# Thread: Spring & Damping Calculations Questions

1. ## Spring & Damping Calculations Questions

Hi everyone,

My name is Nils and I am a current student at Michigan Tech University, and a member our chassis/suspension sub group. In order to better understand springs and dampers, I have gone through OptimumG’s tech tips, and tried to implement the outlined formulas in Excel, specifically in regards to spring rate calculations. To run through some basic damping calculations, I referenced a presentation/PDF on Damping Calculations presented by KAZ Technologies and Jim Kasprzak (http://www.kaztechnologies.com/wp-co...ns-Seminar.pdf). The questions I have revolve around three main areas; roll gradient calculations, third spring calculations, and damping -- I just noticed that I can't attach excel files here so if anyone on this thread is willing to take a look at it, I would be happy to send it to their email address.

- How should a negative value for spring rate be interpreted based on tech tip formula; I assume this is wrong?
- Because the tech tips reference a percent and divide by 100 in the final equation to calculate required front and rear ARB rates, I assume I am supposed to enter the percent value (WD and baseline magic number) as a whole number (i.e. 52 not 0.52). Is this correct?
- Going off of that, is the "magic number" (percentage of roll rate taken by the front of the car) fairly subjective, or is there any rhyme or reason as to selecting a value here? Would it be a safe bet to simply leave it at the advised baseline value of front WD+5% ?
- The variable K_w (see cell B35 - needed to calculate total ARB roll rate required to achieve the chosen roll gradient) in the tech tips refers to “wheel rate” in N/m. Since the front and rear wheel rates are different based on the F/R spring rates, am I supposed to assume an average in this case? Or is that incorrect?
- I also read that “A stiffer roll gradient will produce a car that is faster responding in transient conditions, but at the expense of mechanical grip over bumps in a corner”; I’m not sure I completely understand that. Is someone able to explain this principle in a different way?
- In regards to ride frequency; why is it that a higher front ride frequency allows "faster transient response at corner entry, less ride height variation on the front and allows for better rear wheel traction on corner exit" ?

2 - Third Spring Calculations

- I assume F/R ride frequencies refer to the targeted ride frequency of the car (usually between 1.5-2 Hz for non-aero FSAE cars if I’m not mistaken)? Practically speaking, what does wheel bump frequency refer to in this case? How could a baseline value for this be determined/what is a reasonable range for an FSAE car? I did notice that if the targeted ride frequency for a given side of the vehicle is equal to the wheel bump frequency for both tires, then obviously the third spring rate goes to zero, which intuitively makes sense, as the whole purpose of the third spring is to achieve a lower frequency in single wheel bump than overall ride.
- While from a mathematical standpoint it makes sense that motion ratio of the suspension would not play a role in third spring rates since its change is offset by a subsequently different single wheel spring rate, I just wanted to make sure this was correct? Intuitively I would have expected motion ratio to play a role in determining the third spring rate.

3 - Damping

- In attempting to calculate the ideal knee speed - low speed damping turns into high speed damping - I first calculated the undamped system resonant frequency, and then multiplied this frequency by the sq. root of 2 (as referenced in OptimumG tech tip #4) to determine the crossover point in Hz for the transmissibility plot. To relate this frequency to an absolute velocity, I assumed an arbitrary maximum disturbance height (say 0.04m), divided this value by the (crossover frequency/2) (Tech tip: “The time it takes for the wheel to complete the up-down cycle is the frequency divided by two”). While this gave me an “optimal” knee speed abs. velocity, it doesn’t quite make sense to me, because that would mean that if the crossover frequency [Hz] were to increase, the absolute velocity would decrease. Shouldn’t it be the opposite? If I use the definition that a wave period = 1/f (I divide the crossover frequency by 1/f) then this gives me a different knee speed which increases with increasing crossover frequency as I would have expected. Which method is correct here?

Thank you to everyone for your help, and especially those that read the whole post! I’ve been spending a lot of time trying to understand these calculations and these are the questions I had the most trouble with, so any help would be appreciated!

Best regards,

Nils

2. ## That Dam Ping Time Again

Before the propeller heads strike, let me just give you some free advice:

2) You will need to join the TTC (Tire Test Consortium) and buy into the tire data for a specific tire(s) your team is considering. I show an example of how to get tire Fz spring rates from the TTC data.
There is also a way to get tire damping values from these tests but it seems to be a lost science. The people who proved the Earth was not flat ran similar tire test procedures and have published their work using special machines called 'typewriters' .

3) The 5% rule may not be to your liking because the tires are so load sensitive (They actually Like load). If the FSAE tires had a Facebook Marketplace page, you could "Like" them. ("What color are the tyres". "Do you still have it", " Interested" ==> typical interactions from the Faceplant social network).

4) There is a thread on a recent Eng-Tips Suspension Forum that discusses the TLLTD issue.

5) Do your own analysis of the loads and load distribution(s) necessary to achieve a flat ride at some speed and a stable yet 'quick' turning car. Your thesis will get you a high paying job in an industry of your choice.

6) Modeling time: What software tools do you have available ? What lab test equipment is around to validate your modeling efforts ? Can you build a Mule car to evaluate your results ?

7) How are you at Broomball ? That's also a Team Effort.90112054.jpg Ask these folks to help you.

3. Originally Posted by BillCobb
2) You will need to join the TTC (Tire Test Consortium) ...
Fwiw, Michigan Technological University joined TTC nearly 10 years ago. Register for the TTC secure site at: http://www.fsaettc.org Use your personal email, from your university domain.

4. Nils,

Ahh, poor Nils!

The sad thing is that you have started a thread with a very coherent first post, which I am sure a few years ago would have developed into an interesting and useful resource. But sadly these days it seems that such efforts are too much work for your fellow FSAEers.

Anyway, some points below that may help you. (And BTW, your efforts so far in understanding all this stuff are commendable.)
~o0o~

1. Most importantly, be very sceptical of any "equations", or explanations in general, that you find on the web. Many mistakes, many omissions, and many cases of outright bulldust. The best that can be said about much of this stuff is that it works a treat at confusing legions of students and boy-racers all around the world, about a subject that is really quite simple.

Better is to work directly from the oldest books you can find that cover "Classical (aka Newtonian) Mechanics". Den Hartog's "Mechanics" and "Mechanical Vibrations" are reasonably good US books (ie. quaint colonial units) that cover most of what you need.
~o0o~

2. Second most importantly, always keep in mind that many FSAE competitions have been won by cars with NO SUSPENSION MOVEMENT WHATSOEVER. Well, none from the spring-dampers, but there is usually lots of unintended flex (<- technically "compliance").

Also an increasing number of hi-level comps are won these days by cars with very simple springing systems, such as Direct-Acting-Spring-Dampers (DASDs), with nothing extra. So ARBs or third-springs are NOT NECESSARY.
~o0o~

3. Your F/R roll-rate, or spring-rate split in general, is dependent on many other parts of the car, so there is no hard-and-fast rule as to the best number. The most general rule is that a rear-drive car should lift its inside-front-wheel during fastest cornering, and front-drive lifts its inside-rear, but many other factors in play. The whole-car mass-distribution, tyre sizes F/R, and choice of differential from locked-spool to open-diff, are some of the big factors. So be prepared to change spring-rates once you start testing.

It is because of this uncertainty about exact F/R-roll-rate-balance that many teams have found in testing that simply stiffening all the springs makes the car faster. They keep going in this way, and eventually all the suspension is locked solid and they discover the truth of the old saying "Any suspension will work, if you don't let it!".
~o0o~

4. There are NO "F/R ride frequencies"!!! These are a complete fiction. They are nothing more than clever sounding way of talking about the "stiffness" of the suspension, albeit in a way that is virtually impossible to measure as an actual "frequency". Learn why these numbers are bulldust and you will be a long way ahead of the people who promote them as "real engineering".
~o0o~

5. Lastly, for now, what sort of Spring-Damping do you want for an FSAE-style car, and how do you calculate it?

5a. I suggest quite soft wheel-rates (see below for numbers) for a range of +/- ~1 cm around ride-height. Maybe +/- 0.5 cm for very smooth tracks, going up to +/- 2 cm for the worst tracks in the world. Another +1 cm of progressive bump-stop is useful at the top of the stroke, and the soft springing should be droop-limited at the bottom of the above suggested range of travel. As noted above, DASDs are more than good enough to meet these requirements.

The car SHOULD "ride the bump-stops", which means the suspension should hit those bump-stops a few times a lap, typically on the bumpiest corners. During fast cornering the droop-limiting should come into play a bit before the bump-stops, because this "pulls the car down" for a lower CG.

Damping should be as soft as possible. Start your testing with NO damping, then only add as little as necesssary to control any unwanted oscillations. I am not in USA, but I believe F500 mandates ONLY polyurethane springs, with no dampers, and they go OK.

5b. How do you calculate the (preferably DASD) spring-rates?

Start by thinking in terms of "static deflection", which is the simpler, older-fashioned, and more realistic version of "ride-frequency". This is simply the vertical distance the suspension compresses when the static-weight of the car is applied to it (starting from zero spring load, and assuming linear spring-rates and motion-ratios, etc.).

Next consider that you want the car to be as narrow as possible, for a straighter path through the slaloms, but you do NOT want it falling over in fast corners. So during fastest cornering you want ALMOST all the weight of the car on the outside-wheels, with the inside-wheels almost unloaded. So during fast cornering your outside-wheel vertical loads are close to DOUBLE the static-weight, and inside-wheels have lost almost all their static-weight.

Final step is to ask yourself how much you want the car to lean outwards, or "Roll", during this fast cornering? Say you deem a roll-angle of 1 degree during fastest cornering to be a good starting point. This 1 degree is a slope of ~1:57, which is very close to 1 cm on typical-FSAE-half-track. So 1-degree-roll is 1 cm of outside-wheel compression, and 1 cm of inside-wheel extension.

So, from two paragraphs up, your "static deflection" should be [insert drum-roll] ... 1 cm!

How easy was that? NO alphabet-soup or calculators required!

Repeating this for clarity, when the static-weight is applied to the suspension, it compresses 1 cm. And when, during fastest cornering, the outside-wheels carry double their static-weight, they compress another 1 cm, and the inside-wheels lose their static-weight, so they extend 1 cm.

The actual "wheel-rate" number is now "corner-weight/1 cm", so something like ~100 lbs/cm, or in whatever units you want. And if you are happy with 2 degrees of roll during fastest cornering, then "wheel-rate = corner-weight/2 cm", so maybe = ~50 lbs/cm, or ~125lbs/inch, and so on. Actual spring-rates then need to be adjusted by motion-ratio, and for DASDs they are typically ~double the wheel-rate numbers.

Note that you can have the softer "2-degrees-of-roll" springs above, but still limit roll-angle to 1 degree by "riding the bump and droop-stops". That is, you build these stops to come into play at +/- 1cm travel. Typically, this will cause one of the inside-wheels to lift during fastest cornering, and the "handling balance", namely Over-Steer or Under-Steer, might change a bit through the corner.

But that may be exactly what you want to happen. Think about it.

Z

(Edit: Above "5b" calcs assume NO kinematic anti-roll, so suspension has horizontal lateral-n-lines, or "RCs at ground level". And LLTD = ~F/R-weight-distribution. And probably a few other simplifying assumptions. It is just to show that a ball-park figure for spring-rates can be calc'd "in your head".)

5. Originally Posted by MI906
To run through some basic damping calculations, I referenced a presentation/PDF on Damping Calculations presented by KAZ Technologies and Jim Kasprzak (http://www.kaztechnologies.com/wp-co...ns-Seminar.pdf).
Nils,

I have now had a quick look through that KAZ presentation, and ... it is RIDDLED WITH ERRORS! The equations are nigh-on worthless. As are the numbers, such as the suggested Damping Ratios.

Of course, your fellow students will now accuse me of "shaming" Jimmy K. So, should I bother going on, and point out his errors here, in an effort to help you? Well, the rest of your generation are always saying that they "...couldn't be bothered". Yet they seem to get very "bothered", very quickly. More importantly, could I be bothered? Tough call...

Maybe I will just leave you with this clue. JK seems to have had much difficulty getting to grips with those dang-new-fangled metric units. And since he clearly recognized that his calculated numbers are VERY different to other people's numbers for the same car (ie. he suggests a Damping Ratio of 4!!!) he tries to cover for this obvious discrepancy with his last words "There are MULTIPLE right solutions!".

Good luck in your Brave New World (ie. where DR = 4 is a "right solution").

Z

6. ## Nabisco Fig-Newtons

7. @Nils
Hi! Welcome to the forum.

@Bill
Thank you for your prompt and straight forward guidance.

-William

8. Nils,

The following should be of great assistance,

http://www.chassissim.com/blog/chass...amper-workbook

Enjoy

Danny Nowlan
Director
ChassisSim Technologies

9. ## It's All in the Units,

Well, direct to your point, Z, it's that dammed killer grahams to Fig Newtons conversion error in the previous cloth being properly_gated by formulae without substantiation. But fear not, it will all work out in the durability event via a hydraulic jet stream.

(That probability should be a zeta of about 0.510000000000000000000 instead.) Oops, ...

And we N.A.'s have been metricified for at least 20 years.