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Aircraft landing gear simulation using multidomain modeling technology

LI MING, HAO XIANG-YU, HAN XUE-FENG, JIA HONG-GUANGChangchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences ChangchunJilin 130033China

e-mail: [email protected]

AbstractIn order to accurately analyze the performance and

influence of landing gear system, this paper presents a high

fidelity plant model of an aircraft landing gear to inclusion into

a full aircraft flight simulation. The use of domain specific

modeling software enables detailed modeling of the physics

and facilitates accurate computational simulation of the flight

dynamic, aerodynamic, landing gear dynamic and mechanical

loads that occur when the landing gear are deployed and

retracted during landing and take-off operations. The

parameter design space is easily searched by considering anumber of different landing scenarios including touching down

on one wheel first, to optimize the design. The simulation

results show that the aircraft landing gear system

mathematical model established appropriately reflects the

change of force and moment in the process of taking off and

landing, and it is improve the precision of flight simulation.

Keywords- Landing gear system;flight simulation;multipledomain modeling and simulation;taking off and landing

I. INTRODUCTION

To efficiently employ models for design purposes, it isimportant to capture the physics of the envisioned realization

in as much detail as possible so the design is an accuratereflection of the eventual product. The challenge of themodeler then is to identify and capture a sufficient level ofdetailed dynamic behavior while maintaining computationalperformance. Using general purpose modeling languages tocapture the complexity of such detailed model proportion isdifficult because of the generic concepts that have noimmediate bearing on the domain in which the system underdesign operates. SimMechanics[1,2] is a tool that isdedicated to modeling multi-body systems, for which itincludes specific language elements such as bodies that canbe connected by different types of joints, a variety ofconstraint drivers, and the like. This allows the modeling of amulti-body system to proceed using semantic notions that are

closely related to the specific domain, and the model willclosely reflect the topology of the physically connectedelements.

This paper presents the use of multi-domain modeling forthe study of aircraft landing gear. In particular, mechanicaland aerospace-specific model parts are designed andintegrated into a comprehensive model of the landing gearbehavior. A scenario where the aircraft lands on one wheelset first is analyzed in terms of applied forces required toperform this maneuver safely and effectively.

II. LANDING GEAR CAD MODEL

Modeling of mechanical systems and components oftenstarts with CAD tools. These tools are useful for specifyingthe detailed three-dimensional (3-D) mechanical design of acomponent. Often, different software packages are used foreach step of this process, making it difficult to move frommechanical 3-D modeling to control design and then from

control design to a system level simulation. This paperintroduces a streamlined workflow that enables quick andeasy transition from mechanical 3-D modeling to controldesign and then to system level modeling and simulation.

The landing gear is constructed of four links: a verticalstrut, two bracing links, and a sprung extension (shockabsorber). Joints are analogous to physical connections likehinges, slots, and ball and socket connections. For thelanding gear, the links connect to the airframe and to eachother through revolute joints, which are directly analogous tohinges. These revolute joints are all aligned to rotate aboutthe axes parallel to the longitudinal axes of the airframe.

Mechanical design of mechanical components istypically done using a CAD tool such as UG or

Pro/ENGINEER. Fig.1 shows the landing gear CAD model.As Fig.1a shows, the main landing gear designed in UGrepresents a well-known mechanical construct, the four-barlinkage. Fig.1b shows a Pro/ENGINEER assembly of a four-bar linkage corresponding to the described configuration ofthe landing gear for motion simulation.

a) UG model

vertical strut bracing links

actuator

absorber


actuator

absorber


actuator

absorber

2011 International Conference of Information Technology, Computer Engineering and Management Sciences

978-0-7695-4522-6/11 $26.00 2011 IEEE

DOI 10.1109/ICM.2011.135

279


978-0-7695-4522-6/11 $26.00 2011 IEEE

DOI 10.1109/ICM.2011.135

279


978-0-7695-4522-6/11 $26.00 2011 IEEE

DOI 10.1109/ICM.2011.135

279

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b) Pro/ENGINEER model

Fig.1 Landing gear CAD model

III. LANDING GEARSIMMECHANICSMODEL

Instead of manually constructing a dynamic model from

SimMechanics blocks, the engineer would simply initiate theconversion process of the CAD file to generate the dynamicmodel automatically. In addition to significantly simplifyingthe workflow, this enhancement would eliminate thepotential errors that system engineers or control engineerscould make when manually creating a dynamic model fromthe CAD assembly.

To create a SimMechanics model from this assembly it isnecessary to download and install Pro/ENGINEER-to-SimMechanics Translator. The translators automaticallyexports Pro/ENGINEER assemblies into SimMechanicsmodels[3]. Once this free software is installed, it is possibleto generate a textual description of the assembly that lists themass properties for each body and the characteristics of each

joint defined in the Pro/ENGINEER assembly. Once thePro/ENGINEER assembly has been saved as aSimMechanics XML file, it is possible to automaticallycreate a SimMechanics model out of it. The resultingSimMechanics model with blocks rearranged andbackground colors added for easier understanding is shownin Fig.2. The built-in SimMechanics visualization is usefulfor understanding the behavior of the modeled mechanisms.

Fig.2 Landing gear SimMechanics model

IV. LANDING GEAR DYNAMICS

Once a SimMechanics model has been obtained from theassembly, additional accuracy can be attained by tuning themodel from the actual system that is being modeled[4,5].This is especially important when combining models ofphenomena such as the normal force exerted by the groundand the friction on the tires with detailed physical models.

A. Ground Normal Force

For simplicity, assume that the strut is parallel to theairplanes body zaxis, the tires local z-coordinate is givenby:

31 32 33( ) ( ) ( )L L B B B B B B

g c g c g c g cz z C x x C y y C z z= + + +

The tires coordinates in body axes are( , , )B B Bg g gx y z , and

the coordinates of the CG in body axes are( , , )B B Bc c cx y z .

The compressive force in the strut depends on the total

gear displacementB

gz . The difference between the

uncompressed and compressed tire locations isB

gz .

31 32

33

( ) ( )L L B B B Br c g c g cB B B Bg g g g

z z C x x C y yz z z z

C

+= =

Because the strut is damped, the force also depends on

the rate of landing gear displacement. The displacement rateis given by:

33/B

Lg cz z C

=

A simple model for landing gear displacement force is toassume a linear damped elastic strut, and ignore the tirecompression. Then, the compressive force in the strut is:

stru gt

B

BgzF zK C

= +

where K and C are the spring and damping constants forthe strut. The strut force acts along the axis of strut; however,the force exerted by the ground acts vertically upward. Thevalue of the total ground normal force is the value where thecomponent along the strut axis is the strut force.

33/n strut F CF=

B.

Friction Force

A tire makes sense to resolve the friction force into aforward rolling friction and a sideward sliding friction. Thispaper assumes that the plane of the tires is parallel to thebody x-z-plane. The velocity of the tire in body coordinatesis the velocity of the CG plus contributions due to angularrates.

The friction force in the sideward direction is given byEquation

/ | |

( ) | |

g k k n g k

s

g s n g k

v V F v V F

sign v F v V

>=

The forward force calculation resembles to the sideward

force calculation./ | |

( ) | |

g k k n g k

f

g s n g k

u V F v V F

sign u F v V

>=


actuator

absorber


actuator

absorber


actuator

absorber

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One complication seen with forward force calculations isthe possibility of braking. Braking changes both thethreshold velocity and the kinetic friction coefficient.

, , ,

, , ,

( )

( )

k k roll b k slide k roll

k k roll b k slide k roll

V V V V

= +

= +

V. ANALYSIS OF LANDING GEAR DURING LANDING

The obtained SimMechanics model of the landing gearcan be incorporated into a flight simulation[6,7]. Fig.3 showsa SimMechanics model for the main landing gear. Fig.4shows a flight simulation model for the aircraft. Anadditional wind gust was modeled to inject a roll momentinto the aircraft close to landing. This was achieved bysimply applying a moment about the x-axis of the vehicle(roll) at a specific time and duration just prior to landing.Fig.5 shows the resulting measurements for the landingsimulation.

3

GearPos

2

dz

1

WoW

3

Actuator

2

Conn2

1

Conn1

bearing load

Wheel Force

VerticalStrut

SprungedExtension

B F

Revolute4B

F

Revolute3

B F

Revolute2

B F

Revolute1

Joint Spring & Damper

Joint Sensor3

ap

Fr

Joint Sensor2

ap

Fr

Joint Sensor1

Force Actuator

98

Constant2

10000

Constant1

BracingLink2

BracingLink1F_rmlg

Ang_pos_rmlg

GearPos_rmlg

BearingLoad_RMLG

Fig.3 Main landing gear SimMechanics model

UAV Flight Dynamics Model

1

PlantData

ctrls

XePosLLA

Xe2LLA

SimMechanics6 DoFFlight

E CU c md F M

Propulsion

1/mass

NonGravityAccels

ModelBus

Landing Gear

[ActBus]

[AeroBus]

[AeroBus]

[ActBus]

mEnvData

FCScmd

PlantData

FM

Aero

Actuator

Aerodynamic

4

EnvData

3

LGcmd

2

ECUcmd

1

FCScmd

Ve

Xe

phi_theta_psi

DCM

Vb

pqr

pdot_qdot_rdot

Accels

Fig.4 Flight simulation model for the aircraft

158.5 159 159.5 160 160.5 1610

0.005

0.01

0.015

0.02Landing gear compession

time/s

Compression/m

158.5 159 159.5 160 160.5 1610

1000

2000

3000Landing gear wheel force

time/s

Wheelforce/g

158.5 159 159.5 160 160.5 1610

5000

10000

15000

Bearing load

time/s

Bearingload/N

Left main landing gear

Right main landing gear

Nose landing gear

Fig.5 Results for landing gear simulation

VI. SUMMARIES

The paper presented a method for utilizing CADassemblies of mechanical components for creation ofdynamic models, multi-domain modeling, and systemsimulation. The value of the proposed approach is in thesimplified model development, reuse of CAD assembliesdeveloped by mechanical engineers, and better

understanding of component and system dynamics throughrealistic animation. The domain specific models enabledetailed modeling of physical phenomena. The resultingmodel used the modified block to integrate different domainspecific models and the resultant model was used to quicklysearch the parameter design space.

REFERENCES

[1]

Wood, G. D., and Kennedy, D. C., Simulating Mechanical Systems inSimulink and SimMechanics[R], The MathWorks, Inc., Natick, MA,2003.

[2]

SimMechanics, SimMechanics Users Guide[M], The MathWorks,Inc., Natick, MA, 2010.

[3]

Pro/ENGINEER to SimMechanics Translator, Software Package[M],The MathWorks, Inc., Natick, MA, 2010.

[4]

Flugge, W. Landing-Gear Impact [R] NACA TN 2743. WashingtonDC, USA: National Aeronautics and Space Administration, 1956.

[5]

Ned J Lindsley. A New Tire Model for Aircraft Landing GearDynamics [D]. USA: The University of Akron, 1999.

[6]

LI Ming; JI Yong; JIA Hong-guang; XU Zhi-jun. Hardware-in-the-loop simulation for aircraft based on rapid simulation prototype,Optics and Precision Engineering [J], 2008,16(10)

[7]

Baarspul, M., A Review of Flight Simulation Techniques [J],Progress in the Aerospace Sciences, Vol.27, No. 1, 1990, pp. 1-120.

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