LMS Conference Europe, March 22/23 2006
Landing gear shimmy Detect, understand and fix shimmy problems early in the design using simulation TNO Automotive
Igo Besselink
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Contents introduction: what is shimmy? analytical stability results using a simple model solutions to solve shimmy stability problems detailed shimmy analysis -modelling of the landing gear -tyre modelling • conclusions • • • •
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Introduction Shimmy is an unstable lateral/yaw vibration… 2 examples: helicopter NLG
measurement on aircraft MLG
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Tyre marks on the runway…
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Some notes: • frequency typically in the range of 10 to 30 Hz • degree of instability may vary from annoying vibrations up to structural damage or even a collapse of the landing gear • shimmy can occur on both nose and main landing gears Twin wheeled cantilevered main landing gears as seen on many commercial aircraft may experience shimmy stability problems. Bogie landing gears and levered suspension configurations are generally not sensitive to shimmy
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Landing gear configurations… danger of shimmy!
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The importance of simulation models • full scale shimmy testing on an aircraft may be very risky and dangerous… (also indoor testing on a drum may be not be successful) • no room to “experiment” or create various prototypes: the design has to be “the first time right”! • shimmy is a complex phenomenon: testing only does not directly lead to a solution: trial and error, unclear “solutions” to solve the problem • shimmy stability should be considered in the initial design phase of an aircraft when no hardware is available 23 March 2006
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The cause of shimmy… (1) • interaction between the dynamic behaviour of the landing gear structure and tyre simplified representation tyre lateral force (Fy) results in a side slip angle of the landing gear
due to the side slip angle the tyre develops a lateral force
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The cause of shimmy… (2) • the feedback loop may become unstable! • both the dynamics of the tyre (e.g. relaxation behaviour) and dynamics of the structure (e.g. eigenfrequencies/modeshapes are important) some other views on shimmy: • energy is extracted from the forward motion of the aircraft and converted into a lateral/yaw vibration • for a rolling tyre a combination of lateral and yaw input exists where self-excitation occurs
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Analytical solutions • trailing wheel system with lateral flexibility (topview)
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Analytical solutions… (q=0 and zero damping) also unstable, but generally less problematic
problem area
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What can we learn from the analytical results? • shimmy problems can be solved by changing stiffness, geometry and/or inertia… • just increasing the (yaw) stiffness is no guarantee to solve the shimmy instability effectively two feasible solutions to avoid instability: • small negative trail – yaw stiffness low – lateral stiffness high – large yaw inertia • big positive trail – yaw stiffness high – lateral stiffness low – small yaw inertia note: tyre characteristics will also affect shimmy stability, but are difficult to change in practice
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One step closer to a “real” landing gear… simple multi-body model consisting of: • three rigid bodies -strut -trail body -wheelaxle • two wheels • two tyres (TNO MF-Swift) bodies are connected by means of revolute joints simple, but representative
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Animation (baseline)
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Simulation of a landing event • velocity: 75 m/s (=270 km/h) • asymmetrical spin-up of the wheels on touch down
tyre vertical force
tyre longitudinal force
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Some more simulation results…
tyre side slip angle
tyre lateral force
time scale: 2 sec. 23 March 2006
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Design study – Yaw Stiffness Variation red: nominal (4e5 Nm/rad) green: increased yaw stiffness (5e5 Nm/rad) blue further increase (6e5 Nm/rad)
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Animation (increased yaw stiffness)
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modifying the geometry (negative trail)
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Animation (modified geometry)
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Modelling in an engineering environment so far: (highly) simplified models not suitable for designing a real landing gear …but definitely important to develop some “feeling” for the problem! For an accurate, predictive shimmy analysis both landing gear and tyre have to be modeled accurately! Several component tests may be necessary to validate certain aspects of the model, e.g. stiffness tests, modal testing, tyre testing,… 23 March 2006
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Landing gear structure
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Stiffness modelling • stiffness is dependent on the shock absorber closure due to changes in overlap and torque link geometry (stiffness may change by a factor 2 or more)
• also important: flexibility of the fuselage/wing 23 March 2006
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Modelling of the vertical air spring/damper characteristics
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Non-linear behaviour • free-play: reduces the effective stiffness of a landing gear. Older, worn landing gears may have a reduced stability margin. A simulation study may be necessary to determine the maximum allowable free-play limits • friction: cantilevered landing gear designs may exhibit quite a bit of friction. To get a good agreement with tests on the aircraft and component tests it has to be included in the model. Friction may also “hide” possible shimmy instability problems
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Tyre modelling • traditionally in aircraft shimmy analysis the tyre models of Von Schlippe, Smiley or Moreland are used. Theory of these models dates back to the 1940’s and 1950’s • More up to date models are available • Over 20 years of research at the TU Delft and TNO Automotive under the guidance of professor Pacejka has resulted in tyre models called MF-Tyre and MF-Swift
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Experimental validation (MF-Swift) • yaw oscillation test stand frequency response functions of side force and aligning torque to yaw angle up to 60 Hz amplitude ratio Fy 106
ψ
amplitude ratio Mz ψ 10
10
105
10
6
5
4
110
110 10
3
20 4
10
100
101
Frequency [Hz]
Experiment
20 10
2
10
0
1
10
Frequency [Hz]
Simulation 23 March 2006
V [km/h] 27
MF-Tyre/MF-Swift • originally developed for passenger car tyres • validated extensively by numerous experiments
most recent version: MF-Tyre/MF-Swift 6.0 in comparison to the older MF-Tyre 5.2 and Swift 1.2 much more useable for aircraft simulation studies: • very significantly reduced data requirements • build in parameter estimation procedures • includes turn slip, important for shimmy
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Advantages over “traditional” shimmy tyre models • includes non-linear behaviour with side slip angle, both forces and dynamic behaviour (e.g. reduction of the relaxation length) • combined slip (braking and steering at the same time) • includes gyroscopic effects of the rotating tyre belt • can drive over short wavelength obstacles • includes bottoming of the tyre • includes turnslip for steering/twisting moments at standstill one model which can cover all possible applications!
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Concluding remarks • Simulation allows to identify landing gear shimmy problems very early in the design stage, where you still have the chance to change the design for the better… • Modern tools as LMS Virtual.Lab Motion and TNO tyre model MF-tyre/MF-Swift 6.0 can be applied successfully for the analysis of aircraft shimmy stability • Despite a long history, shimmy is still a very relevant design issue for aircraft landing gears!
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Contact TNO Automotive - Helmond, the Netherlands Igo Besselink (
[email protected]) PhD thesis: Shimmy of Aircraft Main Landing Gears TU Delft, 2000 www.delft-tyre.com www.tno.nl
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