Researching Of Numerical Method For Aeronautic Gear Contact Shakedown

At present an important subject on design of aeronautic gears is to improve its life and reliability, and reduce its weight compared to traditional gears. In this thesis, the numerical theories and computational methods for shakedown of aeronautic gears rolling contact are systematically studied and applied to research of shakedown limit under different curvature radiuses and friction coefficients of tooth contact surface.In this thesis, a series of efficient computational approaches for shakedown analyses are proposed. First, a new analytical model has been developed for shakedown conditions of plastic strain-hardening under different residual stress field based on Melan's shakedown theorem. Here a parameter w is introduced, the residual stresses is controlled by parameter, then shakedown equilibrium equations about all positions in structure are gained, and some convenient conclusions are given to evaluate shakedown limit of structures under cyclic load. Second, a minimum energy theorem is modified based on Koiter theory. The theory is used to develop a method for identifying the ratchet limit for a class of loading histories through the sequential minimisation of two functions. Third, cumulation of residual stresses is important to shakedown analysis. An efficient computational approach is presented through finite element method based on Von. Mises yield criterion. Cumulation of residual stresses of structure under cyclic loading is conveniently gained by approach. The proposed method can make the space and time resources required much less, and make the convergence better.By using the proposed shakedown analysis method, the shakedown of aeronautic gears rolling contact under different mesh positions is investigated and analyzed systematically. Static shakedown limit and kinematic shakedown limit are computed. The result shows that aeronautic gear can reach shakedown state after several rolling cycles. Shakedown limit is directly proportional to contact surface curvature radiuse without friction, and inversely proportional to contact surface curvature radiuse with friction coefficient of surface is 0.3.