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Appendix D: Thermodynamics Calculations
Assignment 1 Code:
Pi = 124.7; %Tank Pressure
Ti = 293;
Pa = 14.7;
n = 1.4;
B = 1.; %Bore
S = 1.5*B; %Stroke
N = 200; %RPM
Le = [0,.35,.65,1]; %intake length
%Le = 0:.01:1; %intake length
Vc = (pi/12)* B.^3; %Clearance Volume
Vd = (pi/4) * (B.^2) .* S; %Displacement Volume
Vi = Vc + (Le .* Vd); %Initial Volume
Vf = Vc + Vd; %Final Volume
Ei = ((Pi) .* Vi .* log(Pa./Pi))/12; %Energy in
We = (((Pi .* Vi ./(n1)) .* (((Vi./Vf).^((n1))) 1)) + (Pi .* Le
.* Vd ))/12; %
Work done by expansion
Wl = (Pa .* Vd)/12; %Work lost
eff_part_a = We ./ Ei %Efficiency (part A)
eff_part_b = (We Wl) ./ Ei %Efficiency (part B)
P_hp = (N * We)./5252 %Power in hp](https://image.slidesharecdn.com/6fa1652c-7ae3-4169-9fa4-4a55cdd6ccc5-160705215208/85/EngineFinalReport-132-320.jpg)
EngineFinalReport
- 2. 2 Table of Contents i. List of Figures………………………………………………………. ii. List of Tables…………………………………………………. iii. List of Equations………………………………………………….. 1. Introduction…………………………………………………….. 2. Engine Concept…………………………………………………. 3. Engine Detailed Engineering & Development………………………. a. Strength of Materials Calculations………………………….. b. Engine Imbalance Study…………………………………………... c. Stiffness of Crankshaft Analysis……………………………………… d. Tolerance Stack Up……………………………………… 4. Thermodynamic Energy and Fluid Flow Models……………………………………… a. Calculations and PV Diagrams……………………………………… b. Discharge Coefficient Valves……………………………………… 5. Strategy, Software Coding for Valve Control, Physical Circuitry……………… a. Strategy……………………………………… b. Software Coding for Valve Control……………………………………… i. Power vs. Efficiency……………………………………… ii. OneCylinder Engine Tests……………………………………… iii. Static Delay of Valves……………………………………… iv. Intake Valve Cutoff Point……………………………………… v. RPM Advance……………………………………… vi. Tank Pressure Influence on Cutoff Point……………………… vii. Additional Tuning……………………………………… c. Physical Circuitry……………………………………… 6. Engine Fabrication and Manufacturing……………………………………… a. Manufacturing Plan……………………………………… b. Design for Manufacturing, Machining, and Assembly………………………… c. Bill of Materials……………………………………… d. Cylinder to Piston Sealing……………………………………… e. Crankshaft Design……………………………………… 7. Mechanical and Valve Timing Testing………………………………………
- 3. 3 a. Mechanical Testing……………………………………… b. Valve Timing Testing: ……………………………………… 8. Testing Day Results……………………………………… 9. Team……………………………………… a. Dominic…………………………………………………………………………… b. Brad……………………………………… c. Forrest……………………………………… d. Wenbo……………………………………… e. Yuting……………………………………… f. Sejun……………………………………… 10. Lessons Learned……………………………………… a. Dominic……………………………………… b. Brad……………………………………… c. Forrest……………………………………… d. Wenbo……………………………………… e. Yuting……………………………………… f. Sejun……………………………………… 11. Course Improvements……………………………………… a. Dominic……………………………………… b. Brad……………………………………… c. Forrest……………………………………… d. Wenbo……………………………………… e. Yuting……………………………………… f. Sejun……………………………………… 12. Appendices……………………………………… a. Appendix A:Detailed Drawings……………………………………… b. Appendix B: Budget: ……………………………………… i. Parts……………………………………… ii. Machining Time……………………………………… c. Appendix C: Digilent Code……………………………………… d. Appendix D: Thermodynamics Calculations…………………………………
- 4. 4 i ‐ List of Figures Figure 1: Team Photo…………………………………………………….. Figure 2: Engine Overview………………………………………….. Figure 3: Crankshaft Overview……………………………………. Figure 4: Loads on piston………………… Figure 5: Side view of piston………………………… Figure 6: Top view of piston………………………………….. Figure 7: Loads on the piston pin………………………….. Figure 8: Loads on the connecting rod……………….. Figure 9: Crankshaft Free Body Diagram…………………………………………... Figure 10: Simplified Crankshaft Free Body Diagram…………………... Figure 11: Crankshaft Shear and Moment Diagrams………………………….. Figure 12: Loads on bearing.…………………………... Figure 13: Basic model of single cylinder engine.…………………………. Figure 14: Typical polar plot of imbalance forces in single cylinder engine.…………… Figure 15: Imbalance plot of one cylinder of the Cylinderella Story engine.…………… Figure 16: Basic model of single cylinder engine with balance mass.…………… Figure 17: Imbalance plot of the Cylinderella Story engine with a balance…………………. mass.…………………………….. Figure 18: Imbalance plot for the Cylinderella Story engine with balance mass of B = .463lb.…………… Figure 19: Crankshaft model used for testing torsional stiffness….. Figure 20: Results of torsional stiffness analysis….. Figure 21: Sketch used to find angle of deformation….. Figure 22: Crankshaft model used for testing bending stiffness…. Figure 23: Results of bending stiffness analysis…. Figure 24: Tolerance stack up sketch…………... Figure 25: Power and efficiency curves for 1 cylinder using parameters specified……... Figure 26: Revised efficiency curve using actual clearance volume……….. Figure 27: PV diagram for when line pressure fills just Vc. The intake is then turned off and the air is expanded……………….
- 6. 6 Figure A12: Cylinder……………………………………… Figure A13: Piston……………………………………… Figure A14: Connecting Rod……………………………………… Figure A15: Assembly guide for crankshaft.…………………………… Figure A16: Crankshaft bill of materials.…………………………… Figure A17: Assembly guide for engine.…………………………… Figure A18: Engine bill of materials.…………………………… ii ‐ List of Tables Table 1: Simplified Free Body Diagram Forces…………………………… Table 2: Results of Thermodynamic Analysis 1.……………………… Table 3: Results of Thermodynamic Analysis 2………….. Table 4: Machined Parts Bill of Materials…………………….. Table 5: Standard Parts Bill of Materials…………… Table B1: Purchased Parts and Materials……….. Table B2: Machined Parts Bill of Materials……………………………………… Table B3: Standard Parts Bill of Materials……………………………………… iii ‐ List of Equations Equation 1: Piston head area…………………… Equation 2: Piston tensile safety factor………………………………… Equation 3: Maximum force on piston head………………………………….. Equation 4: Shear stress on piston head……. Equation 5: Piston shear safety factor……………………………… Equation 6: Pin shear safety factor…………………… Equation 7: Pin tensile stress………… Equation 8: Pin bending moment………... Equation 9: Pin moment of inertia……….. Equation 10: Pin tensile safety factor……. Equation 11: Connecting rod hole area…… Equation 12: Connection rod axial pressure….
- 9. 9 1 ‐ Introduction The engine design and build project presented a unique combination of challenges. The engine was required to run efficiently, as well as produce high power. It had to fit within weight and size constraints, while also staying under a predetermined budget. Furthermore, the engine design had to be simple enough that inexperienced machinists could create it. All of these constraints had to be met under a tight time schedule. A three cylinder, inline engine was chosen as the best available option to meet the project requirements. Thorough engineering analysis was incorporated into making design decisions, including strength of materials calculations, crankshaft strength calculations, and thermodynamic calculations. The cylinders were made from extruded aluminum piping. Bronze pistons were used, with Ucup seals to seal the piston to the cylinder wall. Steel connecting rods connected the pistons to the crankshaft. The bore to stroke ratio for the engine was approximately 1.5, with a bore diameter of 1.000”. The crankshaft was made from a combination of machined rectangular cross section steel “crank blocks” and precision ground three eighths inch diameter steel rod. These parts were connected using spring pins. The crankshaft was supported with four steel support blocks. Each support block contained a pressfitted bronze bushing. The cylinders were held in place between two plates. These plates were clamped together using socket head cap screws to keep the cylinders in place. Pressure was maintained between the top plate and the cylinder using rectangular cross section Orings. Figure 1: Team Photo
- 10. 10 Several design choices distinguish this engine from other inline three cylinder engine designs. First, Ucup seals were used to seal the pistons to the cylinder walls. These seals provide an incredibly tight seal, and mean almost no leakage between the piston and the cylinder. This also meant blowdown ports were not a viable option, because the ports would likely damage the seal. Second, only one top plate was used for all three cylinders, rather than one top plate for each cylinder. The single piece was designed to be connected with only eight socket head cap screws, while a minimum of twelve socket head cap screws would be required if three separate top plates were used. The single piece design was intended to simplify assembly and machining. Finally, the entire engine support structure was manufactured from steel. Though more difficult to machine, steel provides more strength, and therefore rigidity. This rigidity limits vibrational losses within the engine. The rigidity also provides All told, the engine design described in this report meets and exceeds the project requirements, and has advantages that other inline three cylinder engines do not have. Though design difficulties were encountered throughout the course of this project, a well designed, well performing engine was conceived, constructed, and tested to surpass expectations. 2 ‐ Engine Concept At the beginning of the project, a meeting was held to decide the basic geometry of the engine. Several possible alternatives were discussed, including inline, boxer, and radial orientations of the cylinders. After the experience of ME 2900, the radial engine was a natural first choice, but was eventually vetoed due to alignment concerns. LIkewise, a twocylinder boxer was attractive option due to its lack of need for a crankshaft, but was passed on because of a perceived lack of power. In the end, it was agreed upon to go forward with the design of an inline engine. Additionally, a threecylinder setup was selected, since it would provide the power that a twocylinder engine lacks, but is considerably simpler to manufacture than a fourcylinder arrangement. An isometric drawing of the engine is shown below in Figure 1.
- 13. 13 Following a recommendation from Dr. Luscher and Walter Green, the cylinders were designed from standard 1” bore aluminum structural piping, which required relatively little modifications. The bore was reamed so that it was truly 1”, and a shoulder was cut into the top of the cylinders for use with a square oring. An orthographic drawing of the cylinders is available in Figure A12 in Appendix A. Pistons were designed to be manufactured from a bronze rod turned down to size. The pistons were designed to have a relatively loose fit with the cylinder, since it was decided to implement Ucup seals mounted on top of the piston. These seals also necessitated a boss for seating and a tapped hole on the top for securing with a washer. The pistons were designed for use with ¼” diameter pins and ¼” thick connecting rods, and, accordingly, have a hole and a slot for use with these parts. An orthographic drawing of the piston is available in Figure A13 in Appendix A. Finally, the connecting rods were designed from ¼” thick 1018 steel. A relatively simple part, the connecting rod has one hole for attachment to the crankshaft and one hole for attachment to the piston pin. The top hole needed to close to the end to provide clearance with the top of the piston slot without compromising stroke length. An orthographic drawing of the connecting rod is located in Figure A14 in Appendix A. 3 ‐ Engine Detailed Engineering & Development a.) Strength of Materials Calculations In order to choose what size the engine components needed to be, some strength of materials calculations were required. For the strength of materials analysis, the minimum target Factor of Safety (FOS) was taken to be 4. This high FOS was necessary since the analysis was not perfect, missfires and kart dynamics were predicted to cause higher than normal loads, and displacement needed to be allowed for. i. Slider Crank Engine Elements Piston Material: Brass Ultimate Tensile Strength: 469Mpa, 68000psi Yield Tensile Strength: 310Mpa, 45000psi Modulus of Elasticity: 97Gpa,14100ksi
- 14. 14 Poisson’s Ration: 0.31 Figure 4: Loads on piston Piston Tensile Failure Calculations The maximum air pressure is 110 psi. Equation 1 contains a calculation for piston head area. Equation 2 contains an equation for safety factor for tensile loading. 0.5 inr = (Equation 1) π 0.7698 inA = * r2 = 2 (Equation 2).F. 109 4S = P Sy = 110 45000 = >
- 15. 15 Figure 5: Side view of piston Piston Shear Failure Calculations Equation 3 contains a calculation for maximum force on the piston head. Equation 4 contains an equation for shear stress in the piston. Equation 5 contains an equation for safety factor for piston shear failure. (Equation 3) P A 110 psi 0.7698 in 84.678 lbF = * = * 2 = F/2 2.339 lb Fshear = = 4 .04948 inAshear = π * rpin 2 = 0 2
- 16. 16 Figure 6: Top view of piston (Equation 4) 855.68 psiτ = Ashear Fshear = 42.339 0.04948 = (Equation 5).F. 52.59S = 45000 855.68 = Pin Shear Failure Calculations Figure 7: Loads on the piston pin 188 Stainless Steel pin Minimum Yield Strength: 45000psi Minimum tensile strength: 80000psi For the direct shear it should be same as piston as 855.68 psi So the safety factor is:
- 17. 17 S.F = 45000/855.68=52.59 (Equation 6) 52.59>4 The total force is still 84.678lb for the bending stress: σ=My/I (Equation 7) M=L/2*F/2=0.448/2*84.678/2=9.483936lb*in (Equation 8) y=D/2=0.15625 I for circular cross section: I =π*r^4/4=0.00046813 (Equation 9) so the bending stress is: σ=3165.5psi The safety factor is S.F. = 45000/3165.5=14.21 (Equation 10) 14.21>4 Connecting Rod Failure F=P*A=84.678lb Material low carbon steel: 5800psi a. Axial yielding in center section
- 21. 21 Figure 10: Simplified Crankshaft Free Body Diagram Using the simplified beam free body diagram, reaction forces were calculated. The simplified beam problem is statically indeterminate; the reaction forces cannot be calculated with a simple static analysis. More complex methods involving strain energy or superposition are required to solve for the reaction forces. A calculator found on www.sopromat.org solved for the reaction forces in the specific scenario for the simplified crankshaft problem, using the principles of strain energy. The reaction forces are reported in Table 1. Table 1: Simplified Free Body Diagram Forces Location Force (lbs) Rya = Ryg =Fo 30.24 Ryc=Rye = Fi 99.36 Py(b) = Py(d) = Py(f) = Fp 86.40 Based upon these reaction forces, shear and moment diagrams were created for the simplified free body diagram. These diagrams were created using a tool found on www.sopromat.org. Figure 3 shows the shear and moment diagrams created for the crankshaft.
- 24. 24 (Equation 21) 700 psiτmax−tran = 3A 4P = 4 56.16* 3π 0.1875* 2 = Torque Shear in F .75 in 4.8 lbsTmax = p * 0 = 6 For d = 0.25 in (Equation 22) 21000 psiτmax−Torque = T Q = 2 T* π r* 3 = 2 64.8 lbs* π (0.125 in)* 3 = For d = 0.3125 in (Equation 23) 10800 psiτmax−Torque = T Q = 2 T* π r* 3 = 2 64.8 lbs* π (0.15625 in)* 3 = For d = 0.375 in (Equation 24) 6300 psiτmax−Torque = T Q = 2 T* π r* 3 = 2 64.8 lbs* π (0.1875 in)* 3 = Maximum Shear + τmax = τmax−tran τmax−Torque For d = 0.25 in (Equation 25) 1500 psi 21000 psi 22600 psiτmax = + = For d = 0.3125 in (Equation 26) 1000 psi 10800 psi 11800 psiτmax = + = For d = 0.375 in (Equation 27) 700 psi 6300 psi 000 psiτmax = + = 7 Shear Failure For ASTM A36 Steel: (from Solidworks)8000 psiSu = 5 0.6 4800 psiSu−shear = * Su = 3 For d = 0.25 in (fails) 1.54nd−shear = τmax Su−shear = 22600 34800 = For d = 0.3125 in (fails) 2.95nd−shear = τmax Su−shear = 11800 34800 =
- 25. 25 For d = 0.375 in (passes) 5.02nd−shear = τmax Su−shear = 7000 34800 = Bending Stress σmax = I M cmax = πd3 32Mmax For d = 0.25 in 13800 psiσmax = πd3 32Mmax = π 0.25* 3 32 21.168* = For d = 0.3125 in 7100 psiσmax = πd3 32Mmax = π 0.3125* 2 32 21.168* = For d = 0.375 in 4100 psiσmax = πd3 32Mmax = π 0.375* 3 32 21.168* = Axial Failure (due to axial compressive stress in the vertical portion of the crankshaft) For d = 0.25 in 4.20 (passes)nd−bending = Su σmax = 13800 58000 = For d = 0.3125 in 8.21 (passes)nd−bending = Su σmax = 7100 58000 = For d = 0.375 in 14.18 (passes)nd−bending = Su σmax = 4100 58000 = Based upon the strength analysis, the ¼” and 5/16” crankshaft rods both failed the shear stress test. Only the ⅜” crankshaft rod passed both the shear and axial failure tests with a factor of safety of 4.0 or greater. Therefore, ⅜” A36 rod will be used to fabricate the crankshaft. Bushing Failure
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- 41. 41 4‐ Thermodynamic Energy and Fluid Flow Models Two assignments were completed in order to gain a better understanding of the thermodynamics taking place inside the engine. Both assignments performed calculations for only 1 cylinder, and the main goal of each was to investigate the relationship between how far the piston is away from TDC when the intake valve is closed (as a percentage of the total distance from TDC to BDC) and the power and efficiency of the cycle. The first assignment assumes a constant temperature of 293K, a bore of 1”, and an oversquare stroke of 1.5”. The 1” figure for the bore was chosen since it corresponded to the largest available size of aluminum tubing. An oversquare stroke of 1.5x the bore was chosen as a starting point based on a recommendation from Dr. Luscher. Calculations also assume an adiabatic process, venting to atmosphere, infinite flow rate, and a rotational speed of 200rpm. As an initial estimate, the clearance volume was taken to be a perfect hemisphere with a diameter equal to the bore diameter. MATLAB code used for the assignment is shown below, with results following. Since the expansion was taken to be adiabatic, the work done by the expansion was found with the equation We = ((( Pi * Vi/ (n1)) * ((( Vi / Vf ) ^ (( n1 ))) 1)) + (Pi * Le * Vd )) /12 (Equation 43) where We = work of expansion (ftlb) Pi = tank pressure (psia) Vi = initial volume (in^3) n = 1.4 Vf = final volume (in^3) Le = intake length (position of piston at time of intake valve closing, as fraction of length from TDC to BDC) Vd = displacement volume (in^3) 12 is a constant used to get the We quantity in terms of ftlb The work lost (Wl) in expanding the gas to atmosphere is given by Wl = (Pa .* Vd)/12 (Equation 44)
- 43. 43 1 Line pressure fills just Vc. The intake is then turned off and the air is expanded. 33.0% 0.128 2 Intake valve closes when the piston is 35% of the distance away from TDC. 49.6% 0.338 3 Intake valve closes when the piston is 65% of the distance away from TDC. 43.3% 0.431 4 Intake valve is open until the piston is at BDC. 33.8% 0.466 Figure 25: Power (red) and efficiency (blue) curves for 1 cylinder using parameters specified. From the results of this exercise, it was gleaned that the engine operates most efficiently when the intake valve is closed when the piston is about 35% of the way from TDC to BDC, and most powerfully when the intake valve is left open until the piston reaches BDC. The second thermodynamics analysis was performed after the team had a more concrete design. For this reason, the clearance volume could be updated to better reflect the thermodynamics actually taking place in the engine. From Solidworks, the clearance volume was found to be 0.184 in3 , which was somewhat smaller than the value assumed for the first assignment. The engine speed was this time taken as 800rpm. Bore and stroke remained the
- 52. 52 1 Line pressure fills just Vc. The intake is then turned off and the air is expanded. 49.6% 0.030 2 Intake valve closes when the piston is 20% of the distance away from TDC. 73.4% 0.101 3 Intake valve closes when the piston is 40% of the distance away from TDC. 68.4% 0.153 4 Intake valve closes when the piston is 60% of the distance away from TDC. 59.4% 0.189 5 Intake valve closes when the piston is 80% of the distance away from TDC. 48.6% 0.210 6 Intake valve is open until the piston is at BDC. 35.7% 0.218 The efficiency numbers for these calculations are much higher than in the first assignment. It is important to note that these efficiency figures do not take into account any friction effects, leaks, or cart dynamics, and are therefore higher than the actual efficiency one will observe when testing the engine. Again, however, it is apparent that the most efficient intake closure point is somewhere in the 2030% range. Likewise, more power can be developed if the intake is left open longer, though the increase in power begins to level out as the intake length approaches 100%.
- 53. 53 5 ‐ Strategy, Software Coding for Valve Control, Physical Circuitry a.) Strategy The overall strategy we developed for winning each event was pretty simple. For the efficiency event, we wanted to use as little air as possible. So the amount of time that the intake valve is open, also known as the intake length, should be as small as we can possibly get it, while still having the engine turn at a smooth pace. For the power run, we wanted to find the fastest RPM we could possibly get out of our engine, which meant slowly increasing the intake length and testing each value until we found the optimal point. Conserving air was of no concern in the power run, so we used this optimum intake length, even though it ended up being quite large in comparison to the efficiency run. b.) Software Coding for Valve Control With respect to power versus efficiency, the basic code is practically identical. The only aspect that really varies between the codes is the rates at which the intake length and the valve opening delay are iterated. Therefore, both the power and efficiency code follow the following flow chart with respect to actuating the valves. As we can see, the code decides whether or not to actuate the valves based on which of the three possible ranges the encoder is in. During the intake range, the intake valve is open, and the exhaust valve is closed. This allows air to flow into the cylinder, and to force the piston downwards. During the expansion range, both the intake and exhausts are closed. The momentum of the piston from the intake cycle carries the piston downwards until it reaches bottom dead center. At bottom dead center, the exhaust cycle begins. The intake valve is kept closed, while the exhaust valve is opened, to allow air to exit as the piston begins traveling back upwards to top dead center. The encoder lets us know the position of the shaft, and thus allows to know at any given moment where in this cycle each cylinder is. The code references this encoder position to know what to tell each valve to do and when.
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- 64. 64 6 ‐ Engine Fabrication and Manufacturing a.) Manufacturing Plan The engine manufacturing plan developed iteratively as the engine design was refined. Ease of manufacture was a consideration throughout as the initial design was created, and then progressively improved. From the beginning of the design process, manufacture was a key consideration. An initial choice was made to use a single piece, bent crankshaft. The key reason for this decision was ease of manufacture. Though this design was eventually discarded due to unforeseen complications, that decision well represents the design philosophy behind the engine. Several promising designs were passed by because of manufacturing difficulty. Examples of this include the use of single piece cylinders with no top caps, two piece connecting rods, and very tight pistontocylinder tolerances. Each of these design choices have significant upside for engine performance, but were deemed overly complex to manufacture. One of the chief criteria when evaluating a possible design was simplicity of manufacture, and whether another design could perform the same function with less difficult machining Many design choices were made on the basis of ease of manufacture, and they are addressed in the “Design for Manufacturing, Machining, and Assembly” section. Once the design was finalized, the actual manufacturing plan for the engine was relatively simple. First, the support structure would be manufactured. The design on these parts was deemed least likely to change, so they were assigned to be made first. If any flaws in the design became apparent as the engine was being manufactured, other parts could be modified to account for the design flaw. Once the support structure was made, the plan was to make the cylinders. Two of the cylinders were made in this order, but then a reamer jammed in the mill and the machining of the final cylinder was delayed until a later date. Next, the pistons were manufactured, with the exception of the hole for the connecting rod. After that, the crankshaft blocks and rods were manufactured. Finally, the connecting rods were made and the hole was cut in the piston. Once all the parts were made, the crankshaft was assembled. Following some tweaking to limit crankshaft binding, the whole engine was assembled. b.) Design for Manufacturing, Machining and Assembly Several considerations were taken into account to simplify manufacturing and assembly of the engine. First of all, an alternative crankshaft manufacturing method was pursued to save
- 66. 66 c.) Bill of Materials Table4 contains a bill of materials for machined parts created for the engine. Included in the table is the quantity of each part made, a description of the material removed from each part, the holding method used for machining, the number of surfaces machined while making the part, the number of holes machined in the part, and any notes about the machining of the part. Table 4: Machined Parts Bill of Materials Part Quantity Material Removed Holding Method Surfaces Machined Holes Machined Notes Baseplate 1 8 x counterbored thru holes for ø 1/4"20 bolts mill vice 0 8 machined base plate given to team Bushing Support 2 6 sides lightly faced; 1 x ø 0.501" thru hole; 2 x ø 1/4"20 ↧ 0.75" tapped holes mill vice; angle plates 6 3 Connecting Rod 3 1 side faced; 1 side milled to length; 1 x ø 0.251" thru hole; 1 x ø 0.376" thru hole vice 2 2 stock material width and thickness already undersized; only machined two faces Crank Rod A 2 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical Crank Rod B 3 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical
- 67. 67 Crank Rod C 1 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical Crank Rod D 1 1 x ø 0.1885" thru hole; 1 x ø 0.249" ↧ 0.375" hole; 1 side faced; 1 side milled to length mill rotary chuck; rotary table vice 2 2 1/4" ground rod press fit into ø 0.249" hole for encoder shaft Crank Block 6 3 sides faced; 3 sides milled to dimension; 2 x ø 0.376" thru hole; 1 x ø 0.1885" thru hole mill vice 6 3 Cylinder 3 1 side faced; 1 side turned to length; 0.05" long slot cut; 1.000" thru hole lathe chuck 3 1 one cylinder remade due to reamer getting stuck in cylinder while reaming Middle Plate 1 CNC CNC NA NA part made on CNC by Chad Output Shaft 1 1 x ø 0.1885" thru hole; 1 x ø 0.376" ↧ 1.000" hole lathe chuck; mill vice 0 2 hexagonal output shaft given to team Piston 3 1 side faced; 1 side milled to length; OD turned to diameter; seal positioning slot turned to diameter; 3 connecting rod slots milled; 1 x ø 1/4"20 tapped thru hole; 1 x ø 0.251" thru hole lathe chuck; rotary table vice; mill vice 7 1 ø 0.251" thru hole needed to be perpindicular to connecting rod slots; perpindicular located using dial indicator
- 68. 68 Side Upper Plate 2 5 sides lightly faced; 1 side milled to length; 2 x thru hole for ø 1/4"20 bolts mill vice; angle plates 6 2 part made but not used in final design Side Plate 2 5 sides lightly faced; 1 side milled to length;1 x ø 0.501" thru hole; 4 x ø 1/4"20 ↧ 0.75" tapped holes mill vice; angle plates 6 5 Top Plate 1 CNC CNC NA NA part made on CNC by Chad Table 5 contains a bill of materials for standard parts used in the engine. Included in the table is quantity used, quantity ordered, information on the part used, the McMasterCarr part number, and the price paid for the parts. Table 5: Standard Parts Bill of Materials Part Quantity Used Quantity Ordered Notes McMaster Part Number Price Square ORing 3 100 OD 1 5/16"; ID 1 3/16"; thickness 0.070" 4061T13 $10.32 UCup Seal 3 5 OD 1"; ID 1/2" 9691K53 $4.23 Grooved Clevis Pin w/ Retaining Ring 3 5 diameter 1/4"; length 3/4" 92735A220 $7.05 Slotted Spring Pin (1.5" long) 6 25 diameter 3/16"; length 1 1/2" 92373A261 $8.98 Slotted Spring Pin (1" long) 1 given diameter 3/16"; length 1" NA NA ø 1/4"20 SHCS (0.5" long) 3 given NA NA NA
- 69. 69 ø 1/4"20 SHCS (0.75" long) 8 given NA NA NA ø 1/4"20 SHCS (1" long) 4 given NA NA NA ø 1/4"20 SHCS (4" long) 8 given NA NA NA ø 1/4"20 Nut 4 given NA NA NA 5/8" OD Washer 3 given NA NA NA TIP Transistor 6 given NA NA NA Diode 6 given NA NA NA LED 6 preowned NA NA NA Valve 6 given NA NA NA Wire NA given NA NA NA Wire Harness Rail 1 given NA NA NA Resistor 6 given 200k, 10k, 20k ohm NA NA Circuit Board 1 given NA NA NA Battery 2 given 9v NA NA ChipKit 1 preowned Controller NA NA Encoder 1 given Run by chipkit NA NA VGA Cable Set 1 given Used for encoder NA NA Ports and Plugs 14 given NA NA NA Velcro Patches NA given NA NA NA Plastic Box 1 given Electronic Control Box NA NA Wiring Harness Tube NA given Used to package multiple wires NA NA d.) Cylinder to Piston Sealing Many methods were considered for piston to cylinder sealing. Three considerations were evaluated beyond a cursory level. These considerations were a Ucup “bicycle pump”
- 72. 72 rotary vice. After edges were found, the required holes were drilled and reamed into the rod. The rotary vice allowed the 120° offset to be drilled in the third variety rod a high degree of precision. After the holes were drilled, the stock was removed and cut to general size with the band saw. Then, the end of the rod was sanded with a belt sander until it was within 0.020 inches of the nominal size. The crank was then assembled using a press. First, the crankshaft was laid out on the table to ensure all parts were correct. Then, the crankshaft blocks were attached to the rods using spring pins. The springs pins were installed using a press. The connecting rods and crankshaft supports were placed on the crank rods as the crank rods were being fastened to the crank blocks. This fastened them on the crankshaft. Finally, the output shaft was attached to the crankshaft with a spring pin to complete the crankshaft assembly. 7 ‐ Mechanical and Valve Timing Testing When our motor was first assembled and run, there was a massive amount of internal resistance. For the first day, we struggled to even get the motor to run over 200 rotations per minute, even after breaking the engine in for about two hours. We also had severe issues with the motor grinding to a halt very suddenly. After seeking help from Joe West, we realized that we had severe binding in the rods, where they connected to the crank shaft. Joe recommended we try using spacers to keep the rods from shifting over to areas where they were binding. Doing so, allowed us to get up to around 450 rpm, but there was still a large amount of internal resistance. We decided to get the motor running as fast as possible, and then break it in for a few hours. We actually ended up running the engine for about 7 hours straight. After doing so, we noticed significant improvement in the performance of our engine. We were able to get the motor running at about 850 rpm. When consulting with Joe West once again, he recommended loosening the support plates in between the different sections of the crank shaft. Doing this didn’t really help us get the motor running any faster, but it fixed the severe stalling issues we were having. Every once in a while, one of the rods would bind up so badly that the motor would just grind to a halt. Loosening the vertical support plates actually stopped this problem from happening entirely. It should be noted that if we had included a flywheel in the design, much of this could have been avoided. The momentum provided by the flywheel could have prevented stalling by carrying the motor past the binding points, instead of the motor grinding to a halt at those points.
- 74. 74 8 ‐ Testing Day Results a) Efficiency Run (207.5 ft) During our optimization, we concluded that it is most efficient to regulate the air pressure around 26 psi 30 psi. After numerous tests, we realized that the cart’s performance was the most effective, but very unreliable, at 26 psi. In other words, it either performed very well by travelling far, and sometimes hitting the rail, or it stopped prematurely, usually a few feet from the rail. Regulating the air at 30 psi resulted in very reliable performance throughout the distance of the track, but wasn’t nearly as efficient as 26 psi (short of 30 ft in average of the wellperformed 26 psi run). The bottom line is that regulating at 28 psi was safe bet. It was fairly efficient and quite reliable, and that was the choice we made for use in the final testing. Just as in our practice runs, it performed very well for about 150 ft in fifth gear, and allowed us to safely shift down to fourth gear. Shifting, however, had some flaws. This matter was very tricky because the driver has to bet on either safe additional feet by shifting down a little earlier, or shifting down as late as possible to squeeze every distance out of the engine power by staying on high gear as long as possible, which may cause premature stop. This time, we made a decision to shift down early, and expectedly, the driver was able to safely go on 4th gear for about 40 additional feet without any unexpected stop or jerking motion of the cart. However, this obviously caused much faster air consumption and resulted in shifting failure to 3rd gear due to much less angular momentum. Hindsight is that maybe we could’ve shifted 2 gears down to 2nd gear directly, which worked successfully to add a few more feet in the practice runs.
- 81. 81 didn’t require much time to design and build the circuit box but required lots of constant maintenance throughout the project due to the failure of some of the transistors. I was merely waiting on the manufacturing team to finish the engine at one point in the project, and was not doing much. However, when the engine manufacturing was completed, it was only few days before the final testing. Given very short time, we basically had to optimize from A to Z, which forced us to stay the whole day in the lab. Nevertheless, thanks to our concentrated effort to get every result from every minute, we somehow found the best optimization for our engine and managed to execute fairly well in the final testing. With respect to team communication, some of us asked for information that was already announced and learned in the class or carmen posts to other team members. This also wasted effort and time by having to keep each other posted numerous times. It would’ve been nicer if this possibility of miscommunication was warned in the beginning of the class so that everybody can be aware of it and prevent such problems. 10 ‐ Lessons Learned a.) Dominic i) The biggest things that I learned about design in this project were the value of attention to detail, and the importance of doing things right the first time. Since the time of the project was cut by a week due to adverse weather, deadlines at the beginning of the project were very close together. Additionally, that was a busy period in the other classes that I was taking, so I did not have much free time to work towards these deadlines. Under these circumstances, I fell into the trap of making just a quick, sloppy effort so that I could be done with it and have something to turn in before the deadline. As is so often the case with such a strategy, I ended up costing myself far more time in the end than had I done it right the first time. I ended up having to go back and redo nearly everything, all while dealing with the low grade I had gotten for the first attempt. On top of that, I had basically gotten myself back into the same position as before, since I was now far behind where I needed to be and had to rush to catch up. The errors I made while rushing to catch up, however, could have been negated had I spent the necessary time and effort to check over my completed work for accuracy. Instead, the errors were exacerbated by my inattention to detail. Twice I ordered incorrect parts from
- 88. 88 mistakes caused from lack of understanding of circuit system causing me to waste unnecessary time on the part. Therefore, I was more careful about preplanning of circuit soldering by fully understanding every aspect of the breadboard circuit. This positively influenced the circuit board quality especially on correctness of the circuit. For this reason, I did not have to waste unnecessary amount of effort and time to fix and relocate the parts. The only unexpected accident is when we had transistor for intake valve 1 blown out, but neither this can be easily prevented nor there is a ultimate way to prevent soldering error. We easily replaced the parts and were able to keep on going our optimization. I recalled the process I’ve taken as an improvement of my engineering discipline. As to team communication, we exchanged major news fairly well. But when it comes to exchanging details, we failed to do so because it became our habit that we were using cell phone text most of the time. Some of information that requires you to read it carefully was sent from one to another by email but it was never received and reviewed by peers at the right time. Not being able to keep each other posted resulted in confusion and miscommunication between members and caused us to waste unnecessary time. Therefore, I learned that exchanging the information in a timely manner actually saves lots of effort and time. 11 ‐ Course Improvements a.) Dominic While this project can be stressful and frustrating at times, overall it has been a good experience. I learned more about real world skills than in any standard lecture/homework based class. As far as improvements to the course, however, first, I would have preferred to have more time on the engine project, in order to go further in depth with the project and to allow more time for testing and optimization. Accordingly, I believe it would be better to reduce the time allowed for the catapult project and add the resulting time to the engine project. I understand that the goal of the catapult project is to get students prepared for the engine project and to give them an opportunity to fail when the stakes are low, but I think that most people would end up getting much more out of the class if they spent less time painting their Rube Goldberg device and more time analyzing and building their air engine.
- 93. 93 12 ‐ Appendices Appendix A: Detailed Drawings Figure A1: Crank block. Six pieces of this part were used in making crankshaft.
- 108. 108 Due to the difficulty of inserting the spring pins, it is easier to assemble the crankshaft in with the bearing supports and connecting rods already in the correct positions. 1. Insert a Crank Bar B into a Connecting Rod. Put two Crank Blocks on either end of the Connecting Rod and secure to the Crank Bar B with two spring pins. 2. Insert both pieces of Crank Bar A into each of the Crank Blocks from Step 1. Secure each with a spring pin. 3. Press a bronze bearing into each of the Bearing Supports. Slide the Bearing supports over each Crank Bar A. 4. Insert a Crank Bar B into a Connecting Rod. Put two Crank Blocks on either end of the Connecting Rod and secure to the Crank Bar B with two spring pins. 5. Slide a Crank Block from the assembly from Step 4 over one of the pieces of Crank Bar A. Secure with a spring pin. Slide Crank Bar C into the other Crank Block and secure with a spring pin. 6. Insert a Crank Bar B into a Connecting Rod. Put two Crank Blocks on either end of the Connecting Rod and secure to the Crank Bar B with two spring pins. 7. Slide a Crank Block from the assembly from Step 6 over one of the pieces of Crank Bar A. Secure with a spring pin. Slide Crank Bar D into the other Crank Block and secure with a spring pin.
- 110. 110 Figure A18: Engine bill of materials. Crankshaft Assembly 1. Press fit the bronze bearings into the holes of the Side Plates. Slide one Side Plate over each end of the Crankshaft Assembly. 2. Place the Side Plates and Bearing Supports over the appropriate holes in the Base Plate. Secure to the Base Plate with eight ¼20x1 SHCS. 3. Slide the Output Stock over the Crank Bar A and secure with a spring pin. 4. Slide each of the Pistons over a Connecting Rod. Secure by inserting a Piston Pin through the holes in the piston, and clipping with the Piston Pin Clip. 5. Slip the Pistons through the holes in the Middle Plate. Secure the Middle Plate to the Side Plate with four ¼20x1 SCHS.
- 111. 111 6. Slide the Cylinders over the Pistons. 7. Place the Top Plate over the Cylinders, ensuring that each Cylinder fits into one of the counter bores in the Top Plate. 8. Secure the Top Plate the Middle Plate with eight ¼20x3.25 SCHS. The four corner screws connect to the tapped holes Middle Plate, while the four middle screws need to be secured with the ¼20 hexnuts. Appendix B: Budget Estimate of machining time: 55 hours Table B1: Purchased Parts and Materials Part Quantity Ordered Notes McMaster Part Number Price Square ORing 100 OD 1 5/16"; ID 1 3/16"; thickness 0.070" 4061T13 $10.32 UCup Seal 5 OD 1"; ID 1/2" 9691K53 $4.23 Grooved Clevis Pin w/ Retaining Ring 5 diameter 1/4"; length 3/4" 92735A220 $7.05 Slotted Spring Pin (1.5" long) 25 diameter 3/16"; length 1 1/2" 92373A261 $8.98 Low Carbon Steel Bar 2’ length ⅜” thick, 2” width 8910K659 $19.38 Low Carbon Steel Rectangular Bar 3’ length ½” thick, 2” width 8910K949 $32.04 Low Carbon Steel Rectangular Bar 2’ Length ¼” thick, ⅝” width 8910K269 $5.81 Steel Drive Shaft 1’ Length ⅜” OD 1346K11 $6.76 Bearing Bronze, Oversize Rod 6 ½” Length 1” Diameter 8914K736 $26.29 Low Carbon Steel Bar 6” Length ⅜” Thick, ¾” Width 8910K388 $2.76
- 112. 112 Graphite SAE 841 Bronze Flange Bearing 4 ⅜” Thick, ¾” Width, ½” Length 9440T17 $5.76 Total $129.38 Table B2: Machined Parts Bill of Materials Part Quantit y Material Removed Holding Method Surfaces Machine d Holes Machine d Notes Baseplate 1 8 x counterbored thru holes for ø 1/4"20 bolts mill vice 0 8 machined base plate given to team Bushing Support 2 6 sides lightly faced; 1 x ø 0.501" thru hole; 2 x ø 1/4"20 ↧ 0.75" tapped holes mill vice; angle plates 6 3 Connecting Rod 3 1 side faced; 1 side milled to length; 1 x ø 0.251" thru hole; 1 x ø 0.376" thru hole vice 2 2 stock material width and thickness already undersized; only machined two faces Crank Rod A 2 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical Crank Rod B 3 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical Crank Rod C 1 2 x ø 0.1885" thru hole; 1 side sanded to approximate length mill rotary chuck 0 2 sanded to approximate length because length not critical
- 113. 113 Crank Rod D 1 1 x ø 0.1885" thru hole; 1 x ø 0.249" ↧ 0.375" hole; 1 side faced; 1 side milled to length mill rotary chuck; rotary table vice 2 2 1/4" ground rod press fit into ø 0.249" hole for encoder shaft Crank Block 6 3 sides faced; 3 sides milled to dimension; 2 x ø 0.376" thru hole; 1 x ø 0.1885" thru hole mill vice 6 3 Cylinder 3 1 side faced; 1 side turned to length; 0.05" long slot cut; 1.000" thru hole lathe chuck 3 1 one cylinder remade due to reamer getting stuck in cylinder while reaming Middle Plate 1 CNC CNC NA NA part made on CNC by Chad Output Shaft 1 1 x ø 0.1885" thru hole; 1 x ø 0.376" ↧ 1.000" hole lathe chuck; mill vice 0 2 hexagonal output shaft given to team Piston 3 1 side faced; 1 side milled to length; OD turned to diameter; seal positioning slot turned to diameter; 3 connecting rod slots milled; 1 x ø 1/4"20 tapped thru hole; 1 x ø 0.251" thru hole lathe chuck; rotary table vice; mill vice 7 1 ø 0.251" thru hole needed to be perpindicular to connecting rod slots; perpindicular located using dial indicator Side Upper Plate 2 5 sides lightly faced; 1 side milled to length; 2 x thru hole for ø 1/4"20 bolts mill vice; angle plates 6 2 part made but not used in final design
- 114. 114 Side Plate 2 5 sides lightly faced; 1 side milled to length;1 x ø 0.501" thru hole; 4 x ø 1/4"20 ↧ 0.75" tapped holes mill vice; angle plates 6 5 Top Plate 1 CNC CNC NA NA part made on CNC by Chad Table B3 contains a bill of materials for standard parts used in the engine. Included in the table is quantity used, quantity ordered, information on the part used, the McMasterCarr part number, and the price paid for the parts. Table B3: Standard Parts Bill of Materials Part Quantity Used Quantity Ordered Notes McMaster Part Number Price Square ORing 3 100 OD 1 5/16"; ID 1 3/16"; thickness 0.070" 4061T13 $10.32 UCup Seal 3 5 OD 1"; ID 1/2" 9691K53 $4.23 Grooved Clevis Pin w/ Retaining Ring 3 5 diameter 1/4"; length 3/4" 92735A220 $7.05 Slotted Spring Pin (1.5" long) 6 25 diameter 3/16"; length 1 1/2" 92373A261 $8.98 Slotted Spring Pin (1" long) 1 given diameter 3/16"; length 1" NA NA ø 1/4"20 SHCS (0.5" long) 3 given NA NA NA ø 1/4"20 SHCS (0.75" long) 8 given NA NA NA ø 1/4"20 SHCS (1" long) 4 given NA NA NA
- 115. 115 ø 1/4"20 SHCS (4" long) 8 given NA NA NA ø 1/4"20 Nut 4 given NA NA NA 5/8" OD Washer 3 given NA NA NA TIP Transistor 6 given NA NA NA Diode 6 given NA NA NA LED 6 preowned NA NA NA Valve 6 given NA NA NA Wire NA given NA NA NA Wire Harness Rail 1 given NA NA NA Resistor 6 given 200k, 10k, 20k ohm NA NA Circuit Board 1 given NA NA NA Battery 2 given 9v NA NA ChipKit 1 preowned Controller NA NA Encoder 1 given Run by chipkit NA NA VGA Cable Set 1 given Used for encoder NA NA Ports and Plugs 14 given NA NA NA Velcro Patches NA given NA NA NA Plastic Box 1 given Electronic Control Box NA NA Wiring Harness Tube NA given Used to package multiple wires NA NA
- 116. 116 Appendix C: Digilent Code Efficiency Code Went 205 feet during the final test //Sets the points where the intake begins int valve1intake = 0; int valve3intake = 341.3; int valve2intake = 682.6; //the initial pressure in the tank int pressure = 90; int manualvalue = 10; //Setting the points where the intake length ends and expansion begins int initialendofstroke = 120; int endofstroke = initialendofstroke + manualvalue; //Setting the pointos where exhaust begins for each of the cylinders int valve1endexpansion = 512; int valve3endexpansion = 853.3; int valve2endexpansion = 170.6; int valve1endstroke = valve1intake + endofstroke; int valve3endstroke = valve3intake + endofstroke; int valve2endstroke = valve2intake + endofstroke; //Setting the pins for each of the valves int intake1 = 4; int exhaust1 = 7; int intake2 = 8; int exhaust2 = 11; int intake3 = 12; int exhaust3 = 13; //Initializing the encoder location for each of the three cylinders int location1 = 0; int location2 = 0; int location3 = 0;
- 118. 118 void loop() { //This begins reading the state of the button buttonstate1 = digitalRead(buttonpin1); This decreases the delay to 40 PPD after 30 revolutions if(counter == 30) { deltaBit = 40; } //Calculates and returns the RPM every revolution if(revolution==1) { RPM = 1 * (60000/(millis()time1)); //If revolution = 1 time1 = millis(); revolution = 0; Serial.print("RPM: "); Serial.println(RPM); } //When the button is low, this increases the intake length by 10 parts per division. The variable ensures it only goes through the loop once. if(buttonstate1 == LOW & buttonvariable1 == 1) { delay(20); buttonstate1 = digitalRead(buttonpin1); if(buttonstate1 == LOW) { manualvalue = manualvalue + 10; endofstroke = initialendofstroke + manualvalue;
- 119. 119 buttonvariable1 = buttonvariable1 1; buttonvariable2 = buttonvariable2 + 1; Serial.print("Endofstroke: "); Serial.println(endofstroke); } } //When the button is high, this increases the intake length by 10 parts per division. The variable ensures it only goes through the loop once. if(buttonstate1 == HIGH & buttonvariable2 == 1) { delay(20); buttonstate1 = digitalRead(buttonpin1); if(buttonstate1 == HIGH) { manualvalue = manualvalue + 10; endofstroke = initialendofstroke + manualvalue; buttonvariable2 = buttonvariable2 1; buttonvariable1 = buttonvariable1 + 1; Serial.print("Endofstroke: "); Serial.println(endofstroke); } } //Each cylinder is given its own range for the intake, expansion, and exhaust. Basically the same code for all three. if(location1 < valve1endstroke deltaBit) { //Valve 1 INTAKE
- 126. 126 revolution = 0; Serial.print("RPM: "); Serial.println(RPM); } //Ramping up the delay every few revolutions. Honed via testing. Reaches a maximum value of 120. if(counter == othercounter & loopvariable == 0) { deltaBit = deltaBit + 20; othercounter = othercounter + 1; Serial.println(deltaBit); counter = 0; if(deltaBit > 120) { loopvariable = loopvariable + 1; } } //The following two segments of code allows the driver to lower the delay by pressing the button. The code detects a change in the button state, which results in the delay being lowered by 20 each time. if(buttonstate1 == LOW & buttonvariable1 == 1) { delay(20); buttonstate1 = digitalRead(buttonpin1); if(buttonstate1 == LOW) { deltaBit = deltaBit 20; buttonvariable1 = buttonvariable1 1; buttonvariable2 = buttonvariable2 + 1; Serial.print("Delay: "); Serial.println(deltaBit);
- 127. 127 } } if(buttonstate1 == HIGH & buttonvariable2 == 1) { delay(20); buttonstate1 = digitalRead(buttonpin1); if(buttonstate1 == HIGH) { deltaBit = deltaBit 20; buttonvariable2 = buttonvariable2 1; buttonvariable1 = buttonvariable1 + 1; Serial.print("Delay: "); Serial.println(deltaBit); } } //Based on the encoder position, and the ranges for the strokes initialized in the beginning of the code, the code fires different valves. if(location1 < valve1endstroke deltaBit) { //Valve 1 INTAKE digitalWrite(intake1, HIGH); digitalWrite(exhaust1, LOW); } else if(location1 < valve1endexpansion deltaBit) { //Valve 1 EXPANSION digitalWrite(intake1, LOW); digitalWrite(exhaust1, LOW);
- 131. 131
- 132. 132 Appendix D: Thermodynamics Calculations Assignment 1 Code: Pi = 124.7; %Tank Pressure Ti = 293; Pa = 14.7; n = 1.4; B = 1.; %Bore S = 1.5*B; %Stroke N = 200; %RPM Le = [0,.35,.65,1]; %intake length %Le = 0:.01:1; %intake length Vc = (pi/12)* B.^3; %Clearance Volume Vd = (pi/4) * (B.^2) .* S; %Displacement Volume Vi = Vc + (Le .* Vd); %Initial Volume Vf = Vc + Vd; %Final Volume Ei = ((Pi) .* Vi .* log(Pa./Pi))/12; %Energy in We = (((Pi .* Vi ./(n1)) .* (((Vi./Vf).^((n1))) 1)) + (Pi .* Le .* Vd ))/12; % Work done by expansion Wl = (Pa .* Vd)/12; %Work lost eff_part_a = We ./ Ei %Efficiency (part A) eff_part_b = (We Wl) ./ Ei %Efficiency (part B) P_hp = (N * We)./5252 %Power in hp
- 133. 133