Chainless Challenge 2011 -- IIT Chicago Final Report.

IIT Mechanical, Materials and Aerospace Engineering Department

Reciprocating piston hydrostatic vehicle

Illinois Institute of technology 10 West 32ndst.

Chicago, IL 60616

4/6/2012

Submitted by: Arjun Kumar Gopal Noah Jaxon

SaurabhMathur Robert Meyer

Daniel Milewski Vinay Raghu

Advisor: Jose M. Garcia

ILLINOIS INSTITUTE OF TECHNOLOGY Parker 2011/2012 Chainless Challenge

Project Report

IIT Mechanical, Materials and Aerospace Engineering Department i

TABLE OF CONTENTS

1. ABSTRACT ....................................................................................................... 1 2. PROBLEM STATEMENT .................................................................................. 1 3. PROJECT PLAN /OBJECTIVES ...................................................................... 1 3.1 Objectives ......................................................................................................... 1 3.1.1 Design and construction of a hydraulic drive train ...................................... 1 3.1.2 Design an energy recovery add-on ................................................................ 1 3.2 Project educational outcomes ........................................................................ 1 3.2.1 Hydraulic components review ........................................................................ 1 3.2.2 Prototype testing ............................................................................................. 2 3.2.3 Simulation software ......................................................................................... 3 4. DESIGN ANALYSIS .......................................................................................... 3 4.1 Component sizing and analysis of forces ..................................................... 3 4.1.1 Maximum limit of the system based on slipping........................................... 3 4.1.2 Input Cylinder pressure ................................................................................... 6 4.2 Failure Mode Effects Analysis ........................................................................ 8 4.2.1 Buckling/Critical Load: .................................................................................... 8 4.2.2 Critical Stress: ............................................................................................... 10 4.2.3 Analysis of Crank Pin .................................................................................... 10 4.3 Hydraulic simulation ...................................................................................... 12 4.4 Design of the regenerative circuit ................................................................ 14 4.4.1 Motoring (launch assist) ............................................................................... 14 4.4.2 Regenerative (energy storage) ..................................................................... 15 4.4.3 Mag1-2 electronic control ............................................................................. 15 5. DESIGN DRAWINGS ...................................................................................... 17 6. COMPONENT LIST AND COST ANALYSIS .................................................. 18 7. ACTUAL TEST DATA ..................................................................................... 19 8. LESSONS LEARNED ..................................................................................... 21 9. CONCLUSIONS .............................................................................................. 21 10. Apendix ........................................................................................................... 22

IIT Mechanical, Materials and Aerospace Engineering Department 1

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1. ABSTRACT

The Parker Hannifin Corporation Hydraulics Department hosts the annual Chainless Challenge, which challenges universities to design the best bicycle with a hydraulic connection and no chain between its pedals and drivewheel. The objective of our project is todesign a pedaling system that allows a cyclist to continue riding with the help of fluid power. This involves the use of a hydraulic cylinders geared to the pedals and drivewheel, respectively. 2. PROBLEM STATEMENT

Currently, some people commuting to work in urban areas would like to use a bicycle as reliable and economical means for transportation. A good number of cities in the United States are located in areas with lots of hills. This has discouraged the common person from using a bicycle as their preferred daily vehicle. One could say that a small motorcycle or a scooter would be an energy efficient vehicle, but the health and environmental issues of using these types of vehicles would be disastrous. This project presents a solution for the common person, willing to exercise moderately to fulfill his or her transportation needs in an economical and reliable manner. A human powered vehicle with a pneumatic energy recovery system was designed and is presented in this report.

3. PROJECT PLAN /OBJECTIVES

3.1 Objectives

3.1.1 Design and construction of a hydraulic drive train

The first goal of this project was to design and build a hydraulic drive train to propel a human powered vehicle that is economical, reliable, light and easy to use. 3.1.2 Design an energy recovery add-on

The second goal of this project was to design an energy recovery system for the human powered vehicle. This system would allow the operator to store energy to reduce the load required to propel the vehicle. 3.2 Project educational outcomes

3.2.1 Hydraulic components review

During the first three weeks of this project, the students were introduced and asked to review the various types of hydraulic pumps and motors commonly used in industry. The advisor for this project asked the students to disassemble a variable displacement axial piston pump. The students were shown the different parts and functions of the pump. Finally a Parker representative visited the laboratory and showed the students how to use the parts catalog for selection of components.


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3.2.2 Prototype testing

After three brain storming sessions, the team of students decided to implement a hydraulic system using coupled cylinders for the transmission of the hydraulic power. The team first tested the concept using pneumatic grade cylinders filled with water. After the test was completed, the team agreed to build two prototype models that would be mounted on the bicycle frame. The first prototype, an elliptical pedaling style prototype was build using a donor mountain bike frame. It proved the concept for transferring fluid from one cylinder to another and showed that the reciprocating system was feasible (see figure 1).

Figure 1: Elliptical pedaling style prototype

A second prototype that used a road bike frame was built using a crankshaft style connection for the cylinders (figure 2). The advantage of this design was that it allow the operator to ride the bicycle exactly like a regular style one, instead of having to pedal with the elliptical motion of the first prototype.


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Figure 2: Crankshaft style prototype

After comparing the two prototypes it was decided that the crankshaft style model was preferable. This design was selected for final implementation of the competition prototype.

3.2.3 Simulation software

The students in the team were introduced to the hydraulic simulation software, Automation Studio. The purpose of this activity was to facilitate visualization and the design process of the regenerative circuit. 4. DESIGN ANALYSIS

4.1 Component sizing and analysis of forces

The Analysis of the system was done for two separate cases. In the first case, the maximum torque limit of the system was analyzed based on friction coefficient of the tractive tire and the ground. Second analysis was based on the Input cylinder pressure required to power the wheels of the vehicle. 4.1.1 Maximum limit of the system based on slipping

The following physical characteristics of the vehicle were given as input: • Mass • Radius of wheel • Moment of inertia • Coefficient of friction


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First the maximum permissible torque was calculated based on above physical parameters:

a

W

0.25 W 0.75 W

MECHANISM

f1f2

DYNAMIC ANALYSIS

DRIVING FORCE

GOVERNING EQUATION f1-f2 = MT*a ; (f1)max = 0.75 μ

μ

Input

Outputζ

TOTAL MASS MT

Figure 3: Dynamic analysis of the vehicle

Assumptions made: 1) The weight distribution from front wheel to back wheel is 1:3 2) The drag force is neglected Then the system was solved for 2 cases 1) The friction acting on front wheel is maximum 2) The friction acting on front wheel is less than maximum These two assumptions were required because we could not determine physical quantities analytically as friction depends on diverse physical properties.


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Parameters Evaluated: a) Maximum friction on the wheels Based on the coefficient of friction and the above assumptions the maximum permissible friction force is evaluated. F = μ*MT* g b) Maximum acceleration Now the acceleration of the system depends on whether there is slipping or not and can be determined accordingly. c) Permissible Torque The torque can be calculated using Newton’s second law This is the maximum permissible torque as slipping will start on more application of torque! d) Minimum completion time With this maximum acceleration we can calculate the minimum time to complete the 200m Sprint Race using Equations of motion. No one can complete the race before this time e) Friction on front wheel Now friction on front wheel is function of acceleration and a depends on this friction up to certain limit, so a circular reference is given in excel sheet to solve this ambiguity and to determine whether there is slipping on front wheel or not. f) Cylinder pressure Using these maximum conditions the maximum pressure in our output cylinders can be calculated. So it was established that we are operating in safe conditions.


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4.1.2 Input- Cylinder pressure

FRONT WHEEL REAR WHEEL

ROLLS!

F2Rf = Ifαf (αf = a/Rf)

a

Rf Rr

F2 F1

F1 - F2 = MTaζ - F1Rr = Ir a/ RfF2 Rf = If a/ Rf

Solve for F1, F2 and a F2 max

a

Rf

F1 - F2max = MTa

SLIPS!

GOVERNING EQUATIONS

ζ

ζ – F1Rr = Irαr (αr = a/Rr)

Figure 4: Wheel motion conditions

These are torque based calculations.

The following physical characteristics of the vehicle were given as input: Mass Radius of wheels Moment of inertias Coefficient of friction Rated cylinder pressure Number of cylinders used


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Parameters Evaluated:

a) System force

The most important parameter is the cylinder pressure and number of cylinders used. Using this total system pressure can be calculated. Based on the area of piston the System force can be obtained which is used for FEA analysis

b) Torque on rear wheel

Now the torque on the rear wheel varies sinusoidal wrt system force Therefore the average torque can be calculated as system force multiplied by crank length multiplied by 2/pi. This Torque is used to do the further calculations of the time of completion of race. c) Maximum friction on the wheels

Based on the coefficient of friction and the above assumptions the maximum permissible friction force is evaluated. F = μ*MT* g

d) Acceleration of the system

Now the acceleration of the system depends on if there is slipping or not And can be determined accordingly. Now again there are 2 cases: 1) The friction acting on front wheel is maximum 2) The friction acting on front wheel is less than maximum In case 2 the accn can be obtained by solving accn using newton’s second law for the whole bike, front wheel and rear wheel and in case 1 the acceleration can be calculated by using newton’s second law on front wheel with maximum friction e) Friction on the wheels Now friction on wheels is function of acceleration in case 2 and hence calculated using Newton’s second law. It was also determined weather there is slipping on wheels or not.


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f) Time of completion of race With this calculated acceleration we can find the time to complete the 200m Sprint Race using Equations of motion.

4.2 Failure Mode Effects Analysis

4.2.1 Buckling/Critical Load:

Long slender members subjected to an axial compressive force are called columns, and the lateral deflection that occurs is called buckling. Often the buckling of a column can lead to a sudden and dramatic failure of a structure or mechanism, and as a result, special attention must be given to the design of columns so that they can safely support their internal loading without buckling. The maximum axial load (P) that a column can support when it is on the verge of buckling is called the critical load, Pcr, as shown in figure.5(a). Any additional loading will cause the column to buckle and therefore deflect laterally as shown in the figure 5(b). P=PcrP >Pcr

Figure 5 (a): Initial condition Figure 5 (b): Buckling condition

In our case, the cylinder rod undergoes compression during the retraction stroke. The rod end of the cylinder rod encounters the load/force applied by the cyclist and the other


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end by the reaction force applied by the blank end of the cylinder (figure 6(a)). This condition is encountered by both the front cylinders that are cranked at 1800 out of phase between extension and retraction phases. Similarly the rear end cylinder rods also undergo compression during the retraction stroke. The rod end of the cylinder rod encounters the load/force exerted by the crank arms when they are in line with the cylinder rod and simultaneously the other end of therod by the reaction force applied by the blank end of the cylinder. Since the cylinder rod encounters such compressive cycles of loading between phases, it becomes necessary to ensure that the rod is capable of withstanding such loads. Human force of 1300N Restricting force by the cranks Rod end of the cylinder

Cap end of the cylinder Equal reaction force at the Equal reaction force at the blank end of the cylinder blank end of the cylinder

Figure 6 (a) Figure 6(b)

Material of the rod = Stainless Steel Young’s Modulus (E) = 200GPa

Diameter of the rod (D) = 0.00635m Length of the rod (L) = 0.1016m


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Moment of Inertia for a circular c/s rod (I) = = = 7.98*10-11 m4

Formula for determining buckling/Critical load limit; Pcr =

Hence, Pcr = = 15261.84 N Since the approximate load applied by a cyclist is about 1.3KN, the design of the cylinder rod is safe. 4.2.2 Critical Stress:

Stress is also one of the important factors that are considered while designing a column. During the retraction stroke, the column undergoes stresses due to axial compression. The amount of stress the rod can withstand is determined by the critical stress. Critical stress is given by;

cr = = = = 15.33*107 N/m2


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4.2.3 Analysis of Crank Pin

Figure 8: Crank Pin analysis On of the most critical components are the Crank Pin and the screw which holds it with the frame whichconnects the Piston rod to the crank Shaft. The load analysis of this pin and screw is done inorder to ensure its safety

The system force of 13.KN (170 lbf) is considered as input load on Crank Pin and it was established that it will be subjected to both shear and bending stresses.

1”0.2”

SHEAR FORCE

BENDING MOMENT

170 lbf

85 lbf85 lbf

42.5 lbf-inch

Figure 9: Shear force and Bending Moment

170 lbf

1”

0.1”


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Maximum Tensile stress will be at the mid section which will be given as: σmax = Mmax*r/I = 54,140 psi The Shear stress along the cross section is: ζ = V/A = 2707 psi Axial force on the screw = 85 lbf Shear stress on screw = 850 psi Material used = Aluminum Yield stress of Aluminium = 58 kpsi From the calculations it is clear that the design is operating under safe conditions.

4.3 Hydraulic simulation

The hydraulic system was simulated in Automation Studio. Figure 7, shows the schematic representation of the hydraulic system propelling the vehicle. The hydraulic subsystem enclosed by the dotted line represented the pumping action of a human pedaling the bicycle. In the simulation, the lever actuated valve served as the control mechanism to emulate the pedaling motion. One of the requirements of the design was that the cylinders were out of phase with respect to each other by 180°. To do this a pilot operated valve was connected in parallel to the system to control the motion of the cylinder. Moving the main valve between its two positions would automatically actuate the secondary valve controlling the second cylinder.

The geometric and loading parameters found in the previous sections where input to the model. The system simulation showed that upon switching the position of the lever of the primary valve, there was effortless and synchronized motion of the pistons. This proved that the system was feasible and could be used to propel the vehicle.


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Human Pedaling

Figure 7: Hydraulic schematic of the propulsion system

Front Cylinders (Pump)

Rear Cylinders (Motor)


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4.4 Design of the regenerative circuit

Figure 8 Pneumatic schematic of the regenerative circuit

The schematic in figure 8 shows the proposed pneumatic regenerative circuit. The accumulator is essentially a pressure vessel, but it has a bladder filled with nitrogen inside it. The pressure regulator maintains the pressure from the pre-charged accumulator at 150psi so that the system operates at optimum condition. The cylinders (C1 & C2) are both out of phase. The solenoid S1 switches from motoring phase to regeneration phase and the solenoid S2 help us to achieve the neutral position, so that the vehicle stays in constant motion. Initially all the solenoids are switched off. 4.4.1 Motoring (launch assist)

When solenoid S1 and S2 is on and S3 and S4 are off, the fluid flow from the accumulator pushes the cylinders which are coupled with magnetic sensors. The magnetic sensor mag1 is still OFF, so the control valve remains in the same position thus cylinder C1 fully retracts. Once the piston of cylinder C1 reaches the top dead center (TDC), it actuates the magnetic sensor mag1 and thus changes the control valve position. Meanwhile, the cylinder C2 is fully retracted which switches ON the magnetic sensor mag2 changes control valve position and thus starting the motion of cylinder C2.


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Once the cylinders complete half cycle, the control valves are returned back to the original position by spring. 4.4.2 Regenerative (energy storage)

As the vehicle slows down, the motor accepts the torque created by its kinetic energy, converting it to fluid pressure instead of wasting it as heat as in a vehicle with traditional friction brakes. This fluid is then routed to the accumulator, compressing the air in the bladder, leaving potential energy in the form of pressurized air to be used as a boost of acceleration or an assist during the launching of the vehicle. When the solenoid S1 is off and solenoid S2 in on, the system behaves as a regenerative circuit helps assisting the vehicle to stop by pumping air from atmosphere into the accumulator till the vehicle stops.

4.4.3 Mag1-2 electronic control

The magnetic sensors must be sensed and S3/S4 valves controlled using an electronic control circuit. This could be done using either NAND/etc. gates and a dedicated battery power supply (for a net cost of ~$10) or with a microcontroller and similar power supply (~$60). Since we had a microcontroller available in the lab we designed our control circuit based on the conventional logic gates, and planned to implement it using an theArduino Uno microcontroller with commands written in open-source C libraries. The mag sensors can be aligned to produce a pulse signal at the end of a stroke. The input is then these pulse signals from sensors A and B, the output must be the logical 1 or 0 value to either solenoid actuating S3/S4 to drive the other direction which must act as a flip-flop alternated by the driving pulse signals. Following is the truth table and corresponding solution (circuit diagram).

A B Out_last Out 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 ? 1 1 1 ?

Here Out_last is a feedback signal from the last output, and an output of 1 switches the fluid flow direction with S3/S4 to drive the piston toward magB, while an output of 0 drives the piston toward magA. Clearly if neither A nor B is active Out should just be set to Out_last. Otherwise if either is active out should be set such that it drive the piston


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toward the other sensor. Clearly it’s physically unrealistic for both magA and magB to be simultaneously active, but they’ve been included here for completeness

The logic circuit solution for this was the following as illustrated in figure 9:

Figure 9: Logic controller diagram

In this circuit it’s easy to see that if A is ever active, the output will be 1 driving the piston toward magB, whereas if B is ever 1 (and A is of course zero), then Out will be 0 driving the piston towaradmagA. Critically, if neither A nor B is 1, Out is set to be Out_last. As a consequence of this circuit design, our two ?’s above are both 1s. One can imagine that there exist many solutions to this problem.


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5. DESIGN DRAWINGS


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6. COMPONENT LIST AND COST ANALYSIS

The bicycle prototype was assembled utilizing the frame and few parts from a donor bicycle, as well as two sections: the front and rear system. Below is a parts list for each section. Cost may be approximated to the best of our abilities as in some instances; we used a minimal amount of a material, and in other cases, manufacturing a material contributed significantly to its cost. Furthermore, some parts were machined out of existing scrap in the IIT laboratory. Please note that these are the costs of making the prototype, not the cost to mass produce the parts. The prototype has been made utilizing methods that would not be suitable or efficient for mass production.

Front System Part Description Material

Cost Value added

by labor Cost of

component quantity subtotal

Seat Post Clamp $ 10.98 $ 10 $ 20.98 2 $ 41.96 3/8" Threaded rod $1.50/ft $2 $ 1.50 2 $ 3.00 3/8" Nuts $ 0.10 25 $ 2.50 3/8 washers $ 0.15 50 $ 7.50 7/16" Rod $ 0.22/in $ 2 $ 2.22 4 $ 8.88 1 x 0.5" Steel $ 9.92/ ft $ 15 $24.92 4 $ 99.68 1/4"-20 Set Screws $ 0.38 4 $ 1.52 Plastic Spacer $ 4.69/ft 0.25 $ 1.17 7/16" Female Rod Ends $ 5.80 2 $ 11.60 Parker Hydraulic Cylinders $ 251.38 2 $ 502.76

Sum $ 680.57

Rear System Part Description Material

Cost Value added

by labor Cost of

component quantity subtotal

Tricycle Conversion kit $ 429 1 $ 429 Sprocket 40 t $ 68.20 $ 20 $ 88.20 1 $ 88.20 Sprolet 15 t $ 14.02 $ 14.02 1 $14.02 Chain $ 4.50 2 $ 9.00 1/2" Aluminum Sheet $ 48.26 $ 180 $ 228.26 2 $ 456.52 Internal Gear Hub $239 1 $ 239 1x0.5" Steel $ 9.92/ ft $ 15 $24.92 4 $ 99.68 7/16" Rod $ 0.22/in $ 2 $ 2.22 4 $ 8.88 3/8" Rod $1.50/ft $2 $ 1.50 2 $ 3.00 5/8" Rod $4.47/ft $2 $ 1.50 2 $ 3.00 Bearings $ 2.50 4 $ 10.00 7/16" Female Rod Ends $ 5.80 2 $ 11.60 Parker Hydraulic Cylinders $ 251.38 2 $ 502.76 Parker hydraulic hose $19.44 4 $ 77.76 Fittings $ 3.73 8 $ 29.84 Swivel fittings $ 13.09 2 $ 26.18


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Bicycle frame $ 200 1 $ 200 Total $ 2208.44

Grand Total $2889.01

Upon completion of the bike and cost analysis, it is easy to find ways of optimizing the cost of manufacturing. Our grand total came to almost $3000, with over a third of the cost coming from hydraulic components. As we assume Parker has optimized their products, we will focus on the rest of the bike. For example, our cranks are made with 8 individual parts on each side. The steel stock used for the crank arms is listed in the cost analysis at $100. If the bike was to be mass produced, this part could be cast as it is on most bikes, at a cost barely exceeding the cost to produce existing bicycle cranks. This would reduce the cost by more than half, on just this component. The same can be said for the seat post clamp, and the rear bulkheads, which were machined out of solid aluminum, even though their function can be achieved with a relatively simple casting. Casting these pieces would not only reduce cost, but also increase freedom of design for weight savings while preserving strength and rigidity. Furthermore, the costs of our prototype were inflated by the use of an off-the-shelf bicycle frame and internal gear hub. The bike frame contained many parts that were not used for the hydraulic bicycle. If the hydraulic bike was marketed as a complete bicycle and not a conversion or add-on, the original components would be unnecessary. Also, we used a standard internal gear hub to vary gear ratios. This is a rather complex and expensive part, and due to the stock gearing of the hub, necessitated the use of a $90 sprocket. If our design was to be mass-produced, the gear ratios in the hub could be redesigned to eliminate the sprockets, as well as further reducing costs by removing features of the hub which are tailored to traditional bicycles, and not necessary in the hydraulic bicycle. 7. ACTUAL TEST DATA

In the process of creating a final design of our bicycle we performed various tests on its intermediate stages. These generally indicated air leakage issues to be resolved with our bicycle. After completing both our reciprocating and rotating front drive mechanisms we coupled the two together using identical pneumatic cylinders and water as a hydraulic fluid to verify that each achieved the desired mechanical effect. Initially this suggested that certain dimensions of the reciprocating system had to be altered, and once this was done we obtained the following results for continuous un-resisted motion: Drive frequency Output stroke results Input impedance results

60 rpm Visually compete output stroke no-torque region 140 rpm ~1 inch observed damping of output

cylinder no-torque region


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On completing an input stroke, it was also observed that the output would complete its stroke, but with a small time lag. Since water is intrinsically incompressible, any lag had to be the result of a gradual equalization of a pressure differential, only possible if our circuit contained some trapped air. This partially motivated our later switch from pneumatic to hydraulic cylinders. It was mechanical essential that our cylinders complete each stroke to drive the 10cm diameter precisely machined pump-side crankshafts. This meant that any damping of the output motion would no longer result in a complete revolution on our output side. Since this would occur if a significant amount of fluid leaked across the cylinder piston boundary and caused a phase misalignment, or if any component leaked air into the system, to use our original design we had to switch to using hydraulic cylinders. After modifying the bulkhead to use hydraulic cylinders and upgrading to gasket-sealed hose fittings we once again attempted to drive a complete stroke. With both chambers of the cylinders coupled to each other we can now achieve a complete driven stroke allowing the bicycle to run. As a result of using hydraulic cylinders, however, the piston seal and viscous resistance of our hydraulic fluid will contribute to a decrease in overall efficiency. We’d like to mention one curious intermediate result. With a “perfect” seal of the circuit and having purged the circuit of air, but only one chamber of each cylinder active we achieved only partially driven strokes. The reason for this is as follows: Figure 10 depicts a single-chamber charged hydraulic cylinder driven through two operations.

Figure 10: Piston to piston driving system

In the first operation, the left cylinder is driven downwards. Using gasket sealed fittings and the precision hydraulic cylinders used in our final design the right cylinder effectively achieves a complete driven stroke. When we retract the left piston, however, there is an almost un-resisted return motion that doesn’t result in any motion in the output cylinder.


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As a result of the un-resisted retraction the volume contained in the active circuit increases from that of one chamber and the hose to that of two chambers and the hose. Since there is no hydraulic fluid added to the circuit this suggests the additional volume is made up by air leaked into the system, however, repeating the sequence while completely submerged in hydraulic fluid produced the same mechanical response indicating the same effect. The only possible cause of this is then that the additional volume was filled with a vacuum. The force acting on a ½” diameter piston in contact with a vacuum under STP is:

Or slightly less than 3 pounds. Since this is easily achieved by the manual manipulation used in this test it is reasonable to expect that we created a vacuum with this experiment. It is also useful to note that since the piston did not return to close the vacuum created under this negative pressure that the static friction between the piston and the walls of the cylinder exceeded .

8. LESSONS LEARNED

The lessons we learned from this project can be divided into two categories. First, we learned many lessons related to working in a team environment including proper communication, and the value of enthusiasm. Second, working on this bicycle together gave us the chance to trade engineering experience and explore subjects we’d never have had the chance to otherwise. In addition to gaining experience with pneumatic cylinders, hydraulic cylinders, hoses, all the various types of fittings, valves, and circuit simulators; This project gave us a reason to utilize our university student machine shops, search for and locate all kinds of parts online, and taught us how to use funding effectively. In developing a regenerative circuit (which did not materialize in time for the competition) we learned to use a pneumatic circuit simulator, design logic control circuitry, and program a microcontroller.

9. CONCLUSIONS

It can be concluded that for the regenerative circuit, there is a limit to system power requirement which is governed by the friction between the tires and the wheel. For operations within permissible limit, the system force can be obtained which can be used for the FEM analysis of the components. The analysis can also be done for dynamics of the vehicle in order to obtain parameters such as time of completion of race which is an important characteristic to improve the design of the vehicle.


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10. APPENDIX

Calculations

DESCRIPTION UNITS(SI) NOTATION

VALUE VALUE UNITS

Total mass of Bicycle with Rider Kg Mt 100 220 Lb Coffecient of friction between Tyre and Track - μ 0.50 Moment of Inertia of front wheel Kgm2 If 1 2888 lb*in2 Radius of front wheel m Rf 0.32 13 In Radius of Rear wheel m Rr 0.32 13 In Moment of Inertia of Rear wheel Kgm2 Ir 1 2888 lb*in2 Cylinder Rated Pressure psi P 216 Number of cylinder used n 1 Sprint Track Length m L 200

Maximum pressure exerted by cylinder psi P 150 1034212 N/m2

Area of Piston in2 A 1 0.000507 m2 Crank Arm length in l 2.000 0.051 M

Parameters Maximum friction-Rear wheel N f1max 368 Maximum friction-Front wheel N f2max 123 Acceleration of Bicycle m/s2 a 0.66 Friction-front wheel N f2 5 Time to complete sprint s T 25 Friction- Rear wheel N f1 71 Slipping on front wheel 1: Yes;

0:No 0

Slipping on Rear wheel 1: Yes; 0:No

0

Force exerted by a cylinder N F 524 Torque by a cylinder Nm Tau 27

System Force N 756.01 Cylinder Pressure psi P 216 Corrosponding Pressure N/m2 1492372 Torque on rear wheel Nm 24.46

Chainless Challenge 2011 -- IIT Chicago Final Report.

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