Complete 3-D self-calibration of coordinate measuring machines

Abstract

When one attempts to evaluate the measurement accuracy of coordinate measuring machines (CMMs) by use of artifacts such as ball or block array, the ultimate precision of the evaluation is limited by the calibration accuracy of the artifacts. An approach of overcoming the problem is to adopt the concept of self-calibration that aims to perform absolute testing with uncalibrated artifacts. The metrological concept of self-calibration has its base on the congruency between multiple views of measurements of an artifact allows discriminating between the machine error and the artifact error. Self-calibration is particularly useful to test high precision machines or measuring instruments for which no certified artifacts are available because of practical reasons such as fabrication cost or technical difficulty. Self-calibration allows testing machine motion errors, but its implementation has been limited to 1-D and 2-D domains due to lack of suitable 3-D methodology. In this thesis, we present a complete 3-D self-calibration of Coordinate Measuring Machines, allows obtaining a full 3-D map of systematic positioning errors that are necessary for the complete analysis of the volumetric errors of CMMs. To validate the proposed algorithm by experiment, a 3-D rectangular type artifact was built up with a 5x5x5 array of precision steel balls and four separate data sets of measurements are taken with different views of the artifact. Then parasitic errors related to the artifact are identified through an algebraic manipulation procedure, so that a complete 3-D map of machine errors can be accurately constructed. The proposed algorithm also allows reconstructing the 3-D error map of actual ball placements on the 3-D artifact, which tuned out to be much larger than the machine error. Experimental results show that the algorithm provides accurate calibration results, and the practical limit of the calibration accuracy is determined by the measurement repeatability of the CMM und...