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

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. The effect of a changing side-stay plane orientation angle on the bifurcation diagram is investigated. We present a consistent picture that captures the transition of the two-parameter bifurcation diagram as a function of this angle, with a considerable complexity of regions of different types of shimmy oscillations for intermediate and realistic side-stay plane orientations. In particular, we find a region of tristability in which stable torsional, in-plane, and out-of-plane shimmy oscillations coexist

On the nonlinear dynamics of a rotor in autorotation:a combined experimental and numerical approach

This article presents a systematic assessment of the use of numerical continuation and bifurcation techniques in investigating the nonlinear periodic behaviour of a teetering rotor operating in forward autorotation. The aim is to illustrate the potential of these tools in revealing complex blade dynamics, when used in combination (not necessarily at the same time) with physical testing. We show a simple procedure to promote understanding of an existing but not fully understood engineering instability problem, when uncertainties in the numerical modelling and constraints in the experimental testing are present. It is proposed that continuation and bifurcation methods can play a significant role in developing numerical and experimental techniques for studying the nonlinear dynamics not only for rotating blades but also for other engineering systems with uncertainties and constraints.</jats:p

A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism

This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant

Numerical continuation and bifurcation analysis in aircraft design:an industrial perspective

Bifurcation analysis is a powerful method for studying the steady-state nonlinear dynamics of systems. Software tools exist for the numerical continuation of steady-state solutions as parameters of the system are varied. These tools make it possible to generate ‘maps of solutions’ in an efficient way that provide valuable insight into the overall dynamic behaviour of a system and potentially to influence the design process. While this approach has been employed in the military aircraft control community to understand the effectiveness of controllers, the use of bifurcation analysis in the wider aircraft industry is yet limited. This paper reports progress on how bifurcation analysis can play a role as part of the design process for passenger aircraft.</jats:p

Investigation into the interaction of nose landing gear and two DOF fuselage dynamics

Pilots may experience vibrations in the cockpit during ground manoeuvres because of energy being transferred from the nose landing gear to the fuselage. This indicates that the fuselage dynamics could also have an effect on the dynamics of the gear. To study this interaction, a mathematical model of a nose landing gear coupled to a fuselage model with yaw and pitch degrees of freedom is developed. Results obtained by bifurcation analysis show the nature of the interaction between the two systems; in particular the two-DOF fuselage does affect the onset and subsequent severity of nose landing gear shimmy