On estimations of maximum and average interfacial temperature rise in sliding elliptical contacts

Abstract

This study considers the approaches of Blok and Jaeger for the estimation of maximum and average temperatures in sliding elliptical contacts with both uniform and semi-ellipsoidal (Hertzian) heat distributions. The accuracy of each of these methods, which are based on single-point temperature matching between contacting bodies, is assessed relative to a numerical solution of the heat partition problem developed in a previous work, which imposed temperature matching at all nodal points. Comparisons are made for a wide range of Peclet numbers, as well as for moderate ranges of thermal conductivity ratio and elliptical ratio. It is found that the application of Blok's hypothesis yields remarkably accurate predictions of the maximum interfacial temperature, with typical errors less than 3%, whereas the hypothesis of Jaeger leads to predictions of the average interfacial temperature that have typical errors of around 6%. The authors also assess the accuracy of approximate formula developed by Tian and Kennedy to predict the maximum temperature at the interface for the case of sliding circular contacts and find the error to be no more than 2.6% for the full range of Peclet number. Further, the authors of the current study use fundamental heat source solutions developed by Tian and Kennedy to arrive at formulae for average temperature rise for circular contacts that are analogous to the Tian and Kennedy maximum temperature rise formulae. It is found that the formulae for computing the average interfacial temperature rise are also quite accurate, but have slightly more error than the maximum temperature rise formulae. Finally, in the present work, extensions are suggested to the maximum and average temperature rise formulae of Tian and Kennedy to include the effects of elliptical contact geometry. It is found that these formulae are at least 91% accurate for elliptical ratios between 0.4 and 5.0.