Proportioning brake valve

[alfagtv152]

My experience with the transaxle cars is that the difference in pad size (front > rear) alone provides sufficient front bias to prevent rear lock ups.

This isn't exactly correct, pad size actually doesn't have any impact on the braking force generated by the braking system.  Forces generated by friction are independent of surface area,(this does not stand true for tires as they do not work purely by friction). 

I have heard this before and I can't say I believe it,personally I believe the swept area change must change the overall effectiveness of braking efficiency.If you are applying the same clamping force over a much larger area the amount of friction must increase.The valves we are discussing are Pressure control valves not brake bias valves.
Perhaps you could explain it to me,engineering theory doesn't always translate into practice.
I have been using pressure limiting valves on the rear brakes of my Alfetta GTV for years and find it vital for balancing up brake balance which varies due to track conditions especially wet to dry.
When I went to slotted vented rear discs and put front pads in the callipers I suddenly had to much braking on the rear with Volvo 4 spots on the front.Once I slotted the fronts and adjusted the pressure to the rear I got my balance back.Hawk hp plus pads front and rear.
Cheers
Andrew

[Colin Byrne]

If you are applying the same clamping force over a much larger area the amount of friction must increase

Fair enough Andrew I know it can be hard to visualise this sometimes but this comment does go against the second law of friction
(from http://en.wikipedia.org/wiki/Friction)
2.   The force of friction is independent of the apparent area of contact. (Amontons' 2nd Law) (Amontons' 2nd Law does not work for elastic, deformable materials. For example, wider tires on cars provide more traction than narrow tires for a given vehicle mass because of surface deformation of the tire)

I just checked out my copy of Millken/Millken Race Car Vehicle dynamics and I've attached the equation for longitudinal brake force vs Brake fluid pressure.  As you can see the relationship between the two is independent of pad surface area.

engineering theory doesn't always translate into practice.

Been working out pretty well for me so far!

the valves we are discussing are Pressure control valves not brake bias valves.

If your controlling the pressure at one axle isn't that changing the brake bias?

have been using pressure limiting valves on the rear brakes of my Alfetta GTV for years and find it vital for balancing up brake balance which varies due to track conditions especially wet to dry.

Absolutely, getting correct brake balance is critical in decreasing stopping distance and, as you said, in different conditions such as wet vs dry, or anywhere else where weight transfer various due to different deceleration rates, then adjustment is required, I was just saying that I prefer a mechanical brake balance bar rather than a single pressure control valve, but like I said that's just my opinion.

Cheers

[alfagtv152]

Hi Colin,

Thank you for the formula,it does indeed look like a very usefull tool to calculate the brake pressure required for a given set up but that then of course leads to whole lot more calculating of master cylinder diameter and the rest of the other factors you mentioned earlier to generate that pressure.
I am not an engineer but to ignore the pad size in braking efficiency is still not logical in my opinion as it still affects the overall work done by the brakes,which in turn affects the heat generation and disapation,contact pressure etc refered to before.
I found a little bit of information to support my thinking on the web from the US.It is called "brake pad prognosis system",which states"Brake work includes determining braking force as brake pressure times brake pad area times brake pad coefficient of friction.
The amount of work done affects the pad life and is used to predict it.
Thanks for the discussion even if I am "hijacking" the thread.
Cheers
Andrew

[MD]

As I anticipated earlier this topic would generate discussion. Let's face it, it's inevitable.

Colin,

This isn't exactly correct, pad size actually doesn't have any impact on the braking force generated by the braking system.

I gotta say I disagree with that. Let's look at this example. In a braking system without any other parts than the calipers, master cylinder and brake lines, the line pressure is the same at all points. I trust we are in agreement there. Now if the we apply the same pressure to all pads equally and the pad materials are all identical so the friction coefficients are the same, we would expect the same amount of braking forces at all wheels so why dont we have the same sized pads all round?

It is a common practice to reduce the pad area to rear brakes compared to the front brakes to achieve a better braking balance. The usual reason why this is so is because the rear of most cars are lighter than the fronts and the weight transfer to the front axles under braking also takes place making it even lighter. Applying the same line pressure to the same size pads would produce rear wheel lock up. Therefore designers install smaller calipers and pads to effectively try to reduce the effect of the equal line pressure and create less friction with the smaller pads at the rear.

My point was/is that the front brakes have a "natural" bias and negating this bias can be done in other ways than proprtioning valves. It can done by varying rear friction coeficients, rotor diameters.

[MD]

Paul,

I can't see that gorilla behind the wheel in the 35 Gp getting past CAMS..although a good helmet...

[Colin Byrne]

I gotta say I disagree with that. Let's look at this example. In a braking system without any other parts than the calipers, master cylinder and brake lines, the line pressure is the same at all points. I trust we are in agreement there. Now if the we apply the same pressure to all pads equally and the pad materials are all identical so the friction coefficients are the same, we would expect the same amount of braking forces at all wheels so why dont we have the same sized pads all round?

Because the work done, and therefore the heat generated, at the rear of the car, is much less than the front of the car.  Less heat, means smaller pads will be able to stay within in their operating range, smaller pads, dics ect are cheaper, and more importantly in racing applications, are lighter.

MD in your example you didn't appear to take into account one very important factor, and that is the surface area of the brake calliper piston. I've attached an exert from a training manual we use here at work, hopefully this will help illustrate the previous equation I posted

If you still disagree I'm more than happy to keep discussing, but is there a specific part of the equation that you disagree with?  That equation comes from one of the most respected vehicle dynamics text books, but that's not really important as it can be derived from first principles very easily, in fact the attached diagram almost does this

Let me know what you think
Cheers

PS nice gorilla

[MD]

Let me know what you think

...er, I let you know after I consult the gorilla. 

Sorry mate, there's the number crunchers and the geasy knuckles brigade. I am in the latter group.

[alfagtv152]

Hi Colin,
MD did say reduced pad and calliper size which to me implies the piston would be smaller-anyway,I would like to understand the diagram you posted last time,I don't recognise the symbols and the equation.
What do those equations tell you?.If you have the time to explain it I would appreciate it.
Cheers
Andrew

[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