Analysis of the Shimmy Phenomenon

Pacejka, Hans B.

doi:10.1243/pime_auto_1965_180_026_02

Cited by 40 publications

(34 citation statements)

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“…This does in general have an effect on the dynamics of a landing gear system even given high external forces, as the angular rates of these components are high. Such gyroscopic effects act to further couple the DoFs considered [31,33], and herein lies the motivation for their exclusion from this particular study, allowing us to determine the additional coupling arising from a variable side-stay orientation in isolation.…”

Section: Equations Of Motionmentioning

confidence: 99%

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Howcroft¹,

Krauskopf²,

Lowenberg

et al. 2013

SIAM J. Appl. Dyn. Syst.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. Abstract.Commercial aircraft are designed to fly but also need to operate safely and efficiently as vehicles on the ground. During taxiing, take-off, and landing the landing gear must operate reliably over a wide range of forward velocities and vertical loads. Specifically, it must maintain straight rolling under a wide variety of operating conditions. It is well known, however, that under certain conditions the wheels of the landing gear may display unwanted oscillations, referred to as shimmy oscillations, during ground maneuvers. Such oscillations are highly unwanted from a safety and a ride-comfort perspective. In this paper we conduct a study into the occurrence of shimmy oscillations in a main landing gear (MLG) of a typical midsize passenger aircraft. Such a gear is characterized by a main strut attached to the wing spar with a side-stay that connects the main strut to an attachment point closer to the fuselage center line. Nonlinear equations of motion are developed for the specific case of a two-wheeled MLG configuration and allow for large angle deflections within the geometrical framework of the system. The dynamics of the MLG are expressed in terms of three degrees of freedom: torsional motion, in-plane motion, and out-of-plane motion (with respect to the side-stay plane). These are modeled by oscillators that are coupled directly through the geometric configuration of the system as well as through the tire/ground interface, which is modeled here by the von Schlippe stretched string approximation of the tire dynamics. The mathematical model is fully parameterized and parameters are chosen to represent a generic (rather than a specific) landing gear. In particular, the positions of the attachment points are fully parameterized so that any orientation of the side-stay plane can be considered. The occurrence of shimmy oscillations is studied by means of a two-parameter bifurcation analysis of the system in terms of the forward velocity of the aircraft and the vertical force acting on the gear. 1. Introduction. The technical term shimmy is generally used to describe the self-sustained oscillations of a system with one or more rolling wheels and represents a relatively well-studied problem in engineering. Typical examples of shimmy with which the reader may be familiar range from the weaving of a towed trailer at high speeds to the sudden oscillation of a loose trolley wheel. The phenomenon first began to attract research interest in connection with the undesirable oscillation of the steering mechanism of early automobiles. These vehicles shared the common design elements of a single front axle rigidly connected to the front wheels, and the severity of the problem increased further with the development...

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Section: Equations Of Motionmentioning

confidence: 99%

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Howcroft¹,

Krauskopf²,

Lowenberg

et al. 2013

SIAM J. Appl. Dyn. Syst.

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“…Of particular interest for our study is the work by Pacejka [10,11] and by Stépán [15,16], who consider a pulled trailer-a system that is characterized by a large caster length (mechanical trail) with zero rake angle and weak damping, and possible freeplay at the kingpin. Pacejka [10,11] found experimentally and in a 13th-order model that shimmy may occur for a wide range of velocities and may be associated with sudden jumps into and out of shimmy when the velocity is changed.…”

Section: Introductionmentioning

confidence: 99%

“…Pacejka [10,11] found experimentally and in a 13th-order model that shimmy may occur for a wide range of velocities and may be associated with sudden jumps into and out of shimmy when the velocity is changed. Furthermore, he found the first example of quasiperiodic shimmy in the form of beating oscillations where also the translational mode at the kingpin is excited.…”

Section: Introductionmentioning

confidence: 99%

Interaction of torsion and lateral bending in aircraft nose landing gear shimmy

2008

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In this paper we consider the onset of shimmy oscillations of an aircraft nose landing gear. To this end we develop and study a mathematical model with torsional and lateral bending modes that are coupled through a wheel-mounted elastic tyre. The geometric effects of a positive rake angle are fully incorporated into the resulting five-dimensional ordinary differential equation model. A bifurcation analysis in terms of the forward velocity and the vertical force on the gear reveals routes to different types of shimmy oscillations. In particular, we find regions of stable torsional and stable lateral shimmy oscillations, as well as transient quasiperiodic shimmy where both modes are excited.

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“…The presence of dry friciton at the king pin (as used by Pacejka, 1966a) is not essential to explain the experimentally also verified unstable periodic motion (see Pacejka, 1966b). The fact that the nonlinear creep force cannot stabilize the system without additional viscous damping refers to an important approximation in the mathematical model (1), namely that a stationary (or quasi-stationary) creep force is applied in the dynamical equations.…”

Section: Discussionmentioning

confidence: 96%

“…The wheel is considered with an elastic tyre characterized by the creep force presented by Pacejka (1966b). Similar creep forces are often used in railway dynamics (see e.g.…”

Section: Introductionmentioning

confidence: 99%