| Accuracy of a machine tool often limits the dimensional accuracy of parts machined on it. Low rigidity, poor structural design, thermal strains, inaccurate structural members of a machine tool, and assembly allowance result in a positioning error of machine tool's end-effector. Since computer numerically controlled (CNC) machines use their structure as a reference frame, characterization and reduction of these errors call forth an immediate attention.;In general, errors of a machine tool can be reduced either by avoiding them or eliminating them. Error avoidance, as a strategy, attacks and removes the source of errors, thus avoiding the error altogether. In error elimination, the source of errors is left intact instead, and the result of that source, i.e., the error it produces, is eliminated. For successful elimination of such errors, they need to be accurately predicted, and an error prediction scheme requires the following considerations: (1) error modeling, (2) error observation, and (3) error/parameter estimation.;This work is aimed at devising error prediction schemes whose prediction capability has reduced (minimal) dependency on the measurement capability of an error observation system. The first two parts of this work provide two techniques of predicting machine tool errors by constructing error maps based on measurements that are obtained from an inaccurate calibration artifact and an inaccurate displacement transducer, respectively. To overcome the inaccuracy of the measurement setup, two concepts (redundancy and transitivity) are explored and tailored to each of the techniques.;The third part of this work explores the possibility of employing single dimensional measurements in estimating parameters of an error model that has been developed for multi-dimensional measurements. A mechanism of decomposing single dimensional measurement into multi-dimensional components is developed and augmented to the original model to allow the use of the augmented model in a larger calibration region without an added accuracy requirement to the measurement system. This work also investigates the possibility of using L infinity norm in addition to L2 norm in estimating errors and model parameters. |
