Predicting thermal displacements in modular tool systems

Abstract

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new 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 .…”