CK5 - The Full-Size GM Off Road Community

Update:
Just uploaded V1.5. Greg has helped me get it looking alot better with everything layed out in a more fluent manner. He also added some pull down menues for the link materials. If you click on the cell a little down arrow will pop up next to it. Just click on the down arrow and you will be able to pick from a list of choices.

http://home.earthlink.net/~triaged/Files/4LinkCalculatorV1.5.xls

V2.0 is being worked on (by Greg) that will draw a picture of your suspension geometry automatically. He has already drawn up one for the 2D anti-squat excel program he made and is trying to update it for the new 3D spreadsheet (which doesn't sound easy to me!).

I am working on making it cycle your suspension so you can see how some of these values change as your suspension compresses or droops (articulation would be nice as well but I have no idea even where to start on that).

I am also looking for some other people to help out.

I need someone who knows all this math stuff (most likely another mechanical engineer) to check my work and see if my assumptions are valid.

I would also like to have someone acutally use it to analyze their suspension with it and give any notes on how it works in real life.
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Disclamer:
I think this info is correct. If you use it and die (or injure yourself in any way) it is your own fault that you were stupid enough to listen to me.

I finally finished my 4-link calculator. To the best of my knowlage it is correct. It should not be used as a substitute for common sence but as a guide. It also might be fun to play with. It isn't too pollished up but it is there. It requires that you use my "coordinate system" which is based on the ground right under your rear diff...so when you measure stuff start from there.

"X" lengths are from the rear axle centerline forward
"Y" lengths are half (1/2) of the horisontal sepperation.
"Z" lengths are all measured from the ground.

You can end up wiht negative (-) values for "X"...that would just mean behind the axle.
If you do a Wishbone type link you will end up with a "Y" of zero (0) length. If you put in a negative (-) value for "Y" you are stupid because you won't be able to build it (the right link would connect to the left side of the chassis /forums/images/graemlins/rolleyes.gif). If when looking from the top your links are parallel make them "not" by some small # (even as small as .001") or it won't calculate your roll center or roll axis.
If you put in negative (-) "Z" values you just designed a plow...not a 4x4.

BTW: The cells are protected just to keep you from accidentally screwing it up. If you really want to change the formulas there is no password for the protection.


For those of you that care...

Assumptions:

1) Loads are calculated with 100% weight transfer.
2) Tire coeff. of friction of 1.
3) That you have 4 non-parallel links (if you use a wishbone don't forget to double the load to the center rod end)
4) For the F.S. (factor of safety) in bending you have half of the weight of the truck acting on the center of the link.
5) Your links are made of steel with a yield of 63,250 psi (normalized 4130)...if you want to use a different material you will have to find the spec's and plug them in on the 2nd page


Keep this pic handy to help you figure it out
http://home.earthlink.net/~triaged/Files/CordSys4Link.gif
As you can tell from this pic I have a 14B in the rear and a D44 up front /forums/images/graemlins/rotfl.gif

Drumm roll please...










http://home.earthlink.net/~triaged/Files/4LinkCalculatorV1.1.xls



The rest of the list is below:
http://home.earthlink.net/~triaged/Files/LeafSprings.xls
This one has some guessed info, some measured stuff, and some BS...measure up your springs and plug in the #'s.
http://home.earthlink.net/~triaged/Files/PartNumbers.xls
This is some of the part #'s for parts I have used on my truck.
http://home.earthlink.net/~triaged/Files/Swaybars_02.xls
This file will calculate the stiffness of your swaybar in G's per degree. It is made for "fabricated" sway bars...not bent tubes. This is the "Really hard math" stuff and won't be much fun for anybody but...what the hell /forums/images/graemlins/thinking.gif


Edit:

This is an email I sent Greg answering some of his questions

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

The F.S. stands for Factor of Safety. It is how much stronger than failure it it. The lowest F.S. is what will fail first (except for the bending). Ideally you would want to mess with the rod end rating, tube OD, wall thickness, and material (on the 2nd page in blue) to get them all around the same value (no use having a solid 3" diameter link and 3/4" rod end!). In this case a F.S. of 10 might be just a bit overkill...but you sure don't want a number as small as 1 or 2. It is also sometimes called a "Fudge Factor" by engineers because it is tossed in to account for all the stuff they didn't (or couldn't) include in the calculations (like dynamic shock loading in this case). There are also some more general guides for F.S. like "If this fails will someone die, just get hurt, or just property damage?" In this case "Someone might die" so try and keep the F.S. high...esp. for a street driven truck. The bending doesn't have as much of a "someone might die" factor because it will be (I hope!) at slow rockcrawling speeds.

In the case of bending you can see that the link is much weaker than in compression (this is the same reason that cages need triangulation). I think your best bet would be to shoot for something just over 1 and then try not to slam the links all over every rock you see.

The nice thing about a F.S. is that they have no units. At least not normal ones...they are in fact lbf/lbf (which cancles out to just 1). This way you can compair them with any other truck directly (just like AS values in % which is also unitless).

For views I don't see the need for a front view (but it might be cool to see). A top view and side view should be able to show everything.

For the vector algebra:
I took the link length and sepperated it into it's components (how much it went forward, how much it went up...etc.). I then devided each component by the overall link length to get a "unit vector". This is like a arrow pointing in the same direction as the link but it has a length of "1". From that I know in what direction the force in the link is and I just have to find the "magnitude" of it. To do this is I added up all the moments (another word for torques) and set them equal to 0 (zero). This is one of the statics equations that will tell you why something doesn't move (in this case the pinion doesn't point to the sky on acceleration...we just want to know why/how). From there I devide the total link force back into the components (don't know that it is needed for the rest of the equations but it didn't really take any more work...the equation I gave you before calculated only the force in the "x" direction...you can see how it is an OK estimate if the links don't converge too much but it will always be too small...hence giving you a F.S. of 10 to work with...using the more exact forces the F.S. can be reduced some).

Finding the buckling and bending loads was just a matter of "plug and chug" with some equations from an engineering book.

I guess that's about it in writting. You already know how to find the intersections of the lines you'll just have to go back through and figure out how I went about finding them (I actually used alot of your ideas to do this...they were alot cleaner than my origional work).

I looked at all of your spreadsheets and it appears that you have put a lot of work into them.
It's just too bad I'm not a fabricator cause i don't know what tha "F_(&" I was looking at /forums/images/graemlins/rotfl.gif

Very nice, thank you! /forums/images/graemlins/thumb.gif

BTW, you can't use "#" in a URL so you might want to change the name of that parts file...

Somebody help me......

!! MY BRAIN IS SMOKING....MY BRAIN IS SMOKING !!!!

/forums/images/graemlins/angryfire.gif <- Smoking brain emoticon?



Dan, that is WAY cool. As I mentioned in my last e-mail, I am convinced that I can roll all this data up into the "graphical version" which will be a lot more fun to use.

I think if this program does nothing else, it should help people understand some of the forces involved in the rod ends and how critical it is to size these parts correctly. This is my main worry with the "just go out and build it" crowd... for a trail-only rig, a broken rod end is an aggravation....but for a street-driven truck, a broken component is a high-speed CRASH!!! /forums/images/graemlins/eek.gif

I can't wait to see how people start using this program, and the designs that get posted up. Like any collaborative effort.....it sometimes will amaze you what others can do with your initial ideas. /forums/images/graemlins/thumb.gif

Real quick, on the Leaf Spring Calc, when measuring free arch, what are the proper points to take the measurements from? Bottom of the pack, or top of the pack to the top of the spring eye?

By the way, great stuff, thank you /forums/images/graemlins/thumb.gif

BRB,

Here's a link:

http://www.rpmnet.com/techart/leaf.shtml


It looks like it's measured from the spring eye centerline to the bottom (mounting surface) of the leafpack. You'd better read the source too, and see if you agree with my interpretation..... /forums/images/graemlins/deal.gif

Thanks for sharing your brilliance Dan! I really appreciate it. This will really save me and others a bunch of time when starting and fine tuning their 4 link.

Greg is right about the free arch. I quess I should add a picture /forums/images/graemlins/rolleyes.gif...I just suck at making one myself (see posted pick above). /forums/images/graemlins/grin.gif

The intresting thing about measuring this way is you can see that a spring pack with lots of thin leaves will be alot thicker than a pack with just a few thick leaves. This will make it "look like it has less arch" and might be one reason they flex better.

Dan,

Quick question (as I'm currently "modding" your latest version of ExcelCAD!! /forums/images/graemlins/grin.gif)

F.S. = "Factor of Safety"

Is this a multiplier value to be used against the "Link Force" value?

EX.

"Link Force" = 5825 Lbs
"F.S. Rod End" = 9.44

Therefore the load to create failure of the rod end is (5825 x 9.44) = 55,000Lbs???





Interesting coincidence that the number just HAPPENS to be the exact value of BIG rod ends in the Aurora catalog??? /forums/images/graemlins/thinking.gif

[ QUOTE ]
Dan,

Quick question (as I'm currently "modding" your latest version of ExcelCAD!! /forums/images/graemlins/grin.gif)

F.S. = "Factor of Safety"

Is this a multiplier value to be used against the "Link Force" value?

EX.

"Link Force" = 5825 Lbs
"F.S. Rod End" = 9.44

Therefore the load to create failure of the rod end is (5825 x 9.44) = 55,000Lbs???





Interesting coincidence that the number just HAPPENS to be the exact value of BIG rod ends in the Aurora catalog??? /forums/images/graemlins/thinking.gif



[/ QUOTE ]

That's it! Looks like Watson put more thought into those rod ends than you might have realized! I thought it was a good sugestion so I stuck with it.

Your homework:
Now just try and see if you can get the F.S. for the rod end that size with a smaller rod end! /forums/images/graemlins/wink.gif


I updated the name of that file...thanks

[ QUOTE ]
Greg is right about the free arch. I quess I should add a picture /forums/images/graemlins/rolleyes.gif...I just suck at making one myself (see posted pick above). /forums/images/graemlins/grin.gif

The intresting thing about measuring this way is you can see that a spring pack with lots of thin leaves will be alot thicker than a pack with just a few thick leaves. This will make it "look like it has less arch" and might be one reason they flex better.

[/ QUOTE ]


Here's a pic to save Dan from drawing anymore....

http://www.norcalbigdawgs.net/Gallery/albums/album73/Mvc_008f.jpg

the straightedge is across the middle of the springeyes, and you can almost read the tape measure at the base of the springpack (where it sits on the perch)....

BTW -> It's a 4" springpack with what appears to be 9" of "free arch"... Soft Springs, eh? /forums/images/graemlins/wink.gif

[ QUOTE ]
The intresting thing about measuring this way is you can see that a spring pack with lots of thin leaves will be alot thicker than a pack with just a few thick leaves. This will make it "look like it has less arch" and might be one reason they flex better.

[/ QUOTE ]

After going to the 'Way Back' file and a conversation I had with one of the guys at Deaver; I think I can make a call on that one since it wasn't directly said.................And you two better keep the conversation simplistic for my slow mind, y'all engineers might leave me behind /forums/images/graemlins/rotfl.gif

I think the reason for the thin leaves is one, the spring will retain the arch longer than a couple of thick leaves, but more importantly, even though there are more, maybe it's easier to get the thinner leaves to move compared to the thick ones, therefore even for you rock guys this might not back too much of a different, but for something that is hauling butt; the spring can start moving faster and will be keeping up with the terrain compared to what a thick setup will............

Sound right?

Sounds right.


Really, my only experience is in plugging the numbers into the "classic" leaf spring rate formula (yet, ANOTHER spreadsheet I built a while ago).... it became obvious in a hurry that for a given pack thickness....more thin leaves stuffed into that height would provide a softer rate than a few thick leaves.

Sort of like comparing a soft-bound magazine to a single thick sheet of cardboard.... with all those individual sheets of paper in the magazine, is wriggles and moves with a high degree of freedom. The cardboard (even though it's still made of the same material, just thicker) can't do much of anything flexwise.

That's the best analogy I can think of at the moment.

One quick question on the Leaf Spring file, I just got done pluggin the numbers in posted by ntsqd in the Garage forum, but it's been a long time since I messed with an Excel file, how do I get it to calculate the spring rate once I've put in all the numbers?

Use the "=" sign to indicate that you are defining a formula instead of just doing a numeric entry... Then you can click on each of the "involved" cells to add them to the calculation string....add your multiplications, divisions, and ^3s....(or whatever you want)

Once you hit enter, Excel will perform the calculation.

The best part is that every time you change one of the cells involved in the calc....the rate will be automatically recalculated. It will teach you the effects of each change in a HURRY!!!

Fun stuff. /forums/images/graemlins/pimp.gif

Okay, just a few more questions.........

What is Stated Load?

Load F? That would be weight of front end, right?

Loaded Arch looks like would be the measurement of the springs when on the vehicle, and therefore the deflection is the differance between the free arch and loaded arch.

Last but not least, stress? Is that something that I can measure at home, or does it need a special measuring doohickey?

[ QUOTE ]
Okay, just a few more questions.........

What is Stated Load?

Load F? That would be weight of front end, right?

Loaded Arch looks like would be the measurement of the springs when on the vehicle, and therefore the deflection is the differance between the free arch and loaded arch.

Last but not least, stress? Is that something that I can measure at home, or does it need a special measuring doohickey?






[/ QUOTE ]


BRB,

I'll take a crack at these.....Dan will probably followup at 2AM when he logs in here! /forums/images/graemlins/thumb.gif


Stated Load is probably just what the "vendor" says the spring rate is. Just a sanity check against the calculated value, I think.

Load F - I'll bet ya it's the weight on the spring. 1250 looks like exactly 1/4 of the 5000 Lbs of sprung weight that a Blazer probably has.... I don't necessarily think it's FRONT. Curiously my truck when weighed on a set of precise "race scales" had almost perfect 50/50 weight distribution... /forums/images/graemlins/thinking.gif

Load Arch - I think you've got this one right. The arch that's left over once you add the 1250 Lbs on top of it.

Stress - I don't think this is a "measureable" thing, so much as a way to indicate the stresses on the metal itself. Might be an indication of the springs "longevity"...higher values are probably going to sag or fail sooner because the stresses are closer to the limits of the material (in this case spring steel).


Something that can help a lot in Excel, if you don't already know this.... when you click on the cell you're curious about, the formula is displayed in the upper "text window" (duh, obvious right?) BUT!...If you actually move the mouse UP to that text window and single-click.....it will highlight and color-code all of the cells involved in the calc for you!!! It makes it a LOT easier to decode which other cells are being used, and makes it pretty easy to figure out the "meaning" of a calculation that's unclear.



/forums/images/graemlins/cool.gif

Again Greg has it right...
Alot of those springs I got all the info (except for leaf thickness) from the tech section of CK5. I measured the springs that I have laying around and guessed at the leaf thickness for the rest.

The springs I actually measured are
1st gen 4" ranchos (might as well have an I-beam insted of springs)
52" rear (ones that came on my truck...other years might be different)
2nd gen 4" TC EZ-ride (if you notice the calculated value is off by a HUGE amount from the stated rate...I have no idea why)
63" chevy's

See update in 1st post /forums/images/graemlins/pimp1.gif

That spreadsheet is "dead sexy"!!!! /forums/images/graemlins/grin.gif

Hopefully it's becoming more user-friendly, so I wouldn't mind hearing feedback from the rest of the "C.O.G.-Heads" about that.

Adding the coordinate system diagram as a "tab" in the spreadsheet was a good idea. Maybe in v3.0 I'll redraw that silouette.....but for now, it's a great reminder of how simply this whole project started!! /forums/images/graemlins/thumb.gif

Thanks again Dan! /forums/images/graemlins/smile.gif I want to acknowledge your help with this project in a public forum as well.... there is a lot of your brain power and a lot of late nights being spent answering my questions to get this 'little project' where it is today.

I hope that there are other people who appreciate your contributions as much as I do....

I'm a bit too lazy to go back and figure out what exactly I did for max torque values when I figured my link end requirements but I know for the front I found a number somewhere indicating that it would take 10K ft/lb to break a D60 joint so I built the front around breaking both front shafts at the same time. I have no idea if that 10K ft/lb number is even close to right, I kind of suspect it's close knowing that a 32 spline shaft comes close to that strength and a 35 spl. D60 is about 1/8" bigger.

For the rear I did a similar calculation for the 14B shafts. I came up with safety factors around 3 but my lower links are in compression under forward power so I don't know how they would fail. And breaking both shafts in a 14B at the same time is pretty optimistic.

I did purposely err on the side of bigger ends for my suspensions so that durability would be better. I don't want to replace the ends very often and the easy way to make them last is to not stress them much. You also have to watch the bending strength of the threaded shank on the end, I've seen a decent number of broken 3/4" rod ends that just couldn't take the impact on the link arm. That's the nice thing about a 1.25" shank on the end, I'm pretty sure I'm not going to mess it up bouncing on rocks.

There might be room for another spreadsheet calculating the torque loads on the rear end, there can be varying limits of traction, drivetrain strength, or engine output ability. A guy with rockwells and a toyota motor might be able to use the max torque output from the motor and gearing as the absolute limit of torque on the rear suspension linkage.

Another next step might be calculating loads on the links from cornering or lateral forces. I can tell you from my backflip experience, your rig needs to be able to take a couple G's laterally.

The spreadsheet is pretty cool, it does a lot of the work for you, really easy. It makes a lot of my drawings obsolete.

Thanks for all the input.

I like the idea of using axle breaking torque as the starting point. Obviously you can't have any more torque on the axle housing (for the links to resist) than the axle shafts can withstand without breaking. After my first version I ditched the calculation of axle torque as just being a extra un-needed step. I haden't even thought about doing a "sanity check" on it. /forums/images/graemlins/thinking.gif It seems to me that the axle breaking torque would be higher than the tire slipping torque otherwise we would be breaking shafts all the time and having no tire slip. That would be why your safety factor of 3 would corespond to about 6 using my approach. I'll go back through and do the calculations using axle torque..shouldn't take too much work Then if I wanted to I could calculate both ways based off of axle strength or available traction. The available traction approach looks like it would work out well untill you bind up the tire in a crack... /forums/images/graemlins/thinking.gif

[ QUOTE ]
The spreadsheet is pretty cool, it does a lot of the work for you, really easy. It makes a lot of my drawings obsolete.

[/ QUOTE ]
Thanks! Engineers do some strange things when they get board /forums/images/graemlins/grin.gif As for drawings that is how I would have done it if as for only doing it once twice it takes alot less time. I still went through all geometry #'s and checked them in solidworks...I guess I could use cosmos to check the link forces /forums/images/graemlins/thinking.gif

Greg,
Do you have enough measurements from Watson's truck to put it in the spreadsheet?

One enourmous variable we have here is the CG height, it varies a good bit and is very difficult to measure. We need some guidelines for this number to get any of these calculations to work out right. If we just had one vehicle to base everything on, we could add and subtract CG's and locations of various parts to get some kind of baseline.

I've measured CG location once and it was a pain.

We also need to figure out if we want to use the CG height for the total vehicle weight or the sprung weight only and when this transition takes place. I think we might have some artificial AS numbers since unsprung weight is such a big part of out vehicle totals and it usually stays on the ground while the chassis does it's own thing. Watching Jason's video of my K5 in the big hot tub, you can see that this is a big deal. I carried at least one tire at a critical point in that climb and I can guarantee that the AS for that situation is not like anything I calculated for when it's sitting on the ground.

I have always seen it done with the sprung mass CG. The only rule of thumb I have ever heard of for it is camshaft centerline. Sprung mass is way harder to measure than overall! The only reasonable way to do it would be like you sugested to do overall and subtract the CG of the unsprung mass. I have only measured it on small cars that you could just tilt by hand till they balanced and measure the angle. We even did it with different drivers in the car to see how much it changed. Obviously that isn't as easy as it sounds with a heavy 4x4. I think most people will just stick with the rules of thumb for this one.

How did you do the CG measurement? Did do the weigh it on flat ground and then on a known incline? Did you subtract out the unsprung mass CG? How far off was the sprung mass CG from the camshaft or top bellhousing bolt?

This is a good link for overall CG for jeeps
http://www.jeepaholics.com/tech/cog/#_Toc535118705

Maybe you need to bring with a nice set of scales to Blazer Bash and get a bunch of #'s for different K5's /forums/images/graemlins/thumb.gif

I worked on a S-10 tube chassis hill climb truck for a senior project so it's numbers don't apply at all to what we're doing, but the technique worked. I blocked and chained the axle and a-arms so they couldn't move, then picked one end up a LONG ways with a come-along and weighed the other wheel weights. It was a major pain since the cable had to be exactly verical and I had to jack the thing up while it was suspended to get the scales under it. It wouldn't be bad with the right equipment but with what I had, it sucked. I checked the unsprung weight by putting the chassis on stands and removing the coilovers, then weighed the wheel weights. I remember the rear was a 9" with some 325/60R15 (?) BFG's on steel wheels and it weighed about 450#, with suspension linkage and all. This was an easy method to the the unsprung weight since the only thing not connected was the springs and shocks.

For what we do, I think we have to work with both the sprung CG and the total, since it's pretty common for the weight of the front axle to come into play on hill climbs. The rest of the time, it's probably not a big deal till you get into high AS numbers that come close to fully drooping the suspension. To be accurate, we probably need to model the vehicle as just the sprung weight, then model it with the total weight but with the suspension drooped or near full droop. Then I guess we ignore the rebound rate on the shocks. It could also be modeled as the whole vehicle weight in some cases since it's becoming pretty popular to use the winch to suck the axle down on climbs. At that point the sprung and unsprung mass become pretty much the same, at least on the front.

Triaged & Greg72, thank you. I just started playing with version 2.0. It's very easy to use, very thorough, and has come a long way since version 1.0. Your work is truly appreciated.
Why is the FS yield for the lower rod labeled "compression" while the FS yield for the upper rod is labeled "tension"? I thought yield strength for both would be "tension" since the rod will always buckle before it compresses.

On the rear axle the greatist loads will be under acceleration because of weight transfer. In the case of acceleration the upper links are in tension and the lower links are in compression. Obviously a link under tension can't buckle (so the upper links will never buckle under acceleration). If you had no rear brakes you could use a piece of small diameter solid rod (or even cable /forums/images/graemlins/eek.gif) for the upper links as long as it had enough strength to handle the load. Because you do have rear brakes that would be a bad idea. To steer people away from that I added in the buckling of the top link under braking. Because of weight transfer to the front wheels the load will be lower than under acceleration and I didn't take that into account (just to make it easier). This will mean that the calculation for the upper link buckling will be way overkill...oh well. There is one other thing to consider that I didn't exactly put in (but can be infered from the output). That is the slenderness ratio. Think of it this way. If you took a 6" piece of welding rod/wire and put it in compression it would buckle. Now what if you took a piece of 1" steel rod that was 1" long and compressed it it would fail in yield and would never buckle. There is a point at which this transition happens and you find that with the slenderness ratio. What I did was calculate all the F.S.'s and the lowest one would be the one that would fail first. As long as the F.S. for yield is higher than the F.S. for buckling it will buckle first. If the F.S. for Yield is lower than the F.S. for buckling it will yield first. Plug in some huge diameter tube and you will see where this happens. Because of the load under braking is less and because most lower links are close to the buckle/yield transition I did it that way.

Awesome! That's quite a bit of work you've put into this. I'm impressed, and as a (future) mechanical engineer, I can appreciate what kind of stuff you had to incorporate into the calculations.

Now, could you elaborate/explain what the results are telling me? Like what values should I be looking for in the "design overview" that would indicate I've got a "good" setup?

Thanks.

These are what I would shoot for. It is all a matter of opinion and if you asked 10 people you would get 12 different answers.
All of these numbers I have listed below have a very wide range. It is up to you to figure out where in that range you want to shoot for and why.

Anti-Squat: 50-100% (adjustable would be good)
Roll Axis Slope: I don't think in slope so look at the roll axis angle below
Roll Center Height: Somewhere above wheel centerline but not higher than tire diameter
Roll Axis Angle: Keep it in the roll understeer for a street driven truck. The flatter the better up to 10 deg max.
Instant Center X-Axis & Instant Center Z-Axis: These both work together and are what to mess with to get your driveshaft to like you.

Thanks that clears it up. I hadn't thought about the effect of the slenderness ratio.