# Frictional Behaviour of the Microstructural Surfaces Created by Cylindrical Grinding Processes
## 2 Structural Surface Creation and Their Characteristics
### Surface Measurement and Characterization  
The 3D topography of ground micro structural surface was measured by a Wyko white light interferometer. The measuring area is 0.6 \(\times\) 0.4 mm\({}^{2}\) containing 368 \(\times\) 240 points. The typical measurements of micro structural surface topography are shown in Figure 2. Comparing with polish-ground component (test sample 0), many deeper and larger gouges appeared on the ground textural surfaces on the workpieces. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \(a_{d}\) & \(f_{d}\) & \(v_{s}\) & \(n_{s}\) & \(n_{w}\) & \(a_{p}\) \\  & \(\mu\)m & \(\mu\)m/rev & \(m\)/s & rpm & rpm & rpm & \(\mu\)m \\ \hline
1 & 10 & 100 & 35 & 1344 & 3 & 1 \\ \hline
4 & 10 & 100 & 35 & 1344 & 3 & 4 \\ \hline
5 & 10 & 120 & 35 & 1344 & 3 & 1 \\ \hline
6 & 10 & 120 & 35 & 1344 & 3 & 2 \\ \hline
7 & 10 & 120 & 35 & 1344 & 3 & 3 \\ \hline
8 & 10 & 120 & 35 & 1344 & 3 & 4 \\ \hline
0 & 10 & 90 & 35 & 1344 & 30 & 1\(\rightarrow\)0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Grinding experimental conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Structural Axial** & **Structural** & **Structural** & **Structural** \\  & **Interval (\(\mu\)m)** & **Circumference** & **Width** & **Length (\(\mu\)m)** & **Depth (\(\mu\)m)** \\ \hline
1 & 100 & 377 & 10 & 37 & 1 \\
2 & 100 & 377 & 21 & 81 & 2 \\
3 & 100 & 377 & 35 & 133 & 3 \\
4 & 100 & 377 & 53 & 200 & 4 \\
5 & 120 & 377 & 8 & 26 & 1 \\
6 & 120 & 377 & 18 & 54 & 2 \\
7 & 120 & 377 & 27 & 86 & 3 \\
8 & 120 & 377 & 39 & 121 & 4 \\
0 & Polished by dwell sparking out & n/a & n/a & \(\rightarrow\)0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Nominal geometrical parameters of structural surface. Figure 2: Surface topography of microstructural surface. (**a**) Topography of component 0 (polished surface \(S_{a}\) = 0.082 mm). (**b**) Topography of component 2 (textured surface \(S_{a}\) = 0.263 mm). (**c**) Topography of component 3 (textured surface \(S_{a}\) = 0.255 mm). From measured cylindrical surface topography, the surface roughness parameters were extracted for depicting the surface topography amplitude, spatial and other features. Following 3D roughness parameters are considered as microstructural surface features in analysis: \(S_{a}\), \(S_{sk}\) and \(S_{ku}\) from the amplitude parameters, \(S_{vk}\) and \(S_{k}\) from the functional parameter, \(S_{tr}\), \(S_{al}\) from the spatial parameters and the peak count number \(R_{pc}\). These parameters are of statistical geometrical significance and often used for assessing surface quality and surface wear performance. \(S_{a}\) is the most widely used amplitude parameter for surface characterization and is an important roughness parameter for the machining surface. \(S_{sk}\) (Skewness) and \(S_{ku}\) (Kurtosis) of topography height distribution are chosen to evaluate the curvature features of the microstructural surface. The skewness of the texture height distribution is always combined with the kurtosis to describe the shape of the surface topography. By considering the skewness and kurtosis, the proportion of deep valleys and top flat in the microstructural surface can be identified. The functional parameter \(S_{k}\), which defined from Abbott-Firestone curve or bearing area curve, is commonly used to characterize honed surface texture, which might also suit for microstructural grinding surface. It contains the reduced peak height \(S_{pk}\) describing the height at which peaks rise from the core profiles, the core roughness depth \(S_{k}\) and the reduced valley height \(S_{vk}\), which indicates the oil reservoir in the surface that may influence friction. For spatial parameters, the surfaces texture ratio \(S_{tr}\) is used to identify the structural texture pattern and isotropy while the autocorrelation length \(S_{al}\) describes main wavelengths of micro structural surface [19].