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The Official Spring Rate Calculator Thread Part II

BGKYK5

BGKYK5

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Break out your tapes and calipers so you can play along at home. If you haven't had the pleasure of reading Part I of this series, you can find it here. If you have any of the commonly used stock GM springs at home (48, 52, 56, 60, 63", etc.) or any commonly available lift springs (especially from this list) go measure them and post up the dimensions in this thread. I'll crunch the numbers and compare 4 different equations for estimating spring rate.

The dimensions I need are:

L = the length along curve of the main leaf from the the center of one eye to the center of the other
L' = (optional) the distance between the u-bolt centerlines on the same u-bolt. If not provided I will assume 3.5"
N = the number of leaves NOT counting the overload
N' = (optional) the number of full length leaves (usually 1, a military wrap = 2)
W = the width of the spring
T1, T2, etc. = The thickness of each leaf starting at the top measured at the center of the spring (again exclude the overload) Note: the spring rate is highly dependant on leaf thickness, make sure you can accurately measure it to at least 1/32" for best results.
A = (optional) the free arch of the spring

For non-symmetric springs (like 56" springs) I'll also need:
a = the length of the spring ahead of the axle (about 30" for a 56" spring)
b = the length of the spring behind the axle (about 26" for a 56" spring)

A picture would be great as well.


The four equations are:

1. SAE HS-788, R = 32*E*sum(I)*SF/L^3

2. Chassis Engineering, R = ((W X N) / 12) X ((1000 X T) / L)^3

3. Ranger Station Calculator (actual equation unknown, but suspected to be identical to #2 with the exception of an optional adjustment for leaf taper)

4. Equations from a thread on Pirate R = ((2+(N'/N))*(E)*N*W*(T^3))/(6*(L/2)^3)

The other parameters not listed in the dimensions above are:

R = the spring rate in lbs/in (note this is the raw design rate, the as-installed rate will vary depending on the shackle angle etc.

E = Modulus of Elasticity in Tension (about 30,000,000psi for most steels)

I = the Moment of Inertia of a single leaf. Note, this is not a standard Moment of Inertia calculation, HS-788 has a big look-up table that accounts for the unique shape of a leaf spring.

SF = Stiffening Factor. This factor accounts for leaf taper and spacing. Without going into it all, I am going to assume SF=1.15 for everything unless I get a pick of a non-standard looking spring pack (i.e. with leaves pulled out). In that case I might go with SF=1.10

Note: I am going to use the active length for L whenever possible (L-L').


The CK5er who posts up the most useful information will win a cool prize!*








*not really
 
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Here is what I found for my own stock 52" springs from my '91.

L = 52"
L' = 3.5"
N = 4
N' = 1
W = 2.5"
T1 = 0.335"
T2 = 0.335"
T3 = 0.335"
T4 = 0.315

1. SAE HSS-788 - 263lb/in
2. Chassis Engineering - 267lb/in
3. Ranger Station w/ taper - 253lb/in
4. Excel from Pirate - 289lb/in
 
Can these measurements be taken when the springs are installed in the vehicle or do they need to out of the vehicle?
 
On the vehicle is fine (that's how I measured my 52s), you just won't be able to get the free arch, but that isn't even in any of the equations - it's just nice to know.
 
I kinda thought this thread would generate more interest. :( :confused:

Anywho, I remeasured my 52" springs to try and improve the accuracy of the spring rate estimate. This is what I got:

L = 51.75"
L' = 4.2"
N = 4
N' = 1
W = 2.5"
T1 = 0.320"
T2 = 0.308"
T3 = 0.308"
T4 = 0.308"

Which resulted in:

1. SAE HS-788 - 239lb/in (SF = 1.15)
2. Chassis Engineering - 254lb/in
3. Ranger Station w/o taper - 254lb/in
4. Excel from Pirate - 213lb/in

I also did some work to convert the Moment of Inertia table in SAE HS-788 to a simple equation (it was easier than having to do a 2D interpolation for every leaf of every spring I wanted to estimate the rate of). This is what I came up with:

I = W*0.08*T^3

That give a result within 2.5% of the table for all widths from 45 to 90mm and thicknesses from 5 to 12.5mm.

To calculate your spring rate using HS-788, first calculate the moments of inertia for each leaf using the equation above (measurements must be in milimeters, 1 inch = 25.4 mm) and add them up.

Now use that sum of moments of inertia in the main equation:

R = 32*E*sum(I)*SF/L^3

Remember to use mm for the length (and remember to use the active length - the overall length minus the length between the u-bolt holes in the spring plate). In metric units the Modulus of Elasticity for steel (E) is 200,000 MPa. Your result will be in Newtons/mm. To convert N/mm to lbs/in, multiply by 5.710.

A word on the stiffening factor (SF) in HS-788 from the manual itself:

"The value of SF is exactly 1.00 when the leaf lengths and leaf thicknesses are selected to produce a uniform strength beam (spring), and the resultant curvature of the spring in bending is a circular arc with radius R....Selection of the the correct SF value in the final spring design is predicated on factors gained from experience...For the preliminary design calculation, the following SF values may be applied.....

For passenger car and light truck springs with tapered leaf ends and more or less "uniform" stress design: SF = 1.10

For passenger car and light truck springs with tapered leaf ends and extended leaf lengths: SF = 1.15

For truck springs with untapered leaf ends and more or less "uniform" stress design: SF = 1.15

For truck springs with untapered leaf ends and two full length leaves: SF = 1.20"

What they mean by "uniform" is that the shape of the leaf pack is close to an upside down pyramid with the "peak" at the axle. Like:

------------
---------
------
---

Not like:

-----------
-----------
---

Hopefully that makes sense. I am probably going to pick either 1.10, 1.15, or 1.20 depending on the taper, uniformity, and number of full length springs.
 
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I also measured my stock '89 front springs and the 4" lift Trail Master (AFAIK) front springs on my '91. This is what I got:

Stock Front

L = 47.25"
L' = 3.66"
N = 2
N' = 2
W = 2.9"
T1 = 0.400"
T2 = 0.400"

Which resulted in:

1. SAE HS-788 - 399lb/in (SF = 1.20)
2. Chassis Engineering - 373lb/in
3. Ranger Station w/o taper - 373lb/in
4. Excel from Pirate - 422lb/in


Trail Master Front

L = 46.75"
L' = 3.66"
N = 5
N' = 2
W = 2.5"
T1 = 0.375"
T2 = 0.375"
T3 = 0.375"
T4 = 0.375"
T5 = 0.375"

Which resulted in:

1. SAE HS-788 - 844lb/in (SF = 1.15)
2. Chassis Engineering - 687lb/in
3. Ranger Station w/o taper - 672lb/in
4. Excel from Pirate - 619lb/in

Yikes, that is stiff!! :yikes: A perfect compliment to my awful front shackle angle. :doah: Well, now I know what to expect when I finally drive it for the first time. I'll bring a kidney belt. :D
 
ttt

Free Spring Rate Estimation for a limited time only! Act now and I'll throw in a couple "bow" smilies with every order!

Anybody want to post their spring measurements??? :confused:

See first post for the dimensions I need.
 
So the modulus is basically the same for all common spring steels? I guess you CAN estimate static spring rate with a tape measure. What about dynamic spring rate? Are there published fudge factors for teflon pads, etc?
 
Yes, as near as I can tell all spring steels have a very similar value for Young's Modulus. Yes, if you have the spring and a known weight you can estimate the spring rate. But what if you haven't picked the spring you wanna run yet? By dynamic rate I assume you are describing the spring rate plus the damping effect inherent in all multileaf springs. I'll have to check on that. Of course the shock will provide more damping than is caused by interleaf friction anyway, so any dynamic calculations would have to include the shock damping as well.

BTW - reminder to measure your springs this weekend Ryan. :D
 
SAE HS-788 does define a Friction Factor.

Friction Factor = Friction Force/Average Load. For a good low friction spring, the Friction Factor may be between 0.02 and 0.05. For high friction springs it may be as high as 0.10.

The Friction Force can be approximated as half the hysteresis in the force-deflection curve. And the average load is the average of the force in the compression and rebound directions.

It sounds interesting, but not very useful. :dunno:
 
You need both rates to predict ride quality. The friction is not the same as shock damping because of the hysteresis. Looking only at static spring rate is useful only for loading / ride height and "flexiness" in low-speed situations. That's why coil springs ride well, there is almost no additional spring rate added by the friction.

I'm just saying that is IS very useful.
 
Don't get me wrong, I am not saying that understanding the self damping effects of leaf springs isn't very usefull - I'm saying the information in SAE HS-788 isn't very usefull to people like us who lack the ability to quantify it. There is no equation to estimate the effect.
 
Yeah, I agree then. We would have to make careful force measurements to "start" the spring compression and then to keep if from returning.

I'm not trying to mess up your thread. I agree that it's an interesting exercise and could help us all when looking at used springs or something without advertised spring rates. In the end, we're probaby not going to do anything more than put teflon pads or UHMW plastic in them to keep the friction down anyway. And we'll probably always remain blissfully ignorant of the friction and hysteresis in the bushings.

Are there any estimated friction numbers regarding the number and thickness of leaves?
 
Here's my measurements for my springs:

Front 52s:
Length: 52 1/4"
# of leaves: 5
U-bolt distance: 3 3/4"
leaf 1: 5/16"
leaf 2: 5/16"
leaf 3: 5/16"
leaf 5: 5/16"

Rear 64s:
Length: 64"
# of leaves: 3
U-bolt distance: 3 7/8"
Leaf 1: 3/8"
Leaf 2: 3/8"
Leaf 3: 7/16"
 
And here are your results:

52" Springs

1. SAE HS-788 - 286lb/in (SF = 1.15)
2. Chassis Engineering - 279lb/in
3. Ranger Station w/ taper - 265lb/in
4. Excel from Pirate - 235lb/in

64" Springs

1. SAE HS-788 - 186lb/in (SF = 1.15)
2. Chassis Engineering - 152lb/in
3. Ranger Station w/ taper - 138lb/in
4. Excel from Pirate - 141lb/in

How is that for service? :D

BTW, I am using the active length of the springs in all calculations (including the Ranger Station calculator). The exception is the calculators from Pirate where they clearly are using the entire length in the equations.
 
what...Triaged still posts here ???

BGKYK5 said:
...4. Equations from a thread on Pirate R = ((2+(N'/N))*(E)*N*W*(T^3))/(6*(L/2)^3)...
Click to expand...
Is that the one I did you are using or the other one in that thread?

Here is some more good info that MJ scanned from his old Chevy Power Manual. Note the compensation for offset center pins.

ChevPowerManual24.jpg


Here is the rest:
http://www.pirate4x4.com/forum/gall...id=&orderby=title&direction=ASC&cutoffdate=-1
 
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