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 this, many assumptions were made. First,
we assumed that the pressure in the tank was at its maximum of 124.7 psi absolute, and that this
pressure was the same as the pressure in right in front of the valve. In actuality, there is a
pressure drop due to friction and flow resistance in the tube that connects the valve to the tank.
There is also a pressure drop and resistance across the valve, which causes a limitation in the
mass flow rate through the valve. An experiment was done to determine this experimental mass
flow rate, and an equation for volumetric flow rate versus tank pressure was found. Other
assumptions made were that the specific heat of air was constant at constant pressure, the air in
the tank was at room temperature, and that the volume of air in the cylinder varied sinusoidally
with time at a frequency of 800 rpm. The initial conditions were assumed to be at STP with the
mass calculated using a volume equal to the clearance volume of .5 in3. For pressure ratios of
푝푐푦푙푖푛푑 푒푟
푝푡푎푛푘
≥ .528, the mass flow is not at its maximum choked flow and decays rapidly towards
zero with increasing cylinder pressure, so the flow function from my Turbomachinery book was
used to find the mass flow rate at these higher cylinder pressures. The valve was assumed to be
an isentropic nozzle. In order for the this calculated mass flow rate to be less than that found in
21. 21
the electronics valve experiment, the theoretical minimum area of the valve was calculated using
the experimental mass flow rate found.
The pressures were found by first finding the mass flow rate. If the pressure ratio was
greater than .528, the flow function was used to calculate a reduced mass flow rate; otherwise,
the mass flow rate was assumed to be at the maximum value found in the experiment. From the
mass flow rate, the new mass in the cylinder was found by multiplying the mass flow rate by a
predefined time step and adding this to the previous mass in the cylinder. Then, the next pressure
was found by using the ideal gas law, with the next temperature found by using an adiabatic
assumption. Since volume as a function of time is known, the next volume can be found.
푝푛+1 =
푚푛+1푅 (푇푛 (
푝푛+1
푝푛
)
푛−1
푛 )
푉푛+1
After rearranging the recursive formula for pn+1, the next pressure was found to be
푝푛+1 = (
푚푛+1 푅푇푛
푉푛 +1
)
푛 1
푝푛
푛−1
Once the valve was closed, the remaining volume change was assumed to be an adiabatic
expansion. The pressure and volume at the intake closing position were used as the initial
condition to find the constant for adiabatic expansion. The equation for pressure was then found
to be:
푝푛 = 푝푖푛푡푎푘푒 푐푙표푠푖푛푔 ∗ (
푉푖푛푡푎푘푒 푐푙표푠푖푛푔
푉푑푖푠푝푙푎푐푒푚푒푛푡 + 푉푐푙푒푎푟푎푛푐푒
푛
)
where n=1.4 for air.
Since the pressure and volume at each time were known, a pressure vs. volume graph could be
made.
Below is one of these graphs for an intake valve closing position of 75%.
22. 22
40
35
30
25
20
15
10
Pressure vs. Volume at 75% Valve Closure
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Volume (in3)
Pressure (psi)
The useful work was calculated by integrating the pressure vs. volume graphs. The
trapz() function in Matlab was used to approximate this integral using a time step of .0005
seconds. This gave a good approximation since 150 intervals were used in the calculation across
a time range from 0 to .075 seconds. The work done by the atmospheric air on the other side of
the piston was subtracted from this integral so the useful work could be found. On the return part
of the stroke, the pressure on the cylinder was assumed to be atmospheric both above and below
the cylinder, meaning that no net forces acted on it and therefore no work was gained or lost.
This is a strong assumption since the same mass flow limitations for the intake valves will apply
to the exhaust valves, so further analysis will be needed for this part of the stroke. Work will be
23. 23
lost on the exhaust stroke, but because of the valve resistance, the pressure at top dead center will
be higher than atmospheric pressure and that will assist the expansion part of the next cycle so
that more work will be generated on the downstroke. It will need to be determined if this will
result in a net work gain or loss.
With the work for one cycle known, the power is computed by multiplying the work by the
number of cycles per second calculated from the speed of the engine. The efficiency was
computed by dividing the cycle work by the energy required to pressurize the tank. Power and
efficiency versus valve closing position graphs are shown below.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
400
300
200
100
0
-100
-200
Valve Closing Position (Fraction of Displacement Volume)
Power (in-lb/s)
Power vs. Valve Closing Position
24. 24
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10
8
6
4
2
0
-2
-4
-6
-8
-10
Valve Closing Position (Fraction of Displacement Volume)
Efficiency (%)
The maximum efficiency at a valve position of .26 was 9.765%, while the maximum
power at a valve position of 1 was 429.15 in-lb/s.
The work produced for each cycle was strongly dependent on the initial pressure in the
cylinder at top dead center. For example, for an initial pressure of 124.7 psi, the max power was
1001 in-lb/s and max efficiency was 68.1%. Assuming that the pressure was atmospheric at this
point was the reason that the power and efficiency seemed much lower than those from the
infinite mass flow rate assumption. A higher initial pressure condition should give more realistic
power and efficiency values.
Efficiency vs. Valve Closing Position
25. 25
Engine Fabrication and Manufacturing
In order to abide by the DFMA techniques for low cost manufacturing we stringently
used material found at local scrap yards and designed for the least amount of machining as
possible. I believe our design used very little machining compared to other teams. We designed
for maximum adjustability to reduce the need to re-machine parts that were slightly out of
specifications.
The manufacturing plan was developed in order to expedite our machining so that testing
could be done with plenty of time to correct issues in that area. We specifically avoided all
designs that required a lot of precise machining, because our team lacked in machining expertise.
Specifically, we added an adjustment bar at the top of our engine that could expand our
frames, we added slots in the cylinder holder frame so that we could move the cylinder side to
side, clamps that could quickly be loosened so that our cylinders could move back and forth and
rod ends that could be adjusted to set our exact clearance volume.
Our cylinder to piston sealing was accomplished by setting a very precise tolerance of
0.001 between the cylinder wall and piston, and used viscous oil to help seal.
We selected a threaded rod as a crankshaft so that we could fix the crankshaft to the fly
wheels with nuts. The crankshaft is just a straight bar to reduce complex machining.
A bill of materials showing the volume of each stock purchased as well as the volume
removed of each piece of stock can be seen below. We used this to estimate the cost of the
materials we would need and just how much of this stock we would end up having to remove and
wasting.
26. 26
Part Name Quantity Volume of Stock (in^3)
Volume of Finished Piece
(in^3)
Fly Wheels 2 19.24 10.394
Base Plate 1 44 43.65
Shaft Holder 2 19 14.23488
Piston 4 7.069 3.8384
Crank Shaft 1 0.567 0.442
Crank Arm 4 1.787 1.54
Cylinder 2 76.97 64.4
End Cap 2 9.621 9.32
Holder-Shaft 2 6.185 5.74
Stand 2 63 19.68
Volume
Removed
Cost of Stock/piece ($/lb)
Total Cost of Stock
($)
# of faces to be
surfaced
8.846 2 3.77104 2
0.35 2 8.624 1
4.76512 2 3.724 3
3.2306 2 1.385524 2
0.125 2 0.111132 2
0.247 2 0.350252 2
12.57 2 15.08612 2
0.301 2 1.885716 1
0.445 2 1.21226 3
43.32 2 12.348 1
48.498044
27. 27
Mechanical and Valve Timing Testing
Mechanical Testing:
After the engine was completely assembled with the valves and electronics, we tested the
motion of the engine with a basic code. We ran the engine at a low starting pressure with a
medium stroke (20 psi, 50% stroke). The engine made full revolutions; however, it was clear that
binding was slowing down the engine motion at certain locations of revolution. In addition, one
of our frame pieces was moving excessively. The following changes were made to alleviate the
problems: 1) Added an adjustable stabilizer bar connecting the two frame pieces; 2) Loosened
the crankshaft nuts to allow just enough play between the crankshafts and fly wheels. The
adjustable stabilizer bar stabilized our frame pieces and made it possible to adjust if other
problems occurred. We found that imprecise machining made our flywheels wobble about
center. By loosening the crankshaft nuts, we were able to allow the crankshaft to move freely in
the flywheels.
28. 28
The first attempt of the 2-hour burn revealed that we had a severe balancing issue. After a
few minutes into the first attempt it was clear that our engine was not going to survive the whole
duration of the burn-in due to excessive shaking and vibrating. We alleviated this issue by adding
counterweights on the flywheels, opposite the crankshaft. Our analysis team suggested that we
need to add enough weight (approximately 20 ounces) to off-set the weight of our crankshaft and
the components attached to our crankshaft. The weight of choice was lead fishing sinkers that we
attached to the flywheels with metal putty. This addition proved vital in limiting the vibration
and shaking, and also improved our performance in other areas. In just our first attempt after
adding the counterweights we were able to complete the 2 hour burn-in seamlessly using a
simple medium-stroke code.
The dynamometer performance during the pretest provided important information about
our engine. We achieved a maximum power value of 0.059 hp. This was in middle of the pack
compared to other team’s engines. Since we designed our engine specifically for power, we were
not satisfied with that value.
In the process to make the best power-run code for the competition, we relied on the
dynamometer to find where our greatest power occurs by varying our stroke and valve delay
time. It was during this process where we found the values that we were originally expecting.
The raw data from these experiments can be found in the appendix section of this report.
Summarizing, we found our highest power at our expected engine speed (between 400-500 rpm)
to be around 0.075 hp. And our overall maximum power at start-up to be 0.12 hp.
Our analysis team found the gear ratios for each gear. We then determined that the
farthest distance traveled for one revolution of our engine was 5th gear. We assumed that we had
29. 29
enough torque in our engine to produce the maximum rpm given the required start-up torque of
5th gear. To verify our assumption we tested our power code at every gear. Below is the time to
30 feet for each gear using our power code.
Valve Timing Testing:
In order to maximize our efficiency code we needed to find the load torque at our expected
engine speed. The first part of this process included running the engine on the cart with our
default code values in order to get the approximate engine speed. We then used the dynamometer
to match our engine speed to the power/torque. We then adjusted our valve stroke and delay until
we maximized our power and torque values. Our raw data can be found in the appendix. We then
put the engine on the cart and tested our dynamometer results.
0.08
0.075
0.07
0.065
0.06
0.055
0.05
0.045
0.04
Effect of Valve Delay, Stroke 60%
400 425 450 475 500 525 550
Engine Power, HP
Engine Speed, RPM
Run 2 10.75 delay
Run 2 10.5
Run 1 10.25
30. 30
Effect of Changing Stroke, Delay
10.25
400 420 440 460 480 500
Testing Day Results
0.06
0.05
0.04
0.03
0.02
0.01
0
Engine Power, HP
Our engine functioned as well as our previous test runs predicted. Our efficiency matched
our expectations going approximately 113 feet, although it needed a few shoves to keep the
revolutions going. The power run went better than previous runs predicted by nearly a second.
Our power run went for 11.8 seconds when our previous best was 12.8 seconds. Given
additional time we would have decreased our stroke. We would have given up power but gained
in efficiency because of the amount of air we were leaking per revolution.
In conclusion of the testing day results, we were in the top four of the power run and
bottom portion of the efficiency. This is right in line with our initial team commitment to power.
We knew we would do well in power the portion of the testing in sacrifice of our efficiency run.
In terms of overall power, we recorded a value above 0.12 hp, which is the most that any team
recorded on the dynamometer.
Engine Speed, RPM
60 % 10.25
65% 10.25
70% 10.25
31. 31
Testing Day Results
Overall, the final test was a success. We achieved our best time to 30 feet in 11.83
seconds, and the cart traveled 113 feet on one 7 gallon tank of compressed air. We were able to
breakdown the engine in 2 minutes and 24 seconds. In the morning prior to the test, we made
some last minute adjustments to the valve timing and were able to run the engine noticeably
faster on one of the lab tables. The improvement in time can be attributed to the last minute
adjustments in valve position. For the efficiency run, we needed three pushes because we used a
different regulator. The regulator we had used in practice needed 11 turns to get down to a
pressure of 15 to 20 psi, which was insufficient for the one we used on the day of practice. The
engine never really had enough power at these low of pressures to shift consistently, so this was
why we needed 3 pushes in between some of our shifts. If we had some more time, we would
have tested some more on the dynamometer and worked to get the electronics more consistent.
Team
Our team consisted of six members: Joe Mosley, Lucas Gargano, Michael Steiger,
Steven Politowitz, Yichao Ou, and Andrew Daehn. We were then split up into three teams of
two according to the different aspects of the engine design project. These sub-teams were
electronics, design/manufacturing, and analysis. Joe Mosley and Steven Politowitz were
assigned to the electronics team as they had worked on this section previously throughout the
Rube Goldberg Apparatus project previously in the school year. Lucas Gargano and Andrew
Daehn were assigned to the design/manufacture team as they had both taken the ME 2900 course
32. 32
and seemed to have the most experience in the machine shop. Yichao Ou and Michael Steiger
were assigned to the analysis team as they both had the strongest understanding of the theoretical
aspects of engine design.
Communication was paramount for effectively completing this project. Overall, our team
did a very good job of this. Whether it was through e-mail or group text messages we were
always able to get ahold of each other nearly immediately. Everyone in our group got along
extremely well, which enabled us to work long hours beside each other while enjoying one
another’s company. Joe Mosley was definitely the most important member as he unassumingly
became the team leader with his work ethic and overall knowledge. It was important having a
strong leader who had a good understanding of just about every aspect of the project and was
willing to spend as much time was necessary to complete the project no matter what. As a team
we worked very efficiently as everybody was willing and able to complete each assignment
asked of them. We all chipped in equally as far as expenses went and depending on who was
free when we were all willing to help work on whatever needed a little bit extra man power.
We believe we split up our team as best as we could have. Each member’s strengths
were utilized in the sub-team they were put into. Completing assignments and hitting deadlines
were not an issue for us. The communication and overall positive attitude of our group were
some of our best strengths and these may be seen as some of the most important qualities you
can have.
33. 33
Lessons Learned
Design
Engineering design is a very precise, carefully planned process. No manufacturing
advancements are meant to be made until the entire structure has been carefully designed and
verified to work. This does not only mean making sure the pieces fit, this means anticipating
motions and forces that will act on the structure and verifying they will be safe. We conducted
thermodynamic analysis on our structure in order to make sure it would not overheat. We
conducted strength of materials calculations on our structure to make sure it would not fracture.
All this was done before we ever began the physical construction. This is not only a safety
precaution but a financial precaution as well seeing as if something were to go wrong with your
design post-construction you would have to repurchase all the materials used for your engine.
The designing process is easily the most important aspect of building any product.
If we could go back through the design process again what we would do differently is
conduct our analysis as we went, rather than all at once. Often times we would go through and
do a large amount of the design process without stopping to analyze each step. This can lead to
finding out something you did early on would not work with your later decisions which means
you would have to go back through everything once again. Doing your analysis as you go
provides confirmation and reassurance with each design choice you make.
Professional Skills
We became much better at communicating with each other and getting a point across the
right way. We understood we are all in this together and there was no room for anyone to act
like they were a more important member than anyone else. Even as the leader, Joe Mosley
34. 34
would never act like he deserved any more credit than anyone else in the group no matter how
many extra hours he would spend or how much more he understood regarding the project. This
led to respect throughout the group for each member therefore there was no gap of power
between anyone allowing each of us to speak our minds freely. Our closeness as a team might
have been our biggest strength as it would give us all that extra energy and motivation we needed
to spend the tireless hours, as we all felt like we were equally responsible for the final outcome.
We also learned better ways to communicate with those above us; instructors, lab
supervisors, etc. They are the ones who can help the most, so we learned being honest with them
and being as clear as possible was the smartest route. Early on during one of our first oral
presentations we became defensive when Professor Luscher simply asked us a question
regarding a clarification on our Rube Goldberg Apparatus. Our response was rude and useless as
it helped no one and we learned this very quickly. Since then we have learned to respect and
trust our instructors and this led to a much clearer path to success as we were at an understanding
with those who would be critiquing our work. This may be one of the most important lessons we
learned throughout our entire college careers as we will always have someone above us
overseeing our work that it will always be best to respect and get on the same page with.
Manufacturing
We found out how precise of a process the actual manufacturing of our design really was.
We were not permitted to begin machining until we had physical drawings of the exact
dimensions and geometries we would need. The attentiveness that machining requires was also a
major surprise as merely one pass too many could mean disaster for your part and the necessity
35. 35
of starting over on it beginning with repurchasing the material (which, if it wasn’t available
locally, could take days [and we didn’t have days]).
The time it took to manufacture was also a big surprise to most of us. We spent nearly
100 hours machining our engine before we could begin assembling. This amount of time was
hugely more significant then we estimated it to be in the planning phase of our project. Although
we still feel like we did a good job of getting into the shop as early and often as we could, we
would have tried even harder to start earlier during the finals week as that would allow for a
more appropriate time table.
We learned to work a variety of machines through the process of this project. We spent
significant time on the lathe, rotary table, and the mill. We learned how important it is to follow
the rules when operating this machinery as the slightest mistake could be detrimental to the
machine, or even worse, your health. This was no longer concept, nor theoretical, we were in
there physically manufacturing the parts of the engine we designed for real life use.
Programming/Electronics
36. 36
Course Improvements
We felt this course was run very well. The toughest part is not having the proper training
for all the aspects of the engine design going into it and having to learn on the fly with a very
limited amount of time. Although, the instructors were all extremely helpful and if you were
having any sort of trouble going to them was a very good idea as they were always willing and
able to help. They were also all very knowledgeable therefore the help they gave was extremely
strong and efficient. The assignments were at a good level of difficulty as they gave you a good
idea of what they were hoping to teach you without spending too much of your time.
I would say the most improvement regarding this course would have to do with the
preparation prior. Many things we are asked to do and accomplish throughout this course are
things that we have had little to no training on. The recent addition of the Mechanical
Engineering 2900 course is a step in the right direction, but we actually had members on our
team who were not fortunate enough to be a part of that class. Between the Solid Works aspect,
the coding to run the engine, and the manufacturing itself; these were all things each of us were
very new to. This made it especially hard during the four week period we had to get everything
together during the Maymester. Luckily all the instructors were as helpful as could be whenever
we had a question.
Appendices
Budget
Expenses
arduino chip 33.63 Joe Joe
Total
212.06
metal 35.08 Lucas Lucas
Total
110.41
37. 37
bearings 15 Lucas
aluminmum 15.75 Joe
aluminum 29.24 Lucas
Miscellaneous` 10 Lucas
piston rod ends 24 Joe
Alum Rod 31.27 Joe
hardware 33 Joe
cylinder stock 10.75 Lucas
Bearings x2 24.75 Joe
Bar Stock alum 15.49 Joe
Oil, tool, gasket 10.34 Lucas
brass pins, brass pipe 34.17 Joe
Total 322.47
Total for Each 53.745
Engine Balance Code
% All units are english system
clear all
clc
R=1/12; % Radius of rotation (half stroke)
omega=800*2*pi/60; % Engine angular speed (rad/s)
theta=0:.01:2*pi;
m_p=.566/32.2 % mass of piston (pounds to slugs)
m_r=.526/32.2 % mass of connecting rod
CG_r= 3.8/12; % Center of gravity measured from piston side in feet
l_r=5/12; % Length of rod in feet
m_c2=.106/32.2; % mass of rotating portion of crankshaft
% whose mass is centered at the crank radius
m_p1=m_r*(l_r-CG_r)/l_r % Equivalent mass added to piston from con. rod
38. 38
m_c1=m_r-m_p1 % Equiv. mass added to crank from connecting rod
for i=1:100
c=.01*i;
b=R; % balancing mass distance
B=((m_c1+m_c2)+c*(m_p+m_p1))*R/b; % balancing mass
f_c=(m_c1+m_c2)*R*omega^2
f_b=B*omega^2*b
f_cb=f_c-f_b
f_p=(m_p+m_p1)*R*omega^2*(cos(theta)+R/l_r*cos(2*theta));
for k=1:length(theta)
f_net(i,k)=sqrt(f_p (k)^2+f_cb.^2+2*f_p(k)*f_cb.*cos(theta(k)));
end
fmax(i)=max(f_net(i,:));
end
fbest=min(fmax);
c=find(fmax==fbest)*.01
b=R; % balancing mass distance
B=((m_c1+m_c2)+c*(m_p+m_p1))*R/b % balancing mass
f_c=(m_c1+m_c2)*R*omega^2
f_b=B*omega^2*b
39. 39
f_cb=f_c-f_b
f_p=(m_p+m_p1)*R*omega^2*(cos(theta)+R/l_r*cos(2*theta));
f_netbest=sqrt(f_p.^2+f_cb^2+2*f_p*f_cb.*cos(theta));
polar(theta,f_netbest); hold on
Thermo Code
clc
clear all
p_ 0=40:10:(110+14.7); % pressure in the tank
c_p=2241.5; % in-lb/(lbm degR)
T_ 0=529.67; %70 F in Rankine
T(1:100,1)=T_ 0; % Starting temperature
rpm=800; % speed of engine
f=rpm/60; % Frequency (Hz)
R=643.5; % in-lb/(lb,m deg R) for air
d_ 0=1.352*10^(-6); % Not needed?
V_c=.5; % cubic inches
V_D=1.571; % displacement volume
t=0:.0005:.075; % Time from 0 to period of one cycle
dt=t(2)-t(1); % Time step
V=V_c+V_D/2+V_D/2*sin(2*pi*f*t-pi/2); % Volume as function of time
40. 40
% for h=1:4
for j=1:length(p_ 0)
p(1:100,1)=p_ 0(j)/4; % Starting pressure at TDC
m(1:100,1)=p(j)*V_c/R/T_0; % Initial mass in cylinder at TDC
% m_dotmax below calculated from electronics assignment for flow rate
m_dotmax=((.0311*p_ 0(j)^2-6.0719*p_ 0(j)+462.46)*1000/10^3/2.54^3)*p_ 0(j)/R/T_0;
% Area of valve opening below; found so that the mass flow rate
% calculated using the flow function does not exceed the mass flow rate above.
%The area is calculated at the choked condition so F=1.281
% Equations from my turbomachinery book - isentropic nozzle assumption
A_t=m_dotmax/1.281/p_0(j)*(c_p*T_ 0)^(1/2); % in^2
x=0:.01:.99; % Range of valve positions
for k=1:length(x) % For all values of valve position
i=1;
while (V(i)-V_c)<x(k)*V_D % while the valve is open
if p(i)>.528*p_ 0(j) % If back pressure (cyl. pres.) is greater than
% the pressure for choked flow
% Mach number
M(k,i)=(2/(1.4-1)*((p_ 0(j)/p(k,i))^((1.4-1)/1.4)-1))^(1/2);
% Flow function
F(k,i)=1.4*M (k,i)/.4^(1/2)*(1+.4/2*M (k,i)^2)^(-(1.4+1)/.8);
% Use flow function to find mass flow rate
41. 41
m_dot(k,i)=F(k,i)*p_ 0(j)*A_t/(c_p*T_ 0)^(1/2);
else
m_dot(k,i)=m_dotmax; % Choked mass flow rate if cylinder pressure
% is lower than .528*tank pressure
end
m(k,i+1)=m_dot(k,i)*dt+m(k,i); % Find the new mass in cylinder
% after time step
% pressure in cylinder calculated from previous pressure, ideal
% gas law, and adiabatic assumption to find the new temperature
p(k,i+1)=m (k,i+1)^1.4*R^1.4*T (k,i)^1.4/(p (k,i)^.4*V (i)^1.4);
if p(k,i+1)>p_ 0(j) % If mass flow rate is capable of raising the cylinder
% pressure above the tank pressure, just use the tank pressure
% as the next pressure and calculate the mass based on that
p(k,i+1)=p_ 0(j);
T(k,i+1)=(T(k,i)*(p (k,i+1)/p(k,i))^(.4/1.4));
m(k,i+1)=p(k,i+1)*V (i+1)/R/T(k,i+1);
else
T(k,i+1)=(T(k,i)*(p (k,i+1)/p(k,i))^(.4/1.4));
end
i=i+1;
42. 42
end
while V(i)<max(V) % Pressure after valve closes assuming adiabatic expansion
p(k,i+1)=p(k,i)*((V(i)+V_c)/(V(i+1)+V_c))^1.4;
i=i+1;
end
W(j,k)=trapz(V(1:length(p(k,:))),p(k,:))-14.7*V_D; % Work in in-lb
P(k)=W(j,k)*f; % Power in in-lb/s
N(j,k)=W (j,k)/(p_ 0(j)*(x(k)*V_D+V_c)*log(p_ 0(j)/14.7)-14.7*V_D)*100; % Efficiency
fillenergy(j,k)=(p_ 0(j)*(x(k)*V_D+V_c)*log(p_ 0(j)/14.7)-14.7*V_D)*100;
% if N(k)>1 % error correcting
% N(k)=0;
% end
end
maxefficiency(j)=max(N(j,:))
efficiencyposition(j)=find (N==max(N(j,:)))/j
maxpower(j)=max(P);
powerposition(j)=find(P==max(P))*.01;
end
% end
plot(p_ 0,efficiencyposition,'r'); hold on %,p_ 0,efficiencyposition(:,2),p_
0,efficiencyposition(:,3),p_ 0,efficiencyposition(:,4))
43. 43
title('Eff. pos. vs. tank pressure')
% legend('Full TDC Pressure','Half TDC Pressure','1/3 TDC Pressure','1/4 TDC Presure')
Part Drawings
