ARTTU HEININEN MODELLING AND SIMULATION OF AN AIRCRAFT MAIN LANDING GEAR SHOCK ABSORBER Master of Science Thesis Examiner: Professor Kari T. Koskinen Examiner and topic approved in the Faculty of Engineering Sciences meet- ing on 8.4.2015 II TIIVISTELMÄ TAMPEREEN TEKNILLINEN YLIOPISTO Konetekniikan koulutusohjelma HEININEN, ARTTU: Lentokoneen päälaskutelineen iskunvaimentimen mallinnus ja simulointi Diplomityö, 53 sivua, 3 liitesivua Syyskuu 2015 Pääaine: Virtaustekniikka Tarkastaja: professori Kari T. Koskinen Avainsanat: Amesim, mallinnus, simulointi, lentokone, iskunvaimennin, laskuteline Jokaisen perinteisen lentokoneen päälaskutelineissä on iskunvaimennin, jonka tehtävä on ottaa laskeutumisesta aiheutuva isku vastaan, absorboida se ja dissipoida kineettinen energia. Tässä työssä tutkittiin taisteluhävittäjän öljypneumaattisen joustimen mallin- nusta ja simulointia. Iskunvaimentimen toimintaa hallitsevat yhtälöt on esitetty, joihin sisältyvät muun muassa kitkan, kaasujousen ja vaimennuksen käyttäytyminen. Malli on validoitu vertaamalla simulointituloksia referenssimittauksilla saatuihin tu- loksiin. Validoinnin aikana havaittiin korkeita kitkatasoja. Referenssidataa oli saatavilla staattisesta testipenkistä, dynaamisesta testijärjestelmästä sekä oikeasta laskeutumisesta. Työssä esitetty malli tuotti tuloksia, jotka olivat lähellä mitattuja arvoja. Lisäksi suoritettiin simulointeja vaihtelemalla kaasun ja nesteen suhdetta sekä lämpötilaa. Kaasun ja nesteen suhteen merkittävä muutos saattaa aiheuttaa päälaskutelineen vial- lisen toiminnan, mutta asian todentaminen vaatii lisätutkimusta. Lämpötilaa vaihdeltiin kahdella tapaa. Ensin alkulämpötilaa vaihtamalla ja sitten lämmittämällä tai jäähdyt- tämällä iskunvaimenninta simuloinnin aikana. Jos iskunvaimentimen täyttölämpötilan ja ulkolämpötilan välillä on lämpötilaero, paine iskunvaimentimen sisällä kasvaa tai pienenee, riippuen lämmitetäänkö vai jäähdytetäänkö iskunvaimenninta, mikä voi aiheuttaa viallisen toiminnan. Mallia voidaan käyttää työkaluna kunnonvalvonnan kehit- tämisessä sekä vikatilojen tutkimisessa. Suunnitteilla on myös uusi mittalaite, jonka suunnitteluvaiheessa mallia voidaan käyttää hyödyksi. Työssä esitetty malli approksimoi todellisen iskunvaimentimen kaasujousen sekä kur- istustapin toimintaa hyväksyttävällä tarkkuudella, mutta ei ota huomioon mahdollisia muodonmuutoksia, jotka voivat syntyä korkeiden paineiden takia. Parannusehdotuksia on esitetty sekä pohdittu ja tavoitteena on, että nämä esitetyt parannusehdotukset liitetään malliin lähitulevaisuudessa. Myöhemmin tavoitteena on liittää paranneltu malli suurempaan päälaskutelineen malliin, jonka avulla laskeutumista ja siihen liittyviä ilmiöitä voidaan tarkastella kokonaisuutena. III ABSTRACT TAMPERE UNIVERSITY OF TECHNOLOGY Master’s Degree Programme in Mechanical Engineering HEININEN, ARTTU: Modelling and simulation of an aircraft main landing gear shock absorber Master of Science Thesis, 53 pages, 3 Appendix pages September 2015 Major: Fluid dynamics Examiner: Professor Kari T. Koskinen Keywords: Amesim, modelling, simulation, aircraft, shock absorber, landing gear Every traditional aircraft has a shock absorber in its main landing gear. A shock ab- sorber takes the brunt of the shock imparted to the landing gear, absorbs it and dissi- pates the kinetic energy. This thesis is based on the construction of a realistic analytical model of an oleo-pneumatic shock absorber for a combat aircraft. The governing equa- tions presented here include the effects of friction, gas spring and damping, among other things. The model was validated with a wide range of reference data, which revealed excep- tionally high friction levels detected during the validation process. The reference data consists of measurements from a static test bench, a dynamic test system and an actual aircraft landing, and the corresponding simulations are presented in this thesis. The re- sults of the simulations closely match the measured data. The effects of variations in the gas-liquid ratio and temperature on the pressure behaviour inside the shock absorber were simulated. If the gas-liquid ratio is distorted, the damping ability of the shock ab- sorber is diminished, which may lead to faulty operation of the landing gear. Tempera- ture variation was examined in two ways, firstly by varying the initial temperature and secondly, by heating and cooling the shock absorber. Filling the shock absorber in con- ditions which differ from the environment in which the aircraft will operate causes the pressure to decrease or increase, depending on whether the shock absorber is cooled or heated. The utilization of simulations as a tool in condition monitoring and fault detec- tion is discussed, and as a result of that a new measuring instrument is proposed, whose design can be facilitated with this simulation model. Although the model presented in this thesis is not complete, it adequately mirrors the behaviour of the gas spring and the metering bin. However, the model does not include the deformations caused by high pressures. A number of possible improvements to the model are presented and discussed. In its present form, the load-stroke behaviour of the model is close to the real shock absorber, and the model can be used to analyse the forces and pressures generated by different shocks. Future work will involve improving the model and incorporation of the model into a larger main landing gear model so that a comprehensive investigation of the dynamics of an aircraft landing can be performed. IV PREFACE I would like to express my gratitude to my supervisors Professor Kari T. Koskinen and M.Sc. Jussi Aaltonen for their guidance and advice during the process of working on this thesis. I would also like to thank the Department of Mechanical Engineering and In- dustrial Systems and the Finnish air force for giving me this opportunity to carry out this research. I am grateful to B.Sc. Juha Huitula from the FDF Logistics Command for the inform- ation he provided. I would also like to express my gratitude to all the teaching person- nel, who have taught me during my studies here at Tampere University of Technology. Tampere, November 24, 2015 ______________________ Arttu Heininen V CONTENTS 1. Introduction..............................................................................................................1 2. State of the art..........................................................................................................4 2.1 Literature review..........................................................................................4 3. The shock absorber model.......................................................................................6 3.1 The main parts of the shock absorber...........................................................6 3.2 Principles of operation................................................................................10 3.3 System model and governing equations.....................................................10 3.4 Modelling the gas.......................................................................................20 3.5 Modelling the hydraulic fluid.....................................................................22 3.6 Solving the differential equations...............................................................23 4. Model validation....................................................................................................24 4.1 The static case............................................................................................24 4.2 The dynamic case.......................................................................................28 4.3 Real landing................................................................................................30 5. Utilizing the simulation for condition monitoring and fault detection..................34 5.1 The effect of variations in the gas-liquid ratio on the operation of the shock absorber......................................................................................................35 5.2 The effect of temperature variation on the pressure behaviour..................37 5.3 Discussion on the new measuring instrument............................................40 6. Model limitations and future improvements..........................................................43 6.1 Gas-liquid interaction.................................................................................43 6.2 Other improvements...................................................................................47 7. Conclusions............................................................................................................49 References..............................................................................................................51 Appendix 1: Amesim submodel symbols...............................................................54 VI LIST OF SYMBOLS Greek symbols: α Volumetric expansion coefficient [1/K] α Thermal diffusivity [m2/s] T α Volumetric expansion coefficient [1/K] V β Fluid bulk modulus [Pa] Γ Polytropic index δQ Heat exchange with surroundings [W] Δp Pressure difference [Pa] λ Flow number λ Critical flow number crit θ Angle of inclination [rad] μ Dynamic viscosity [Pa·s] μ Coulomb friction coefficient c ν Kinematic viscosity [m2/s] ρ Density [kg/m3] ω Pitzer's acentric factor Latin symbols: a Attractive term [(N·m)/kg] a Inner mass acceleration [m/s2] 1 a Envelope acceleration [m/s2] 2 A Orifice cross section [m2] A High pressure chamber cross-sectional area [m2] HP A Metering pin cross-sectional area [m2] mp A Seal outer surface [m2] S A Effective piston ring area [m2] PF A Annulus area of the primary piston head [m2] ph b Covolume [m3/kg] c Specific heat capacity [J/(K·kg)] p c Flow coefficient q VII c Maximum flow coefficient q C Specific heat of the fluid [J/(kg·K)] P d Clearance between an envelope and a piston [m] c d External piston diameter [m] p dh Heat flow rate [W] dp Piston diameter [m] dr Piston rod diameter [m] dm Mass flow rate [kg/s] dmh Incoming enthalpy flow rate [W] dmh Downstream enthalpy flow rate [W] down dmh Upstream enthalpy flow rate [W] up dv Zero velocity interval [m/s] D External piston diameter [m] P Db Higher limit contact damping coefficient [N/(m·s)] max Db Lower limit contact damping coefficient [N/(m·s)] min F Dry friction force [N] dry F Higher limit contact force [N] max Higher limit contact force between the envelope and the F [N] max2 fixed reference Higher limit contact force between the inner mass and F [N] max3 the fixed reference F Lower limit contact force [N] min Lower limit contact force between the envelope and the F [N] min2 fixed reference Lower limit contact force between the inner mass and F [N] min3 the fixed reference F Piston force at the positive port [N] 1 F Piston force at the negative port [N] 2 F Added force [N] added F Force on the inner mass [N] sum1 F Force on the envelope [N] sum2 F Force acting on port i [N] exti F Coulomb friction force [N] C F Piston friction force [N] FP F Normal force [N] N VIII F Stiction force [N] S F Viscous friction force [N] V F Coefficient of viscous friction [N/(m·s)] V F+ Envelope friction force [N] F- Piston friction force [N] g Gravitational acceleration [m/s2] h Specific enthalpy of the volume [J/kg] k Thermal conductivity [W/(m·K)] K Constant Kb Higher limit stiffness [N/m] max Kb Lower limit stiffness [N/m] min K Henry's law constant [Pa] H l Contact length [m] c L Seal ring axial length [m] m Mass of the fluid [kg] m Mass of the shock absorber [kg] sa m Mass of the inner mass [kg] 1 m Mass of the envelope [kg] 2 p Pressure [Pa] p Initial pressure [Pa] init p Normal service pressure [Pa] ns p Upstream pressure [Pa] up P Pressure [Pa] P Atmospheric pressure [Pa] atm P Critical pressure [Pa] crit P Piston pressure [Pa] P Pd Higher limit penetration for full damping [m] max Pd Lower limit penetration for full damping [m] min Q Volumetric flow rate [m3/s] r Specific gas constant [J/(kg·K)] r Radial clearance [m] c R Viscous friction between the piston and the envelope [N/(m·s)] visc1 Viscous friction between the envelope and the fixed R [N/(m·s)] visc2 reference T Temperature of the volume [K] IX T Critical temperature [K] crit T Upstream temperature [K] up v Relative velocity [m/s] v Specific volume of the fluid [m3/kg] s v Stribeck velocity [m/s] s v+ Envelope velocity [m/s] v- Piston velocity [m/s] V Volume [m3] V Envelope velocity [m/s] 2 V Relative velocity [m/s] rel W Windage friction between the piston and the envelope [N/(m·s)2] 1 Windage friction between the envelope and the fixed W [N/(m·s)2] 2 reference x Gas content [(N·m)/kg] X Higher displacement limit [m] max X Lower displacement limit [m] min X Relative displacement [m] rel X Inertial reference position [m] ref Z Compressibility factor X LIST OF FIGURES Figure 1.1. A generic oleo-pneumatic shock absorber.......................................................1 Figure 1.2. A modified oleo-pneumatic shock absorber from a combat aircraft...............3 Figure 3.1. The modified oleo-pneumatic shock absorber assembly. 1) The orifice support, 2) the primary piston assembly and 3) the high pressure chamber......................7 Figure 3.2. The primary piston assembly..........................................................................8 Figure 3.3. The primary piston head and the piston ring position.1) during compression; 2) during extension............................................................................................................9 Figure 3.4. 1) The secondary piston head, 2) the orifice support, 3) the snubber plate, 4) a shoulder bolt...................................................................................................................9 Figure 3.5. Schematic of the oleo-pneumatic shock absorber.........................................11 Figure 3.6. The block diagram of the oleo-pneumatic shock absorber............................12 Figure 3.7. The symbol of the mass envelope [13]..........................................................13 Figure 3.8. Friction forces and the Stribeck effect..........................................................16 Figure 3.9. The normalised cross section of the metering pin against normalised displacement....................................................................................................................18 Figure 4.1. The normalised displacement used as an input signal in the static case simulation........................................................................................................................25 Figure 4.2. A normalised force-displacement curve of an unpressurised modified shock absorber............................................................................................................................26 Figure 4.3. A normalised force-displacement curve of a normally serviced shock absorber............................................................................................................................27 Figure 4.4. A normalised force-displacement curve of a shock absorber serviced with quarter pressure................................................................................................................27 Figure 4.5. The normalised force used as an input signal in the dynamic case simulation. .........................................................................................................................................29 Figure 4.6. The compression velocity during the dynamic test.......................................29 Figure 4.7. The displacement during the dynamic test....................................................30 Figure 4.8. The normalised displacement of the shock absorber measured during landing.............................................................................................................................31 Figure 4.9. Normalised pressure inside the orifice support during landing....................32 Figure 4.10. Normalised pressure inside the high pressure chamber during landing......33 Figure 5.1. Force-displacement curves of the static case simulation with varying nitrogen volume...............................................................................................................36 Figure 5.2. Displacement during the dynamic case simulation with varying nitrogen