James A.C. Knowles

Numerical Continuation Applied to Landing Gear Mechanism Analysis

A method of investigating quasi-static mechanisms is presented and applied to an overcenter mechanism and to a nose landing gear mechanism. The method uses static equilibrium equations along with equations describing the geometric constraints in the mechanism. In the spirit of bifurcation analysis, solutions to these steady-state equations are then continued numerically in parameters of interest. Results obtained from the bifurcation method agree with the equivalent results obtained from two overcenter mechanism dynamic models (one state-space and one multibody dynamic model), while a considerable computation time reduction is demonstrated with the overcenter mechanism. The analysis performed with the nose landing gear model demonstrates the flexibility of the continuation approach, allowing conventional model states to be used as continuation parameters without a need to reformulate the equations within the model. This flexibility, coupled with the computation time reductions, suggests that the bifurcation approach has potential for analyzing complex landing gear mechanisms.

Numerical Continuation Analysis of a Dual-sidestay Main Landing Gear Mechanism

A model of a three-dimensional dual-sidestay landing gear mechanism is presented and employed in an investigation of the sensitivity of the downlocking mechanism to attachment point deflections. A motivation for this study is the desire to understand the underlying nonlinear behavior, which may prevent a dual-sidestay landing gear from downlocking under certain conditions. The model formulates the mechanism as a set of steady-state constraint equations. Solutions to these equations are then continued numerically in state and parameter space, providing all state parameter dependencies within the model from a single computation. The capability of this analysis approach is demonstrated with an investigation into the effects of the aft sidestay angle on retraction actuator loads. It was found that the retraction loads are not significantly affected by the sidestay plane angle, but the landing gear’s ability to be retracted fully is impeded at certain sidestay plane angles. This result is attributed to the lan...

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 mechanisms 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.

Self-repairing design process applied to a 4-bar linkage mechanism

Despite significant advances in modelling and design, mechanical systems almost inevitably fail at some point during their operative life. This can be due to a pre-existing design flaw, which is usually overcome in a revision, or more commonly due to some unexpected damage during operation. To overcome a failure during operation, a new method in designing machines or systems is proposed that creates a result, that is, resilient to both expected and unexpected failure. By shifting the focus from a detailed assessment of the underlying cause of failure to how that failure will manifest, a system becomes inherently resilient against a wide range of failure modes. The proposed process involves five steps: cause, detection, diagnosis, confirmation and correction. This is demonstrated with an application to a generic 4 bar linkage mechanism. Through this process, the system is able to return to a near perfect state even after a permanent deformation occurs in the mechanism. These results show the potential that this self-repairing design process has applications including robotics, manufacturing and other systems.

Numerical investigation of aircraft high-speed runway exit using generalized optimal control

To aim at reducing aircraft turnaround time and improving airport operation efficiency, this paper considers the optimization of aircraft ground manoeuvres such as a high-speed runway exit. The aircraft on the ground is a highly nonlinear dynamical system described by a fully parameterized mathematical model. The full aircraft model used in this paper has been further developed to include combined slip tire model. An iterative simulation-based optimization algorithm known as Generalized Optimal Control is employed to investigate the optimal solution for the control input such as nose-gear steering, main-gear brakes and engine thrust. To achieve different control objectives, the cost function is defined accordingly and then minimized by GOC. The optimization results of GOC will help to explore the safety boundary of ground handling and guide the design of a real-time controller.

Optimization of a main landing gear locking mechanism using bifurcation analysis

A key part of the main landing gear of a civil aircraft is its locking mechanism that holds the gear in the deployed or downlocked state. The locking is driven by a spring mechanism and its release...

Bifurcation study of a dynamic model of a landing gear mechanism

This paper presents a new modeling 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 overcenter mechanism and a nose-landing-gear mechanism. In both cases, selecting a sufficient stiffness for the elastic joint is shown to provide accurate continuation results. The advantages of this new modeling 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...

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 mechanisms 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.