Spring rates!

[Raj]

Hi friends,
Can someone please help me with the correct formula for determining the spring rate of a shock absorber? I have read different books/articles & have found different formulas for the same! the different formulas lead to different answers, hence the confusion.

till now, i have been using the formula:
Spring rate = Gd^4 / 8nD^3
where,
G = modulus of rigidity
d = wire dia
n = no. of active coils
D = mean coil dia

is this formula correct? is there any alternative method to find out the spring rate if value of 'G' is not known?

Also, i have read,
wheel rate = spring rate x motion ratio
whereas, in some books, i have read,
wheel rate = spring rate / (motion ratio)^2

which is the correct formula?

[-francisco-]

According to what I've read:

wheelrate = spring rate/ motion ratio^2
WR=k/MR^2

or:

WR=k*IR^2

IR= instalation ratio = shock travel/wheel travel

Check out this (http://pirate4x4.com/tech/billavista/coilovers/Part_1/) a great article that also covers spring rate formulae.

Also, what spring rates are people running? The lowest i can find for MTB shocks is 250lbs springs, which on our 260kg car with a motion ratio of 1.1 gives us a natural frequency of 3,6 which is pretty high. I know some teams are running 150lbs springs, are they getting them custom made, or something?

[Mike Macie]

edited to fix errors

When you calculate your wheel rate you should calculate your ride rate which includes your tire spring rate since it is part of the same system. For better accuracy it should be something like

Wheel Center Rate = (spring rate / MR^2)

Ride Rate = (Tire Rate * Wheel Center Rate)/(Tire Rate + Wheel Center Rate)

[HenningO]

In every discussion involving MR, one should also present how they define MR - since there are two ways to define this. This will affect the the above formulas.

MR = wheel/spring

or

MR = spring/wheel

[J.R.]

I've always thought of it as MR = Wheel/Spring and called the other Installation Ratio, IR = Spring/Wheel. Supposed to help keep them straight, but I still always get them mixed up in my head.

[Chris_S]

Originally posted by -francisco-:
Also, what spring rates are people running? The lowest i can find for MTB shocks is 250lbs springs, which on our 260kg car with a motion ratio of 1.1 gives us a natural frequency of 3,6 which is pretty high. I know some teams are running 150lbs springs, are they getting them custom made, or something?

Try H&R for custom wound springs. They sorted us out last year for our cane creeks

[BilletB]

Originally posted by -francisco-:
According to what I've read:

wheelrate = spring rate/ motion ratio^2
WR=k/MR^2

or:

WR=k*IR^2

IR= instalation ratio = shock travel/wheel travel

Check out this (http://pirate4x4.com/tech/billavista/coilovers/Part_1/) a great article that also covers spring rate formulae.

Also, what spring rates are people running? The lowest i can find for MTB shocks is 250lbs springs, which on our 260kg car with a motion ratio of 1.1 gives us a natural frequency of 3,6 which is pretty high. I know some teams are running 150lbs springs, are they getting them custom made, or something?

Haha, nice. I may possibly know the authors of that piece. =] Fun to see it posted here! If you look hard enough you can find 150 lb springs. What is the ID and free length you need for those shocks? We run the Cane Creeks and 150's are out there for them.

Raj,
You should always know what G is. If your spring is steel, you know G. If it's ti, you know G. Etc. However, I've found that formula is very inexact for predicting the rate of a coil spring. If the spring isn't marked your best bet is to throw it in a machine and actually test for the rate.

[BilletB]

Originally posted by Mike Macie:
When you calculate your wheel rate you should include your tire spring rate since it is part of the same system. For better accuracy it should be something like

Total Spring rate = (Tire Rate * Spring rate)/(Tire Rate - Spring Rate)

Wheel Rate = (total spring rate / MR^2)

Technically, wheel rate doesn't include the tire. It's the rate at the wheel center. Ride rate then accounts for the rate of the tire. You really need to calculate and know both.

And it would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate)

[BilletB]

Originally posted by BilletB:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Macie:
When you calculate your wheel rate you should include your tire spring rate since it is part of the same system. For better accuracy it should be something like

Total Spring rate = (Tire Rate * Spring rate)/(Tire Rate - Spring Rate)

Wheel Rate = (total spring rate / MR^2)

Technically, wheel rate doesn't include the tire. It's the rate at the wheel center. Ride rate then accounts for the rate of the tire. You really need to calculate and know both. Also, installation ratio won't effect the tire rate. Your equations are a lil off.

It would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate) </div></BLOCKQUOTE>

and

wheelrate=springrate*ir^2

where

ir=shocktravel/wheeltravel

Remember ir changes dynamically.

[Mike Macie]

Originally posted by BilletB:

And it would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate)


My bad, should of checked it before posting. Don't know how i mixed up ride rate and wheel rate. But I'm pretty sure you subtract the wheel rate from the tire rate when calculating the ride rate.

[-francisco-]

Originally posted by BilletB:
Haha, nice. I may possibly know the authors of that piece. =] Fun to see it posted here! If you look hard enough you can find 150 lb springs. What is the ID and free length you need for those shocks? We run the Cane Creeks and 150's are out there for them.


Thanks. But yeah, last year pirate4x4's article on suspension design was what really taught me how to draw a linkage suspension system, well it only gave me the basics, but it was all i needed, first for mountainbike design and now for Formula Student. Going to the second year in college, now i could have easily figured out how to do it with a bit of applied physics, but still, the complete lack of information on the matter at car suspension books is patethic.

[-francisco-]

Originally posted by BilletB:
[QUOTE]

Technically, wheel rate doesn't include the tire. It's the rate at the wheel center. Ride rate then accounts for the rate of the tire. You really need to calculate and know both.

And it would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate)

It makes sence, but then what do you use for natural frequency calculation? wheel rate or ride rate? I entered the team this year and my job was to develop a new pushrod system for last year's car (we'll be on class 1-200) keeping the overall A-arms geometry and thwe same tyres, so i didn't really looked in tyre performance.

Also what formula are you guys using for Fn? I'm using:

Fn = sqrt ((386.088 * WR ) / CSW ) / 2pi

But i've seen guys using diferent formulae/convertion factors in forums and such, so I'm really not sure what is the correct one.

As for springs we just got a local spring shop to wound custom springs for us.

[BilletB]

Originally posted by Mike Macie:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BilletB:

And it would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate)


My bad, should of checked it before posting. Don't know how i mixed up ride rate and wheel rate. But I'm pretty sure you subtract the wheel rate from the tire rate when calculating the ride rate. </div></BLOCKQUOTE>

Your ride rate is your wheel rate and tire rate as springs in series. How do you find the equivalent spring rate of springs in series?

(1/k_eq)=(1/k_1)+(1/k_2)+...+(1/k_i)

For just two springs in series it reduces to the product of the rates divided by the sum of the rates.

[BilletB]

Originally posted by -francisco-:
It makes sence, but then what do you use for natural frequency calculation? wheel rate or ride rate? I entered the team this year and my job was to develop a new pushrod system for last year's car (we'll be on class 1-200) keeping the overall A-arms geometry and thwe same tyres, so i didn't really looked in tyre performance.

Also what formula are you guys using for Fn? I'm using:

Fn = sqrt ((386.088 * WR ) / CSW ) / 2pi

But i've seen guys using diferent formulae/convertion factors in forums and such, so I'm really not sure what is the correct one.

As for springs we just got a local spring shop to wound custom springs for us.

Thanks for saying that about the pirate article. That's really what we were going for.

As you said, physics, statics, and dynamics are the fundamentals of what we're dealing with. I came up with that natural frequency equation for that article because it was simpler to just say that for the non-engineers. You are an engineer. For you, fn=sqrt(k/m)/2pi. Then, you can derive your own equations for shortcuts if you wish, but don't use the shortcut equation until you understand and derive it. You should also understand where sqrt(k/m) comes from. Think equations of motion and solutions to those equations. That is how you model and help design suspensions.

Do you use the nat freq of wheel or ride rate (I call these suspension frequency and ride frequency respectively)? Which do you care about more? Well, those are questions for YOU to answer. I can tell you that you damn well better know both. The best suspension designers can blend some logic and art with their science.

[Mike Macie]

Originally posted by BilletB:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Mike Macie:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BilletB:

And it would be

ride rate = (wheelrate*tirerate)/(wheelrate+tirerate)


My bad, should of checked it before posting. Don't know how i mixed up ride rate and wheel rate. But I'm pretty sure you subtract the wheel rate from the tire rate when calculating the ride rate. </div></BLOCKQUOTE>

Your ride rate is your wheel rate and tire rate as springs in series. How do you find the equivalent spring rate of springs in series?

(1/k_eq)=(1/k_1)+(1/k_2)+...+(1/k_i)

For just two springs in series it reduces to the product of the rates divided by the sum of the rates. </div></BLOCKQUOTE>


Again i mixed up ride rate and wheel rate. You would subtract when calculating the wheel center rate using the ride and tire rate. I'm used to calculating the desired ride rate and working my way back.

[-francisco-]

Originally posted by BilletB:
Thanks for saying that about the pirate article. That's really what we were going for.

I came up with that natural frequency equation for that article because it was simpler to just say that for the non-engineers. You are an engineer. For you, fn=sqrt(k/m)/2pi.

So, you know the guys that wrote the article or were you the one who wrote it?!
The Fn formulae always get me in trouble because of working with the imperial system and its wicked conversions factors from mass to weight and such. But know i ave everything straight.

One question, i did all the maths for our suspension with all the wheel travel visualized in Solidworks, but everyone is bashing me cause i ordered 215, 225 and 250 lbs springs to play with, and we haven't tested the car yet, susp everyone is saying the susp is gonna be too soft.

We have a car with 200kg -444lbs sprung mass, about 50-50 distribution front to back, the push rod is at 40º working in a plane. and the rocker's MR is 1,1:1.

The general Motion ratio is about 1,18:1. Down on paper i have ride frequencies between 3 and 3.4hz (MR is adjustable). I told them that's what most people run on their cars.

Any advice?

[Adambomb]

I'd say 3-3.4 is a bit higher than I'd prefer for an FSAE car; surely not too soft.

I hear you on everybody saying the suspension is going to be too soft. I've heard that a lot over the last couple years. The only advice I have on that is that most of those naysayers (including the engineers), quite honestly, don't have a damned clue what they're talking about, and I can almost guarantee haven't looked at the problem with the level of depth presented here.

Most of them have gained all their knowledge from movies like "The Fast and the Furious," and will swear up and down that the "best" suspension for performance is the stiffest. Not true at all.

Sorry, got off on a bit of a rant there, but yeah, you're in the ballpark at least. Ride rate is a bit high for my tastes (I've seen some really good publicly posted papers from Optimum G on the subject), but other than that the numbers sound reasonable.

[flavorPacket]

Instead of guessing on what is 'too soft' or 'too stiff', why don't you evaluate the effects of these parameters on tire load variation, force transmissibility to the sprung mass, etc? Or even better, just test both setups?

[Yellow Ranger]

force transmissibility? now we're just making up words http://fsae.com/groupee_common/emoticons/icon_wink.gif

We tested a few different ranges last year, and kept going stiffer and stiffer cause we were trying to get our tires temps up (scrub wasn't bad but can't remember the figures). The problem was, we were used to running the old harder compound tires and when we got the new hoosiers, they were like butter. So now we're stepping down in the freqs, but hey, thats why you test these things... oh, and were were near the 3 and 3.5 range.

what tires are you planning on running?

[flavorPacket]

force transmissibility = transmission of force

transmissibility is not limited to examining displacement, though that's the most common. Force and displacement transmissibility are only the same for 1 DOF linear systems. If you think your car is one of those...

[-francisco-]

and will swear up and down that the "best" suspension for performance is the stiffest.

That sentence pretty much sums up my last 2 months!

Everyone knows a alot about engine but no one knows a thing about suspension other than "it has" to be really stiff. I got all kinds of crap said at me during these last months. They laughed at me when i said these shocks take less beating on our cars than they do on a mountainbike, even after my efforts to try to explain them the 3:1 leverage ratio applied on the rear susp of a downhill bike, or the 12mm aluminum sheet of a mtbike rocker compared to the 3mm sheet they used for ours last year.
Same with their assumptions that the rear springs have to be stiffer than the front because of the engine's weight! I guess the OptimumK papers on higher front Fn wasn't prove enough. They almost beat me when i talked about revalving the shocks!

I'm not yet at the level of force transmissibility but the car will be tested in a few days. Let's see how the springs old on.

[Buddy Fey]

Speaking from experience, there is absolutely NO substitute for testing. You can calculate and simulate til the cows come home, but your model and knowledge will ALWAYS be incomplete.

Have a look at my new blog post (7-9-09) on spring tuning.

[Adambomb]

Same with their assumptions that the rear springs have to be stiffer than the front because of the engine's weight!

Yes, I also hear a lot of completely un-scientific rubbish like that. Sure, the engine is heavy, but not as heavy as the driver!!! Do any of the folks talking this trash actually know the car's weight distribution? Throw that in there next time they try to tell you something crazy.

Of course I can't add anything to Buddy Fey's suggestion...I am now way out of my league! http://fsae.com/groupee_common/emoticons/icon_wink.gif

I can tell you this on my past FSAE suspension testing experience: The team, generally knowing more about the engine and assuming that the suspension is "witchcraft," will generally want to focus 95% of the time on things like throttle response. If I could, I would like to test everywhere from 1.5 to 3 Hz, just to get a general feel for it. Just be forewarned, if it doesn't work perfectly the instant you make changes, all the engine guys will try to tell you "it didn't work," and it's not worth messing with. Then just ask them how much time they spent on the dyno before the engine was even bolted in the car...

[Raj]

the weight of our car is 130 kg in the front & 150 kg in the rear. the M.R. for front is 0.6 & M.R. for rear is 0.7, SR for front is 100 N/mm^2 & SR for rear is 120 N/mm^2.

any views on this?

[BilletB]

Originally posted by -francisco-:

So, you know the guys that wrote the article or were you the one who wrote it?!

One question, i did all the maths for our suspension with all the wheel travel visualized in Solidworks, but everyone is bashing me cause i ordered 215, 225 and 250 lbs springs to play with, and we haven't tested the car yet, susp everyone is saying the susp is gonna be too soft.

We have a car with 200kg -444lbs sprung mass, about 50-50 distribution front to back, the push rod is at 40º working in a plane. and the rocker's MR is 1,1:1.

The general Motion ratio is about 1,18:1. Down on paper i have ride frequencies between 3 and 3.4hz (MR is adjustable). I told them that's what most people run on their cars.

Any advice?

I tech'd it and Bill wrote it. It was an enjoyable project for me and I like working with 'ol Bill.

Don't worry what everyone says they think the car should be. You are the suspension man so you know better and don't be afraid to stick to your guns. You have testing to do ahead of you, but the best advice has already been given. What do those different rates do to your normal load variation? Which direction does that suggest you go? What are the limiting factors that tell you "you've gone too far"? After you get in some testing, I seriously doubt you'll have any desire to go stiffer and remind your engine team you guys are a mechanical grip car and without grip their engine is useless. If they can't answer the few questions I posed, you don't need their advice.