QwkTrip

iTrader: (22)

Below is a method to estimate braking torque of any brake package. Topics include,

* How to calculate braking torque
* Explanation how the stock proportioning valve works and how to calculate the proportioning ratio
* How to modify your stock prop valve to produce a different proportioning curve
* Lists of physical data of braking systems

You're going to see a little bit of rounding error here and there because I'm copying numbers from my spreadsheet. Just go with the flow and don't worry about it.

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Step 1: Applied force to Master Cylinder

QwkTrip

iTrader: (22)

This is the method to predict the proportioning curve of any stock valve, or any mix of parts you throw in it.


The Components

First order of business is to understand how the valve works. High pressure fluid from the Master Cylinder enters the Proportioning Valve. Fluid passes through unaltered at full line pressure to the front brakes (not shown here). Fluid to the rear brake lines gets proportioned, meaning the pressure is altered. The task of proportioning the rear brake line pressure is done by a Piston, Cup-Seal, and Spring. And it's genius how they did it. A diagram of the rear brake passage is shown below.

The piston sits in the prop valve with a spring on one end and a cup-seal on the other. When the piston moves to the right it pushes against the cup-seal and deforms the seal. The deformation cause the cup-seal to lose its ability to hold a seal and fluid passes thru to the rear brakes. (ya, I know, it's not intuitive) When the piston moves to the left, the cup-seal can reform and make a seal again and stop fluid flow to the rear brakes.




Step 1: When brakes are applied

The native state of the valve is with the spring pushing the piston to the right and allowing fluid to flow to the rear brakes. Fluid pressure in the forward chamber is same as pressure in the rear chamber. The key thing here is that the piston is not fully submerged in the fluid -- one end of the piston protrudes out of the chamber into the outside air (atmosphere). As fluid pressure rises in the brake line it causes a hydraulic force to be applied to the piston that tries to push the piston out of the valve into the atmosphere, and the only thing resisting it is the spring. During this period the pressure will rise at a 1:1 ratio (same) with the front brake lines because the cup-seal is allowing fluid to pass freely to the rear brakes.


Step 2: The hysteresis point - the point where rear brake proportioning begins

Eventually the spring is overcome and the piston will move far enough to the left that the cup-seal will form a seal and shut off the rear brake line and stop fluid flow. This is called the hysteresis point where pressure to rear brake line begins to be "proportioned". From now on pressure to the rear brake lines will increase at a slower rate than the front brakes, with a slope that is equal to the "proportioning rate" of the valve. Increasing the spring rate will increase the rear line pressure where hysteresis occurs.

(Note: Saying a prop valve reduces rear line pressure is a misnomer. The pressure is actually increasing as the brake pedal is pushed harder, but the rate of increase is less than the rate of increase in the front brakes. The rear brake line pressure is "proportioned" as a ratio of the front.)


Step 3: The proportioning rate

At this point the rear line pressure is stagnant because the line is sealed off from the front chamber. As pressure rises in the front chamber it causes a hydraulic force to be applied to the piston that pushes it to the right again. As the piston moves right the cup-seal is deformed and pressure can rise in the rear chamber again..... but this time pressure doesn't equalize with the front. From now on the rear line pressure will always be less than the front line pressure. The secret is in unequal surface areas for hydraulic pressure to act on.

The piston is basically stuck floating between the point where the cup-seal opens and closes. The forces pushing the piston to the right are in balance with the forces pushing the piston to the left. However, the hydraulics in the rear chamber are pushing against a larger surface area than the hydraulics in the front chamber, so the rear chamber ends up at lower pressure than the front in order to balance forces. And that's how the prop valve proportions rear brake line pressure. This situation won't change until the brakes are released and the pressure goes below the hysteresis point again.


Doing The Math

All the calculations in this example are for a 3rd gen "NB code" prop valve. Some measurements of the piston are needed.




We know that inlet pressure equals outlet pressure in the range of operation before reaching the hysteresis point. And the hysteresis pressure is found by,

Assembled spring force = (hysteresis pressure) * (spring tube area)
(9.8 lb) = (hysteresis pressure) * (0.06335 inch2)
hysteresis pressure = 155 psi

After the hysteresis point, rear line pressure is found by the following method.

Assembled spring force = (spring rate) * (compressed length)
Assembled spring force = (19.6 lb/inch) * (0.5 inch)
Spring force = 9.8 lb

Calculate the area of the piston on which the hydraulic pressure acts to cause a force to the right (--->)

Area on inlet side = (shelf area) - (spring tube area)
Area on inlet side = [ (shelf diameter)^2 - (spring tube diameter)^2 ] * pi / 4
Area on inlet side = [ (0.420)^2 - (0.284)^2 ] * pi / 4
Ai = 0.0752 inch2

Calculate the area of the piston on which the hydraulic pressure acts to cause a force to the left (<---)

Area on outlet side = (spring tube area) + (Ai)
Area on outlet side = [ (0.284)^2 * pi / 4 ] + (0.0752)
Ao = 0.1385 inch2

Calculate the total force by which the piston is pushed to the right (--->)

Total force = (Hyd force inlet side) + (spring force)
Total force = [ (Ai) * (master cylinder pressure) ] + (9.8)

The forces must balance on the inlet side and outlet side of the piston. The right side of the piston has only a hydraulic force element. Calculate the hydraulic pressure in the outlet.

Total Force = (Hyd force outlet side)
Total Force = (Ao) * (rear line pressure)
rear line pressure = (Total Force) / (Ao)

And now you have the ability to calculate rear line pressure. If you iterate this a few times you can also generate curves for any stock prop valve, such as below.

QwkTrip

iTrader: (22)

Modifying the OE prop valve

The "Grainger spring swap" is a well known modification to get the rear brakes to participate more. As shown earlier, swapping springs changes the hysteresis point but it does not change the proportioning rate of the valve. By swapping springs you end up with two parallel curves with one higher than the other (see graph below).

I've read a lot of threads on this site about the Grainger spring swap and one thing is clear -- different people get different results, sometimes wildly different. The reason is because they're only paying attention to advertised spring rates and don't understand what's really happening. It's not the spring rate you need to pay attention to. The key feature is the spring force that is applied to the piston when the spring is fully assembled into the valve. And that spring force will be different depending what valve you have.

The spring sticks out the end of the valve body before assembly and the spring is compressed when the vent cap is screwed in place. The spring force on the piston is,

spring force = (spring rate) * [ (free length) - (compressed length) ]

There are multiple piston designs that I know of, maybe more. The NB code disc brake piston I have results in a spring compressed length of 1.0 inch. I've never had a drum brake piston in my hands, but it definitely has a longer pocket for the spring and the spring is not compressed as much. So putting the same spring in a disc valve vs. a drum valve will give two different results. But there is a much bigger difference than that between disc and drum valves. The other factor is the piston "spring shaft diameter", and it is different between the various valves.

The shaft diameter also is a powerful tuning tool and has a massive effect on how the valve behaves. A smaller spring shaft diameter will increase the hysteresis point, but it will also increase the proportioning rate of the valve (slope of the curve). The chart below compares a mid-'80s disc brake NB valve to a later LF valve used on the 1LE cars. The LF valve uses the same spring as a stock NB valve, but has a smaller piston shaft diameter that results in a more aggressive proportioning slope. Even swapping out for a 2x more powerful spring in the NB valve doesn't make up for the difference at high braking pressures. So it's no wonder the later disc/disc valves are so desirable: they have a higher proportioning rate.

But don't throw away your drum brake valve yet! Turns out the drum valves have an even smaller piston shaft diameter than the later disc/disc LF valves, and that means an even higher proportioning rate. All you need to do to make your drum valve work is choose the right spring. For example, tossing a Grainger 1NCF1 spring into your old NC code drum valve will produce more aggressive braking curve than the later model LF valve used on 1LE cars.

So now you know how to do the calculations and what to watch for. Doing so can literally make the difference between lackluster brake performance and having a panic attack when rear brakes lock. At the end of the day these calculations are only an aid to help guide you which direction things will move with a particular change. You'll still need to get out there with the car to see what happens and go from there.

QwkTrip

iTrader: (22)

Here is the technical data needed to do calcs. Some of this data has measurements to back it up, some I am guessing. I need help from members here to check & verify. The better we make these data tables the better the results.

The "Spring Force Assembled" is what you use for calculations to create prop valve curve. One column is the force when spring is assembled with a piston from disc/disc valve. The other column is the force when the same spring is assembled to a piston from a drum valve, because the spring doesn't compress as much. I am looking for volunteers to take some measurements of stock parts for me. Just post up and I'll explain what I need from you. I think the stock springs are music wire and I highly recommend staying with music wire.




Dimensions of the piston inside the prop valve. A lot of this is guesses and I need help from members to put the right data in here.





Stock 3rd gen prop valve codes. The broadcast code is stamped onto the body of the prop valve.




This doesn't help with calcs but it's hard to find information that I think is worth sharing.

QwkTrip

iTrader: (22)

And here is the information needed about the brakes. I am unsure about numbers in red text. And there are blanks in the table that I would like to get filled out. Again, hoping people can check & verify to help get this data right.

daferris

iTrader: (8)

Still wrapping my head around all of this info... Thank YOU for the hard work in compiling it!

QwkTrip

iTrader: (22)

You're welcome. It was a fun little hobby last winter.

This came about because I kept guessing and making changes to improve braking performance and wasn't getting the results I wanted. Finally got tired of all that hassle and figured this out. Being able to run calculations and comparisons in a spreadsheet made all the difference in the world. I suddenly knew what changes to make and what to expect. It was freakin' fantastico.

I have a spreadsheet where you can choose the front and rear brakes from a pick-list and it will do the calculations for you. But it's not as user friendly as you might think so I never offered it up to everyone. I can give you a copy if you really want it but you're kind of on your own using it.

Bow_Tied

iTrader: (1)

I was able to follow along with the math and have no complaints on the explanation, it follows engineering logic as far as I can see. Very nice work and strong explanation; well done. Are you a mech engineer?

The thing that kept occuring to me as I read the threads on swapping springs is the effective spring rate over actual travel seemed to be talked about. I think you have shown that this is an important pc of the puzzle. Same with the spool valve dimensions.

QwkTrip

iTrader: (22)

Thanks for the feedback. Your input is appreciated and valued!

By education, yes, but have forgotten 99% of everything by lack of use. You know how it is, 90% of engineers run elements of the business while 10% or less are the hardcore designers. I'm the 90%.

Bow_Tied

iTrader: (1)

You have stated assumptions and maintained units in your calculations so you haven't forgotten too much! I'm a mech eng tech that does design work and likely wouldn't have met the bar of your post.

In consideration that there are a number of assumptions in the calculations would it fair to suggest that going through this exercise is primarily about understanding the concepts and how the components impact the outcome - and then to use the output as a comparison tool vs. an actual specific calculation of one's car? At least I see the greatest value here is to evaluate how changing components changes the relative output more than defining the actual results. I think that is why you have suggested that results ought to be confirmed individually.

QwkTrip

iTrader: (22)

Exactly. I used it to make relative comparisons, and decide if a change was directionally correct or not. I already had seat time in my car so I wasn't flying blind either.

There are some rule of thumb guidelines for overall braking torque and front/rear bias, depending on application. I found some good info at pro-touring.com where the guys from Kore3 and Ron Sutton are talking about brakes.

ResIpsa

iTrader: (1)

It’s funny when you look at the math so many common brake system beliefs just get thrown out the window. Such as six piston calipers (or eight piston, 12 piston, etc...) have more braking force than single piston calipers.

When the reality is it’s just a function of total piston area. You can have one large piston or multiple tiny opposed pistons if they (divided by 2) add up to the same total piston area they will brake with the same force.

Or that by upgrading to larger brakes (i.e. more braking force) will make your car stop In a shorter distance. When the reality is adding more braking force to the front generally results in a longer stopping distance. ( Quick hint, on a normal street car slightly increasing rear brake force generally results in shorter breaking distances).

But I guess that is the beauty of a brake proportioning valve.

KyleF

What a lot of people overlook is braking performance is usually tied to the tires more than anything else. Their ability to grip the road and not lock up is what determines how hard the pads can squeeze the rotors and dissipate energy. The main point of bigger brakes and multiple pistons is to handle heat, spread it out, and dissipate it to prevent fade.
Multiple pistons versus single piston doesn't necessarily change total force applied (depends on cylinder sizes), but it spreads it more equally out across the pad surface.

alan91z28

Qwktrip, this is a very nice thread and summary and would be a good stickie

Also anyone interested in understanding more about design of brake systems, the book Brake Design and Safety by Rudolf Limpert is an excellent resource

QwkTrip

iTrader: (22)

Thanks.