## 3 Results  
The primary parameter to be considered is the overall specific energy consumption (OSEC). The obtained simulation's results are depicted in Figure 2 and resumed in Table 5.  
Figure 2 shows the results of the simulations in terms of the overall specific energy consumption (OSEC) versus the gearbox ratio percent variation (GRPV), for each motor from M2 to M7. The decameter speed is controlled at 4916 rpm, although with a varying gearbox ratio. The minimum OSEC is achieved using the M7 motor at +7% GRPV, operating the M7 motor at a velocity of 2646 rpm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coefficient** & **Value** & \
\begin{tabular}{c} **Lower 95\%** \\ **Confidence Bounds** \\ \end{tabular} &
\begin{tabular}{c} **Upper 95\%** \\ **Confidence Bounds** \\ \end{tabular} \\ \hline p00 & \(-\)13.27 & \(-\)21.36 & \(-\)5.186 \\ p10 & 548.6 & 548.1 & 549.1 \\ p01 & 612.5 & 546.7 & 678.3 \\ p11 & \(-\)1109 & \(-\)1111 & \(-\)1106 \\ p02 & 1736 & 1372 & 2101 \\ p12 & 1487 & 1466 & 1508 \\ p03 & \(-\)27,486 & \(-\)29,220 & \(-\)25,750 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The polynomial surface fit model poly13 coefficients and their 95% confidence bounds when considering the M4 motor and the decameter not loaded. Figure 2: Simulink simulation results of the overall specific energy consumption (OSEC) versus the gearbox ratio percent variation, for each motor from M2 to M7. Furthermore, the graphs in Figure 2 show that the curves have a parabolic law behavior and that the motors are operated at a speed over 3000 rpm that corresponds to the synchronous speed of these three-phase motors (being f = 50 Hz and PolesPairs = 1, then the synchronous speed is 60\(\times\)f/PolesPairs = 3000 rpm), except for the M7 motor, which is operated at 2646 rpm to reach its minimum OSEC and, therefore, below its synchronous speed. Table 5 resumes the objective of this work: to determine when the OSEC reaches its minimum value and for which electric motor power and gearbox ratio value. Table 5 also reports the minimum reached OSEC, showing the optimum GRPV and the operated electric motor. These values represent the minimum values as shown in Figure 2. In addition, the OSEC percent saving related to the reference (the M4 motor operated directly online) is reported in Table 5.  
The decanter speed is controlled at 4916 rpm. The minimum OSEC is achieved by the M7 motor at +7% the optimum gearbox ratio percent variation; in this condition, the related energy saving resulted in +4.01% for the OSEC with reference to the M4 motor operated directly online (DOL). In addition, Figure 3 shows the existing relation between the minimum OSEC and the electric motor nominal power. The data suggest the interpolation using a Gompertz sigmoid function as this function models very well the asymptotic behavior observed at 11 and 15 kW of motor power. The Gompertz sigmoid function correlates very well (R\({}^{2}\) = 0.99427) and predicts what happens to the OSEC when using a motor with a different rated power; thanks to this, the equation can be considered very helpful. In addition, the equation suggests that, although the general behavior recommends that IM heavy oversizing can improve the process's overall energy saving, this should be compared to the asymptotic behavior of the equation itself. In fact, at higher motor mechanical power values, an increment of the mechanical power brings a decrement of OSEC that can be unimportant if compared to the higher costs required to purchase both the IM and the VFD. This last consideration should be considered by adding it to the correlation equation of Figure 3: in this manner, an optimal minimum for the size of the IM could be obtained. Moreover, to investigate the predictive capability of the results found, the OSEC curves have been modeled through a multiple linear regression, using as dependent variables the motor power (called x1) and GRPV (called x2). As the independent variable, or result variable, the OSEC (called y) was used.