Numerical and experimental methods for viscoelastic circular contacts in dry and lubricated conditions

The present thesis is focused on the development of a Boundary Element formulation to assess two-dimensional steady-state circular contact problems. In particular, the methodology paves over an ad-hoc defined steady-state viscoelastic Green’s function, which takes into account the circular hallmark of the contact domain, typical, for example, of a mechanical pin joint. Crucially, it is able to manage any real viscoelastic material, characterized by a continuum spectrum of relaxation times. The contact problem can be easily formulated in the form of a spatial convolution product between surface stresses and displacement, which blazes the trail to solving contact problems of a countless number of engineering-relevant systems, where multiple contacts occur, such as viscoelastic rolling element bearing. Incidentally, to correctly formulate the contact problem, the definition of the spatial Green’s tensor is crucial. Specifically, the entries of such tensor, namely the radial and tangential displacements associated to concentrated radial and tangential unit forces, are determined via a complex variable method. Conversely to the usual method employing the Airy’s stress function, the complex variable method allows, through the definition of appropriate complex potentials, a modus operandi which does not entail the solution to fresh differential equations whenever the coordinates are changed. Once the viscoelastic Green’s function is derived, the conformal contact problem of a rigid pin in contact with a deformable space with a cylindrical hole is investigated. At first, the methodology is validated against the analytical solution provided by A. Persson for a purely elastic case; then, the case of a linearly viscoelastic space is analyzed: as expected in a viscoelastic contact system, at the leading edge, the pressure distribution peaks, whilst the displacements are larger at the trailing edge, due to the different relaxation in the two regions. Indeed, at the trailing edge, the material has been just deformed and is still relaxing. Moreover, this process is speed-dependent as, at very low and very high speeds the material enters the rubbery and glassy regions respectively, where it behaves as a solid elastic body, and the energy dissipation is negligible. The latter is significant at intermediate speed, where proper viscoelasticity effects arise. Notably, thanks to the well-known computational efficiency of Boundary Element methods, the present methodology is employed as a valid and numerical more efficient alternative to Finite Element approaches to assess the multiple contact problem in a rolling element bearing, where the raceways are linearly viscoelastic, and the rolling elements are assumed to be rigid. From an applicative point of view, the assessment of the contact problem is crucial. In fact, it is shown that the distribution of the load among the rolling elements deviates significantly with respect to the purely elastic case, with some rollers eventually losing the contact with the raceways for some speed values. This has consequences not only on the rolling element durability but may impact the rotor dynamics of the system supported by the bearing. Finally, to corroborate the model, numerical predictions for a rolling element bearing with the outer ring made of Polytetrafluoroethylene (PTFE) are compared, with good agreement, to experimental outcomes. This is further supported by a successive comparison between numerics and experiments, for the outer ring of the bearing is made of Polyamide 6 (PA6). Crucially, it should be observed that possible implications of the Boundary Element methodology are not limited to dry contact mechanics, but the integral formulation could be very useful in lubrication problems involving conformal surfaces. Specifically, the case of a polymer journal bearing is studied and the importance of the definition of an appropriate Green’s function to take into account of the conformity of the problem is highlighted. In fact, making use of the classical half-plane Green’s function significant deviations are observed in the case of such conforming contact conditions: this aspect is then critical in design processes. Furthermore, it is overt that the complex rheology of the viscoelastic material is strongly coupled with the lubricant viscous losses, thus affecting the bearing capacity of the system. Hence, the pressure and film thickness distributions for different contact configurations are determined, highlighting that viscoelastic lubrication is governed by three parameters, i.e., the Hersey number and the dimensionless velocities of the interacting pair.