Analyzing the Probabilities of Natural Resting for a Component With a Virtual Resting Face

Abstract

This paper introduces a new approach to predicting the natural resting behavior of a part of irregular prismatic cross-sectional shape. The methods proposed by Boothroyd, Redford, Poli, and Murch (1972) and Boothroyd and Ho (1977), successfully analyzed parts whose centers of gravity were located at the geometric center. The hypothesis presented here employs the centroid solid angle of parts of irregular cross-sectional shape with virtual resting faces, such as the L-section. It postulates that the probability of the respective natural resting surfaces of a part coming to rest is directly proportional to the centroid solid angle and inversely proportional to the height of the center of gravity from that surface. The proposed hypothesis is compared with the Energy Barrier Method and experimental results obtained from drop-tests of the L-shaped part. The theoretical results agree well with the experimental results, with the maximum deviation not exceeding 6 percent.