Damping Rates

[Karam Atteia]

Hello everyone,

This is my first time dealing in such subject, the damping rates. I know that this topic is mostly through empirical and iterative researches. But i did an approach to damping rates selection for our front suspension. My references in this approach are Kaz Technologies Seminars, Optimum G technical Tips and RCVD.

Here some data about our vehicle:
total vehicle weight= 350 kg
front vehicle weight/corner= 77.5 kg
front unsprung weight/corner= 12.5 kg
motion ratio= 0.66
front ride rate= 19518.4 N/m
front wheel rate= 21429 N/m
Tire spring rate= 218908.54 N.m
front sprung ride frequency= 2.52 Hz
front unsprung ride frequency= 22 Hz
front sprung critical damping= 2460 N/(m/s)
front unsprung critical damping= 3464 N/(m/s)

Here some decisions taken for the approach:
Knee speed= 60 mm/s
Compression/Rebound ratio= 1:2
low speed damping ratio= 0.65
high speed damping ratio= 0.45

In this approach, The heave and single wheel bump were only took in consideration and nothing for the Roll and Pitch motions. We've done an estimation for our Roll and Pitch inertia and frequency, but don't know where to use. I need your experience in such a trim as we didn't make any track testing nor test rigs before since we started participating in the FS and i can't feel these numbers if it is in the right ballpark.

Here the calculated Damping Rates:
low speed compression damping rate= 1599 N/(m/s)
high speed compression damping rate= 1558.8 N/(m/s)
low speed rebound damping rate= 3198 N/(m/s)
high speed rebound damping rate= 3117.6 N/(m/s)

thanks for your attention

Karam

[Claude Rouelle]

350 KG for a FSAE? Forget it!

[Karam Atteia]

Mr. Claude,

with the driver, sir.

Please, give me your advice about these decisions and calculation results.

If these results are a good starting point?? If the decision on the Knee speed and damping ratio and the comp/rebound ratio are reasonable ??

thanks in advance

karam

[Claude Rouelle]

350 KG with or without driver is still insane.

[Warpspeed]

Originally posted by Karam Atteia:

This is my first time dealing in such subject, the damping rates. I know that this topic is mostly through empirical and iterative researches.
There are some very good practical real world reasons why that is so Karam.

The best approach would be to obtain some fully adjustable dampers with suitably wide adjustment ranges, and then do some track testing with the completed car.

If you wish to be a bit more scientific about it, a simple to make home made single wheel variable frequency vibration table and some instrumentation will tell you what is actually happening, as opposed to what you think is happening, and provide some useful data.

[Karam Atteia]

Mr. Claude,

Thanks for your attention,

Sir, I might be wrong on something. Its my first time in this subject and i really want to learn more about.

Please comment on these results and decisions, really that would be appreciated.

Excuse my ignorance,

Karam

[Karam Atteia]

Warpspeed

thanks for advice.

Karam

[Claude Rouelle]

Karam Atteia

If you are able to calculate the spring and unsprung masses natural vertical frequencies, I don't see why you would not be able to calculate your suspended mass natural frequencies in roll and pitch.

In the usual f = 1/2 sqrt (K/M), replace K by the anti-roll stiffness (Spring and ARB) at the wheel in Nm / rad and your M by the SM inertia around the roll axis in Kgm2.

Same calculation for pitch natural frequncies.

Worth to calculate also the suspended mass roll and pitch damping ratio. You will see that unfortunately in most of the case when you have a good damping in heave it is far from good in roll.

Also

1. Look at your numbers: if your "low speed" damping ratio is 0.65 and your "high speed" damping ration is 0.45 don't you think there is an issue with you 1599 and 1558 compression numbers and 3198 and 3117 rebound numbers?

2. Ultimately, you need to calculate the damping that you need at the damper, not only at the wheel. Your MR has to be used to do that.

3. Your tire spring rate is in Nm?

4. How do you want people to check your calculation if you do not publish your suspension spring stiffness?

5. How do you define motion ration: wheel mvt / spring mvt or spring mvt / wheel mvt?

6. Why do you make the calculation for front AND rear?

If you have the guts to publish the new numbers on this forum I will take you step by step in your calculations and tell you what is right or wrong with it. When you will get it right I will share our simple calculation software with you

BUT

- I already posted some answers in this forum. Make some research.

- For God sake use a 250 kg car (70 kg driver included) in your calculation! A 350 Kg car with (even worse) or without driver is ridiculous.

[Karam Atteia]

Mr. Claude

Again thanks in advance for your support

About the roll and pitch inertia and frequency, I mentioned above that we had an estimation about.
here how we estimated for:
first its an approach for the roll and pitch inertia, assuming the vehicle is a solid cuboid (l*w*h)= (2 m *0.9 m *0.8 m)
Roll inertia= 1/12 * M * ( w^2 + h^2 ) = (1/12)*(250)*(0.9^2 + 0.8^2) = 30.2 kg.m^2

Pitch inertia= 1/12 * M * ( l^2 + h^2 ) = (1/12)*(250)*(2^2 + 0.8^2) = 96.6 kg.m^2

Roll frequency= (1/2*pi)*sqrt[(180*K_roll_des.)/(pi*I_roll)] = 7.3 Hz

Pitch frequency= 1.2 Hz

Roll Damping Rate: low speed= 56.1 Nm/deg/s
high speed= 33.84 Nm/deg/s

Pitch Damping Rate: low speed= 18.6 Nm/deg/s
high speed= 12.6 Nm/deg/s


1-sorry for this stupid mistake
low speed compression damping rate= 1599 N/(m/s)
high speed compression damping rate= 1107 N/(m/s)
low speed rebound damping rate= 3198 N/(m/s)
high speed rebound damping rate= 2214 N/(m/s)

2-should i divide these damping rates by the MR to get the forces at the dampers.

3-another mistake, its N/m.

4-front spring stiffness= 49194.2 N/m
rear spring stiffness= 81693.7 N/m

5- MR= spring mvt. / wheel mvt.

6-different sprung masses and ride frequencies.

excuse me if there is any fatal mistakes above

Karam

[ChassisSim]

Karam,

My friend you might find the following really helpful,

http://www.chassissim.com/blog.../the-damper-workbook (http://www.chassissim.com/blog/chassissim-news/the-damper-workbook)

It's been of great use to me and my colleagues and I trust it will be of use to you.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[Claude Rouelle]

Karam,

OK let's continue the game and let me help you to find practical results. No theoretical BS here.

Your inertia calculation is a bit exaggerated. A good FEA or, better, measurements will be better but it is OK for now.

BTW Would be worth for you to also calculate your yaw inertia; no need for this exercise but you could use it later for different calculations.

Show me how you calculate your roll damping rate, your roll frequency I need to see the equations. Explain it to me as if I am able to understand it but I never saw those calculations. For example what is roll-des. ?

Also

- Use Motion Ratio as wheel mvt divided spring mvt like everybody else in racing (except Nascar....... but is Nascar racing?)
- Do you think you need to use the whole mass to calculate the roll and pitch inertia?
- What is the point or the axis around which the mass (which mass: see above question) rotates? Does the parallel axis theorem tell you something?
- Are you showing the roll and pitch damping or the roll and pitch critical damping?
- With the choice of damping you made for heave what is is your roll and pitch damping ratio?
- You need to show the damping at the damper not only at the wheel. "should i divide these damping rates by the MR to get the forces at the dampers." I will not answer such basic question. Do the math and tell me.
- Show the numbers for both front and rear
-
-

[Karam Atteia]

Mr. Claude

For the roll frequency and roll damping rates, i'm using Optimum G tech tips equations !!
sorry, i might have wrote them in an unfamiliar way.

Roll frequency= (1/2*pi)*sqrt[(180*K_roll_des.)/(pi*I_roll)]
Roll damping rate= pi^2 * zeta_pitch * Roll frequency * Roll inertia / 45

K_roll_des: desired roll stiffness
I_roll: roll inertia

-"Do you think you need to use the whole mass to calculate the roll and pitch inertia?"
i think for the way i'm calculating the roll and pitch inertia, i should use the total mass (i assumed the vehicle as a solid cuboid).

-"What is the point or the axis around which the mass (which mass: see above question) rotates? Does the parallel axis theorem tell you something?"
For roll: the mass will rotate around the roll axis (axis between front and rear roll centers).
For Pitch: the mass will rotate around a horizontal transverse axis through the CG.
Parallel axis theorem: yes, i think i should have used on calculating the Roll inertia.

-"Are you showing the roll and pitch damping or the roll and pitch critical damping?"
i'm showing the roll and pitch damping
Roll Damping Rate: low speed= 56.1 Nm/deg/s
high speed= 33.84 Nm/deg/s

Pitch Damping Rate: low speed= 18.6 Nm/deg/s
high speed= 12.6 Nm/deg/s

-"With the choice of damping you made for heave what is is your roll and pitch damping ratio?"
low speed damping ratio= 0.7
high speed damping ratio= 0.4

-"You need to show the damping at the damper not only at the wheel. "should i divide these damping rates by the MR to get the forces at the dampers." I will not answer such basic question. Do the math and tell me."
Here the damping rates at the dampers: (C_damper = C_wheel / MR^2)
low speed compression damping rate= 3670.8 N/(m/s)
high speed compression damping rate= 2541.3 N/(m/s)
low speed rebound damping rate= 7341.6 N/(m/s)
high speed rebound damping rate= 5082.6 N/(m/s)

-"Show the numbers for both front and rear"
front sprung mass= 155 kg
front ride frequency= 2.52 HZ
rear sprung mass= 195 kg
rear ride frequency= 2.82 Hz

thanks a lot

Karam

[Warpspeed]

All this has one purpose, and one purpose only (for a race vehicle) to keep the tires in most intimate contact with the track and hopefully dissipate any excessive stored spring energy and resonance that reduces tire TRACTION and GRIP.

You can calculate all manner of things, taking into account many non linearities and coming up with some magic theoretical number after making a whole bunch of possibly wild and erroneous assumptions, which is basically at best an informed guess, at worst totally wrong, and come up with the perfect theoretical damper.

But alas !!!
Such a beast does not exist in any damper catalogue, you have to buy an adjustable damper that does not provide shock dyno curves for each and every of the hundreds of possible combinations of settings and possible test velocities.

So you are right back where you started, and have to rely on some empirical, practical, do it yourself, down and dirty TESTING.

Nothing wrong with that at all.
It's just like engine tuning, you test it within an inch of it's life and find out what the engine is happiest with.

Likewise you tweak your shocks for whatever feels right to an experienced driver on a particular vehicle on a particular smooth or bumpy track.

Like adjusting aero, gearing, brake balance, or antiroll bar bias, different shock settings and wheel rates are appropriate for different situations.

Don't sweat it, just fit some fully adjustable dampers and play with it after the car is at the stage of being drivable.

[Z]

Originally posted by Claude Rouelle:
If you are able to calculate the spring and unsprung masses natural vertical frequencies, I don't see why you would not be able to calculate your suspended mass natural frequencies in roll and pitch.

In the usual f = 1/2 sqrt (K/M), replace K by the anti-roll stiffness (Spring and ARB) at the wheel in Nm / rad and your M by the SM inertia around the roll axis in Kgm2.

Same calculation for pitch natural frequncies.
Claude,

Given that this issue was recently covered on another thread (and is adequately explained in most good VD textbooks, and has been since the 1920s), why do you keep promoting the above nonsense?

Do you, in fact, know how to do the calculations correctly?!
~~~o0o~~~

Karam,

Read Tony's post above, especially the last line.

Or putting it simply, you are wasting your time (and the team's resources) on these largely meaningless calculations.

Z

[Karam Atteia]

Danny

thank you, that was really helpful.
I learned from your posts too much .. Keep it up http://fsae.com/groupee_common/emoticons/icon_smile.gif

Tony


It's just like engine tuning, you test it within an inch of it's life and find out what the engine is happiest with.

Likewise you tweak your shocks for whatever feels right to an experienced driver on a particular vehicle on a particular smooth or bumpy track.

Like adjusting aero, gearing, brake balance, or antiroll bar bias, different shock settings and wheel rates are appropriate for different situations.

Don't sweat it, just fit some fully adjustable dampers and play with it after the car is at the stage of being drivable

Its my first time in FS and we are a relatively new team that have no experience in such aspect. Even no Automotive industry nor MotorSport in my country. But this year i think we are on the right track for building a good drivable car and i 'm totally excited to play with the dampers and ARBs and spring rates and feel the numbers.


Mr. Z

I really don't think i'm wasting my time at all. Doing these calculations will help me a lot to understand the issue.

Again i'm from Egypt, where no one can help me in such subject. It took me a lot of time to understand alone.

Please put all that in consideration and give me your advice.

thanks in advance

Karam

[Claude Rouelle]

Karam,

- If the front sprung mass is 155 KG and the rear sprung mass is 195 Kg (bottom of your last post) how can you have the whole car mass at 250 Kg? Even if your all car was 350 KG (which I remind yo is unreasonable for a FS / FSAE car) and if you have 4 unsprung masses of 12.5 KG, how can you come with 155 Kg ad 195 Kg of front and rear sprung masses?
- Why do you want to use the total mass to calculate the damping? Are the dampers between the tires and the ground or between the suspended and non suspended masses?
- You are now correct; You need to use the MR^2 to calculate the damping needed at the damper from the damping number at the wheel.

Lets start from fresh ans please answer the following question step by step. Some answers are input some are already your calculation. Please show both equations and result numbers.

1 What is your wheelbase and what are the front and rear tracks?
2 What is your car total mass (driver included)?
3 What is your car mass distribution?
4 What are the total car mass CG x and z coordinates (we will assume the car is symmetrical and the y coordinate of the CG is 0)
5 What are the front and rear non suspended masses? Chose different numbers for the sake of the exercise.
6 What are the front and rear non suspended masses CG height? To make things easy you can assume that the non suspended mass CG z coordinate is the wheel center height. We will assume that the Y coordinate of the non suspended mass CG is the 1/2 track (no camber)
7 What is the car suspended mass distribution?
8 What are the car suspended mass x and z coordinates. I guess you understand that they will not necessarily be the same as the total mass CG x and z coordinates
9 What are your front and rear spring stiffness. In N/mm please
10 What are your front and rear spring motion ratio. We will define the motion ratio as wheel movement / spring movement.
11 What is your front wheel rate (effect of the spring at the wheel)
12 What is your rear wheel rate?
13 What are your front and rear ARB stiffness? in Nm/deg or Nmm/deg please. Some will argue in this forum that Anti Roll Bars are not needed. It is their opinion, they are entitled to theirs. Mine is different.
14 What are your front and rear ARB motion ratio. We will define ARB Motion Ratio as roll angle / ARB twist angle.
15 What is your tire vertical stiffness?
16 What are your front and rear suspended masses natural heave frequencies?
17 What are the front and rear roll centers altitude (we assume that the roll cents y coordinate is 0)
18 What is your suspended mass inertia around an horizontal axis going though the suspended mass CG
19 What is the shortest distance between the roll axis and the suspended mass CG.
20 What is the suspended mass inertia around the roll axis?
21 What are the left and right pitch center x and z coordinates z. Do not worry about the y coordinates of the left and right pitch centers: an axis is an axis. Let's assume that the pitch axis will be perpendicular to the car longitudinal axis and parallel to the ground
22 What is the shortest distance between the suspended mass CG and the pitch axis? What is the suspended mass inertia around the pitch axis?
23 What is the anti-roll stiffness coming from your front spring? in Nm/deg please.
24 What is the anti-roll stiffness coming from your front ARB? in Nm/deg please.
25 What is the anti-roll stiffness coming from your rear spring? in Nm/deg please.
26 What is the anti-roll stiffness coming from your rear ARB? in Nm/deg please.

For 23 to 26 we obviously speak about the effect of spring and ARB at the wheel not at the suspension elements. The motion ratio has to be taken into account but I guess you already know that.

Note that some guys in this forum will argue that the suspended mass do not rotate around the kinematic roll axis; they are right. The spring stiffness, the tire grip, the compliance (one of the compliance being the chassis torsion stiffness), (and in transient the damping rates and the chassis torsion damping ) has to be taken into account.
Let's make it simple for the moment. Simple and useful then complicated; not the other way around. The same observation goes for the pitch.

27 What is your suspended mass natural roll frequency?
28 What is your suspended mass natural pitch frequency?

29 What is your choice of front and rear low speed compression damping ratio?
30 What is your choice of front and rear low speed rebound damping ratio?
31 What is your choice of front and rear high speed compression damping ratio?
32 What is your choice of front and rear high speed rebound damping ratio?
33 What is your choice of the "knee speed: at which the damping slope change for the front damper in compression?
34.What is your choice of the "knee speed: at which the damping slope change for the front damper in rebound?
35 What is your choice of the "knee speed: at which the damping slope change for the rear damper in compression?
36.What is your choice of the "knee speed: at which the damping slope change for the rear damper in rebound?

Note that answer to 33 to 36 can be different.

37 What is the front damping in low speed compression at the wheel?
38 What is the front damping in low speed compression at the damper?
39 What is the front damping in low speed rebound at the wheel?
40 What is the front damping in low speed rebound at the damper?
41 What is the front damping in high speed compression at the wheel?
42 What is the front damping in high speed compression at the damper?
43 What is the front damping in high speed rebound at the wheel?
44 What is the front damping in high speed rebound at the damper?
45 What is the rear damping in low speed compression at the wheel?
46 What is the rear damping in low speed compression at the damper?
47 What is the rear damping in low speed rebound at the wheel?
48 What is the rear damping in low speed rebound at the damper?
49 What is the rear damping in high speed compression at the wheel?
50 What is the rear damping in high speed compression at the damper?
51 What is the rear damping in high speed rebound at the wheel?
52 What is the rear damping in high speed rebound at the damper?

53 What is your front critical damping at the wheel?
54 What is your front critical damping at the damper?
55 What is your rear critical damping at the wheel?
54 What is your rear critical damping at the damper?

Based on the choice of damper ratio you made above,

55 What is the suspended mass roll critical damping
56 What is the suspended mass roll damping ratio (use only damper low speed numbers)
57 What is the suspended mass pitch critical damping
58 What is the suspended mass pitch damping ratio (use only damper low speed numbers) in acceleration
59 What is the suspended mass pitch damping ratio (use only damper low speed numbers) in braking

Note about 58 and 59. With a pitch center between the front and rear wheel (Yeah... I know to be discussed) in acceleration your rear dampers are in compression and your front dampers are in rebound. The contrary in braking. As your front and rear dampers have probably different compression and rebound and their motion ratios are probably different I bet you there is great chance that answer to 58 and 59 will be different.


Lets go though this first and then I will explain to you what is right and wrong (insufficient) with these calculations.

Unless you have a 7 post rig, a mathematical definition of the road profile (road excitation^2/ frequency) and/or you want to go through difficult system of differentials equations first.

Then we will go to some practical approach about how your tune the dampers in testing (I honestly do not have all the answers but I already have given some decent hints in this forum)

Put that in an Excel spreadsheet and make this Excel downloadable.

Good luck!

[Claude Rouelle]

Karam,

Ooops I forgot. I think it is useful you also put somewhere in this list (as input or output) what is your roll and pitch stiffness in Nm/deg or in deg/G.

[Warpspeed]

Originally posted by Claude Rouelle:
Then we will go to some practical approach about how your tune the dampers in testing.
Golly Claude, do you mean that after all those calculations you still need to actually tune the dampers during testing.
WHY ???

Hint.
Pure design can take you a long way, but tuning is a very different thing to design.

Chassis designers work with hard numbers which are more often than not a compromise solution.

Chassis tuners do not.
If increasing or decreasing something makes it go quicker around the track, then the only numbers that are important to the tuner are the results coming out of the data logger.

You still definitely need to understand the theory, and experience and insight is also a very important part of that, to understand what variables effect what.

But tuning is just iteratively increasing or decreasing things to give the car what it seems to want, without the need to quantify every setting to five significant figure accuracy.

[Claude Rouelle]

Tony,

What a strange reaction...

Besides your public profile (RMIT) I don't know who you are, what you do and how well you do it (RMIT has not been on the top of its game in the last few years) but I can tell you that if you do not know theses numbers you will not impress me or nay vehicle dynamics judges in the FSAE design competition. Not that I am dogmatic about numbers but simply because, even if you win, if you do not know WHY (sometimes with a decent car you just need a very good driver), then you won't know why you lose.

Do I mean that after all those calculations you still need to actually tune the dampers during testing. Yes you bet!

Professional racing teams use both theoretical and practical methods
- sophisticated calculation (way more complicated that the ones presented)
- 7 post rigs
- track testing with good objective (car) and subjective (driver).

I think you need both perspectives. The numbers which are in my previous post are just the beginning. With our consulting job (LMP2 1st and 2nd last weekend in Le Mans, win today in European GT today.... I could not help!) we go much further but we won't go there unless we have these basic numbers

Unless you know perfectly your tires (even the tire manufacturers do not know them super well), your micro and macro road profile, what your ambient and track temperatures will be the day of the race, and you can quantify your driver style and predict his mood (good luck), you will always need testing; I am with you.

But unless you have unlimited testing time and budget these calculations will help you to narrow the zone in which the dampers will work and your car and driver will be "happy". Worse case if you are lost you have quantitative comparisons and references.

If you have the recipe to tune the dampers by just testing, then make it your job: you will make tons of money.

[Z]

Originally posted by Karam Atteia:
Z ...
Please put all that in consideration and give me your advice.
Karam,

I have given you my advice. It is up to you to choose whether to follow it or not.

But I will try one more time. Which of the following two scenarios do you think is more likely.

1. After going through Claude's 59+ "Let's make it simple for the moment" questions above, you build a car with dampers that are so accurately specified (yes, to maybe 10 significant digits, or more!) that you can drive so fantastically fast that you score N points more than if you took Tony's dumbed down, but more practical, approach.
(Please supply your best estimate for the "N" extra points you gain in this case.)

2. You again follow Claude's suggestions and prevent your chassis designer from finishing his job for several months, because you're not sure what size the dampers must be. You eventually specify the most expensive dampers on the planet, and embark on a long-winded, out-sourced, damper testing program to ensure that the dampers are accurate (well, at least to 5 significant digits). These time delays and extra costs result in your team arriving at comp with a never-driven car (but with thoroughly tested dampers!). So you fail to pass scrutineering, and so fail to score any Dynamic points at all. But you do impress the Design Judges with your damper knowledge, and so score N extra points in the Design event.
(Please supply your best estimate for the "N-675" points you gain in this case.)
~~~o0o~~~

Claude,

All that bluff and bluster above is a sure sign that you do not understand this subject.


16 What are your front and rear suspended masses natural heave frequencies?
...
28 What is your suspended mass natural pitch frequency?

If these "natural frequencies" have any connection with reality (which is what I take the word "natural" to mean), then could you please describe what they look like (ie. what sort of motion they exhibit) and how someone could empirically measure them.

Also, are you currently including in your seminars the subject of "longitudinally (F-R) interconnected springing". If not, then why not? (After all, why bother calculating "~pitch" frequency if you cannot independently control it.)

Z

[Warpspeed]

Originally posted by Claude Rouelle:
I think you need both perspectives. The numbers which are in my previous post are just the beginning.
That is a very realistic assessment with which I wholly agree.

[Tim.Wright]

Honest question Erik, because you and Tony have touched on this.

The natural frequency calcs are a simplification. Everyone will agree on this.

Why then, do you see the need to complicate these initial design calcs when it is very likely that the spring rate will be changed on track during tuning?

[Claude Rouelle]

Tim,

If I may.... Here are a few parallel perspectives.

There is effectively a great chance that the springs will be changed. And the damper and the tire pressure, toe, camber, Ackermann etc...

You are never spot on in design. And, in any case, "ideal" (i there is such thing) suspension stiffness depend on your tire, your driver, you track (bumpiness just to name one characteristic), ambient conditions such as temperature ..etc... The parameters will change.

However you do want to look at the tuning of other parameters at the same time you change the spring.
Examples:
- If you change the springs you change the critical damping (in heave, and pitch and maybe roll) and you may want to modify the damper tuning to get the best possible compromise.
- If you change the spring and the car is very ride height sensitive in aerobalance you may have to adjust the static ride heights.
- If the driver is happy with the balance but you want stiffer springs because for example the driver finds the car lazy, or the track is smoother than expected, or you want mote tire temperature (although there are other ways to get tire temperature; playing with the amount of damper compression is on of them ,... but that is another story)
and you want let's say 160 lb/in but the only springs you have are 160 and 175 lb/in, you will have the tune the ARB to get back to the "happy" elastic weight transfer distribution.

All that can be done quickly with the use of a few Excel spreadsheets which take a few hours to build but that will be useful for years. They do not need to be 6 digits precise http://fsae.com/groupee_common/emoticons/icon_smile.gif They will not decrease the design process but they will accelerate the development process and the understanding of the car.

Yes, some could say that the initial natural frequencies calculation is a simplistic way to look at suspension stiffness. There are other more complicated ways which for example look at the car as a complete system (virtual 7 post rig for example) but I feel that it is easier as a first step to look at heave, roll and pitch frequency separately and experiment what the best compromise is. This the FSAE forum, not the engineering meeting of an LMP1 race car manufacturer. Let's make is simple (the list of numbers I asked look long but it is a step by step list and it not that complicated) and useful before we make it complicated, not the other way around.

With these basic spreadsheets you "walk less in the dark" and you are able to make easier correlations between some of their numbers numbers, the driver comments, the tire temperatures and the lap times.

[Z]

Tim,

I, like Tony, am suggesting to Karam that he is better off not doing these calculations. Given that he is from an inexperienced team, he should just buy readily available and affordable dampers, as used on other FSAE cars, then adjust them to suit the car once it is running. Meanwhile, get busy building the car!

Of course, if he wants to learn about "the damping of natural vibrations", then, sure, he can do as many calculations as he wants (providing he doesn't slow down the rest of the FSAE program). But now he shouldn't waste time on the unrealistic "front and rear heave frequencies", or "pitch frequencies". These are not "natural frequencies" at all. They are an artificial fiction.

Elsewhere I have criticised the auto industry's almost universal adoption of two-dimensional thinking when it comes to suspension design. The 3-D kinematics are more useful, more accurate, just as easy to learn, but unfortunately never taught to auto-engineering students (at least I have never seen them mentioned).

The really disappointing thing about this particular topic (re: damping) is that the correct analysis of the two degree-of-freedom vibration of a car body in pitch and heave was done in the 1920s (independently) by Rowell and Guest. When properly taught it is remarkably easy to understand, and gives good insights into the vehicle's dynamics.

But nowadays we have Claude and other educators dumbing this down to two separate 1 DoF systems, and these separately give much less insight into how the vehicle behaves. And then Claude is demanding that Karam do these and 50+ other mostly useless calculations ("I can tell you that if you do not know theses numbers you will not impress me or nay vehicle dynamics judges in the FSAE design competition.")...

It is mindless quantity, replacing thoughtful quality.

Where does it all end? How much longer before we all descend into Idiocrasy?

Z

(Edit: Claude just posted while I was writing this. Will read that and respond later...)

[Tim.Wright]

Claude,

Actually I agree. These simple calcs should be done for the reasons you mentioned. They are not perfect but I find them a nice tool. Also, I'm quite aware of their limitations.

My point was mainly to Erik, I would like to know what advantage I'm likely to see by replacing the simple intuitive 2x1D calculations with a more complicated 3D one.

A fun story. I have a load transfer spread sheet basically like Claude's. Assumes constant evil geometric roll centre position, constant spring rates in ride and roll etc.

I used it to find the spring rates for a number of setups and for two different suspension design for a road car. Not only did the trend of the roll rates match the physical tests, but the absolute value of the roll rate was within 1%. I wish I could get my Adams model to do that.

And you want to tell me that these calculations are a waste of time?

Granted, I know this is not a typical level of accuracy for these kind of calculations, but really I'm scratching my head as to why I should throw them in the bin and do everything in 3D. Especially for the case where you have no front/rear interconnection.

[GSpeedR]

Originally posted by Tim.Wright:

The natural frequency calcs are a simplification. Everyone will agree on this.

Why then, do you see the need to complicate these initial design calcs when it is very likely that the spring rate will be changed on track during tuning?

Why not code these 'more complicated' equations in Matlab (or even Excel if necessary) and update them for every spring change? Isn't that exactly what you do with your 1DOF natural frequency formulas?

[Tim.Wright]

Well no... Once you have found a spring rate that works, there is no need to go back to the calcs. This is the point I'm trying to make. The calcs are done once, in a simplified form, to give you an initial spring rate from which you can use as a baseline.

It doesnt make any sense to have this extra complexity for a calculation that is done once. There is just no return for the increase in complexity. Outside of uni, Matlab doesn't lie on every computer in the office.

[SNasello]

I would have to agree with the posts here on all fronts to some extent.

Are the calculations posted by Claude complete (or correct, however you want to look at it)? No. Are they useful? Absolutely.

Lets say that a first year (or second year team) is looking to purchase a damper with a so called 'Wide adjustment range' so that they can test their damper on the track. There are many dampers that fall under the category of wide adjustment range (note that 'Wide' in this sense is relative) with a damping stiffness that could or could not be useful for a car of this weight class. How would this team know if the damper they are purchasing is even in the range that could be useful? What motion ratio is required to put the damper in the correct wheel damping range? How 'Wide' is the adjustment range when you factor in motion ratio?

So on the one hand Z, you are suggesting to not make any calculations, because they will be wrong anyways, and hope that the damper that fits in this teams budget just happens to provide the proper range of adjustment for them, with the motion ratio that they also just happen to choose blindly.

On the other hand, the team can sit down and make some 'back of the napkin' calculations, with some assumptions of vehicle weight, spring stiffness, etc. and relatively quickly get an idea of the range of damping forces that are needed to produce a half properly damped car. These calculations should not take more than an afternoon.

After that it is still going to be a game of suspension refinement (or 'tuning'), which could also include further calculations or models which go a step further, and try to make a more accurate representation of what is actually going on.

[Claude Rouelle]

Tim,


A fun story. I have a load transfer spread sheet basically like Claude's. Assumes constant evil geometric roll centre position, constant spring rates in ride and roll etc.

I used it to find the spring rates for a number of setups and for two different suspension design for a road car. Not only did the trend of the roll rates match the physical tests, but the absolute value of the roll rate was within 1%. I wish I could get my Adams model to do that.

And you want to tell me that these calculations are a waste of time?

You made my day. Thank you. I am going to work with another smile.

[Claude Rouelle]

Stefan,


Are the calculations posted by Claude complete (or correct, however you want to look at it)? No. Are they useful? Absolutely.

Thank you. You made my day too. These are close to the words I keep using is the seminars I teach; "Is it perfect? No. It is useful? Yes"

Make useful before you make it complicated.

Cheers,

[GSpeedR]

Originally posted by Tim.Wright:
Well no... Once you have found a spring rate that works, there is no need to go back to the calcs. This is the point I'm trying to make. The calcs are done once, in a simplified form, to give you an initial spring rate from which you can use as a baseline.

It doesnt make any sense to have this extra complexity for a calculation that is done once. There is just no return for the increase in complexity. Outside of uni, Matlab doesn't lie on every computer in the office.

The calcs should be updated during the tuning process, whether we are talking about simple formulas or simulations. Otherwise you are simply throwing darts.

You are right about limited computer resources, so sometimes these things need to be post-processed or a parameter sweep can be performed beforehand.

[Tim.Wright]

Originally posted by GSpeedR:
The calcs should be updated during the tuning process, whether we are talking about simple formulas or simulations. Otherwise you are simply throwing darts.

Sometimes yes sometimes no. Once you have reached a setup the driver is happy with, you move on to the next thing to tune.

On the other hand you might have some problems finding a good balance and you find that you are recalculating things every setup change.

I've been through both cases.

I think with springs you can get a decent amount of accuracy with simple calcs like I've mentioned. Dampers on the other hand (moving back to the original topic)... I personally will hold my hand up and admit I don't have a feel for what simplifications are appropriate and which aren't. I, myself look at a damper diagram, particularly a racing one which is quite complicated and think "how the hell is it valid to reduce that to a single linear velocity coefficient".

All of the damper tuning I've been involved in (which admittedly is not a lot, but covers both race and road cars) has been based completely on the test driver feedback.

[SNasello]

Originally posted by Tim.Wright:
I, myself look at a damper diagram, particularly a racing one which is quite complicated and think "how the hell is it valid to reduce that to a single linear velocity coefficient".


I had just about written this very same thing.

[Karam Atteia]

Mr. Claude

Here is my spread sheet for what you requested. excuse me if there is any mistake. I did my best http://fsae.com/groupee_common/emoticons/icon_smile.gif.

http://www.mediafire.com/?yxj6lxm7x2x50po

But here also some problems,
How to take the decisions about the Knee speeds and the low speed and high speed damping ratios ??

no.58 & 59 .. i didn't understand your point.

thanks for your support

Karam

[Warpspeed]

Originally posted by Tim.Wright:I, myself look at a damper diagram, particularly a racing one which is quite complicated and think "how the hell is it valid to reduce that to a single linear velocity coefficient".

All of the damper tuning I've been involved in (which admittedly is not a lot, but covers both race and road cars) has been based completely on the test driver feedback.
That sums it up very nicely Tim.

Spring and antiroll bar calcs are absolutely fundamental, and the results entirely predictable within a very close margin.
Definitely no argument on that score.
But that is not at all what this thread is about, the topic is damping rates.

Precise predictive damper tuning is far more elusive.
It's one of several parameters on the car that are best optimised during testing rather than calculated.

As to initially selecting suitable damper valving, it's just a case of telling the damper supplier (roughly) the anticipated spring poundage that will be fitted onto his damper.

The damper will be then be supplied with appropriate valving and have a fully usable and sufficiently wide adjustment range to suit that spring range.

Even in FSAE, spring poundages can vary greatly with the extreme motion ratio differences possible between direct springing, and a really radical rocker setup.

Calculate the springs (free length, solid stack height, and poundage) and just tell the damper supplier the required shock collapsed and extended eye lengths, and the spring poundage.

Just make sure the spring physically fits onto the damper, and all the various lengths and dimensions jive, the approximate required spring poundage, and that is all you really need to know at the damper ordering stage.

[Flight909]

Originally posted by Warpspeed:
As to initially selecting suitable damper valving, it's just a case of telling the damper supplier (roughly) the anticipated spring poundage that will be fitted onto his damper.

The damper will be then be supplied with appropriate valving and have a fully usable and sufficiently wide adjustment range to suit that spring range.


So you trust a third party to do the work for you? What method is the damper supplier using then?

[Warpspeed]

Originally posted by Flight909:

So you trust a third party to do the work for you? What method is the damper supplier using then?
Yes I would trust a well known reputable damper supplier that has carried out a lot of continuing R&D, and has had feedback from customers to provide a safe and reliable product capable of providing a WIDELY ADJUSTABLE damping range, valved appropriately for the spring rate that I specify.

In the end it is the actual spring itself that needs the damping, everything else is pretty much taken care of by the motion ratio.

Let me ask you a question.
Would you trust a manufacturer that provides ball bearings, high tensile bolts, fuel injectors, tires, brake calipers, steering racks, and a wide range of other vehicle components to actually know what they are doing?

In reality we are mostly building a car by specifying and assembling parts designed by other people, and supplied through the normal commercial supply chain.

[Tim.Wright]

Originally posted by Flight909:
So you trust a third party to do the work for you? What method is the damper supplier using then?

Dampers are one of the components where this is generally the best way forward. From what I understand, the best damper manufacturers use a mix of experience of rig testing and track testing to arrive at a set of damping curves.

I personally have not had the same success with damping calculations that I have had with spring and anti roll bar calculations.

Though I'm interested to hear if Claude has a different story.

[Francis Gagné]

Having a ballpark idea of what you need is still a good idea. We already bought custom dampers from a "reputable manufacturer". When they proposed us their damping ratio they were way off (about 5 times over), since we had ballpark specs we challenged them and the revised their aim. If we hadn't validated the values we would have received dampers that had been useless. It was maybe a honest mistake, or they were out of their confort zone with a FSAE car.

Plus, they came installed with springs 1" longer than the damper. And late.

So, in most cases your better listening to the experts in place, but you still have to do your job and understand what you are working with and have an idea of what is realistic, and what is needed for YOUR application. Blind trust is never a good idea.

I do trust high tensile bolts manufacturer sold by trusted reseller, but if the told me their bolts were two times stronger than every other available on the market, I'd be sceptic...

[GSpeedR]

If your FSAE team is at a stage where they are ready to purchase (possibly expensive) dampers, then you need have some general idea of a damping target. I imagine first-year teams are getting used dampers or buying cheap ones, so they can be forgiven for using quick and dirty methods to get damping estimations.

[Claude Rouelle]

Karam,

Sorry for the late reply; I was busy with several other things.

First I want to congratulate you for having the guts to make this spreadsheet visible to everybody who read this forum. You have the courage to expose your strengths and weaknesses. You take the risk to expose yourself to criticism from me or others. But ultimately if you build a FSAE car, that car will be exposed to criticism anyway. You can't solve a problem unless you know have one, so the earlier you work on this, the better and the earlier you will make a decent car.

I wish other pople could do the same and show their own calculations or car design or pictures and openly ask what others (students and/or judge) like or do not like. Whether these students are right or wrong (I could be wrong and I have been) I think it would be very profitable for EVERYBODY.

So here is my list of questions and comments at this stage. If you are interested please take these remarks into account, remake your spreadsheet accordingly and we will go from there.


- To make your life easy E 18, E 32, E 33, E 34 E 37, E 39, E 42 E 46, E 47, E 55, E 116 should be an automatic calculation, not an input. In that way you can use the spreadsheet repeatedly: if you change any input, all the calculations will be made automatically. The machine helps the man, not the other way around. Also having these cells as calculations will help me to check your equations. Help me to help you.
- Same issue for E 19, E 28, E 39 (in case your car has left-right asymmetrical weight distribution).
- How was E 39 calculated if the non-suspended masses CG heights are not part of the input?
- How was E 42 calculated? Is this the vertical distance between the roll axis and the total mass CG or the vertical distance between the roll axis and the suspended mass CG?
- Why do you repeat E 43 as you already have it as an input in E20?
- I cannot check your calculation in E 66 and E 67. These should be calculation not input.
- In E 73 why do you use the total mass? Don’t you think that you should use the suspended mass? Isn’t there a 9.81 missing somewhere? Have you checked that your units are the same on the left and right of the equation? Also you should not us the average track.
- In E 73 I advise you to calculate independently the elastic weight transfer (from ARB and Spring) and the geometric weight transfer (due to roll centers height) I also advice you to calculate the non-suspended weight transfer. To do that you would need the non suspended mass CG heights.
- E 89: You are interested in the suspended mass damping at least in this simple, first approach. So the tire stiffness is not useful at this stage.
- I don’t know how E 116 has been calculated. Is it the suspended mass inertia around its own suspended mass CG or around the roll axis? How could I know? Even around it is own CG a FSAE suspended mass inertia of a 40 kgm2 is a bit high for a FSAE, use ½ of that amount as a basic number
- Same question for E 117.
- E 48 and E 49. How did you come with this number of 38 mm? What does the rule say about the minimum suspended mass Vs wheel movement? That will influence your E 77 and E 78 numbers.
- E 81 and E 82 can only be calculated with wheel rate and suspended mass not the complete mass. At least as a first stage
- About the chose of the knee speed. Basic explanation. Imagine (simplified numbers) that your suspended mass per corner is 50 Kg and the motion ratio is 1. If your compression damping is 10 N/mms, once your relative wheel speed vs the suspended mass is 50 mm/sec (with a MR=1 that will also be your damper speed) the force in the damper will be equal to the suspended weight; the whole car will lift up. This is oversimplified: you should solve a differential equation including mass, suspension stiffness and damping and of course the road input. Unless you know your road profile you will work buy experience. The choice of your knee speed is largely dependent of your circuit; for example if you take curbs or not. If I was you I would choose a knee speed at about 25 mm/sec for the moment. More explanation later.
- If E 55 is 56 % FRONT who do you come with bigger number rear than front in E 66 and E 67? In any case in a first approach, without tire data, I would chose an antiroll stiffness distribution percentage [(front spring + FARB) effect at front wheels] / [(front spring + FARB) effect at front wheels + (rear spring + RARB) effect at rear wheels)] about 0.5 % bigger than your suspended mass distribution. Too long to explain why here and now.
- Make sure you give all input of the same family the same number of decimal, Write the “0” if there is one. For example, the front track should be 1.350 m and not 1.35 m. No big deal, I am just picky. Same issue for E 27 and E 29.
- Put E 51, E 52 in the reverse ratio: wheel mvt. divided by the spring mvt. That is what the majority of people do.
- Same for E 53 and E 54.
- Why are E48, E 49 E 58, E 59, E 62, E 63 necessary? (see further comments)
- In E 94 you should only use the suspended mass.
- In E 94 check you units. The numerator of the fraction is N * m. The denominator is Nm/deg. How can the answer be in deg/G?
- The calculations in 105 and 106 would be valid IF the ARB arms would not bend. That will never be the case. You assume that only the bar is twisting. If I was you I would try to find what is the front and rear ARB that you need to satisfy both your roll gradient (deg/G) or roll stiffness (Nm /deg) and your target antiroll stiffness distribution. Then I will worry after that if this is mechanically possible and if you do not break (going in the plastic zones) the ARBs.
- Something fundamentally wrong in E 117 and E 178. The answer should be in Nm/(deg/sec) or Nm/(rad /sec). In any case when you calculate a critical damping in roll (or in pitch) you should use the suspended roll (or pitch) INERTIA, not the suspended mass.

A few comments not related to the exercise itself.

- Cell E 11 and E 12. With 46 % front weight distribution you are at the limit of what is acceptable to use the same front and rear tires. The front/rear tire cornering stiffness ration should be within 1 or 2 % of the weight distribution.
- E 20. That is pretty high! A good FSAE CG height with driver should be in the 250 mm region, if not lower
- E23 and E 24. IF you build a FSAE car target something in the 10 kg region, ideally lower.
- E 50 seem a bit high for a FSAE tire.

I hope this helps. I look forward your next spreadsheet. It won't be perfect next time but if you want it will be better step by step. Then we will go to an holistic multidimensional approach. Simple tan complicated. Not the other way around.

Good luck, good work.

PS: This a FSAE forum not a political forum but I can't help to follow and admire the search of a better life and real democracy that the people of your county are fighting for. Some violences are hard to watch and accept but the determination your people to fight for democracy, less corruption, better heath and education deserve a lot of respect. Turkey, Brazil, Egypt.... fascinating and high speed changing world. (Not that Europe or US are perfect; we also have work to do here)
You do not have to comment on this. I just want to quickly share my perspectives and encouragements.

[Lemon Lime]

Mr.Claude Rouelle,
Mr.Karam Atteia,

Pardon me if I stick my nose where it shouldn't be .. But I really admire you Mr.Claude .. You have a fascinating way of teaching and encouraging .. I would like to thank you a lot Mr.Claude for your nice reply giving the circumstances that Karam is my friend and we both are in the same team and in the same department as well .

If I can just meet you in person .. I would be honored for the next millennium http://fsae.com/groupee_common/emoticons/icon_smile.gif " As Walter Isaacson said << I hope that some day scientists can be considered heroes again, instead of Paris Hilton ! >> " You're my hero Mr.Claude http://fsae.com/groupee_common/emoticons/icon_smile.gif ...

I do realize that this forum is not meant for such sort of speech .. But I couldn't hold it anymore ... Once you told me Mr.Claude that you're one of the 7.23 billion " Yes they increased from 7.1 to 7.23 billion ! " .. But you Mr.Claude are one of a kind .. Can not find someone like you anywhere .. And about the last three lines you wrote Mr. Claude ; Thank you for supporting our case and for caring ... But I must add ; for everything there is a price .. we pay much " away from the violence " As you know Mr.Claude that FSAE race cars needs funds .. in such conditions in Egypt ; It's nearly impossible to find a sponsor , We " As FSAE teams " sacrifice as individuals who want to play an effective role in the society !! ..

Again I never wanted to mock this forum and to start speaking emotionally and in a dramatic way ! Nevertheless ; Mr.Claude you do inspire me a lot http://fsae.com/groupee_common/emoticons/icon_smile.gif .. Thank you again .

[Claude Rouelle]

Lemon Lime,

Claude, not Mr. Claude. Please.

Thank you for your kind words.

I don't think there is any hero in me. Surely less than you guys fighting for your freedom!

But is there is such thing in me than there must at least as much of it than in Paris Hilton http://fsae.com/groupee_common/emoticons/icon_smile.gif

Never thought I would have seen my name in the same forum, let alone a FSAE forum, near her name. My all life is now changed!


********

We will meet one day. Sooner than you think. I don't yet how and why but I am pretty sure of it.

[Karam Atteia]

Mr. Claude

Again thanks for your time and effort, I appreciate that too much.

About my country, politics, violence, democracy,........etc. I think my only way to freedom is doing what i love to do, and what i love to do is learning about the subject and one day i may work in this subject. My country is very important for me and i think doing this is for its sake.

Back to the subject,

-I added the equations for what u recommended, but still there are few cells that can't use equations. Cells like the (E 39)Suspended mass CG height, (E 42)distance from CG to Roll axis.

-for these coordinates, i don't use equations as i'm getting my numbers for the suspended mass CG height and lateral distance from vehicle center line from SusProg3D i'm using in kinematic and force analysis.

-(E 39) from SusProg3D

-(E 42) is not calculated. I get the number from the CAD.

-(E 43) is deleted now. It was repeated for nothing.

-(E 66), (E 67) the front and rear roll stiffness are assumptions to start the iterations for calculating the ride and roll rates.

-(E 73), (E 74) yes there is a problem in the units, i think because i used the total vehicle weight in (N). Edited to be the vehicle suspended mass in (kg). I'm using front track width for the front load transfer and the rear track for the rear one.

-"In E 73 I advise you to calculate independently the elastic weight transfer (from ARB and Spring) and the geometric weight transfer (due to roll centers height) I also advice you to calculate the non-suspended weight transfer. To do that you would need the non suspended mass CG heights."

i don't know how to calculate them independently !!

-(E 116), (E 117) i added how they were calculated, and i illustrated before that i'm assuming the car as a solid cuboid for the simplification as i can't do this on CAD yet. they are about the roll and pitch axis (parallel axis theorem).

-" E 48 and E 49. How did you come with this number of 38 mm? What does the rule say about the minimum suspended mass Vs wheel movement? That will influence your E 77 and E 78 numbers."

here i assumed to have 38 mm bump and 38 mm rebound.

-I changed the knee speed to be 25 mm/sec. I do understand your example and waiting for the more explanation.

-" If E 55 is 56 % FRONT who do you come with bigger number rear than front in E 66 and E 67? In any case in a first approach, without tire data, I would chose an antiroll stiffness distribution percentage [(front spring + FARB) effect at front wheels] / [(front spring + FARB) effect at front wheels + (rear spring + RARB) effect at rear wheels)] about 0.5 % bigger than your suspended mass distribution. Too long to explain why here and now. "

sry .. i did a mistake there, check! .. edited

-"In E 94 check you units. The numerator of the fraction is N * m. The denominator is Nm/deg. How can the answer be in deg/G?"

yes there is something wrong .. but if i divided by g=9.81 it would be wrong also !!
a problem i can't really solve .. Same equation at the OptimumG tech tips no.2


About the CG height, it was an assumption as I don't have a vehicle to make the experiment to get the CG height. We are using wider rear tires 8" at the rear and 6" at the front. I get the number of the tire stiffness from Hoosier data on the site.

I think i've fixed (remaked) the spread sheet according to your comments.

http://www.mediafire.com/?k8z0pvw38syab33

Excuse my ignorance and faults again !!

Karam

[mdavis]

Karam,

I've downloaded your spreadsheet, but yet to look at it, so I will only comment on some of what you posted.

"-"In E 73 I advise you to calculate independently the elastic weight transfer (from ARB and Spring) and the geometric weight transfer (due to roll centers height) I also advice you to calculate the non-suspended weight transfer. To do that you would need the non suspended mass CG heights."

i don't know how to calculate them independently !!"

Think about what each one does, and where the force comes from. I'll give you a hint about the one that was more difficult for me (geometric) to understand. If the roll center is simply the point at which the lateral force from the tires is imparted, and your CG is a certain distance above this point, then you have a radius (or a moment arm). If you know the force being applied at the roll center (you have a lateral acceleration for that axle, which it's probably safe to approximate as the vehicle lateral acceleration and a vehicle mass) then you should be able to calculate the moment created by that portion of weight transfer.

-I added the equations for what u recommended, but still there are few cells that can't use equations. Cells like the (E 39)Suspended mass CG height, (E 42)distance from CG to Roll axis.

Why can't you use equations to define these values? Is the suspended mass CG height not related to the total vehicle cg height and the non-suspended mass cg height by way of a weighted average? And can you not find the distance between a point and a line, if you know the 3-d coordinates of the point (you have them in your sheet) and 2 points on the line (front and rear roll centers)?

Like I said, just a few quick thoughts.

-Matt

[Claude Rouelle]

Kamar,

I only have the time for a few basic remarks. I will go in depth later.

1. You need to have the front and rear non suspended mass CG has coordinates input.
From
- the whole mass CG coordinates
- the non suspended masses CG coordinates. YOU NEED THESE NUMBERS AS INPUT
- the suspended and non suspended masses number (kg)
It is easy to calculate the coordinates of the suspended mass CG in E 39
E 39 is still an input. It should be a calculation. Saying it comes from a software without knowing how it was calculated will not get you approvals from design judges.

2. E 42 is an input. It should be a calculation. If you know where the suspended mass CG is, where you front and rear roll centers are (and there fore where your roll axis is) is pretty easy to calculate the delta z coordinate between the suspended mass CG and the roll axis. Please do that.

Remarks 1 and 2 oblige you to make a very simple work. If you cannot do that then I have worries about next calculations....

3. I suggest you make E 81 and E 82 an input 2.5 HZ front and 2.8 Hz rear are reasonable numbers) and then make the calculation of the wheel rate and, via the spring motion ratio, the spring rate.

4. E 94 should be an input (0.5 deg/G is a decent input. E 66, E 67 and E 68 should be output based on E 55 and the decision that you make in E 94.


Other pieces of advice

- Pleaaaase use the same number of decimal for each kind of dimension. Not make sense to see 1.6 m and 0.872727 m. Lock each cell decimal amount so that for example you would have 1.600 m and 0.872 m.
- You may want to color the cells with input in one color and the cells with output in another one

I will come back to you later with other comments.

Meanwhile send me your email address at engineering@optimumg.com; I could send you a few documents which could help you to better understand.

[Karam Atteia]

Mr. Claude,

http://www.mediafire.com/?9f0uurp8a4178a2

I do edited (remade) the spread sheet again. Hope to have done it as expected.

(Green >> input) AND (Red >> Calculated)

Thanks

Karam

[jlangholzj]

I'll attach this as a picture, but what I've shown is something that I like to do for input/output spreadsheets.

Your inputs are the white background boxes and the outputs are a bolded background box. The reason why I tend to do this is so that I can much easier use conditional formatting on your outputs.

Ie...say in this picture you wanted your total lateral load transfer distribution to be less than 60%. You could apply conditional formatting so that anything over 60% is red and anything under your target is green. (which is exactly what I did just as an example)

Is this necessary? No. However if you're trying to focus on several key values it can be very helpful.

Some people like this....others may not. Just sharing something that I've found working in spreadsheets that has made my life easier.

http://i260.photobucket.com/albums/ii35/jlangholzj/loadxfr_snip_zps5512609a.png (http://s260.photobucket.com/user/jlangholzj/media/loadxfr_snip_zps5512609a.png.html)

[Karam Atteia]

Mr. Claude,

http://www.mediafire.com/?9f0uurp8a4178a2

I do edited (remade) the spread sheet again. Hope to have done it as expected.

(Green >> input) AND (Red >> Calculated)


Sorry, I've posted it 5 days ago. Supposing You didn't see it.

Excuse me for being rude like that. But I told you before it is very important to me.

Thanks in advance.

Karam

[Claude Rouelle]

Karam,

I want to help you but it is not the only thing I am working on. I hope you can be patient. If you were on my university student that would be another case but here I do it only when I have time.

[Karam Atteia]

Mr. Claude

Ok no problem, I appreciate that a lot. Never mind sir.

I'm waiting

Thanks in advance

Karam

[Claude Rouelle]

Karam

Here are a few additional comments. Wish I could do more but quite busy. Take these and the info I sent you to improve the calculations and we will go to the next steps.

E 8 why do you need to calculate the average track? Where do you use this?

E 11 and E 12 I would prefer them to be a calculation and the mass distribution percentage to be an input that you decide at the moment of the car concept

E 13 and others similar cells. I would put a 9.81 somewhere else in the spreadsheet and calculate the weight with the $$ function. No big deal for the moment. But I guarantee you that this 1.9 % difference between 10 and 9.81 will end up making a difference in the car behavior when the tire model will be included.

E 16 why do you need this for now? You may want to know that the tire loaded radius and rolling radius are 2 different things

E 20 nothing wrong here in the calculation. In fact that is an input, not a calculation but I would not want you to keep in your mind that 350 mm of CG height is acceptable for a FS / FSAE car. 250 mm is more the norm for a decent FSAE
E 25 Is this a car with 2 wheels or 4 wheels? For me the total non-suspended mass is 52 kg. I guess your non suspended mass is 12.5 kg per front wheel and 13.5 kg per rear wheel, correct? But E 34 is correct.

Somewhere after E 25 you should calculate the non-suspended mass distribution. Here is 100 * (12.5*2) /[ (12.5*2) + (13.5*20]
E29 You should have the possibility to have different non suspended mass CG height front and rear

E 38 is not necessary; you should not use this as the lateral geometric weight transfer will be calcate separately front and rear

E 39. If you imagine 1 G of lateral acceleration you will agree that the roll moment on the total Mass should be = Mass * Mass CG height and that should be equal the total of the 3 roll moments on the suspended mass and the front and rear non suspended mass, correct? So Mass * Mass CG height should be equal to (SM * suspended mass CG height * 1 G) + [(front nsM* front nSM CH height* 1G) + (rear nsM * rear nsM CG height * 1 G)] In other words (250 * 0.350*1*9.81) should be equal to [(198 * 0.409*1*9.81) + (12.5*2*.260*1*9.81) + (13.5*2*.260*1*9.81)], correct? well try that and it is not. So something should be wrong in your 0.409 calculation. Also as E 39 is wrong E 42 will be too. I find E 39 to be 373.6 mm. What about you?

E 42. I already mentioned this before: you are looking for the vertical distance between the SUSPENDED MASS CG and the roll axis (not the vertical distance between the total mass and the roll axis). Why is E 20 in this calculation?

I suggest you make these new corrections and publish a new spreadsheet. It does not make sense to check the next values if the basic numbers at the beginning of the spreadsheet are wrong.

[Claude Rouelle]

Karam,

Additional comments

Put the front or rear roll center altitude at 0 and your spreadsheet crashes in the roll rates .....

Something is wrong here....

Back to the very basics....

Make sure you make some simple sanity checks, If the front and rear roll centers are on the ground then the vertical distance from the suspended mass to the roll axis is the suspended mass CG altitude.

Make sure also that if roll centers under the ground (negative z) it will give you negative geometric weight transfers and also more roll angle for all other parameters / input being the same; that is another simple basic sanity check.

[Karam Atteia]

Mr. Claude,

I used (E 8) the average track to calculate the additional ARB roll stiffness needed to reach the desired roll stiffness.
You can see it in (E 97)

I do edited the spread sheet according to your comments again, sir.

http://www.mediafire.com/?8q8yf3m31ui3dry

Special Thanks,

Karam

[Claude Rouelle]

Karam,

E 28 12.5 kg non suspended mass front and 13.5 kg rear and x of the non-suspended mass CG is at about ¼ of the wheelbase?

E 72 Why do you use the whole mass in this calculation? If you use the vertical distance between the suspended mass CG and the roll axis to calculate the suspended mass roll moment why do you use the whole mass?

Re-arrange the Excel spreadsheet so that we can find all the inputs (green) first. It does not make sense to find the explanation of what E 72 is while E 03 is way below.

As I suggested earlier use a constant 9.81 to make the conversion from mass (kg) to weight or force (N)

[Claude Rouelle]

More to come later when and if I can find a bit of time. I will be in Europe in the next 3 weeks (Spa 24 hours, FSG and seminar)

[Karam Atteia]

Mr. Claude,

I do edited it for the last comments.

http://www.mediafire.com/?e6l8vwniz57i6zk

Take your time sir, I'll be patient this time. Cause i appreciate your time.

thank you for your attention

Karam

[Claude Rouelle]

Karam,

We are getting closer...

It looks a bit more professional although it would be nice to see the input on the left and the output on the right so that the user do not have to scroll up and down all the time to see the logical connection between input and output

E 58 You cannot simply make an average here. What if your front and rear non suspended masses CG heights would be different?

E 72 use the same number of displayed decimals even if the last number is a 0. In this case 0.070, not 0.07. Although it won't change the calculations, just be consistent in the numbers alignment and your presentation. Same issue for example between E 122 and E 123

I still do not understand what you try to accomplish in E 90 and E 91. To calculate E 87 and E 88 you should use E 84 and E 85... Unless I am missing something...

Try to present the calculations in a logical order which follows the row number. For example it is difficult to understand a calculation made in E 78 making a reference of a cell in E 82

Where is the choice you made in E 157 coming from?

E 160 Something is wrong. Check your units. To get your answer in Hz (which is 1/sec) under the square root you should have a fraction of which the numerator should be in Nm/rad and the denominator should be in Kgm2. The issue is the same in E 161. You just missed a few parenthesis in your formula. By experience I knew that your natural roll frequency was too high and unusual.

E 199 and E 200. I am confused about your units: either you should have Nm / (rad /sec) or Nm / (deg /sec) but not N/(m/sec)

Work on both the calculations and the presentation; you are on the right track

[Karam Atteia]

Mr. Claude,

Wish you a good day http://fsae.com/groupee_common/emoticons/icon_smile.gif

http://www.mediafire.com/?xo29obikoemlwwg

I do edited the spread sheet, please have a look.

but now having a question, now i calculated the roll and pitch frequency and critical damping. So how to combine between these and the already calculated damping rates (where Heave motion only where took in consideration) and get the damping rates that is appropriate for this vehicle.

Thanks

Karam

[Karam Atteia]

Mr. Claude

http://www.mediafire.com/?1he7neboqbuuvee

Same as last posted spread sheet, but aligned better.

Thanks

Karam

[Claude Rouelle]

Karam

What is the square root of 49?

What is the square root of 64?

What is the square root of 57.3? Somewhere in between the first answer right?

Now check your unites in AB18.

I have mentioned this issue in a previous post but you have not corrected it.

When you write an equation please make sure that the units are the same on the left and of the right of the equal sign.

You mix Nm/deg and Nm/rad.

Will come back with more comments later

[Karam Atteia]

Mr. Cluade

Sorry, it was a mistake in writing the equation. Excuse me !!

(AB 18)
?_roll = (1/2?)* Sqrt[(180*K?)/(?*I_roll)]
1/sec = 1/sec

where, K? in N.m/deg.
I_roll in kg.m^2

Edited !!

http://www.mediafire.com/?1he7neboqbuuvee


Karam

[Claude Rouelle]

Karam,

No excuse needed. WE are all learning.

Now the advice I can give you is the following.

If it is true that 0.7 of damping ratio (and that is gross average because there is bump and rebound, low speed and high speed compromise) is a good first target (before you go testing and / or before you use more sophisticated models with, for example, road profile simulation) it is worth you "play" with this spreadsheet (still a few corrections to be made... will speak about that later) to see how you can get the best 0.7 of suspended mass damping ratio in heave, roll and pitch. Not obvious.

There are some racing categories where you cannot change everything you want of an existing car and where you will see that to have 0.7 in roll (springs and 0.7 in heave ARBs against roll inertia) you will be to compromise and you will have more than 0.7 in heave. If you look at some cars like DTM you can really see that they are over-damped in heave: practically no movement of the chassis and the wheel in the pit-lane but they do have reasonable damping ratio in roll. At the end it is how and where on the circuit you make the car going fast. It is all about COMPROMISE. That is where lap time simulation comes in the picture.

I hope this helps to enlarge your perspective. you are only at the beginning. WE are all at the beginning anyway http://fsae.com/groupee_common/emoticons/icon_smile.gif

Life is a journey not a destination. Have fun!

[Karam Atteia]

Mr. Claude,

Here are few questions and thoughts.

1- On calculating the Non-Suspended mass natural frequency, should i use the tire spring stiffness only. or should i treat the non-suspended mass as a body between two springs (in parallel)and use (Kt_tire stiffness + Ks_spring stiffness) ??

2- Add to the spread sheet the Roll and Pitch Damping that will occur due to damping rates calculated to reach the 0.7 damping ratio in Heave. then by calculating the Roll and Pitch Critical damping, we can get the Damping ratio in Roll and Pitch. then start to iterate till we get a compromise between Heave, Roll and Pitch. Is that true ??

Thanks

Karam

[Claude Rouelle]

Karam,,

Your spreadsheet is evolved a lot and well.

I only see one more issue remaining before we go to a next step.

AB 36 and 37. In your opinion are the springs in series or in parallel?

[Karam Atteia]

Mr. Claude,

http://s17.postimg.org/gzmr2kd4r/image.jpg (http://postimg.org/image/gzmr2kd4r/)

In my opinion, i can see that the wheel (non-suspended mass) is suspended between two springs. The Tire spring (K_tire) and the suspension spring (K_spring) and for me they look in parallel.

I can see a mistake in my spread sheet, at AB 36,37 where i used the wheel rate instead of the spring rate.

Karam

[Karam Atteia]

Mr. Claude,

I hope you still remember this topic, Please reply when you are free.
Sorry for my late reply.

1-I do edited the spreadsheet again and added the damping ratios in roll and pitch. I found that when targeted to have 0.65 as a damping ratio in bump and rebound for low speed damping, the roll damping ratio is 1.46 and the pitch braking damping ratio is 0.88 while the pitch accelerating damping ratio is 1.91. if these numbers are reasonable??

If so, to compromise these numbers i should decrease the damping ratios in heave to get damping ratios in ROLL and PITCH near the 0.7. and if i used a third damper that works only on HEAVE to increase the damping ratio in HEAVE. Is that right??

2-In my opinion, i can see that the wheel (non-suspended mass) is suspended between two springs. The Tire spring (K_tire) and the suspension spring (K_spring) and for me they look in parallel. So, on calculating the Non-Suspended mass natural frequency, should i use the tire spring stiffness only. or should i treat the non-suspended mass as a body between two springs (in parallel)and use (Kt_tire stiffness + Ks_spring stiffness) ??


http://www.mediafire.com/download/lx0jyg51sksqsg6/damping_rates_..._8th_edit.xlsx

[Claude Rouelle]

Karam,

In calculating the pitch/roll damping values Cells - AB 62, 63 and 64 you use the Non-Suspended Mass Critical damping and Suspended Mass Damping ratio, instead of Suspended Mass critical damping and suspended mass damping ratio.

It seems like a simple oversight. Its under the title 'Damping rates on HEAVE' - Cells - AA 52, 54, 56 and 58.

Will come back with other comments later

[Karam Atteia]

In calculating the pitch/roll damping values Cells - AB 62, 63 and 64 you use the Non-Suspended Mass Critical damping and Suspended Mass Damping ratio, instead of Suspended Mass critical damping and suspended mass damping ratio.


Mr. Claude,

Here i used cells - AA 52, 54, 56 and 58 because IMO when the vehicle is in ROLL, this means that one side is in compression and the other side is in rebound. And that's what i applied in calculating cell AB 62. And same thought for the PITCH damping in braking and accelerating, the front axle is in compression and the rear in rebound or viceversa.

Excuse me if any fatal mistake.
Thanks.

[Claude Rouelle]

Karam,

I agree with what you said and that's how our weight transfer spreadsheet is setup too.

But that's not what I'm talking about though.

For example, in Cell AA52, to calculate the 'Front Damping in Low Speed Rebound' at the wheel, you use the non-suspended mass critical damping, when you should be using the suspended mass critical damping.
But for Cell AA51- 'Front Damping in Low Speed Compression' at the wheel, you use the suspended mass critical damping.

So you are using suspended mass critical damping for compression and non-suspended mass critical damping for rebound, which I would say is incorrect.

You have to use suspended mass critical damping for both compression and rebound cases to calculate the Suspended mass Roll/Pitch Damping values. If not, this would mean you're considering a different mass-spring combinations under compression and rebound!

[Karam Atteia]

Mr.Claude,

" The Damper controls the suspended mass in bump, and the non-suspended mass in rebound "
that's what made me confused, and hazy to use the non-suspended mass critical damping in rebound. Is this phrase isn't correct ?? or does it refer for another thing ??

Thanks

[Claude Rouelle]

Karam,

" The Damper controls the suspended mass in bump, and the non-suspended mass in rebound "

1. Where did you read this? Where is the logical?

2. Lets also be sure we use the right word here. The load can change because the acceleration changes. But unless you go on another planet with different gravity the masses of give unmodified objects do not change. So when I read that a damper control a mass I am already lost.

[Karam Atteia]

" The Damper controls the suspended mass in bump, and the non-suspended mass in rebound "


Mr.Claude,

First of all i wrote it wrong, i should have wrote "the non-suspended mass in bump ........etc." , Sorry for that.

my reference for that was, "Bump Damping: Bump damping controls the unsprung weight of the vehicle. It controls the upward movement of the suspension as when hitting a bump on the track. It should not be used to control the downward movement of the vehicle when it encounters dips. Also, it should not be used to control either roll or bottoming." QUOTED from: KONI's published instructions for damper adjustment at the track.

i do edited the spreadsheet and used the suspended mass critical damping in both bump and rebound damping calculations.

http://www.mediafire.com/?6dazrgwiaehlz81

sorry i mixed up things, Excuse my ignorance.

[Claude Rouelle]

There is no ignorance for the people who want to learn. there is only new horizons to discover and experience to acquire

Will be back to you later

[Z]

Karam,

2. Lets also be sure we use the right word here. The load can change because the acceleration changes. But unless you go on another planet with different gravity the masses of give unmodified objects do not change. So when I read that a damper control a mass I am already lost.
Claude,

Hmmm... I hope that is only a Franco-English translation problem...
~~~~~o0o~~~~~

Students wondering about the above might try this Quick Quiz. (In answering the following questions, NO calculators/Matlab/etc., allowed! You should be able to answer all these in your heads (or maybe on a small scrap of paper)!!!)

You are floating about in Deep Space when you come across two small metallic meteors. These particular lumps of stainless steel have a high Tungsten content, so their "specific gravities" (to keep this simple) are equal to 10 (ie. "density" = 10 g/cc).

One meteor has a volume = 300 cc, and the other has volume = 900cc.

Question 1a. What are the "masses" of these two meteors?
Q 1b. What do they "weigh" out there in Deep Space?
Q 1c. What would they "weigh" on the surface of Earth?
Q 1d. What would they "weigh" on the surface of our Moon (take Moon's gravitational intensity on its surface to be 1/6th of Earth's)?

You get bored looking at all the blackness, so you decide to do an experiment. You get a long length of springy wire (assumed to be of negligible "mass") and fashion it into a coil-spring 1 metre long, with spring-rate = 100N/m. You attach the two lumps of meteor to each end of the coil-spring. You stretch the two meteors apart so the spring is now 1.1 metres long, and you then simultaneously release both meteors.

(For double marks.)
Q 2a. Describe the ensuing motions of the two meteors.
Q 2b. Would these motions be different if the experiment was done on the surface of Earth (perhaps on a frictionless "Air Hockey" table)?
Q 2c. Or different on the surface of the Moon?

(For triple marks.)
Q 3. How many "natural resonant frequencies" are there for this system (remember, two meteors, but only one spring)?

(For quadruple marks. )
Q4. What is/are the natural resonant frequency/frequencies?

Students scoring less than 50% should look for a job in Management. Or maybe in Teaching! :)

Z

(PS. Remember that 40+ years ago US and Russian engineers had to design suspensions for their Moon-Buggies/Lunakods!)

[MCoach]

Claude,

Hmmm... I hope that is only a Franco-English translation problem...
~~~~~o0o~~~~~

Students wondering about the above might try this Quick Quiz. (In answering the following questions, NO calculators/Matlab/etc., allowed! You should be able to answer all these in your heads (or maybe on a small scrap of paper)!!!)

You are floating about in Deep Space when you come across two small metallic meteors. These particular lumps of stainless steel have a high Tungsten content, so their "specific gravities" (to keep this simple) are equal to 10 (ie. "density" = 10 g/cc).

One meteor has a volume = 300 cc, and the other has volume = 900cc.

Question 1a. What are the "masses" of these two meteors?
Q 1b. What do they "weigh" out there in Deep Space?
Q 1c. What would they "weigh" on the surface of Earth?
Q 1d. What would they "weigh" on the surface of our Moon (take Moon's gravitational intensity on its surface to be 1/6th of Earth's)?

You get bored looking at all the blackness, so you decide to do an experiment. You get a long length of springy wire (assumed to be of negligible "mass") and fashion it into a coil-spring 1 metre long, with spring-rate = 100N/m. You attach the two lumps of meteor to each end of the coil-spring. You stretch the two meteors apart so the spring is now 1.1 metres long, and you then simultaneously release both meteors.

(For double marks.)
Q 2a. Describe the ensuing motions of the two meteors.
Q 2b. Would these motions be different if the experiment was done on the surface of Earth (perhaps on a frictionless "Air Hockey" table)?
Q 2c. Or different on the surface of the Moon?

(For triple marks.)
Q 3. How many "natural resonant frequencies" are there for this system (remember, two meteors, but only one spring)?

(For quadruple marks. )
Q4. What is/are the natural resonant frequency/frequencies?

Students scoring less than 50% should look for a job in Management. Or maybe in Teaching! :)

Z

(PS. Remember that 40+ years ago US and Russian engineers had to design suspensions for their Moon-Buggies/Lunakods!)


I believe I'm walking through this correctly, but it's lunch time and I've got to run.

10g/cc each

10g*300cc= 3kg = m1
10g*900cc= 9kg = m2

weight = m*a. a = 0 m/s^2,
in deep space, weight = 0 N

weight on Earth = m*9.81 m/s^2 (~10 for head calcs) = 30N, 90N respectively

weight on Moon = m*10*(1/6) = 5N, 15N


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

Neither end of the of the meteors are fixed, the spring is unbalanced with m2 = m1*3
The compression of the spring with this unbalance will cause the system to move in plane axially, while vibrating, towards the direction of m1 continuously with a fully undamped system.

This motion would not be different on a frictionless table (assuming absolute ideal conditions and the meteors lay on the plane of the table and not normal to it). This would also not be different on the surface of the moon either because gravity is only acting perpendicular to the system, against the frictionless surface. With a frictionless surface, this lead to an acceleration and a force, but no Coulomb to act as resistance axially to the oscillating system.


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


The system has two dependent masses attached to it, and therefore qualifies as a two DOF system. The amount of freedom in the system needs an equal amount of natural vibration modes.


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

resonant frequencies in cycles/sec are governed by the EQ:


f = 1/2*pi*sqrt(k/m)

However it is much easier to just find the radian frequency for head math:

%spring stiffness
k= 100 N/m

%define both masses, calc
m1= 3 kg
m2= 9 kg

w_n1 = sqrt(k/m1)
w_n2 = sqrt(k/m2)

w_n1 = ~ 5.78 rad/sec
w_n2 = 3 1/3 rad/sec

submitting for interest in topic retention and openly testing myself. :)

[nowhere fast]

I believe your frequencies are incorrect. One of the natural frequencies will be zero (i.e. the two masses move together as if they were a single rigid body). There will actually be six of these rigid body modes, but only one resonant mode.

For the description of the motion; the smaller mass will oscillate further than the larger mass, but the system will not move from where it was released.

[Z]

Dear Messrs MCoach and Nathan,

"Z's Institute for Vocational Studies" thanks you for taking the above Quick Quiz. We are pleased to present your scores below, together with suggestions for your future life directions.
~~~~~~~~~~o0o~~~~~~~~~~

Mr MCoach
=========

Q1a,b,c,d - 4/4.
Congratulations on knowing the difference between "mass" and "weight"! This means that you are probably NOT suited to a career as an Educationalist (at least not in the Automotive Industry).

Note that an acceptable answer to Q1b is that BOTH meteors (assumed 1 metre apart in Deep Space, with no other bodies nearby) have the SAME WEIGHT of 1.8 nanoNewtons, this being their mutual gravitational attraction. However, if you gave this answer we would have to mark your card "SmartAr$e Know-It-All - Unemployable!!!".

Q2a - 0/2.
Here it seems that you are thinking about the fabled "Inertial Drive". If you can get this working, then forget about FSAE and the like, and instead start "M's 2-Infinity-And-Beyond CoachWorks". You'll become a squillionaire!

Q2b,c - 2 points each, so 4/4.

Q3 - 3/3.
This one is debateable (as Mr Nathan indeed does), but we accept your answer.

For future reference the ends of the massless spring may be considered attached by frictionless ball-joints to the CGs of the meteors, so that rotational and other DoFs of the meteors may be neglected. So just two "point masses" moving along a straight line passing through them.

Q4 - 1/8.
One point for showing the correct equation, but unfortunately your two frequencies are incorrect.
~o0o~

Total Score = 12/21 = 57%.

Congratulations! You have (only just!) proved yourself suitable for a position as a lowly paid, and under-appreciated, Engineer!

However, if you spend more time taking long-lunches (with lots of heavy drinking), shmoozing your superiors, and so on, then your score may well drop low enough that you become better suited to a much more highly paid role in Management. :)
~~~~~~~~~~o0o~~~~~~~~~~

Mr Nathan
=========
The brevity of your answers suggests that you are most definitely NOT SUITED to roles in Marketing or Politics.

Your suggestion that "There will actually be six of these rigid body modes" indicates a tendency to "roll-the-dice". Why not 2 x 6++ DoFs, given that there are two, sort of rigid, bodies? Hmmm... So, perhaps a job in the Gambling Industry?

Nevertheless, your last paragraph is correct, so a lowly paid Engineering job beckons... Note that if you actually gave some numbers, then we could guarantee you a place in one of the deepest Engineering dungeons, with an occasional bone being slipped under the locked door. :)
~~~~~~~~~~o0o~~~~~~~~~~

More applicants welcome...

Z

(PS. This is a very simple problem. Many hints given above. The numbers can be worked out easily. Just one conceptual insight required. And you cannot understand "damping" until you understand "vibrating mechanical systems"...)

[MCoach]

Ah, yes. I'll admit defeat.

Nathan is correct in part II, as they will follow Newtons laws, of equal action and reaction. Silly mistake on my part. m1 will oscillate further than m2, but the system will remain stationary. Thanks for the equally silly response, Z.

Now that I have time to look and think about, Q4 has me a little stumped because I can't think of where to ground the system... In my head at this point, I want to combine the mass amounts acting on the spring, so 3 + 9 = 12kg

sqrt(k/(m1+m2)=w_n1
w_n1 = sqrt( 100/12) = sqrt(8 1/3) = ~2.89 rad/sec

And assuming Nathan's answer on the latter part of 0 rad/sec

This is based on the assumption of stiffness/equivalent mass, while being able to neglect the distance the spring is actually displaced. Still, without a thought out place to ground the system I cannot promote full confidence in my answer. However, when the system oscillates so that the masses both move in the same direction, it's a rigid body, with spring displacement of 0 in that cycle. When the reach their apex in opposite directions, both masses will act on the spring in opposite directions. Can't tell if this reasoning is sound, but I expect some sort of snarky answer :)

[SNasello]

Interesting problem Z.

Im not going to touch on Q1 because it was already answered correctly.

Q2: When the two masses are stretched apart and released, they will both be subjected to the same force, but in opposite directions. As there are no other forces acting on the individual masses they will accelerate towards each other. With an equal force acting on the masses, the lighter mass will have a higher initial acceleration (3x higher to be exact) than the heavier mass. At the moment when both masses have the same force acting in the opposite direction, pushing them away from each other, the lighter mass will have travelled 3x farther than the larger mass, meaning m1 will have travelled 3/4*0.2m or 0.15m and m2 will have travelled 1/4*0.2m or 0.05m. This is very important for part 4.

Q3: As this is a system with two degrees of freedom, it has to have two natural frequencies. The natural frequency of both masses are the same.

Q4: There is a point on the coil spring which does not see any motion, which means we can take this as our effective virtual ground point, and split the one spring into two springs with different stiffnesses. How do we find them?

The first mass travelled a distance 0.15m due to an initial force of 10N. This gives it an amplitude of 0.075m. The effective spring stiffness will be 10/0.075m or 133.33... N/m
The second mass travelled a distance of 0.05, giving it an amplitude of 0.025. The effective spring stiffness is 10/0.025 or 400 N/m

the natural frequency is then sqrt(400/9) or sqrt(133.33/3) , which is 6-2/3 rad/s.

[Z]

... Q4 has me a little stumped because I can't think of where to ground the system...
MCoach,

And where better to "ground the system" than ...... at the system's Centre of Gravity (or Centre of Mass)!

From Newton's Laws, and the fact that no external forces act on the system, it follows that after the meteors are initially "released" their combined CG will always remain "inertially stationary" (ie. possibly moving at constant velocity wrt Newton's "absolute space", but not accelerating).

And since the CG is found by a simple linear relationship (see below), and the spring's Force-Deflection behaviour is also linear, it follows that a point on the spring which is at the CG at a certain given time, will always be at the CG at all other times. So that point can be "the ground" for calculations.
~~~~~o0o~~~~~

Stefan,

Congratulations! You receive full marks!

You may now proceed straight to the bowels of any big Engineering Corporation, where you can work endless hours as a "back room boffin", for almost no pay at all. Well, they might throw you that occasional bone... :)
~~~~~o0o~~~~~

BTW, my approach to Q4 is this.

As above, the combined system's CG is stationary, and the spring is also stationary at that point.

The CG is 3/4 of the spring's length from the lighter mass m1, and 1/4 of the spring's length from the heavier mass m2 (since 3/4 x L x 3kg = 1/4 x L x 9kg).

The "3/4 length spring" has a spring-rate of 4/3 x the original whole spring-rate (from "springs in series" equations, etc.). So the lighter mass is "bouncing" against a spring-rate of 4/3 x 100 N/m.

Similarly, the heavier mass is bouncing against the "1/4 length spring", which has a spring-rate of 4/1 x 100 N/m.

From MCoach's earlier equation for natural frequency (ie. Frequency = 1/2.Pi x Sqrt(k/m)).

Freq1 = 1/2.Pi x Sqrt((4/3 x 100)/3) = 1/2.Pi x Sqrt(400/9) = 1/2.Pi x 20/3 = 10/3.Pi = ~10/9 = ~1+ Hz.

Freq2 = 1/2.Pi x Sqrt((4 x 100)/9) = 10/3.Pi = ~10/9 = ~1+ Hz.

(Or a bit more accurately, since Pi = ~22/7, Freq1,2 = ~70/66 = ~1.06 Hz.)

Take out the 2.Pi and both radian frequencies are as Stefan's at Sqrt(400/9) = 20/3 rad/s.
~~~~~o0o~~~~~

Finally, it might be a good idea to look back to page 2 where Claude lists his 59 "let's make it simple" damper calculations. Several of those calculations suggest that the car's Sprung-Mass oscillates rotationally in Roll and Pitch about axes that do NOT pass through the SM's CG. That is, it seems to me that Claude is suggesting that "Roll and Pitch damper calcs" should be done around the "Roll and Pitch axes", which are well below the SM's CG.

Does anyone think this makes sense? Especially given that tyres have soft sidewalls that let the wheel move sideways, and wheels can roll freely longitudinally, so the wheels are most definitely NOT pin-jointed to the road? (Think about what the car's CG would do during these Roll and Pitch oscillations, with reference to the above meteor problem.)

Claude???

Z

[MCoach]

Congrats, Stefan.

This has been enlightening. I haven't thought much about a system vibrating without a "ground", but this helps a lot.

[dynatune]

Karam,

have a look at www.dynatune-xl.com. You will find the tool you have always wanted there. It is straightforward and based on MS Excel. Many Students in Europe are using it during their education and I hope it will bring gret knowledge to you too.

Dynatune

[Z]

Finally, it might be a good idea to look back to page 2 where Claude lists his 59 "let's make it simple" damper calculations. Several of those calculations suggest that the car's Sprung-Mass oscillates rotationally in Roll and Pitch about axes that do NOT pass through the SM's CG. That is, it seems to me that Claude is suggesting that "Roll and Pitch damper calcs" should be done around the "Roll and Pitch axes", which are well below the SM's CG.

Does anyone think this makes sense? Especially given that tyres have soft sidewalls that let the wheel move sideways, and wheels can roll freely longitudinally, so the wheels are most definitely NOT pin-jointed to the road? (Think about what the car's CG would do during these Roll and Pitch oscillations, with reference to the above meteor problem.)

Claude???

Z
Claude,

Do you really think that the car's Sprung-Mass oscillates rotationally in Roll and Pitch about (your particular definition of) the "Roll and Pitch" axes?

If, in the Design tent, students gave you more realistic, and SIMPLER, calculations for Roll and Pitch oscillations than the ones you are suggesting in this thread, then would you give them low marks for not complicating it enough?

Z

[dynatune]

Karam,

have a look at our excel based tool that will certainly help you understand. There is a free download version to play with. www.dynatune-xl.com

dynatune