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Old Wed, Jul-04-2012, 05:08:14 PM   #2
p0lar
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Default Re: How to Calculate Brake Bias

Edit by TerraPhantm 01.09.18

I've unembedded p0lar's pictures (though the attachments are still present) as they were causing too much confusion and misinformation. The master cylinder does *not* impact brake bias. This was mathematically and experimentally proven by e36 332ti

You can see further detail in his posts here (reproduced below):
Quote:
Originally Posted by e36 323ti View Post
Some more reflections regarding if stepped bore influences the brake bias or not…

Short version:
Stepped bore does not influence the brake bias. The pressure front and rear are the same, and hence the pressure to all 4 calipers are the same. In static bias calculations, the master cylinder bore size used shall be the front (or primary) only. Due to the beauty of math, it cancel out, since it appears both in the numerator and de-numerator.

Long version:
Opened an e46 master cylinder with stepped bore “22”mm front and “20”mm rear. The “22”mm is in fact 22.2mm and “20”mm is 20.64mm.



The dismantled master cylinder is shown in the picture above. The front (primary) and rear (secondary) piston are two separate parts. The spring constants for the primary and secondary spring was measured to (approximate values):

Spring constant secondary piston: kH = 4700 N/m.
Spring constant primary piston: kV= 9700 N/m.

The purpose of the tiny pin shown in the picture is to lock the secondary piston. By this the secondary piston is pre-tensioned to FH0=51.7 N, i.e. the force on the secondary piston must exceed 51.7N in order to move. Since the “forces” set up by the brake fluid is much larger than this, it is clear that the spring constants can be neglected.

By looking up any text regarding “How does the master cylinder work”, they all give the explanation that the secondary piston is driven by the pressure setup by the brake fluid when the primary piston is moved.

If the the secondary piston is driven by the pressure from the primary piston, the system must follow Pascal’s principles. Hence:

-The pressure front and rear are the same (suppoted by INPA measurements).
-The diameter of the secondary piston has no meaning when it comes to the pressure delivered to the rear calipers.

The next question is then, why use stepped bore?
Quote:
Originally Posted by e36 323ti View Post
Tried to see if the stepped bore had any influence on how fast the pistons in the calipers moved. Answer: No, it has no influence.

Quote:
Originally Posted by e36 323ti View Post
... and finally, measurements from the brake pressures from an MY2003 e46 m3 MK60.

Measured bias is in average 66.74%, while modelled bias for the e46 m3 is 66.9%.



To me it seems like all the numbers in the tables in the second post in this thread deserves a revision.




This is a quick chart I've constructed using Excel to illustrate the bias generated by various combinations of brake calipers/rotors. Please eMail me any additional caliper/rotor/pad combinations you would like to see crossed, and dimensions of the pad swept area, rotor diameter and piston size and count, if possible.

Edit | 08.02.2012: Added WilWood SL6R to front calipers with 325mm rotor

Edit | 08.09.2012: Added C6 Z06 Corvette to front calipers with 355mm rotor

Edit | 09.23.2012: Added a multitude of calipers. Included FULL bias, inclusive of master cylinder as well as % bias front/rear. Added deviation from standard/ZCP E46 M3 biases in terms of %F (front) or %R (rear) movement - this could give more data to the layman. This was a massive update, please review to let me know if there are any issues with my calculations or data presentation.

Edit | 09.24.2012: Added 4-Piston RacingBrake caliper.

Edit | 03.27.2013: Removed differentiation from OEM bias charts - they were causing way too much confusion. Added charts for differences in DSC (MK60 (>09/2002) vs DSC3 (<09/2002). Also added a small table to show calculated bias results for OEM E46 M3s and a warning for those who wish to downgrade to ZCP/CSL brakes on a DSC3-based system from <09/2002.

FULL BIAS INCLUDING MASTER CYLINDER PISTON DIFFERENTIATION

E46 M3 with MK60-based Master Cylinder (Front: 25mm, Rear: 22mm) (post-09/2002)
http://www.m3forum.net/m3forum/attac...1&d=1364397539

E46 M3 with DSC3-based Master Cylinder (Front: 25mm, Rear: 20mm) (pre-09/2002)
http://www.m3forum.net/m3forum/attac...1&d=1364397540

Warning: If you replace your pre-09/2002 DSC3-based OEM E46 M3 brakes with ZCP/CSL brakes, including the rear caliper, you are doing yourself a grand disservice. This causes an almost 5% shift in rear bias from the actual ZCP configuration, which was never designed for the DSC3-based master cylinder. Consider upgrading to a MK60-based master cylinder at the same time - the MK60-based power-booster may also be required.
Attached Images
File Type: png E46 M3 MK60 Bias Calcs v0.144.png (419.9 KB, 3174 views)
File Type: png E46 M3 DSC3 Bias Calcs v0.144.png (417.6 KB, 3069 views)

Last edited by terraphantm; Tue, Jan-09-2018 at 10:31:09 PM.
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