## 4 Conclusions  
This study aims to present a structured method to compensate errors of a MT when it is affected by undesired external factors. This point is a critical process since it allows for the instantaneous compensation of geometrical or thermal errors, thereby guaranteeing the machining performance. The conventional approaches are based on models that are able to predict the MT deformations, studying a relationship between machine accuracy and undesired loads. Nevertheless, it is difficult to identify a general robust relation and these models need to be calibrated for every machine variant, thereby limiting their success, and increasing both costs and the implementation time. The proposed solution is based on a novel approach to calibrate a machine tool in real-time, analyzing the thermo-mechanical errors through fiber Bragg grating (FBG) sensors embedded in the MT frame. This configuration consists of an adaptronic structure of passive materials, Carbon Fiber Reinforced Polymers (CFRP), equipped with FBG sensors that are able to measure in real-time the deformed conditions of the frame. By using a proper thermo-mechanical kinematic model, the displacement of the end effector may be predicted and corrected when it is required. By starting from a set of FE simulations, a relationship between the FBG behaviors and TTP displacement was evaluated. The simulations were performed by varying a static load at TTP and the structure temperature. The multiple regression allowed for the identification of a model to be validated through a set experimental tests. A prototype (a ram of a commercial milling machine) was fabricated integrating the FBG sensors in the MT frame. In the first part of the experimental tests, the model was validated applying a set of static loads. This analysis showed a good matching between the real and the predicted position of the MT tool tip point. In the same way, the tests were replicated varying the \begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Advantages**} & \multicolumn{1}{c}{**Limitations**} \\ \hline - & high sensitivity (0.2 \(\mu\) = 0.2 \(\mu\)m/m = 0.00002\% & - & due to their high sensitivity, the measurement of one quantity (e.g., strain) may be influenced by another quantity; \\  & & strain 1\%; able to measure local strain & - \\  & and temperature; & - & fibers cannot be repaired; \\  - & small size (diameter \textasci{-}0.5\) mm) and light weight; & - & complexity in fibers handling due to their brittleness; \\  - & immunity to chemical agents; & - & relatively high costs, but that depends on the type of application; \\  - & geometrical versatile; & - & not always easy to install to obtain an effective application; \\  - & temperature range \textasci{-}40\)\({}^{\circ}\)C to 300\({}^{\circ}\)C; & - & not always easy to install to obtain an effective application; \\  - & ability to be embedded or laminated & - & effective application; \\  & into structures; & - & complexity in statistical data management to identify a robust model. \\ - & high durability and lifetime over 20 years. & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A comparison between the main advantages and limitations of the FBG sensor application. Figure 9: Thermo-mechanical effects: the real tool tip displacement vs. the predicted displacement. environmental temperature over time (36 h). The results obtained from the FBG measurements allowed for the regression model to be tuned and for the error prediction to be improved. The last campaign of experimental tests illustrated a substantial coherence between the real and predicted position of TTP. This study highlights the significant advantages of applying FBG sensors in measuring MT deformations, such as their high sensitivity, geometrical versatility, light weight, immunity to electromagnetic interference or chemical agents, and high durability. Nevertheless, it also underlines the limitations of this method.