to the point of fatigue , I doubt that mild steel would be an improvement.

Share this post


Link to post
Share on other sites

The spring on my power hammer is mild-ish steel. It has been running for 1 1/2 years with no problems.

20170408_204215.thumb.jpg.0d2afd7c59d39124771970a6b765b6b6.jpg20180817_135425.thumb.jpg.20e0c0aba6fa773c1b4ee7981281d7f5.jpg

Edited by Jeremy Blohm

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.


×
×
  • Create New...