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Portable Environmental Electromechanical Voltage

Supply

Final Design Report December 8, 2009

April Hougey

Ken Luo Ben McKune

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Table of Contents Requirements Specification 4 Overview 5 Problem Statement 5 Operation 5 Deliverables 6 Draft User’s Manual 6 System Testing 7 Final Design 9 Updated Functional Description of Blocks 10 Updated System Block Diagram 12 Crankshaft and Power Supply Mount Design 13 Faraday Apparatus Design 19 Electrical System Design 26 Ideal Power Generation 27 Electrical System Overall Diagrams 30 Overcharge Protection Circuit 31 Discharge Cutoff Circuit 38 Electrical Losses and Efficiencies 42 Rider Power Requirement 43 Electrical System Current Discussion 44 Full-Wave Rectifier Simulation 45 Filtering Circuit Simulation 46 Energy Generation Method Decision Matrix 47 Battery Selection Decision Matrix 48 Project Status 49 Updated Budget and Analysis 50 Updated Gantt Charts and Schedule Analysis 51 Appendices Appendix A: DC/DC Converter Appendix B: NPN Transistor Appendix C: LED Appendix D: Electromechanical Relay Appendix E: Magnet Wire Appendix F: Power Inverter

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Appendix G: Lead Acid Battery Appendix H: Capacitor Appendix I: Rectifier Diode Appendix J: Voltage Detector Appendix K: Polycarbonate Sheet Appendix L: Aluminum Rod Appendix M: Phenolic Rod Appendix N: Main piston cylinder Appendix O: Outer piston casing Appendix P: Piston Rod Appendix Q: Power Supply Mount Appendix R: Power Supply Mount Support Appendix S: Flywheel Appendix T: Connecting Rod

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Requirements Specification

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Overview: Our project team will design and build a portable generator powered by the rotary action of a bicycle wheel, capable of generating environmentally clean energy which may be used for supplying low power applications (up to 100 W). The energy storage unit may either be simply charged exclusively while pedaling, or some of the power may be routed to an attached headlight, lowering the charge rate on the energy storage unit by a small amount (not more than 20 W). Once charged, the energy storage unit may be detached and later used as a standalone power supply. Problem Statement: In a world where more people in our society are exhibiting environmental conscientiousness, bicycles are rapidly becoming the most economically and ecologically viable alternative transportation method. This can be attributed to the bicycle’s lack of emissions and gasoline expenses. Consumers who have already acknowledged the benefits of this form of transportation would undoubtedly be attracted to a way to increase the bicycle’s positive environmental impact even more. Through P.E.E.V.S., we aim to reach out to these potential consumers. By designing a portable energy storage unit which uses the bicycle as a renewable mechanical source of energy in order to supply low power loads (cell phones, laptops, etc.), we will add yet another benefit to the list of the bicycle’s environmental contributions. Operation: Operation of the device will be simplistic and intuitive, such that the bicycle is not any more difficult or unwieldy to ride (based on O2 consumption) than any other conventional bicycle. While in use, the movement of the bicycle’s wheel automatically stores energy to the unit through a generator. The user may flip a switch attached to the handlebars if he/she wishes to instead power a mounted headlight. Once charged, the user may detach the energy storage unit from its housing on the bicycle, which may then be used to power other electrical loads once an on/off switch allowing electrical discharge has been flipped to the ‘on’ position. The user will be notified once the supply has been depleted of energy and has cut off discharge, so that the user may then reattach it to the bicycle in order to charge it again.

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Deliverables:

• Mobile bicycle with gear shifting capabilities and power supply mount

• Detachable energy storage unit with LED indicators

• Generator

• LED headlight with on/off switch

• User’s manual

• Circuit diagrams/schematics including analysis and simulations

• CAD drawings and analysis

• Final report including test results, list of materials, and final design

Draft User’s Manual: Setup:

• Flip power supply discharge switch to the ‘off’ position

• Mount power supply - Fasten and tighten housing clamps - Plug in LED headlight (ensure headlight switch is in the ‘off’

position) - Connect energy storage unit to generator system

Operation:

• Ride bicycle in order to charge power supply

• For night riding, user should flip both the power supply switch and the headlight switch to the ‘on’ position to power the headlight

• Once the power supply has been fully charged as indicated by an LED on the power supply, the supply may be detached after ensuring that both switches are in the ‘off’ position

• At this point, one or two low-power loads (not to exceed 100W) may be plugged into the energy storage unit

• Charging of the low power device will begin once the user has flipped the discharge switch to the ‘on’ position

• The energy storage unit will no longer discharge once the voltage level drops to a predetermined threshold, as indicated by a low power LED

• Repeat setup instructions for further use

Maintenance:

• Store bicycle in a dry location protected from the weather

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• Ensure that the discharge switch is set to the ‘off’ position when not in use

• Normal bicycle maintenance applies (chain tension and lubrication, tire pressure, etc.)

User Interface:

• On/Off switch for headlight

• On/Off switch for energy storage unit

• LEDs indicating maximum charge and low power Physical Capabilities:

• Easily rideable (such that the supply may be fully charged in 2.5-3 hours of pedaling at a rate of approximately 50 rpm with the rider’s oxygen consumption ranging from 1-1.5 L/min.)

• 12-14 W headlight operated by an On/Off switch with a 15-20o beam dispersion, able to illuminate a distance in front of the rider up to at least 30 meters with maximum intensity of at least 20 candela.

• Headlight will run continuously (with constant luminosity, beam dispersion, etc.) as long as the power supply discharge switch is in the ‘on’ position and the charge level in the supply is above the cutoff threshold

• Will be able to support two low-power electrical loads (up to 100 W each for two hours)

• Generator able to generate 125-150 watts

• Energy storage unit maximum capacity of at least 400 watt-hours

• Waterproof power supply casing

• Automatic cutoff when the charge drops below 5% of its maximum capacity

System Testing: Supply testing: The energy storage unit will be tested over 20 complete charge/discharge cycles at a supply rate of no less than 40 W*hr to confirm that the system performs as well as originally specified. The cutoff system must be shown to occur within a 20% tolerance of the 5% charge level cutoff threshold.

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Peripheral testing: Through night-time testing it must be demonstrated that the headlight is capable of meeting all of the above listed physical qualities. Mechanical testing: Due to the addition of external parts on the bike, testing will need to be done to ensure that the structural integrity of the bicycle is not compromised. We will measure and record the initial tire pressure, tread height, bolt tightness, etc. of the bike. We will then ride it at a steady rate of 40-50 pedal rpm for a total of 25 hours and record the new measurements, which will then be compared quantitatively. All measured values should be within 10% of the original values. Ease of ride testing: In order to verify the comparative ease of riding the bicycle with existing industry standards, the oxygen consumption for a batch of three students will be measured while riding for 2.5-3 hours at an average of 50 RPM, and aiming for an oxygen consumption of 1-1.5 L/min.

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Final Design

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Updated Functional Description of Blocks

Train Wheel Mechanism: By converting the rotational motion (approximately 60 pedal RPMs) of the wheel into translational motion of the Faraday piston (up to a maximum of 160 strokes per minute), this device harnesses the power generated by the rider (≈ 342 W) to provide energy through the angular displacement of the crankshaft to the Faraday apparatus for conversion into electrical potential. Faraday Apparatus: This subsystem is composed of a phenolic piston with a magnetic neodymium head, an aluminum inner casing, a copper coil, and a plastic outer casing. By oscillating the magnet within the inductive coil, a magnetic flux is created, inducing a potential across the coil of approximately 20 V @ 8 A. Full-Wave Rectifier: A simple array of four diodes, this circuit, placed after the generator, converts the negative portions of the electricity generated by the Faraday apparatus into a completely positive waveform, which can then be stored to a battery for later use. DC/DC Converter: Also called a switching regulator, this component uses a form of pulse width modulation to create a duty cycle for an input voltage, stepping it down with significantly less losses than a linear regulator. In our design, the charge phase converter will step down the potential produced by the Faraday apparatus from roughly 20 V to the 13 V necessary to charge our lead acid battery. Overcharge Protection Circuit: Centered around the MAX8211 voltage detector IC and a solid state relay, this circuit prevents the battery from being charged once the potential across the battery has reached 13 V. No current limiting circuit is in place because the dimensions of the copper wire utilized in the Faraday apparatus were iteratively selected to produce current that would not only maximize our power generation, but also limit the current from potentially damaging electrical components and/or the battery. Lead Acid Battery: This is our energy storage device for the design. Rated at 12 V and 40 A∙h, this particular unit can potentially store up to 480 W∙h, 80 W∙h above the 400 W∙h stipulated in the requirements specification.

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Discharge Cutoff Circuit: Very similar to the overcharge protection circuit, this subsystem prevents the battery from discharging once its potential has dropped below 11.8 V, preventing loads attached by the user from being undersupplied and potentially damaged. LED Indicators: Two LEDs, a “charge complete” indicator and a “low charge” indicator (green and red, respectively) are implemented within the protection and cutoff circuits to update the current status of the battery to the user. Headlight: A standard 12 W LED headlight which will be mounted to the front of the bicycle. Its batteries will be removed so that the device can be powered by the bicycle’s battery. Inverter: A car’s cigarette lighter adapter will be modified to accept a signal from the battery and step it up for use in a load.

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Figure 1

System Block Diagram

*Note: The maximum current level shown immediately after the overcharge protection block is only true when the system is only charging, and the maximum current level shown immediately preceding the discharge cutoff is only true when the system is only discharging.

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Crankshaft and Power Supply Mount Design

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The power supply mount, crankshaft, and piston will all be made as one assembly (see figure 1). The power supply mount will have one vertical support on each side of the bicycle, which will be bolted at the bottom to the bike frame where it attaches to the rear axle. A hole close to the top of the right side support will hold a small bearing. This bearing will provide for the rotation of a 13 tooth chain-ring and a 7 ½ in. (19.05 cm) aluminum flywheel. The 13 tooth chain-ring will be driven by a secondary bike chain threaded over the smallest gear on the existing gear cassette, which also has 13 teeth. Four small bolts will connect the flywheel to the 13 tooth chain-ring so that they rotate together. The crankshaft connecting rod will be connected to the flywheel approximately an inch (2.54 cm) from its edge by a spacer (to provide clearance between the bolts and the rotating connecting rod) and a bearing (which will allow it to rotate). The piston will be mounted underneath the power supply mount.

The power supply mount will be fabricated using 3/16” aluminum (chosen for its light weight). It will extend 20” back from the seat post over the rear wheel. Starting at the rear it will have four equally spaced (4” apart) ¾” supports, and two more supports crossed at the front. The front of the mount will be clamped around the seat post to provide stability.

One of the constraints that came up in the design of the crankshaft and power supply mount was the amount of space available. A Solidworks drawing was generated to determine the placement and spacing of all of the mechanical components (see figures 1 and 2).

The highest gear ratio we can achieve within the constraints of our system is 2.667:1. This ratio is achieved by having the bicycle’s chain around the largest front gear (48 teeth) and the third smallest gear on the rear cassette (18 teeth), and with the secondary chain around the smallest gear in the rear cassette (13 teeth) and another 13 tooth gear mounted onto the side support of the power supply mount. Pedaling at 50 rpm with this gear ratio will result in 133 piston strokes per minute, which is low enough that it won’t cause premature wear on the crankshaft and the piston, but unfortunately won’t be able to generate as much power as we predicted in our requirements specification. The secondary 13 tooth gear was chosen because a gear with more teeth would have lowered the gear ratio unnecessarily. While the gear ratio of 2.667:1 is the highest that can be achieved for this system, the rider may still utilize all of the gears on the bike transmission except for the two smallest gears on the rear cassette which need to be avoided for clearance purposes.

It was important that the gear that is farthest out from the wheel be used as the gear to drive the crankshaft so that the power supply mount could be as wide as possible. The gear driving the crankshaft must be outside the frame of the power supply mount so that the chain can be placed around both gears without interfering with any other parts. It was considered to replace the smallest gear with a larger gear in order to achieve a higher gear ratio, but clearance with the bike frame would have been an issue.

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Figure 2

Crankshaft and Power Supply Mount Layout Side View

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Figure 3

Crankshaft and Power Supply Mount Layout Top View

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Using the estimated force exerted on the pedals as 350 N, the torque was calculated by

multiplying the force times the length of the pedal arm, which is .19 m. With this information, the forces on each component of the crankshaft and the forces on the piston were generated using Matlab.

Figure 4

Graph of Forces on the Crankshaft

With the knowledge of the forces on each component of the crankshaft, a stress analysis was done to determine the necessary yield strengths of the materials used.

Table 1 – Material Selection Refer to Figure 4 for pin locations Component Maximum Stress Material Yield Stress Pin 1 7.14 kpsi 2011 Aluminum Alloy 24.5 kpsi Flywheel 23.32 kpsi 2024 Aluminum Alloy 43.0 kpsi Pin 2 3.71 kpsi 2011 Aluminum Alloy 24.5 kpsi Connecting Rod 58 kpsi 1035 CD Steel 80.0 kpsi Pin 3 10.71 kpsi 2011 Aluminum Alloy 24.5 kpsi

0 50 100 150 200 250 300 350 400-300

-200

-100

0

100

200

300

Input Angle, θ2, (deg)

Mag

nitu

de o

f For

ce, N

Magnitude of the Forces on each pin of the crankshaft

F12

F32F43

F norm

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Figure 5

Bearing Locations

Three ball bearings will be needed at points 1, 2 and 3 (see figure 4). The maximum force on each of the points was used to determine the load rating of the bearings needed.

C10L101/a = FL1/a

This equation is used to calculate the catalog rating of a bearing, C10. For ball bearings, a = 3. L10 is the rating life in revolutions, and it is equal to L, the life that we wish for the bearing to have. F is the maximum radial load that the bearing will experience. This means that we need bearings with a catalog rating larger than the maximum load in the bearing.

Table 2 – Bearing Selection Maximum load on bearing Bearing 1 270 N Bearing 2 270 N Bearing 3 260 N

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Faraday Apparatus Design

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Design Principle The purpose of the Faraday apparatus is to transfer kinetic energy into electrical energy.

A critical part of the design, this mechanism needs to be sturdy and rugged. Regardless of environmental conditions, the Faraday component has to work well to generate electricity, and thus must be completely waterproofed. Because a magnet is used to produce the electricity using the Faraday principle, all the materials which comprise it must be non-magnetic, so as not to interfere with the magnetic field created by the motion of the magnet. Also, as much friction will be incurred by the motion of the piston within the casing, the casing must be durable and wear-resistant. The Faraday apparatus, shown in Fig. 1, is connected to a crankshaft which is used to transfer the rotational motion of the wheel to vertical motion of the piston. Because the magnet is fastened to the piston, the magnet also undergoes the same motion within the piston casing. The faster the magnet moves, the more electricity we can generate. Materials The mechanism includes two parts: one is dynamic, which is made up of the magnet and piston, and the stationary portion, which has an inside casing and an outside casing. To prevent the magnet from chipping or shattering, its diameter is slightly less (about 1.27mm) than that of the casing. In order to meet this requirement, we intend to use a piston of slightly greater diameter than the magnet, such that the piston is still in contact with the housing wall to prevent gouging as much as possible. In this way, we are able to both increase the operational life of the magnet and decrease our mechanical losses by using a material with a low coefficient of kinetic friction.

And, to this end, we chose phenolic for our piston material (decision matrix below). Phenolic is very easy to machine, heat and wear resistant, and has good mechanical strength and dimensional stability. In our design, the piston is the only component which touches the casing directly, and thus its abrasion is greater than any other portion of the apparatus.

Moving outward from the phenolic piston, the inside casing is made of aluminum. Aluminum has large corrosion resistance, thermal conductivity, and is cheap and easily fabricated. When the piston is moving, the temperature will rise because of the friction between the piston and casing. Using aluminum will help ensure that the temperature will not rise too much to influence the normal work of the mechanism.

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Piston Material Decision Matrix

Lexan Phenolic Aluminum Plastic

Non-magnetic 10 10 10 10

Low friction coefficient 5 9 6 5

Light weight 7 9 5 9

High wear property 4 9 8 5

Easy to fabricate 7 8 5 9

Durability 8 9 10 2

Cost 3 8 9 7

Total 44 62 53 47

Figure 6 Piston Material Decisio Matrix

The decision matrix above shows the reasoning behind our selection of phenolic as the

piston material. Because we have a limited budget and don’t have suitable equipment for us to machine any material, cost and fabrication are the two most important factors in our design. A low coefficient of friction and weight are both less important factor to our design because they are both a little part to the total system losing and total bicycle weight. From the table, we found that aluminum and phenolic are the better choices for us. Because the density of phenolic is less than that of aluminum, phenolic is better-suited for use as the piston because it will make the bicycle easy to ride. The inner casing, which will be made of aluminum, will help keep the temperature of the Faraday component under control because of its higher thermal conduction.

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Figure 7 SolidWorks Representation of Faraday Apparatus

Dimensions of the Main Components Table 2 shows the dimension of the main components. Figure 2 shows all the dimensions of the Faraday apparatus.

Length of inner casing 200mm Small diameter of inner

casing 5.4mm

Width of inside casing 8.73mm Length of magnet 25.4mm

Diameter of magnet 22.22mm Length of piston 154.6mm

Diameter of piston 24.13mm Figure 8

Faraday Apparatus Dimensions

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Power Requirement for a Typical Bicycle There are two main resistances to ride the bicycle. One is wind resistance; another one is rolling resistance. The total resistance force, which can be calculated by the equation shown below, is 17.7 N.

= ( +12 )

Where Fw is the wind resistance, m is the mass of rider and bicycle and Crr is rolling resistance coefficient. We assume the bicycle is at speed of 30 km/h, then the wind resistance should be 15 N, the rolling resistance is 0.00555 for BMX bicycle tires. Then the power need to ride a bicycle is

= = 17.7 ×303.6 = 147

Mechanical Losses and Efficiencies The efficiencies of the mechanical components can be divided into two parts. One is from the drive chain to the Derailleur gears, and another one is from the Derailleur gears to the gear where we setup. The efficiency from the drive chain to the Derailleur gears (the original bicycle) is 88%-99%. The efficiency from Derailleur gears to the setupped gear is 90%-93%. We choose small efficiencies to calculate the total mechanical efficiency.

μ = 0.88 × 0.9 = 0.792

The system has two main types of losses, electrical and mechanical. Comparing electrical and mechanical losses, electrical is the main loss in our system. The mechanical losses are mainly caused by friction force. The friction force is different at different angles, so the average friction force should be calculated. Figure 2 shows how the frictional force changes over one stroke. is the angular of the rotated bar to horizontal direction. The average value of friction is 69.2 N per one cycle (calculated by Matlab).

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Figure 9

Frictional Force Between the Inner Casing and Piston The gear ratio of the pedal and setup gear is 1:2.667, the average velocity of the piston is

=2.667

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Where n is the number turns of the pedal in one minute, and S is the distance that the piston moves in one period. The power to get over the frictional force is calculated by

= /

yielding a value of 194 watts. If lubrication is used within the piston and inside cylinder, the average friction force is significantly reduced to 8.65 N, because the friction coefficient is reduced from 0.4 to 0.06, and the power required to compensate for the frictional force is reduced to 15.2 watts.

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Heat Expansion

Temperature rise will cause the dimension of the mechanism to change. Small change of the temperature and small heat expansion coefficient will keep the materials’ dimensions. The materials we chose both have small heat expansion coefficient, and it makes sure that the diameter of the piston will not expand too much to touch the inside casing and cannot move any move. Here is the heat expansion equation:

∆ = ∆ Assuming the temperature change is 100 oC.

Aluminum Phenolic

Heat expansion coefficient (m-6/oC) 0.5842 1.397

Radius of material (m) 0.00218 0.01111

Temperature change (oC) 100 100

Radius change (m-6) 0.1274 1.552

Figure 10 Heat Expansion of Piston Materials

In Table 3, we assume that the temperature within the apparatus rises to 100 oC, but the length change due to heat is very small. The result shows that the materials and dimensions we chose are both good for our purposes, as the space between piston and inner casing is 0.004365 m. Strength Analysis and Durability The force acting on the piston in X direction is 225 N, and 350 N in the Y direction, meaning that the force on the insider of the aluminum casing is 350 N. The pressure in the X direction is 0.123 MPa, and in the Y direction is 654 Pa. However, the tensile yield strength of aluminum is 276 MPa and that of phenolic is 41-57 MPa. Comparing the pressures, we find that the theoretical applied pressure is very small in comparison to what our materials are able to handle, and as a result the safety factor reaches nearly 330. Because of this, the durability of the Faraday apparatus is high enough to meet our requirements.

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Electrical System Design

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Ideal Power Generation Calculation

To calculate the power generation of our system before losses, we first use Faraday’s Law to calculate the voltage generated:

=

Here, e is the potential generated across the inductive coil, N is the total number of

coils, and

is the rate of change of magnetic flux within the system (proportional to the linear

velocity of the magnet within the Faraday apparatus. At this point, an assumption is made to simplify calculations: assume that the difference in the diameters of the magnet and the copper coil is negligibly small. This allows us to say that

= ×

That is, the maximum flux generated by the generated by the magnet is theoretically equal to the magnetic flux density of the magnet times the cross-sectional area of the magnet or the coil (both are assumed to have the same diameter). Knowing this maximum flux, we can solve for its rate of change as follows:

= sin This simply says that the flux can be expressed as a sinusoidal function of time operating at a given frequency (for which our maximum gearing ratio serves effectively as a coefficient), and that the amplitude of that sinusoid is the maximum flux we solved for above. Taking the derivate of this equation with respect to time yields:

= cos

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where G is the gearing ratio of the mechanical system. Simplifying this by taking the root mean square of the sinusoidal term yields

=

√2=

2√2

= √2

The maximum flux is already known to us, and the rotational frequency ω is simply determined by how quickly the pedals are rotating. The next step, then, is to determine the number of coils in the length of the wire. This is found as shown below, where N is the number of coils, ℓ is the total length of the coil through which the magnet passes, and d is the diameter of the copper wire.

= ℓ

Referring back to Faraday’s Law above, we now have all the information one needs to solve for e, the potential generated across the inductive coil. However, it is desirable to know more than just the voltage: the overall goal is a figure the power generation of the system. To determine that power, one can use the form of the power equation shown below.

=

V, obviously, is the same potential e which was just determined above. Because that potential is across the coil itself, the resistance R must be the inherent resistance in the copper wire, given by the following equation:

=

Here, ρ is the resistivity of copper (0.00000000172 Ω∙m), L is the length of the copper wire in meters, and A is the cross-sectional area of the copper wire, which is found using the diameter. We now know everything necessary to calculate the average power generated by the system before electrical and mechanical losses. Plugging in 0.11 m for the coil length, 0.0004 m

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for the wire diameter, a maximum gearing ratio of 2.667:1, 1.6 T for the magnetic field density, and 0.022 m for the magnet diameter, we obtain an average power generation of approximately 57 W before losses. This does not meet our required power generation as define in the requirements specification. However, our planned countermeasure is to layer additional levels of inductive coil around the piston, which, while not capturing the mechanical energy input quite as efficiently (a result of increased coil resistance), will result in a higher energy transfer overall.

It should also be noted that this particular derivation became very important to us in the process of optimizing the power generation through the selection of the dimensions of the parts of the Faraday apparatus. One of the most important of these was the diameter of the copper wire used in the inductive coil: as the diameter increases, the total resistance of the wire for a set coil length decreases faster than the voltage decreases because of the reduced number of turns. In other words, as the diameter is made larger, the denominator of the power equation gets smaller more quickly than the numerator does. This can be good in that it is a quick way to increase our efficiency and thus our total energy generation, but the drawback is that decreasing the resistance in such a manner, must, by way of Ohm’s Law, lead to a proportional increase in current. After some trial and error, we determined that coated copper wire of a diameter of 0.16 mm gave us the highest achievable theoretical power generation while still keeping the resulting current low enough that the electrical components and the lead acid battery will not be damaged (refer to the block diagram for specific voltage and current values).

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Electrical System (Charge Phase)

Figure 11

Multisim Representation of Electrical System Charge Phase

*It should be noted that several more components (capacitors and resistors) must also be included in the DC/DC converter circuit. Application layouts are prescribed in the data sheet in the Appendices section.

Electrical System (Discharge Phase)

Figure 12

Multisim Representation of Electrical System Discharge Phase

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Overcharge Protection Circuit

Figure 13

Multisim Representation of Overcharge Protection Circuit

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Overcharge Protection Circuit Discussion

For the diagram shown on the previous page, the goal is to cease charging from the Faraday generator if the lead acid battery reaches a potential of 13 V. The MAX8211 reads the potential across the battery, using a series of resistors to normalize that potential to an internal threshold of 1.15 V at typical operating temperature (25 C). As can be seen on the voltage detection data sheet, variation in the operating temperature will not alter this threshold by more than a few hundredths of a volt, which is acceptable for our application. The resistors were chosen under the constraints that the potential at the threshold pin be 1.15 V when the battery is at 13 V, that the potential at the hysteresis feedback pin be approximately 75 mV (a sufficient amount to ensure that the relay stays open once it has been given enough power to switch), and that the resistors be within a reasonable range for limiting current to the appropriate level. The selection of 75 mV for the hysteresis threshold comes from the example on the MAX8211 data sheet, page 5. It should be noted that if experimentation proves that inconsistencies in the output level of the DC/DC converter result in the relay “bouncing” between its open and closed states, it may become necessary to raise this hysteresis potential higher than 75 mV. Using voltage division, two equations are generated:

13 V ∗R

R + R + R= 0.075 V

13 V ∗R

R + R + R= 1.15 V

We select R2 to be equal to 2.2 MΩ and solve simultaneously for the other two resistances, such that R1 = 214.9 kΩ and R3 = 14.0 kΩ. The conditions for the selection of R2 are that it be attainable within commonly available resistances (as well as with R1 and R3) and that the resulting value for R1 falls between 10 kΩ and 10 MΩ, which it does. This second requirement is delineated in the MAX8211 data sheet, page 5. Because all calculated resistances can only be applied using real resistors, there is a small disparity between the ideal resistances and the implemented resistances. However, as shown in

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the Multisim simulations in the next section, these minor differences in value result in very little change in the hysteresis voltage and the cutoff voltage within the circuit. Thus, a tolerance in both the overcharge protection and the discharge cutoff subsystems is permissible, although we aim to keep the cutoff thresholds as close as possible to their originally intended values. After iterating DC sweeps in Multisim the final selected design values for R1 and R3 are 215 kΩ and 14 kΩ, respectively. The electromechanical relay used is an NC type, or “normally closed.” When the battery is not fully charged to 13 V, the output of the voltage detector is low, and the base potential of the NPN transistor is not greater than the approximately 0.7 V necessary to begin current flow to the LED and relay. Thus, the relay, which is normally closed, would be allowing continued current to flow from the generator to supply the battery. However, once 13 V across the battery is attained, the logical output from the voltage detector goes high (higher than the required potential to turn on the LED and switch the relay). At this point, current flows through the transistor, the “fully charged” LED is lit, and the relay switches, opening the circuit to prevent any more charge from reaching the battery until the charge level drops back down below the threshold minus the hysteresis potential. Approximately 30 mA must be supplied to both light up the LED and switch the relay.

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Overcharge Protection Circuit Simulation

Figure 14

Multisim Voltage Detector Simulation Circuit (Charge Phase)

Looking below, we can see the resulting potential at the threshold pin for various input voltages to the overcharge protection circuit, varying from 12.8-13.2 V using a DC sweep. With the resistances selected, the threshold is crossed almost exactly at 13 V across the battery, which is exactly what we want to see.

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Figure 15

Battery Potential vs. Threshold Pin Input Voltage

Because the hysteresis potential is equal to the voltage drop across R3, we can plot the hysteresis for a varying input as the difference of the input and the voltage drop across the other two resistors (voltage division). The result is shown below. Notice that as the input voltage crosses 13 V in its sweep, the hysteresis voltage at that point is approximately 74.9 mV, only 0.00001 V away from our calculated goal.

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Figure 16

Battery Potential vs. Hysteresis Pin Input Voltage

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Discharge Cutoff Circuit

Figure 17

Multisim Representation of Discharge Cutoff Circuit

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Discharge Cutoff Circuit Discussion The resistances are chosen in the exact same way for this circuit as for the overcharge protection circuit. R2 is again chosen to be 2.2 MΩ, and R1 and R3 are again found through solving two simultaneous voltage division equations. The only difference in the calculation of the resistances for this voltage detector chip is that now our critical threshold is at 11.8 V, not 13 V as before (shown below).

11.8 V ∗R

R + R + R= 0.075 V

11.8 V ∗R

R + R + R= 1.15 V

R1 and R3 are found to be approximately 239.2 kΩ and 15.6 kΩ, respectively. Using real resistances, we approximate these values to get 239.3 kΩ and 15.9 kΩ. The voltage division simulations shown below demonstrate that these resistances are still close enough to be valid for implementation. Because the purpose of this circuit is to stop discharge when the potential across the battery drops below a certain point, a logical inverter is used to reverse the cutoff generated by the overcharge protection circuit. When the potential across the battery drops below 11.8 V, the voltage detector sends a logic low, which is converted to high by the logical inverter. This allows current to flow through the transistor, turning on the “low power” LED and switching the relay, opening the circuit leading from the battery to the load. A “normally open” type relay could easily be used to replace the logical inverter and NC relay in order to achieve the same switching functionality; however, because the LED is in series with the relay, the LED would always be lit until the relay switched, which is the opposite of what we want. For purposes of simplicity and cost-effectiveness, simply adding the logical inverter at the converter output is the best solution for our application.

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Discharge Cutoff Circuit Simulation

Figure 18

Multisim Voltage Detector Simulation Circuit (Disharge Phase)

For this simulation, a DC sweep was performed with the input voltage ranging from 11.6-12 V. The resistances selected give the response shown below. Notice that at 11.8 V, our critical threshold for the discharge cutoff circuit, the potential at the threshold pin of the MAX8211 chip is almost exactly 1.15 V.

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Figure 19

Battery Potential vs. Threshold Pin Input Voltage

Finally, the hysteresis potential for the discharge cutoff circuit is shown below. Here, the hysteresis potential at 11.8 V battery potential is roughly 76.4 mV, about 0.0014 V away from our goal of 75 mV. However, as this is only a 1.87% overshoot, it should have very little impact on the cutoff subsystem functionality (especially considering the function of the hysteresis feedback, which is simply to prevent rapid switching of the chip’s logical output).

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Figure 20

Battery Potential vs. Hysteresis Pin Input Voltage

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Electrical Losses and Efficiencies Losses within the electrical system can be divided into energy lost before current reaches the battery and energy lost between the battery and the load. Energy lost before the battery affects the charge time of the battery by reducing the amount of current the battery receives (and thus its charge rate), and energy lost after the battery lessens the total amount of time for which a load may be supplied by causing the battery to be depleted faster while charging a load with a given power draw. Critical efficiencies for parts in these two divisions of the electrical system are shown below, taken from the individual component data sheets. Input Efficiencies

• Full-Wave Rectifier (90%)

• DC/DC Converter (92%) Output Efficiencies

• Lead Acid Battery (92%)

• Inverter (90%) Thus, the total output efficiency = 92% * 90% = 82.8%, and the overall electrical efficiency = 90% * 92% * 82.8% = roughly 68.56%. This efficiency may have been possible to increase slightly, but such losses are inherent in the nature of our design; any energy generation method we could have chosen would still have roughly the same electrical system, with approximately the same electrical efficiency.

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Rider Power Requirement

One of the criteria by which the design will be evaluated is the device’s ease of riding; that is to say, how much effort the rider must go through to simply use the bicycle. As such, it is important to know how much more difficult our bicycle will be to ride than an unmodified bicycle. The increased difficulty of riding our bicycle can be determined through two factors: the mechanical and electrical efficiencies. As demonstrated in the mechanical section of the report, the mechanical efficiency of the system was calculated to be 79.2%, while the electrical efficiency between the generator and the battery was determined above to be 82.8%. When riding the bicycle without charging the battery, there will be no power draw on the generator, and only the mechanical losses will have an effect on the difficulty the rider experiences in operating the bicycle. As mentioned in the mechanical analysis, a typical rider would exert roughly 130 N of force on the pedals when riding at an average rate of 60 pedal RPMs. Given 0.17 m lever arm on the pedals, the resultant torque will be 130 N * 0.17 m = 22.1 N*m. Also, at 60 pedal RPMs, the frequency f = 1 Hz, such that ω = 2π rad/s. Knowing that, the mechanical power P = T ω = 22.1 * 2π = 138.9 W. However, to account for the mechanical losses of the system, we divide this power by the mechanical efficiency, and 138.9 / 0.792 = 175.4 W. This means that the rider must provide roughly 165.2 N of force at the pedals in order to counter the mechanical losses expressed between the pedals and the Faraday apparatus. Once the battery begins charging from the generator and current begins flowing, however, the additional power draw of the charge phase of the electrical system on the generator results in yet another term for which the rider must compensate. Assuming the rider is providing the 164.2 N listed above, 138.9 W of energy reaches and is utilized by the Faraday apparatus. In order to have that same power output at the battery, the rider must provide force for an additional amount of power, given by the power input of the electrical system divided by the electrical efficiency, or 138.9 / 0.828 = 167.8 W. The summation of these mechanical and electrical power requirements comes to 167.8 + 175.4 = 343.2 W. Solving for the related force then yields 321.2 N. Thus, a rough estimate would be that the rider will be required to be pedal 321.2 / 130 ≈ 2.47 times harder in order to overcome the power losses inherent in the device.

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Electrical System Current Discussion

A critical portion of our analysis involves ensuring that the levels of current present within the electrical system are acceptable in terms of safety and feasibility. In both cases, those criteria are met by making sure nothing blows up or catches on fire. For a 16 mm. wire wrapped around a cylinder 11 cm. long, the inherent resistance of the copper is roughly 4.1 Ω. Given a maximum generate potential of about 25 V, this will result in a generated current peaking at 6.1 A. Knowing that, it is important to determine if all of the components within the charge phase of the electrical system can handle such an input current. Firstly, both the rectifier diodes in the full-wave rectifier and the DC/DC converter are rated at 10 A, and should easily be able to handle such a current. It should also be noted that the capacitors in the filtering circuit are rated at 35 V, well above any spike voltage that could be generated by the Faraday apparatus. The battery itself, rated at 40 A∙h, can be guaranteed to be safely fast-charged at 30% of its rated current, or 12 A. This high charge rate should not, however, be maintained during the last 30% of the total charge of the lead acid battery. This is because lead acid batteries, while rugged and charge tolerant, handle shallower charges and discharges much better, especially as they approach the fully charged state. Still, a current half that of the safety margin for our battery, while too high to be considered ideal, is certainly within safe bounds for our design considerations. Next, the current during the discharge cycle of the electrical system must be considered. The ideal discharge rate for most lead acid batteries is approximately 0.05 C, or 0.05 * 40 = 2 A in our case. Discharging more quickly than this, perhaps at a rate of 4 A as depicted in the system block diagram in Figure 1, is feasible, but drains the battery much more quickly (thus reducing its output efficiency). It must be said here that part of the safety aspect of the design demands that the user not attach a load to the outlet which requires a higher power supply than the battery can handle, so as to avoid not damaging the battery. After a point, the power inverter has an internal cutoff which will stop delivering power to the outlet if the inverter is not receiving enough current to meet the power demand, but it’s much better to be safe than sorry.

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Full-Wave Rectifier Simulation In order to prevent current with a negative phase from being sent to the DC/DC converter, a diode circuit (shown below) is used to rectify the signal produced by the generator. The output is then smoothed by the filtering capacitors between the rectifier and the DC/DC converter.

Figure 21

Multisim Representation of Full-Wave Rectifier w/ AC Input

The resulting waveform is viewed using an oscilloscope and shown below. Notice how the negative phase regions of the originally sinusoidal AC current are made positive by the rectifier.

Figure 22

Multisim Oscilloscope Output of Full-Wave Rectifier

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Filtering Circuit Simulation

After passing through the rectifier, the AC current is leveled off to something more closely resembling DC using capacitors. By storing excess energy during the peak of the rectifier output signal, the capacitors can discharge during the troughs so that the voltage is smoothed to a much more consistent potential. The circuit is shown below, followed by an image from Multisim’s oscilloscope tool demonstrating the resultant waveform.

Figure 23

Multisim Representation Rectifier w/ Filtering Capacitors

Figure 24

Multisim Oscilloscope Output for Filtering Circuit

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Energy Generation Method Decision Matrix

Coefficients Bearing System Flywheel System Faraday Concept

Technical Depth 5 5 3 9

Originality 4 1 1 7

Efficiency 3 5 7 3

Implementation Cost 2 7 5 3

Marketability 1 7 9 5

Totals 65 59 93

Figure 25 Energy Generation Method Decision Matrix

Above is a decision matrix describing the factors motivating our decision to use a

Faraday piston and train wheel mechanism as the means of generating electrical energy in our design. The three considered design options are shown across the top row, and options are scored by multiplying their individual assigned values for each parameter by coefficients associated with that parameter, which represent how critical meeting a given parameter is to the overall success of the design. Here, we see that the Faraday concept won out by a margin of about 43%, making it unlikely that any minor adjustments of the order of the parameters would have changed the end result. Technical depth is chosen as the most important step because the entire focus of the class is on the design process, of which there is very little if the design our group is attempting to realize is overly simplistic. Originality was very important to us because of the creative nature of what we wanted to design, and the Faraday apparatus concept is the only one of the three generation methods listed above that has not already been mass manufactured. It should be noted that we scored the Faraday concept fairly low on efficiency, as the greater number of moving parts incurs many mechanical losses which must be evaluated. However, as long as we are able to meet the minimum power specified by our requirements specification, our goal is only to create proof of concept.

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Battery Selection Decision Matrix

Coefficients Nickel-Cadmium

Nickel-Metal Hydride

Lead Acid (SLA)

Lithium Ion

Capacity 9 5 5 9 7

Cost 8 7 7 9 1

Efficiency 7 5 3 9 7

Environmental Friendliness

6 5 7 3 3

Charge Tolerance 5 3 3 9 1

Longevity 4 9 5 5 7

Energy Density 3 5 7 1 9

Memory Effect 2 3 3 5 9

Self-Discharge 1 3 5 7 9

Totals 241 231 319 233

Figure 26 Battery Selection Decision Matrix

Much more complex than the energy generation method design matrix, this matrix

outlines our decision to use a sealed lead acid battery as our form of energy storage, despite some of its technical shortcomings. Looking above, it is apparent that if the weighting coefficients were even close to being ordered correctly, an SLA is almost certainly the best choice for our design, having scored more than 32% greater than the next best option according to the matrix. For the parameters, order was determined based on how definitively they apply to our requirements specification document. Because we have a very limited budget and because we must meet our 125 W generation goal to be successful, capacity and cost held the two highest places in the list of factors critical to the design. Things like self-discharge and memory effect, which are indeed very present in SLA batteries, are less important because the bicycle will charge often, as long as it’s used often.

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Project Status

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Updated Budget and Analysis Already purchased: Item Vendor Cost Bicycle Wal-Mart $214.92 Headlight B2Cshop24.com $7.34 Copper wire Smallparts.com $26.59 Magnets Bunting Magnetics $40.60 Pencil Sharpener (mock-up) Staples $10.79 Power Inverter Wal-Mart $19.59 Lead Acid Battery BMF Batteries $152.04 12 x 330 µF Capacitors Pololu Robotics $11.15 4 x Rectifier Diodes Allied Electronics $9.68 34 AWG Magnet Wire Powerwerx $13.21 2 x Voltage Detectors Maxim $0.00 (Samples) 2 x DC/DC Convertors Maxim $0.00 (Samples) Total Spent: $300.24

To be purchased: Item Possible Vendor Cost Phenolic Radford Brothers $18.00 Aluminum Amazon $16.00 Polycarbonate Sheet Amazon $18.00 Electromechanical Relays

Pickering Electronics $15.00

Circuit Board See Appendix A $30.00 LED indicators Harding Lab $1.00 Connectors Lowe’s $10.00 Crankshaft Bar(s) Lowe’s $15.00 Bike Rack www.meijer.com $10.00 Bike Chain www.meijer.com $8.00 Gear Cassette www.meijer.com $14.00 Contingencies $234.76 Total $549.76

Analysis of Budget: As of now, 82.2% of our projected budget (excluding contingency costs) has been expended. Purchases yet to be made will be ordered early in the spring semester and potentially over Christmas break. It should be noted that because our DC/DC converter is free, the originally intended expense of $20.00 for that item was converted to contingency, bringing our total contingency fund to $234.76.

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Updated Gantt Chart (Fall 2009)

Gantt Chart (Spring 2010)

Analysis of Schedule: Because of complications in the design of the Faraday piston and crankshaft subsystems, our original intention to have the mechanical aspects of the project constructed and partially tested by the end of the semester has had to be put on hold. However, nearly all of our components will have been ordered and received by finals week, and we plan to make up for lost time by getting most if not all of our individual components testing out of the way before the end of the semester. The electrical system is on schedule, with its various design modules completed and nearly ready for assembly and testing. The most pressing issue in that area of the project is the

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selection of the DC/DC converter, which will have a serious impact on our power generation. Once we can settle on an appropriate choice, however, the circuit layout for either one of our potential choices is outlined clearly in each IC’s data sheet, such that we should not be delayed too much in our design by the time it will take to design the DC/DC converter PCB layout. Finally, we are on schedule for our parts selection and ordering. The final major components necessary to push us over the 80% budget requirement for the fall semester will be purchased and on their way by the end of the week. The only components whose purchase will be put off until next semester are several of the mechanical components for the crankshaft, whose dimensions may change slightly after the Faraday piston is completed and attached.

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Appendices