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Parameterization of environmental influences by automated characteristic diagrams for the decoupled fluid and structural-mechanical simulations

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Glänzel J. , Kumar T. S. , Naumann C. , Putz M.

tom Vol. 19, No. 1

98--113

Thermo-elastic effects contribute the most to positioning errors in machine tools especially in operations where high precision machining is involved. When a machine tool is subjected to changes in environmental influences such as ambient air temperature, velocity or direction, then flow (CFD) simulations are necessary to effectively quantify the thermal behaviour between the machine tool surface and the surrounding air (fluid). Heat transfer coefficient (HTC) values effectively represent this solid-fluid heat transfer and it serves as the boundary data for thermo-elastic simulations. Thereby, deformation results can be obtained. This two-step simulation procedure involving fluid and thermo-structural simulations is highly complex and time-consuming. A suitable alternative for the above process can be obtained by introducing a clustering algorithm (CA) and characteristic diagrams (CDs) in the workflow. CDs are continuous maps of a set of input variables onto a single output variable, which are trained using data from a limited number of CFD simulations which is optimized using the clustering technique involving genetic algorithm (GA) and radial basis function (RBF) interpolation. The parameterized environmental influences are mapped directly onto corresponding HTC values in each CD. Thus, CDs serve as look-up tables which provide boundary data (HTC values along with nodal information) under several load cases (combinations of environmental influences) for thermo-elastic simulations. Ultimately, a decoupled fluid-structural simulation system is obtained where boundary (convection) data for thermo-mechanical simulations can be directly obtained from CDs and would no longer require fluid simulations to be carried out again. Thus, a novel approach for the correction of thermo-elastic deformations on a machine tool is obtained.

Comparison of basis functions for thermal error compensation based on regression analysis – a simulation based case study

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Naumann C. , Glänzel J. , Putz M.

tom Vol. 20, No. 4

28--40

It is a well-known problem of milling machines, that waste heat from motors, friction effects on guides, the environment and the milling process itself greatly affect positioning accuracy and thus production quality. An economic and energy-efficient method of correcting this thermo-elastic positioning error is to gather sensor data (temperatures, axis positions, etc.) from the machine tool and the process and to use that information to predict and correct the resulting tool center point displacement using regression analysis. This paper compares multilinear characteristic diagrams, B-spline characteristic diagrams, Radial Basis Function fitting and Wavelet fitting in general and also in the context of thermal error compensation. The demonstrations are made using FEM simulation data from a machine tool demonstrator. The results show that all of the above kernel types, if properly used, are able to create good compensation models. However, high-dimensional multivariate analysis usually only works by adding grid structures and regularization.