Parameter Optimization of Nose Landing Gear Considering Both Take-off and Landing Performance of Catapult Take-off Carrier-Based Aircraft

Zhang Ming，Nie Hong，He Zhihang

1.Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China；2.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China（Received 18March 2015；revised 26May 2015；accepted 23June 2015）

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Parameter Optimization of Nose Landing Gear Considering Both Take-off and Landing Performance of Catapult Take-off Carrier-Based Aircraft

Zhang Ming1＊，Nie Hong1，2，He Zhihang1

1.Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle，
Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China；
2.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China
（Received 18March 2015；revised 26May 2015；accepted 23June 2015）

Optimization of the parameters of landing gear systems with double-stage air springs of catapult take-off carrier-based aircraft is here studied based on the mathematical equations of the classic dual mass spring-damper dynamic model.Certain standards for both take-off and landing performance are put forward.The contradictory factors between take-off and landing processes are analyzed.The optimization of oil in the pin area and the area near the rear oil hole is performed.Then these optimized parameters are used to assess the influence of the initial pressure of the low chamber，the ratio of the high chamber to the low chamber，and the tire inflation pressure on the performance of arresting landing and catapult take-off.The influences of these parameters on carrier-based aircraft and the aircraft-carrier on aircraft catapult take-off is also assessed.Based on the results of the simulation，respective take-off criteria must be drafted considering different types of aircraft and different take-off load cases，all of which must be matched to parameters relevant to catapult take-off.

carrier-based aircraft；buffer performance；fast-extension performance；aircraft design；optimization；sensitivity analysis

0 Introduction

Carrier-based aircraft are different from ground-based aircraft.They must take off and land on an aircraft carrier，which is much smaller than conventional runways.Catapult take-off allows planes with heavier loads and longer ranges than ski-jump take-off does.Due to the limited length of the deck，carrier-based aircraft often use arrested landing（excepting vertical takeoff and landing aircraft）.At the end of a catapult take-off process，the bumper of the nose landing gear extends quickly to pitch up the aircraft to the required angle of attack，therefore to generate the necessary lift［1，2］.Carrier-based aircraft also land much faster than normal aircraft.This arrested landing process calls for more energy absorption of landing gear than that of normal aircraft.Fastextension performance and buffering performance are both crucial standards for the landing and the take-off of carrier-based aircraft.

（1）U.S.military standards and reports about the design of carrier-based aircraft landing gear are available for reference.U.S.military standard MIL-L-22589provides details of the design，improvement，structure，analysis，experiment and relevant criteria and standards of the nose gear of carrier-based aircraft［3］.U.S.military standard MIL-A-8863defines the strengthand stiffness standards for carrier-based aircraft［4］.The Performance of five different models of carrier-based aircraft is discussed［5］.Other works expounded the principal theories and criteria for hold-down and release systems［6，7］.Researchers in China have thoroughly investigated multiple fast-extension modes，the effect of fastextension on aircraft track，and the sensitivity parameters of the extension［8-14］.Concerning arresting landing，the arresting hook dynamics and load issue of landing gear have been studied［15，16］. However，contemporary studies have some limitations，for example，the research background has focused solely on fast-extension and bumping issues，and no thorough and systematic analysis on landing gear performance.Some research models used are not practical for engineering.

We，standing on the results of previous works，present a novel design for the nose landing gear of carrier-based aircraft and establish a dynamic model.The technology targets of nose landing gear performance are put forth with respect to both landing and catapult take-off.Optimization is conducted on the oil pin cross section and the size of back oil hole，which requires a trade-off between landing and catapult take-off performance.The sensitivity of the effect of nose landing gear filling parameters on landing and catapult take-off performance is analyzed based on optimization results.

1　Mathematic Model of Nose Landing Gear

1.1 Mechanics model of landing gear and relevant hypothesis

A structural figure of the landing gear buffering with double stage air chamber is shown in Fig.1.A mechanical model of the landing gear based on the classic dual mass spring-damper model is shown in Fig.2.

The air spring is used to absorb and reserve energy while the oil damper and friction damper are to dissipate energy.The mass of elastic supporting means the mass of the airframe along with the buffer′s outer tub，while the mass of rigid supporting is comprised of the piston rod and wheel.

Fig.1　Structure of damper with double-stage air spring

Fig.2　Mechanical model of landing gear

In order to guarantee the precision of the calculations，we assume（1）The effect of wheel spin-up is ignored.（2）The axis of the buffer aligns with that of the landing gear.

1.2 Mathematical equations

The positive direction is along the axis of the damper downwards.Local coordinate system of elastic and rigid supporting is established，and the centers of mass of respective objects is set as the origins of coordinate.Then dynamic differential equations are constructed for the landing gear.

The initial condition is as followsThe boundary condition is as follows

where m1，m2are the mass of elastic supporting and rigid supporting mechanisms，respectively，and x1，x2the displacements of elastic supporting mass and the rigid supporting mass，respectively. gis the gravitational acceleration，Tthe positive axial contact compression force between piston rod and outer tub（when damper is compressed，T=0），Fathe air spring force，Foilthe oil damping force，Ffthe friction force between outer tub and piston rod，Lthe lift force，and Fvthe supporting reaction force from deck to tire.

The equation for calculating air spring force is shown as follows

where Aais the effective area of pressure in the air chamber，Sthe stroke of the damper，γthe gas polytropic index which varies between 1.1and 1.4，and Patmthe air pressure.P0，V0indicate the initial pressure and the volume of air in the chamber，respectively.

Calculation of oil damping force is given as follows

whereρis the density of the oil.Cd，Cdsare the coefficients of contraction of main oil chamber and back oil chamber，respectively，and Ah，Ahsthe area of oil pressure of the main oil chamber and back oil chamber，respectively.

Equations for calculating friction force of leather cup is displayed as follows

where Kmis the friction coefficient of leather cup andμbthe bending friction coefficient of the damper.Nu，Nlare the normal forces of the upper and the lower supporting points when damper bends.

The processes of landing and catapult takeoff are analyzed，and Eq.（1）is changed.During landing analysis，the time point when wheel just touches the deck with damper and the wheel is not compressed is set as initials.During catapult take-off analysis，the time point when the ejection force as just come into effect is set as initials.

1.3 Performance index for nose landing gear

Based on the working condition of the landing gear of carrier-based aircraft，two sets of performance index are put forward with respect to landing buffering and the fast extension of nose gear during take-off.

Landing buffering［17-19］：

（1）The landing gear damper ought to absorb work induced by the aircraft with a 7m/s vertical landing speed in less than 0.8s.

（2）The stroke of the damper should not exceed 90%of the max design stroke，and tire compression should not exceed 90%of the maximum，and tire force should remain in the linear phase. Only during rough landings should the damper or tire reach their respective limits.

（3）The damping system should be capable of absorbing the vibrations caused by repeated shock and prevent bouncing and wheel-deck separation.

Fast extension of nose gear during takeoff［20，21］：

（1）The extension should provide enough attack angle for a safe take-off within the length of deck before the nose wheel leaves the deck.

（2）After the ejection force disappears，nose landing gear must extend rapidly while the wheel is still in contact with the deck during the process.

（3）The extension time ought to be as short as possible，and it must end within the given length of deck.

Given the index above，several performance parameters are put forth as follows：

Sis the stroke of the damper，l the load of the landing gear，and ethe efficiency of the damper.

Parameters listed below are for analysis of landing buffering.

t is the time of fast extension，dthe displacement of fast extension，vthe velocity of the mass of elastic supporting when extension ends，andα the attack angle when aircraft leaves deck.

2　Structural Parameter Contradictions and Relevant Optimization

2.1 Analysis on structural parameter contradictions

Structural parameters refer to the parameters of nose gear′s main oil hole and rear oil hole.In order to control and configure the transient damping while working and to ensure the efficiency of the damper，the slope of the damper pillar force must remain to stroke figure positive.Therefore，the variable section main oil hole is used.A valve is installed to configure the positive and negative strokes of the damper.

Fig.3　Oil damping force

The curves in Fig.3are the damping force of main oil hole and back oil hole during one stroke，respectively.During positive strokes，damping force generated by the main oil hole dominates，which indicates that main oil hole plays the main role in absorbing energy during landing.During negative strokes，the rear oil hole generates more damping force and prevents wheel from jumping and the damper from extending too fast. The damper absorbs at least 60%of the energy involved in the first compression while landing，which necessitates greater damping force from the main oil hole during the positive stroke and solid contact between the wheel and deck during the first negative stroke.This means a large oil damping joint force of negative stroke，which suggests a relatively small cross-section of the back oil hole during the negative stroke.For carrier-based aircraft，the fast extension period is during the negative stroke of damper，so fast extension requires a small damping for the negative stroke of damper，which necessitates a large cross-section of the negative stroke of rear oil hole.

2.2 Optimization on structural parameters

Based on the findings given in section 2.3，some key performance factors of landing buffering and the fast extension are here used as optimization objectives，as listed in Table 1，where Fdis the damping force of fast extension and n the maximum overload factor.

Table1　Optimization objectives

The oil pin areas and oil hole areas in positive and negative strokes of the rear chamber here serve as design variables，as listed in Tables 2，3.

The constraint functions of the optimization are as follows：

（1）The landing gear damper ought to absorb work induced by the aircraft at 7m/s vertical landing speed in less than 0.8s.The time required for one buffering stroke should be less than 0.3s.

（2）The stroke of the damper must not exceed 90%of the max design stroke.

Table2　Oil pin area of nose landing gear before optimization

Table3　Oil hole area of back chamber of nose landing gear before optimization

（3）The extension must provide a sufficient attack angle for a safe take-off within the length of deck before the nose wheel leaves the deck. The attack angle must be greater than 5°.

（4）The aircraft wheel should not rebound from the deck.

Integrate ADAMS/Aircraft software through simcode module of ISIGHT-fd system，the optimization procedure of nose gear damper structural parameters is given in Fig.4.

We use non-linear quadratic programming method in ISIGHT-fd software to optimize the shape of oil pin and back oil.The most popular method of stroke-controlled cross-section of oil hole is faciliated by dividing the stroke into several phases.Then the shape of cross-section of the oil pin during the entire stroke can be put forward through quadratic curve fitting method.For rear oil hole parameters，the values of the range of areas for the stroke are given for the optimization process.

Optimization is conducted in two ways，one for landing alone，and another is for landing and fast extension.The optimized oil pin area and the oil hole area of the rear chamber of the nose landing gear are shown in Tables 4，5.

The optimized figure of the buffer is shown in Fig.5.

Fig.4　Optimization procedure of nose gear damper structural parameters

Table4　Oil pin area of nose landing gear after optimization

Table5　Oil hole area of the rear chamber of nose landing gear after optimization

Fig.5shows that landing performance after optimization is better than the unoptimized；And the one only optizmized for landing is better than that optimized both for landing and fast extension.The axial force of the damper during the negative stroke on the condition of landing is smaller than that for both landing and take-off. This shows that a rapid rise in the nose while tak-

ing off could be easier to effect.

Fig.5　Working of the damper

Fig.6　Attack angle over time while leaving deck

Fig.6depicts the curve of attack angle while the plane is leaving the deck.After optimization，the attack angle increases，which means the aircraft can generate more lift force while leaving the deck.

The objectives for landing gear are optimized in two ways，based on initial structural parameters and on two groups of optimized parameters. Results are shown in Table 6.

Table6　Optimization objectives of nose landing gear

Several conclusions can be drawn from the data in Table 6.For landing，the optimized structure can decrease the landing gear overload and increase the efficiency of damper by 10%.For take-off and fast-extension，length is increased by 90mm within the length of deck.

3　Sensitivity of Filling Parameters

While designing the landing gear，filling parameters should include initial inflation pressure of low chamber PL0and that of high chamber PH0；Initial volume of low chamber VL0and that of high chamber VH0，and tire inflation pressure Vt.Nevertheless，these parameters are not all independent of each other.It is here suggested that the stroke of the damper is a constant value. Then the pressure of chambers and inflation volume of chambers are connected to each other through gas state equations.Moreover，inflation pressure in the high and low chambers is related to the transition stroke.For this reason，the sensitivity of relevant parameters is analyzed in this paper.

3.1 Initial pressure of the low chamber

As shown in Table 7，when initial inflation pressure increases from 1.13MPa to 2MPa，maximum axial force of damper during landing drops by 10kN，damper efficiency increases by 5%，and the stroke of the damper decreases by around 17mm，which indicates that increasing the initial pressure of low chamber boosts the performance of the damper.In terms of fast extension performance，as initial pressure of the low chamber increases，the time of extension increases by 0.3s.The axial velocity of upper supporting mass increases somewhat，with a 70mm increase of the extension length.Nevertheless，velocity of aircraft while leaving deck does not increase with the increase of inflation pressure. With the limited length of the deck，the off-ship attack angle become the key parameter for take-off analysis.As a result，both increases and decreases in initial pressure of the low chamber leads only to disadvantages.

Table7　Effect of initial pressure of the low chamber

3.2 Initial pressure of the high chamber

As shown in Table 8，as the ratio increases from 3.5to 7.2，the maximum axial force of the damper during landing increases by 46kN，the efficiency of the damper drops by 7%，with a decrease in damper stroke of 54mm.This indicates that a greater ratio brings a weaker performance for buffering.In terms of fast extension performance，as the ratio increases，time of extension occurres 0.5searlier.Although extension length shrink by 95mm，the axial velocity of upper supporting mass at the end of extension increases by 0.23m/s，and the off-ship attack angle increases by 1.2°.This suggests that a high ratio between pressure of high chamber and low chamber may improve the performance of fast extension.

Table8　Initial pressure of the high chamber

3.3 Tire pressure

As shown in Table 9，as the tire pressure increases from 1.5to 2.2，the maximum axial force of the damper during landing decreases by 7.6kN，the efficiency of the damper increases by 2%，with a decrease in damper stroke of 2.4mm.The efficiency of the entire damping system increases by about 3%，so increases of the initial pressure of the lower chamber has good effects on damping performance.However，when tire pressure is below 1.65MPa，tire compression does not remain linear stage.With respect to fast extension performance，extension takes place 0.1 s earlier as pressure increases.The axial velocity of the upper supporting mass at the end of extension drops slightly，and the off-ship attack angle decreases by 0.05°with a 34mm increase in the length of extension.It can be concluded that low tire pressure leads to better performance of fast extension，but the effect is limited.Tire force may exceed its linear stage due to insufficient tire pressure，so it must maintain a suitable value and damping performance must be taken into serious consideration.

Table9　Tire pressure

4　Parameter Match Between Carrier-Based Aircraft and Aircraft-Carrier

Parameter matches between carrier-based aircraft and the aircraft carriers refers to parameters concerning ejection force provided by aircraft catapult，the length of take-off runway，wind over the deck when carrier cruises windward，initial load of the aircraft，and the trust force of engine.Initial parameters shared between carrierbased aircraft and the aircraft-carrier are used for analysis as listed in Table 10.

Table10　Initial parameters for simulations

4.1 Ejection force

The American C13-1catapult is used for the analysis for the simulation，as there are neither relevant standards nor steam catapult in this country.In the simulations，initial parameters of deck length，aircraft mass，and engine thrust force are applied.Wind over the deck is disregarded，and the ejection force of catapult is changed by 10%each time，and three different curves of force-stroke are given，as shown in Fig.7.Theeffect of thrust force on take-off performance is here analyzed by harnessing these data.Results are listed below.

Based on Table 11and Figs.7—11，it is evident that as ejection force increases from 545PSI to 660PSI，off-deck time of nose wheel starts 0.2searlier，off-deck velocity increases by 5.4m/s，and the off-deck attack angle drops by 0.4°.This explains that large ejection force grants a higher acceleration during the take-off run，and the aircraft leaves the deck so quickly that nose gear can not make full contact with the deck，which leads to an insufficient fast-extension.As ejection force increases，the maximum axial force of the nose damper increases by 67kN and maximum axial force of main damper increases by 47kN，due to an increasing component of force along axial direction.When ejection force reaches 545PSI，the deflection quantity reaches 0.91mand does not exceed 3m.After leaving the deck，the vertical velocity of the aircraft is lower than 3m/s，so the take-off process still results in failure in this case.

Note that the aircraft fails to take off when ejection force reaches the maximum value，a large off-deck attack angle still benefits the take-off process.This is because the taxi run velocity is so short that the aircraft stays on the deck too long，which guarantees a large off-deck attack angle. However，after leaving the deck，the attack angle fails to compensate for the negative effects of the low off-deck velocity and the loss of the ground effect.

Table11　Simulation results under different ejection forces

Fig.7　Pulling forces over stroke under different ejection forces

Fig.8　Attack angles under different ejection forces

Fig.9　Velocities under different ejection forces

Fig.10　Lengthways gravity center displacements under different ejection forces

4.2 Deck length

During catapult take-off，the end of thestroke of the catapult does not reach the end of the deck.The distance between them ranges from 5.8mto 44.2m.This interval profoundly affects how long the ground effect lasts after ejection force disappears，as well as the time of contact between the wheel and the deck.Therefore，this interval is important for the analysis of off-deck attack angle and deflection quantity of flight path.

Initial parameters of aircraft mass，engine thrust force，ejection force of the catapult are applied，the wind over the deck is ignored，and three sets of deck length are put forth：d1= 103m，d2=115m，d3=127m.The effect of deck length on performance of take-off is analyzed based on these sets of data.

Conclusions can be drawn（See Table 12）. With the increase in deck length，the nose wheel can leave deck safely，the off-deck velocity increases by 1.7m/s，the off-deck attack angle increases by 3°，and the maximum axial force of both nose and main landing gear remains unchanged. The deflection of flight path gradually decreases to zero.In conclusion，extending deck length is a fine option for increasing off-deck speed and offdeck attack angle and providing sufficient ground effect.A long deck is also good for the flight path and boosts take-off performance.

4.3 Mass at take-off

Initial parameters of length of deck，engine thrust force，ejection force of catapult are used，and wind the over deck is ignored.Three sets of take-off loads are here put forth：m1=25 000kg， m2=29 000kg，m3=33 000kg.Analysis of the effect of take-off mass on take-off performance is conducted based on the previous sets of data.

It is deduced from Table 13that off-deck time of nose wheel is put off by 0.5sand the offdeck velocity decreases by 14.6m/s as take-off load increases from 25 000kg to 37 000kg，because the acceleration of the aircraft drops due to the increasing load and invariant ejection force and deck length.Therefore，the velocity ejector delivered to the aircraft is greatly limited，and aircraft lingers longer on the deck.The smallest off-deck attack angle is observed when take-off load is 25 000kg，because the aircraft does not stay on the deck long enough，leading to an insufficient fast-extension.As the take-off load reaches 37 000kg，its off-deck attack angle decreases instead of increasing because of the relatively low off-deck velocity.As the take-off load increases，so does the maximum axial force of both nose and main dampers.When take-off load reaches 37 000kg，the deflection of off-deck flight path exceeds 3m，and the vertical upward velocity of aircraft fails to increase，which causes it to fail.

Among the sets of data applied in the simulations，the minimum off-deck attack is observed when aircraft mass does not exceed 25 000kg，but there is no deflection of flight path.This can be attributed to the fast off-deck velocity and the upward vertical velocity continuing to increase after leaving the deck，as does the attack angle，which facilitates safe take-off by offering sufficient lift force against gravity.

4.4 Engine thrust force

If the length of deck is inadequate，the flight path is deflected.To ensure safe take-off，engine thrust force must be able to maintain enough thrust force to enable the aircraft to climb after a period of descent 3safter reaching maximum deflection.Engine thrust force depends only on engine attributes.

Initial parameters of aircraft mass，deck length，and ejection force of catapult，are used. the wind over the deck is disregarded，and four sets of deck length are applied by configuringthrust 20%at a time：T1=174.2kN，T2= 209.7kN，T3=250.88kN，T4=301.06kN. The effect of engine thrust force on take-off performance is analyzed using such sets of data.

It is concluded from Table 14that，as the engine thrust force increases from 174.2kN to 301.06kN，off-deck time of nose wheel takes place 0.2searlier，and off-deck velocity drops by 5.47m/s.This is primarily because the increment of thrust force significantly increases the acceleration under the invariant ejection force and take-off mass.As a result，the velocity of aircraft at the end of deck and the off-deck attack angle both increase，and the time range during which the aircraft remains on the deck decreases.The maximum axial force of the nose gear increases，and that of main landing gear decreases，but the variations are limited.If thrust force is under 250.88kN，flight path is deflected after the aircraft leaves the deck.When the force is equal to 174.2kN，aircraft drops profoundly after the aircraft left the deck and fails to climb up.When thrust force is 209.7kN，the deflection of flight path is 1.13m，which does not exceed 3m. However the rate of climbing does not reach 3m/s within 3sof leaving the deck.This is an unsuccessful take off.

Table12　Simulation results at different deck lengths

Table13　Simulation results with different take-off loads

Table14　Simulation results under different thruster forces

5　Conclusions

（1）Nose landing gear performance is explored with respect to both landing and catapult take-off.Optimization of the oil pin cross-section and the size of back oil hole can necessitate a tradeoff between landing and catapult take-off performance.Optimized structure can decrease the landing gear overload and increase the effi-ciency of buffer by 10%.For take-off，fast-extension length is increased by 90mm within the length of the deck.

（2）Inflation pressure in the low air chamber has little effect on buffering or fast-extension performance.It is unwise to modify its parameters in practical situations.Inflation pressure in the high air chamber has profound effects on fast-extension performance，the higher the pressure，the betterthe fast-extension performance.Nevertheless，if pressure grow too high，the buffering effect is weakened.Lower tire pressure will be good for fast-extension performance to an extent.Considering that a high tire pressure prevents the tire from entering a nonlinear stage，the value of inflation pressure tends not to be too low，and buffering performance should be taken into consideration.

（3）Match parameters between carrier-based aircraft and aircraft-carriers affect each other. Larger ejection forces and thrust force benefit offdeck velocity.However，if the deck is too short，this ejection force and thrust force can cause only a small off-deck attack angle.Extended deck length can compensate for the inadequate thrust force and ejection force.Safety criteria specific to different types of aircraft and types of take-off loads must be established with several ejection parameters modified for their specific cases.

Acknowledgements

This work was supported by the National Natural Science Foundation of China（Nos.51305198，11372129）.

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Dr.Zhang Ming is currently an associate professor in Col-lege of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics.He received his Ph.D.degree in Aircraft Design from Nanjing University of Aeronautics and Astronautics in 2009.His research interests include aircraft design，dynamics and landing gear system.

Dr.Nie Hong is currently aprofessor and doctoral supervisor in Nanjing University of Aeronautics and Astronautics. He received his Ph.D.degree in Aircraft Design from Nanjing University of Aeronautics and Astronautics in 1992. His current research interests include aircraft design，dynamics and landing gear system.

Mr.He Zhihang is currently a M.S.candidate in Nanjing University of Aeronautics and Astronautics.His current research interests include aircraft design，dynamics and landing gear system.

（Executive Editor：Xu Chengting）

V226 Document code：A Article ID：1005-1120（2016）02-0187-12

＊Corresponding author，E-mail address：zhm6196@nuaa.edu.cn.

How to cite this article：Zhang Ming，Nie Hong，He Zhihang.Parameter optimization of nose landing gear considering both take-off and landing performance of catapult take-off carrier-based aircraft［J］.Trans.Nanjing Univ.Aero.Astro.，2016，33（2）：187-198.

http：//dx.doi.org/10.16356/j.1005-1120.2016.02.187