Sanity check for my braking calcs

[Bazanaius]

Hey guys, actually posting on behalf of another team member who isn't registered on here (yet :-).

He has done some good work on looking at our braking system and modelling its performance. So far all seems well - the system we are looking to use this year is quite similar to last years and so far things seem to agree with what we saw quite well (including predicting just how close we were to not passing brake test last year!).

We're now looking at the thermal side of things and we'd just like a sanity check on the kind of numbers we're getting out as they seem quite high. The plot below is the predicted brake disc temperature over a 20 lap period, for three different diameters.

Yellow is 200mm diameter, and as you can see it reaches a stable temp of about 750deg Celsius!

Pink is 215mm and the blue is 254mm, stabilizing at around 490 deg Celsius.

To us this seems a bit high, particularly as the data we've got from our pad supplier suggests 600deg is where the performance starts to drop off significantly. We used tool (gray) steel last year for our discs with no problems, however I'm having trouble getting hold of any really useful data in terms of operating temperatures for this material, particularly with the regular thermal cycles it will be subjected to.

What kind of brake disc temps do you guys normally see/predict/measure? Bear in mind our car isn't the lightest (expected ~350kg with driver)!

For those inclined, in terms of modelling the brake disc has been subjected to the heating rate taken from some on-track data received a few years ago. This has been decreased by the expected cooling rate due to convection and radiation, and then this net heating rate integrated over time.

http://img398.imageshack.us/img398/9338/tempplotsfb1.th.jpg (http://img398.imageshack.us/my.php?image=tempplotsfb1.jpg)

cheers!

Baz

[Bazanaius]

Hey guys, actually posting on behalf of another team member who isn't registered on here (yet :-).

He has done some good work on looking at our braking system and modelling its performance. So far all seems well - the system we are looking to use this year is quite similar to last years and so far things seem to agree with what we saw quite well (including predicting just how close we were to not passing brake test last year!).

We're now looking at the thermal side of things and we'd just like a sanity check on the kind of numbers we're getting out as they seem quite high. The plot below is the predicted brake disc temperature over a 20 lap period, for three different diameters.

Yellow is 200mm diameter, and as you can see it reaches a stable temp of about 750deg Celsius!

Pink is 215mm and the blue is 254mm, stabilizing at around 490 deg Celsius.

To us this seems a bit high, particularly as the data we've got from our pad supplier suggests 600deg is where the performance starts to drop off significantly. We used tool (gray) steel last year for our discs with no problems, however I'm having trouble getting hold of any really useful data in terms of operating temperatures for this material, particularly with the regular thermal cycles it will be subjected to.

What kind of brake disc temps do you guys normally see/predict/measure? Bear in mind our car isn't the lightest (expected ~350kg with driver)!

For those inclined, in terms of modelling the brake disc has been subjected to the heating rate taken from some on-track data received a few years ago. This has been decreased by the expected cooling rate due to convection and radiation, and then this net heating rate integrated over time.

http://img398.imageshack.us/img398/9338/tempplotsfb1.th.jpg (http://img398.imageshack.us/my.php?image=tempplotsfb1.jpg)

cheers!

Baz

[Drew Price]

That sounds pretty hot to me....

How thick are your rotors?

I feel like you might be misrepresenting the cooling of the rotors, but without going through your whole analysis it's impossible to say, you'll want to take a look over it again.

I will say that we used <STRIKE>"1/4"</STRIKE> 0.188" thick 8.25" dia (about 210 mm) and they never got anywhere near that hot with Ferodo DS3000 pads, I don't know what the peak temps were though, but we had no trouble passing brakes, and never any fade issues with Wilwood 570 fluid, and Wilwood PS-1 calipers.

Best,
Drew

[Bazanaius]

Hi Drew,

our brakes are only 5mm thick, a bit thinner than yours.

We're aware that the brake model is based upon some approximate coefficients in the cooling model, particularly for the convection model. This is why we're looking for comparative figures, to see whether we're off base or it just needs further refinement.

Ideally we'd be able to match these to real numbers from last years car, but it doesn't look like we're going to be able to test until it's too late :-( I'm wondering if maybe there's something we can do on a bench...

B

[Drew Price]

You know, now that you say that, I remember that our rotors are 0.188" thick, not 0.25", so 4.75mm, sorry about that.

No way you can do any testing, even taking it out for a few runs up and down with hard stops and hit it with an IR temp gun, just to see what you get after a min?

I don't imagine your weather is any better than ours for testing right now though, hopefully someone else chimes in with some numbers.

Best,
Drew

[Bazanaius]

Alas, the weather is the least of our problems! Last time we had it running it was -2 degC (which might be normal for somewhere like Finland, but is flipping cold for the UK!). Unfortunately our problem is a lack of somewhere to go for a spin, and currently a lack of ability to get there :-(

If anyone has any numbers we would be very appreciative. I think it is simply that our coefficients are not accurate at the moment, despite our model not being bad. If anyone can provide numbers for a Gray Steel (or similar) brake disc along with dimensions we might be able to at least make something we can then confirm when we finally get a test in.

B

[jrickert]

Why not make different rotors and test. On the cheap you can buy temperature sensitive paint that changes when it gets over a certain temp.

[Bazanaius]

Changing the size of the rotors would mean that we'd need to move the brake calipers, and therefore make different uprights for each one no?
We really just don't have the budget for that expenditure, but certainly temp sensitive paint will probably be what we use when we finally get last year's car out on the track.

B

[terra_dactile]

Hi Bazanaius,
Have you thought of doing simple hand calculations using basic formulas to evaluate your heat disiipation needs based on energy to decelerate your car from say worst case 100km/h in comp to Zero. Once you have this qty of energy from Total energy = (Mass with driver) *(Vint-Vfinal)squared; where energy is in joules and mass in kilograms and velocity in m/s. This total energy has to dissipated by 4 disks. When you do load tranfer calculations you see how much of the percentage of braking torque is accomplished by the front (say 60-75 % of energy), Next split the energy calulated above into front / rear energy then use the equation in thermodynamics that tell you your raise in temperature depending on totaly energy dissipate, material properties and mass of say one disk. The mass of the disk will be the unkown parameter since you will set your maximum temperature raise depending on what temperature it is out side(ambient) and what is your max safety temp recommended by pad manufacturers. With these simple calculations you will have a amount of mass that would scare you to put on the car. It ussually is pretty low and you cant forget that once the discs reaches it operating temperature you might need to due this type if braking manuever. The point is that as is repeated often a model is only as usefull as the precision of parameters you enter, the more assumed variable the less chance you have of getting a valid model.
I have recorded temperature upwards of 275 deg C on the front discs using infrared temp sensors that are on the car during a endurance validation. It gives a tendency similar to what you have showed from simulation, but since it was a autocross style track, their are much more variations in temperature then in your model. I dont think that it will follow your trend exactly but you have already chosen a steel that has better heat dissipation properties per mass then what i use, Grey is much better then our O1 tool steel. But our tool steel is precision ground and has good wear proerties because it is between 60 and 62 rockwell C.

We have a 150-160 kg car with a 70-80 kg driver and our disks in the front have a mass of 300-375 grams. Hand calculations recommend 100-150 grams per corner.

Their are other concerns though since our disks are floating, with solid mounted disk the max temp we could attain was much lower because it would warp so bad that even when not pushing on the brakes the disk was pushing one piston of the caliper to its max travel (PS1) MEANING IT WAS STEALING USEFULL hp.

A quick solution would be to check with the calipers you had last year to see if you can get thicker disks, we use 1/8 thick disks (3.175mm).
But I WOULD BE CAUTIOUS: If your only basis to say that you current disk are over heating is the simulation I would validate with the car using some sort of temeprature paint, hand held infrared tool or live infrared sensors ( best Choice). We saw upwards of 100 deg C drops in temperature from track running temp 10 seconds later when finally stopped in the pits meaning a hand held sensor with a non adjustable imissivity setting is pretty much a rule of thumb tool to use and does not have much meaning if you are look more maximum conditions of the brake. Temperature paint is cheap and the most will give you good results.

Sorry for this long message/ramble ( I feel like that Geoff guy from RMIT)

Hope that some of this long essay was usefull to you.

Jude Berthault
ETS FSAE 2004-2009
Technical Director

[Bazanaius]

Hi Terra,

Indeed the calculations for how much energy needs to be dissipated by the disc stopping from (say) 100km/hr was a starting point for the brake thermal design, and we came up with a delta Temp of around 200degC for our front discs from last year. Which sounds about right since 100km/hr is pretty quick!

From here, we moved on to looking at how the discs would behave over repeated applications of the brakes with cooling periods in between, as is the case during autocross/endurance. For this we managed to gather some data from a past track which detailed the time of application of brakes, and periods of no brake application for a lap. This was then fed into a simulation which calculated the instantaneous power in (analagous to the energy calc done above) and the rate of cooling out; this net heat rate was then summed over time to establish the temperature of the brake disc during a race.

I think that the additional weight that you require in your brake discs, different to that suggested by your energy calc above, is that the brake doesn't have time to cool fully between applications. For this reason, it must be able to operate at higher temps (or hold more heat) and thus be heavier. At some point the in/out will reach equilibrium at a certain disc temp, which is what we're seeing in the plot in my first post.

It's looking more and more like we're gonna have to go safe and then confirm our results with testing later unless someone can provide concrete data - although your 275+ deg is good for guidance Terra. Cheers!

Baz

[dazz]

Be sure to look at the whole picture when comparing different size rotors. 254 'vs' 200mm dia. gives 27% longer moment arm and an increase in relative speed of the pad contacting the rotor. Total work done (heat generated) should still be the same, but brake feel & feed back to the driver needs to be considered. Better feel leads to later, harder braking. More sudden & higher temp spikes in your data? Longer cooling periods between brake applications? Of course this all depends on your driver & the track conditions & layout...

All I'm trying to say is that your calcs are only one piece of the puzzle.

[Bazanaius]

Agreed Dazz. We've got hold of some other logged data and we'll be running this through the same model to see how it compares. In addition we'll be running a data logger for the first time this year and we'd look to get it hooked up to the 2008 car for some testing later this term - this will give us some more data (and also include in it the different driving styles of our driver) and hopefully help us develop this further.
This is the first year we've looked into this in detail and the hope is that the development will continue into next year as well, so if nothing else this year's choice will provide some useful data for next years :-)

[Alastair Clarke]

A few years back we used some of the temperature sensitive paint on the outer edge of our disks and this we logged just under 200 deg C as a max temp. This won't be the highest temp the disk get to though, but it's quite hard to get paint to stay on your friction face of the disk!!!! Could have coated the bore of one of the cross drilled holes though - next time!!!!

Al