## 2 Experimental Procedure
### Taguchi Method and Polishing Parameters  
Before designing the experiments using Taguchi' orthogonal arrays, it is worth mentioning here that in surface polishing, it is always desired to remove less material to achieve the smooth surface as higher material removal can easily deform the shape of the workpieces, especially at the edges. Therefore, the target is to remove the peaks in the surface roughness profile of the surface to be polished, which is only possible with the optimal polishing force. Figure 4 shows the surface roughness height profile of the surface of the watch bezel before and after the initial polishing tests. Besides the surface  
Figure 3: Equipment used in experiments: (**a**) surface roughness tester (Mitutoyo, SJ-210); (**b**) torque sensor (Forsentek, FX02); (**c**) tachometer. Figure 2: Polishing wheel and workpiece: (**a**) Top view of the polishing wheel and workpiece interaction; (**b**) isometric view of the workpiece (watch bezel). roughness (\(R_{a}\)) of the height profile, skewness (\(R_{sk}\)), and kurtosis (\(R_{kt}\)) are also mentioned here because these parameters help to understand the distribution of the peaks and valleys present in height profile. Before polishing height profile have many high peaks and deep valleys (\(R_{sk\ (before)}=-0.505\), and \(R_{kt\ (before)}=3.409\)). After the surface polishing, the height profile became highly negatively skewed (\(R_{sk\ (after)}=-1.530\)) because more high peaks are removed compared to the valleys. For the precise interaction workpiece is allowed to rotate upon wheel interaction to avoid the extreme frictional force. This interaction can be optimized by controlling the gripper's rotational friction or moment of inertia (it is the amount of torque required to rotate a rigid body about its rotational axis). Moment of inertia depends on the mass of the body as \(I\ =\ mr^{2}\), where \(m\) is mass and \(r\) is the distance from the pivoted point. Therefore, the rotational friction of the gripper can be control by adding friction to the axi or by adding the mass to the gripper. In this gripper, mass (circular ring with a mass of 0.303 Kg) is added to the rotational part of the gripper to change its load or startup torque or moment of inertia. Taguchi based DOE is used to analyze the effect of machining input parameters on the proposed system for the polishing of watch bezel. The input parameters are wheel rotation speed (\(w\)), normal contact force (\(F_{z}\)), gripper vibratory motion velocity (\(V_{f}\)), and gripper start-up torque (\(T_{g}\)). These parameters are tested for polishing efficiency (\(PE\)) and polishing torque (\(T\)). Input polishing parameters for the system with its levels are shown in Table 1. To analyze the \(T_{g}\) effect on the process two different levels are created by adding weight to the rotating part of the gripper as discussed previously. The polishing wheel speed and normal force are two important parameters that work collectively for economical polishing. Wheel speed is usually measured in surface feet per minute (SFPM) as: \(SFPM=\ \pi\ [(1\ f\ x\ D\ /\ 12\ in)\ \times rpm]\), where \(D\) is the wheel diameter and \(rpm\) is the rotation per minute. Depending on the initial testing, material removal requirement, related literature study [32], and the experiences of the experts working on the steel polishing, three levels are selected for the speed (3500, 4000, and 4500 rpm). In polishing particularly to achieve the mirror-like shine from the semi-polished surface, a higher material removing rate is avoided. Additionally, higher contact forces damage wheel shape, reduce its life, and increase power consumption (torque), which is not good for economical polishing.