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.

Decoupling approach presents a novel solution/alternative to the highly time-consuming fluid-thermal-structural simulation procedures when thermal effects and resultant displacements on machine tools are analyzed. Using high dimensional Characteristic Diagrams (CDs) along with a Clustering Algorithm that immensely reduces the data needed for training, a limited number of CFD simulations can suffice in effectively decoupling fluid and thermal-structural simulations. This approach becomes highly significant when complex geometries or dynamic components are considered. However, there is still scope for improvement in the reduction of time needed to train CDs. Parallel computation can be effectively utilized in decoupling approach in simultaneous execution of (i) CFD simulations and data export, and (ii) Clustering technique involving Genetic Algorithm and Radial Basis Function interpolation, which clusters and optimizes the training data for CDs. Parallelization reduces the entire computation duration from several days to a few hours and thereby, improving the efficiency and easeof-use of decoupling simulation approach.

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