Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made.

The use of numerical and experimental methods to determine the stress field of mechanical components is well known. In particular, 3D photoelasticity can be considered the only experimental technique for the complete stress state evaluation of 3D components. The advent of rapid prototyping techniques has allowed the manufacturing of complex models in a matter of hours by using birifrangent materials. The present paper is focused on the description of a Computer Aided Engineering (CAE) approach which combines Finite Element (FE) simulations and automatic photoelastic investigations for the stress analysis of face gear drives, made by stereolithography. Computer Aided Design (CAD) geometries, used to manufacture the stereolithographic models, are directly used to perform FE analyses, thus allowing the stress analysis process to become simpler and easier. The substantial agreement observed between experimental and numerical results proved the potentialities of the adopted approach and the usefulness of FE simulations to optimize photoelastic analyses through cost- and time-effective experiments even for complex 3D shapes.

This paper reviews the current knowledge on turbulence effects in tilting pad journal bearings. Turbulence is becoming increasingly important in the design of hydrodynamic bearings due to the trend to increase power density in turbomachines and consequently the operating speeds of the hydrodynamic bearings. Turbulence has a series of effects on the bearing performance which may be beneficial or detrimental, depending on the operating conditions. The main turbulence models are recalled and a historical overview on the evolution of numerical simulations of turbulent flow in tilting pad journal bearings is presented. The two broad simulation strategies used are the generalized Reynolds equation and computational fluid dynamics. The main experimental works are then reviewed, and a unified comparison of these works is provided. Novel results on the critical Reynolds number in a tilting pad journal bearing are reported. Much emphasis is given on the experimental evidence for laminar-to-turbulent transition. The evidence used in the literature is reviewed and its reliability is discussed. Lastly, some future research directions are suggested.