Three-dimensional modeling of coordinate measuring machines probing accuracy and settings using fuzzy knowledge bases: Application to TP6 and TP200 triggering probes

Sofiane Achiche and Adam Wozniak


One of the fundamental elements that determines the precision of coordinate measuring machines (CMMs) is the probe, which locates measuring points within measurement volume. In this paper genetically generated fuzzy knowledge based models of three-dimensional (3-D) probing accuracy for one- and two-stage touch trigger probes are proposed. The fuzzy models are automatically generated using a dedicated genetic algorithm developed by the authors. The algorithm uses hybrid coding, binary for the rule base and real for the database. This hybrid coding, used with a set of specialized operators of reproduction, proved to be an effective learning environment in this case. Data collection of the measured objects' coordinates was carried out using a special setup for probe testing. The authors used a novel method that applies a low-force high-resolution displacement transducer for probe error examination in 3-D space outside the CMM measurement. The genetically generated fuzzy models are constructed for both one stage (TP6) and two stage (TP200) types of probes. First, the optimal number of settings is defined using an analysis of the influence of fuzzy rules on TP6 accuracy. Then, once the number of settings is obtained, near optimal fuzzy knowledge bases are generated for both TP6 and TP200 triggering probes, followed by analysis of the finalized fuzzy rules bases for knowledge extraction about the relationships between physical setup values and error levels of the probes. The number of fuzzy sets on each premise leads to the number of physical setups needed to get satisfactory error profiles, whereas the fuzzy rules base adds to the knowledge linking the design experiment parameters to the pretravel error of CMM machines. Satisfactory fuzzy logic equivalents of the 3-D error profiles were obtained for both TP6 and TP200 with root mean squsre errors ranging from 0.00 mm to a maximum of 0.58 mm.

(Received January 28 2010)
(Accepted April 11 2011)

Correspondence: Reprint requests to: Sofiane Achiche, Department of Mechanical Engineering, École Polytechnique de Montréal, University of Montreal, P.O. Box 6079, Station Centre-Ville 2900, Montreal, QC H3C 3A7, Canada. E-mail: