Proportioning brake valve

[Colin Byrne]

Happy to explain the diagram a little better

Starting at the brake fluid end, the master cylinder creates pressure (p), pressure is measured in force per unit area, so if the pressure is acting on a known area, in this case the brake piston Apiston we can calculate the resultant force, in this case the force of the piston (Fn). This gives us the first equation

Force of the piston = Brake Pressure x Area of the piston
Fn = p . Apiston

(the term “Normal force” just implies a force that is perpendicular or at 90deg. To a surface, in this case the brake disc)

Because the piston is directly acting on the pad and the pad to the disc we can say that the resulting force on the disc is the same as the piston (Fn), 
Friction coefficient, mue, is unitless, its this way because it is a ratio, and it is a ratio of the resulting force due to friction in the direction of travel  to a normal force.  This gives us our second equation for brake force (Fr)

Brake Force due to friction = Friction coefficient of pad x Force of the Piston x 2
Fr = 2 .  muepad . Fn
(the 2 is because it is a slideing calliper so the force acts on both sides, no different to if it just had another piston on the other side)

A torque is simply a force at a certain distance, now we have our brake force from our last equation, to get our braking torque (T) we simply multiply it by the effective radius of the disc (Ra)

Brake Torque =  Effective radius x Brake Force
T = Fr . Ra

Following this to get the longitudinal force (Fl) at the tyre we simply divide this torque by the radius of the wheel Rw

Longitudinal force = Brake Torque / Radius of the wheel
Fl=T/Rw

So just for completeness I’ve re-arranged these equations and put them in the form of the first equation I posted (attached)

And just for the record, I’m not just a number cruncher!
 

[alfagtv152]

Hi Colin,
Thank you,I don,t think for a minute that you are just a number cruncher.You have shown me the more scientific/technical side of things I practice and made me learn a few things,thank you.
One last question, what is Cp in the equation from the bosch book please?.
Cheers
Andrew

[Colin Byrne]

The Cp is just a compilation of all the physical properties of the braking system in one term, to give a very simple way of calculating resultant brake torque for a known pressure, this is important for the kind of work I do, but not so important for the explanation so I left it out.  Drum brakes are sometimes specified with a Cstar value from manufactures, and this is the same thing