Motion Ratio, Natural Frequency and Spring Rate

[turboshad]

And all that Jazz.....


I am trying to decide on my spring rates which stem off the natural frequency of the suspension. Frequency is used because the number can be corrolated between vehicles. Two vehicles with similar suspension frequencies will have similar ride qualities. The lower the frequency, the softer the ride and vice versa. I knew if I asked what frequecy other were running most wouldn't know so I did a bit of the work.

To find the frequency you need to know the motion ratio and corner weight of your car. Since all of our cars (except the L guys) have more or less the same front and rear suspension geometry I went to the garage and found those numbers. This is with the cast control arm but I think it will be very similar with the stamped. The rear is the same for all the genereations AFIK.



The graph shows a y=mx+b equation. m is the slope which represents the motion ratio so the front has a MR of 0.897 and the rear is 0.788. Using this motion ratio I made some charts for front and rear correlating spring rate, coner weight and natural frequency.



So once you know your coner weight, draw a straight line up until you hit the spring rate you are using and then go across to find the frequency. This only applies to linear springs so most likely those using coil overs.

I am curious what frequency others are using and how their cars ride. Currently I am looking at using 1.8hz in the front and ~1.9Hz in the rear but have no conception of how rough this will be. Anyone care to share their experiences?

DJ

[turboshad]

Well, I guess I'm on my own here.

The good news is last night I confirmed that I can make the rear work with 8" free length springs which would be the same length as the front. That means if I buy a 300lb/in set I can go 380/300 or 300/250 fron/rear giving me two diffrent ride sets (I already have the 380 and 250 set). The softer set might be nice for long trips.....like the 32hr one to SDAC ......hopefully. These rates give me 1.8Hz/1.9Hz and 1.6Hz/1.7Hz respectively.

I will let people know how it works out so hopefully someone else can use this when choosing coilovers.

DJ

[2.216VTurbo]

Uh oh, no way Mister! You'll do no such thing till you build those control arms! One revolutionary product at a time for you bud

BTW i have the 8" springs on the coild over Konis in the S and the Rampage. 275 pounders in the S which sounds light and there was some body roll in Vegas at Carroll's 86th bash but I dont think anyone could say the car didn't handle well there 300 pounders in the Rampage becuse it is heavier int he nose with AC, power steering, and that chunk called a Lotus TIII I think I might drop some 325's in that thing becuse it needs a little more and I am still *adding* weight to it

[BadAssPerformance]

Alan, you car does ride nice and handle well, at least from teh passenger seat how did you like Craig's 600# springs when you could feather the throttle enough to point it straight?

turboshad, nice analysis, but spring rates are kind of going to depend on how you like the ride vs. handling vs. your driving style more than anything.

[2.216VTurbo]

Alan, you car does ride nice and handle well, at least from teh passenger seat how did you like Craig's 600# springs when you could feather the throttle enough to point it straight?

turboshad, nice analysis, but spring rates are kind of going to depend on how you like the ride vs. handling vs. your driving style more than anything.

Actually, his car 'chatters' around the corners when pushed hard, IMO if he dropped the spring rates 20% or so it would handle better. His car is the most uh, *entertaining* turbo Mopar I have ever driven I told Stimac he should throw a steering rack in it for Craig, I think that will cure its 'behavior'

[turboshad]

Uh oh, no way Mister! You'll do no such thing till you build those control arms! One revolutionary product at a time for you bud

lol, don't worry Allan, I was acutally checking back in on things while I waited for another FEA to finish on an updated design. The wheel sure sticks in further than I had imagined at first.

spring rates are kind of going to depend on how you like the ride vs. handling vs. your driving style more than anything.

Exactly. The best way to compare the ride is through suspension frequency which is what I was looking for. I was really looking to see if someone had tried something and found it to be back breaking or not. I also figured most people wouldn't take the time to figure it out which is why I posted the graphs.

The whole give and take of handling vs. ride is definately subjective though. I'm sure with stiffer suspension I could take corners better but I do still want to enjoy the car. At the same point, suspension as stiff as you can get away with on a road course may be dangerous on the street if your tires can't keep in contact with the ground over the bumps.

[Reaper1]

I believe that the Pro-Kit Eibach's are 300#/in in the front and 330#/in in the rear. Now, I know those are "progressive springs, but the "progressive" part is usually bound on on the cars I've ever seen them installed on making it basically a linear rate spring.

I find it absolutly awsome that you are doing alalysis on all kinds of stuiff we are doing in my Vehicle Dynamics class right now! It's also stuff I'm interested in presenting in my project.

BTW, the book we are using: "Race Car Vehicle Dynamics" by Milliken suggests that "typical" 'sports cars and small formula cars' have natrural frequencies in the 70-90 cycles per minute, or 1.17-1.5 cycles per second(Hz, IIRC).

Also, keep in mind that the rear spring does not directly compare to the wheel rate becuase it has an installation ratio, so that has to be taken in to account when choosing the spring rate back there...

[supercrackerbox]

This is the kind of stuff that makes me think I don't actually know anything about cars.

[Reaper1]

Believe me, there is a reason that there are so many different engineering teams that usually design a car! There is SO much to know it's incredible!

That book I mentioned in my above post is VERY good. It is a bit heavy on the engineering side of things, but it does explain what is going on pretty darn well IMHO. I think it's about $120 or so. Or, find it in the library and just look at it! I've read about half of it becuase once I start reading it I can't put it down! It's like a good novel!!! LOL

[turboshad]

Ya, it's been a few years since I've milled throught Milliken. I should really buy it one of these days b/c it is definately the suspension bible.

I knew the rear would react different because the left and right side aren't independant and I would think the spring rates are in some form coupled. The problem is that 90% of the info out there for solid rear axle is for a live axle which behaves different b/c of the torque. I couldn't find anything satisfactory that seemed to work with the trailing arm so I figured treating it like an independant system and finding the motio ratio experimentally would give a "close enough" result. I would be very interested if you have any more theory to shed some light on determining spring rates for a trailing arm suspension.

DJ

[Reaper1]

Yeah, I'll read through that section again, but the book gives a refference for better information on beam axles. I'll have to look it up....

[turbovanman²]

I had these on the van, they were brutally hard,

I used Eibach springs that were 12 inchs long, 2.5 diameter and 300 lbs on Bilstein coilover's, it was bouncy and very hard.

[Reaper1]

I posted this information in my "corner wieghts" thread, but I figured ot would be good to post here too!

I'd like to say that I have not completed my analysis by a long shot, but the report was due, so I had to put something together! LOL This information is all first iteration and VERY rough. I did not take in to account roll gradients, the front instalation ratio(I set it at "1", but it it different in reality due to the angle of the strut), the rear information was all based on educated guesses becuase I hadn't really done any rear measurements.

For a car with 3" of jounce travel a natural frequency(NF) should be around 1.92Hz or 115cpm. Based on the equations I used found in my Milliken Vehicle Dynamics book this should equate to about a 405lb/in spring up front.

My front Eibachs provide a NF of 1.81 or 108.6cpm on my car.

I set the rear jounce travel at 3.5" and came up with an instalation ratio of .65 based on a LOT of guessing. This yeilded a spring of 447lb/in back there. That equates to a NF of 1.68Hz or 101cpm.

The current Eibach springs out back (330lb/in) provide a NF of 1.45Hz or 87cpm.

Also some interesting info...the CG changed less than a full inch in either the font/rear or CL of the car.

My front roll center is 3.3" BELOW the ground surface.

OK...I'm VERY tired and am crashing. I hope this helps ome people!

[Aries_Turbo]

but the "progressive" part is usually bound on on the cars I've ever seen them installed on making it basically a linear rate spring.

maybe on a daytona the progressive part is collapsed at rest.... on a kcar it definitely isnt. the ride is supple on small bumps and cracks in the road, but when it collapses to a linear spring, its very firm.

Brian

[Reaper1]

I've only ever seen them installed on Daytona's. But even the one baseline(read: should be fairly light) had all of the progressive coils bound.

What is the weight of a K-car then? I'm guessing in the 2400-2700# range, but at the upper limit of that they WILL be bound, I promise!

To add a little more feedback as far as the ride is concerned, all the cars I've ridden in that have the Pro Kit Eibachs on them ride BETTER than factory, even though the spring rates are definatly higher. This *may* have to do with the progressive coils, but seeing as those cars I've ridden in bind them all I don't think that is really the case....

[Aries_Turbo]

k car is around 2400lbs.

it does ride well and soak up the small stuff.

Brian

[turboshad]

When you say installation ratio do you mean the same as motion ratio? If so, how did you come up with those numbers b/c they shouldn't be much different from what I found. Also, what corner weights do you have?

[Reaper1]

k car is around 2400lbs.

it does ride well and soak up the small stuff.

Brian

The lighter weight makes a HUGE difference on EVERYTHING.

When you say installation ratio do you mean the same as motion ratio? If so, how did you come up with those numbers b/c they shouldn't be much different from what I found. Also, what corner weights do you have?

It depends on what you mean by motion ratio. The installation ratio is the ratio between how much the wheel center moves in relation to how much the spring acutally gets displaced. It is defined as the change in spring displacement (delta y) over the change in wheel center displacement (delta x): (delta y/ delta x) = instalation ratio.

There is another parameter which I did not take in to account because I had absolutly NO information to figure it out and that is the geomtetric rate. That is defined as the change in instalation ratio with respect to wheel displacement. I kinda feel that our rear suspension MAY have this and it will effect what the final wheel rate ends up being. Simply measureing distances and then graphing the information will tell whether we need to take it in to account.

I don't know how this will work on the front suspension, but I was told that a sine function needs to be used to figure out the instalation ration up there. I have a feeling that it is going to be negligable becuase of the small angle the strut is on, but I could be wrong....

[turboshad]

So we are talking about the same thing. If you look at my charts for motion ratio they are made experimentally (not by drawing it out on paper) by taking the spring out of the front and rear and then incrementally changing the wheel center heights and the measuring the spring change. As you can see the scatter isn't bad at all so I'm pretty confident in them as being right. It also shows that the geometry proves to be decently linear or at least enough to call it so.

The only difference I can see in the rear is from the solid axle which from what I can figure would mean the left and right spring would be partially coupled. This would in essence make the real life frequency higher than the calculated frequency since there would be some opposite spring compression. I was thinking about it and I think if you raised the right wheel center and kept the left constant and then took the delta of both springs together over the delta of the wheel center you would get a closer match.

[Reaper1]

Cool! So since you found out the instalation ratios experimentally that saves some work for me! I'm surprised that the front is that far from being 1, I would have figured it to be closer.

As for the rear, foget about coupling the springs. Make both sides raise the same amount and get the ratio that way.

As is stated in the book, there is a different refference used for twist beam axles. The roll rate and such will definatly be effected by the ratio, but the ratio itself is the same side to side, so just make sure both right and left wheel centers move the same amount and all should be well!