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

On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

This paper investigates the effect of model uncertainty on the nonlinear dynamics of a generic aeroelastic system. Among the most dangerous phenomena to which these systems are prone, Limit Cycle Oscillations are periodic isolated responses triggered by the nonlinear interactions among elastic deformations, inertial forces, and aerodynamic actions. In a dynamical systems setting, these responses typically emanate from Hopf bifurcation points, and thus a recently proposed framework, which address the problem of robustness from a nonlinear dynamics viewpoint, is employed. Briefly, the notion of robust bifurcation margin extends the concept of mu analysis technique from the robust control theory. The main contribution of this article is a systematic investigation of the numerous scenarios arising in the study of nonlinear flutter when uncertainties in the model are accounted for in the analyses. The advantages of adopting this framework include the possibility to: quantify relevant information for the determination of the nonlinear stability envelope; gain a more in-depth understanding of the physical mechanisms triggering subcritical and supercritical Hopf bifurcations; and reveal properties of the nominal system by identifying isolated branches not straightforward to detect with conventional numerical approaches.Open Access funding provided by Swiss Federal Institute of Technology Zurich This work has received funding from the Horizon 2020 research and innovation programme under grant agreement No. 636307, project FLEXOP