Braking 101

Brake Handles

  
     Braking starts with the operator at the handlebar lever. Using a force of 2 to 7kg, The operator squeases the brake handle. By leverage action, this force movement is transfered to the cable to move it with-in the cable housing. At the other end of the cable a similar leverage action is used to engage te pads on the braking surface. The amount of braking pressure is direct proportion between effort source and effort at the destination. Typically, there is only 1 inch of cable movement at the source. At the destination this is also true but, and there is always a but, while the pads are not in contact with the stopping surface, pressure at the handle lever is very light. As the pads make contact pressure at the handle increases. The stopping power is governed by the ability of the operator add additional pressure.

     For a child, limits of 2kg maximum pressure is typical and so child bikes rarely have hand brakes and opt for foot operated coaster brakes where a back pedal pressure of 8 to 15kg supplies better pressure. For women typically, they have stronger grip and can excerpt 4-6kg, 40 - 60N. Men have a typical range of 5-7kg, 50 - 70N. To even the playing field, An electronic brake handle that does not rely on grip strength would be a bonus. A tensile spring return of 2kg supplies a constant pressure as a minimum. An aditional 1 to 1.5kg stretches the spring and the cable or rod would be used to adjust a potentiometer to identify the amount of brake pressure to apply. Electric bike accelerators already use this for speed control. As such a Thumb throttle or twist grip moved to the opposite handbar handle can be repurposed to supply braking pressure.

Rim Brakes

  
     Rim brakes use a cantilever design to double the pressure from the 1" of cable pull into an effective 1" per side of movement. As such pads move against the rim from both sides. Actual movement free of the rim is less than 0.5 inch per side. This leaves up to 0.5" travel to convert into pressure. The circumphrance of the wheel rim provides the stopping surface and the length and height of the pads provide the friction to the surface. As pads wear, more travel is required to supply the same stopping pressure. Friction causes heat and pad wear as well as potential warping of the rim to cause tires to deflate. It depends on the rim circumphrance to disipate the heat.

     Besides loss of pad depth from wear, cables can stretch and even brake. On long downhill braking there may not be enough time for heat on the rim to disipate properly.

     To implement electronic breaking on a cantilever brake, you would still have the cable to the cantilever but the cable would be pulled by a solenoid type servo or motor type servo with a > 1" stroke.

Brake Rotors

 
     Rotors are the next stage in braking. They can be mounted only to wheel hubs designed for them. They start out about 1.8mm to 2.0mm thick and when they wear down to 1.5mm it's time to replace them. You will note they have all kinds of holes in them. These are used to help disipate heat and lower noise during braking. Where a rim pad is 0.5" x 2", the disc pads are normally 1.5" x 3". This means that Disc Pads cover 4.5 Sq in vs rim brakes that have 1 Sq in. This is 4.5 times more stopping area. The brake calipers that strattle the rotor are mounted to the frame forks on the left side of the bike.

Cable Disc Brakes

 
     Above left you see a customary Cable Disc brake. The Caliper mounts to the fork, strattles the rotor and has a brake cable that pulls a lever which rotates against the piston to move a brake shoe out against the pad. As this happens the shoe is forced against the rotor pushing the rotor sideways against a brake shoe on the other side. This causes much more friction and heat than a rim brake. More friction and larger pad surface to rotor becomes far superior stopping power. As pads wear, there is an adjustment to compensate. As Brake Cables stretch, there is another adjustment to compensate.

     Heat and poor weather combined with long downhill use for slowing can and do contribute to accelerated pad and rotor wear and warping of the rotor. A warped rotor can increase friction against the inside pad while riding with the brakes not even applied.

     In an electric brake situation, a servo or PWM motor would mount to the fork above the Caliper and draw the Cable the 1" or so needed for brake full travel.

Cable hydraulic Disc Brakes

  
     If you have a cable type hand brake lever and the hydraulic reservoir is at the Caliper then you have a Cable-Hydraulic brake. If the reservoir is up at the brake lever, then the system is pure hydraulic. In the pure hydraulic system The brake lever forces the hydraulic fluid into the line. The fluid is non-compressible so the fluid forces into the caliper and agaimst the piston. Since the piston is the only thing that can move in the system, the hydraulic fluid expands the piston into contact with the brake shoe which in turn comes into contact with the rotor.

     Down at the Disc rotor, the caliper will be either single or dual acting. A dual acting provides brake pressure from both sides of the Disc. Single on the other hand has a fixed pad on one side and the moving pad on the other side.
 
     The single sided Caliper suffers from the same problems as the Cable Disc brake. Loss of braking if too hot, or too wet. The disc can be warped by heat and single sided pressure. The dual acting does not force the Disc into a stationary pad. Both pads are moved to the rotor and apply equal braking force. The strength of the hydraulic system is based on the fact that a large piston at the hand grip lever forces a large volume of fluid into a relatively narrow line. Reaching the Caliper the fluid fills 1 (single) or 2 (dual) piston chamber and the piston(s) is/are forced to move.
     On the down side, care must be taken to bleed air and moisture from the lines. Only pure hydraulic fluid should be present. Air and water can compress but hydraulic fluid can not. Seals in the calipers can deteriorate and leak. As they leak air can be drawn in to the lines causing spongy brakes. With natural heating and cooling moisture develops in the lines which attacks the seal integrity. While some Calipers are auto adjusting to reduce over working the calipers and thus avoiding potential seal leaks, most are not. You will find bleeder screws and pad adjusters.

     For the Cable-hydraulic an electric brake system as mentioned for Cable Disc brakes can be used. For the pure hydraulic, it is likely that the whole system from the handbars to the wheel rotors would need replacing. While a servo can easily push a plunger and if that plunger is on a reservoir of hydraulic fluid, we could possibly move the hand grip brake lever with reservoir from the hand grip to some other location and put an electric brake deselerator where the old hand brake was.

Servos

     There are many ways of turning electrical signal into mechanical motion. An electromagnet in a relay mechanically switches contacts from one state to another. An electromagnet door lock gives access or denies access to a doorway in a security system. A motor rotates or spins a shaft when power is applied. A Stepper motor can rotate in precise increments both clockwise and counterclockwise directions. A solenoid can either push or pull it's plunger when power is applied. A bi-directional solenoid can be told to move it's plunger one way and back to center then the other way. Each movement produces both a pull action and a push action with 3 defined states of action A, action B, or center=off

  
     There is a close love hate relationship between the motor, stepper motor, linear actuator, and servo. The motor without PWM (pulse width modulation) spins at full speed with a finite torque. If you need it to spin faster or slower you have it drive gears to change the rate of spin, use an H-bridge and PWM control to set spin direction and speed, or if an AC type motor you can alter the frequency for even more control such as current vs torque. But alas, the motor can't be a stepper, an actuator, or a servo by itself.

  
     The basic stepper uses an H-bridge and PWM to control direction and rotation in a count of steps. It can precisely move based on the number of steps to take. So if a given stepper has 200 steps per rotation, and it is told to move CCW 6 steps then CW 215 steps then CCW 300 steps, it's final point is -6+215-300= -91 steps from the start position. Often external sensing is needed so a controller knows exactly where the stepper possition is. The stepper really does not have good torque or holding strength. You will note that so far all motor devices have been rotational in nature.

     The linear actuator actually marries a stepper to a lead screw to move a linear shaft. The stepper rotates the lead screw. A threaded block on the lead screw moves up and down on the lead screw as it is turned. A piston shaft on the block is therefore moved laterally up and down on command. Enormously heavy objects can be lifted and moved as long as the stepper motor has the strength to turn the lead screw with the load on it. To increase this turning strength, the motor is removed from the lead screw and a gear is substituted. The motor is then moved to the side to drive the gear. Torque increases, rotational speed usually is decreased and the motor can now lift and lower heavier loads.

     Thus far we have rotate continuous, rotate in incremented steps CW or CCW. And we added laterally lift or lower an object of light weight and heavy weight classes. But what if we want to move from one extreme to another extreme with a central home between the extremes. These are the time for servos. They can move from a set ccw limit (usually -60 or -90) passing through 0 to a set cw limit (usually +60 or +90). A PWM signal where in the 180 degree total spectrum to go to. Where a Linear activator uses an H-bridge to control direction and movement amount, a servo actuator uses just a PWM signal to determine what extreme or portion thereof to rest at. A pulse at 50% duty = 0 or center in travel extremes.
     ServoCity has this handy web based way to find and select just the right servo, linear actuator, or stepper. Below is just an example of a general servo search.

     We can see from the above that we are looking for a servo that can run using 6v DC. we need it rotate at least 113 degrees to a maximum of 198 degrees. It needs at least 200 oz in of torque but want as much torque as we can get. And left the speed to any speed. Under these parameters it found 6 candidates. Four standard size servos and two Large size. If our need was for 7Kg of torque, our absolute bare minimum torque would be 247 oz in (35.274/Kg). Five of the six would have enough torque. Speed is fairly consistant allowing for for full travel between 0.28 seconds and 0.37 seconds @ 60 degrees per rated speed. These are under no load conditions. For load conditions, we need to check out whether the servo has weaker nylon gears or stronger brass, titainium, or steel gears. Servo size may play a role depending on planning a new project or doing replacement on an existing one.




     Expanding the torque range greatly increases the options. In some cases you accomplish a task by engineering a solution to work with a lighter duty servo in a different way to result in comparable work. The servo torque is measured 1' out. moving the load closer by 0.5" doubles the torque and likewise moving the load out to 2" halves the torque. A lever is one way to increase mehanical advantage. The ratio of the output force FB to the input force FA is obtained as:
   MA = FB/FA = a/b , which is the mechanical advantage of the lever.

   This equation shows that if the distance a from the fulcrum to the point A where the input force is applied is greater than the distance b from fulcrum to the point B where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point A is less than from the fulcrum to the output point B, then the lever reduces the magnitude of the input force.

     As such, if we have a servo with an arm extending 4" and rotation is 180 degrees, the rotation is a span of 8" of movement. If the final torque at the end of 8" is 1 oz in, then supplied torque is 2^8 * 1 = 256 oz in assuming no losses. If we can lesson the travel to 4" we can reduce the required torque to 16 oz in. And we can do this by mechanical advantage. We move the bar closer by 4" from the end. If the bar was also 8" to the load, then the load would have moved 8" on the extremes. Moving it in by 4" also lessoned the load movement by 4" and moved the load closer by 4". Using a lever and a pivot we can create a mechanical advantage such that the 4" bar pulls and /or pushes against a lever moving source side A 4" and with the pivot placed such that side B travels 8". A servo with 1/16th the torque now can do the job.


     So using a lighter servo with mechanical advantage is definately a possible solution for substituting electric mechanical control.
 
     Another is the linear servo which again can be used using mechanical advantage. A servo with a series of built-in gears convert 180 degrees of rotation into linear motion with huge weight capacity. Here we have the micro size measuring 3.2" to 8.2" retracted and 2" stroke. You will note THRUST replaces the oz in spec as we are using linear force as oposed to angular rotation. So 256 oz in becomes 16lbs lateral. Our above rating of replacing a servo with 1oz in end point load needed 256 oz in servo. Usng linear the 1 oz in end becomes 0.062 lbs of load.

Electric Brakes

     OK! enough of the theory, lets get on with designing an electric brake. We had determined that our hand brake lever had 0 - 7kg of effort from the operator which pulled a cable about 1" at each end. This 1" movement pulled a lever of a cantilever or caliper to move pads inbound by as much as 1/8" inch when properly adjusted. We can definately put a servo of rotational or linear style to pull a cable or two (if a trike) to reduce stress at the hand grip and shorten the cable paths.

     Or as in the above, we can mount the servo right to the forks above the brake and directly pull the levers of the brake by even shorter cables or rods.

     The first true cableless / hydraulicless pure electromechanical brake is shown above. The servo in this case uses its gear end as a pinion gear. the motor is stationary and the pinion is sandwiched by two gear tracks either side. For every action there is an equal and opossite reaction. The pinion turns gainst 2 oposing gears. One gear track is forced left and the other right. Then direction reverses causing the left bound track to switch and move right and the right bound track moves left. We secure 2 perpendicular rods both facing away from the tracks but in the same direction. This forms a Pincer. CW rotation closes the pincer and CCW opens the pincer. Place brake pads at the ends of the pincer and we can now use the brake on rim or Disc rotor brakes. Ideally, servo extremes would be 60 degrees between open and close and each arm would be moved up to 0.52" when we are really looking for 0.125" to engage the pad to the brake surface and increased pressure on the arms/pads for stopping.


     In this rendition of a true electric brake, it is also a pincer but this time 2 lead screws and lead screw mount blocks get moved in oposing directions by the source gears. When the Motor turns cw, gear 'B' turns cw and gear 'A' & 'C' turns ccw and 'D' turns cw. This forces the pincer open (no braking). When the motor turns ccw the pincer closes ( brakes on). For a Disc brake we need to move the pincer 3.1mm per side with a 1.5mm to 2mm disc. So pincers full open are 8.2mm (0.32") apart and full together are 1.5mm (.06") apart. The assembly measures 6.25" long, 3" Wide, and 2.25" high (plus length of arms to pads). For rim brakes the arms must clear a 2.25" wheel width so the glide path has to increase from 1" to 3.5" and that increases the width from 3" to 5.5"
     As for mounting, the one for Disc brakes has the pad arms that fit center over the disc. So the brake assembly is 1/2" either side of Disc center. The motor then sticks out 2"