engin1000: 2009 Fall:Eddy Current BrakeWhy Change Designs?The Problem: My original design was tested in the first prototype and produced at maximum 1.21 V. This low voltage outputforced me to reconsider my calculations, which had predicted much greater voltage. I discovered that my initial calculationshad not converted Teslas (flux density) to Webers (total flux). Because of this error, I had used Faraday's Law to predict fargreater power output than was actually possible in my design. Considering the alternatives: Returning to basic electrodynamics, I realised that my initial design produced no force vectorsopposed to the direction of the wheel's motion. I understood how the Lorentz force is opposite the direction of motion in aneddy current brake, but had dismissed the design after the brainstorming phase. I rejected this design because theelectromagnets required too much weight and a complicated design. But I now realised that I may be able to generate aneddy current with permanent magnets instead, reducing complexity and weight. The concept was to place magnets on typicalbicycle brake pads, thus when pulled close to the rim the Bfield would be perpendicular and through the aluminum bicyclewheel rim. This would induce eddy currents in the rim whose interaction with the Bfield would s low the wheel. But first I hadto test the practicality of the idea.

Second Prototype: Eddy Current Test rig.My second prototype has an eddy current brake (an aluminium disc about the s ize of three stacked CDs) on a shaft connectedto a motor. A photodiode mounted to the rig measures angular speed in revolutions per second (PASCO scientific) by countingthe amount of time that passed between holes that let the IR beam through. A Magnet holder provides a ~.15T Bfield acrossthe disc.A top View of the Test rig.

A Side View. The 8 holes halfway between the axis and the rim allow IR light through to the photodiode.

A video of the Rig in Action.

Based on the mass of the disc I calculated its moment of inertia:

I=.106kg*.062m/2=1.91E-4Having measured the spin down rate, average frictional torque could be calculated:Tavg=I*Δω/Δt=1.91E-4*(21-0)/(0-1.31)=0.003NmDue to Newton's first law, the rubber band-drive must be providing about this much torque to overcome the bearing's frictionand keep the disc rotating at a constant speed.The same calculation was preformed with the data gained when the disc decelerated due to the introduction of a magneticfield across the disc. The torque generated was T=0.012Nm. Power: P=T*2π/t=0.012Nm*2*π/0.357=0.211WActing at the radius of the disc the force exerted was calculated: T=F*r 0.012Nm=F*0.06m F=0.15N Since the eddycurrent brake generates a Lorentz force: F is proportional to V assuming negligible E. Thus I could

proportionally scale my results to see if an eddy current induced in the rim of a moving bicycle could produce enough powerto s ignificantly s low the wheel. The rim of the brake in my test rig was moving at 2.8r/s*2*π=17.6 rad/s, prior to theintroduction of the magnetic field. Since V=ω*r the speed at the rim is V=17.6rad/s*0.06m=1.06m/s.The design parameter was 15MPH=6.7m/s thus the same system would produce F=0.15N*(6.7/1.06)=0.95N.Allowing for 5 magnet pairs , and the increased rim s ize of the bike wheels this still only amounted to:T=5*(0.95N*0.29m)=1.38Nm. Power would be just P=1.38Nm*2*π/0.225s=38.5WThis estimated maximum power was still well short of my design goal, as well as being less than the power generated by alightly pedaling rider. This dispiriting fact caused me to reconsider my design yet again.

Final DesignThe essential problem was that the bicycle wheel rim moved too s lowly to produce a substantial Lorenz force at any normalriding speed. This led to the obvious conclusion that if only I could increase the speed of the eddy current brake relative tothe wheel speed I could produce a substantial braking force. This condition necessitates a drivetrain by definition, a systemthat adds complexity and weight to the system, two things I had been trying to avoid. More importantly it undermined my goalof having a contactless braking system. By scaling up my result from the previous test rig however, it appeared thatsubstantial power could be generated. For example the bike wheel would spin at about 3 revolutions/second at 15MPH, but a 1 inch diameter shaft driven off of thatwheel's tire would spin at 82r/s . Scaling proportionally the result from my second prototype, my eddy current brake's rimwould be traveling at 30.9m/s and would produce 4.4N of force, 0.26Nm of torque, and diss ipate a power of 134 W. Multipliedby a couple sets of magnets, I would quickly be at my 500W goal. Finally I had a mathematically promis ing design. The Final Design I decided on would have a shaft connected to a brake disc surrounded by several magnet pairs , whenbrought into contact with the wheel this shaft would spin at a great enough angular velocity to produce substantial brakingforces in the disc. I envis ioned this shaft being held by bearings on the end of rods that could pivot on frame-mounts,allowing the brake to be selectively applied. A spiral tors ion spring in the frame mount would hold the system off of the bikewheel during normal riding, a Bowden cable would pivot the brake shaft down into contact with the tire

. One downside of this design is that when the stationary shaft is brought into contact with the spinning tire it will s lip, wearingboth parts , particular at high speed. However for my purpose of keeping a moderate speed down a hill this would not be sucha problem as the brake would be applied prior to descending the hill, when the wheel is not spinning that fast. Unfortunately at this point in the semester there was not enough time remaining to fully design, construct, install and testsuch a system. Instead I decided to build a proof of concept prototype which would be s imple enough to quickly build and test.I reduced the design to it's most essential components: a bearing, a shaft, a brake disc and a magnet holder. This prototypewould demonstrate that us ing a shaft could increase the speed of the brake disc and produce s izable braking power, butbecause it would have no selective application it would be breaking all the time and thus render the bicycle impractical.

Proof of Concept (Prototype 3)Despite the fact that most breaking occurs at the front wheel due to weight transfer under deceleration, especially whenriding downhill, the easiest mounting point on my bicycle was the rear frame just below the seat, so this is where I put thebraking system in this prototype. For expedience and s implicity a s ingle bearing is used. A steel shaft 5/8" in diameter wasmachined to interface with the brake disc, this removed the majority of the perpendicular load on the screw that held the discto the shaft. This perpendicular load had caused many screws to break on prototype 2. The proof of concept prototypeinstalled on the test bicycle can be seen below.

The steel rectangle is the magnet holder. Below one can see the radial arrangment of the magnets in the holder and thebrake disc (out of focus).

TestingNow I had to test this system to asses its efficacy. I did so by riding the bike down a s lope of known angle and legnth, andtiming the trip. The angle and legnth told me how much higher the start line was than the finish line. Knowing this mypotential energy could be calculated By dividing the potential energy lost over the course by the time of the course I could estimate the rate of energy convers ion,Power.The test was preformed on Wriston quadrangle, and runs were repeated three times so that the average transit time couldbe taken. After the first test the magnet holder was removed, after the second test the entire eddy current braking systemwas removed.The course had a s lope of 3° and a legnth of 46.3m, thus the height h=46.3m*SIN(3°)=2.42m.

The test bicycle and myself together have a mass of 82kg. ΔU=mgh=82kg*9.81m/s2*2.42m=1947J

Test Normal Bicycle w/ Shaft, Bearing and Brake Disc (No Magnets) Full Eddy Current Braking System

ΔU (potential) 1947J 1947J 1947J

tavg 9.27s 12.34s 14.43s

Power Diss ipated 210W 158W 135W

ΔPower 52W 23W

Thus in this test the braking system developed a total power of 75W, of which more than 2/3 was from the friction of thebearing and the shaft-tire interface. Subjective test resultsMy first attempt to collect a useful dataset failed because the bicycle traveled faster with the full eddy current braking systemthan without the magnet holder. This cause of this was the observed s lipping between the tire and the shaft, this had notoccurred without the magnet holder installed because in that case the shaft was unloaded. I readjusted the bearing mount toforce the shaft to press harder into the tire to try and eliminate s lippage. This adjustment resulted in the successful data setseen above, although intermittent s lipping still did occur. This s lipping should be less of a problem in my final design becausethe force pushing the shaft onto the tire can be modulated by the rider (via the bowden cable) to prevent s lipping. The proof of concept prototype was effective at drastically reducing acceleration when riding downhill, with the systeminstalled my run over the course was effectively at constant speed, with only s light accelerations during moments of s lippage.Without the system the bicycle accelerated during almost the entire downhill run. In this way the proof of concept prototypewas effective at carrying a constant moderate speed downhill.

Final ResultsAnalys is of my design goals

Design Goal Met Why

produce at least 500Wof braking power

No Even scaling my results form the proof of concept prototype linearly with speed, at 15MPH only140W of braking would be generated, of which only 41W are due to eddy currents

brake a bicycle onlevel ground from15mph to 4 mph

Yes* My proof of concept prototype will decelerate a bicycle on level ground, however it does not do soparticularly quickly. * My goal should have specified a distance or time for this deceleration, If Ihad it is doubtful that my prototype would have met this goal.

allow normaloperation of thebicycle when not inuse

Yes My final design does not interfear with normal bicycle use or braking.

Present only the mostminor electrocutionrisk while in use

Yes All of the current generated is contained in the brake disc, which is ins ide an insulatedcase/magnet holder, thus there is no risk of electrocution.

The proof of concept prototype showed that the eddy current braking system of my final design is effective at maintaining asafe downhill speed. Slipping between the shaft and tire will always be a problem with this design, however intelligentlyapplied Bowden cable pressure can limit this problem. The largest compromise in my final design is that it wears both thebraking shaft and tire when in use, thereby creating servicing needs. The minimization of maintenence was one of themotivations to undertake this design project. Future work could implement my final design to test its real-world braking andwear.