Analysis of the Elastic Contact of a Hollow Ball With a Flat Plate

Abstract

This paper presents the analysis of the stress field in a hollow sphere in the vicinity of the contact area. The sphere is subjected to a normal load applied through a flat plate. The elastic contact shape and extent are developed for a load of 1000 lb applied to a 1-in-dia hollow ball with a 0.08-in-thick wall. Hollow ball shell bending stresses have a significant effect upon the subsurface stress field. Fatigue life estimates for the hollow ball vary significantly depending upon the selection of decisive stress amplitude. Comparison of the maximum value and location of the reversing orthogonal subsurface shear stress with solid ball data according to the Lundberg-Palmgren dynamic life theory predicts a 91.6 percent life reduction for the hollow ball contact. The use of the unidirectional subsurface shear stress results in a prediction of hollow ball contact life over 30 times the solid ball contact life.

Crush Strength Analysis of Hollow Glass Microspheres

“…Data collected from nanoindentation was used to determine the failure load using the method based on previous nanoindentation work by Carlisle et al [32]. The stress acting on the microsphere was calculated using Equation (21) from the analysis of a hollow sphere between two flat plates by Rumbarger et al [53]. Results from previous nanoindentation work on microspheres showed a tip displacement vs applied load graph with three regions.…”

Relative contact width evaluation of end hemispherical cavities rollers as an indication of Hertzian contact pressure

“…Filetti and Rumbarger 21 had used the footprint technique using copper plating for validating their presented general analytical techniques applicable for rolling element bearings and realized that the experimental determination of the roller load distribution by “footprint” measurement techniques showed excellent agreement with the analytical predictions in their analysis. Furthermore, Rumbarger et al 22 had used the footprint technique for validating their proposed method of computer solution in order to investigate performance of hollow rolling elements where the accordance of experimental footprint results with calculated contact radius demonstrated the accomplishment of their method of analysis for contact type problems and concluded that the hollow rolling element bending stresses are the origin of the competing modes of failure and hence should not be simply disregarded. Furthermore, Heydari and Gohar 23 compared their numerical solutions for rolling element bearings with the experimental findings by observing the footprints obtained on a Perspex plate for a steel roller using a micrometer microscope and realized that rollers with larger dub-off radii imperil lesser severe pressure peaks than rollers with smaller radii and, therefore, the life of bearings should improve with reasonable augmentation in end radii of the rollers.…”

Bending Stresses in Spherically Hollow Ball Bearing and Fatigue Experiments

“…Rumbarger, Herrick, and Eklund [8] reported the result of a finite element computer analysis of a hollow ball contacting a flat plate. The ball model had a diameter of 25.4 mm (1 in.…”