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.

Development of Vibratory Part Feeder for Material Handling in Manufacturing Automation: A Survey

“…This method was proposed by Lee et al [7]. A solid angle is defined as one steradian unit subtended by a part of the spherical surface whose area equals the square of the radius of the sphere.…”

Determining the most probable natural resting orientation of sector shaped parts

“…These three methods are capable of determining the probability of natural resting orientations based on parts' geometry. Ngoi et al (1997) and Lee et al (1997) presented the centroid solid angle method to predict the most probable natural resting orientation of various parts. A solid angle is defined as being of one steradian unit subtended by portion of a spherical surface whose area is equal to the square of the radius of the sphere.…”

Vibratory orienting and separation of small polygonal parts

“…This research presents three methods of determining the natural resting aspect. The first method is a simple falling experiment, the second is an analytical method using the centroid solid angle (CSA) hypothesis introduced by Lee et al [13], and the last method utilizes the simulation program. In fact, the most reliable way of determining the resting aspect is to execute a falling experiment with the target part by setting a vibrating bar on the part feeder.…”