Calculating Individual Leaf Spring K value

[Kritter]

Ok guys and girls I searched and searched for this but could not find it. I know there was a post on coils but it did not have regard to leaf srings.

I need an equation that calculates the k value of individual leaf springs as a function of material, length, width, and height and any other variables needed. I have seen a calculator that used lenght width and height for them on a website but they want 100 bucks for the license. I searched elsewhere for the equation to solve my dilema and have come up empty handed. Please help me out.

Also I am pretty sure that the k factors for each individual leaf can be added together in parallel to get the total spring rate (k effective = k1+k2+k3+....) but correct me if I am wrong.


1st leaf k-value is 23#/in
2 nd leaf K-value is 32#/in
3rd leaf K-value is 35#/in
4th leaf 35#/in

So the total k for the pack is 125#/in

Thanks

Kris

"Revenge is best served cold"

 

[ntsqd]

Kritter, I think my Norton book on Machine Design has the equation you're looking for. It's at work. I'll try to remember to look tomorrow just in case someone else doesn't answer first.
As memory serves, assuming all leaves are the same thickness, you 'take' the spring apart and make a single, triangular, leaf out of them of equivalent volume and thickness. Then you can calc the k as a single leaf. Sorry my description of the process isn't real good, maybe that's enough to get you going. BradM & I talked about this a while back, he may be able to confirm or correct me on this.

TS

"Teach you all I know and you're still stupid"
-- Howdy Lee

 

[BradM]

Kritter, I don't recall the conversation that Thom does but since he brought me into it, I did a little digging myself. I found some data on flat springs of various end conditions and material selections for leaf springs. I don't know if it is directly applicable (I don't believe it accounts for arc) but it may get you started in the right direction. As for the combined effective rate, I would tend to agree that they are in parallel.

Load (P) = (4 * E * b * t^3 * F) / (L^3)

That is for a flat spring of uniform thickness without fixed end conditions.

Parameters are as follows:

P = Load (pounds)
E = Modulus of Elasticity in Tension (psi)
b = widest width of rectangular wire (inches)
t = thickness (inches)
F = Deflection (inches)
L = Active length (inches)

Also, from what I have seen, typical SAE alloys for leaf springs are 1085 and 9260.

I hope that is of some benefit to you. Perhaps someone with a better understanding of leaf springs can offer some additional insight.



"The only source of knowledge is experience." - Albert Einstein

 

[Dylan]

I did my senior project @ school on a quarter elliptic spring and we used the analysis that Thom described. It’s been a couple of years but I think its called a curtailed trapezoidal spring???? I’ll dig up the info when I get home. You kind of need to do the front and rear half of the spring pack separately because the rear half of most spring packs is usually longer and when you have L^3 it makes a drastic change. BradM’s equation for each individual leaf is good also. If you want to use that equation for each half individually in terms of K you can use:
K=(E*W*T^3)/(4*L^3)

E= Modulus (30E6)
W= width
T= thickness
L= length form edge of spring pad to eyelet
K= rate (lb/in)

The problem with this equation is that it doesn’t work for packs that have a lot of leaves because the shorter leaves don’t see the same end deflection as the long leaves and they support the leaf above them part way down the length and this equation does not account for that kind of loading. I would only use it for a stock Toyota or similar pack that has 2 leaves where the second leaf is almost full length. Of coarse as the pack settles on to the overload leaf its shoots the whole thing out the window.
There is a little program Called Dave’s Spring Calculator that approximates leaf spring rates. I think its share ware, if so I’ll try to find a way to make it available for down load.
Thom if you can’t find that analysis I’ll try to dig it up and post it.

 

[rdc]

If you are really interested, there is an SAE book we have on spring design, it is pretty much the bible of automotive suspension springs. It will tell you anything known about leaf springs, coil springs, torsion bars and other miscellanous springs. You can get it at the SAE website/bookstore, it is book # AE21, 421 pgs, and is $109. Dylan will probably study up on it and give you the lowdown later.

 

[Kritter]

Thanks guys. I wrote a little spreadsheet that figured it out by individual leafs and then jsut added it together for the total K factor. It is kind of off though because it does not account for "stiction" between leaves.

The reason I am going through this is because I have a deaver race pack that has a K of 160 and I need to get it down to around 120 for my application. I am going to remove 2 or 3 leaves and hopefully I will be right on target.

Kris

"Revenge is best served cold"

 

[ntsqd]

Sorry Brad, my memory isn't what it used to be. Now that Dylan has posted I'm reasonably certain he and I talked about it in the shade of the E-Z Up @ OCD II while dodging flying ice cubes.

TS

"Teach you all I know and you're still stupid"
-- Howdy Lee

 

[drtdevil93]

kritter- i strongly disagree with you taking leaves out of the pack on your own. it will throw off the progression, causing odd handling through the cycle; and it can cause breakage as the leaves wont have the support we put into them. if you buy a pack from us, we will make it right for you. if you decide to do that on your own, we cannot warranty and breakage of the spring. as far as calculating rates, weve learned from experience how to tune a spring. you tell us the weight, we just know how many leaves to put in, at what length, and with how much preload (another thing we do that a spring calculator wont be able to take into account). i believe you have a ranger, and you got the f31 pack (stock shackle). that spring is already built very light. it just isnt possible to take 2-3 leaves out and expect it to last for any length of time. what shocks do you run? have you had them adjusted or are they off the shelf. we have had issues with people saying it rides too stiff. we send them to a shock tuner, and that is the problem every time.

erik