Hydraulic disc brakes - how they work and troubleshooting
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[edit] Hydraulic disc brakes - how they work
[edit] Overview
All bicycle brakes work on the simple premise of providing a torque that slows the rotation of the wheel. The torque is provided by the rider pulling a brake lever at the handlebar, which by some means or another, actuates the brake. Torque is defined by essentially two things: force, and the perpendicular distance between where the force is applied and the point about which the body is rotating. For a brake system on a bike wheel, the force is applied at the brake caliper, the wheel is rotating about the axle, and the distance between them is the distance from the centre of the axle to the centre of the braking track on the brake rotor (so slightly less than the outer radius of the rotor), which we will call "r".
[edit] Inside the caliper
At the caliper, you have a pair of brake pads that are pushed into the rotor from opposing sides. In a perfectly set-up brake, this means the rotor doesn't have to move sideways or flex at all, because the force from each pad cancels out. The amount of friction provided by the brake pads against the rotor is proportional to two things: the Coefficient of Friction (Cf) between the pad and rotor, and the force pushing them together (the clamping force, we'll call it Fclamp). Coefficent of friction is, in reality, affected by temperature, clamping force (so it's not perfectly linear, though for stiff materials with smooth surfaces it's close enough) and to a lesser extent the speed at which the two surfaces are moving relative to each other. This is why sometimes brakes can feel "grabby" at very low speed but not be noticeably grabby on the trail.
So, frictional force Ff is:
- Ff = Cf * Fclamp
And again, since the braking torque is a function of the rotor radius (to the centre of the braking track) times the frictional force, the brake torque T is:
- T = Ff * r
- T = (Cf * Fclamp) * r
What provides the clamping force though? This is provided by brake fluid (DOT fluid or mineral oil usually) being pressurised and pushing against the back of the pistons (known as slave pistons, slave cylinders or caliper pistons) in the caliper, which in turn forces the piston to push the pad against the rotor. Any static fluid (fluid can refer to liquid or gas) that is under pressure exerts the same pressure in all directions. This means that it exerts the same pressure against any surface that holds it.
The total clamping force is proportional to the total area of the piston or pistons on ONE side of the caliper, multiplied by the brake fluid's pressure. This is because of the relationship between pressure and force: Pressure (P) = Force (F)/Area (A) In other words, P = F/A We can rearrange this equation to be:
- F = P * A, which is Force equals Pressure multiplied by the area (perpendicular to the force) over which the pressure is applied.
Technical aside: Why does the relationship only account for the pistons on one side of the rotor, doesn't it make a difference if you have another piston or pistons directly opposite instead of a static pad in the caliper? The reason for this is that the forces cancel out since the rotor is always clamped from both sides anyway - whatever force you put in on one side has to be equalled by the force pushing on the rotor from the other side. The pressure in the caliper in a normal two-piston caliper (eg Hayes, Juicies, newer Shimano stuff) pushes on the piston in one direction and the caliper in the other, which essentially "pulls" the far side of the caliper against the rotor (in reality it pushes the rotor over against the caliper, but the effect is the same) in the same way that it would if there was simply fluid on that side of the caliper pushing the piston against the rotor too. When you have the opposing piston, the pressure against the caliper on each side balances out (so the caliper is not pushed in a particular direction relative to the rotor, or vice versa), as does the pressure on the two opposing pistons.
Anyway, so far we have now established that the braking force you can apply is proportional to a few things: 1. Rotor radius 2. Pad coefficient of friction 3. Total piston area on one side of the caliper 4. Pressure in the brake fluid
Before we move onto point 4 in more detail, let's examine point 3 a bit more closely and clarify a couple of things. First up, it should be noted that the area of a piston is proportional to the SQUARE of its diameter/radius. The equation for the surface area of a circle is:
- A = pi * r^2, where pi is the well known constant, being equal to roughly 3.14
This relationship has a critical implication as far as the difference between 4-piston brakes (ie 2 pistons per side) and 2-piston brakes (1 piston per side). If, for example, you have a 2-piston caliper with 20mm diameter pistons (r = 10mm), this will not be equivalent to a 4-piston caliper using 10mm diameter pistons (r = 5mm). For the two-piston brake:
- A = pi * r^2
- A = 3.14 * 100
- A = 314.16mm^2
For the four-piston brake:
- A = 2 * (pi * r^2)
- A = 2 * (3.14 x 25)
- A = 157.08mm^2
As you can clearly see, having twice as many pistons at half the diameter gives only half the surface area (and thus braking power).
[edit] How pressure is generated in the brake fluid
As shown above, the pressure in the brake fluid is directly proportional to how much clamping force and thus friction you have. But how is the fluid pressure generated? It's done by pulling the brake lever, which in turn pushes a piston in the lever body (known as the "master piston" or "master cylinder"). This piston pushes fluid down to the caliper, and the force you put into the master cylinder is directly proportional to the pressure generated in the system. Brake systems have what is known as a Pressure-Volume (P-V) characteristic, which is the relationship between the volume of fluid pushed by the master cylinder and the pressure generated in the system. This is essentially a measure of the elasticity of the system as a whole, in other words, if your caliper/pads/pistons/brake lines/master cylinder are stiffer, you will need to push less fluid to generate any given brake pressure. This does not mean that you will need to pull on the lever less HARD but it does mean the lever will move less FAR.
What is important to note here is that the force/pressure/area relationship still applies to the master cylinder, however because you're applying a FORCE to the master cylinder (via the brake lever), the pressure generated in the system is inversely proportional to the surface area of the master cylinder. That means a smaller master cylinder piston will result in a higher pressure for a given input force at the brake lever. Another factor requiring consideration is the leverage ratio of the lever blade itself, that is, the ratio between the length of the lever blade from pivot to finger-hold and the distance from lever pivot to pushrod pivot. The higher this ratio is, the more power the brakes will have (for a given force on the brake lever), but also the brake lever will move further.
[edit] Clamping Force
The clamping force of the brake is the product of all the above factors, which multiply together to give a ratio which determines the overall mechanical advantage. Mechanical advantage refers to the ratio of forces output and input to a system. For example, say at one end of a system, you input 15 Newtons of force, and the output is 60 Newtons. This means that you have a mechanical advantage of 4:1, as the output force is 4 times as high as the input force. However, in a closed mechanical system (no external "boosters" or other power sources), this also means that for a given input distance, the output distance will be the inverse multiple of the mechanical advantage. In this case with a mechanical advantage of 4:1, say the input movement distance was 80mm, the output movement would only be 20mm, which is 1/4 the input. The same applies to hydraulic systems - if you use a master piston with say 1/4 the area of the slave pistons (assuming again that you have a two-piston setup), the distance the slave pistons move will be 1/4 as far as the master piston. This is sometimes referred to as a "hydraulic advantage ratio", however it is effectively the same thing as mechanical advantage.
Why is this the case? It's simply a factor of a term called "work". Work refers to force multiplied by the distance moved. This is the absolute fundamental principle of leverage - you can apply a much larger force if you use a longer lever, but you have to move the input much further to do so. For a given amount of work required, if you decrease the amount of force being used, you must increase the distance over which it is applied.
How is this relevant to brakes? When you pull on the brake lever, you move the lever perhaps 30mm, yet the caliper pistons themselves only move a very small distance, let's say about 1.5mm in total. This means that whatever clamping force your hand can apply to the lever is being multiplied by about 20 at the pads. A reasonably strong person can squeeze over 300N into a brake lever fairly easily, with this mechanical advantage ratio of approximately 20:1, this means the clamping force at the caliper could be 6000N (the equivalent of about 600kg). These numbers are estimations, not measurements, but the purpose of them is simply to highlight how the force your hand can apply is multiplied greatly by the brake system.
[edit] Braking "power"
The job of a brake is to convert kinetic energy (movement of a mass) into thermal energy (heat) by means of friction. Power is defined as:
- Power = Force * Speed
or
- Power = Torque * Speed
So the power a brake system is generating at any given time is proportional to the torque it's generating, multiplied by the speed at which the bike is travelling.
[edit] Brakes and heat generation/dissipation
Most modern brakes thankfully have little or no issues with the brake fluid itself overheating. This means that "brake fade" is typically to do with the pads themselves being overheated. As stated above, brakes are specifically designed to generate heat, so it is imperative that they also be able to deal with the temperatures they generate. As a general rule, more surface area for the braking surfaces (that means the braking track of the rotor, and the faces of the pads) means better heat dissipation. Brakes with bigger pads (and rotors) will be harder to overheat, because there is more surface area to dissipate the heat energy, which results in a lower temperature across that surface. If you suspect you're overheating your brakes, there are a few things you can try:
- Larger rotors. This is the simplest one and it has the added benefit of giving you more braking power for less force at the lever.
- A brake system with larger brake pads. Typically 4-piston and 6-piston brakes have bigger pads than 2-piston brakes, which while it might not offer more outright power, is inevitably going to provide better cooling.
- Laying off the brakes. The major reason that brakes ever get overheated in the beginning is that riders drag them for too long. On top of continually generating heat, this doesn't let air run over the brake pads (since they're pressed against the rotor) to cool them. Because rear brakes in particular are very easy to drag, they are often overheated in spite of not ever being able to generate the same braking torque under full load that front brakes have the opportunity to.
Also, heavier riders generate more braking heat because more force is required to stop them. This might seem obvious but if you're a 120kg rider you're going to need to dissipate twice as much heat as a 60kg rider all the time. If you're both using the same brake system, guess who's going to have overheating issues.
Another factor in heat generation is pad compound. To understand why this is, we must look at the different pad compounds available and their characteristics. The two most common forms of bike brake pad materials are sintered metal (metal powder pressed and bonded) and "organic" brake pads (carbon/resin-based compounds). Sintered pads provide lots of friction and a very long life, but also generate lots of heat. Organic pads on the other hand, generate quite a bit less heat but also don't last as long. The reason for this is that the kinetic energy is being used in two different ways during braking. On a sintered pad (which is a harder compound), as the molecules of the brake pad slide over the molecules of the rotor, they hit each other and induce vibrations at a molecular level - this is exactly what heat energy is. However, on a softer organic pad, some of the kinetic energy is used to break the molecular bonds in the pad material, which results in less energy being converted to heat as well as more wear in the pads.
[edit] Brake operation problems - diagnoses and common misconceptions
As with any troubleshooting, the best way to do it is to be totally methodical. There are only a few things that can go wrong with brakes:
- Mechanical failure, leakage etc. Pull the lever and either oil comes out of the outside of the brake, or the lever goes straight to the bar. This is usually fairly obvious.
- "Spongey"/soft lever feel. This happens when the system is too elastic - usually because there are air bubbles present in the system, which compress when you pull the lever. This reduces the gradient of the P-V (pressure-volume) characteristic so that the lever needs to be pulled further to reach any given fluid pressure/clamping force. This is usually solved by bleeding the system thoroughly, shortening the brake lines, or installing new lines/pads with lower elasticity. Another common cause is misalignment of the caliper/rotor - if they're not straight, they'll need to flex for the pads and rotor to meet squarely, which will make the brakes feel soft and make the engagement point of the brakes harder to discern.
- Lack of power. People commonly attribute this to brakes requiring a bleed, but if the lever feel is firm, the bleed is absolutely not to blame. All the brake fluid and indeed the whole brake system up to the caliper does, is transmit and multiply the force your fingers put in, to clamp the pads against the rotor. In fact, even with a poor bleed, whatever force you put into the lever will result in the same multiplied output force as with a good bleed, because in order to keep equilibrium in the system, the fluid pressure (including any compressed air bubbles) acting on the master piston must be sufficient to balance the force you're putting into the lever with your hand. The point being? If your brakes are lacking actual stopping power, bleeding them won't help.
If your brakes don't have enough bite or power, the problem nearly always lies in your pad/rotor interface. This can be because of:
- Contamination by oil/lubricants or other deposits on the brake pads/rotor, requiring new brake pads and a thorough cleaning of the rotor with a suitable solvent such as acetone or isopropyl alcohol
- The pads/rotor haven't bedded in to each other yet - very common on new bikes, which often results in people trying a brake in a shop and thinking it's bad
- Overheating of the pads. If your pads have been overheated, they will tend to "glaze over". If this has been done badly enough it will result in a visibly shiny pad surface, but as often as not you won't actually be able to see it. What can you do to solve it? New pads is always a possibility, but generally just continuing to ride on the brakes and making sure not to overheat them again is the best method to fix them. You can try sanding/filing the pads but chances are that you won't be able to keep it flat enough, and the pads will need to be bedded in again. If the pads have been badly overheated, it's possible that the whole pad's braking material will have been hardened somewhat and as a result they will never work quite as well again.
- Brakes dragging/rubbing. This is most commonly caused by simple caliper misalignment, which can be fixed by simply realigning the caliper. Other causes are warped rotors, which need straightening or replacement to prevent rubbing, or occasionally sticky caliper pistons. If the pistons are not moving evenly, one may tend to rub on the rotor. If you suspect this is the case, consult the manufacturer's service guides - usually found on their websites - for instructions on how to service the caliper pistons.
