Abstract
Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest.
Highlights
Machine tools, such as milling machines, grinding machines, or lathes, are complex mechatronic systems and key components in the manufacturing process
This work presents a model order reduction (MOR) approach to deal with the parametric dependency of the convective boundary conditions in weakly coupled thermo-mechanical models
The Krylov Modal Subspace (KMS) method proposes a reduction basis combining the information of the Krylov subspace basis with an expansion point at a low frequency and the thermal eigenmodes
Summary
Machine tools, such as milling machines, grinding machines, or lathes, are complex mechatronic systems and key components in the manufacturing process. The thermo-mechanical model described the thermal response of a machine tool column to localized heat sources, representing the losses of a drive and friction of the ballscrew nut. Efficient thermo-mechanical models of machine tools need to consider the position dependency of the thermal and mechanical response. Parametric MOR approaches with global reduction bases are more suitable for the models under investigation These methods create a single set of projection bases for the values of the parameter space. This paper proposes a novel parametric MOR reduction approach for thermo-mechanical models of mechatronics systems, such as machine tools. The presented MOR method considers the characteristic behavior of these models in order to build the reduction basis, enabling the possibility to trace the parameters describing the convective boundary conditions. The reduced model needs to evaluate the thermally induced structural deformations
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