Jonny Rochester
03-31-2015, 05:34 AM
I am looking at brakes. To preserve the UTAS 2014 we must buy everything again.
Background: 2014 car used 3 Wilwood Dynalite brakes, with aluminium discs, and 3/4" MC's. It worked well. To buy again we will probably use steel discs, but first I must do calculations for the old car to see if the numbers work out. But also I am thinking from first principles for designing brakes. Please forgive my language as I wrote the following for myself, or internal use...
Thinking out loud:
Consider our desired acceleration goal with a 600cc. If we are able to accelerate to 75 meters in 4.0 seconds, s=ut+(1/2)at2 → acceleration is 9.4m/s^2 or nearly 1g. To feel confident in a vehicle you want the brakes to be better in deceleration than the car is in acceleration. We aim for braking of more than 1g.
Also consider, our best decelerating (braking) needs to be limited by the tyres. This is a requirement for our brake lockup test. Our brakes need to be more capable of decelerating the car than our tyres (otherwise lockup can't be achieved).
From some info on the forums, at FS Austria one year they measured deceleration. Some of the best cars got to 95km/h then came to a stop in 22 meters. v2=u2+2as → means a deceleration of 16m/s^2 or about 1.6g. This would be limited by tyres, which may have a mu of 1.6. Some cars got over -1.6g. (With no aero 1.6g means tyre mu of 1.6).
From this info, new tyres are capable of 1.6g. We need brakes that are better than this. If we design for 1.6g then include a safety factor that may work OK.
Under max braking the vertical weight on the front wheels is higher than the rear. This could be calculated knowing CoG and other things, or we assume about 65 or 70% weight (and braking) is on the front. (Weight% on the front changes with CoG and deceleration. It maybe more like 80% at 1.6g).
With a chosen brake setup, we can use all the measurements to calculate fluid pressure and brake pedal force at 1.6g deceleration. And we check that fluid pressure is less than the component manufactures limit, and also that the drivers leg force required is not going to cause fatigue.
Also, we have selected a new brake calliper, 2 piston fixed. At this point our faculty adviser suggests we use 4 piston callipers because of their "feel". I say we can't account for that with this level of calcs so can't consider it.
Moving along... The next thing is to use energy calculations to size the thermal mass of the brake discs.
KE=(1/2)mv2 gives the energy required to convert into heat energy. Using v as the max speed, decelerating to 0km/h, and m the mass of the vehicle. Q = Cp.m.ΔT is the amount of heat energy put into the discs. m is the weight of all discs in grams. Cp is the thermal capacity of the disc material. Putting this together:
(1/2)mv2 = Cp.m.ΔT
Also checking the temperature range of the pads used to avoid pad fade. Some general assumptions are needed thinking about brake cooling and heat soak of other components, and duty cycle. For reference, another teams steel disc is 417g which is on the small side of OK.
Some general numbers I found:
max fluid pressure 1000psi, (Brembo say 1015psi, Wilwood say 1500psi)
Brake pedal has 6:1 ratio to the tip of the pedal, but effective 5:1 where the foot presses
Foot force between 250N and 500N
Brake pad pressure not over 12N/mm^2
Organic pads mu ~ 0.4
Sintered pads mu ~ 0.65 (Wilwood have graphs of brake pad specs)
Aluminium disc mu 0.47 (Wilwood PolyMatrix Q)
Front and rear master cyl. diameters maybe different.
Assume balance bar provides 1/2 pedal force to the front brakes, can be adjusted.
Cp for steel is 0.466
Cp for aluminium is 0.897 (Joules per gram per kelvin)
Brake pad fade temp ~400 degrees or 700 degrees for racing pads?
I calculated out our 2014 car with these assumptions and to brake at 1.6g we would have a foot force of about 300N.
Fluid pressure = 2.6 N.mm^2 = 377psi
Brake disc (aluminium) after 1 braking event from 150km/h, 173 degrees C.
I did this again thinking about a 5mm thick steel disc, braking from 150km/h I think it gets to ~700 degrees C if using a 500g disc. This is assuming all kinetic energy is transferred to heat energy in the discs. With the basic outer dimentions of our disc it would be 1kg, so we drill holes in it till its ~500g, which also increased cooling by convection...
So... this is all a embarrassing mess.
What model should I be using? Our faculty adviser says we should not make our own brake discs because it would take too long (a PhD or someone spending 18 months research) to understand material properties and do enough testing... :eek:
Background: 2014 car used 3 Wilwood Dynalite brakes, with aluminium discs, and 3/4" MC's. It worked well. To buy again we will probably use steel discs, but first I must do calculations for the old car to see if the numbers work out. But also I am thinking from first principles for designing brakes. Please forgive my language as I wrote the following for myself, or internal use...
Thinking out loud:
Consider our desired acceleration goal with a 600cc. If we are able to accelerate to 75 meters in 4.0 seconds, s=ut+(1/2)at2 → acceleration is 9.4m/s^2 or nearly 1g. To feel confident in a vehicle you want the brakes to be better in deceleration than the car is in acceleration. We aim for braking of more than 1g.
Also consider, our best decelerating (braking) needs to be limited by the tyres. This is a requirement for our brake lockup test. Our brakes need to be more capable of decelerating the car than our tyres (otherwise lockup can't be achieved).
From some info on the forums, at FS Austria one year they measured deceleration. Some of the best cars got to 95km/h then came to a stop in 22 meters. v2=u2+2as → means a deceleration of 16m/s^2 or about 1.6g. This would be limited by tyres, which may have a mu of 1.6. Some cars got over -1.6g. (With no aero 1.6g means tyre mu of 1.6).
From this info, new tyres are capable of 1.6g. We need brakes that are better than this. If we design for 1.6g then include a safety factor that may work OK.
Under max braking the vertical weight on the front wheels is higher than the rear. This could be calculated knowing CoG and other things, or we assume about 65 or 70% weight (and braking) is on the front. (Weight% on the front changes with CoG and deceleration. It maybe more like 80% at 1.6g).
With a chosen brake setup, we can use all the measurements to calculate fluid pressure and brake pedal force at 1.6g deceleration. And we check that fluid pressure is less than the component manufactures limit, and also that the drivers leg force required is not going to cause fatigue.
Also, we have selected a new brake calliper, 2 piston fixed. At this point our faculty adviser suggests we use 4 piston callipers because of their "feel". I say we can't account for that with this level of calcs so can't consider it.
Moving along... The next thing is to use energy calculations to size the thermal mass of the brake discs.
KE=(1/2)mv2 gives the energy required to convert into heat energy. Using v as the max speed, decelerating to 0km/h, and m the mass of the vehicle. Q = Cp.m.ΔT is the amount of heat energy put into the discs. m is the weight of all discs in grams. Cp is the thermal capacity of the disc material. Putting this together:
(1/2)mv2 = Cp.m.ΔT
Also checking the temperature range of the pads used to avoid pad fade. Some general assumptions are needed thinking about brake cooling and heat soak of other components, and duty cycle. For reference, another teams steel disc is 417g which is on the small side of OK.
Some general numbers I found:
max fluid pressure 1000psi, (Brembo say 1015psi, Wilwood say 1500psi)
Brake pedal has 6:1 ratio to the tip of the pedal, but effective 5:1 where the foot presses
Foot force between 250N and 500N
Brake pad pressure not over 12N/mm^2
Organic pads mu ~ 0.4
Sintered pads mu ~ 0.65 (Wilwood have graphs of brake pad specs)
Aluminium disc mu 0.47 (Wilwood PolyMatrix Q)
Front and rear master cyl. diameters maybe different.
Assume balance bar provides 1/2 pedal force to the front brakes, can be adjusted.
Cp for steel is 0.466
Cp for aluminium is 0.897 (Joules per gram per kelvin)
Brake pad fade temp ~400 degrees or 700 degrees for racing pads?
I calculated out our 2014 car with these assumptions and to brake at 1.6g we would have a foot force of about 300N.
Fluid pressure = 2.6 N.mm^2 = 377psi
Brake disc (aluminium) after 1 braking event from 150km/h, 173 degrees C.
I did this again thinking about a 5mm thick steel disc, braking from 150km/h I think it gets to ~700 degrees C if using a 500g disc. This is assuming all kinetic energy is transferred to heat energy in the discs. With the basic outer dimentions of our disc it would be 1kg, so we drill holes in it till its ~500g, which also increased cooling by convection...
So... this is all a embarrassing mess.
What model should I be using? Our faculty adviser says we should not make our own brake discs because it would take too long (a PhD or someone spending 18 months research) to understand material properties and do enough testing... :eek: