Application Research On A Scaled Boundary Finite Element Method For Gear Crack Growth Problems

Gear transmission is widely used in the field of structure transmission, because it possesses the advantages of high efficiency,reliable operation and stable transmission ratio,etc.In general, gears work in complex environment, some gear sometimes runs at low speed and high torque conditions, sometimes runs at high speed and low torque state in a vehicle transmission, therefore highly reliability and long gear life of the gear are required,and it is ensured that the gear can not be broken.The main failure mode is fatigue cracking,which is a main factor that results in a let of structural failures.So it possesses an important theoretical and application value in engineering to investigate the gear fatigue crack problems.The scaled boundary finite element method is a new kind of effective numerical method in engineering after the finite element method and boundary finite element method. The scaled boundary finite element method is a more effective method than the finite element method and the boundary finite element method for solving the stress concentration problem based on linear elastic body, elastic crack problem with stress singularities, the crack propagation problem in brittle materials, and stress problems of local plastic elasto-plastic with local plastic,etc. In this thesis, the scaled boundary finite element method was investigated and adopted to solve an elastic crack problem.In this thesis, firstly, a special isoparametric element was adopted to discrete the boundary domain, the higher-order Chebyshev polynomial was selected as a new mapping function and shape functions, and a set of static equilibrium equations was established based on the principle of virtual work. By use of an eigenvalue method with Jordan decomposition or a function matrix technique, the numerical solutions of structural displacements and stresses were derived, being integrated with a transferring method dealing with the complex eigenvalues and eigenvectors with zero eigenvalues.Secondly,two sets of typical engineering models without cracks and with cracks were given, based on the Abaqus platform, and a set of complete analysis and calculation software was programmed by use of the Fortran language, being integrated with some Matlab subroutines and data files.The software was applied to the model data file based on Abaqus,and a comparison research between its numerical solution and its analytical solution was given to verify the accuracy and effectiveness of this method.Finally,for an elastic crack problem, two set of spur gear tooth models without crack and with crack were constructed, based on the involute equation that is derived by the meshing principle. Accurate contact stresses, comprehensive gear shape factors and the bending strength of these two models were obtained by adopting the programming software system.The stress intensity factor of the gear teeth with crack was calculated by adopting the software and, by use of multiple proportion centers established, and by applying a substructure block idea. At the same time, the relation curves of crack growth with respect with to loading ways,and load magnitude, crack length, and crack configurations were given and investigated. The application range of the scaled boundary finite element method was further extended.