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The Applicability of the Hertzian Formulas to Point Contacts of Spheres and Spherical Caps

Authors :
Enrico Ciulli
Alberto Betti
Paola Forte
Source :
Lubricants, Vol 10, Iss 10, p 233 (2022)
Publication Year :
2022
Publisher :
MDPI AG, 2022.

Abstract

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.

Details

Language :
English
ISSN :
20754442
Volume :
10
Issue :
10
Database :
Directory of Open Access Journals
Journal :
Lubricants
Publication Type :
Academic Journal
Accession number :
edsdoj.4c81839ab28e425ea5b724e8adc2a09b
Document Type :
article
Full Text :
https://doi.org/10.3390/lubricants10100233