There is an increasing diffusion of the industry 4. 0 concept today. The fourth industrial revolution, following three other previous industrial revolutions, is considered related to the introduction of modern information and communication technologies in production. Tribological concepts are much older than industry. Tribology has always been connected to industrial problems from the birth of industry. It was strongly connected with the previous industrial revolutions and it is surely related to industry 4.0. In this work, the main aspects of the four industrial revolutions and the main evolutions of tribology are firstly reviewed from a historical point of view. The relationships between tribology and industry are described with particular attention to the aspects that relate the modern tribology 4.0 to industry 4.0. Tribology can have in particular a big impact on the industrial needs to reduce losses and wastes, for instance with the development of new tribological components and materials also in connection with electronic smart systems and taking advantage of the information and communication technologies.

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.

Tribology is related to all studies on friction, wear, and lubrication. One of the main aims of these studies is a reduction in friction and wear. Tribology is extremely vast, being also multidisciplinary and interdisciplinary. Therefore, it is very difficult to organize the several tribology subjects in an unique way and different classifications have been proposed by different authors. In this work, several subjects treated by tribology are reviewed and organized in six branches: Fundamental Tribology, Tribology of Materials and Lubricants, Micro and Nanotribology, Industrial Tribology, Biotribology, and New Frontiers of Tribology. The main subjects treated by the six branches are briefly reviewed in this paper in order to highlight the vastness of tribology and its important contribution to sustainability. Particularly, friction and wear reductions are strictly related to greater efficiency and material saving, which means less energy losses and material wastes, less pollution and therefore a more sustainable life according to the sustainable development goals. The connections among the latter and the several different tribological subjects are discussed.