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SIMPACK»News, November 2008

» APPlICAtIoN

Prashant Khapane, INTEC

Simulation of Landing Gear Dynamics using SIMPACK

Fig. 1: SIMPACK as a virtual test-bed

Fig. 2: Slip-optimised braking algorithm

Fig. 3: Landing gear vibration modes

In a variety of mechanical systems fric-tion induced vibrations are a major concern. the aircraft landing gear is by nature a complex multi-degree-of-free-dom dynamic system. It may encounter various vibration modes which can be induced by brake frictional character-istics and design features. these brake induced oscillations can lead to very high loads in the landing gear and brake structure which may result in passenger discomfort and sometimes even component failure.

Along with the serious fore and aft oscillations of a landing gear, often referred to as gear walk, and shimmy, other vibrations in aircraft landing systems are not only annoying and disconcerting but can also affect the stability of the aircraft during take-off, landing, and rolling. Although equa-tions for representing various parts of a landing gear are well established, solving the problems manually with mathematical programs can be slow and laborious. Simplifications made to reduce problem size may introduce in-accuracies such that a design modifica-tion to correct a problem in one area causes unforeseen vibration in other parts of the structure.

INtroduCtIoN

Originally, Multi-body Simulation (MBS) software was designed for the analysis of purely mechanical rigid

body systems, sometimes added by force laws from other fields such as hy-draulics or electronics, mostly included as source code. Since rigid body MBS is not relying on the exact structure and geometry of its components its main applications were principle dynamic in-vestigations in the early development phase of a project. Today the request for the features of MBS-software is much more demanding. Modern MBS-software packages enable interdiscipli-nary modelling and analysis, either by user enhancements of the MBS func-tionality or via interfaces to other CAE tools or both. As a rule, the individual extensions of MBS programs are well adapted to the needs of MBS compu-tation but limited in their facilities and performance. Interfaces to other CAE software on the other hand not only offer the entire possibilities and func-tionality of proven software tools but widely reduce the modelling effort as most of these models already exist, e.g. for CAD drawings or FEA stress analysis only appropriate conversion is needed. Computer Aided Engineering (CAE) tools such as Flexible Multi-body Meth-ods are an excellent test-bed for mod-elling a landing gear and complete air-craft system, see Fig.1. Since the MBS tools such as SIMPACK are modelled as an open system they can accept inputs from many other standard software tools such as Matlab etc. With the help of these sub-modules one can simulate important ground manoeuvres in the

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Prashant Khapane, INTEC

Fig. 5: Effect of mechanical trail

Fig. 6: Shimmy Analysis

Fig 4: Complex ground manouvre

pre-design phase to save high costs of flight-tests. Clearly MBS is the favoured tool for analysis of the dynamics of the landing gear and brake system. It also allows concurrent engineering with other Computer Aided Engineering (CAE) tools such as Nastran which ensures ac-curate modelling for the purpose.

ModellINg lANdINg geAr IN SIMPACK

In SIMPACK this multi-body system is represented by rigid body elements such as main-fitting, the shock tube, and two or four wheels, respectively. The shock absorbers (oleo) are located between the shock tube and main fit-ting. All landing gears have one trans-lational degree of freedom for the shock absorber and one rotational de-gree of freedom for each wheel.

The main landing gears may have an additional bogie attached to the shock tube with a rotational degree of free-dom along the y-axis with 4 wheels at-tached to it. To model landing gears of large aircraft such as A380 main land-ing gear which has 6 wheels, a bogie, and a pitch trimmer in addition can be more complex. To model the system successfully one needs to define prop-er force elements to simulate the be-haviour of the system. SIMPACK has a built-in library of many force elements and it is also possible to write so called user-routines which gives additional freedom to model different systems. Force elements apply external or inter-nal forces and torques in the system. They may depend upon the state of the system, e.g. the distance between two points, and upon time. Force elements do not affect the degrees of freedom of the system, but may introduce addi-tional states, or boundary conditions, to the differential equation system of the MBS model. The force elements describing the landing gear characteristics have been modeled in detail for this work by means of so-called user-routines in SIMPACK. While the equations of the physical phenomena as such are valid independently from the exact aircraft type and can be taken from standard textbooks the parameters for the force elements are usually proprietary. It is also possible to model individual body elements in a tool like NASTRAN and then import it in SIMPACK using the

interface FEMBS [3].For transport aircraft the main task of vertical energy dissipation is almost ex-clusively taken over by an oleo-pneu-matic shock-strut. This device combines a gas spring with oil and additional friction damping [1]. Damping force is provided by oil flow forced through an orifice by vertical strut motion. Often the oil flow is “controlled” by means of a metering pin. The gas spring is represented by a law of polytropic expansion as with spring force. The properties of the passive damper are determined by the laws describing the flow of a viscous fluid, e.g. oil, through an orifice. It is possible to program ac-tive, semi-active, and passive elements using either library elements or by means of user-elements in SIMPACK. Tyre elements can also be modelled the same way. One can make use of ‘Con-trol Elements’ in SIMPACK or SIMAT interface to model an ABS algorithm based on slip-optimization principle. It can be further enhanced as shown in Fig. 2. For further details about the force elements please refer to the lit-erature [1, 3].

reSultS ANd ANAlySIS

The results presented here are for a two mass model main landing gear of the Embraer regional aircraft and a complete large transport aircraft. It is possible to simulate complex ground manoeuvres using these sub-modules, see Fig. 5. With the help of modelling elements one can study landing gear and brake interaction and the related friction induced vibrations such as gear walk and shimmy, see Fig. 4. One can also perform parameter variation to study and optimize various parameters affecting landing gear shimmy. For the simulation of rolling and braking ma-noeuvres it is safe to assume that the aircraft is in static-equilibrium on the ground. This work was conducted by Dr. Khap-ane during his employment at DLR.

literature1. W.R. Krüger and M. Spieck, Interdisciplinary

Landing Gear Layout for large Transport Air-

craft. AIAA, 4964, 1998.

2. R. Lernbeiss, Simulation eines Flugzeugfahr-

werks bei elastischer Betrachtung des Feder-

beines. Dipl.Arbeit at DLR, Oberpfaffenhofen.

3. P. Khapane, Gear walk instability studies using

flexible multibody methods in SIMPACK. Jour-

nal of Aerosp.Sci.Technol., 10:19-25, 2006.