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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.

Film thickness is the most important parameter of a lubricated contact. Its evaluation in a cam-follower contact is not easy due to the continuous variations of speed, load and geometry during the camshaft rotation. In this work, experimental apparatus with a system for film thickness and shape estimation using optical interferometry, is described. The basic principles of the interferometric techniques and the color spaces used to describe the color components of the fringes of the interference images are reported. Programs for calibration and image analysis, previously developed for point contacts, have been improved and specifically modified for line contacts. The essential steps of the calibration procedure are illustrated. Some experimental interference images obtained with both Hertzian and elastohydrodynamic lubricated cam-follower line contacts are analyzed. The results show program is capable of being used in very different conditions. The methodology developed seems to be promising for a quasi-automatic analysis of large numbers of interference images recorded during camshaft rotation.

Der Einfluss von elastohydrodynamischen Kontakten (EHD) auf das nichtlineare Schwingungsverhalten von Systemen wird untersucht. Aufgrund der numerischen Komplexität des kontinuierlich modellierten EHD-Problems muss für Schwingungsanalysen ein vereinfachtes Kontaktmodelle entwickelt und validiert werden. Die durch EHD-Kontakte induzierten nichtlinearen Schwingungsphänomene werden zunächst an Modellbeispielen demonstriert. Abschließend wird ein Rotor in Zylinderrollenlagern betrachtet.

Kinematic couplings are often used in synchrotron radiation facilities to achieve high-precision positioning and relocation of opto-mechanical components. The analytical and numerical modeling of their stress-strain behaviour is however difficult, as it implies the necessity to deal with the Hertz theory of point contacts between elastically deforming solids. This work adresses the limits of applicability of the analytical approaches available in literature for the calculation of high-precision kinematic couplings. The validity of the theoretical models, as well as the achievable repeatability of the couplings, is assessed experimentally for various loading conditions and material types.

A three V-groove (Maxwell-type) kinematic mount design configuration constrains all degrees of freedom of the apparatus mounted onto it, thus allowing its high-precision positioning and re- positioning. The analysis of this mechanical assembly comprises force and moment balances, as well as expressions for stress-strain and error motion calculations. For determined loading conditions and the geometry of the mount, the resulting loads across each groove-ball interface imply, however, the necessity to consider the complex nonlinear Hertz theory of point contacts between elastically deforming solids. The available analytical approaches to the calculation of the conditions at the ball-V groove contacts are hence recalled in this work with the aim of establishing the respective limits of applicability. The obtained results are validated experimentally. A structured calculation procedure is then used to assess the stability of a kinematic mount employed to support a large mechanical component at a particle accelerator facility, depending on the value and orientation of the external loads acting on the studied assembly. Stability conditions for different design configurations are consecutively established.