Landing Gear Project Final Report
- 1. 1 Project 3: Landing Gear Design & Analysis December 19th , 2014 Kevin Osman
- 2. 2 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
- 3. 3 Executive Summary Using 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 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 shockabsorber, a piston cylinder, a wheel and tire assembly (with a wheel axle serving as a pin), and at least six pins with caps. Propermaterial 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 approachtheir max stress values during deployment and retraction. Forthe spring analysis, a spring was inputted into the shockabsorber 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.
- 4. 4 Introduction The 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 efficiencyof 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. Figure 1 Generic View of the Project Three Landing Gear
- 5. 5 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 efficientlypiece 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). Figure 2- Wheel Axle (Pin). Figure 3- Generic Pin (required dimensions) with a total length of 2.75 in
- 6. 6 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. 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.
- 7. 7 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 AssemblyII). 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.
- 8. 8 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.
- 9. 9 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 retractionhad 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. Figure 8- Finite-element Analysis (FEA)of Pin D generated by the forces from Link 1
- 10. 10 Results of Analysis: Table 1- Max Force, Max Stress, and Safety Factor at each of the Pins Pin MaximumForce (lbf) MaximumStress(psi) SafetyFactor 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 CalculatedValue % Error BendingMoment (PinD) 48080 psi 42069 psi 14.28 ResultantStress (ShearonPinF) 291785.5 psi 35097.79 psi 16.87 SpringForce N/A 29997.50 psi N/A AngularVelocity 6.8 rad/sec 6.7 rad/sec 1.32% 𝐹𝑜𝑟𝑐𝑒 𝑜𝑛 𝑆𝑝𝑟𝑖𝑛𝑔: 𝑘 ∗ ∇𝑠 Equation 1-Force on a Spri0ng 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦 ( 𝑁) = 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑌𝑖𝑒𝑙 𝑑 𝑆𝑡𝑟𝑒𝑠𝑠 𝐷𝑒𝑠𝑖𝑔𝑛 𝑆𝑡𝑟𝑒𝑠𝑠 Equation 2- Factor of Safety
- 11. 11 Discussion of Results: Aftergeneratingresults,stressevaluationsfor eachof the pinsare essential inevaluatingthe conditions that eachundergodue to the appliedsimulations(retraction,deployment, andapplied force witha spring). Note thatit isessential tosetthe boundaryconditionsandappliedforcesinthe appropriate spotsin orderto generate the mostaccurate information. Boundaryconditionswere setateachendof the pins. This seemedtobe the mostappropriate method of measurement for eachof the pinsbecause setting the boundaryconditionsat each endtheoreticallyimposesthe largest bendingstressthat a pincan undergo. Because the stresseswill be higherwith these conditions,thiswillsupplythe designerwiththe lowest safetyfactorsthat a pinundergoes(observeFormula1for safetyfactor). Utilizinggoodengineeringjudgment,pinDwasfurtheranalyzedbyhandcalculatingthe bendingmoment. Althoughthe projectrequiredthatthe handcalculationwasforthe largestpin,it seemedmore importanttoevaluate the bendingmomentwere the smallestsafetyfactoroccurred(pin D had a safetyfactor of 1.33 whereasthe largestpinhada value of 2.77). As shownat the endof the report,the hand calculationrevealedabendingstressof 42069.00 psi. Compared to Creo’svalue of 48080.00 psi,there wasa percenterror of only14.29%. This revealstothe designerthatalthoughCreo can simulate stressesdistributedthroughoutthe pin,itsvalue shouldnotbe fullytrusted. Similarly,a handcalculationat PinF revealedashearstressof 35097.79 psi, whereasCreo’sFEA revealeda shear stressof 29178.50 psi. The percenterrorcalculatedwas16.87% thus supportingthe claimabove tonot trust Creo’scalculations withoutfurtheranalysis. Nevertheless,the percenterrorwaswithin20%of the 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.
- 12. 12 handcalculations,andsince eachof the analysisestablishedboundaryconditionsformaximumpossible bendingmoment,the FEA resultsshownatthe endof the reportare reliable andsufficientfordesign. In addition,the angularvelocitypercenterrorwasapproximately1.32%,thusmakingCreo’skinematic analysisveryaccurate and reliable. Summary and Conclusion: Aftercreatingall necessarypartsandassembliesrequiredforthe landinggear,itisaffirmedthat the landinggearmechanismadherestothe desiredconditionsandrequirementsstatedonthe project description. Dynamical andkinematical analysiswere performedonthe landinggearmechanismunder realisticscenariosthat mostlandinggearsundergo. Maximumradial forceswereobservedafter runningthe simulationandexaminingthe force vs.displacementgraphs produced bythe piston cylinder. Fromhere,finite-elementanalysisallowedustoobserve the stressandstrainenergy conductedonall of the pins. Table 1 showsthe othersafetyfactorsforeach of the pinsutilizedinthe mechanism. Manymainlandinggearstructuresrequire asafetyfactorof 1.25. Aftercomparingsome of these safetyfactorvaluestothe 1.25 safetyfactor,all of the pinssurpassthe 1.25 safetyfactorthus establishingasatisfactoryperformancethroughoutthe entirelandinggearmechanism. Some even pass withflyingcolors(PinA andB have a safetyfactorof 3.623 and 2.77 respectively). Lastly,the maximumbendingmovementandshearstresses calculatedbyCreo were validatedbyhand calculations,andwere observedtobe within20% error. Afterdesigningthe landinggearinmany differentways,itis alsoimportanttonote that the symmetricdesignseemedtobe the mostefficient wayfor reducingthe maximumstress exertedoneachof the pins. Finally,itwasveryvaluable to compare Creo’sgeneratedresultswithhandcalculations. The lessonlearnedisthatthere are tradeoffs to usingcomputergeneratedcalculationsinCreo. AlthoughFEA analysissavestimeandisfairly accurate,it is notas accurate or as good as the conventional methodof hand calculations.
- 13. 13 Appendix A: Assembly Drawings: SubAssembly1………………………………………………………………………………………………………………………………..……14 Sub Assembly 2……………………………………………………………………………………………………………………………….……15 Sub Assembly 3 ..…………………………………………………………………………………………………………………….……………16 Final Assembly……………………………………………………………………………………………………………………………………….17
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- 18. 18 Appendix B: Detail Drawings: Piston………………………………………………………………………………………………………………………………………………….19 Cylinder……………………………………………………………………………………………………………………………….………………20 Wheel……………………………………………………………………………………………………………………….…………………………21 Tire……………………………………………………………………………………………………………….………………………………….….22 Link2 Slider1……………………………………………………………………………………………….……………………………………..23 Link2 Slider2…………………………………………………….………………………………………….…………………………………….24 ShockAbsorberSlider……………….………………….……………………………………….…………………………………………….25 Link1………………………………………………………………………………………………………………………………………………..…26 Link3 &4……………………………………………………………………….…………………………………………………………………….27 Link7…………………………………………………………………………………………………………………………………………………..28 Axle Wheel…………………………………………………………………………………….…………………………………………………….29 PinsF & A…………………………………………………….……………………………………………………………………………………….30 PinsD & C…………………………………………………………………………………………………………………………………………….31 PinE…………………………………………………………………………………………………………………………………………………….32 PinB…………………………………………………………………………………………………………………………………………………….33 GenericCap……………………………………………………………………………………………………..………………………………….34
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- 35. 35 Appendix C: Graphs & Calculations: PinA…………………………………………………………………………………………………………………………………………………….36 PinB…………………………………………………………………………………………………………………………………………………….37 PinC…………………………………………………………………………………………………………………………………………………….38 PinD…………………………………………………………………………………………………………………………………………………….39 PinE……………………………………………………………………………………………………….…………………………………………….40 Axle Wheel (Pin)……………………………………………………………………………………………………………………………….….41 PinF……………………………………………………………………………………………………….…………………………………………….42 PistonCylinder(Displacementvstime)………………………………………………….…………………………………………….43 Force vs. Displacement atEach Pin(RetractionandDeployment)………………………………………………………..44 Hand Calculations………………………………………………………………………………………………………………………………….51 BendingMomentValidation………………………………………………………………………………………….………….52 ShearStressValidation……………………………………………………….…………………………………………………….53 AngularVelocity……………………………………………………………………….……………………………………………….54
- 36. 36 FEA Analysis Fringe Plots & Convergence Plots Spring: Pin A1 to link 4A
- 37. 37 Spring Force: Pin B to link 4A
- 38. 38 Retraction Force: Pin C to Shock Absorber
- 39. 39 Spring Force: Pin D to link 1
- 40. 40 Spring Force: Pin E to piston
- 41. 41 Spring Force: Wheel axle to link 7
- 42. 42 Spring Force: Pin F to piston
- 43. 43 Piston Cylinder Displacement vs Time
- 44. 44 Force vs. Displacement at Each Pin (Retraction and Deployment)
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