A bifurcation study of a dynamic model of a nose landing gear mechanism subjected to external disturbances

This paper presents a new modelling approach for the analysis of landing gear mechanisms. By replacing the mechanism's rotational joints with equivalent high-stiffness elastic joints, numerical continuation methods can be applied directly to dynamic models of landing gear mechanisms. The effects of using elastic joints are considered through two applications --| an overcentre mechanism, and a nose landing gear mechanism. In both cases, selecting a suffcient stiffness for the elastic joint is shown to provide accurate contiuation results. The advantages of this new modelling approach are then demonstrated by considering the unlocking of a nose landing gear with a single uplock/downlock mechanism, when subjected to different orientations and magnitudes of gravitational loading. The unlocking process is shown to be qualitatively insensitive to changes in both load angle and load magnitude, ratifying the robustness of a previously- proposed control methodology for unlocking a nose landing gear with a single uplock/downlock mechanism

Bifurcation study of a dynamic model of a landing gear mechanism

This paper presents a new modelling approach for the analysis of landing gear mecha- nisms. By replacing the mechanism's rotational joints with equivalent high-sti ness elas- tic joints, numerical continuation methods can be applied directly to dynamic models of landing gear mechanisms. The e ects of using elastic joints are considered through two applications | an overcentre mechanism, and a nose landing gear mechanism. In both cases, selecting a su cient sti ness for the elastic joint is shown to provide accurate con- tiuation results. The advantages of this new modelling approach are then demonstrated by considering the unlocking of a nose landing gear with a single uplock/downlock mechanism, when subjected to di erent orientations and magnitudes of gravitational loading. The un- locking process is shown to be qualitatively insensitive to changes in both load angle and load magnitude, ratifying the robustness of a previously-proposed control methodology for unlocking a nose landing gear with a single uplock/downlock mechanism

Optimization of a main landing gear locking mechanism using bifurcation analysis

A key part of the main landing gear (MLG) of a civil aircraft is its locking mechanism that holds the gear in the deployed or down-locked state. The locking is driven by a spring mechanism and its release by the unlock actuator. This paper considers this mechanism in terms of its stability and the locking and unlocking forces required for down-locking. To study this an analytical model was developed. The equations, consisting of geometric constraints and force/moment equilibriums, were derived using the coordinate transformation method. Using numerical continuation to solve these equations, the effect of the unlock force on the MLG retraction cycle was analyzed. The variation of a fold bifurcation point, which indicates the transition between the locked state and the unlocked state, gives further insight into the required unlock force that governs the sizing of the unlock actuator. Moreover, some important information, such as the critical position for the lock-links’ stops, the unlock position and the unlock force, are discussed using the bifurcation diagrams for the MLG retraction/extension cycle. Then, the effect of three key geometry parameters of the locking spring (the spring stiffness, unstrained spring length and spring attachment point) on the critical over-center angle and the unlock force are investigated. Finally, an optimization of the critical unlock force is carried out with a constraint on the initial over-center angle. The results show that the spring parameters have significant effects on the MLG’s retraction performance. A 37% reduction of the required unlock force is obtained through optimizing for the gear considered here

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