Brake system design formulas...?

[Homemade WRX]

Hi, I'm having a hard time finding formulas for designing brake systems. I was wondering if anyone had any info or any particular books that were of any great help to them.
Thanks, Micah

[audi fan]

The Brake Handbook from Fred Puhn is an excellent place to start. I designed the brakes for the '05 UoG Car using it and they work like a charm. I entered all the formulae into an Excel spreadsheet and played around with master and caliper bore sizes to see what would work best.

Chris Quinke
Gryphon Racing '04, '05

[Homemade WRX]

Originally posted by audi fan:
The Brake Handbook from Fred Puhn is an excellent place to start. I designed the brakes for the '05 UoG Car using it and they work like a charm. I entered all the formulae into an Excel spreadsheet and played around with master and caliper bore sizes to see what would work best.

Chris Quinke
Gryphon Racing '04, '05
thanks for the help...I will have to find it.

[jack]

uh..like..carroll smith, dude...

and..like..do a search..all the equations are probably on this forum somewhere

...uh ..yeah..

[RaID]

Originally posted by audi fan:
The Brake Handbook from Fred Puhn is an excellent place to start. I designed the brakes for the '05 UoG Car using it and they work like a charm. I entered all the formulae into an Excel spreadsheet and played around with master and caliper bore sizes to see what would work best.

Chris Quinke
Gryphon Racing '04, '05

definately check out this book easy to follow and covers a wide range on info

i picked up mine on Amazon for $5 second hand,
designed brakes that did job quite well

[rjwoods77]

Raid,

Does Fred book include stuff about kinetic energy into the rotors, heat loss and all that stuff. We wrote our one spreadsheet using the same equations out of a different book and we are now trying to figure out what size rotors(diameter and thickness)will be suitable for the job.

[B]

I'm in the same boat.... need to find out what size rotors to use....

If anyone knows how to calculate what dimensions required to disipate the heat given the braking conditions and material properities then you'd b a life saver!!!

Brett

[Homemade WRX]

the searches I have been able to do have yeilded some help but I'm going to go ahead and buy the fred puhn book, and see if we have anything on it in our carroll smith collection at the lab.
take it easy, Micah

[John Bucknell]

As a former brake engineer, the books out there don't tell you how to figure out the heat capacity necessary for a good brake. Most make the mistake of designing for a single brake apply, and not for the stabilized temp. How to find the stabilized temp to design to?

The german auto magazine Auto Motor und Sport does a test on all the cars that come through that I think is a good indicator of how to size brakes. They run the car up to 100 kph (62 mph) and do a stop with the brakes cold and record stopping distance. Then they let the brakes cool down again, then do max effort 0-100-0 kph ten times in a row and compare the stopping distance first stop to last. A car that has no fade in that test is effectively race quality (not Le Mans race-quality, but sedan racing). In a FSAE car, you would spike about 100 kW into the brakes every 5 seconds during that test. Remember that radiant heat transfer is your friend and figure out whether your friction material will function in a brake that is glowing and maybe it is now about the right size. Not hot enough to glow isn't that much heavier, and considerably easier to work with (ie it won't start melting nearby components). This isn't everything to be sure, but it should give you a feel for the duty cycle.

[Homemade WRX]

thanks for the helpful testing method...I would like to see how our past car holds up

[Dr. Bob Woods]

My textbook "Modeling and Simulation of Dynamic Systems" from Prentice Hall has a complete math model and sizing example for a FSAE car in Chapter 10.

-Dr. Bob Woods
Faculty Advisor, UTA

[romkasponka]

You can find some useful info here http://www.stoptech.com/technical/

[rjwoods77]

I just got my hands on "Brake Design and Safety" second edition by Rudolf Limpert. This book is so good. Even goes into details of caliper design and it is written so the average fsae guy can understand it well. I would definitly go and get it if you want to do brake system design.

[Homemade WRX]

Originally posted by Rob Woods:
I just got my hands on "Brake Design and Safety" second edition by Rudolf Limpert. This book is so good. Even goes into details of caliper design and it is written so the average fsae guy can understand it well. I would definitly go and get it if you want to do brake system design.
thanks for the lead...I will have to buy that book as well...you can never have too many resources http://fsae.com/groupee_common/emoticons/icon_wink.gif
-Micah

[Mark Bacchetti]

Numerical Prediction of Brake Fluid Temperature Rise During Braking and Heat Soaking (http://www.delphi.com/pdf/techpapers/1999-01-0483.PDF)

This SAE paper discusses the duty cycle that John Bucknell mentioned earlier in this thread.

-Mark
Cal Poly Pomona

[Homemade WRX]

thanks for the link...still waiting on my books

[Marshall Grice]

Remember that radiant heat transfer is your friend and figure out whether your friction material will function in a brake that is glowing and maybe it is now about the right size. Not hot enough to glow isn't that much heavier, and considerably easier to work with (ie it won't start melting nearby components).
Here I thought our glowing brake rotors was bad, good thing I'm not the brake designer. I'm curious though, with all this talk about rotor size and temp. What about caliper/pad size? Do you know of any simple rules for how much heat goes into the pads/calipers?

[John Bucknell]

Originally posted by Marshall Grice:
Here I thought our glowing brake rotors was bad, good thing I'm not the brake designer. I'm curious though, with all this talk about rotor size and temp. What about caliper/pad size? Do you know of any simple rules for how much heat goes into the pads/calipers?

The caliper sizing is another issue all together. That you can find equations for elsewhere. Pad sizing is bit more of a black art, because you need the material properties of the pad at operating temp for heat transfer coefficient, stiffness, etc (and that is harder to get). In general though, the thermal mass of the rotor is huge compared to the pad - so it's all you can do to prevent the heat from getting through the pad, to the piston and from there to the fluid (ie why there are water-cooled brake calipers out there - or you gotta size everything bigger than necessary from a friction material performance point of view, some of these carbon-based pads will operate WAY up there in temp). Many times you'll set fire to the rubber seals, which bakes the phenolic piston, etc. if you overdo it. Also keep in mind pad wear is usually an upward slope with temp, up to a 'knee' where it accelerates dramatically. Differential bore calipers came about because of uneven pad wear - you get down to a lo mu backing plate much too soon without it.

[rjwoods77]

Thats another point. I was planning on basing my caliper off of wilwoods thermolock 1 or 2 pistons. Doing it more or less for just less stuff to design. You said phenolic piston. Would is the current school of though on what to use for a piston and thermal insulator. Straight titanium? Aluminum with a spacer? Wilwoods setup? I know it is about minimizing heat transfer to the fluid so ....

[Adam D. Bell]

Hello I'm just testing how this system works

[John Bucknell]

Rob,

You've reached the limit of my knowledge. I've been away from the front lines of brakes for six years - so piston design advice from me will be out of date. However, differential thermal expansion is a pretty big issue (Ti and stainless being bad boys in that regard) so using somebody elses developed piston/seal is probably a real good idea.

[Z]

Rob,

IF your brakes get too hot, then make a small duct to catch the wind and blow air on them - problem solved! (Use pistons with a ring of holes near the pad, to let the breeze flow through. http://fsae.com/groupee_common/emoticons/icon_smile.gif )

Since I've never seen brake ducts on FSAE cars I must assume that brake cooling is not a big problem. Maybe if they introduce a "Brake Test" dynamic event, as in John Bucknell's post, then yes, you'll have to add cooling...

Better yet, increase your corner speeds, then you don't have to brake as much.

Z

[rjwoods77]

My rotors are outboard(between the upright and the car, reverse side of the upright that they normally go) and it is a solid rotor so I think I have the airflow thing taken care of. I just want to minimize heat transfering into the fluid and make sure the pads wear even and clean okay.

[Z]

Good brake ducts make a huge difference. A well directed blast of air gives much more cooling than just having the disc "out in the breeze". However, I really don't think brake cooling is a big issue in FSAE (yet). If it ever becomes important then brake ducts will pop up everywhere.

I think just reasonable size brakes now (ie. motorcycle size), test hard, then if any problems (fluid boiling, stuff burning) add ducts.

The "ring of holes" around the piston is good for keeping heat out of the fluid, and easy to do.

Z

[Cement Legs]

Hey Z could you clarigy 'where' the ring of holes around the piston would be? I don't think I have ever seen something that resembles what you are reffering to so my imagination is running away with me.

[Chris Boyden]

Z,

by ring of holes, do you mean around the skirt of the piston? Would this create a thermal choke or relief? They do something similar for circuit boards before they get soldered. On parts that are attached to a ground plane, i.e. a big thermal sink, they'll create a thermal relief for the parts that are grounded which helps to keep the large ground plane from sucking heat away from the part to be soldered.

[Denny Trimble]

Here's a resource for some quality brake information:

http://www.stoptech.com/technical/

[Homemade WRX]

Originally posted by Cement Legs:
Hey Z could you clarigy 'where' the ring of holes around the piston would be? I don't think I have ever seen something that resembles what you are reffering to so my imagination is running away with me.
I'm in the same boat, trying to imagine what he means...

[markocosic]

Originally posted by Cement Legs:
Hey Z could you clarigy 'where' the ring of holes around the piston would be? I don't think I have ever seen something that resembles what you are reffering to so my imagination is running away with me.

I'm picturing a drinking glass, with the rubber seal at the base and pad on the top, and a ring (or two) of holes in the side of the glass up near the pad end?

[Z]

Re: "ring of holes".

Marko's got it. The piston is a cup with its bottom pushed into the caliper, the o-ring seal around its upper-middle (sitting in caliper), and its open-end rim pushing against the pad backplate. The "ring of holes" is just below the rim, and just above the o-ring when new pads are fitted (ie. holes must be above o-ring when piston pushed fully into caliper!). Sometimes the "holes" are just notches in the rim.

The idea is partly to provide a "thermal choke" (Chris ^), but mainly to let a bit of cooling air to circulate through and inside the piston. This slows the heat from the pad getting to the fluid. These holes used to be quite common - maybe out of fashion now? If you do need extra cooling (which at the moment I don't think is necessary) some of the ducted air should be fed between the pad backplates and pistons, with the rest going to the disc (both sides!).

Another way to stop fluid boiling is to use two sets of brake lines to each caliper, each line having a one-way (non-return) valve in it. Each time you pump the brake the fluid goes into the caliper through one line, and then when you release the brake the fluid exits through the other line (eventually returning to the M/C reservoir). This circulates the fluid allowing it to cool in the brake lines, and also acts as a self bleeder. There were/are commercial versions of this, but you'll have to look... Again, I don't think this is necessary for current FSAE conditions -too complicated and the valves can get stuck leaving too much residual pressure.

Z

[t-4ever]

Originally posted by jack:
uh..like..carroll smith, dude...

and..like..do a search..all the equations are probably on this forum somewhere

...uh ..yeah..

so plzz where i can find these formulas
thanx

[ben]

In brief

Force applied to pedal by driver * pedal ratio = force applied to balance bar
Balance bar force split in proportion to balance bar fulcrum position
Master cylinder force * master cylinder area = line pressure
Line pressure / caliper piston area = pad normal force
Pad normal force * pad friction coefficient = pad tangential force
Pad tangential force * disc effective radius = brake torque
Brake torque / tyre loaded radius = braking force at tyre contact patch

The brake system is just a big lever in the end

Ben

[Chris Boyden]

Uhhh...that doesn't jive.


Master cylinder force * master cylinder area = line pressure

Isn't Pressure(lbs/in^2) = Force(lbs) / Area(in^2)?

[scooter2131]

Line Pressure * caliper piston area instead of dividing. Just incase anyone didn't catch on after the last post.

[TG]

Z,

Brembo does that ring of holes trick on their high end brake pistons. The bike calipers they are on tend to run in the vacinity of $1000-2000... not FSAE stuff. Just another note, Alcon has a technology call (I think) Through Piston Venting. The pistons have a hole in the center of them (sealed so the brake fluid only goes to the outer portion of the piston) and guide air through it. They noticed dramatic decreases in pad and fluid temperatures in NASCAR. They spent three years developing it so you know it's definately not for FSAE yet.

One thing I am curious about is if anybody has experimented with ceramic coatings on the piston surfaces to try to prevent heat transfer to the brake fluid?

[rjwoods77]

http://patentlaw.typepad.com/patent/Brembo.claims.pdf

[ben]

Originally posted by Chris Boyden:
Uhhh...that doesn't jive.

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Master cylinder force * master cylinder area = line pressure

Isn't Pressure(lbs/in^2) = Force(lbs) / Area(in^2)? </div></BLOCKQUOTE>

Ooops finger trouble on my part.

Ben