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Connecticut Corsair Capstone Project
Interim Report January 2014
Team 10Mechanical EngineeringLauren BradleyArthur PodkowiakMichael TurnerTeam 194Electrical EngineeringRandy BertrandAmanda SweatDavid TartaglinoComputer EngineeringZachary Mosch
Faculty AdvisorsDr. Stephen StagonDr. Rajeev Bansal
SponsorConnecticut Corsair
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Table of Contents1 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
2 PRELIMINARY ASSESSMENT........................................................................................5
2.1 SIMULATOR MOTION AND REQUIREMENTS.......................................................5
2.2 PARAMETRIC MODEL DEVELOPMENT..................................................................6
2.3 PREPAR3D....................................................................................................................7
3 MOTOR SELECTION.........................................................................................................7
3.1 THEORY........................................................................................................................7
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
4 PROTOTYPE DESIGN.....................................................................................................18
4.1 PURPOSE OF PROTOTYPE.......................................................................................18
4.2 STRUCTURE OF PROPOSED PROTOTYPE............................................................19
5 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
6 CONCLUSIONS.................................................................................................................24
6.1 PROJECT ACCOMPLISHMENTS..............................................................................24
6.2 PLAN OF ACTION......................................................................................................24
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6.2.1 Project Schedule...................................................................................................25
7 APPENDICES......................................................................................................................26
7.1 Appendix I: References.................................................................................................26
7.2 Appendix II: Supplementary Analysis Data..................................................................28
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1 PROJECT OVERVIEW1.1 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 BACKGROUNDConnecticut 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.
1.3
SIMULATOR BACKGROUNDConnecticut 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 3, 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.
Figure 2. F4U-4 Corsair in flight 22Figure 1. F4U-4 Corsair with wings folded 27
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1.4 PROBLEM STATEMENTAs 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 4.
1.5 PROJECT DELIVERABLESThe 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
Figure 3. Original Gyro IPTTM Simulator Base 13Figure 4. Donated Gyro IPTTM Simulator Base
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incorrectly sized model by the Phase I senior design team. The objective will be 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 ASSESSMENT2.1 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 Range of Motion Speed AccelerationPitch +/- 25 deg/sec 0-25 deg/sec 0.5-75 deg/sec2
Roll +/- 30 deg/sec 0-25 deg/sec 0.5-75 deg/sec2
Yaw 360 degree continuous 0-150 deg/sec 0.5-15 deg/sec2
Heave +/- 10 cm 30 cm/sec 90 cm/sec2
Sway +/- 10 cm 20 deg/sec 60 deg/sec2
Surge +/- 10 cm 20 deg/sec 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
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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 RequirementVoltage 220-240 Volts ACFrequency 50/60 HzPhase Three PhaseNominal Current Rating 10 AmpsSurge Current Rating 13 AmpsProtective Device Rating 16 AmpsExpected Operating Temp Range +13°C to +35°CExpected Humidity Range 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 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 DEVELOPMENTIn 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 drawing so that valid dimensions from point to point 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 new lower scissor
Figure 5. Axes of motion for simulator platform
Figure 6. Rendering of Solidworks Parametric Model 25
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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 software, and the design team will work to 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 SELECTION3.1 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 usages19. 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 CoefficientDue 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 restore the simulator platform to a neutral flat position. The free
Figure 8. Central universal joint and spring motion
Figure 7. Screenshot of Prepar3D Flight Simulation 20
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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.
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
F s r cosΦ+F s r cosΦ−Fw l cosΦ=0 (Equation 1)
The force of the spring is defined as:
F s=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.
F s=ky3 (Equation 2b)
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:
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k=3 Fw l
2r2 sin Φ(Equation 4)
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: SupplementaryAnalysis Data.
3.1.2 Free Body Analysis: Torque RequirementsIn 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.
Figure 11. Plot of Weight vs. Displacement for Spring Coefficient
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02100
110
120
130
140
150
160
170
180
190
200
Weight vs. Displacement of Spring
Displacement (m)
Wei
ght (
lbs)
Figure 10. Components Contributing to Static Weight of Simulator
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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 τ m is the motor torque.
To determine the torque requirement of the motor the moments were summed about Point A and Point M.
+↺∑Ma
F pl sin β−Fc l=0 (Equation 5)
+↺∑Mm
τm−F p 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.
Figure 12. Free body diagram for torque analysis based on vertical lift
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τ m=F c a sin α
sin β (Equation 7)
The value of F c 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.
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.
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
-100 -80 -60 -40 -20 0 20 40 60 80 1000
20
4060
80
100120
140
160180
200
θ vs α and β
αβ
θ (Degrees)
Ang
le (D
egre
es)
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)
Figure 14. Plot of relationships between θ vs . α and θ vs . β
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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
force on the cam. After analysis the torque required to lift the simulator in a vertical z-direction was found to be 2894.3 in-lbs.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.
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 between the horizontal plane and the platform, θ is the angle between the horizontal plane and the cam, and τ m is the motor torque.
Figure 15. Plot generated using MATLAB showing torque calculated at each θ . The maximum torque occurs at θ=0
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
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Through summing the moments about Point A and Point M the following two equations are established.
+↺∑Ma
F s r cosΦ+F s r cosΦ−l F c cosΦ+F pl sin γ=0 (Equation 8)
+↺∑Mm
τm−F p 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.
τ m=a sin α [ F c cos Φsin γ
−2kr 2cosΦ sinΦ3 l 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. Figure17 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.
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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 in-lbs. 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.
3.1.3 Torque RequirementsAfter 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 in-lbs 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 CalculationsUtilizing the previous studies, two angular velocities were generated using the
ETC recommended speeds from Table 1. ETC recommends 30 cm/sec of heave which
Figure 19. Plot generated using MATLAB shows torque calculated at each θ. The max torque occurs at θ=27°
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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:
ΔθΔz
degreescm
∙30 cms=degrees
s (Equation 11)
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:
ΔθΔϕ
degreesdegrees
∙81 degreess
=degreess (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 RequirementsIn 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:
rpm= 120 f¿of poles
=120 ∙60 Hz4
=1800 rpm (Equation 13)26
The gear ratio is then calculated using:
R= ω¿
ωout=1800rpm
85rpm=21.1 (Equation 14)26
Where ω is the speed. Input torque is evaluated using the calculated torque output and the gear ratio.
τ ¿=τ out
R=3500∈∙lbs
21.1=165.9∈∙ lbs ∙ 1 ft
12∈¿=13.8 ft ∙lbs ¿ (Equation 15)
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Finally, the horsepower requirement is calculated using:
P= τ ¿∙ ω¿
5252=(13.8 ft ∙ lbs) ∙(1800 rpm)
5252=4.7hp (Equation 16)26
Since 4.7hp is not a standard motor size, the number was rounded to 5hp.
3.1.6 User-Interface RequirementsRestoration 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. InductionThe 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 box. The speed and torque of an induction motor is controlled by the external VFD19.
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. Existing induction motor connection with
position encoder (in red box)
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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. 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 ServoAdvantages
ServoDisadvantages
InductionAdvantages
InductionDisadvantages
Mot
or
Encoder Encoder integrated Accurate position
control
Program required to correct gearbox ratio
Program required to correct gearbox ratio
Encoder separate Not very accurate
Size
Less weight than induction
Smaller overall size
Similar in size to original motors; will not interfere
Heavy Up to 50% larger than
servo
Price
Approx. $6000/motor Expensive due to
high quality materials and integrated feedback
Approx. $3300/motor Less expensive due to
external encoder
Efficiency
90% efficient Magnet rotors lose
less power between stator and rotor
60%-70% efficient High power loss due to
metals used in motor structure
Heat Waste
Low operating temperature
Low heat production
High operating temperature; tendency to overheat
High heat production
Operating Current
Low current draw No magnetizing
current required due to rotor being permanent magnet
High current draw Magnetizing current
required to make magnetic field for rotor rotation
Prototyping
Hobby servo motors available and inexpensive to prototype proof of concept
Coding development libraries available
Difficult to prototype proof of concept as small scale induction motors are not readily available
Dri
ves
Software
Most have manufacturer software included
Reduced programming complexity
Some servo drives do not come with manufacturer software
All codes would need to be produced
Controllers Microcontrollers
may be an option depending on brand
Many drives require a controller which is difficult to code
More expensive than microprocessors
Microprocessors can be used in combination with VFDs which are easy to code
Cheaper than controllers
Price Servo drives are expensive
VFDs are less expensive than servo drives
Compatibility Motors and drives Any VFD brand will
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must come from same manufacturer
work with any induction motor
Control
Positional control is easy using servo drives due to built-in encoder
Speed control is easy using VFDs. Speed is directly proportional to input frequency
Positional control is complicated and less accurate
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) capabilities2. Identical brand and motor wear (if used)3. Positional feedback4. 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 SpecificationsAlthough 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 specificationsCriteria Gyro IPTTM Corsair Simulator
Motor Type Induction ServoSpeed 26 rpm 85 rpm
Torque Output 1212 in-lbs 3500 in-lbsPower 1.5 hp 5 hp
4 PROTOTYPE DESIGN4.1 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
19
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.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.
Table 5. Arduino Uno specifications3
Parameter SpecificationMicrocontroller Type ATmega328Operating Voltage 5VRecommended Input Voltage Range 7-12VCritical Input Voltage Range 6-20VTotal Digital I/O Pins 14PWM Output Pins 6/14 of Total I/O PinsAnalog Input Pins 6DC Current for I/O Pins 40 mADC Current for 3.3V Pin 50 mAFlash Memory 32 KB, 0.5 KB used by bootloaderSRAM 2 KBEEPROM 1 KBClock Speed 16 MHz
5 SCISSOR ARM DESIGN5.1 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
Figure 22. Arduino Uno microcontroller3
Figure 25. Free body diagram for upper scissor arm analysis
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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 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 Figure23.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 REDESIGNThe 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 THEORY5.3.1 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
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 26. Upper scissor arm simplified into a two-force member
Figure 28. Side plates of upper scissor arm modeled in Solidworks
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bearing holes can be expected. Therefore, the arm will either fail in buckling or at the bearing holes due to yielding5. 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 member2. The pins at each end of the member3. The plates on each side of the member
The total member is shown in Figure 27 with just the plates shown in Figure 28.
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.
Figure 27. Entire upper scissor arm modeled in Solidworks
Figure 29. Bearing stress area shown in Solidworks model
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5.3.3 Finite Element AnalysisThe program used for analysis was Abaqus CAE1. When compared to ANSYS,
another option for FEA, Abaqus provides better meshing capabilities as well as a user-friendly interface that was more intuitive to a new user than ANSYS8. In order to 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 PropertiesThe 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 69
69 x109 Nm2 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 ConditionsThe 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.
LoadingsThe 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:
σ b=PAb
(Equation 17)
X
Z
Y
Figure 30. Bearing stress contact surface in Abaqus
23
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.
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 Figure33. 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 Figure34.
Figure 31. Bearing stress loading
Figure 32. Stress analysis of beam with low mesh density in Abaqus
Figure 33. Stress analysis of beam with high mesh density in Abaqus
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5.3.4 Finite Element Analysis ResultsThe 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.
6 CONCLUSIONS6.1 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
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0500
1000150020002500
Mesh Convergence
Number of Elements
Max
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Figure 35. Stress distribution on upper scissor arm
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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 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, Figure36.
Figure 36. Proposed project timeline
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7 APPENDICES7.1 Appendix I: References1. "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.
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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-speed-
d_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>
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7.2 Appendix II: Supplementary Analysis Data
Table 1-1:Spring CoefficientWeight (kg) Angle (Rad) Displacement (m) Spring Coefficient (N/m)
2.27 0.007 0.001 648644.54 0.01 0.001 92664
6.8 0.016 0.002 864899.07 0.017 0.002 109249
11.34 0.017 0.002 12973413.61 0.024 0.003 11120615.88 0.024 0.003 12974118.14 0.026 0.003 13839220.41 0.026 0.003 15569122.68 0.029 0.003 15726827.22 0.033 0.004 16389731.75 0.035 0.004 18165636.29 0.043 0.005 16949240.82 0.047 0.005 17303445.36 0.052 0.006 17304949.9 0.054 0.006 184220
54.43 0.059 0.007 18325358.97 0.063 0.007 18750863.5 0.07 0.008 181767
68.04 0.07 0.008 19475072.57 0.072 0.008 20023777.11 0.079 0.009 19623581.65 0.085 0.01 19281686.18 0.089 0.01 19357588.04 0.093 0.011 18923592.57 0.096 0.011 19285297.11 0.099 0.011 196601
101.65 0.105 0.012 194162106.18 0.108 0.012 196307108.04 0.12 0.014 179560112.57 0.124 0.014 181854117.11 0.128 0.015 183276121.65 0.134 0.015 182219126.18 0.138 0.016 183306130.72 0.141 0.016 185237135.25 0.145 0.016 187077139.79 0.148 0.017 188834144.33 0.152 0.017 190513
Table 1-2: Lift Angular Velocityθ α β Distance (cm) Angular Velocity Of Cam(deg/s) Cam RPM
90 163.47 73.47 36.29 534.68 89.11
80 176.4 76.4 36.86 1933.06 322.18
70 170.79 79.21 36.7 356.94 59.49
60 158.18 81.82 35.86 204.7 34.12
50 145.83 84.17 34.39 149.51 24.92
40 133.82 86.18 32.39 122.67 20.45
30 122.18 87.82 29.94 108.2 18.03
20 110.98 89.02 27.17 100.5 16.75
10 100.25 89.75 24.18 97.19 16.2
0 90 90 21.1 97.15 16.19
-10 80.25 89.75 18.01 99.92 16.65
29
-20 70.98 89.02 15.01 105.45 17.57
-30 62.18 87.82 12.16 113.98 19
-40 53.82 86.18 9.53 126.24 21.04
-50 45.83 84.17 7.15 143.56 23.93
-60 38.18 81.82 5.06 168.61 28.1
-70 30.79 79.21 3.28 207.03 34.5
-80 23.6 76.4 1.84 272.39 45.4
-90 16.53 73.47 0.73 408.54 68.09
-100 9.51 70.4
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Table 1-3: Roll Rate vs. Cam Angular VelocityAngle of Platform Φ Angle of Cam θ Angular Velocity of Cam RPM Cam
22.59 80 1100.69 183.4521.86 70 487.01 81.1720.2 60 336.29 56.0517.79 50 271.75 45.2914.81 40 238.43 39.7411.41 30 220.28 36.717.73 20 211.05 35.173.89 10 208.05 34.67
0 0 210.13 35.02-3.85 -10 202.41 33.73-7.86 -20 248.25 41.37-11.12 -30 247.99 41.33-14.39 -40 275.38 45.9-17.33 -50 315.41 52.57-19.9 -60 375.49 62.58-22.05 -70 471.2 78.53-23.77 -80 641.38 106.9-25.03 -90 1017.59 169.6
