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Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235239
05/19/12 12:44 AM
05/19/12 12:44 AM
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Quote:

where engineers begin frothing at the mouth




Mechanical advantage of the lever at the pedal, area ratio from the master to the caliper, lump capacitance of the fluid system / materials, torque on the wheel from the braking force, coefficient of friction at the pad rotor interface dependent on: brake pad material(s) - rotor material - rotor surface condition - pad surface condition - temperature - humidity, reaction torque from the tire road interface, coefficient of friction at the tire interface as a function of the slip ratio.. nooooo... let it goooo...


OK Kevin, I think I am OK now...

---------------------
Michael
AS in Automotive Technology (1990)
ASE Certified Master Tech (1991)
BS in Mechanical Engineering (1997)
MS in Mechanical Engineering w/ a concentration on Dynamic Systems and Controls (2005)

Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish] #1235240
05/19/12 12:47 AM
05/19/12 12:47 AM
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Anyone want to see the bond graph representation of a torque converter?

Oh... never mind...


Michael Plano, TX 68 Barracuda Notch Pro Patina
Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235241
05/19/12 01:37 AM
05/19/12 01:37 AM
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Quote:

Dividing by 4 brake pads gives you a total of .0041" of movement.




Kevin - this is where modeling the system gets really "fun". Not picking on you or anything, this is the good stuff. All the numbers and ratios and everything you are tossing out there all assume a steady state A/B type ratio. Those numbers are what comes into play when the brake pads are in contact with the rotors and we are slowing down. What is really cool - and may be one of the more important things is what happens before that. The actual travel you have before the pad - or shoe - engages is going to be different front to rear. So you actually have several different states each with a different model. #1 - foot on pedal, no pads touching yet; #2 - first set of pads engage; #3 second set of pads engage. Before contact the pistons in the rear are moving at a different speed than the ones in the front. If we assume the force to get the piston / pads moving is about the same, the front pistons have more leverage and thus less reflected force back into the system. This means you would get considerably more movement on the front and they will engage first, then, as they meet more resistance at the pad rotor interface the slack in the rear would be taken up. Interesting - be nice to go out and slowly press the pedal with someone turning each wheel to see if this is indeed what happens. The only way around this would be separate master cylinders and a balance bar, you could then tune it to your liking.

I feel like a nerd... forgot how much I like this stuff.


Michael Plano, TX 68 Barracuda Notch Pro Patina
Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish] #1235242
05/19/12 02:05 AM
05/19/12 02:05 AM
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Quote:

Interesting - be nice to go out and slowly press the pedal with someone turning each wheel to see if this is indeed what happens. The only way around this would be separate master cylinders and a balance bar, you could then tune it to your liking.
...




On of the advantages to dual masters with balance bar setup. We've done that very test on our circle track cars. We've caught cars with rears that grab first or at the same time.


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Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish] #1235243
05/19/12 03:05 AM
05/19/12 03:05 AM
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Michael, I am aware of most of the stuff you listed but didn't want to get into that stuff. It would make the post totally useless for most folks.

Also, when I was referring to the movement of the 4 brake pads, I meant the front brakes. The rear brakes were not addressed in the post. I didn't want to go there due to the different proportioning valves in use.


Again, I believe the stuff I dumped out there will be good enough to get someone in the general ball park.
Obviously, the brake torque calculation shows a perfect scenario where the real world will see the number cut by as much as 65% with the use of poor quality brake pads.

Sometimes it's just fun to fiddle around with numbers.

Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1] #1235244
05/19/12 10:54 AM
05/19/12 10:54 AM
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Quote:

Excel file is available for download here:

http://www.3gduster.com/brakes.html

Enjoy!




When I suggested in the other thread that it would be nice if this was all in an excel spreadsheet, I didn't think anyone would actually do it! I was thinking of trying to do it myself, but it would have taken a week, and I still would not have gotten it right.

Thanks to both of you for all the time you have put into this. This sheet has been downloaded, saved, and backed up for future reference.


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Re: Disc brakes: All the math that you never wanted to know [Re: DynoDave] #1235245
05/19/12 11:11 AM
05/19/12 11:11 AM
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one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C


They say there are no such thing as a stupid question.
They say there is always the exception that proves the rule.
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Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda] #1235246
05/19/12 11:58 AM
05/19/12 11:58 AM
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Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Less leverage is less stroke at the pedal. Stroke at the master is determined by the system downstream.


Michael Plano, TX 68 Barracuda Notch Pro Patina
Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish] #1235247
05/19/12 01:00 PM
05/19/12 01:00 PM
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Quote:

Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Less leverage is less stroke at the pedal. Stroke at the master is determined by the system downstream.




Stroke at the pedal is irrelevant. Stroke at the M/C is, Frankenduster had an issue with his manual all disc setup I am thinking is volume out the M/C related. The problem cured up with him swapping to power (less leverage at the pedal, more stroke at the M/C, same MC).

In a lever situation, which this is, stroke and leverage are directly related.


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Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda] #1235248
05/19/12 06:23 PM
05/19/12 06:23 PM
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Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Look at the chart again.

The third input requested is pedal ratio. 7 in the example.
The sixth (and last) input requested is how far you moved the pedal. 5 inches in this example.

The third output listed is "the master cylinder moved this far". .7143" in this example.

There's your stroke by pedal ratio.


You referenced FD's power booster conversion. I specifically stated that the math in these examples was for a manual brake system only and that if you used a booster you were on your own.

If you want to get into pedal effort by master cylinder size, start punching numbers.
Put in a 1" master with 100 lbs pedal effort and see what the brake torque is.
Put in a 1-1/8" master with 100 lbs pedal effort and see what the brake torque is.
Start putting higher numbers in the pedal effort until you get back to the same brake torque.

Going from the example's 15/16" master cylinder to a 1-1/8" master cylinder shows that the pedal effort increases from 100 lbs to 144 lbs to get the same brake torque. A 44% increase in pedal effort is not going to make for a happy driver.

Go back and play with the numbers and see what the spreadsheet will do for you. It's kinda fun.

Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235249
05/19/12 07:40 PM
05/19/12 07:40 PM
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I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.


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They say there is always the exception that proves the rule.
Don't be the exception.
Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda] #1235250
05/19/12 07:54 PM
05/19/12 07:54 PM
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Quote:

I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.




Steve - what does the power booster have to do with the volume output from the master? The only time that is going to make any difference is if he ran out of pedal before the brakes were fully applied. In that case, he could have also cured the issue by going to a larger diameter bore on the master. So, was the root issue too much pedal travel?


Michael Plano, TX 68 Barracuda Notch Pro Patina
Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda] #1235251
05/19/12 08:18 PM
05/19/12 08:18 PM
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Quote:

I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.




Again, go back and play with the numbers. You can see how far the calipers move with different size master cylinders as well as the pedal force required to generate enough brake torque.

It won't magically tell you everything you want to know. Playing with it and reading all of the results will help you understand what is going on.

Again, it's not the final word in brake info. Instead, it will get you in the ball park assuming you read and understand the info presented.

Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish] #1235252
05/19/12 08:22 PM
05/19/12 08:22 PM
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A 15/16" bore master cylinder should have ample volume in this case, because the caliper pistons only move a fraction of an inch.

Re: Disc brakes: All the math that you never wanted to know [Re: DoctorDiff] #1235253
05/19/12 11:35 PM
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I think we bore that out in the math.




The 15/16" master worked fine once he put the booster back in.

Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235254
05/19/12 11:50 PM
05/19/12 11:50 PM
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Hmm, only 408lbs from the master cylinder. I sure hope the booster is actually doing its thing

I ordered the pressure gauge and adapters today to make sure


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Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit] #1235255
05/19/12 11:53 PM
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Perhaps you could build some sort of electric brake controller that will vary the brake pressure based on speed, traffic conditions, and the presence of radar emissions directed at the vehicle.


Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235256
05/19/12 11:56 PM
05/19/12 11:56 PM
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Quote:

I think we bore that out in the math.




The 15/16" master worked fine once he put the booster back in.




The manual 15/16" master cylinder wasn't likely to blame, since I also had trouble with the other two manual units that I tried. The 15/16" unit I have on the car NOW with the power booster is an iron unit spec'd for a 75 Dart with power brakes.

Something wierd was happening and I still don't know what is to blame.

Re: Disc brakes: All the math that you never wanted to know [Re: feets] #1235257
05/20/12 12:14 AM
05/20/12 12:14 AM
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Quote:

Perhaps you could build some sort of electric brake controller that will vary the brake pressure based on speed, traffic conditions, and the presence of radar emissions directed at the vehicle.




No more of this ABS stutter-stop stuff. Just lower the pressure in the event of wheel lockup. And/or change the rear pressure based on road speed and current load (for trucks). Should work great!


If you ever find yourself in a fair fight, your tactics suck.
Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit] #1235258
05/20/12 12:17 AM
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When you decrease the pedal ratio, you increase the stroke in the M/C. Power brakes systems use less pedal ratio, therefor more stroke at the MC for a given pedal travel.

Same bore M/C going from manual to power sends out more volume for a given pedal travel.

That's what is different.


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They say there is always the exception that proves the rule.
Don't be the exception.
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