Moments of Inertia

[scott_rfr]

So I am in the process of witting my own simulink simulation for our car. At this point I am a bit stuck at what to use for roll/pitch and yaw moment of inertia. While I plan to physically test our car I was wondering if anyone has any recommendations for calculating something by hand to use.

Thanks,
Scott
Rutgers FSAE
Suspension Guy

[Trevor]

You could always use a number similar to last year's car (modified accordingly)...
Or if you know the mass of the major components and their locations on the car, you could get a rough value with a little math.

[Rickertsen2]

Sorry to distract from the original topic but how many people measure this? Everything I can come up with requires spinning the car on some sort of overly elaborate rig.

[bahous]

overly elaborate, no.
big, yes.

[scott_rfr]

Yes I could just measure lasts years car however as you stated the rig will take up a bit of space and while currently building the new car we do not have enough room in the shop. This is the reason I was asking for some advice on how to come up with some rough numbers...

Scott

[HenningO]

Use your CAD assembly, select the 25 or so heaviest components, assign them their actual weights. Let your CAD software calculate it. It should get you in the ballpark.

You should also verify this number with some hand calcs. Estimate the car with boxes/cylinders, and use Steiners theorem to add all the boxes/components.

I'm guessing you want to measure the MOI of your coming car, so I have to agree with the previous posts, build a rig now. Make it demountable and space shouldn't be an issue, plus you already got it built for when your car is finished.

[Adambomb]

The CAD method or hand calc method should get you surprisingly close, we made a weight distribution spreadsheet in Excel and were within 1%.

As for a test rig, the simplest method I've seen is the "pendulum" method, where you hang the whole car, time how long a cycle takes, then use the parallel axis theorem to back the point mass inertia out of total inertia to find roll or pitch inertia (depending on which way it's swung). Yaw inertia is only slightly less straightforward.

[PatClarke]

Moments of Inertia ??

Yes, I have them.

I usually open a beer and sit in my favourite chair and watch the Simpsons =]

Pat

[ben]

Anyone got any thoughts on the errors on inertia between a CAD model and a measured value?

From a design judging point of view it would obviously be better to have a measured number, but if the team's got a mass distribution estimate from the CAD model and it's close to the car on the scales then is the inertia estimate from the same CAD model good enough?

I suspect it is, but obviously the distance squared terms are going to lead to a higher error. But then the experimental errors on swinging the car are high and how many people have a discussion about that?

If I was in the OP's position I'd do as suggested. Pick the largest masses and do a hand calc. The order of magnitude should at least be correct.

Ben

[Zac]

In my experience, inertia measurements are kind of a crapshoot, particularly with any sort of a simple/student built rig.

For a lab activity in one of my tech electives we had to measure the inertia of a con-rod using a couple different setups: a torsional pendulum, using a knife edge to turn the con-rod into a pendulum, and using a cad model with mass properties. There was about a +/- 50% spread between the three techniques.

My advice would be to come-up with a rough estimate(using one of the ideas others have suggested) of last year's car, put that into your simulation, compare the simulation to track data, and adjust accordingly.

[exFSAE]

Better question is how important are these MOI numbers? What are you trying to simulate?

For the vast majority (if not entirety) of what I'd be simulating and predicting I wouldn't worry much about them, or they shouldn't change much in the end.

I'd just stick with a real rough CAD approximation.

[ben]

Originally posted by exFSAE:
Better question is how important are these MOI numbers? What are you trying to simulate?

For the vast majority (if not entirety) of what I'd be simulating and predicting I wouldn't worry much about them, or they shouldn't change much in the end.

I'd just stick with a real rough CAD approximation.

I wouldn't say they're unimportant the question is do you have the tools to assess the effect? Not the same thing.

Ben

[scott_rfr]

The way the model works is I input a steer angle at some constant velocity. Or I take out the steer angle/constant velocity part and I input a pitching moment. Model is used to test various tire, damper, arb, etc... settings. There are vertical displacment, yaw, roll, and pitch dof. When I came up with the equations for roll, yaw, and pitch they all ended up something like this;
Ixx(theta_roll_accel)=some terms
Iyy(theta_pitch_accel)=some terms
Izz(theta_yaw_accel)=some terms

So when I solved the above equations plus some others in simulink I needed to know the MOI. Maybe there's an easier way to write out the equations but this is just what I did. I do have track data to compare results of simulation to however I feel there is more than just adjusting the MOI to get the correct results as there are other terms that also affect things.

Scott

[flavorPacket]

Originally posted by Zac:
In my experience, inertia measurements are kind of a crapshoot, particularly with any sort of a simple/student built rig.

True. The differences between our CAD model, self-built rig, and professional rig results were enough to change our wheelbase and track.

[exFSAE]

Good point, Ben. Though I still maintain that as far as simulation goes in designing a car at this level that will handle very well, I would put a high priority on quasi-steady state work.

The TTC data is pretty iffy even on that (quasi steady state), much less anything really abrupt and dynamic.

I guess the better question, Scott, is what exactly is your end goal? What is the design criterion or objective for which you are building this tool?

When I was doing the "kinetic" half of our suspension design I was doing something very similar in Simulink. Wanted to see if I could pick damper rates that would critically damp the chassis roll and/or pitch, and what the effect would be. Not convinced that was the right approach when I look back at it... and if I should really have been looking at how the FORCES ramped at the tire or sprung mass, rather than how the sprung mass position was changing. I believe a good bit of 7-post damper tuning is aimed toward minimizing TLV, and without having really detailed data on tire, suspension, inertias etc I'm not convinced you could get very well in the ballpark from an analytical approach. Plus the competition surfaces at these events tend to be very smooth these days.

Also used an extension of it to look at effects of frame rigidity with step roll inputs. Again, don't think that was the right approach. I'm more convinced now that frame rigidity is more of a steady-state critical item.

I'll stop rambling now.

[scott_rfr]

exFSAE this tool is being built for several reasons. One is to pick damping rates as you have already stated. I wanted to build a model such that I can through some inputs at it and see how the car reacted given different, damper, spring, arb, settings or with different tires. Next reason was to further my understanding of both what was going on during the transient phase and build up more knowledge ( I have learned a lot building this model).

Maybe the approach I have taken at this problem is correct, maybe not. You said that you did something similar and looking back your not sure it was correct. If you were doing it all over again how would you approach the problem?

So the end goal of all of this is come up with different spring, damper, arb settings to go test.

Scott

[exFSAE]

Right, understood. Allow me to rephrase...

What model output are you looking for, that you could say "ok this is a good damper rate." Are you looking at a position vs time plot? Ie setting a rate that will critically dampen the sprung mass in heave / pitch / roll / whatever?

Or are you looking at force vs time? Stiff dampers will slow down the movement of an object, but will make the force ramp very quickly. Is that a good thing or a bad thing.

Or, are you looking at amplitude vs frequency? Ie looking at transmissibility and trying to tune your damper rates to minimize force transmission to the chassis, and minimizing tire load variation?

Or something else?

There's definitely "ride" items to be considering as well as "handling." Unfortunately of all the suspension bits, I have very little intuition regarding damper settings. I couldn't say off hand what having really stiff or soft dampers on either end of the car would do for handling.

I'm tempted to think that the dampers just give you additional temporary roll stiffness on entry and exit. Stiff rear dampers -> momentary shift of TLLTD to rear -> momentary "loose" tendency, and the opposite for stiff front dampers. But then you get into bump vs rebound and blah blah blah. There's the "rules of thumb" a la C. Smith's "Engineer in your Pocket" but until I see an explanation of WHY tune X has effect Y, I don't buy it.

The other thing to consider is just how long these "transient" events are, and if they're really dynamic or if they're almost quasi steady state in themselves. Is your driver using step-steer inputs, or are they smooth? With an overly stiffly sprung vehicle (like many FSAE cars) the time constant for the chassis taking a set in any mode of travel might be small compared to the duration of most maneuvers.

Dampers would be last on my tuning list. After springs, bars, differential, steady state fuel map, transient fuel map, camber, toe, and pressures. I'd set em so I have my "half way" setting picked to have the corner car model critically damped in bump, and then go from there and hope for the best.

[ben]

Not strictly on topic but an interesting passage I found googling the topic:


With regard to the yaw moment of inertia, a common concept in race car design is to concentrate the masses as much as possible near the centre of gravity. However, modern Formula One cars generate very large tyre lateral forces thanks to aerodynamic downforce. This fact and the usually long wheelbase allow to generate a very large moment about the vehicle yaw axis. Hence, it is not unexpected to find that the sensitivity of the performance with respect to yaw inertia is negligible for a very large range of inertias. At this stage the controllability issue appears more important, as it appears that increasing the yaw moment of inertia makes the car easier to control without penalising the performance.

" On Minimum Time Vehicle Manoeuvring: The Theoretical Optimal Lap"� D. Casanova Cranfield University PhD Thesis November 2000 (I think Mr Casanova now works for Red Bull, although the thesis was done with Renault F1)


Ben

[murpia]

For most racecars weight distribution and yaw inertia are not independent. Moving a mass to affect one will affect the other. When I once did a test on this, the weight distribution effect was dominant, i.e. you should go for the fastest weight distribution and not worry about inertia.

Doubly-so if you have to compromise CG height to get a target yaw inertia.

Writing this gives me deja-vu, so possibly the search will show up an older post on this topic...

Regards, Ian

[Zac]

Scott, it might be worth doing a sensitivity study for your model.

[scott_rfr]

Ben- that paper is really good. For anyone reading this if you go to Cranfield's site you can view a lot of dissertation papers for free.

Second right now I am looking at force vs. time. I am not exactly sure what my end criteria is going to be of "hey this is good". Right now I am stuck in a phase of well I could do x,y and z. They all have their pros/con but what will get me the fastest car with amateur drivers. I feel that in the past the springing of the car was way to stiff and I find this with many cars. While we need a fast responding car I feel that to many people (including my self) just through lots of spring at the car to get this. I'm not really sure what the best way to simulate the car or best way to look at the outputs to get the results I want. In the end I want to be able to say if I have this setting how will the car react; what will be the response, grip levels of tires, where exactly is the load going, etc... I know that a professional package such as Adams or Carsim is best for this we don't have the money for carsim at this point and I have Adams but need to find some time to learn. In the meantime I just started witting my own code and was going to build upon that as a good learning exercise and see what happened.

The comment about dampers giving you temporary additional roll stiffness is pretty interesting. For those who read RCE there was an article about preloading springs and the handling effects it has with shifting the roll moment distribution.

Scott

[ben]

I think if I was doing a car now I'd be looking at much softer springs and much higher roll centres/instant centres/FAPS/ delete as applicable http://fsae.com/groupee_common/emoticons/icon_smile.gif

Ben

[J. Vinella]

Oh good topic for a thread Ben. If you could do it all over again what would you do? Coming soon.

[BillCobb]

Couple of things to suggest:

Writing your equations in terms of mass to inertia ratio instead of mass and inertia will save you a lot of headache. There you find that that position of objects is more important than the total weight by itself. In fact the yaw and pitch radii of gyration can be boiled down even easier as the departure from 1.0 (Dynamic Index). Then from a database of real measurements, we find values for yaw (for example) of roughly -.2 to +.2 . This is something to connect with because the driver, motor and fuel loads are big hitters in changing it. (Lower numbers are "better").

Secondly, don't forget that you need the inertia and cross products of the heavy pieces, when adding up the total. The motor, driver, transmission and even wheels+tires need to be factored in. Just adding up point masses to get an inertia value is "pointless" and can be 40% off the actual and final value. A CAD 3d model with the right mass properties should be very close if you have correct dimensions and mass density figures. Some knife edge with springs table measurements to augment the CAD output are necessary. Don't forget the driver and helmet. Put them in a rocking chair seat and time how long it takes to put them to sleep....

[scott_rfr]

Ben you hit the nail right on the head of where I was heading design wise this year. Over the summer I tested (to the extent that I could adjust rch's) increasing rch and softening the springs. From the limited amount I was able to do it did improve performance. The negative side is you add the jacking force and has the cornering loads and rch get higher they start to become a factor. Neat way to do things it to make some 3d plots of rch, fy and f jacking for the lateral direction; then fx,fz,pch. You can quickly see where your point of no return is.

Bill how exactly would I write equations in "mass to inertia ratios". Not exactly sure how to do this.

Scott

[ben]

Interesting. Sort of where Mike Cook was headed in the thread the other week on RC migration. Some simple hand calcs show that jacking forces are negligible relative to the attitude towards them as being the root of all evil.

Question is; if you reduce the yaw inertia and increase the rate of load transfer are the transients too short for the driver to handle?

Ben

[scott_rfr]

Not really sure at which point the car responds faster than the driver can handle. Above I was kind of hinting at that with my comment on amateur drivers. Do you have any recommendation's as to how fast this should occur? This is an area I have been poking around with due to the fact that our yaw inertia should be decreasing along with the other things I have already said.

Scott

[murpia]

Originally posted by ben:
I think if I was doing a car now I'd be looking at much softer springs and much higher roll centres/instant centres/FAPS/ delete as applicable http://fsae.com/groupee_common/emoticons/icon_smile.gif

Ben
Mmmm... Warp soft...

Regards, Ian

[exFSAE]

Keep in mind, at these low speeds the tire may be a limiting factor in how quickly the car responds, rather than chassis with high RC's.

[B Hise]

A good dynamic sim that you can put some tire loads through is a great tool. It can also spit out enough data to keep you busy for a year. Finding metrics that can help you boil down the info is important.

One pitfall of 7 post work (sim and testing) is that it can lead the designer/engineer/whoever to soften the car too much or end up with something that drives like shit. Obsession with histograms and transfer functions can lead you down the wrong road. Common sense is important.

Studying the dynamic balance of the car is fruitful, and can really help you get a fast car comfortable. It doesn't have to be scary and twitchy to be fast.

Accurate MOIs are important, and knowing the axes that your inertia tensor moves about is too. If you could find somewhere to measure the car (old or new, compare as necessary) I would highly recommend it.

Jacking forces (x/y) are great when used properly.


Take everything you get out of your simulation with a grain of salt and make sure your findings make sense to the stopwatch and driver. Complete that loop and your car will be quick and you'll have learned a ton. Never use rules of thumb either, get to know YOUR car and tire.

-Bryan

[ben]

Originally posted by exFSAE:
Keep in mind, at these low speeds the tire may be a limiting factor in how quickly the car responds, rather than chassis with high RC's.

Good point - it would be interesting to see how much that varied between different tyres.

Ben

[Zac]

Originally posted by ben:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
Keep in mind, at these low speeds the tire may be a limiting factor in how quickly the car responds, rather than chassis with high RC's.

Good point - it would be interesting to see how much that varied between different tyres.

Ben </div></BLOCKQUOTE>

On the tire side I'd agree that transient effects are fairly significant. I've seen some tires on these cars that have less steady-state grip but run faster lap times because of improved turn-in response. Whether or not this is going to be more of a limiting factor than whatever someone does with suspension design or car setup I really can't say.

[ben]

Originally posted by ben:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
Keep in mind, at these low speeds the tire may be a limiting factor in how quickly the car responds, rather than chassis with high RC's.

Good point - it would be interesting to see how much that varied between different tyres.

Ben </div></BLOCKQUOTE>

Update: Stiffening lower sidewall = fun...

http://www.ubracing.co.uk/ubr2009/

Ben

[exFSAE]

-3 seconds on a 30 second lap. Not bad I guess http://fsae.com/groupee_common/emoticons/icon_smile.gif

[ben]

That says more about how horrificaly bad the first spec was and the variation in driver skill in this competition.

I'd say a solid second or two better than what we raced this season. New compound was good two. One more test early next year to determine final compound choice, but new construction's definitely confirmed.

Ben

[Sander]

On the website of our team (University Racing Eindhoven) is a video of how we measured the moments of inertia. http://www.universityracing.nl/?p=484

The results are being processed now, we dont think it is deadly accurate because there are a few errors but after filtering those out with calculations, it will give us a good impression.

[mech5496]

Sorry for bringing this back from the dead, but I am trying to find a discussion on track width and MoI and its effects on laptime I have found some time ago. I think somebody has plotted a trajectory vs track in a slalom somewhere (if this helps). Sorry again, but I am messing around with the search function for about an hour but with no luck!

[Crispy]

Thread: "Any way to objectively choose engine?" - Page 17

maybe?

[nowhere fast]

It sounds like you might be reffering to my post in the thread mentioned by Chris.

Link here:
http://www.fsae.com/forums/showthread.php?1389-Any-way-to-objectively-choose-engine&p=29439

[mech5496]

Yeah! No wonder WHY I could not find it by using the search function on thread titles! Chris and Nathan thank you very much!