Air Motor Report

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  1. 1 *The following is the final written report regarding my engineering team’s air motor design senior project. We were asked to come up with and develop our…
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  • 1. 1 *The following is the final written report regarding my engineering team’s air motor design senior project. We were asked to come up with and develop our own design, conduct our own analysis, and machine each part ourselves. The final product was used to power a miniature go-kart. Engine Design Team Muscles Lucas Gargano Joe Mosley Andrew Daehn Steven Politowitz Michael Steiger Yichao Ou
  • 2. 2 Table of Contents Introduction Engine Concept Engine Detailed Engineering and Development Thermodynamic Energy and Fluid Flow Models Strategy, Software Coding for Valve Control, Physical Circuitry Engine Fabrication and Manufacturing Mechanical and Valve Timing Testing Testing Day Results Team Lessons Learned Course Improvements Appendices List of Figures List of Tables List of Equations
  • 3. 3 Introduction Beginning our engine design project, we made sure to identify each of our team members’ strengths and assign them to each team accordingly. The team was broken up into groups of analysis, electronics, and design/manufacturing. Andrew Daehn and Lucas Gargano were assigned to design/manufacturing portion of the project. Steven Politowitz and Joseph R. Mosley were assigned to the electronics section of the project, which left Michael Steiger and Yichao Ou to the analysis team. No matter which sub-group they belonged to, each team member was encouraged to aid the other skill teams in order to help balance the work load given to everyone. Finding a solid direction to go when designing our engine was the first step to a successful project. Our engine design is a bit unconventional by layman’s terms. We designed it to be a four cylinder engine with two pistons firing in each cylinder body. These pistons are also programmed to be in phase when firing (meaning that they pump at the same time). This gives our four cylinder design the function of a two cylinder design. We also have two fly wheels that are used to support the crank shaft, which is used to transfer the linear motion of the pistons into the angular motion we desire. Our engine is predominantly made of aluminum, while our pistons are made of bronze and our connecting rods are made of steel. Our materials were acquired in numerous ways. We made several to trips to a local scrap yard to obtain much of the aluminum we used to machine the cylinders as well as the support plates. We also ordered material from a few different suppliers online. We were able to obtain bearings to support the main shaft of our design. The
  • 4. 4 aluminum piping used to manufacture the drive shaft was also obtained through the online suppliers. Nearly over one hundred hours were spent in the machine shop manufacturing our engine’s components. Even as we were very diligent when scheduling our manufacturing appointments, the project took longer than expected and the time slots filled up fast as well so finishing our engine took until nearly the last minute. The pre-test was pushed back from Monday, May 19th to Wednesday, May 21st as apparently we were not the only group going through this. Andrew Daehn’s father also works on campus and was able to give us some spare time on the machines he watches over. Walter Green was also very helpful in the machining process as we are all very new to the shop. The electronics team would have never been able to successfully complete their assignments (on time anyway) had it not been for Joe West’s, and each of the Jasons’, constant willingness to offer help and guidance. The weekly meetings that began in May with Professor Luscher also proved extremely helpful as it gave us reassurance to the track we were on as well as direct access to ask any question we may have had regarding the project, as he was always willing to clarify and suggest the best way we could go about anything. Without these people it would have been a very rocky road and we were lucky to have instructors who were so easy to communicate with helping us. The learning curve throughout the project was incredible. Every single one of us was challenged to complete assignments involving things we had little to no experience with. With very little Solid Works experience, minimal machining experience, and no electronics experience; each team was challenged not only by their knowledge, but their ability to learn on the fly, as well. This design project was the strongest real life experience we have had as
  • 5. 5 undergraduates as far as learning to work on your own and finding ways to complete something when all the answers may not be lying there in front of you.
  • 6. 6 Engine Concept When developing our engine design we decided to keep our main focus on power. We designed the engine keeping in mind our limited experience using CAD programs and working in the machine shop. Our design was meant to allow as much precision error as possible when designing and machine as we anticipated a significant amount of setbacks. We also attempted to keep our pieces and parts designed as simply as possible so as not to bring on something that would be potentially too difficult for such an inexperienced group. This proved vital as our machined parts nearly never were machined precisely where we wanted them, yet our engine was able to accommodate to these mistakes and still operate. We developed a four cylinder engine that worked like a two cylinder engine. It had two cylinders on each side that fired in phase with each other, while each respective side fired a half cycle out of phase. We designed this to maximize power and in this we succeeded as our max hp output ended up being .12. This proved vital during the power testing as we had one of the fastest engines with a run time of 11.83 seconds. Drawings of each and every part of of our engine design can be found later on in the appendices.
  • 7. 7 Engine Detailed Engineering and Development Crankshaft Stiffness Analysis Torsional Analysis: For the torsional analysis, an arbitrary torque was applied to the crankshaft and its deflection was measured so that a stiffness constant, torsional, could be found. This was done using a static analysis within the simulation tool in Solidworks. Since our crankshaft is off center at a constant radius from the center of the flywheel, the torque was assumed to result in only an applied shear force to one end of the crankshaft. By doing this, it is assumed that the all of the crankshaft’s material is at the constant radius of 1”. This is not actually true, since the crankshaft’s outer-most point is at a radius of 푅표 = 1 푖푛푐ℎ + 푑푐푟푎푛푘푠ℎ푎푓푡 2 = 1.25", and the crankshaft’s inner-most point is at a radius of 푅푖 = 1 푖푛푐ℎ − 푑푐푟푎푛푘푠ℎ 푎푓푡 2 = .75". In other words, it is assumed that the crankshaft’s diameter is small compared to the radius at which it rotates. Because the smaller torsion in the rod is neglected, the crankshaft’s deflection will be less in the simulation than in practice all other things being equal. A smaller deflection for the same applied torque will give a larger stiffness value. Below are the results of the Finite Element simulation for an arbitrary applied torque of 11.24 in-lb, causing a 50 N shear force at the end of the rod.
  • 8. 8 Study Results Name Type Min Max Stress1 VON: von Mises Stress 147204 N/m^2 Node: 409 3.61192e+007 N/m^2 Node: 851
  • 9. 9 Name Type Min Max cshaft-Study 1-Stress-Stress1 Name Type Min Max Displacement1 URES: Resultant Displacement 0 mm Node: 1 0.220161 mm Node: 638
  • 10. 10 The maximum displacement of the free end was .2202 mm, or .00867 inches. This displacement at a radius of 1” is equal to an angular displacement of .00867 radians. The stiffness can then be found as 푘푡표푟푠푖표푛푎푙 = 휏 휃푑푖푠푝푙푎푐푒푚푒푛푡 = 11.24 푖푛 − 푙푏푠 . 00867 푟푎푑 = 1296.4 푖푛 − 푙푏푠 푟푎푑 Bending Model and Analysis: The bending model was done to determine the stiffness of the crankshaft under just the loads from the piston. For this analysis, the force of the piston was assumed to be greatest at the piston’s top dead center position. At this position, the line of the force goes directly through the crankshaft as well as the crankshaft’s axis of rotation. The two pistons that are in phase on our engine were grouped as one for simplicity since they are close together, 1” apart. The force was placed across a 1” section of the crankshaft because the two connecting rods contact the crankshaft across a 1” portion of it. An arbitrary force of 50 N was applied for the Solidworks Simulation. The two ends of the crankshaft were fixed, and the maximum displacement was found. Below are the results of the Finite Element Analysis. Study Results Name Type Min Max Stress1 VON: von Mises Stress 4209.9 N/m^2 Node: 9755 4.83335e+006 N/m^2 Node: 5
  • 11. 11 cshaft-Study 2-Stress-Stress1 Name Type Min Max Displacement1 URES: Resultant Displacement 0 mm Node: 1 0.00196683 mm Node: 9035 cshaft-Study 2-Displacement-Displacement1
  • 12. 12 For the arbitrary applied force of 11.24 lbs, the maximum displacement was .001967 mm, or 7.743x10-5 inches. This results in a bending stiffness of 푘푏푒푛푑푖푛푔 = 퐹푝푖푠푡표푛 훿푐표푛푛푒푐푡푖푛푔 푟표푑 = 11.24 푙푏푠 7.743푥10−5 푖푛 = 145163 푙푏푠 푖푛 For a maximum piston force of 196 lbs (two pistons at 124.7 psi), this results in a deflection of only .001”, which should not cause any problems like a phase differences between the two sets of pistons. From this Finite Element Analysis, our current crankshaft should be stiff enough in bending and torsion so that if we have any problems with our engine, we can safely assume that crankshaft flexibility is not contributing to the problem. Stress Analysis Rod Axial Yielding: From the basic axial yielding equation with a 3/8” diameter rod, 휎푐푟 = 퐹 퐴 = 퐹 휋 ( 3 8 ) 2 4 = 27푘푠푖 퐹푐푟 = 2982 푙푏푠 From a Free body diagram analysis, the maximum force at the bottom of the stroke is: 휋푑2 4 퐹푚푎푥 = 120푝푠푖 ∗ ( ) = 94.2 푙푏푠 Therefore, the factor of safety is very high (>10). Rod hole tear out: Using the approximations from a rivet-plate tear out, 휏푒 = 퐹푠 2푥푒 푡 = 94.2 푙푏푠 2 ∗ 푥푒 푡 , 푠표 푥푒 푡 ≥ .00302
  • 13. 13 For a thickness t=1/4”, xe only needs to be greater than .012”, and our connecting rod will have at least an eighth of an inch of material surrounding the pin. Buckling: The equation for buckling was used assuming a pin to pin connection type. Our connecting rod is 3/8” by 3.8” long. The equation for critical buckling load is: 푃푐푟 = 휋 2퐸푡 퐼 퐿푒 2 = 휋 210.3퐸6푝푠푖 ( 휋 ( 3 8 ) 4 64 ) 3.82 = 6834 푙푏푠 > 94 푙푏푠 Piston: The piston cylinder should easily be able to react to the maximum pressure of 120 psi. Since the maximum yield strength of Aluminum is 27 ksi, the piston is easily capable of supporting the maximum 120 psi load. Piston Pin: The piston pin must be able to withstand double shear. The maximum force of 94 lbs is split between its supporting ends. For a factor of safety greater than or equal to 4: 휏 = 퐹 2퐴 = 94푙푏푠 2 ( 휋 4 2 ) (푑푝푖푛) = 27000 √3퐹푂푆 The pin therefore must be at least .112”, rounding up gives a nominal diameter of 1/8”. Bearings/Bushings: We initially tried bushings for supporting the radial load between the engine supports and the crankshaft. Assuming the crankshaft’s forces are symmetrical means that the total radial load on the bearing/bushing is equal to one of the two max piston forces since only two pistons fire at one time. This means that one bearing/bushing will have to support a 퐹푚푎푥 = 94 푙푏푠. Using a factor of Safety of 2, this increases to 188 lbs. Using the bushing design criteria and a bearing thickness of ¼” and diameter of ¼”, 푃푚푎푥 = 188푙푏푠 . 25 ∗ .25" = 1504푝푠푖
  • 14. 14 This P_max is only slightly less than the maximum Pmax for a porous bronze bushing, 2 ksi. Since the factor of safety is low, we decided bearings would be a safer option. We assumed a reliability of 90%, an impact factor of 1.5 (Moderate impact), and a bearing life of 120,000 revolutions, corresponding to 10 hours at 200 rpm. From the bearing design criteria, 푃푒 = 푋푑퐹푟 + 푌푑 ∗ 퐹푎 = 1 ∗ 188푙푏푠 = 188푙푏푠 = 푃푠푒 Therefore, the required ball bearing factor calculation is: [퐶푑 (. 90)]푟푒푞 = ( 퐿푑 퐾푅(10)6) 1 푎 (퐼퐹) ∗ 푃푒 = ( 120000푟푒푣 1 ∗ 106 ) 1 3 ∗ 1.5 ∗ 188 푙푏푠 = 139.1 푙푏푠 Most of the light duty bearings we looked at online were rated at around 600N or 134.9 lbs, meaning we would most likely need a medium duty radial single ball bearing. This is by far the most critical failure point in the engine due to the high required loads on the engine. Additionally, the loads are dynamic, that is, they vary rapidly from 0 to 139.1 lbs within one stroke of the engine. This adds in an additional element that we must make sure is covered by using a high enough factor of safety. Crankshaft: Our crankshaft rod lies at a radius equal to 1.5”, and since it is fixed at both ends to the rotating flywheels, the moment provided at the ends act to decrease the maximum bending moment in the bar. For this reason, the worst case scenario for this bar is simple supports, so we chose our analysis based on this. From the free body diagram analysis on the rods, it was determined that the maximum moment occurs at the points of applied force. Assuming a rod diameter of ½” and a length of 5”, the maximum moment is: 푀푚푎푥 = 5 3 ∗ 퐹푝 = 94푙푏푠(5/3") = 156.7 푖푛 − 푙푏푠 휎푚푎푥 = 푀푐 퐼 = (156.7 푖푛 − 푙푏푠) ∗ .25")/(휋 ∗ .5^4/64) = 12769 푝푠푖 ≪ 200000푝푠푖 = 푈푙푡. 푇푒푛푠푖푙푒 푠푡푟푒푛푔푡ℎ 표푓 푠푡푒푒푙
  • 15. 15 휏푚푎푥 = 퐹 퐴 = 94푙푏푠 휋 ∗. 52 64 = 7664 푝푠푖 ≪ 115470푝푠푖 = 휏푢,푠푡푒푒푙 Since we are using a steel rod as the crankshaft, these maximum stresses are well below the limiting strength of steel in tension. Fasteners: To attach the engine to the provided base, screws will be used. The only major force acting on the screw or bolt will be a shearing force on the bolt due to the acceleration of the pistons. Assuming the engine is moving quickly at 500 rpm, and there is only one bolt holding the assembly in place, the shear force generated is: 휏 = 4푝푖푠푡표푛푠(휌푉휔2푅) 퐴푏표푙푡 = 4 ∗ ( 5.2푠푙푢푔 푓푡3 ) (휋(12)2")/12^3*(500rpm(2π/60 ))^2*1.5/12) 휋 (푑)2 = 200000 √3 = 휏푢,푠푡푒푒푙 Solving for the nominal bolt diameter, d: 푑 ≥ .0085" All of the bolts we use will be larger than that diameter, so even one of them will be able to withstand the engine’s shear forces. In conclusion, the critical design components will be the bearings, the tear out from the connecting rod hole, and the piston pins to a lesser extent. All of these components currently have a design factor of safety of around 4 or less, so care must be taken when selecting these particular parts. Strength of Materials Reciprocating engines in a crank-slider arrangement produce unbalanced forces due to the inertia of the piston, crankshaft, and connecting rods. While it is difficult to completely
  • 16. 16 balance many engines, a properly sized balancing mass can reduce the unbalanced force significantly. Our engine experienced a considerable amount of shaking or unbalanced force during a preliminary test, so to reduce this, a basic engine balancing analysis was conducted. The engine was assumed to be operating in a constant velocity reference frame. This assumption is close enough because the maximum acceleration of our cart is probably going to be small compared to the acceleration experienced by the piston during the engine’s operation. The piston’s acceleration has a primary and secondary component given by: 푎푝 = −푅 휔2 (cos(휃) + 푅 퐿 cos(2휃)) with the cos 휃 term being the primary component and the cos (2휃) term being the secondary one. The phenomenon of dynamically equivalent bodies was used to split the mass of the connecting rod between the crankshaft and piston so that there were only two point masses, a rotating one to represent the crankshaft and a reciprocating one to represent the piston. Since our crankshaft was at a radius of 1”, its mass was assumed to be centered at that radius. The overall mass of the crankshaft was divided by four so that each of the four pistons was assumed to be connected to an equally partitioned piece of crankshaft. The Law of Cosines was used to find the magnitude of the vectorally added horizontal piston unbalanced force with the radially directed centripetal force from the crankshaft equivalent mass. The net force as a function of crank angle was found: 2 + 푓푐 푓푛푒푡 = √푓푝 2 + 2 푓푝 푓푏 cos(휃) The net force as a function of crank angle is given in the polar plot below.
  • 17. 17 Net Unbalanced Force Without Balancing Mass (lbs) 25 20 15 10 5 30 150 180 0 210 60 120 240 90 270 300 330 To balance the engine, a mass was placed opposite the location of the crankshaft. In order to balance this with a rotating mass, the sum of a fraction, c, of the reciprocating piston mass and all of the rotating mass was used. 퐵 = (푚푒푞,푐푟푎푛푘 + 푐 푚푒푞,푝푖푠푡표푛 )푟 The new net unbalanced force was computed from the same reciprocating piston force with a modified rotating force that consisted of the difference between the old rotating force and the new centripetal force due to the rotation of the balancing mass. The balance mass that produced the lowest total unbalanced force was found to be .9073 lbs at a distance of 1” from the center. This mass was found by varying the fraction of reciprocating mass balanced until the smallest net maximum unbalanced force was found. This fraction, c, was found to be .58. The new unbalanced force is graphed with the original unbalanced force below.
  • 18. 18 Net Unbalanced Force With Balancing Mass (lbs) 25 20 15 10 5 30 150 180 0 210 60 120 240 90 270 300 330 Original Unbalanced Force Unbalanced Force with Balancing Mass From the graph, the maximum unbalanced force with the balancing mass added is less than the minimum unbalanced force without balancing. This is clearly an improvement, but since this is the best possible revolving balancing mass, the engine cannot be perfectly balanced with a rotating balancing mass. To completely balance the engine, some type of reciprocating mass would need to be added. By reducing this shaking force, the engine will experience less vibration, which could possibly extend its life and prevent any bolts from loosening. This balancing could also help the speed and pressure sensors, whose measurements could be altered by excessive vibration. Thermodynamic Energy and Fluid Flow Models Thermodynamic methods were used to estimate the power and efficiency of our engine. The analysis is based on an engine that rotates at a constant speed of 800 rpm with a bore of 1 inch and a bore-stroke ratio of 1:2. A clearance volume of .5 in3 was used; this gives an ample clearance distance in between .5” and 1”. Initially, we assumed that there was no pressure drop across the line and the valve and that the mass flow rate into the cylinder was infinite. Varying
  • 19. 19 the valve closing position, the theoretical power and efficiency curves were calculated assuming adiabatic conditions across the cylinder boundary. The power and efficiency graphs are shown below. 2500 2000 1500 1000 500 0 Power vs. Valve Position 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 50.00% 55.00% 60.00% 65.00% 70.00% 75.00% 80.00% 85.00% 90.00% 95.00% 100.00% Power (in-lb/s) Valve Close Percentage 60 50 40 30 20 10 0 Efficiency vs. Valve Position 0% 20% 40% 60% 80% 100% 120% Efficiency (%) Valve Close Percentage
  • 20. 20 The maximum efficiency resulted from a 20% valve closing position, while the power reached a maximum when the valves were opened for the entire downstroke. In order to get a more realistic graph of valve position closure versus power and efficiency, the work at each value of valve closure needed to be calculated. To do this, Matlab was used to calculate the work, power, and efficiency at each valve closing position in increments of 1 percent in valve position. Once the valve position was assumed, the absolute pressure was found at each point before and after the valve was closed. In order to do t
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