Numerical Analysis of Brake Rotors

[KeithYoung]

Posted

http://racingtech.wordpress.com/2012/04 ... e-problem/

[KeithYoung]

Let me hear any criticism.

I have yet to sort out why exactly the order of accuracy is 1 insetad of 2. Central Differences, I think, are often 2nd order accurate. So I will have to explore my truncation error. I should find the answer to this soon.

I also plan on releasing the current math model in the near future, right or wrong. If it's wrong, I may delay release in order to explain in the same writing why it is wrong. Otherwise I will explain any mistakes in a later writing.

[KeithYoung]

The math model used for the initial run has been released.

[riff_raff]

rough_wood,

I can't really comment on your math model because I don't have any expertise in this area. But with regards to carbon-carbon material properties there are a few peculiar issues to consider. As others noted, the thermal conductivity and Mu can vary with temperature. I also understand that thermal conductivity can vary with respect to lateral/transverse/longitudinal directions.

CRC materials also have definite temperature limits due to oxidation. The number I recall seeing is about 1500degF, but I don't have any data for current F1 brake materials.

Lastly, since this seems to be related to an engineering undergrad study, I'd recommend that you try contacting the racing brake manufacturers (Brembo, AP, etc.) and see about getting them to support your efforts. What you are attempting to do is quite ambitious, and I would imagine creating such an analytical model is beyond what the racing brake suppliers would typically attempt. They don't have the manpower or financial resources for such efforts.

Regards,
riff_raff

[KeithYoung]

rough_wood,

I can't really comment on your math model because I don't have any expertise in this area. But with regards to carbon-carbon material properties there are a few peculiar issues to consider. As others noted, the thermal conductivity and Mu can vary with temperature. I also understand that thermal conductivity can vary with respect to lateral/transverse/longitudinal directions.

CRC materials also have definite temperature limits due to oxidation. The number I recall seeing is about 1500degF, but I don't have any data for current F1 brake materials.

Lastly, since this seems to be related to an engineering undergrad study, I'd recommend that you try contacting the racing brake manufacturers (Brembo, AP, etc.) and see about getting them to support your efforts. What you are attempting to do is quite ambitious, and I would imagine creating such an analytical model is beyond what the racing brake suppliers would typically attempt. They don't have the manpower or financial resources for such efforts.

Regards,
riff_raff

Yes, those assumptions are only temporary.

As far as the temperature, they are below failing temperatures in carbon carbon heat shielding on re entry vehicles, however I don't know maximum temperatures of brakes. Another thing to note, is it's still just a slab and I assumed a duty cycle of 3 G braking since for now the model is treated as steady state.

As far as contacting companies that's not a bad idea, but I'd care to bet they've done some homework themselves. I know owning brake dynos is standard operating procedure for racing brak manufacturers.

Thanks for the input.

[Jersey Tom]

So how long does it take to solve? Didn't need a super computer after all?

[KeithYoung]

Once I included a relaxation factor by longest run was 871s, or 14.5min.

The problem will begin when I an accounting for laminar and turbulent flow within brake vents around a cylindrical system, as well as non constant properties such as thermal conductivity, nusselt number/convection, and emissivity. Given my lack of experience I don't know how many iterations will be required for a decent residual, or how many iterations can be done in a minute given the extra complexities. I am currently working on both changing to cylindrical as well as eliminating loops and replacing them with matrix operations to speed up the code.

For the time being though, yeah I'll be sticking with Matlab on my 5 year old laptop (poor thing).

[riff_raff]

.......As far as the temperature, they are below failing temperatures in carbon carbon heat shielding on re entry vehicles, however I don't know maximum temperatures of brakes. Another thing to note, is it's still just a slab and I assumed a duty cycle of 3 G braking since for now the model is treated as steady state.......

rough_wood,

Sorry if it's not helpful to your modelling, but just a couple more comments about CRC brake materials:

There are two basic types of commercial CRC friction materials, PAN based and pitch based. In general, the PAN based materials tend to have better structural properties, and the pitch based materials tend to be tougher. I believe both types are used for aircraft brakes, but I don't know about racing brakes.

When both the rotor and pads are made from CRC, it presents a different wear situation than that existing in conventional metal brake rotors. With CRC pads and rotors, both are subject to significant wear. The section and mass properties of the CRC rotor may change appreciably over the course of a race. Many years ago when CRC brakes were first introduced to F1 racing the rotor wear rate was quite high, but I don't know what it currently is. Reduced thermal mass and section thickness will affect both heat transfer and mechanical stress in the rotor.

Just more things to consider in your brake model.

slider

[KeithYoung]

.......As far as the temperature, they are below failing temperatures in carbon carbon heat shielding on re entry vehicles, however I don't know maximum temperatures of brakes. Another thing to note, is it's still just a slab and I assumed a duty cycle of 3 G braking since for now the model is treated as steady state.......

rough_wood,

Sorry if it's not helpful to your modelling, but just a couple more comments about CRC brake materials:

There are two basic types of commercial CRC friction materials, PAN based and pitch based. In general, the PAN based materials tend to have better structural properties, and the pitch based materials tend to be tougher. I believe both types are used for aircraft brakes, but I don't know about racing brakes.

When both the rotor and pads are made from CRC, it presents a different wear situation than that existing in conventional metal brake rotors. With CRC pads and rotors, both are subject to significant wear. The section and mass properties of the CRC rotor may change appreciably over the course of a race. Many years ago when CRC brakes were first introduced to F1 racing the rotor wear rate was quite high, but I don't know what it currently is. Reduced thermal mass and section thickness will affect both heat transfer and mechanical stress in the rotor.

Just more things to consider in your brake model.

slider

No man thanks for your input. Keep it comin.

[riff_raff]

rough_wood,

Here's some useful data on CRC rotor wear and operating temps for GT/LMP race applications on AP's website:

http://www.apracing.com/Info.aspx?InfoI ... ductID=979
http://www.apracing.com/Info.aspx?InfoI ... ductID=979
http://www.apracing.com/Info.aspx?InfoI ... ductID=979

Hope it helps.
riff_raff