Numerical Analysis of Brake Rotors

[KeithYoung]

Transient will be more complicated, certainly. That's why I'm ignoring it at first. However once I have my model dialed in adding it in won't be prohibitively difficult. Plus there is alot of literature on transient braking, more so in fact that on steady state brake heat (which is difficult to find).

Also it looks like I'll have some access to help. This morning when I go to school I have a professor that wants to see the project. He has simulated the 1D acceleration and braking of a car negotiating a given race line. With my model coupled with his, we could theoretically model the brake temperature over a lap on some famous circuits. Plus I am involved in some of his funded research so I have more access to his help and time than most students.

Thanks for the input Riff.

FYI everyone, I have started my first article (mostly because I ran in to my first brick wall in trying to change to a cylindrical system. There are basically 11 equations I have to put in that are 2 full widths of a page in length. I need to find a way to simplify these MESSY equations, but in the mean time, it's easier to write ) It should be posted in the near future.

[you_nes]

Would love to see this, so many input variable and non-linearities in an f1 brake system!

When you say simulate brake rotors, what exactly do you mean?
Flow, thermal, friction,...?

I would not even know where to begin on a flow prediction through a moving rotor.

I have however done several energy balance style hand calculations for thermal capacity of steel/ceramic brake rotors in the past, assuming constant mue and linear thermal emissivity wrt temperature and excluding conduction. These are usually pretty safe because they always over estimate energy in and under estimate energy out, so in reality your rotor runs cooler than the calc says.

I would imagine though that with a carbon carbon brake system the constant mue assumption would produce bad results, since its well documented that mue is heavily temperature dependent in this system.

Still, would be great to see your methods.

[olefud]

I’m probable missing something; but what is “steady state” as you use the term. It suggests equilibrium between heat generated and heat rejected. I suppose there is a light clamping pressure under which this can be obtained, but at least iron rotors are pretty much duty cycle devices, i.e. the rotor functions as a heatsink that net accumulates heat during a limited claming cycle and rejects the heat while clamping is released. But then maybe carbon brakes can run 100% duty cycles at high temps since radiant cooling is the primary heat-rejection mechanism.

[PlatinumZealot]

His input parameters are constant. Instead of changing over time.

[KeithYoung]

Would love to see this, so many input variable and non-linearities in an f1 brake system!

When you say simulate brake rotors, what exactly do you mean?
Flow, thermal, friction,...?

Mainly temperature distribution

I would not even know where to begin on a flow prediction through a moving rotor.

To begin that I would assume a brake duct inlet area, airspeed, and equal air flow through each vent.

I have however done several energy balance style hand calculations for thermal capacity of steel/ceramic brake rotors in the past, assuming constant mue and linear thermal emissivity wrt temperature and excluding conduction. These are usually pretty safe because they always over estimate energy in and under estimate energy out, so in reality your rotor runs cooler than the calc says.

Currently emissivity is constant but that is one among many simplifying assumptions I will be eliminating.

I would imagine though that with a carbon carbon brake system the constant mue assumption would produce bad results, since its well documented that mue is heavily temperature dependent in this system.

Non constant friction coefficient is currently assumed and may be eliminated later.

Still, would be great to see your methods.

The current, simplest form will be released shortly. It's current form is NOT a good indicator of the temperature distribution. It is an initial step to make sure my code is functional

I’m probable missing something; but what is “steady state” as you use the term. It suggests equilibrium between heat generated and heat rejected. I suppose there is a light clamping pressure under which this can be obtained, but at least iron rotors are pretty much duty cycle devices, i.e. the rotor functions as a heatsink that net accumulates heat during a limited claming cycle and rejects the heat while clamping is released. But then maybe carbon brakes can run 100% duty cycles at high temps since radiant cooling is the primary heat-rejection mechanism.

The code is full of simplifying assumptions, one of which is steady state. In my method of producing steady state, I guessed the duty cycle of a car braking around sebring this way. A certain amount of heat enters the brakes when entering hte hairping. I divided that by time for a heat rate. I then watched onboard laps and decided this amount of heat rate happens for 10% of the lap.

I doubt real F1 brakes can operate at 100% duty cycle. Now that you mention that it will be interesting to eventually see how much duty cycle they can handle, for example Canada GP

His input parameters are constant. Instead of changing over time.

Correct.

[olefud]

Understood. Thanks

[Caito]

What's wrong with Fortran? I'm not a software/computer guy, so please educate me. The reason I'd see possibly doing it is Matlab is horrible when it comes to loops, and in order to have a small step size/large number of elements that greatly increases the number of loops required. Also, I don't think our "supercomputer" run Matlab code. Switching to Fortran would enable an immense jump in computing power due to the code and circumstances.

Plus I thought Fortran was free, isn't it? Matlab isn't free to most people here. Let alone if I use a command that happens to be in some special toolbox.

Let me know. Thanks!

A small intake into this. If matlab is too expensive, use octave, or the french version of matlab which is free and I really don't remember the name.

Matlab is not optimized to do loops, that's right. Matlab means MATrix LABoratory, it's highly optimized to do matrix calculations. In most of the cases a loop can be transformed into matrix form. Might or might not be your case.

BTW, you can usee all cores and the GPU to greatly increase the speed of matlab if you're using a personal computer.

[Jersey Tom]

Matlab is not optimized to do loops, that's right.

I'd say the JIT compiler they've put in sometime in the past few years makes a pretty big difference.

By far, poor pre-allocation of an output matrix is a much much much bigger computational killer than anything with how it does loops. IMO anyway.

[KeithYoung]

I may try to incorporate repeated matrix operations. Then problem with it is there will be very large matrices, and likely sparse matrices, which may become unwieldy. In fact now would be the time to try it while the model is at it's simplest. I'll look in to that.

[Jersey Tom]

Also, don't believe you'll be able to take advantage of multiple cores or parallel processing for this type of problem where you have to solve each time step before the next. Doesn't lend itself to distributed computation.

[Caito]

Also, don't believe you'll be able to take advantage of multiple cores or parallel processing for this type of problem where you have to solve each time step before the next. Doesn't lend itself to distributed computation.

What you can do with multicores is something like this:



yn=a*x +b*x'+c*x'' .. etc.


a*x is solved by one processor,
b*x' is solved by another and so on.
the addition is made at the end.

GPU can have over 60 processors. Any cheap GPU nowadays has at least 16.

[ringo]

enough talking guys. Start the theory. I mean numbers not paragraphs.

[KeithYoung]

enough talking guys. Start the theory. I mean numbers not paragraphs.

That should happen soon. My apartment was struck by lightning (again) and this time it fried some stuff.

FYI there will be numbers, but there will also be alot of paragraphs. I wrote this in Word, when I put it in WordPress I have no idea how it will look. But yes, there will be numbers, and some pictures, but also a lot of paragraphs.

[PlatinumZealot]

Also tell us what principles, equations and even algorithms you are using for each step. I think it there is something to learn from this.

[KeithYoung]

That will be after this post. I do have it documented. I don't want to explode WordPress with a writing over 15 pages