Determining the probabilities of natural resting aspects of parts from their geometries

Abstract

Proposes a computationally‐simple method, based on the centroid solid angle, for computing the probability distributions of the natural resting aspects of small parts, the fore‐knowledge of which can improve the design of vibratory feeders and orienting devices. The centroid solid angle (CSA) hypothesis postulates that the probability of a part coming to rest on a particular aspect is directly proportional to the solid angle subtended by the aspect with respect to the centroid (the centroid solid angle) and inversely proportional to the height of the centroid from the aspect in question. When benchmarked against Boothroyd’s energy barrier method, its results did not deviate from those of the energy barrier method by more than 0.04. Examines studies of a cylindrical prismatic part and a symmetrical T‐shaped prism. The drop tests used to obtain the authors’ empirical data were validated by experiments conducted on vibratory bowl feeders, subjected to different vibration frequencies. The tracks of one of the bowls was coated with urethane to simulate a soft surface. In the case of both frequencies, the empirical results are in generally good agreement with the predictions of the CSA hypothesis; the largest deviation was 0.07. As for the urethane track, the largest deviation was 0.08, thereby corroborating the results of the drop test method.