Landing-Gear Drop-Test Rig Developmentand Application for Light Airplanes

Cai-Jun Xue,∗ Yu Han,† Wen-Gang Qi,† and Jian-Hua Dai†

Nanjing University of Aeronautics and Astronautics,

210016 Nanjing, People’s Republic of China

DOI: 10.2514/1.C031913

A drop-test rig is developed for the landing gear of a light multifunctional amphibious airplane based on its

drop-test specifications. Several key technologies (including the schematic design of the light-aircraft drop test, the

control-system design for the drop test, the high-speed turn of the wheel, the accurate lifting of the drop system,

design of the measuring platform, and the imitation of the runway) are studied. Simultaneously, the system can

realize accurate measurement and conduct the light-aircraft drop test with high-speed belt turn. Based on a drop

test under initial parameters to get the friction between the tire and platform, and the elastic parameters of the

wheel to simulate the interactions of components, the simulation models are repeatedly modified by analyzing the

results of comparisons between drop test and simulation. Thus, an accurate model is established with optimal

parameters, which verifies that the shock-absorbing properties of the landing gear with the optimal parameters

meet the requirements of airworthiness rules, and the properties are greatly improved. According to the

requirement of China Civil Aviation Regulations Order No. 132 (CCAR-23-R3) and the application of virtual

prototype technology for the light multifunctional amphibious airplane, the adjusting-parameter drop test, the

limited drop test, and the reserve-energy absorption drop test of the nose landing gear are accomplished. The

limited load measured in the test is less than the design load, and the landing gear can bear the reserve-energy

absorption drop test. The study shows that the adjusting-parameter drop test for establishing a simulation model

is an available and reliable way to optimize the shock-absorbing properties of an amphibious-aircraft landing

gear. The test system can be applied for the landing-gear drop-test of other light airplanes. Moreover, the test

results can be used as the certification of the airworthiness for this airplane.

Nomenclature

Aa = area where the piston rod squeezes out the air (exceptfor the oil-hole area)

Ah = area where the piston rod squeezes out the oil (exceptfor the oil-hole area)

A0 = sectional area of oil holeat = acceleration of hanging basketCd = flow coefficient of the oil holeC� = vertical damping coefficient of the wheeldm = diameter of the main oil holeds = diameter of one-way oil holeFm�t� = total friction force between platform and the four

supported pillarsFx = horizontal load acting on the wheelFY�t� = vertical load of the wheelFz = vertical load acting on the wheelK� = vertical deformation coefficient of the wheelkva = calibration value of vertical acceleration sensor fixed

on platform.kvg = calibration value of vertical load sensorM1 = mass of platformN = number of wheelNY�t� = inertia force of platformnn = inertial overload coefficient

PS = atmospheric pressurePy�t� = resultant force measured by four sensorsP0 = initial pressure of bufferp�t� = tension–compression load of platform in the drop testS = stroke of bufferSmax = maximum stroke of buffert = first buffering circle timeV0 = initial volume of the air chamber� = oil density

I. Introduction

N OWADAYS, an aircraft landing-gear drop test basically relieson the design of the drop-test rig. For instance, the American

drop-test rig is designed into a dynamic form as well as being set onactive ground. The American test rig consists of rack car, sprinklersystem (which is used to provide driving force), and a track withbilateral rails. The simulation accomplished on the drop-test rig isclose to actual landing conditions. The vertical drop-test rig is widelyused in Russia. The working principle of the rig is using the motor todrive the landing-gear tire, which is fixedwith a flywheel through thebelt. With the rapid development of the aviation industry, aircraftlanding-gear drop-test technology has received much attention, andseveral key technologies have been broken through. The dynamicanalysis and drop tests for specific aircraft landing gear have beenextensively studied by scholars from various countries at differentviewpoints.

As early as 1937, Franz established a linear spring-damper modelfor an aircraft landing-gear system [1]. The landing-gear dynamicmodel became more meticulous since then. More factors wereconsidered in the dynamic model, such as nonlinear buffer, tiredamping, and the stiffness of the landing gear. In 1952, Fliiggeapplied the method of entering nonlinearity force-displacementcurves and damping formulas, which was related to the verticalvelocity [2]. By this way, the nonlinearity behaviors of the oil bufferwere taken into consideration for the dynamic model. In the sameyear, Milwitzky and Cook studied the behavior analysis of a

Received 5 April 2012; revision received 3 May 2012; accepted forpublication 4 June 2012. This material is declared a work of the U.S.Government and is not subject to copyright protection in the United States.Copies of this paper may be made for personal or internal use, on conditionthat the copier pay the $10.00 per-copy fee to theCopyright Clearance Center,Inc., 222RosewoodDrive, Danvers,MA01923; include the code 0021-8669/12 and $10.00 in correspondence with the CCC.

∗Associate Professor, Key Laboratory of Fundamental Science forNational Defense–Advanced Design Technology of Flight Vehicle;cjxue@nuaa.edu.cn.

†Graduate Student, Key Laboratory of Fundamental Science for NationalDefense–Advanced Design Technology of Flight Vehicle.

JOURNAL OF AIRCRAFT

Vol. 49, No. 6, November–December 2012

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conventional landing gear during its landing impact process literally[3]. Several key factors of landing gear were discussed, and theanalysis model for the landing-gear system model was simplifiedrationally. In 1967, Garba described the correlation between thepredicted and measured dynamic behavior for a full-size surveyordrop test [4]. In 1974, Daughetee described a laboratory facilitydeveloped by Vought Systems Division of the Ling–Temco–VoughtAerospace Corporation and techniques used to realistically simulatelandings of full-scale aircraft under precisely controlled conditions[5]. He reported that the load of the landing gear had reached the peakin the first 0.2 s when the wheel touched down, and the wheel’spassing through deckwith obstacles caused an increase about 16% inlanding-gear load during the landing progress. From 1979 to 1982,Ross [6] and Ross and Edson [7–10] presented the design of anactive-control landing-gear system that was motivated by anelectronic controller. The control effect of the controller was verifiedby the landing-gear drop test.

In the early 1970s, Bender et al. [11] and Corsetti and Dillow [12]elaborated on the feasibility of the research and design scheme of themain landing gear. From then on, NASA plunged a lot of human andmaterial resources to carry out the research [13]. In 1976, McGeheeand Carden established a mathematical model of an active-controllanding gear for load control during impact and rollout with thesimulation technology being applied in the study of its performance[14–17]. In 1979–1982, the results of an evaluation of an active load-control landing-gear computer program for predicting the landingdynamics of airplanes with passive and active main gears werepresented. It showed that the active gear reduced airframe-gear forcesand airplane motions following initial impact and had the potentialfor significant reductions in structural fatigue damage relative tothat which occurred with the passive gear [18]. In 1990, Howelland McGehee conducted an experimental investigation on theseries-hydraulic active-control nose gear of an F106-B [19]. Theexperiments involved testing the gear in both passive- and active-control modes. Results of this investigation showed that a series-hydraulic active-control gear was feasible and that such a gear waseffective in reducing the loads transmitted by the gear to the airframeduring ground operation. In 1997, Underwood described the finalsystem drop test of the disk–gap–band parachute system [20]. Thesystem consisted of three disk–gap–band parachutes of differentdesigns, each of which was optimized for its own task within themission [21,22]. In 1999, Wang and Udo simulated the operation ofan Airbus A320 as an example and set up the main landing-gearmodel [23]. The highly nonlinear aircraft dynamics coupled withvarying landing and runway conditions were handled with theproposed fuzzy controller.

At the end of 20th century, the landing-gear dynamics model haddeveloped to the depth of making a complete layout from thewhole aircraft. The structural flexibility of the body, dynamic loaddistribution between the nose and main landing gear, aerodynamicresponse on the body, and its influence on landing-gear impact loadswere fully taken into account. In 2000, Ghiringhelli used a two-freedommodel to investigate the simulation of a semi-active-controllanding-gear test with different subsidence velocity [24]. In 2004,Ghiringhelli used a multibody dynamics software ADAMS to set upa complete model without considering the flexibility of the airframe,and the Proportion Integration Differentiation (PID) controller wasdesigned and improved to carry out simulation research on the semi-active landing-gear control [25]. In 2004, Adams summarized thetesting and analysis used to quantify the expected airbag landingloads for the Mars exploration rovers [26]. The airbag drop-testsetup, landing instrumentation, and the test-data-reduction methodwere discussed to provide an understanding of the empirical loads. Afavorable comparison was made between the empirical data andavailable computational airbag models, boosting confidence in theresults. In 2006, Lernbeiss and Plöch introduced an Multi-BodySystem (MBS)-based landing-gear model and investigated thenumerical simulation of a simple static and dynamic load bycomparing with a finite-element model [27]. In 2009, Kong et al.conducted drop-impact analyses for the landing gear of smartunmanned aerial vehicles using the explicit finite-element code

LS-DYNA [28]. Experimental data were used to revise the impactmodel for the landing gear. Structural particularity and airworthinessspecifications should be considered in the landing-gear drop testof light aircraft. For the light-aircraft landing-gear drop-testtechnology, a test and control system had been introduced by Xueet al. in 2011 [29].

Conclusion demonstrates that Chinese scholars have investigatedvarious aspects of airworthiness drop test, including airworthinesstest systems and dynamics investigation of the adjusting-parametertests. They have some achievements, and they have laid thefoundation for the research and execution of airworthiness tests. Butthere are quite a few reports on the systemic investigation of theairworthiness certification test for civil aircraft, few reports about theapplication of the drop test to amend and verify the drop-simulationmodel, and none about the application of the simulation result toguide the adjusting-parameter test. To meet the requirements of theairworthiness of a Seagull 300 aircraft landing gear, this paper reportsthe systemic investigation of the airworthiness drop test as well aseffective combination between the advanced simulation technologyand the actual engineering needs. The research possesses certainacademic values and engineering application values. And theachievement can be used as the reference of drop test and dynamicsanalysis for light-airplane landing-gear drop test.

II. Drop-Test System

A. Structure of the Test System and Working Principle

The vertical drop-test system consists of the platform system, thelow-friction sliding system, the up and down system, the wheel’sturning-speed system, the impact-platform system, the fixturesystem, and the acquisition system, as shown in Fig. 1.

We must simulate the aircraft landing weight, angle of attack,sinking velocity, forward velocity, wing aerodynamic force, and ratioof the friction between the wheel and the runway at the moment oftouchdown. The drop test is in progress by adapting to theway of freefall. In this test, the effective dropping weight (which consists oflanding gear, fixture, core barrel, and additional weight) is simulatedby the weight of the drop system. The ways to adjust the fixture ofthe landing gear and the height of the drop test are used to simulatethe angle of landing attack and the sink velocity, respectively. Thereverse rotation of the wheel at a preset velocity and the concrete flatare used to simulate the horizontal landing velocity of aircraft and thesurface of the pavement, respectively. The friction coefficientbetween the wheel and the contact flat is varied through modifyingthe toughness of the flat. Meanwhile, the reasonable methods forimitating rotating loads and spring-back drag loads are studiedthrough using different imitation platforms. The research is carriedout under the condition of guaranteeing the friction coefficient.

B. Design of Core Barrel and Sliding Way

The core barrel is connected with the rack by eight tackles, and itsfree sliding along the rack is accomplished through the tackles.

Fig. 1 Drop-test rig for a landing gear.

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Meanwhile, four axles with a diameter of 60 mm are installed underthe big core barrel to increase the balance weight of the landing-gearsystem; thus, the equivalent load exerted on the real landing gear willbe imitated conveniently. The three-dimensional graphic of the corebarrel is shown in Fig. 2.

The free sliding of the core-barrel system is accomplishedthrough the tackles. The sliding way should be of certainsmoothness so that the friction between the core-barrel system andthe sliding way will be decreased fully. Thus, the errors occurred inthe instantaneously sinking velocity of the dropping test will bedecreased, and the test to imitate the sinking velocity in the processof landing will also be enough. Considering the parking problem ofthe core-barrel system, the top as well as the bottom of the slidingway should be stretched so as to park the core-barrel systemconveniently. The three-dimensional graphic of the sliding way isshown in Fig. 3.

The core barrel consists of the framework structure, counter-balance component, guide wheel, and fixed plate for the landinggear. The low-friction sliding way adopts four cylindrical columnswith 180 mm diameter and is fixed at both ends with bearings on thebench column. To ensure the free fall of the drop-test system, the corebarrel is fixed with a concave guide wheel to combine with thelow-friction sliding way. The dimensions of the core barrel are1600 � 1700 � 450 mm.

The verticality of the sliding way is guaranteed by setontechnology in the process of installation. Simultaneously, thecombination between the guide wheel and the sliding way isregulated. Before the formal test, we should make the guide wheelslide along the low-friction sliding way 100 times, and then we needto smear lubricating oil on the surface of the slidingway. It is difficultto measure the dynamic friction between the guide wheel and thesliding way directly. Therefore, we can collocate several pull-pressure sensors around the hook tomeasure the tension subjected tothe guide wheel when it locates at different height. Thus, we can getthe percentage of effective weight loss. The effective weight loss

caused by static friction is less than 5%, and the average loss is 3.7%,as shown in Table 1.

C. Design of the Wheel’s Turning-Speed Mechanism

As the effective diameter of the wheel for aircraft landing gear isrelatively small, the effective way to imitate the horizontal landingvelocity is to improve the rotational speed of the wheel.Simultaneously, it is quite necessary to improve the evacuationspeed to decrease the loss of the wheel’s turning speed.

The wheel’s turning-speed mechanism consists of the hydraulicpressure moving tube, the stent, the dc motor, and the friction wheel,as shown in Fig. 4. The friction wheel is in contact with the wheelthrough the hydraulic-pressure moving tube, and the dc motor drivesthe friction wheel to rotate. Then the friction wheel turns thewheel inreverse. After the tangential velocity of the wheel achieves thedesired speed, the hydraulic-pressure moving tube will shrink, andthe friction wheel will return rapidly.

D. Impact Platform and Measuring System

The impact platform is composed of three layers. As shown inFig. 5, the upper layer filled with concrete is used to simulate the

Fig. 2 Design of the core barrel.

Fig. 3 Low-friction sliding way design.

Fig. 4 Working theory of the wheel’s turning-speed mechanism.

Fig. 5 Measuring flat for a landing-gear drop test.

Table 1 Efficient weight expense due to friction

Height , mm Weight loss, % Height, mm Weight loss, %

100 3.2 152 2.8204 4.2 246 4.0300 5.0 353 3.7410 2.4 452 3.4501 2.9 548 4.3595 4.3 average 3.7

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runway. Four sensors tomeasure heading load are installed alongsidethe upper layer, and the other four sensors to measure side loads areinstalled alongside with the middle layer. The bottom layer issupported by three pillars, and there are vertical sensors in it.There are circular guide grooves that are perpendicular in theinterface. The steel balls are used here to keep point contact andreduce the friction.

The parameters needed to be measured in the drop test are asfollows: the horizontal vertical loads of the wheel, the verticaldisplacement of the wheel center, the axial compression of the bufferand the wheel’s compression. Four load sensors are installed on theforce platform tomeasurewhat can be converted into thevertical loadFz acting on the wheel. Two load sensors and an accelerometer areinstalled alongside the force platform to measure what can beconverted into the horizontal load FX acting on the wheel. A guyeddisplacement sensor is installed between the hanging basket and thepillars to measure the vertical displacement of the hanging basketcenter. An acceleration sensor is installed at the center of the bottomof the hanging basket to measure the acceleration of the hangingbasket (at). A linear displacement sensor is installed at the twoends of the buffer to measure the compression of the threesupported pillars. The sensor-installation schematic diagram isshown in Fig. 6.

E. Control System

The whole control system consists of the hydraulic system, the upand downmechanism, the structure of turning speed, and telecontrol.Just after the drop system is dropped by the electric motor to a presetheight, the hook will be locked. Then the structure of turning speedturns the wheel in reverse and evacuates when the speed of wheelreaches to the preset one. As long as the drop system is ensured to belocated safely, the drop system is dropping down and the test data arecollected.

The drop test is dominated by the Programmable Logic Controller(PLC) control system, which adapts an OMRON CP1H-XA40Dprogramming with CX Programmer version 7.3. The computer isconnectedwithCP1HbyRS232, the type of host link, 9600 baud ratefor the port, 7 bit even parity check. The software of King Viewversion 6.5 is used to monitor the process of the drop test. All I/Os ofthe input and output signals are adapted to the photoelectric isolatingequipment. Thus, the anti-interference ability of the deoxidizationdevice and the electrical circuit inside the controller can be insulated.

The software of King View is used to realize the development ofthe control interface for the drop test, and the prompt communicationwith the PLC control program is also enforced. Correspondingprocesses are used to realize high-precision, good-trackingperformance and a high level of visualization. According to thespecialties of the aircraft landing gear and the requirements ofairworthiness certification, the interface of the control system isdeveloped to meet the requirements on the platform of King Viewsoftware. The adjusting-parameter drop test, the limited drop test,

and the reserve-energy absorption drop test for the light-aircraftlanding gear are accomplished by operating the interface of thecontrol system.

The design proposal of the hydraulic servo system is achievedaccording to the design research of a control system for a landing-gear drop test, which includes the following:

1) The pressure supplement for the system is proposed in view ofthe high pressure supplied for the prototype pump.

2) The actuation time of the executive components is set upjudging by the requirements and the project design of the drop test.

3) The maximum working stroke is determined in view of thereference height of the drop test, the limited dropping height, and thesimulation results.

4) The maximum load of the actuator cylinder is calculatedaccording to theweight of thewheel’s turning-speed mechanism, therequirements of the test, and the contact force between the frictionwheel and the wheel of the landing gear.

The original design parameters are as follows:1) The time of protracting the structure of turning speed is 8–20 s,

and the time of withdrawal is 1–3 s.2) The maximum effective diameter of the actuator cylinder is

24.62 mm.3) The maximum stroke of the actuator cylinder is 400 mm.4) The biggest load is 10,000 N.5) The temperature is �50 to 50�C.6) The pressure of the oil sump tank is 0.15 MPa.The technical index is shown in Table 2.

F. Test System

1. Transient Rotational Speed Test

In the measuring of the rotational speed of thewheel, wewill meetthe following troubles:

1) The structures of different landing gears are compact so that thefix of sensors is limited.

2) The wheel will generate vibration and deformation when itimpacts the platform, and the test requirement should be somehowhigher than ever.

3) The drop-test platform will bring electromagnetic interferenceto the measuring sensors.

On account of these reasons, the rotational speed of the wheelshould be measured by noncontact photosensors and grating trays.Then, the variation curve of the rotational speed of the wheel can bemeasured by time counting. As shown in Fig. 7, as the room of thewheels is compaction, the directed sensor and grating tray are notsuitable to install here, so the reflective sensor is applied and thegrating tray is replaced by the grating patch, which are uniformly

Fig. 6 Sensor-installation schematic diagram.

Table 2 Major technical index of hydraulic system

Name of parameter Technical index

Pump motor 1.5 KWHydraulic pump Pmax � 20 MPa, dextrorotationSystem rated flow Q� 20 L=minControl voltage DC24V

Fig. 7 Measurement of the wheel’s transient rotational speed.

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distributed in the wheel. Then, the transient rotation speed of thelanding-gear wheel will be measured in the counting way.

The turning system turns around the wheel in the oppositedirection to simulate the horizontal velocity of the aircraft, and thehorizontal velocity of the wheel is based on the Eq. (1):

N � 60Vx2�R

(1)

2. Horizontal Load Test

In recent studies, the horizontal and vertical loads are measured bythe drop platform, which is supported by three points. In this paper,the platform is supported by four points and the impact platform isconstituted by three layers. As shown in Fig. 8, the upper layer filledwith concrete is used to simulate the runway. Four sensors tomeasurethe heading load are installed alongside the upper layer, and the otherfour sensors to measure side load are installed alongside the middlelayer. The bottom layer is supported by four pillars, and there arefour sensors in them. There are circular guide grooves that areperpendicular in the interface. The steel balls are used here to keeppoint contact and reduce friction, which applies the upper layersliding along the course and side direction.

After turning, the rotating wheel of the landing gear drops on theplatform and the friction force is produced as the horizontal load ofthe wheel. It is difficult to measure the friction force directly, and theindirect method which is to arrange dynamic force sensors on bothsides of the platform along the course onlymeets. The heading load isshown in Eq. (2):

Fx � p�t� � Fm�t� � Nx�t� (2)

3. Vertical Load Test

The measurement of general loads usually adopts the method ofpasting the strain gauges on the test sample or fixing the force sensorsdirectly on it. However, it is difficult to measure the vertical load ofthe landing gear directly, and so the indirect method is used. Beforemeasurement of the vertical load, we assume that the platform andsteel balls are both rigid bodies. Four sensors are symmetricallyinstalled under the laminate of platform. When the landing gear

drops on the platform, the impact load of the wheel is passed by theplatform and steel balls, and it is gained from the sensors. Theconversion relationship between the vertical load of the wheel andthe load measured by the sensors is based on the theorem of staticforce balance, and Eq. (3) is based on the mechanism mode shownin Fig. 9:

Fy�t� � kygPy�t� � kyaay�t�M1 (3)

4. Axial Compression of Buffer and Wheel Compression

The drop test is to verify whether the buffer system satisfies itscapacity of absorbing energy and thewheel compression satisfies therequirements of design. According to the original parameters of thebuffer pillar stroke and the wheel stroke, a cable-type displacementsensor is installed between the basket and the pillar to measure thevertical displacement h of the basket center, and another sensor isinstalled at the end of buffer to measure the compression � of thebuffer. The wheel’s compression can be obtained from the verticaldisplacement h, the compression �, and the strut front angle of thelanding gear, which is also the angle of attack.

5. Data Collection of Drop Test

The data measured in the drop test are collected by the system ofimpact test data acquisition with 48 channels, concurrent working,100–512kHz frequencies fromNanjingUniversity ofAeronautics andAstronautics. Table 3 is the list of the equipment needed in the droptest.

The parameters needed to be measured in the drop test are asfollows: the horizontal load and vertical load of wheel; the verticaldisplacement of the wheel center; and the axial compression of thebuffer and the wheel compression. Four load sensors are installed onthe force platform to measure what can be converted into the verticalload FZ acting on the wheel. Two load sensors and an accelerometerare installed alongside the force platform to measure what can beconverted into the horizontal load FX acting on the wheel. A guyeddisplacement sensor is installed between the core barrel and pillars tomeasure the vertical displacement of the core-barrel center. Anacceleration sensor is installed at the center of the bottom of the corebarrel to measure the acceleration of the core barrel (at). A lineardisplacement sensor is installed at the two ends of the buffer tomeasure the compression � of the three supported pillars.

wheel Pysensor

N(t)

Fig. 9 Vertical mechanical model of the platform.

Table 3 Measuring instruments and their precision

No. Equipment Type Precision Quantity

1 Collection system DH5927 0.5% 12 Force sensor 5114 0.1% 83 Acceleration sensor DH311 0.1% 24 Displacement sensor DH801 0.5% 25 Speed sensor DH5640 0.3% 16 Electronic scale OCS 2T=0:2 kg 1

Fig. 10 Force diagram of the landing gear’s various parts.

Fig. 8 Measuring flat for landing-gear drop test.

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III. Drop Test and Simulation Underthe Adjusting Parameters

A. Dynamic Model of Landing Gear

In accordance with the characteristics of movement to variousparts, the structuremass of the landing gear is divided into three parts:

the elastic supporting mass, the inelastic supporting mass, and the

rotating mass. By this means, the mechanical model can preferably

imitate the actual condition and simplify the dynamic equation. The

elastic supporting mass is the mass of the upper air spring buffers

including the mass of the fuselage, the wing, and the outer cylinder,

Table 4 Results of formal test under initial parameters

Maximum stroke ofbuffer (S)

Maximum verticalloads FZ

Energy absorption ofsystem (Ac)

Limited vertical loadfactor n

Efficiency factor ofbuffer

Efficiency factor ofsystem

126 mm 17,980 N 1521 J 4.37 64.9% 55.1%

Table 5 Initial parameters of the formal drop test

Drop height H Effective drop weightWe Diameter of main oil hole (dm) Diameter of one-way oil hole (ds) Initial pressure P0 Rolling speed

410 mm 329.8 kg 2.6 mm 1.8 mm 0.6 MPa 1300 rpm

Table 6 Results of auxiliary drop test under initial parameters

Test programnumber

Releaseheight H,

mm

Maximum strokeof buffer (S),

mm

Verticalloads Fz,

N

Energy absorptionof system (Ac), J

Limited verticalload coefficient n

Efficiencycoefficient ofbuffer, %

Efficiencycoefficient ofsystem, %

1 250 96 14,769 989 3.56 62.1 52.32 300 99 15,342 1159 3.73 67.5 59.03 350 106 17,520 1532 4.26 64.5 54.4

Fig. 11 Energy absorption of the buffer.

Fig. 12 Simulation results of the energy absorption.

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which is the mass supported by the air spring. The elastic supportingmass is themass of the lowair spring buffers including themass of thepiston cylinder, the brakes, and the tire, which is the mass supportedby the nonair spring. The rotating mass is part of the nonelasticsupport quality, which includes themass of thewheel and the rotatingpart of the brake apparatus.

The stress states of the wheel, the inner cylinder, and the outercylinder are shown in Fig. 10. The interaction between the bufferpillar and the wheel forms a commonly used two-mass model. Thefollowing assumptions are contained in the model:

1) All the forces of the landing gear are exerted within the verticalplane of the landing gear.

2) The elastic supporting mass can be idealized as rigid bodiesconcentrated near the trunnion.

3) In addition to the horizontal deflection of the buffer pillar, theother deformations of the structure are ignored.

1. Motion Equations of System

Coordinate System: Here, the coordinate refers to the localcoordinate system, which is moving along with the mass. The originof the coordinate is located at the mass centroid. Based on theassumption, the centroid of the inelasticity supporting mass islocated in the landing-gear axle. The Z coordinate’s positivedirection is vertically downward, and the X coordinate isperpendicular to the Z coordinate. The reverse course is referencedas the positive direction.

Motion Equations of Wheel Rotating Stage: This is thesynchronous motion stage of the elastic supporting mass and theinelastic supporting mass (only the wheel is compressed, whereasthe buffer pillar is not). The horizontal gliding speed of the wheel is

_" X �� _Xm � �R� �=3�!� VX (4)

At the buffer compression stage (while the tire continues tocompress), the horizontal motion equation of concentrated massretains the same, while the vertical motion equation is shown inEq. (5):

�Z M � g �FSM

cos�n �Nu � NlM

sin�n �L

M(5a)

�Z m � g�Ft � Fzm

(5b)

ZM � S cos�n � Zm (5c)

Motion Differential Equation of the Rebound Stage:

�X U ��Nt�R� ���R � �=3�Im �m�R� ���R � �=3�

(6a)

_!� Nt�R � ��Im �m�R� ���R � �=3�

(6b)

2. Stress Analysis of Buffer Pillar

The stroke of the buffer (S) is zero:

FS � �m �Xm � Fx� cos�n � �m �Zm � Fz �mg� sin�n (7)

Table 7 Contrast between results of simulation and test

System performance Maximum stroke ofbuffer (S), mm

Maximum verticalloads FZ, N

Energy absorption ofsystem (Ac), J

Efficiency factor ofbuffer, %

Efficiency factor ofsystem, %

Result of simulation 126.0 18,590 1885 65.8 53.6Result of test 126.0 17,980 1721 64.9 55.1Deviation of two results 1.5 3.4 9.5 1.9 3.5

Fig. 13 Simulation model for optimization.

Fig. 14 Iteration history of optimization.

Table 8 Energy absorbed by the buffer system corresponding

to different parameters

Diameters of themain oil hole(dm),mm

Diameters ofone-way oilhole (ds), mm

Initial pressureof the buffer(P0), MPa

Energyabsorption ofthe system(Ac), J

3.4 1.8 0.6 19433.8 1.8 0.6 19734 1.8 0.6 19882.6 2 0.6 19243 2 0.6 19483.4 2 0.6 19743.8 2 0.6 20024 2 0.66 20144 2 0.62 20124 2 0.64 20114 2 0.68 20074 2 0.7 2006

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The stroke of the buffer (S) is larger than zero:

FS � PhA1 � Pa�A2 � A1� � Ff (8)

The buffer stroke (S) equals the mechanism stroke:

FS � Fa � Ff � Fl (9)

whereFa can be calculated from Eq. (9) The chamber volume can becalculated by subtracting the result, which is the gas pressure beingmultiplied by the area from the initial volume of structural itinerary.

3. Oil Damping Force

The oil damping force is produced due to the pressure differencecaused by the flow of hydraulic oil through both ends of the hole. Thecalculation formula of oil damping force is shown in Eq. (10):

Fh ��A3

h

2�CdA0�2_Sj _Sj (10)

4. Air Spring Force

The air spring force is determined by the initial pressure, the areacovered by the gas pressure and the instantaneous compression ratio.The calculation formula of oil damping force is shown in Eq. (11):

Fa � Aa�P0

�V0

V0 � AaS

�n

� Ps�

(11)

5. Internal Friction Force

The friction emerged at the collar between inside and outside of thebuffer cylinder is only taken into consideration. The calculationformula of oil damping force is shown in Eq. (12):

Ff � ��ujNuj � �ljNlj� (12)

6. Stress Analysis of the Wheel

The wheel suffers the vertical reaction force from the ground. Thecalculation formula of oil damping force is shown in Eq. (13):

Fz � NK�Zm � NC� _Zm (13)

B. Dynamic Simulation Under Adjusting-Parameter Drop Test

1. Analysis of Simulation and Test Under Initial Parameter

The results of the initial drop test and the adjusting-parameter droptest are shown in Tables 4 and 5. Comparing the shock-absorbingperformance parameters of the initial drop test with that of theadjusting-parameter drop test on the requirements of shock-absorbing capacity, we can find that the energy absorbed by the

buffer system and the maximum stroke of the buffer are less thanthe requirement; the maximum vertical load of wheel is larger thanthe requirement (15,362 N); and the limited vertical load coefficientis larger than the requirement. According to the analysis of theinfluence of buffer parameters toward the shock-absorbingproperties, the following adjustments should be done: 1) enlargingthe oil hole of the buffer, and 2) enhancing the initial pressure of thebuffer. The results of auxiliary drop test are shown in Table 6 andFig. 11. According to the maximum strokes of the buffer and themaximum vertical loads at different heights, it can be deduced thatthe maximum stroke of the buffer and the maximum vertical load ofthe wheel can meet the requirements when it is released at the heightof 410 mm.

Figure 12 is the dynamic simulation results of the energyabsorption. Figure 12a is the energy absorbed by the buffer.Figure 12b is the energy absorbed by the buffer system. Contrastbetween results of simulation and test has been listed in Table 7. Asshown in the table, the maximum vertical loads in simulation is 4.5%higher than in the test; deviation of the maximum stroke of buffer is1.5%; and the deviation of energy absorbed by system is 9.5%.Considering that the error of themodel is quite small, it can be used inparameter-optimization analysis.

On the basis of the virtual prototype of the landing gear, the droptest under initial parameters has been simulated. The initial conditionparameters including the drop height, the rolling speed, and the initialair pressure are set as shown in Table 7. The friction coefficientbetween the wheel and the platform is defined by the �z � � curve,and the elastic constant of the wheel is defined by the kT � � curve.The two curves are all measured from the test. The friction factorbetween the inner barrel and the piston rod of the buffer is set at 0.11,which is the calculated test result.

2. Optimization Model for Buffer Parameters

The appropriate allocation of the buffer parameters should befound to meet the design requirements. Actually, we optimize theshock-absorbing performance on the basis of adopting the bufferparameters as design variables. The model of optimization isdescribed as follows: 1) objective function (energy absorption of thebuffering system, Ac), and 2) design variables (dm, ds, four one-wayholeswith same diameters, andP0). Considering the actualminimumadjustmentmount of the initial pressure of the buffer and the diameterof the main oil hole (dm), we regulate dm, ds, and V0 as discretevariables. The step sizes ofdm andds are all 0.2mm.And the step sizeof P0 is 0.02 MPa.

Table 9 Optimization results of the buffering performance

dm ds P0 Smax FZ n nn t Ac

4.0 mm 2.0 mm 0.66 MPa 153 14675 4.39 3.56 0.38 s 2014 J

Fig. 15 Optimized energy absorption.

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The constraint functions are Smax, Fz, nn, and t, which aremathematical expressions of the optimization model on shock-absorbing performance. The aforementioned functions are shown inEq. (14):

8>>>>>><>>>>>>:

Smax � 156:3 mm

Pz � 15362 N

n � 4:42

t � 0:8 s

maxAc�dm; ds; V0�

(14)

According to the results of the initial drop test, we can concludethat the diameters of the oil holes and the initial pressure of the buffershould be enhanced. Combining with the practical experience, therange of design variables is determined, as shown in Eq. (15):

dm 2 �2:8; 3:0; 3:2; . . . ; 5:2� ds 2 �1:8; 2:0; 2:2; . . . ; 3:6�(15)

P0 2 �0:60; 0:62; 0:64; . . . ; 0:80�

3. Optimization Analysis of Shock-Absorbing Performance in LMS

Virtual.Lab Software

Design variables and the response function are set in thesimulationmodel; the range of designvariables are added as shown inEq. (15). Variation ranges of the constraint function are applied, andthe objective function is set as maxAc. The simulation model foroptimization is established as shown in Fig. 13. The optimization iscarried out through software, and the iteration process is shown inFig. 14. The curve shows that the objective function that representsthe energy absorbed by the buffer system is increasing greatly. Partsof the objective functionvalues corresponding to the designvariablesare output during the iterative process, which are shown in Table 8.

The results of the optimization, design variables, values ofconstraints, and objective functions are shown in Table 9.We can seethe shock-absorbing performance has been further enhanced. Theoptimized energy-absorption curves are shown in Fig. 15. The curvesare much better than the initial ones, which are the simulation resultsunder initial parameters. It indicates that the buffering performancehas been improved.

4. Drop Test with Optimized Buffer Parameters

Other parameters, such as rolling speed, release height, andeffective drop weight are kept the same as the parameters listed inTable 6. Test procedures are also kept the same as that in the initialtest. The auxiliary drop test is done at first. The drop heights are 200,250, 350, and 380 mm in turn. Attention should be paid in the test;before each test, the landing gear should be hung in the air for morethan half an hour to ensure that the oil and gas are separatedadequately, and the pressure in the buffer should be kept the sameduring each test. The results of the auxiliary drop test are shown inTable 10, and the shock-absorbing capacity is listed in the appendeddrawing. According to the results, we can concludewhen the landinggear is released at the height of 410 mm in the drop test, the maxi-mum stroke and the maximum vertical load can meet the designrequirement.

The auxiliary drop test has verified the security of the test. Thelanding gear should be hung for half an hour before the formal test.The capacity curves of the buffer and the system are shown in Fig. 16.The capacity curve of the buffer has four humps, which are the sameas that in the initial test. The curve is much better than the initial one.It indicates that the buffering performance has been improved. Thecalculated buffering parameters are listed in Table 10. The data showthat the maximum stock of the buffer is increased, the maximumvertical load is reduced, and the energy absorbed by the system isslightly less than beforewhen compared with the results of the initialtest. As a result, the following modifications should be done:1) enlarging the oil hole of the buffer, and 2) enhancing the initialpressure.

5. Buffer Parameter Optimization with the Pulleys-Sliding Friction

Taken into Account

The coefficient of friction between the wheel and the sliding waycauses an average loss of 3.7% in acceleration. The average loss ofacceleration is taken as the loss of acceleration at random time. Thus,we can compute that the drop height should be increased to 427 mmto keep the sink rate atVy � 2:84 m=swhen thewheel touches down.

There is no loss of sink rate in the simulation without the additionof thewheel-sliding way friction coefficient. It results in a little error;thus, the model should be modified. The specific methods arekeeping the drop height at 410mm and setting the acceleration of thefalling body as 9:8 � �1–3:7%� � 9:44 m=s2 with the friction being

Table 10 Results of the drop tests with 4 mm main oil hole

Maximum stroke ofbuffer (S)

Maximum verticalload FZ

Capacity of buffersystem (Ac)

Limited vertical loadcoefficient nn

Efficiency coefficient ofbuffer (�s)

Efficiency coefficient of thebuffer system (�)

152.9 mm 15,789 N 1841 J 3.83 64.6% 56.8%

Fig. 16 Energy capacity of drop tests with 4 mm main oil hole.

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taken into account. The results of the simulationwithmodifiedmodelare shown inTable 11. The table shows that the error of the simulationresults is less than 8%, and so the model is sufficiently accurate. Thenext step for optimization can be taken.

The optimization results are listed in Table 12, which shows thatshock-absorbing performance has a further improvement. Thecapacity curves shown in Fig. 17 are very similar to the test with amain oil-hole diameter of 4.0 mm, and the curves are much betterthan the initial ones.

C. Results of Adjusting-Parameter Drop Test

The drop test has been done three times based on theaforementioned simulation results. In the test, the drop height isincreased to 427mm, the diameter of themain oil-hole is 4.2mm, theinitial pressure of the air cavity is kept at 0.7 MPa, and the other

parameters are kept the same. Attention should be paid in the test;before each test, the landing gear should be hung in the air for morethan half an hour to ensure that the oil and gas are separatedadequately; and the pressure in the buffer should be kept the sameduring each test.

The capacity curve of the second test is shown in Fig. 18, which issimilar to the ones with the main oil-hole diameter of 4.0 mm. Thecurves also present four peaks, and the buffer compressionscorresponding to the peaks are almost consistent. They are preferablewith the optimum parameters. In the capacity curve of the buffer, thechange of the load is smooth at the maximum axial force point (at thesecond peak). In the capacity curve of the system, the change ofthevertical load is smooth at the second and thirdfluctuation. The testresults with optimum parameters are recorded, which are shown inTable 13.

Table 11 Simulation result of buffering performance

dm ds V0 Smax Fz n nn t Ac

4.2 mm 2.0 mm 0.70 MPa 152.7 mm 14,226 N 4.40 3.45 0.71 s 2008 J

Table 12 Contrast between results of test and simulation with modified model

System performance Maximum stroke of buffer (S) Maximum vertical load Fz Energy absorption of system (Ac)

Simulation result 158.2 mm 15,480 N 2014 JTest result 152.9 mm 15,789 N 1841 JError between results of test and simulation, % 3.5 2.2 9.4

Fig. 17 Energy absorption of drop tests with 4.2 mm main oil hole.

Fig. 18 Energy absorption with optimal parameters.

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Table 13 Test results with optimum parameters

Serial number Item First Second Third Average value

1 Stroke of buffer (S), mm 155.6 157.6 155.2 156.12 Vertical load Fz, N 15,283 15,324 15,522 15,3093 Energy absorbed in system (Ac), J 1964 2013 1972 19834 Efficiency of buffer 70.7 69.2 64 67.95 Efficiency of system 55.3 59 55.3 56.5

Table 14 Drop parameters for the limited drop test

Drop height Theoretical drop weight Theoretical drop work Rolling speed

0.4108 m 325.0 kg 1967 N m 1366.5 rpm

Table 15 Result of the limited drop test

Stroke ofbuffer, mm

Verticalload, N

Vertical loadfactor

Testingcapacity, J

Error ofcapacity, %

Efficiencyof buffer, %

Efficiencyof system, %

Friction coefficientof platform

152.9 15,789 3.9 1841 �6:4 64.6 51.8 0.62155.8 14,996 3.6 1985 0.9 69.2 59.0 0.71158.0 16,766 4.1 1884 �4:2 64.0 55.3 0.55

Fig. 19 Energy capacity of the drop test.

Fig. 20 Energy capacity of the reserve-energy absorption drop test.

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IV. Limited Drop Test

According to the certification of airworthiness, drop parametersfor the limited drop test of the Seagull 300 are shown in Table 14.After the drop test is repeated three times, the test data are collectedcomprehensively. The result is shown in Table 15. Analysis suggeststhat consistency of the result is relatively superior. The drop test isaccomplished.

The limited drop test has been repeated three times for theHO300 nose landing gear. The buffer’s capacity and the system’scapacity of the limited drop test are shown in Fig. 19. FZ is thevertical load, and FX is the horizontal load. As can be seen from thebuffer’s capacity of the limited drop test, the axial load of the bufferhas a similar trend in the repeated tests. The peak exists four timesin the first compression, and the maximum value exists at thesecond peak, which is about 70 mm off the stroke. The maximumpeak is caused by the increase of the buffer-damping force. Fromthe system’s capacity of the limited drop test, we can also find thesimilarities. With the declining of the center of gravity, themaximum vertical load exists at the second peak, which is causedby the increase of the buffer’s axial force. The experimental resultsagree with the expected results of the theoretical analysis, whichsatisfies the airworthiness requirements.

The sample is examined after the test, and there is no permanentplastic deformation. This result indicates the strength of the landinggear meets the design requirements. As can be seen from Fig. 20, theconsistency of the three tests is rather high. The following conditionsare all satisfied: the buffer efficiency is more than 60%, and thesystem efficiency is more than 50%. The limited drop test meets theairworthiness standards, the experimental results meet the designrequirements, and the limited drop test gets through the airworthinesscertification.

V. Reserve-Energy Absorption Drop Test

The reserve-energy absorption drop test has been repeated twotimes for the Seagull 300 nose landing gear. The buffer’s capacity andthe system’s capacity of the reserve-energy absorption drop test areshown in Fig. 20. As can be seen from the buffer’s capacity of thereserve-energy absorption drop test, the axial load of the buffer hassimilar trends in the repeated tests. The peak exists three times in thefirst compression, and the maximum value exists at the first peak,which is about 80mmoff the stroke. Themaximumpeak is caused bythe increase of the buffer-damping force. From the system’s capacityof the reserve-energy absorption drop test, we can also find thesimilarities. With the declining of the center of gravity, themaximumvertical load exists at the first peak, which is caused by the increase ofthe buffer’s axial force. This result indicates the strength of thelanding gear meets the design requirements, and the consistency ofthe three tests is rather high. The following conditions are satisfied:the buffer efficiency is more than 65%, and the system efficiency ismore than 55%. The system’s capacity of the reserve-energyabsorption drop test satisfies the airworthiness requirements. Dropparameters for the reserve-energy absorption drop test of Seagull 300are shown in Table 16. After the drop test is repeated twice, the testdata are collected comprehensively. The result is shown in Table 17.Analysis suggests that consistency of the result is relatively superior.

According to the relative provisions of airworthiness, the censorsreview the test materials and the test equipment calibration certificateas well as the test personnel qualifications certificate and examine thetest pieces and the manufacturing compliance of the test equipments.The aforementioned items all satisfy the airworthiness requirement.The installation of the test pieces is examined, which meets therequirement of the test programs. The limited drop test and thereserve-energy absorption drop test are performed successfully, andthewhole process was witnessed. This itemmeets the requirement ofthe test programs. The test records are checked, and it is complete.The test data-processing method is examined, and it is reasonable.After the test, the applicants of the airworthiness test complete thetest report and submit it to the airworthiness authorities. Then, we getthe conclusion: the airworthiness certification test is in line with theprovisions of the ordinance, and the test results meet the designrequirements. The airworthiness certification for the drop test of theHO300 nose landing gear is approved on 11 July 2011.

VI. Conclusions

A drop-test rig is developed for the landing gear of a lightmultifunctional amphibious airplane based on its drop-testspecifications. The system can realize accurate measurement andconduct the light-aircraft drop test with high-speed belt turn.Simultaneously, several key technologies including the schematicdesign of the light-aircraft drop test, the control-system design for thedrop test, high-speed turn of the wheel, accurate lifting of the dropsystem, design of the measuring platform, and imitation of therunway have been accomplished. The test shows that the test systemis secure and reliable, which can be applied for the landing-gear drop-test of other light airplanes.

According to the requirement of China Civil Aviation RegulationsOrder No. 132 (CCAR-23-R3) and drop-test outline for the Seagull300 light multifunctional amphibious airplane, the adjusting-parameter drop test, limited drop test, and the reserve-energyabsorption drop test of the nose landing gear are accomplished. Thedrop test with initial parameters is executed on the base of the drop-test system, and the uncertain parameters including the initial shock-absorbing performance and friction coefficient are obtained in thesimulation. The adjusting-parameter process will not stop beingrepeated until we get the optimal parameters. Finally, we obtain thebuffer-parameters configuration that meets the design requirements.The optimized configuration parameters of the buffer are adjusted asfollows: enlarging themain oil hole from2.6 to 4.2mm, enlarging theone-way hole from 1.8 to 2.0 mm, and enlarging the initial pressurefrom 6.0 to 7.0 MPa. All testing results show that the limit load islower than the design load and the landing gear could bear thereserve-energy absorption drop test. Moreover, the test results can beused as the certificate of the airworthiness for this airplane.

Acknowledgments

This work is supported by the operating expenses of basicscientific research project (number NS2012081) and the Foundationof Graduate Innovation Center (number KFJJ20110201) in NanjingUniversity of Aeronautics and Astronautics.

Table 16 Drop parameters for the reserve-energy absorption drop test

Drop height Theoretical drop weight Theoretical drop work Rolling speed

0.5916 m 305.1 kg 2427 N m 0 rpm

Table 17 Result of the reserve-energy absorption drop test

Stroke of buffer, mm Vertical load, N Vertical load factor Testing capacity, J Error of capacity, % Efficiency of buffer, % Efficiency of system, %

153.0 18,897 4.60 2442 0.6 71.3 58.4153.6 19,135 4.67 2373 �2:2 71.2 59.8

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