## 2 Materials and Methods
### Pad Wear Shape Simulation  
Figure 4a shows a schematic of the kinematic model related to the rotation of the conditioner disc, the sweep of the conditioning arm, and the rotation of the pad, where the distance between the rotational centers of the pad and the swing arm hinge is defined as \(L\). The conditioner disc rotates in the same direction at an angular velocity \(\omega_{c}\), sweep velocity of the swing arm \(\omega_{s}\), and pad at angular velocity \(\omega_{p}\). A conditioning arm of length \(l\) sweeps back and forth between the center of the pad and the edge of the pad.  
The kinematics of an abrasive at point C on a conditioner disc can be described by the following equations:  
\[\stackrel{{\rightarrow}}{{R}}=\stackrel{{ \rightarrow}}{{L}}+\stackrel{{\rightarrow}}{{l}}+ \stackrel{{\rightarrow}}{{r}}=\left\{L_{x}(t)+l_{x}(t)+r_{x}(t) \right\}\hat{t}+\left\{L_{y}(t)+l_{y}(t)+r_{y}(t)\right\}\hat{J}, \tag{1}\]  
\[L_{x}(t)=L\cos(\theta_{1}+\omega_{p}t), \tag{2}\]  
\[L_{y}(t)=L\sin(\theta_{1}+\omega_{p}t), \tag{3}\]  
\[l_{x}(t)=l\cos(\theta_{1}+\theta_{2}+\left(\omega_{p}+\omega_{s}\right)t), \tag{4}\]  
\[l_{y}(t)=l\sin(\theta_{1}+\theta_{2}+\left(\omega_{p}+\omega_{s}\right)t), \tag{5}\]  
\[r_{x}(t)=r\cos(\theta_{1}+\theta_{2}+\theta_{3}+\left(\omega_{p}+\omega_{s}+ \omega_{c}\right)t), \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Zone**} & \multicolumn{1}{c}{**1**} & \multicolumn{1}{c}{**2**} & \multicolumn{1}{c}{**3**} & \multicolumn{1}{c}{**4**} & \multicolumn{1}{c}{**5**} & \multicolumn{1}{c}{**6**} & \multicolumn{1}{c}{**7**} & \multicolumn{1}{c}{**8**} & \multicolumn{1}{c}{**9**} & \multicolumn{1}{c}{**10**} & \multicolumn{1}{c}{**11**} & \multicolumn{1}{c}{**12**} & \multicolumn{1}{c}{**13**} & \multicolumn{1}{c}{**14**} & \multicolumn{1}{c}{**15**} \\ \hline Parabolic & 11 & 9.1 & 7.6 & 6.3 & 5.3 & 4.6 & 4.1 & 4.0 & 4.1 & 4.6 & 5.3 & 6.3 & 7.6 & 9.1 & 11 \\ \hline Inverse Parabolic & 3.2 & 4.7 & 5.9 & 7.0 & 7.8 & 8.3 & 8.7 & 8.8 & 8.7 & 8.3 & 7.8 & 7.0 & 5.9 & 4.7 & 3.2 \\ \hline Step Center Fast & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 & 6.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 \\ \hline Step Edge Fast & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 4.0 & 6.0 & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 & 8.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Relative occupancy time (ROT, %) of profile cases; parabolic, inverse parabolic, step center fast, and step edge fast.  
Figure 3: (**a**) Schematic of conditioning zone and Relative occupancy time (ROT), (**b**) Schematic of the eight conditions used in experiments and predictions.  
\[r_{y}(t)=l\sin(\theta_{1}+\theta_{2}+\theta_{3}+\left(\omega_{p}+\omega_{s}+\omega_{c }\right)t) \tag{7}\]  
where \(\theta_{1},\ \theta_{2},\ \text{and}\ \theta_{3}\) denote the initial angular position of the center of the swing arm with respect to the center of the pad, the initial angular position of the center of the conditioner disc, and the initial angular position of an abrasive on the conditioner disc, respectively.  
In this study, \(l\) and \(L\) are set the same. Figure 4b shows a schematic of the concept of integrating the trajectory made in a certain area where the working diamond abrasives are defined. We calculated the relative wear amount for the areas of \(dx\) and \(dy\), and then integrated the length of the trajectory in the area of \(dx\) and \(dy\). The total length trajectory is proportional to the amount of pad wear, which can represent the wear profile.