17 Non-probabilistic Uncertainty Evaluation in the Concept Phase for Airplane Landing Gear Design 163 • derivation of an mathematical model M.ˇ/ with the vector ˇ that comprises (i) model parameters such as material and geometry assumptions as well as properties like damping and stiffnesses, and (ii) state variables such as displacements, velocities, accelerations, forces and moments assumptions • derivation of an uncertainty model U.ˇ0; h/ D (ˇ W j ˇ ˇ0j ˇ0 h); h 0 (17.1) taking into account assumed uncertainty in the vectors ˇ around the vector’s nominal entities ˇ0. The variation of ˇ is limited by the uncertainty horizonh. A simple uncertainty model could be an interval jˇ ˇ0j related the nominal valueˇ0 • performance requirement P M.ˇ/ Pcrit (17.2) to specify a critical level such as limit loads etc. • robustness to uncertainty b h D maxfh W maxP M.ˇ/ Pcritg (17.3) with the highest tolerable uncertainty horizon b h. 17.3 Uncertainty Quantification in Landing Gear Design Concepts via INFO-GAP Approach 17.3.1 Guideline For each landing gear design concept (a) to (d), the authors derive a mathematical model M.ˇ/ Dza.px;vx/ (17.4) to calculate the absolute compression stroke progress za.px;vx/ as a function of model parameters px such as density of material, geometric dimensions and other properties like stiffness k as well as state variables vx such as static absolute loading Fa assumed to act on all models of the four landing gear design concepts (a) to (d). All model parameters and state variables are listed in [12]. Table 17.1 lists only a selection of model parameters and state variables that are relevant for the uncertainty evaluation in this present contribution. Next, the uncertainty model U.k0; h/ D (k W j k k0j k0 h); h 0 (17.5) comprises only one varied model parameter in ˇ: the stiffness k of the suspension rod, Sect. 17.3.2. The performance requirement for the landing gear design, P za px.k/;vx Pcrit Dza; max (17.6) specifies the critical or maximum allowable absolute compression stroke za; max as a result of increasing static loading Fa. For za px.k/;vx in (17.6), only the stiffness k out of all model parameters and state variables listed in [12] is assumed to be uncertain and is varied according to (17.5). Of course, all other model parameters and state variables may vary too. To the authors’ opinion, however, relative to varied stiffness of the suspension strut, the variation of material and geometric parameters can be neglected due to today’s high precision and accuracy in manufacturing and assembling. Stiffness variations are considered to be more likely to occur due to influence of temperature, fatigue etc.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==