How do brakes work (aka: where's the spring?)

[Jeff S]

In replacing the brake system on my Z900RS, I realized I don't understand brakes. Here's what I think I know:

1. Ideal braking system has perfectly rigid lines - zero change in internal volume (not a spring)
2. Ideal braking system is 100% filled with fluid - zero air - and the fluid is perfectly incompressible (not a spring)
3. Ideally, the brake lever and calipers (and other mechanical bits along the way) are perfectly stiff (not a spring)
4. Braking force is due to friction, meaning the only difference in 10% braking force and 100% braking force is the normal force of the pads against the rotor (different force but same position - zero internal displacement difference)
5. The master cylinder changes displacement linearly as it goes from 10% to 100% braking force

It SEEMS that we try to remove the springiness from a brake system to improve it's performance, but is also seems that fundamentally, a brake system is closer in theory to a spring (transform MC displacement to brake pad force) than to a closed hydraulic system (transforms two displacements by the ratio of cylinder diameters).

So, where's the spring? It seems like the "spring" that's critical to performance of the system is really just the "accidental" leftovers of not being perfect at #1, #2, #3 from above. We talk about spring rates in shocks - why not talk about spring rates in brakes... if that's what actually makes them work? It's hard for me to imagine that the only reason brakes work like they do is from our inability to achieve the ideals for 1, 2, and 3.

This only works if 4 and 5 are also true. So one MUST be wrong. Right?

I think #4 above is totally true. This is why you can "upgrade" from a 4 pot to as 6 pot caliper (+50% surface area) and a) not change the MC diameter and b) actually get better "performing" brakes. If the braking force caused any measurable piston displacement - then you'd HAVE to increase MC displacement... which you don't. 50% larger piston area means larger pads - so the same force is being applied over a larger area - which is good for heat dissipation, and more even pressure on the pads for lower flex, etc.

So, is #5 wrong? The lever clearly moves between 10% and 100% braking force - I am not applying more force to a perfectly stationary lever. Is the spring in the system that makes brakes work lever flex? Even the cheapest aluminum levers feel pretty darn close to perfectly rigid to me.

I'm ignoring the 0% to 10% range of braking force - clearly at 0% the pistons retract and the pads measurably move until the normal force on the pad is essentially zero. Brake pads are clearly not perfectly smooth, so perhaps they actually are deforming (acting as springs) thru some tiny displacement amount? Anyway, I can imagine a lot of "slop" in the very low brake-force ranges where both spring and displacement is in play - so I'm trying to only think about the part where the rotor, nor pads, nor piston walls, nor caliper body are flexing (acting springy).

I'm aware there IS a spring in a brake system - in the MC behind the piston - but it's tiny and just there to ensure the lever returns as I lower force on it (I think?).

Summary: brakes are springs: displacement at the MC and force but zero displacement at the caliper. We try to lower the springiness (increase k), but if we perfectly achieved this, brakes would feel totally broken (no lever movement, no "feel" at all. Right?

 

[btrider]

When the shoes contact the drum a gradual slowing will begin. If unit has just gone thru a low water crossing then you are in trouble. That there is how brakes work!

 

[FE_Rex]

1. Ideal braking system has perfectly rigid lines - zero change in internal volume (not a spring)

"softlines" on brake system are not truly as rigid as hard lines - even if they are SS braid over Teflon

2. Ideal braking system is 100% filled with fluid - zero air - and the fluid is perfectly in-compressible (not a spring)

DOT fluids are somewhat compressible as are all liquids (maybe not so much at working brake pressures). Matter of fact, DOT5 silicone based fluids are compressible enough not to be suitable for ABS

3. Ideally, the brake lever and calipers (and other mechanical bits along the way) are perfectly stiff (not a spring)

They also have a little flex - put you hand on a caliper when you strongly apply brakes

4. Braking force is due to friction, meaning the only difference in 10% braking force and 100% braking force is the normal force of the pads against the rotor (different force but same position - zero internal displacement difference)

There is a LOT going on here that isn't explained by the simple linear friction model (friction force = coefficient/normal force). In theory, you can have a force without displacement, but in "real--life" Hooke's Law is an undeniable fact - cause nothing is ever truly perfectly rigid.

5. The master cylinder changes displacement linearly as it goes from 10% to 100% braking force

The displacement of the master cylinder is certainly related to the increase of pressure, but very small line ballooning and system flex is where your "feel" comes from. It doesn't take much flex to give "feel" - think about the volume of that last bubble you got out the last time you bled your brakes and also realize that for every 15psi in brake pressure that bubble halves in volume

 

[one Wolf]

Don't miss the fine point, that when the lever is in the released position, the system is essentially open to the atmosphere at the master cylinder reservoir. Until the lever is moved enough to cover the master cylinder port to the reservoir you get lever movement "spring" then the system is hydraulically solid.

Mostly.

Prove me wrong...

 

[FE_Rex]

Don't miss the fine point, that when the lever is in the released position, the system is essentially open to the atmosphere at the master cylinder reservoir. Until the lever is moved enough to cover the master cylinder port to the reservoir you get lever movement "spring" then the system is hydraulically solid.

Mostly.

Prove me wrong...

I’m thinking that movement to close the port is take-up similar to freeplay on a cable clutch

 

[DFW_Warrior]

Summary: brakes are springs: displacement at the MC and force but zero displacement at the caliper. We try to lower the springiness (increase k), but if we perfectly achieved this, brakes would feel totally broken (no lever movement, no "feel" at all. Right?

Not really. There is still lever movement to close the port in the master cylinder. There is a small gap between the rotor(s) and pads. There is also probably a small gap between the pistons and pads. So you will get quite a bit of lever movement just from all those things tightening up when you apply the brakes. Then, when the brakes are applied, pad material is most certainly compressing. Calipers can also flex to a certain extent as well. If you remove all the slop from the system, you will still have those things that will always have to have slop or the brakes would just burn themselves up in short order.

 

[Cagiva 549]

Back before disc brakes were invented racers used metallic brake shoes and drum brakes , mid 70 s or so I put a set of those metallic shoes on my old beater 140 mph ElCamino , one night I had the opportunity to need to hit the brakes at around 120 , at arounf 70 I was easing up on the pedal to keep my face from planting in the windshield . The hotter they got the better they stopped . Only modern vehicle I have ever had with brakes that good is my mid 90s F 350 fords with 12 x 3 inch rear drum brakes . I never used trailer brakes till I started towing with a truck with 4 wheel disc . Those metallic brake shoes were still on that ole beater truck when I sold it ten years latter and they would still out stop a whole lot of what was on the road back then . And chinese brakes that have flooded the market these days dont even get me started on that crap .

 

[Jeff S]

Not really. There is still lever movement to close the port in the master cylinder. There is a small gap between the rotor(s) and pads. There is also probably a small gap between the pistons and pads. So you will get quite a bit of lever movement just from all those things tightening up when you apply the brakes.

Totally get that... This is why I was considering only the 10% to 100% brake force range... thinking all that play will be accounted for by that point.

Still, I think I get 1/2 to 3/4" MC piston travel with no perceptual piston/pad travel. Hard to believe all of that is "flex" and give and "springiness" from not-perfectly-rigid parts. But, guess it is.

 

[DFW_Warrior]

Totally get that... This is why I was considering only the 10% to 100% brake force range... thinking all that play will be accounted for by that point.

Still, I think I get 1/2 to 3/4" MC piston travel with no perceptual piston/pad travel. Hard to believe all of that is "flex" and give and "springiness" from not-perfectly-rigid parts. But, guess it is.

That's because the volume that the master cylinder is pushing is very VERY small compared to the volume inside the calipers. One full squeeze of a lever is only going to move those pistons maybe 0.5-0.75mm.

And you brought up that you can change the calipers out for larger volume ones with more pistons without changing out the master cylinder. By most brake people that is almost always regarded as not wise precisely because the volume at the master cylinder stays the same, but the volume at the calipers increases to the point where you will actually degrade your braking instead of improve it.

So at the end of the day, it really isn't a spring, but it really is a pretty standard hydraulic system. The tricky part is that it is both an open and a closed system depending on the condition of the brake lever and the port that can be open or closed.

 

[Jeff S]

One full squeeze of a lever is only going to move those pistons maybe 0.5-0.75mm.

Indeed: MC diameter is I think 17mm and I have 8 pistons, each over 25mm (two different diameters, interestingly), so nearly 12:1 ratio. Thus: 12mm MC displacement ~= 1mm per piston. That should be apparent and measurable.

The two pad faces that contact the rotor experience zero displacement during that 10% to 100% range (the rotor is not deforming). That means there's a little spring just between the piston surface within the caliper to the rotor surface (meaning: piston walls, piston/pad interface (mine have small sheetmetal component in there) and pad body).... if the piston/fluid interface surfaces really are moving 1mm. I can't see ANY movement at the piston/pad interface in this range. I'll see if I can find a way to measure this.

 

[FE_Rex]

Actually in your example the ration would be ~17:1 - displacement goes by square of diameter.

Also we have not mentioned the lever ratio - the ratio on my K1300S looks to be 4 or 5 to one @ the middle of the lever

 

[DFW_Warrior]

17mm for a master cylinder piston diameter on a motorcycle? Are you sure about that?

 

[Jeff S]

No, I am not

 

[Jeff S]

Actually in your example the ration would be ~17:1 - displacement goes by square of diameter.

Also we have not mentioned the lever ratio - the ratio on my K1300S looks to be 4 or 5 to one @ the middle of the lever

Math: Uhh, yeah, that should have been obvious.
Lever: yeah, and at least one of my bikes has adjustable lever ratios. But, if we consider only the MC piston displacement, this ratio is 'outside' that interaction.