Modeling Thermal Displacements in Modular Tool Systems

Abstract

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.

Nonlinear additive autoregressive model-based analysis of short-term heart rate variability

“…The maximal correlation and optimal transformation approach were applied recently to nonlinear dynamic systems to identify delay in lasers [35] and partial differential equations in fluid dynamics [37]. The ACE algorithm turned out to be a very efficient tool for nonlinear data analysis [16,35,39,43,44]. …”

Nonlinear Methods of Cardiovascular Physics and Their Clinical Applicability

“…These approaches on the one hand aim at modeling one or more regulation processes, and on the other hand provide model parameters which should be used to answer clinically relevant questions. In this tutorial we have introduced an approach which is very promising in data-driven modeling and modelbased data analysis [Wessel et al, 2000b;Wessel et al, 2004a;Wessel et al, 2004b;Wessel et al, 2006]. We have found that the maximal correlation method is a powerful tool for medical data analyses and for solving mechanical engineering problems.…”

“…This makes the result less sensitive to the data distribution. The maximal correlation and optimal transformation approach have recently been applied to nonlinear dynamical systems especially to model river flow data [Chen & Tsay, 1993], to identify delay in lasers [Voss & Kurths, 1997] and partial differential equations in fluid dynamics , to predict thermal displacements in modular tool systems [Wessel et al, 2004a;Wessel et al, 2004b] and to medical data analyses [Wessel et al, 2000b;Wessel et al, 2006]. A more general review on nonlinear system identification is given in .…”