## 3 Experimental Tests and Results
### The Time-Variant Experimental Tests for Model Validation  
In the second part of the experimental campaign, a set of time-variant experiments was executed. In particular, the prototype was subjected to the application of thermal loads over a prescribed time period of 36 h. By starting with an environmental temperature close to 30 \({}^{\circ}\)C, the frame conditions were monitored by measuring the thermal stresses in the different positions of the frame surface. A preliminary investigation allowed for the improvement of the regression coefficients extrapolated from the FE study in order to obtain a robust model of the thermal effects. In this way, a multivariate regression model was studied to fit the \(z\)-axis thermo-mechanical deformations. Figure 8 presents the displacement variability detected by the sensors during the experiment time. The temperature of the structure was automatically collected by integrated circuit temperature sensors (LM53) located along the ram. By using the experimental data, a Multi Regression Analysis was performed, estimating the thermal-mechanical model coefficients. In addition, further temperatures of strategical positions (\(\Delta T_{bulk}\), \(\Delta T_{surf}\), and \(\Delta T_{flange}\)) were collected by a set of thermocouples and included in the model as independent variables. Figure 8: Variations measured by FBG sensors arranged over 36 h experimental tests. Figure 7: The static force effects: a comparison between the real tool tip displacement and the predicted position when a static force is applied to the tool tip point. Equation (13) represents the mathematical formulation of the MRA technique. \[\Delta Y_{pred}=\alpha_{0}+\alpha_{1}\cdot\Delta L_{1}+\alpha_{2}\cdot\Delta L_{2 }+\alpha_{3}\cdot\Delta L_{3}+\alpha_{4}\cdot\Delta L_{4}+\alpha_{5}\cdot\Delta L _{5}+\alpha_{6}\cdot\Delta T_{bulk}+\alpha_{7}\cdot\Delta T_{surf}+\alpha_{8} \cdot\Delta T_{flange} \tag{13}\]  
where \(\Delta T_{bulk}\) is the variation of \(z\)-axis bulk temperature between the starting time and the instant of measure, \(\Delta T_{surf}\) is the difference between bulk RAM temperature and Surface temperature, and \(\Delta T_{flange}\) is the temperature range measured between the spindle case and the structure. Table 1 summarizes the results of the MRA model with the use of a stepwise software. Figure 9 presents the thermal study results. A substantial coherence between the real and predicted position of the tool tip point is noted over time (36 h). The curves have the same change trends. The MRA models is able to fit the thermos-mechanical deformations with some mismatching due to the limited number of sensors integrated into the structure. The obtained accuracy of the predicted model varies from 5% to 8%, guaranteeing a substantial effectiveness of the model to predict the tool tip deviations. In the proposed experiments, the temperature effects had an important influence on the TTP position, in fact the maximum detected deviation was equal to 51 microns. If compensation is not provided, the total error due to the thermo-mechanical effects is described by the dotted curve in Figure 9. By using the predicted model the TTP position may be corrected. The potential compensation is equal to the difference between the dotted line and the solid line in Figure 9. In this case, the maximum model error is close to 9 microns. The presented model is particularly valid for external loads lower than 1000 N, as shown by conventional machining (e.g., milling cutting forces or temperature gradients). In this configuration, the rotations are considered as displacements, assuming the small displacement hypothesis. This paper also presents a set of simulations and tests based on loads that are over the expected operational range. This choice allows for the investigation of all potentialities of FBG technology applied to a novel MT structure made of CFRP and for the evaluation of further utilizations when high external loads are present.