landing gear project final report
TRANSCRIPT
Project 3: Landing GearDesign & Analysis
December 19th, 2014
Kevin Osman1
Table of Contents:Executive Summary.....................................................................................................................................3
Introduction.................................................................................................................................................4
Inputs/Details of Analysis........................................................................................................................9
Results of Analysis.....................................................................................................................................10
Discussion of Results.................................................................................................................................11
Summary and Conclusion..........................................................................................................................12
Appendix A: Assembly Drawings...............................................................................................................13
Appendix B: Detail Drawings.....................................................................................................................18
Appendix C: Graphs & Calculations...........................................................................................................35
FEA Analysis Fringe Plots & Convergence Plots.....................................................................................36
Piston Cylinder Displacement vs Time...................................................................................................43
Force vs. Displacement At Each Pin (Retraction and Deployment)........................................................44
Hand Calculations..................................................................................................................................51
Executive SummaryUsing the Creo 2.0 Parametric software for modeling, the objective of this project is to design, model, animate and test a landing gear for planes. Given limited
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dimensions in the parts that were required in the assembly of this landing gear, good engineering judgment was essential in the entirety of this project. Most of the parts shown in further in this project required the basic knowledge of statics, dynamics, solid mechanics and science in engineering materials. Certain criteria and features needed to be fulfilled in order to adhere the projects requirements. The Landing gear assembly needs to maintain the vertical displacements from Pin F to fuselage as well as Pin F to the ground (2 and 44 inches respectively). Nine components were requested to be used: 4 links (1,3,4,7) a shock absorber, a piston cylinder, a wheel and tire assembly (with a wheel axle serving as a pin), and at least six pins with caps. Proper material were assigned to their respective parts (whose values were found from MatWeb) in order to perform a finite-element analysis and observe the stress distribution and strain energy on each pin. Two servo motors were required for the assembly as well as spring totaling three different simulations that the landing gear had to undergo. The servo motors were inputted into the piston cylinder whose velocity was a function of time in order to allow the pins to slowly approach their max stress values during deployment and retraction. For the spring analysis, a spring was inputted into the shock absorber and was observed as a force of 26,500 lbf was imposed on the tire from the ground. Pins were constrained to links as pin connections and were observed during these simulations in order to analyze the maximum loads on each of the pins as well as the angular velocity and acceleration. The maximum forces on each of the pins were then applied to each part individually to observe stress distribution and strain energy through the use of FEA. In addition the angular velocities at each of the pins were measured as well. After interpreting the data and collecting important mechanical properties of each pin, hand calculations were made in order to compare the accuracy of Creo. By comparing the three methods and seeing that their percent error was relatively low, the computer generated calculations were considered accurate and reliable. Lastly, safety factors were observed on each of the pin to establish the overall structural safety of the landing gear mechanism. After verifying that the project requirements were met, and critically analyzing the results, Creo 2.0 had verified that the design of this landing gear perfectly safe to be used and manufactured for aircrafts.
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IntroductionThe Landing plays a significant role in the
world of jets and planes. Its importance in
maintaining its structural integrity allows
planes to land smoothly as well as takeoff
efficiently. Most, if not all airline
companies, allow the landing gear to fold
up inside the fuselage in order to increase
the efficiency of the plane’s travel (this
reduces the surface area of the plane thus decreases drag). Figure 1 depicts the generic
version of the landing gear extended in its deployed position. Pins F, A, and D are
considered grounded or “fixed” points thus restricting their motion as the four-bar linkage
both deploys and retracts. Naturally because of this the dimensions of these pins are to
maintain the precise dimensions that were given in the project requirements. Some other
features whose dimensions were to be maintained were the explicit dimensions of the tire
and wheel, the vertical distance (42 inches) separating the ground to the fuselage, and the
distance between the centers of each of the joints. Lastly, the shock absorber assembly
needed to be designed in such a way that mechanism could properly compress during
retraction. The rest of parts included in Figure 1 lacked definitive dimensions since they
were either not included or produced global interferences after modeling/assembling.
This lack of information therefore required the designer to utilize good engineering
judgment in order to determine the proper dimensions to use as well as efficiently piece
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Figure 1 Generic View of the Project Three Landing Gear
the missing dimensions together. Ultimately, there were a variety of modifications that
needed to be implemented in order to effectively execute the everyday functions of an
average landing gear. Requiring the knowledge of materials science, statics, dynamics
and solid mechanics, the following modifications described below were taken under
heavy consideration and later implemented in the design. The following figure (3)
depicts one of these modifications as the wheel axle takes a unique shape from most of
the designed pins in this design. Although very unique from other pins, its exact
dimensions were required in order to create a snug yet stable
constraint with the wheel and tire assembly. Next to the figure is
the conventional generic pin used in
the assembly to show the general
level of ingenuity and engineering
judgment required due to the vague
dimensions given to the designer
(figure 2).
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Figure 3- Generic Pin (required dimensions) with a total length of 2.75 in
Another important modification that should be noted is the design of the piston that
attaches to the cylinder. The general dimensions of the original design did not allow the
free movement of the Link 1 bar in order for the landing gear to properly retract and
deploy. Utilizing Creo’s simulation and global interferences applications, the problem
was easily found.
The global
interferences tool
supplied the
designer with a
quantitative measurement of the interference by displaying the total number of volume of
intersection. After noting the issue, it was an appropriate revision to reduce the end
diameter of the rod attaching the two pronged rings on the piston. The two pronged rings
were kept in the final revision because it would later be helpful in maintaining the
symmetry of the entire mechanism which allowed easier stress analysis and calculation.
Figure 4 displays the modified piston whereas figure 5 displays the original outlook of
the piston. Note that the part was also rounded by the modifications in order to reduce
stress concentrations in sharp edges.
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Figure 4- Modified Piston. Oriented in order to convey the varying curves required for the part. Shaded with edges to enlarge the texture of the rounds.
Figure 5- Original design of the piston. The end of the 1.97 diameter
connecting the ring maintained its diameter throughout the 23.5 inches.
The most obvious modification of the
landing gear however is the shock
absorber. The shock absorber needed to
be evaluated as a rigid structure during
deployment and retraction analysis. Yet
it also needed to compress when a spring was implemented inside the shock absorber and an
external force was exerted onto the tire. To increase the freedom of the compression and reduce
possible friction generated during the spring simulation, both sides of the piston were free to
move along the central axis of the shock absorber. It is important making two freely moving
sliders because it allows the landing gear to deploy/retract without causing buckling of one of the
sliders if let rigid. Also note that the diameter at the opposite sides of the rings of the sliders
have a diameter of 3.0 inches, creating a tight yet snug fit between the sliders and the shock
absorber during the landing gears operations. This restricts the angle of rotation that the sliders
can undergo with the shock absorber thus decreasing the chances of buckling and snapping from
torque. Figure 6 is the modified shock absorber assembly.
Figure 6- Shock Absorber assembly (Sub Assembly II). The sliders are free to move along the central axis of the shock absorber
yet are constrained within the edges of the shell of the shock absorber.
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The right slider of the shock absorber in figure 6 (termed as link 2 slider 2 in the detailed
drawing section of this report), has also been modified. This length of this slider had been
reduced and expanded outwards in order to prevent global interferences with link 7 during the
landing gear’s deployment operation. Shown below is link 2 slider 2 (highlighted in yellow) as it
allows link 7 (highlighted in orange) to freely pass during deployment. The two pronged rings
also served the purpose of making the entirety of the landing gear symmetrical (useful for same
reasons described when discussing the piston cylinder assembly).
Figure 7- Deployment Simulation. Without the reduced length of link 2 slider 2, link 7 would go through this slider thus causing
global interference thus making deployment an impossible process.
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Inputs/Details of Analysis:After proper pin placement and constraints, a snapshot was taken at precisely 44 inches
down from Pin F. After simulating the shock absorber as a rigid body, gravity was
enabled in order to make the retraction simulation more realistic. Both servo motors for
deployment and retraction had inputted velocity as a cosine function. This allows the
mechanism to slowly yet safely retract and deploy while shocking the landing gear pins
with an instant force. Simulation requirements included a motor that allowed the entire
wheel to fit above into the fuselage (retraction), as well as a motor that extended the edge
of the wheel to precisely 44 inches (acting as the ground). During this simulation,
measurements were placed on each of the pins (force vs. displacement). As shown in the
picture on the cover of this report, the entire mechanism is symmetrical, indicating that
reaction forces theoretically are the same on either side (pins A,D, and B should therefore
experience the same force reactions at their respective connections due to symmetry). In
order to further understand the efficiency of the landing gear, FEA was utilized. Each of
the pins underwent finite-element analysis to simulate testing for failure. The maximum
forces measured and recorded during deployment
and retraction were imposed on the respective
areas of each pin as shown in Figure 8.
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Figure 8- Finite-element Analysis (FEA) of Pin D generated by the forces from Link 1
Results of Analysis:
Table 1- Max Force, Max Stress, and Safety Factor at each of the Pins
Pin Maximum Force (lbf) Maximum Stress (psi) Safety Factor
A 11075.69 17637.5 3.628632
B 11082.62 23042.1 2.777525
C 30929.6 25821.3 2.478574
D 41957.71 48080 1.331115
E 33825.66 38240.5 1.673618
F 33837.92 29178.5 2.193396
Wheel Axle 16565.8 36123.7 1.77169
Table 2- Hand Calculations: Bending Moment on Pin D & Shear Stress imposed on Pin F (smallest pin). Spring force and Angular velocity are shown as well.
CREO Value Calculated Value % Error
Bending Moment (Pin D) 48080 psi 42069 psi 14.28
Resultant Stress (Shear on Pin F) 291785.5 psi 35097.79 psi 16.87
Spring Force N/A 29997.50 psi N/A
Angular Velocity 6.8 rad/sec 6.7 rad/sec 1.32%
Force onSpring :k∗∇ sEquation 1-Force on a Spri0ng
Factor of Safety (N )=UltimateYield StressDesignStress
Equation 2- Factor of Safety
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Discussion of Results:After generating results, stress evaluations for each of the pins are essential in evaluating the conditions
that each undergo due to the applied simulations (retraction, deployment, and applied force with a
spring). Note that it is essential to set the boundary conditions and applied forces in the appropriate
spots in order to generate the most accurate information.
Boundary conditions were set at each end of the pins. This
seemed to be the most appropriate method of measurement
for each of the pins because setting the boundary conditions at
each end theoretically imposes the largest bending stress that
a pin can undergo. Because the stresses will be higher with
these conditions, this will supply the designer with the lowest
safety factors that a pin undergoes (observe Formula 1 for
safety factor). Utilizing good engineering judgment, pin D was further analyzed by hand calculating the
bending moment. Although the project required that the hand calculation was for the largest pin, it
seemed more important to evaluate the bending moment were the smallest safety factor occurred (pin
D had a safety factor of 1.33 whereas the largest pin had a value of 2.77). As shown at the end of the
report, the hand calculation revealed a bending stress of 42069.00 psi. Compared to Creo’s value of
48080.00 psi, there was a percent error of only 14.29%. This reveals to the designer that although Creo
can simulate stresses distributed throughout the pin, its value should not be fully trusted. Similarly, a
hand calculation at Pin F revealed a shear stress of 35097.79 psi, whereas Creo’s FEA revealed a shear
stress of 29178.50 psi. The percent error calculated was 16.87% thus supporting the claim above to not
trust Creo’s calculations without further analysis. Nevertheless, the percent error was within 20% of the
hand calculations, and since each of the analysis established boundary conditions for maximum possible
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Figure 9- Imposing the cylinder's measured force on Pin F. This is inputted by the designer in order to review stresses and strain energy via FEA.
bending moment, the FEA results shown at the end of the report are reliable and sufficient for design.
In addition, the angular velocity percent error was approximately 1.32%, thus making Creo’s kinematic
analysis very accurate and reliable.
Summary and Conclusion:After creating all necessary parts and assemblies required for the landing gear, it is affirmed that the
landing gear mechanism adheres to the desired conditions and requirements stated on the project
description. Dynamical and kinematical analysis were performed on the landing gear mechanism under
realistic scenarios that most landing gears undergo. Maximum radial forces were observed after running
the simulation and examining the force vs. displacement graphs produced by the piston cylinder. From
here, finite-element analysis allowed us to observe the stress and strain energy conducted on all of the
pins. Table 1 shows the other safety factors for each of the pins utilized in the mechanism. Many main
landing gear structures require a safety factor of 1.25. After comparing some of these safety factor
values to the 1.25 safety factor, all of the pins surpass the 1.25 safety factor thus establishing a
satisfactory performance throughout the entire landing gear mechanism. Some even pass with flying
colors (Pin A and B have a safety factor of 3.623 and 2.77 respectively). Lastly, the maximum bending
movement and shear stresses calculated by Creo were validated by hand calculations, and were
observed to be within 20% error. After designing the landing gear in many different ways, it is also
important to note that the symmetric design seemed to be the most efficient way for reducing the
maximum stress exerted on each of the pins. Finally, it was very valuable to compare Creo’s generated
results with hand calculations. The lesson learned is that there are tradeoffs to using computer
generated calculations in Creo. Although FEA analysis saves time and is fairly accurate, it is not as
accurate or as good as the conventional method of hand calculations.
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Appendix A: Assembly Drawings:
Sub Assembly 1………………………………………………………………………………………………………………………………..……14
Sub Assembly 2……………………………………………………………………………………………………………………………….……15
Sub Assembly 3 ..…………………………………………………………………………………………………………………….……………16
Final Assembly……………………………………………………………………………………………………………………………………….17
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Appendix B:
Detail Drawings:
Piston………………………………………………………………………………………………………………………………………………….19
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Cylinder……………………………………………………………………………………………………………………………….………………20
Wheel……………………………………………………………………………………………………………………….…………………………21
Tire……………………………………………………………………………………………………………….………………………………….….22
Link 2 Slider 1……………………………………………………………………………………………….……………………………………..23
Link 2 Slider 2…………………………………………………….………………………………………….…………………………………….24
Shock Absorber Slider……………….………………….……………………………………….…………………………………………….25
Link 1………………………………………………………………………………………………………………………………………………..…26
Link 3 &4……………………………………………………………………….…………………………………………………………………….27
Link 7…………………………………………………………………………………………………………………………………………………..28
Axle Wheel…………………………………………………………………………………….…………………………………………………….29
Pins F & A…………………………………………………….……………………………………………………………………………………….30
Pins D & C…………………………………………………………………………………………………………………………………………….31
Pin E…………………………………………………………………………………………………………………………………………………….32
Pin B…………………………………………………………………………………………………………………………………………………….33
Generic Cap……………………………………………………………………………………………………..………………………………….34
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Appendix C: Graphs & Calculations:
Pin A…………………………………………………………………………………………………………………………………………………….36
Pin B…………………………………………………………………………………………………………………………………………………….37
Pin C…………………………………………………………………………………………………………………………………………………….38
Pin D…………………………………………………………………………………………………………………………………………………….39
Pin E……………………………………………………………………………………………………….…………………………………………….40
Axle Wheel (Pin)……………………………………………………………………………………………………………………………….….41
Pin F……………………………………………………………………………………………………….…………………………………………….42
Piston Cylinder (Displacement vs time)………………………………………………….…………………………………………….43
Force vs. Displacement at Each Pin (Retraction and Deployment)………………………………………………………..44
Hand Calculations………………………………………………………………………………………………………………………………….51
Bending Moment Validation………………………………………………………………………………………….………….52
Shear Stress Validation……………………………………………………….…………………………………………………….53
Angular Velocity……………………………………………………………………….……………………………………………….54
FEA Analysis Fringe Plots & Convergence Plots
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Spring:
Pin A1 to link 4A
Spring Force:
Pin B to link 4A
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Retraction Force:
Pin C to Shock Absorber
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Spring Force:
Pin D to link 1
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Spring Force:
Pin E to piston
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Spring Force:
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Wheel axle to link 7
Spring Force:
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Pin F to piston
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Piston Cylinder Displacement vs Time
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Force vs. Displacement at Each Pin (Retraction and Deployment)
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Hand Calculations
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