Brake Single Stop and Fade Stop temperature rise

Could you please indicate where you found the equations?

It is better to analyse them in their context.

I had a look at the equations as you describe them. there is a major error since the flux is per area unit and the temperature is deducted from a total energy balance. The factor which was missed is the area upon which the flux is directed to the brake.

But please give the origin as stated it helps to analyse how this error occured.

My experience in this area applicible to passenger cars and light trucks.

The standard text for brake calulation is

Brake Design and Safety

By Rudolf Limpert

http://books.google.com/books?id=Oq6p4owZhn4C&dq=brake+limpert

major point missing in your question is what temperature do you want for your answer?

Do you want Surface Temperature? (harder)

or

Do you want bulk Temperature? (easier)

Here is the calculation for bulk from Page 159 of Limpert's book.

Temperature Rise for one front brake (Celcius) =

(Front braking percentage/2)*((W*(Vi^2-Vf^2)/(2*g*RHOr*Cr*Vr))

where Cr = rotor specific heat, Nm/Kg*k

Vi = initial velocity, m/s

Vf = final velocity, m/s

Vr = rotor volume, m^3

W = vehicle weight, N

RHOr = rotor density, Kg/m^3

standard grey cast iron specific heat Cp = 420 Nm/Kg*k

if you need rotor density use 7220 Kg/m^3 for grey cast iron

Through FEA and testing we have found that only 80-90% of the heat gets into the rotor. Part of the equation misses the heat lost into the brake pads. Different pad materials require a different factor. Most non asbestos organic compound (passenger car long life) pads match FEA best using 85% correction factor.

Thanks Smith for the reference, you are right in saying I have to decide which temperature I should consider and in my opinion it should be the surface temperature. The purpose of my calculations however is for concepting of a full transmission including the brake and I don't want to have exact figure just a ballpark. Therefore it would be sufficient for me to have an empirical temperature based on the bulk temperature translated to a surface temperature (if that would be at all possible). I could say for example that the surface temperature is twice the bulk temperature and most likely I would be incorrect as it very much depends on the thickness (volume) of the disc. Another option could be to consider a minimum thickness of the disc hoping that this would sufficiently approximate the surface temperature. I am talking about allowable inaccuracy of say 10%. Any suggestions are appreciated.

One item that might help you is to consider the bulk and the surface temperature initially diverge but at the onset of brake fade temperatures they converge again. The fade action decreases the heat flux into the rotor. So most high decel stops have almost constant temperature across the rotor after about 5 seconds of constant decel apply time. This holds true for light trucks and passenger car rotors but not for racing, aerospace, train or heavy duty truck applications.

Oops, does that mean I am stuffed then? My application is for heavy duty machinery like dumper trucks etc. Do you have any idea on how it is different for this type of application. Think weights of 4 to 10 tonnes and speeds of say 25kph and decelleration of maybe 1.5m/s^2 would it still be critical in that case and if yes where does it start to become critical.

I know this is a lot of questions to ask but I am completely new in the brake side of engineering so I hope you guys will be patient with me.