## 5 Results and Discussion  
Given the typical conveyor belt speed used throughout this work (\(V_{L}\) = 600 mm/min = 1 cm/s) and the relatively large tool head diameter (\(d\) = 435 mm), condition 1 is easily obeyed, even for small transverse speeds (see Table 1). As expected, increasing the transverse speed requires larger rotational speeds to fulfil condition 2. Decreasing \(x\), from \(x=r\) to \(x=r/8\), to further obey condition 2, requires even larger rotational speeds. Experimental results (see Figure 9) for surface gloss as a function of transverse velocity \(V_{T}\), for \(x=r\), \(x=r/2\), \(x=r/4\), and \(x=r/8\) conditions, show a significant increase in gloss from 40 to 200 mm/s for all four \(x\) conditions. For higher transverse velocities, gloss remains essentially constant, showing that a maximum threshold has been attained and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(I\) (mm)} & \({V_{T}}\) & \({V}\) & \multicolumn{5}{c}{\(\omega\) (rpm)} \\ \cline{3-8}  & (mm/s) & (mm/s) & \(x\) & \(r\) & \(r\)/2 & \(r\)/4 & \(r\)/8 \\ \hline
120 & 40 & 41.58 & & 10 & 20 & 45 & 90 \\
64 & 75 & 75.80 & & 20 & 40 & 80 & 165 \\
53 & 90 & 90.67 & & 25 & 50 & 100 & 200 \\
48 & 150 & 150.33 further increasing the energy spent in the polishing process (by increasing the transverse and rotational speeds) does not lead to a refinement of the surface quality. The results clearly show that a better surface quality is obtained for smaller \(x\) values when the rotating action is more effective. For \(x=r\), the maximum attainable gloss is below 65 GU while for \(x=r/2\), \(x=r/4\), and \(x=r/8\) the maximum gloss is above 70 GU; essentially the same value in the three cases. However, for \(x=r/8\), this limit is reached sooner for lower transverse (and rotational) speeds. Simulation results (see Figure 10) for the same conditions show the same general trends, although the flat region for higher transverse velocities is not observed because the simulator simply adds abrasion contacts between the tool and the stone in a linear way, without considering any asymptotic effects. Clearly, gloss increases with transverse velocity and rotation velocity (which increases from \(x=r\) to \(x=r/8\)), with a slope that essentially matches the values obtained from the  
Figure 10: Abrasion as a function of transverse velocity \(V_{T}\), for \(x=r\), \(x=r/2\), \(x=r/4\), and \(x=r/8\). Figure 9: Gloss as a function of transverse velocity \(V_{T}\), for \(x=r\), \(x=r/2\), \(x=r/4\), and \(x=r/8\). experimental curves. Figure 11 shows, for three different transverse velocities (for the curve for \(x=r/8\)), that as the zigzag trajectories become more parallel (when the transverse velocity increases), the polishing intensity and surface homogeneity should also increase, as indicated by experimental and simulation results. Figure 12 compares experimental gloss with simulation abrasion, as a function of transverse velocity, for \(x=r/8\). While the simulated abrasion increases linearly with transverse velocity, experimental gloss shows a less predictable evolution, although the overall trends are similar for both types of data. In both cases the polishing quality increases substantially when the transverse speed increases (and rotational speed, to obey condition 2). However, the data in Figure 9 and Table 1 clearly show that increasing these two speed parameters separately is not sufficient to achieve a good polished surface. Decreasing \(x\) from \(x=r\) to \(x=r/2\) is crucial to achieve a good polished surface. Decreasing \(x\) even further to \(x=r/8\) permits obtaining the same results at lower transverse speeds. In our case, working at \(x=r/8\) with \(V_{T}=150\) mm/s (w = 330 rpm, from Table 1) provides essentially the same final quality (Figure 10) as working at \(x=r/2\) with \(V_{T}=200\) mm/s (\(w=110\) rpm). On the other hand, working at low \(V_{T}\) speeds, such as 90 mm/s, a good polished surface is never attained, even for \(x=r/8\) and high rotational speeds (\(\omega=200\) rpm).