There is an important interest in compensating thermally induced errors of modular tool systems to improve the manufacturing accuracy. In this paper, we test the hypothesis whether we can predict such thermal displacements by using a nonlinear regression analysis, namely the alternating conditional expectation algorithm (ACE [Breiman & Friedman, 1985]), reliably. The data analyzed were generated by two different finite element spindle models of modular tool systems. As the main result, we find that the ACE-algorithm is a powerful tool to model the relation between temperatures and displacements. The maximal correlation is larger than 0.999 in both cases, which demonstrates the suitability of the ACE algorithm. Furthermore, preconditions for the applicability of this approach, such as the length and the support of measured data sets, are studied. Hence, this approach seems to be promising for the application to real modular tool systems.
Precision and productivity are very important criteria for the evaluation of modular tool systems and require a thermally stable process with tolerances in the micrometer range. During the past decades there has been an increasing interest in compensating thermally induced errors. In this paper we investigate wheather a prediction of thermal displacement based on a nonlinear regression analysis is possible, namely using the alternating conditional expectation algorithm (ACE) introduced by Breiman and Friedman, 1985. The data we are analyzing were generated by two different finite element spindle models of modular tool systems. As the main result we find that the ACE-algorithm is a powerful tool to model the relation between temperatures and displacements. It could also be a promising approach to handle well-known hysteresis effects. Limitations of this study are the model restricted results, next our findings have to be validated on real data.
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