Brake system design module equations, and notes

Hello, I am in the process of going through the Brake System Design and Optimization course. I am having trouble finding equations used through out the Brake System Design section. Discs, Calipers and Pads 7:33. Where are we getting the brake pad radius and swept pad radius measurements from?

I am following along with the onscreen math in this section and there are some discrepancies.

Calculating Braking Capacity: 7:27 Lateral Load transfer math is off, answer should be 252kg not 254kg, following math uses 252kg (636kg+252kg = 888kg).

Discs, Calipers and Pads: 7:54 The Effective Radius equation is off, (Effective radius = Outer radius - Pad radius) is shown as (370/2)-53, according to the solution it should be (370-53)/2.

Proportioning Valve, Pedal Feel and Master Cylinders: 5:46 MC Diameter equation is incorrect on screen. Currently is MC Diameter = 2(√Area/π) should be MC Diameter = 2*√(Area/π).

Hi Matt,

Regarding brake radius dimensions. I got these measurement simply by measuring the pads that are used in this example. Since the outside of the pad should line up with the outer edge of the disc then we know from those calculations on the screen where the centre of the pad and therefore the effective radius of the disc are.

Is anything still unclear here?

"Calculating Braking Capacity: 7:27 Lateral Load transfer math is off, answer should be 252kg not 254kg, following math uses 252kg (636kg+252kg = 888kg)"

Good catch, Must have been a typo in my script on the teleprompter. I'll fix this when I get the chance.

"Discs, Calipers and Pads: 7:54 The Effective Radius equation is off, (Effective radius = Outer radius - Pad radius) is shown as (370/2)-53, according to the solution it should be (370-53)/2."

Same thing again, thanks for pointing that out. My works would have been correct but then the script is wrong. Will fix.

Again good catch, brackets are in the wrong place, will get the graphics guys to update this asap.

Thanks for your help, anything else pops up please let me know.

Thank you for the response. I am trying to pass the quiz at the end of the module but for the life of me I cannot identify or find the equation to be used in the brake torque calculation question.

I know there is a lot in the brake calculator but maybe a glossary of equations, especially in these math heavy courses?

I've made a note to make a "equation cheatsheet"

Which of the questions in the quiz is giving you trouble specifically?

A tire is loaded vertically with 200kg, has an assumed COF of 1.2, and a loaded rolling diameter of 650mm, approximately how much brake torque can it sustain without starting to lose traction?

If a brake package has an effective radius of 150mm, a total piston area of 2500 mm^2, and a pad coefficient of friction of 0.4, how much brake torque will 3500 kPa of pressure generate?

I thought it was only 1 but I am stumped on both of those questions.

1. A tire is loaded vertically with 200kg, has an assumed COF of 1.2, and a loaded rolling diameter of 650mm, approximately how much brake torque can it sustain without starting to lose traction?

- So the max tire force that can achieved before loosing traction is found by our friction force equation: F=N.mu=200kg x 1.2 = 240kg

- Torque is this force multiplied by the distance to the centre of rotation (diameter/2): T = 240 x (0.650/2) = 78 kg.m

2.If a brake package has an effective radius of 150mm, a total piston area of 2500 mm^2, and a pad coefficient of friction of 0.4, how much brake torque will 3500 kPa of pressure generate?

- first let's convert some units 2500mm^2=0.0025m^2 and 3500kPa = 3500000Pa

- Piston Force = Preassure x Area = 3500000 x 0.0025 = 8750 N

- Friction Force = Piston Force x Mu = 8750x0.4 = 3500 N

- Torque = Friction Force x Effective Radius = 3500x0.15 = 525 N.m

Keep in mind that these calculations are just to give indications of theoretical values, the real life values will be different.

Thank you, numbers I was coming up with were nowhere close. I defiantly wasn't changing/converting any of the measurements.

Just to clarify.

1: We need to find the force of the tire before it looses traction/locks up, so the lateral load transfer mass. This data is found through corner weights, in this case 200kg, and the G force from data logging, in this case 1.2, which would also be our COF for this calculation?

Yes, so if we know we can pull max of 1.2Gs on deceleration then it's a fair assumption (albeit massively simplified) that the COF of the tire is 1.2.

We should know the Static weight distribution of the car (corner weights) and then factor in the load transfer under braking to find the vertical load on each tire.

Then we use the friction force equation to calculate the tire forces and use this with the radius values to find the torques.

Thank you for clearing this up.

No problem more than happy to help!