Knowles James A C, Lowenberg Mark H, Neild Simon A, Krauskopf Bernd
Department of Aeronautical and Automotive Engineering , Loughborough University , Loughborough LE11 3TU, UK.
Department of Aerospace Engineering , University of Bristol , Bristol BS8 1TR, UK.
Proc Math Phys Eng Sci. 2014 Dec 8;470(2172):20140332. doi: 10.1098/rspa.2014.0332.
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.
本文讨论了分岔分析在设计机构时所能提供的见解。可以推导一组耦合稳态方程形式的模型来描述该机构。通过数值延拓，在一个或多个参数同时变化的情况下，可以在机构的状态与参数空间中追踪该模型的解。利用这种方法，可以识别响应曲面中的关键特征，如分岔点。通过在适当的参数空间中对这些点进行数值延拓，得到的分岔图可用于指导参数选择和优化。在本文中，我们通过考虑一种飞机前起落架来展示这种技术的潜力，该起落架采用了一种新颖的锁定策略，即使用组合式上锁/下锁机构。起落架在收起或放下状态时被锁定。这些锁定状态与解锁状态（此时起落架是一个机构）之间的转换取决于两个折叠点分岔的位置。通过进行双参数延拓，追踪临界点以确定操作边界。随着折叠点在参数空间中的变化，确定了使起落架能够锁定在收起状态的最小弹簧刚度。分岔分析还表明，收起的起落架解锁时应使用解锁力测量，而不是位置指示器，以消除收放和锁定执行器的影响。总体而言，该研究表明，分岔分析可以增强对设计选择在非线性显著的广泛工作范围内的影响的理解。
