# Correction of Thermal Errors in Machine Tools by a Hybrid Model Approach
## 5 Structural Model
Segmentation allows for the simulation of asymmetric load cases (e.g., one-sided heat input on the right side). For example, if a moving part slides over a static part (denoted by vertical arrows), one of them is divided into several segments and after every 10 s of solver time step, 2500 signals of data (i.e., based on a 4 ms data sampling rate \(\rightarrow\) 10/0.004 = 2500) are averaged over the divided segments to generate a position-dependent load profile. Preliminary results indicate feasible approximation of thermal behavior when tested with the control's data, i.e., load cases. The structural model is subjected to a series of tests to investigate the simulation time. Figure 15 elaborates on the simulation time comparison and a temperature profile visualization of the structural model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Block** & **Description** \\ \hline Main Code & Here, the interconnections of each block are defined and with the help of additional function scripts (\(f\)), the overall process parameters are implemented and performed, such as time domains (solver time step, data sampling rate, and correction rate), machine model calculation, pre-processing of imported data, post-processing of the output, and visualization. \\ \multicolumn{2}{c}{A complete machine is assembled including the imported data of each AP, contacts, sensors, axes, convection blocks, and FEM-to-MOR pre-processing. Once the configuration of sub-blocks is finalized, creation of the model is a one-time process and the created model can later be directly loaded into the main code saving compilation time for different load cases. \\ \multicolumn{2}{c}{\begin{tabular}{c} Sensor \\ \end{tabular} } & Heat flow/generation scripts are generated separately for each surface to impose thermal values found by experiments. \\ \multicolumn{2}{c}{\begin{tabular}{c} Convection \\ \end{tabular} } & Scripts are generated separately for each surface to impose convection values found by experiments on specific renamed imported surfaces. \\ \multicolumn{2}{c}{\begin{tabular}{c} Axes \\ \end{tabular} } & Spatial parameters are defined and prepared to gather data from the load cases incoming from machine controller. These load cases together with axes block are then communicated to moving contact blocks for thermal load calculation. \\ \multicolumn{2}{c}{\begin{tabular}{c} Contact \\ \end{tabular} } & Contacts could either be linear or angular and moving or static. Depending on the case, the respective contact block is generated. In the presented case, contact scripts mainly act as a medium to incorporate load case by machine controls and generate a position-dependent temperature profile. These scripts \\ \multicolumn{2}{c}{\begin{tabular}{c} Fortract \\ \end{tabular} } & \begin{tabular}{c} work simultaneously, i.e., active AP contact + passive AP contact, with other blocks. \\ \end{tabular} \\ \multicolumn{2}{c}{\
\begin{tabular}{c} FEM block \\ \end{tabular} } & Finite Element Modeling (FEM) numerical procedure is introduced and integrated with CreateModel \\ \multicolumn{2}{c}{
\begin{tabular}{c} MOR block \\ \end{tabular} } & Krylov-based Model Order Reduction (MOR) method is introduced, which is used to downsize the DOF of whole system and retransform into temperature points for output block. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Block characteristics of structural model. An example load case was simulated in both the FE model and the structural model. A comparison between the two models revealed an error ranging from 10% to 15% (subject to change with further development) in the structural model when compared to the FE model, while exhibiting similar temperature behavior. It was further observed that 24 h of reality was simulated in 48 h through a conventional FEM procedure (ANSYS), while a structural model based on MOR (MATLAB) took less than 30 min. The structural model's significant reduction in simulation time enhances its suitability for real-time decision making.