Real-time error compensation on machine tools through optimal thermal error modeling.

Abstract

This dissertation presents a real-time error compensation approach, which combines finite element analyses and a developed optimization method with error modeling, measurements and real-time control system. The proposed approach introduces a generic error synthesis model, eliminates metrological constraints, reduces required experiments, and improves thermal error model accuracy. A generic error synthesis model was derived for linkage systems using prismatic joints. An error component link metrology was introduced to relax the metrological constraints imposed on error component measurements. The use of the link metrology yielded a flexible error synthesis model, which is applicable to error measurements taken arbitrarily in space. An optimization method was developed to select appropriate temperature variables as well as to ensure accurate thermal error models. An optimization objective was designed to avoid unnecessary temperature variables into thermal error models. A search method was proposed for the particular unknown-order temperature variable domain. In contrast to other modeling techniques, the developed optimization method determined the optimal models consistently. By using directly measured temperature and error data, the optimal thermal error models were found for two similar machines, an AC300 and an AC1000 turning centers. Two real-time error compensations were implemented successfully on the two machines. Machine accuracy, for both machines, was improved by a factor of 5 to 10 times. The maximal error of the AC300 turning center was reduced from 100 to 10 $\mu$m. In addition, a systematic scheme of numerical temperature variable optimization was developed without requiring the measured data. Temperature distributions and thermal deformations of machine structures were solved numerically by utilizing finite element methods. The best temperature variables in terms of temperature sensor locations were determined by using the finite element data through the developed optimization method. The accomplished numerical optimization not only reduces required experimental time and cost, but also improves the reliability of thermal error models.