Finite element incremental contact analysis with various frictional conditions

Abstract

Abstract The use of contacting components such as gear teeth in mesh and shrink‐fitted shafts is very common in engineering practice. This paper deals with the development of a theoretical method which gives a solution for non‐linear contact problems with irreversibility resulting from stick‐slip phenomenon. The method is based on the finite element method and load incremental theory. The geometrical and the statical boundary conditions on contact surfaces are treated as additional conditions being independent of stiffness equations. As a result, the algorithm of calculation is simplified and only a part of the simultaneous equations related to the contact surfaces is required to be solved instead of the overall stiffness equations at each step. Furthermore, the magnitude of load causing a change in a contact condition of one contact nodepair is taken as a load increment, in analogy with the incremental iterative procedure for elastic‐plastic problems. Therefore, the method provides a general and efficient method for analysis and design of such problems. As illustrative examples, the stick‐slip behaviour of turbo‐alternator end‐bells and other problems are discussed. The calculated results show a reasonable agreement with experimental data and other solutions.