A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field, Using Multilevel Techniques

The most time-consuming routine in the present EHL and dry contact computations is the calculation of the elastic deformation integrals. Using Multilevel Multi-Integration (MLMI) these integrals can be computed in O(n log n) instead of O(n²) operations. This fast integration is applied to the dry contact problem. To make optimal use of this integration, it is also necessary to construct an efficient solver for the integral equation. This is again accomplished using multilevel techniques. The total complexity of the new dry contact solver is O (n log n) which gives a big reduction in computing time over “classical” solution methods, enabling the solution of contact problems on grids with so many points that a realistic modelling of the surface roughness lies within reach. The fast integration is then applied to compute the stress distribution below the surface. As an example, the stress distribution under a smooth surface with a bump in contact is calculated for both a 2-dimensional and for a 3-dimensional contact case, and for a 2-dimensional rough surface in contact