Torusity Tolerance Verification using Swarm Intelligence

Measurement technology plays an important role in discrete manufacturing industry. Probe-type coordinate measuring machines (CMMs) are normally used to capture the geometry of part features. The measured points are then fit to verify a specified geometry by using the least squares method (LSQ). However, it occasionally overestimates the tolerance zone, which leads to the rejection of some good parts. To overcome this drawback, minimum zone approaches defined by the ANSI Y14.5M-1994 standard have been extensively pursued for zone fitting in coordinate form literature for such basic features as plane, circle, cylinder and sphere. Meanwhile, complex features such as torus have been left to be dealt-with by the use of profile tolerance definition. This may be impractical when accuracy of the whole profile is desired. Hence, the true deviation model of torus is developed and then formulated as a minimax problem. Next, a relatively new and simple population based evolutionary approach, particle swarm optimization (PSO), is applied by imitating the social behavior of animals to find the minimum tolerance zone torusity. Simulated data with specified torusity zones are used to validate the deviation model. The torusity results are in close agreement with the actual torusity zones and also confirm the effectiveness of the proposed PSO when compared to those of the LSQ.