Connecticut Corsair Capstone Project
Interim Report
Team 10
Mechanical Engineering
Lauren Bradley
Arthur Podkowiak
Michael Turner
Team 194
Electrical Engineering
Randy Bertrand
Amanda Sweat
David Tartaglino
Computer Engineering
Zachary Mosch
Faculty Advisors
Dr. Stephen Stagon
Dr. Rajeev Bansal
Sponsor
Connecticut Corsair
January 2014
1
Table of Contents
1
2
3
PROJECT OVERVIEW ....................................................................................................... 3
1.1
ABSTRACT .................................................................................................................... 3
1.2
SPONSOR BACKGROUND .......................................................................................... 3
1.3
SIMULATOR BACKGROUND..................................................................................... 3
1.4
PROBLEM STATEMENT ............................................................................................. 4
1.5
PROJECT DELIVERABLES ......................................................................................... 4
PRELIMINARY ASSESSMENT......................................................................................... 5
2.1
SIMULATOR MOTION AND REQUIREMENTS ....................................................... 5
2.2
PARAMETRIC MODEL DEVELOPMENT .................................................................. 6
2.3
PREPAR3D ..................................................................................................................... 7
MOTOR SELECTION ......................................................................................................... 7
THEORY ......................................................................................................................... 7
3.1
4
5
6
3.1.1
Free Body Analysis: Spring Coefficient .................................................................. 7
3.1.2
Free Body Analysis: Torque Requirements ............................................................. 9
3.1.3
Torque Requirements............................................................................................. 14
3.1.4
Angular Velocity Calculations............................................................................... 14
3.1.5
Horsepower Requirements .................................................................................... 15
3.1.6
User-Interface Requirements................................................................................. 16
3.1.7
Motor Comparison: Servo vs. Induction ............................................................... 16
3.1.8
Final Motor Specifications .................................................................................... 18
PROTOTYPE DESIGN ...................................................................................................... 18
4.1
PURPOSE OF PROTOTYPE ....................................................................................... 18
4.2
STRUCTURE OF PROPOSED PROTOTYPE ............................................................ 19
SCISSOR ARM DESIGN ................................................................................................... 19
5.1
SCISSOR ARM OVERVIEW ...................................................................................... 19
5.2
PURPOSE OF REDESIGN ........................................................................................... 20
5.3
THEORY ....................................................................................................................... 20
5.3.1
Free Body Analysis ................................................................................................ 20
5.3.2
Finite Element Analysis Model Selection .............................................................. 21
5.3.3
Finite Element Analysis ......................................................................................... 21
5.3.4
Finite Element Analysis Results ............................................................................ 24
CONCLUSIONS .................................................................................................................. 24
6.1
PROJECT ACCOMPLISHMENTS .............................................................................. 24
6.2
PLAN OF ACTION ...................................................................................................... 24
2
Project Schedule .................................................................................................... 25
6.2.1
7
APPENDICES ....................................................................................................................... 26
7.1
Appendix I: References ................................................................................................. 26
7.2
Appendix II: Supplementary Analysis Data .................................................................. 28
3
1
PROJECT OVERVIEW
1.1
ABSTRACT
Connecticut Corsair has sponsored an interdisciplinary team of senior engineering
students to restore a damaged Gyro IPT flight simulator with obsolete components to
working condition. The goal of this project is to have the simulator respond to user input
via a joystick throttle such that the simulator mimics the flight patterns of an F4U-4
Corsair aircraft. To accomplish this the team will need to replace the lower scissor arms
of the system, integrate the simulator with Prepar3D flight simulation software, and
accurately select and obtain gearboxes, motors, and drives for the system.
1.2
SPONSOR BACKGROUND
Connecticut Corsair is a non-profit organization, founded in 1991, dedicated to
restoring an F4U-4 Corsair to flying condition12. The F4U Corsair was used primarily in
World War II and the Korean War as a fighter aircraft. The wings on the aircraft folded
upward for storage aboard aircraft carriers and the pilot was positioned over the wings in
a domed cockpit, allowing for a full view during flight27. Craig McBurney, the founder of
Connecticut Corsair, is sponsoring this project. Craig has helped to maintain vintage
aircrafts at more than 400 aviation museums throughout the country, and therefore is very
knowledgeable in the flight characteristics of the F4U-4 Corsair aircraft.
Figure 1. F4U-4 Corsair with wings folded 27
1.3
Figure 2. F4U-4 Corsair in flight 22
SIMULATOR BACKGROUND
Connecticut Corsair received a donated flight simulator system from
Environmental Tectonics Corporation® (ETC), a company based out of Pennsylvania
specializing in aviation and space training equipment for both military and civil
applications2. The original simulator was a first generation ETC Gyro IPTTM simulator,
shown in Figure 4, which mimicked the flight patterns of large jets. The current simulator
contains three induction motors to control the pitch, roll, heave, and vestibular
movements of the simulator. These motors are not capable of running the simulator for an
extended time period due to their tendency to overheat. To combat this problem ETC
installed cooling fans on the motors, however for the new Corsair design, the motors will
not be sufficient13. The motors also lack feedback elements that will be necessary for
integrating the mechanism with the proposed software.
4
Figure 3. Donated Gyro IPTTM Simulator Base
Figure 4. Original Gyro IPTTM Simulator Base 13
1.4
PROBLEM STATEMENT
As stated previously, Connecticut Corsair is an entirely volunteer organization
relying solely on donations in order to complete the restoration. The senior design team
will be working on renovating the flight simulator to mimic the flight characteristics of an
F4U-4 Corsair and serve as a registered flight trainer for pilots. Connecticut Corsair
intends to use the simulator for promotional purposes to raise support for the restoration
of the original aircraft12. This project is a multi-disciplinary venture which was broken
into three proposed phases. Phase I of the design project focused on the analysis and
research of the simulator. As of September 2013, the project entered its second phase,
which includes the restoration of multi-axis movement, the analysis and modification of
the Prepar3D software to emulate the F4U-4 Corsair, the determination of necessary
auxiliary systems, and the determination of IO requirements for software and hardware
integration. In order to pursue restoration, a team composed of multiple engineering
disciplines is required. The donated simulator base is shown in Figure 3.
1.5
PROJECT DELIVERABLES
The Phase II team consists of senior year mechanical engineering, electrical
engineering and computer engineering undergraduate students. The deliverables for the
project are distributed among the disciples depending on the expertise required for
accomplishing the goal.
The first deliverable of Phase II is the selection of effective motors to drive the
motion of the simulator along its axes. The motors must not interfere with other
moving simulator components and must be able to be adapted to the existing actuator
arms. Both mechanical and electrical specifications must be derived in order for motor
options to be explored. Motor selection will also drive the selection of gearboxes,
drivers, control systems, and the user interface for motor operation. This deliverable will
be accomplished through a collaboration of the mechanical and electrical engineering
students.
The second deliverable of Phase II will be the redesign of the lower scissor arm
that attaches the upper triangular base piece to the simulator base. The scissor arms act
as a damper to the simulator's heave motion, creating the feel of turbulence and landing
conditions. The scissor arms must be redesigned due to an over-engineered and
incorrectly sized model by the Phase I senior design team. The objective will be
5
accomplished by analyzing the failing criteria of the upper scissor arm and incorporating
the findings in the design process of the lower scissor arm. The team will also ensure that
the arms are compatible with existing linkages so that no physical interferences occur
with other components on the simulator. This goal will be pursued primarily by the
mechanical engineering students due to the student’s experience with parametric
modeling and analysis software.
The final deliverable of Phase II will be the control of the drive motors through
the integration of simulation software, specifically Prepar3D, as well as establishing
user control of the motors with a joystick. The computer and electrical engineering
students will specifically focus on this goal. The experience that the students have will
be crucial in understanding the driver system of the selected motors, programming the
motion of the motors, and implementing the Prepar3D software with the simulator.
2 PRELIMINARY ASSESSMENT
2.1 SIMULATOR MOTION AND REQUIREMENTS
The Gyro IPT flight simulator model has a triangular base plate where the cockpit
is situated, with three actuating pushrods, three scissor arm attachments, and a central
universal joint surrounded by a supportive spring. As stated previously, the current
simulator contains three induction motors to control the pitch, roll, heave, and vestibular
movements of the simulator. Pitch is defined as the rotation of the simulator about its
center x axis and is controlled solely by the front drive motor. The pitch of the simulator
about the center x-axis is used to simulate climbing, diving, and acceleration maneuvers
of an actual Corsair. Roll is defined as the rotation of the simulator about is center y-axis
and is controlled by the two side drive motors. Rotation of the simulator about its y-axis
allows for the simulation of turns and rolls during flight. The yaw is the rotation about
the vertical z-axis, or spin. This maneuver is controlled by the ‘spin’ motor and is out of
the scope of Phase II. Heave is defined as any vertical excursions from the home position
in the z-direction and is controlled by all three drive motors working in unison to lift the
system. The heave function is designed to simulate runway roughness, rough landings,
and turbulence. Vestibular movements are defined as those movements which stimulate
the inner ear balance system. Certain movements of the simulator will allow the pilot to
feel acceleration and other movements because of vestibular stimulation18.
The range of motion for the Corsair simulator is expected to correspond with the
original Gyro IPTTM simulator characteristics and can be found in Table 1.
Table 1. Gyro IPTTM Simulator Range of Motion18
Displacement Type
Pitch
Roll
Yaw
Heave
Sway
Surge
Range of Motion
+/- 25 deg/sec
+/- 30 deg/sec
360 degree continuous
+/- 10 cm
+/- 10 cm
+/- 10 cm
Speed
0-25 deg/sec
0-25 deg/sec
0-150 deg/sec
30 cm/sec
20 deg/sec
20 deg/sec
Acceleration
0.5-75 deg/sec2
0.5-75 deg/sec2
0.5-15 deg/sec2
90 cm/sec2
60 deg/sec2
60 deg/sec2
The original simulator is powered through three phase power with the environmental and
physical specifications listed in Table 2. It is important to note that many operating
6
specifications from the original Gyro IPTTM will remain the same in order to preserve the
system integrity.
Table 2. Operating Conditions for Gyro IPTTM Simulator18
Parameter
Voltage
Frequency
Phase
Requirement
220-240 Volts AC
50/60 Hz
Three Phase
Nominal Current Rating
10 Amps
Surge Current Rating
13 Amps
Protective Device Rating
16 Amps
Expected Operating Temp Range
Expected Humidity Range
+13°C to +35°C
10% to 80% non-condensing
The pitch and roll movements are dependent upon the
center of the simulator platform having a fixed pivot point.
The pivot point is obtained by connecting the center of the
simulator platform to a spring and universal joint
combination. The universal joint is connected to the
simulator platform and the guide rod ring which eliminates
any translational linear movement of the simulator platform
in the x and y directions but allows for rotational movement
Figure 5. Axes of motion for
simulator platform
about the x and y axes.
The three motors used to drive the motion of the simulator utilize a gear box and
cam pushrod system to induce motion in the simulator platform. The gearbox output
shaft is used to rotate the cam. The purpose of the cam is to translate the rotational
motion of the gearbox shaft into linear motion. Translation from one form of motion to
the next happens through a ball pivot joint that allows the pushrod to rotate perpendicular
to the cam. The opposite end of the pushrod is connected to a knuckle joint that is
attached to the simulator platform. A knuckle joint allows the pushrod to move in both
the x and y plane. Freedom of the pushrod to rotate about both the knuckle joint and cam
is critical to allow the pushrod to apply force to the simulator platform regardless of the
orientation of the simulator platform.
2.2
PARAMETRIC MODEL DEVELOPMENT
In order to perform a finite element analysis and
derive the necessary equations for torque, accurate model
of the simulator base needed to be created. A parametric
model was developed using Solidworks by replicating
every component in the base that was critical to the
structure as separate part files. Each part was measured
using calipers with a tolerance of ±.001 in. These part
files were then mated and given relations in an assembly
Figure 6. Rendering of Solidworks
drawing so that valid dimensions from point to point
Parametric Model 25
could be found. The accuracy of the upper scissor arms
and springs were especially imperative to the model as those parts will be mating to the
7
new lower scissor arm that will be designed. The upper scissor arm model was also
exported into Abaqus to perform a finite element analysis. The full model is shown in
Figure 6.
2.3 PREPAR3D
Prepar3D is a flight simulation software
developed by the company Lockheed Martin that
allows the user to create flight scenarios in order
to train pilots on an aircraft. The software
branches from the original Microsoft Flight
Simulator package and is incorporated into
numerous flight simulator mechanisms20.
Connecticut Corsair has a license to use this
20
software, and the design team will work to Figure 7. Screenshot of Prepar3D Flight Simulation
integrate the program with the new simulator control system. Currently the software is
used in conjunction with the supplied Windows 98 OS that the Gyro IPTTM was delivered
with, however the product key will be used to install the software on the team’s Windows
XP system6. The program structure will need to be analyzed in order to determine
appropriate I/O requirements so that a functional software to mechanical component
connection can be used to operate the simulator.
3 MOTOR SELECTION
3.1 THEORY
The original motors specified by ETC in the original Gyro IPT prototype were 1hp
induction motors. These motors were replaced in later models due to their tendency to
overheat during prolonged use13. The motors overheat when the duty cycle of the motor
is exceeded. A duty cycle is the maximum amount of time that a motor should be
continuously used for and the minimum amount of time a motor can be turned off before
being turned back on. If the duty cycle is exceeded, the windings and other parts of the
motor begin to overheat as there is not enough time to cool the motors between usages 19.
The induction motors obtained by the Phase I team are 0.5hp induction motors with a 90°
offset on the output shaft and therefore cannot be integrated into the Phase II design. In
order to obtain a reasonable torque requirement for each of the motors, a free body
analysis was performed on the entire mechanical system including a derivation of the
central spring constant as well as the forces experienced by the cam arm. In addition, the
motors also needed an output angular velocity which depends on motor and gearbox
combinations.
3.1.1 Free Body Analysis: Spring Coefficient
Due to the presence of the central universal joint, the
spring cannot act in lateral z-direction compression or tension.
For the analysis and derivation of the spring constant it is assumed
that the only motion the spring experiences is rotational about the
central pivot point, thus acting as a ‘bobble-head’ of sorts17. It is
assumed then that the spring constant can be derived by assuming
the right side of the pivot point provides an upward force, while
the left side of the spring applies a downward tilting force to
Figure 8. Central universal
joint and spring motion
8
restore the simulator platform to a neutral flat position. The free body diagram of the
platform is shown in Figure 9. The central spring and universal joint is depicted in red
and the platform in teal.
Figure 9. Free Body Diagram for Calculating Spring
Coefficient
Using knowledge from statics14, the moment about the pivot point, consisting of
the spring and tilting forces, can be summed and set equal to zero.
+↺ ∑𝑀𝑎 𝐹𝑠 𝑟 cos Φ + 𝐹𝑠 𝑟 cos Φ −𝐹𝑤 𝑙 cos Φ = 0
(Equation 1)
The force of the spring is defined as:
𝐹𝑠 = 𝑘𝑦
(Equation 2a)
Where k represents the spring constant in N/m and y is the linear displacement of one
side of the spring. This equation, however, becomes Equation 2b due to the shared
spring force between the three arms.
𝐹𝑠 =
𝑘𝑦
(Equation 2b)
3
The free body diagram reveals the relation between the angle Φ, and the displacement of
the simulator in the y-direction. This relation is expressed in:
𝑟 sin Φ = 𝑦
(Equation 3)
After substituting Equation 2b and Equation 3 into Equation 1 the following equation is
obtained for the spring constant:
3𝐹 𝑙
𝑤
𝑘 = 2𝑟 2 sin
Φ
(Equation 4)
9
With the relation between the spring constant and the force acting on the platform
derived, and experiment was conducted to determine the value of the spring constant. An
angle finder was place on top of the simulator platform in line with the pivot point and
pushrod location. The angle finder was accurate within .5 degrees, as a result the
experiment was limited to be only accurate within this tolerance. A chain was then
attached to the simulator platform at the pushrod location and weights ranging from 5
pounds to 320 pounds were hung off of the edge (as depicted in Figure 9). The weights
represented the varying amounts of pulling force that a pushrod could exhibit on the
simulator platform. Each of the weights had been calibrated by a certified metrologist
therefore ensuring that the weights were accurate within ±.001 lbs. Each weight and
corresponding displacement was recorded and plotted to verify that the spring constant is
a linear relationship. The spring constant was determined to be 189000 N/m. As seen on
Figure 11, only the weights between 110 pounds and 320 pounds were used in the
derivation due to measurement tool limitations. The angle measuring device was only
accurate within ½ of a degree, and the range of weights between 5 pounds and 105
pounds did not result in a noticeable displacement due to the large spring constant. Raw
data from the experiment is included in Table 1-1 of Appendix II: Supplementary
Analysis Data.
Weight vs. Displacement of Spring
Weight (lbs)
350
300
250
200
150
100
0
0.002
0.004
0.006
0.008
0.01
0.012
Displacement (m)
Figure 10. Components Contributing
to Static Weight of Simulator
Figure 11. Plot of Weight vs. Displacement for Spring Coefficient
3.1.2 Free Body Analysis: Torque Requirements
In order to determine the torque requirement for the motor, it was necessary to
find the total static weight of the simulator that the motors would have to overcome in
order to move the system. The weight of the system includes the pushrods, central
spring, universal joint, and the platform, and is important because this weight cannot be
altered. These components are shown in Figure 10. Using a platform scale, this weight
was determined to be 240lbs.
10
Figure 12. Free body diagram for torque analysis
based on vertical lift
Also included in the weight of the simulator was
the overall weight of the cabin which was broken into
two distinct sections: the pilot weight and the structure
weight. The pilot was estimated to be at a maximum of
250lbs as set in ETC’s original Gyro IPT user manual18.
Secondly, the cabin structure was estimated to be
750lbs which includes both external features and the
installed instrumentation. This estimate was determined
by the Phase I senior design team based on the
components that were installed in the original simulator.
This is considered to be an overestimate as all of the
new components will be lighter weight than the original
due to the updated technology, therefore the weight
estimate of 1240 lbs total has a safety factor built in
Next, the kinematic equations for the simulator’s
vertical lift and heave were derived which represents
the maximum torque the three motors must output in
order to move the simulator in the z-direction. The lift
sequence was analyzed as the distance the platform
travels from the ‘off’ rest position, to the highest point
that the platform assembly can be lifted. To develop the
kinematic equations, the free body diagrams were
drawn of the cam, pushrods, simulator platform, and
central spring joint. The diagram depicts the analysis of
only one motor, as the loading for each motor in this
case is identical.
In this diagram, Point A is the platform pivot point, Point M is the motor output
shaft, 𝐹𝑐 is the weight of the platform assembly, 𝐹𝑃 is the force of the pushrod, 𝑙 is the
length from Point A to the pushrod, 𝑎 is the length of the cam, 𝛼 is the angle between the
pushrod and the cam, 𝛽 is the angle between the platform and the pushrod, 𝜃 is the angle
between the horizontal plane and the cam, and 𝜏𝑚 is the motor torque.
To determine the torque requirement of the motor the moments were summed
about Point A and Point M.
+↺ ∑𝑀𝑎 𝐹𝑝 𝑙 sin 𝛽 −𝐹𝑐 𝑙 = 0
(Equation 5)
+↺ ∑𝑀𝑚 𝜏𝑚 −𝐹𝑝 𝑎 sin 𝛼 = 0
(Equation 6)
Solving Equation 5 for the push rod force and substituting the results into
Equation 6, an equation for the torque requirement for vertical lift is developed.
𝜏𝑚 =
𝐹𝑐 𝑎 sin 𝛼
sin 𝛽
(Equation 7)
11
The value of 𝐹𝑐 does not represent 1240 lbs, the full weight of the platform
assembly, but rather 413 lbs which is one third of the total weight. This assumption was
made because the weight will be equally distributed over the simulator platform. Equal
distribution of weight can be assumed because the pilot will be centered on the simulator
platform.
It is important to note the relationship between 𝛼, 𝛽, and 𝜃 that Equation 7
depicts. The relationship between these three angles is not linear due to the non-linear
motion of both the cam and simulator platform. In order to understand this relationship, a
3D model of the simulator was created in Autodesk Inventor.
Figure 13. Autodesk Inventor simulating vertical lift: 𝜃 less than zero (pictured left), 𝜃 equals
zero (pictured center), and 𝜃 greater than zero (pictured right). This simulated the relationship
between the cam (green), pushrods (red), and platform (blue)
The cam is shown in green, the pushrod is shown in red, and the simulator platform is
blue. Using this model, the cam was driven by 𝜃 in both the positive and negative
z-direction from -100° to +90° in increments of 10°. This range was selected based on
the range of motion that the cam can reach. At each increment the angles 𝛼 and 𝛽 were
measured in the 3D model. Through plotting the relationship between these angles in
Microsoft Excel, and determining the line of best fit, two equations were established to
find angles 𝛼 and 𝛽 as a function of 𝜃 shown in Figure 14. These equations were used in
a MATLAB code to calculate the torque based on any given 𝜃 and Equation 7.
θ vs α and β
Angle (Degrees)
200
150
100
α
50
β
0
-100
-50
0
θ (Degrees)
50
100
Figure 14. Plot of relationships between 𝜃 𝑣𝑠. 𝛼 and 𝜃 𝑣𝑠. 𝛽
Figure 15 shows the torque curve for the range of 𝜃 between -100° and 90°
showing that the maximum torque occurs when 𝜃=0, when both the cam and simulator
platform are perpendicular to the pushrod. Achieving maximum torque at this point is
valid because all of the pushrod force is perpendicular to the cam, creating the largest
12
force on the cam. After analysis the torque required to lift the simulator in a vertical zdirection was found to be 2894.3 in-lbs.
Figure 15. Plot generated using MATLAB showing torque calculated at each 𝜃 . The maximum torque occurs at 𝜃 = 0
The next simulation to be analyzed is the pitching and rolling of the simulator. For this
analysis it is again assumed that all three motors must provide an equal amount of force
to induce movement due to the equal distribution of weight. The free body diagrams
were derived and are shown in Figure 16.
Figure 16. Free body diagram for torque analysis based on the pitch and roll of the simulator
In this diagram, Point A is the platform pivot point, Point M is the motor output
shaft, 𝐹𝑐 is the weight of the platform assembly, 𝐹𝑃 is the force of the pushrod, 𝑙 is the
length from Point A to the pushrod, 𝑎 is the length of the cam, 𝛼 is the angle between the
pushrod and the cam, 𝛾 is the angle between the platform and the pushrod, Φ is the angle
13
between the horizontal plane and the platform, 𝜃 is the angle between the horizontal
plane and the cam, and 𝜏𝑚 is the motor torque.
Through summing the moments about Point A and Point M the following two
equations are established.
+↺ ∑𝑀𝑎 𝐹𝑠 𝑟 cos Φ + 𝐹𝑠 𝑟 cos Φ − 𝑙𝐹𝑐 cos Φ + 𝐹𝑝 𝑙 sin 𝛾 = 0
(Equation 8)
+↺ ∑𝑀𝑚 𝜏𝑚 − 𝐹𝑝 𝑎 sin 𝛼 = 0
(Equation 9)
Equation 8 was solved for the pushrod force, and substituted into Equation 9. The spring
force was also substituted as derived in Equation 2b and Equation 3. This substitution
yielded an equation for the torque necessary to pitch or roll the simulator.
𝜏𝑚 = 𝑎 sin 𝛼 [
𝐹𝑐 cos Φ
sin 𝛾
−
2𝑘𝑟 2 cos Φ sin Φ
3𝑙 sin 𝛾
]
(Equation 10)
As with the previous torque calculation, it is important to note that the angles do
not vary linearly with each other. In order to understand the relation between 𝛼, 𝛾, Φ,
and 𝜃 a 3D model was created of just the cam, pushrod, and simulator platform. Figure 17
shows this model with green representing the cam, red representing the pushrod, and blue
representing the platform. The model again used 10° intervals between -100° and 90° for
𝜃. For each 𝜃, the angles 𝛼, 𝛾, and Φ were recorded. Each of these angles were plotted
against 𝜃 in Microsoft Excel, and curve fitting was done to establish relationships
between 𝜃 and the other three angles. This relationship is shown in Figure 18.
Figure 17. Autodesk Inventor
model of cam (green), pushrod
(red), and platform (blue)
relationship
Figure 18. Plot of relationships between 𝜃 𝑣𝑠. 𝛷, 𝜃 𝑣𝑠. 𝛼 and 𝜃 𝑣𝑠. 𝛾
14
An additional MATLAB code was written to determine the torque based off of
any given 𝜃 value. Figure 19 shows the torque curve for the range of 𝜃 between -100°
and 90° showing that the maximum torque occurs when 𝜃=27° with a value of 3484.1 inlbs. The max torque does not occur when 𝜃=0° due to the addition of the spring force.
The further the simulator pitches and rolls the higher the torque that the motor receives
from the cam.
Figure 19. Plot generated using MATLAB shows torque calculated at each θ. The max torque occurs at θ=27°
3.1.3 Torque Requirements
After evaluation of the three main movements of the simulator, the total torque
requirements are 3484.1 in-lbs and 2894.3 in-lbs. The larger torque value was selected
and rounded up to 3500 in-lbs.
The validity of this number was assessed by two means. First, when comparing
the two calculated torque values, they were both within 600 in-lbs of each other. These
numbers analytically should be within a reasonable range from each other as the only
difference in the assessments is the addition of the spring force. The second validity
check consisted of phone and email correspondence with a professional in the field. Our
professional reference, Charles Bartel, works at Moog Motors4. This company develops
motors for flight simulation equipment and has an entire department devoted specifically
to flight simulators. Mr. Bartel has designed a flight simulator very similar in style to the
ETC simulators where he utilized a motor and gearbox combination that yielded 3500 inlbs per pushrod. This number is almost identical to the calculated torque requirements.
A safety factor was included in the selection of the torque requirement. The
previous simulator was able to provide motion and mimic all the required movements of
a jet simulator, therefore the torque requirements from the existing motors proved
adequate for the purposes of the project. Although the minimum requirements for the
motor motion is able to be performed by the existing motor specifications, the renovated
simulator will have an increased acceptable torque range to handle the quicker
movements of a Corsair aircraft ensuring that the motors do not overheat.
3.1.4 Angular Velocity Calculations
Utilizing the previous studies, two angular velocities were generated using the
ETC recommended speeds from Table 1. ETC recommends 30 cm/sec of heave which
15
was combined with the change of height of the simulator platform as calculated in the
first torque derivation. To calculate the degrees per second necessary to achieve the
desired lift rate the following equation was derived:
Δ𝜃 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
Δz
𝑐𝑚
𝑐𝑚
∙ 30
𝑠
=
𝑑𝑒𝑔𝑟𝑒𝑒𝑠
(Equation 11)
𝑠
This equation states that for every 10° that θ travels, the simulator platform has traversed
a certain distance in the z-direction. The value is then multiplied by the maximum rate at
which the simulator traverses the z-axis. The calculated value for required velocity based
on heave criteria was found to be 59.5 RPM.
The required angular velocity for pitch and roll could not be found in a similar
manner as the relationship is not linear like the heave motion. Instead, the roll velocity
for a Corsair was researched and found to be 81°/sec18. Using the analysis from the
second torque calculations, the follow equation was developed for the pitch and roll
angular velocity:
Δ𝜃 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
Δϕ 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
∙ 81
𝑑𝑒𝑔𝑟𝑒𝑒𝑠
𝑠
=
𝑑𝑒𝑔𝑟𝑒𝑒𝑠
𝑠
(Equation 12)
This equation states that for every 10° that θ travels, the simulator platform will have
rolled a distance represented by ∆Φ. The equation was then multiplied by the required
roll rate of 81°/sec. Roll rates based on 𝜃 are displayed in Table 1-3 in Appendix II:
Supplementary Analysis Data. The greatest angular velocity was chosen from Table 1-2
also in Appendix II: Supplementary Analysis Data to be 85 RPM.
As a result, the simulator requires a gearbox-motor combination that will operate at 85
RPM.
3.1.5 Horsepower Requirements
In order to calculate the power requirements of the motors the following
calculations were performed using the system specifications from Table 2.
To calculate the necessary motor input speed:
120𝑓
𝑟𝑝𝑚 = # 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠 =
120∙60 𝐻𝑧
4
= 1800 𝑟𝑝𝑚
(Equation 13)26
= 21.1
(Equation 14)26
The gear ratio is then calculated using:
𝜔
𝑅 = 𝜔 𝑖𝑛 =
𝑜𝑢𝑡
1800 𝑟𝑝𝑚
85 𝑟𝑝𝑚
Where 𝜔 is the speed. Input torque is evaluated using the calculated torque output and
the gear ratio.
𝜏𝑖𝑛 =
𝜏𝑜𝑢𝑡
𝑅
=
3500 𝑖𝑛∙𝑙𝑏𝑠
21.1
1 𝑓𝑡
= 165.9 𝑖𝑛 ∙ 𝑙𝑏𝑠 ∙ 12 𝑖𝑛 = 13.8 𝑓𝑡 ∙ 𝑙𝑏𝑠 (Equation 15)
Finally, the horsepower requirement is calculated using:
16
𝑃=
𝜏𝑖𝑛 ∙𝜔𝑖𝑛
5252
=
(13.8 𝑓𝑡∙𝑙𝑏𝑠)∙(1800 𝑟𝑝𝑚)
5252
= 4.7 ℎ𝑝
(Equation 16)26
Since 4.7hp is not a standard motor size, the number was rounded to 5hp.
3.1.6 User-Interface Requirements
Restoration of the simulator’s 3-axis movement requires interfacing a joystick
throttle to a processor. This processor will talk to three separate motor drives, which in
turn will drive three rotational braking motors via an amplified signal. The motor shafts
will be connected to gearboxes which modify the output torque and speed. Figure 20
below is a high level visual representation of this control scheme.
Figure 20. Schematic showing control scheme
3.1.7 Motor Comparison: Servo vs. Induction
The two primary motor types that are considered for this project are
servo motors and induction motors. Induction motors are consistent with the
motors used in the original Gyro IPTTM simulator however servo motors
provide numerous benefits that induction motors do not.
Induction motors are controlled using variable-frequency drives, or
VFDs, to vary the frequency of the input signal. This, in turn, changes the
speed and output torque of the motor shaft. Position control is difficult using
induction motors as they require a separate encoder on the output shaft to get
position feedback; the current position encoder is shown in Figure 21 in a red Figure 21. Existing induction
motor connection with
box. The speed and torque of an induction motor is controlled by the
position encoder (in red box)
19
external VFD .
A servo drive receives a command signal from a control system, amplifies the
signal, and then transmits and electric current to a servo motor23. The motor, in turn,
produces motion proportional to the command signal. The command signal typically
represents a desired velocity, but it can also represent a desired torque or position.
Unlike induction motors, servo motors have an integrated feedback sensor which reports
the motor’s status back to the servo drive. The servo drive then compares the actual
motor status with the commanded motor status. It then alters the applied voltage
frequency, or pulse width, to correct for any deviation from the desired status.
In terms of feedback on induction motors, a small gear can be connected to the
gearbox output shaft so the encoder can pick up rotational rates and positions, shown in
Figure 21. The servo motors come with an encoder already installed within the motor.
An advantage that induction motors have over servo motors is that induction motor drives
do not depend on the motor brand and can be purchased independent from the motors.
17
An extensive comparison of both induction and servo motors and drives can be found
below in Table 3.
Table 3. Comparison of servo and induction motors and drives24
Criteria
Servo
Advantages
Encoder
 Encoder integrated
 Accurate position
control
Size
 Less weight than
induction
 Smaller overall size
Motor
Heat Waste
Operating Current
Prototyping
Software
Drives
Controllers
 90% efficient
 Magnet rotors lose
less power between
stator and rotor
 Low operating
temperature
 Low heat
production
 Low current draw
 No magnetizing
current required
due to rotor being
permanent magnet
 Hobby servo
motors available
and inexpensive to
prototype proof of
concept
 Coding
development
libraries available
 Most have
manufacturer
software included
 Reduced
programming
complexity
 Microcontrollers
may be an option
depending on brand
 Positional control is
easy using servo
drives due to builtin encoder
Induction
Disadvantages
 Program required to
correct gearbox ratio
 Encoder separate
 Not very accurate
 Heavy
 Up to 50% larger than
servo
 Approx. $3300/motor
 Less expensive due to
external encoder
 60%-70% efficient
 High power loss due to
metals used in motor
structure
 High operating
temperature; tendency
to overheat
 High heat production
 High current draw
 Magnetizing current
required to make
magnetic field for rotor
rotation
 Difficult to prototype
proof of concept as
small scale induction
motors are not readily
available
 Some servo drives do
not come with
manufacturer
software
 All codes would need
to be produced
 Many drives require a
controller which is
difficult to code
 More expensive than
microprocessors
 Motors and drives
must come from same
manufacturer
Compatibility
Control
 Similar in size to
original motors; will
not interfere
 Servo drives are
expensive
Price
Induction
Advantages
 Program required to
correct gearbox ratio
 Approx. $6000/motor
 Expensive due to high
quality materials and
integrated feedback
Price
Efficiency
Servo
Disadvantages
 Microprocessors can
be used in combination
with VFDs which are
easy to code
 Cheaper than
controllers
 VFDs are less
expensive than servo
drives
 Any VFD brand will
work with any
induction motor
 Speed control is easy
using VFDs. Speed is
directly proportional to
input frequency
 Positional control is
complicated and less
accurate
18
It is important to note that servo motor drives must be an identical brand to the
motor due to the unique design of each brand of servo motor. The following criteria are
required for the drive motors on the simulator:
1. Motors with braking (holding) capabilities
2. Identical brand and motor wear (if used)
3. Positional feedback
4. Compatible drives
Servo motors are the best choice for this application due to their integrated
encoder, minimal size, and power efficiency. Servo motors also are easier to perform a
small scale proof of concept due to the similar coding style to the full size servo motors.
Although induction motors are half the price on average of a servo motor, the sponsor has
asked the team to disregard cost when performing motor analysis for the system.
In order to select an effective gearbox, drive, and motor combination, three
companies were contacted; Moog, Yaskawa, and Bosch Rexroth. The motors do not
need to be new as Connecticut Corsair has developed a relationship with the company
ServoTech that overhauls used servo motors24. ServoTech advised the team to avoid
Panasonic servo motors for this specific application as these motors are not as durable,
and tend to break more frequently than other brands. Yaskawa motors, on the other hand,
are a much higher quality but expensive compared to some other servo motor brands.
Moog, as previously mentioned, has a branch completely dedicated to flight simulation.
They are one of the only companies that sell both servo motors and drives.
3.1.8 Final Motor Specifications
Although final motor specifications are inherently dependent on gearbox ratio
selection, the calculations performed dictate the systems overall speed and torque
requirements. Table 4 contrasts the original Gyro IPTTM specifications with the new
Corsair simulator specifications.
Table 4. Original Gyro IPTTM specifications vs new Corsair simulator specifications
Criteria
Gyro IPTTM
Corsair Simulator
Motor Type
Induction
Servo
Speed
26 rpm
85 rpm
Torque Output
1212 in-lbs
3500 in-lbs
Power
1.5 hp
5 hp
4 PROTOTYPE DESIGN
4.1 PURPOSE OF PROTOTYPE
The servo motor design will be prototyped on a smaller scale using hobby servo
motors. The purpose of the prototype is to gain experience in positional feedback motor
control in a low-risk environment. This will ensure that when the simulator motors are
overhauled and received, the team will have an adequate understanding of the computer
code’s logical structure. The first goal of the prototype will be to implement proportional
speed control without braking. The second goal is to synchronize the motors such that
they rotate and brake at appropriate times to simulate holding the simulator at a specific
position.
19
4.2
STRUCTURE OF PROPOSED PROTOTYPE
The first prototype iteration will use an Arduino Uno and LEDs to symbolized
motor speed using light intensity. The second prototype will be to implement miniature
motors that will be purchased for proof of concept purposes. The prototype will be
constructed using the Arduino Uno microcontroller, a 3D printed simulator base model,
small hobby servo motors, a deconstructed joystick, and a personal computer.
The Arduino microcontroller will be used to control the shaft speed and position.
Arduino technology has numerous open source libraries available, many of which are
servo motor specific libraries. A log file will be created on the computer that will take
the input from the joystick and communicate the data to the controller. The first
prototype will utilized the deconstructed joystick to access its two internal
potentiometers. This will eliminate communication protocol issues. Positional feedback
will also need to be established. The Arduino Uno specifications are outlined in Table 5.
Figure 22. Arduino Uno microcontroller3
Table 5. Arduino Uno specifications3
Parameter
Microcontroller Type
Operating Voltage
Specification
ATmega328
5V
Recommended Input Voltage Range
7-12V
Critical Input Voltage Range
6-20V
Total Digital I/O Pins
14
PWM Output Pins
6/14 of Total I/O Pins
Analog Input Pins
6
DC Current for I/O Pins
40 mA
DC Current for 3.3V Pin
50 mA
Flash Memory
32 KB, 0.5 KB used by bootloader
SRAM
2 KB
EEPROM
1 KB
Clock Speed
16 MHz
5 SCISSOR ARM DESIGN
5.1 SCISSOR ARM OVERVIEW
The three scissor arms are designed to cushion the simulator
as it mimics a Corsair suddenly losing altitude due to a descent or
turbulence. Each arm consists of two separate members that are
connected to each other by means of a pin joint. The lower member
connects to the shock system spring as well as the base of the
simulator, and the upper member connects to the central universal
joint structure below the platform. The springs connected to the
Figure 23. Scissor arm system in Solidworks
model of simulator
20
lower arms are essentially what creates the “cushioning effect” for the simulator when it
moves in the z-direction. The scissor arm system is shown in Figure 23.The upper scissor
arms are shown in green, the lower scissor arms are shown in red, and the shock
absorbing springs are shown in blue.
5.2
PURPOSE OF REDESIGN
The previously manufactured lower scissor arm was incorrectly
designed and over engineered. The existing upper scissor arms from the
Gyro IPTTM consists of aluminum plates welded together as well as internal
pin structures. The existing lower scissor arm is made from 1.5in steel
tubing with welded on pin tabs. The built-in safety factor of this component
is nearly seven times the failing criteria of the upper scissor arm. The arm
also adds a significant amount of weight to the lifting of the central spring
unit, with each arm weighing approximately 10lbs. The scissor arm also
collides with the motor in rest position and does not allow for the unit to
rest on its base when it is turned off, as shown in Figure 24 in a red box. The
redesign allows the arm to use less material, eliminates interference between
components, and will be designed based on the failing criteria of the upper
scissor arm to avoid over-engineering.
5.3 THEORY
5.3.1 Free Body Analysis
In order to perform the finite element analysis of the
upper scissor arm it is necessary to understand how the
loadings are applied to the arm, the different failure
scenarios that can potentially break the arm, and the
different assumptions that will need to be made in order to
design a stable system. A free body analysis of the entire
scissor arm system is shown in Figure 25. For the analysis,
the upper scissor arm is the point of interest. There are only
two forces acting on this component, and therefore it can be
simplified into a two force member, shown on the bottom of
Figure 25.
From the free body diagram, it can be seen that the
upper scissor arm is in compression. The forces acting on
the arm are a portion of the weight of the simulator and the
force of the lower arm pushing back on the upper arm at the
pin joint. To further simplify the loading case, one pin can
be assumed to be fixed, while the other provides a
compressive load against the bearing hole in a direction
purely along the arm, Figure 26. Realizing that the load is
being concentrated on the bearing holes rather than the end
of the arm itself, a high concentration of stress inside of the
bearing holes can be expected. Therefore, the arm will
either fail in buckling or at the bearing holes due to
yielding5.
Figure 24. Old lower scissor arm
installed on system. Notice gap
between upper ring and lower
ring on base indicated by the red
box.
Figure 25. Free body diagram for upper scissor
arm analysis
Figure 26. Upper scissor arm simplified into a
two-force member
21
5.3.2 Finite Element Analysis Model Selection
Prior to analysis in Abaqus it was crucial to ensure that the upper scissor arm drawn
in Solidworks included every detail of the member including the internal support pins.
Through observation of the model and understanding of the finite element analysis (FEA)
software it was determined that the model could be simplified so as to not over
complicate the analysis. Initially, there were three points of interest to consider in the
upper scissor arm analysis8:
1. The welds connecting the plate to the member
2. The pins at each end of the member
3. The plates on each side of the member
The total member is shown in Figure 27 with just the plates shown in Figure 28.
Figure 27. Entire upper scissor arm
modeled in Solidworks
Figure 28. Side plates of upper
scissor arm modeled in Solidworks
Figure 29. Bearing stress area shown in
Solidworks model
Out of the three points of interest, it was determined that the welds would be the most
difficult to model. In order to model these points the material properties would need to
be altered around specific sections, which would complicate analysis. The welds are not
interfering with the location that the load is being applied or the area that the member is
fixed therefore the decision was made not to model the welds in SolidWorks and
ABAQUS. Although the decision will affect the results of the analysis, there will not be
a drastic difference.
The second point of interest were the pins that sit in the bearings allowing the
arms to pivot about a point. In order to assess if the pins were necessary in the FEA
model, the load distribution between the pins and member was explored. The load is
transferred through the pins only at the location where the pin is in contact with the
member. Assuming that the majority of the load is then transferred onto the bearing hole
surfaces rather than the pin itself, the pins can be safely removed without impacting the
results of the FEA analysis on a large scale. The area that the force will be distributed is
shown in Figure 29.
The third point of interest in determining the model used for FEA are the plates
on either side of the upper scissor arm. These plates are welded to the member on either
side and provide extra support to the member during loading. Since it is unknown how
both loading cases will be impacted by keeping or removing these plates, two models
were created; one with the plates as part of the solid model and one without.
5.3.3 Finite Element Analysis
The program used for analysis was Abaqus CAE1. When compared to ANSYS,
another option for FEA, Abaqus provides better meshing capabilities as well as a userfriendly interface that was more intuitive to a new user than ANSYS8. In order to
22
achieve accurate and usable results, it was imperative that appropriate inputs were
provided including material properties, boundary conditions, loading scenarios, and
meshing and mesh convergence. These inputs are outlined in the subsections below.
Material Properties
The material used to manufacture the upper scissor arm was 6061 Aluminum.
The relevant material properties of this material include a Young’s Modulus of 69x109
𝑁
6969𝑥109 𝑚2 and Poisson’s Ratio of .33.29 These properties were assigned to all parts of
the upper scissor arm as it was all manufactured using the same material.
Boundary Conditions
The boundary conditions used in the analysis were difficult to determine, as the
decision was made to exclude the pins from the analysis. This created a challenge
regarding fixing one end of the member in order to constrain it from rotating or moving
about the x, y, and z-directions. To determine the quality of the chosen boundary
conditions prior to analysis, three working engineers were consulted as resources8. The
most accurate way of performing the analysis was discovered to be through fixing one set
of bearing holes. The holes were fixed on only one half of the surface, as only that half
would be in contact with the pin during compression. This is depicted in Figure 30.
Z
Y
X
Figure 30. Bearing stress contact surface in Abaqus
Loadings
The majority of an effective and accurate FEA depended on understanding the
way that the component was loaded, therefore determining the way the member deformed
at failure. The member is subjected to a compressive force that acts on the bearings,
therefore indicating a bearing stress scenario. This loading can be summed up using the
bearing stress equation:
𝑃
𝜎𝑏 = 𝐴
𝑏
(Equation 17)
Where 𝐴𝑏 is the surface area of the hole, or in this case the diameter of the hole
being multiplied by the thickness of the hole, and 𝑃 is the magnitude of the load. This
loading is shown in Figure 31.
Figure 31. Bearing stress loading
23
Since the pin was omitted from the analysis, the bearing stress was assumed to
distribute uniformly over the bearing hole. As a result, during the FEA the load was
applied to half of the bearing hole as shown in Figure 30. This caused deformation only
to occur on the z-axis and created an accurate output stress concentration in the bearing
holes.
Meshing and Mesh Convergence21
Abaqus requires the user to mesh the part based on the number of seeds along
each edge. Meshing the member was simplified due to the symmetry in the part,
therefore ordinary meshes could be used for the FEA. The mesh convergence was
critical in this analysis because depending on the mesh density size an incorrect
maximum stress can be evaluated. This phenomenon is shown in Figure 32 and Figure 33.
To test mesh density, a mesh convergence test was performed to compare the amount of
elements in the mesh to the maximum stress output. The mesh density was determined to
be the location of where this plot leveled out. The number of elements required for this
analysis was evaluated to be 9038. The mesh convergence graph is shown in Figure 34.
Figure 32. Stress analysis of beam with low mesh density in
Abaqus
Figure 33. Stress analysis of beam with high mesh density in
Abaqus
Maximum Stress in Entire
Member
Mesh Convergence
2500
2000
1500
1000
500
0
0
2000
4000
6000
8000
Number of Elements
Figure 34. Mesh convergence graph of Abaqus iterations
10000
24
5.3.4 Finite Element Analysis Results
The FEA was completed using the aforementioned criteria and Abaqus. Using
9038 as the number of elements in the mesh density resulted in a stress distribution
shown in Figure 35. It can be clearly seen that the member will fail at the bearing holes
before any other member deformation. This failure occurs at approximately 2400 N, or
540 lbs, for each upper scissor arm. The maximum weight of the simulator with a pilot is
approximately 1240 lbs, therefore each arm will have an additional 126 lbs beyond the
maximum weight that they can hold before failure occurs.
The results of the FEA allow the design, analysis, and manufacturing process of the
lower scissor arms to match the characteristics of the upper scissor arm. This will help to
prevent over-engineered components, thus saving money.
Figure 35. Stress distribution on upper scissor arm
6 CONCLUSIONS
6.1 PROJECT ACCOMPLISHMENTS
At the end of the first semester of work, a number of milestones have been reached.
An understanding of the overall simulator motion and function has been determined as
well as the expected project deliverables for Phase II. The upper scissor arms have been
reverse engineered and the failure loading has been analyzed. This information will be
used in the design of the lower scissor arm. A plan for the structure of a small scale
prototype has been defined as well as an outline for the overall control system of the
simulator. The team has also established relationships with multiple companies to
appropriately size and purchase the driving system for the simulator.
6.2 PLAN OF ACTION
The team has collaborated to create a plan of action for the remainder of Phase II.
The requirements for motor output have been finalized, and motor selection is in progress
through correspondence with three companies; Moog Motors, Yaskawa, and Bosch
Rexroth. The companies will be aiding in both sizing and purchasing the drives,
gearboxes, and motors required. Quotes will be acquired from each of the three
companies and the most competitive estimate will be selected and presented to the
sponsor.
As soon as motors are officially selected, the redesign of the simulator base will
commence. This redesign includes ensuring the shaft of the gearbox aligns with the cam
in the same location as the original design, as well as modifying the motor mounts. All
25
modifications to the base will have an FEA performed to ensure strength and fatigue
resistance.
With this information, the lower scissor arms will be designed to the same standard
as well as designed to integrate without interference with the other existing components.
Once the design has been finalized, an FEA will be done on the arm to ensure strength
and fatigue resistance as well.
A prototype will be created using a scaled down 3D printed model of the simulator
base. This prototype will integrate small hobby motors that will be purchased over the
winter break. The electrical engineering students will be focusing on creating a code to
manage the motion of the simulator, and interface the code with the simulator using a
joystick.
Overall, the project is on schedule and the team is expecting to present all Phase II
deliverables by the scheduled date.
6.2.1 Project Schedule
The proposed project timeline for the spring semester can be found below, Figure
36.
Figure 36. Proposed project timeline
26
7 APPENDICES
7.1 Appendix I: References
1.
"Abaqus CAE." Finite Element Analysis. N.p., n.d. Web. 15 Nov. 2013.
<http://www.3ds.com/products-services/simulia/overview/>.
2.
"Advanced Pilot Training." ETC Corporate. Environmental Tectonics
Corporation, n.d. Web. 30 Sept. 2013. <http://www.etcusa.com/>.
3.
"Arduino - ArduinoBoardUno." Arduino - ArduinoBoardUno. N.p., n.d. Web. 10
Dec. 2013. <http://arduino.cc/en/Main/arduinoBoardUno>.
4.
Bartel, Charles, Product Application Manager, Simulation Department. “Motor
Sizing Inquiry.” Phone Interview. 20 Dec. 2013.
5.
Bearing Stress. N.d. Photograph. Missouri University of Science and Technology,
Web. 15 Nov 2013.
<http://classes.mst.edu/civeng110/concepts/01/bearing/index.html>.
6.
Boucher, Henry. “Prepar3D Inquiry and Help.” Phone Interview. 4 Oct. 2013.
7.
Boyd, Graham, CAPINC. “SolidWorks Course Opportunities.” Chester Airport
Site Visit. 29 Sept. 2013
8.
Cassenti, Brice, PhD. "ANSYS Tutorial." Personal interview. 2 Oct. 2013.
9.
Cassenti, Brice, PhD. "ANSYS Tutorial." engr.uconn.edu. N.p.. Web. 10 Oct
2013. <http://engr.uconn.edu/~cassenti/>.
10.
Cassenti, Brice, PhD. "Finite Element Analysis." engr.uconn.edu. N.p.. Web. 10
Oct 2013. <http://engr.uconn.edu/~cassenti/>.
11.
"Chance Vought F4U Corsair." F4U Corsair History. N.p., n.d. Web. 1 Dec.
2013. <http://www.f4ucorsair.com/history.html>.
12.
Connecticut Corsair LLC. "Connecticut Corsair." Connecticut Corsair. N.p., n.d.
Web. 20 Sept. 2013. <http://www.connecticutscorsair.com/>.
13.
G. King, Environmental Tectonics Corporation; C. McBurney, Connecticut
Corsair; Y. Liu, D. Synnott, M. Winczura, University of Connecticut; Site
Meeting at University of Connecticut. 17 Nov. 2012
14.
Malla, Ramesh, PhD. "Spring Constant Analysis and Approach." Personal
interview. 7 Oct. 2013.
15.
"McMaster-Carr." McMaster-Carr. McMaster-Carr, n.d. Web. 30 Sept. 2013.
<http://www.mcmaster.com/>.
16.
Mealy, Tom. "Project Storage and Fabrication." Site Meeting at University of
Connecticut. 2 Oct. 2013.
27
17.
Mechanical ANSYS APDL. Vers. 14.5. Cecil Township, Pennsylvania: ANSYS,
2013. Computer software.
18.
Motaref, Sarira, PhD. "Spring Constant Analysis." E-mail interview. 6 Oct. 2013.
19.
Operations & Maintenance Manual (2000). Gyro IPT: Integrated Physiological
Trainer. Environmental Tectonics Corporation, Southampton, Pennsylvania.
University of Connecticut.
20.
Popoli, Bill. "Interview with IBAG." Personal interview. 20 Sept. 2013.
21.
Prepar3D. Vers. 1.4. Bethesda, Maryland: Lockheed Martin, 2012. Computer
Software.
22.
Phung, Lam. Abaqus Tutorials. 2013. Video. www.YouTube.comWeb. 1 Nov
2013. <http://www.youtube.com/user/ngoclam250?feature=watch>.
23.
"Picture of the Vought F4U-4 Corsair Aircraft." Photos: Vought F4U-4 Corsair
Aircraft Pictures. N.p., n.d. Web. 10 Dec. 2013.
<http://www.airliners.net/photo/Vought-F4U-4-Corsair/0869430/L/>.
24.
Ratliff, Christian, Servo Tech Representative. “General Servo Motor Inquiry.”
Personal Interview. 18 Sept. 2013.
25.
"Servo Tech, Inc." Servo Tech Products. Servo Tech, Inc., n.d. Web. 29 Sept.
2013. <http://servotechinc.com/>.
26.
SolidWorks. Vers. 2014. Vélizy-Villacoublay, France: Dassault Systemes, 2014.
Computer software.
27.
"Synchronous Speed of Electrical Motors." Synchronous Speed of Electrical
Motors. N.p., n.d. Web. 1 Dec. 2013.
<http://www.engineeringtoolbox.com/synchronous-motor-frequency-speedd_649.html>.
28.
"Vought F4U Corsair." Wikipedia. Wikimedia Foundation, 16 Dec. 2013. Web.
12 Nov. 2013. <http://en.wikipedia.org/wiki/Vought_F4U_Corsair>.
29.
"Young’s Modulus." Engineering Toolbox. N.p.. Web. 15 Oct 2013.
<http://www.engineeringtoolbox.com/young-modulus-d_417.html>
28
7.2
Appendix II: Supplementary Analysis Data
Weight (kg)
2.27
4.54
6.8
9.07
11.34
13.61
15.88
18.14
20.41
22.68
27.22
31.75
36.29
40.82
45.36
49.9
54.43
58.97
63.5
68.04
72.57
77.11
81.65
86.18
88.04
92.57
97.11
101.65
106.18
108.04
112.57
117.11
121.65
126.18
130.72
135.25
139.79
144.33
θ
90
80
70
60
50
40
30
20
10
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
α
163.47
176.4
170.79
158.18
145.83
133.82
122.18
110.98
100.25
90
80.25
70.98
62.18
53.82
45.83
38.18
30.79
23.6
16.53
9.51
Table 1-1:Spring Coefficient
Angle (Rad)
Displacement (m)
Spring Coefficient (N/m)
0.007
0.001
64864
0.01
0.001
92664
0.016
0.002
86489
0.017
0.002
109249
0.017
0.002
129734
0.024
0.003
111206
0.024
0.003
129741
0.026
0.003
138392
0.026
0.003
155691
0.029
0.003
157268
0.033
0.004
163897
0.035
0.004
181656
0.043
0.005
169492
0.047
0.005
173034
0.052
0.006
173049
0.054
0.006
184220
0.059
0.007
183253
0.063
0.007
187508
0.07
0.008
181767
0.07
0.008
194750
0.072
0.008
200237
0.079
0.009
196235
0.085
0.01
192816
0.089
0.01
193575
0.093
0.011
189235
0.096
0.011
192852
0.099
0.011
196601
0.105
0.012
194162
0.108
0.012
196307
0.12
0.014
179560
0.124
0.014
181854
0.128
0.015
183276
0.134
0.015
182219
0.138
0.016
183306
0.141
0.016
185237
0.145
0.016
187077
0.148
0.017
188834
0.152
0.017
190513
β
73.47
76.4
79.21
81.82
84.17
86.18
87.82
89.02
89.75
90
89.75
89.02
87.82
86.18
84.17
81.82
79.21
76.4
73.47
70.49
Table 1-2: Lift Angular Velocity
Distance (cm) Angular Velocity Of Cam(deg/s)
36.29
534.68
36.86
1933.06
36.7
356.94
35.86
204.7
34.39
149.51
32.39
122.67
29.94
108.2
27.17
100.5
24.18
97.19
21.1
97.15
18.01
99.92
15.01
105.45
12.16
113.98
9.53
126.24
7.15
143.56
5.06
168.61
3.28
207.03
1.84
272.39
0.73
408.54
Cam RPM
89.11
322.18
59.49
34.12
24.92
20.45
18.03
16.75
16.2
16.19
16.65
17.57
19
21.04
23.93
28.1
34.5
45.4
68.09
29
Angle of Platform Φ
22.59
21.86
20.2
17.79
14.81
11.41
7.73
3.89
0
-3.85
-7.86
-11.12
-14.39
-17.33
-19.9
-22.05
-23.77
-25.03
Table 1-3: Roll Rate vs. Cam Angular Velocity
Angle of Cam θ
Angular Velocity of Cam
80
1100.69
70
487.01
60
336.29
50
271.75
40
238.43
30
220.28
20
211.05
10
208.05
0
210.13
-10
202.41
-20
248.25
-30
247.99
-40
275.38
-50
315.41
-60
375.49
-70
471.2
-80
641.38
-90
1017.59
RPM Cam
183.45
81.17
56.05
45.29
39.74
36.71
35.17
34.67
35.02
33.73
41.37
41.33
45.9
52.57
62.58
78.53
106.9
169.6