# Effect to the Surface Composition in Ultrasonic Vibration-Assisted Grinding of BK7 Optical Glass
## 2 Experimental Setup  
In order to investigate the effect of grinding and ultrasonic vibration parameters on surface composition and surface roughness, ultrasonic vibration-assisted grinding experiments of BK7 optical glass materials were carried out on a 5-axis precision ultrasonic machine center (DMG Ultrasonic 70-5 linear). The Schott ultrasonic hollow nickel electroforming diamond grinding wheel was used, whose diameter was 4 mm, average grain diameter was 64 um, and the diamond concentration was 100%. Automatic laser measuring device was used to measure the length and radius of the tool. The grinding tool oscillates along the axial direction of the spindle. The ultrasonic frequency of the cutting tool was detected by the machine tool measurement device and its value was 30,047 Hz. The BK7 optical glass material workpieces were in the form of cuboid with 50 mm in length, 50 mm in width, and 6 mm in height. In order to preclude the influence of coolant on machining process, grinding coolant was not used in these experiments. The glass workpiece was fixed to a steel plate using strong adhesive. After sticking, the object was allowed to stand for 24 h at room temperature. Experimental setup and scheme of the process kinematics is shown in Figure 1.  
To extensively investigate the influencing law of machining parameters on surface composition and surface roughness, a single factor design was employed in the experiments. The spindle rotation speed, grinding depth, feed rate, and ultrasonic vibration amplitude were defined as the experimental parameters. Since the resonance frequency is the best vibration frequency of the cutting tool during the process of ultrasonic vibration machining, the ultrasonic frequency was not considered as the parameter during the experiments [32; 33]. The concrete experimental parameters are given in Table 1. A total of 32 groups of experiments were carried out on BK7 optical glass based on this experimental design.  
Figure 1: \(Cont.\)  
After the experiments, the surface morphologies of the machined surfaces were observed by SEM, and the surface roughness of the machined surfaces were measured by AFM manufactured by Nanosurf Nanite, Switzerland, whose average error in the X/Y direction is less than 0.6%, the number of sampling lines set in the X/Y directions are both 256, the number of sampling points of each line is 256. In order to eliminate the random error, three sampling areas are taken randomly on the machined surface, and the average value is taken as the final result of surface roughness. The surface arithmetic  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Serial No.**} & **Spindle Rotation** & **Feed Rate** & **Grinding Depth** & **Ultrasonic** \\  & **Speed \(\boldsymbol{n}\)/(\(\boldsymbol{\mathrm{r}}\)pm)** & \(\boldsymbol{V_{p}}\)/(\(\boldsymbol{\mathrm{r}}\)mm/\(\boldsymbol{\mathrm{m}}\)) & \(\boldsymbol{a_{p}}\)/(\(\boldsymbol{\mathrm{\mu}}\)m) & **Amplitude \(\boldsymbol{A}\)/(\(\boldsymbol{\mathrm{\mu}}\)m)** \\ \hline
1 & 1000 & 110 & 60 & 7 \\
2 & 3000 & 110 & 60 & 7 \\
3 & 5000 & 110 & 60 & 7 \\
4 & 7000 & 110 & 60 & 7  
mean deviation (\(Sa\)) is selected as an index for evaluating the quality of the machined surface, and the specific algorithm is shown in Equation (1).  
\[Sa=\frac{1}{MN}\sum_{j=1}^{N}\sum_{i=1}^{M}\bigl{|}\eta i\bigr{|} \tag{1}\]  
where  
\(\eta_{ij}\)--the protrusion height at the measuring point of the \(i\)th row and the \(j\)th column;  
\(M\)--total number of rows in the measurement area;  
\(N\)--total number of columns in the measurement area.