# Measuring Procedures for Evaluating the Surface Roughness of Machined Parts
## 2 Methodology
The surface tester used has a manufacturer-defined resolution for the \(Z\)-axis, i.e., for measuring height characteristics with a value of 0.02 \(\upmu\)m. This data applies to the largest measurement range that this device has available. Since the device has an automatic selection of the measurement range, for reporting measurement uncertainty, we will consider this resolution value as a potential source of measurement uncertainty. The resolution is not defined for the \(X\)-axis, but this data can be determined from the sampling that the device performs at individual settings (Table 1). For individual setting values of the cut-off filter parameter, the sampling for the \(X\)-axis also changes. This device for evaluating individual quantities uses the course of the surface roughness profile curve with resolution values for individual measurement axes (\(X\)-axis in the horizontal plane and \(Z\)-axis in the vertical plane). These are longitudinal measurements, from which the values of individual surface roughness values are then indirectly determined by calculation in accordance with the relevant standards. Thus, determining the measurement uncertainty for \(Ra\), for example, is a rather complicated task beyond the scope of this article. In this article, we will attempt at least an approximate estimation of the measurement uncertainty because, in our opinion, each measurement must have an \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cut-Off Filter (mm)** & \begin{tabular}{c} **Evaluation Length** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Number** \\ **of Samples** \\ \end{tabular} &
\begin{tabular}{c} **\(X\)-Axis Resolution** \\ **(\(\upmu\)m)** \\ \end{tabular} \\ \hline
0.08 & 0.4 & 800 & 0.5 \\
0.25 & 1.25 & 2500 & 0.5 \\
0.8 & 4 & 8000 & 0.5 \\
2.5 & 12.5 & 8330 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Surface tester sampling and resolution at different settings. Figure 1: Stylus-based surface roughness measurement using a surface tester. associated measurement uncertainty in order to be able to evaluate the reliability of the mentioned experimental measurements [41; 42; 43; 44; 45; 46; 47; 48; 49]. Therefore, if we consider the differences in measurement in both directions as a significant source of uncertainty, then we can state them as the standard uncertainty determined by method B:  
\[ \begin{array}{c}u_{BX}=1.5\ \upmu\text{m}\\ u_{BZ}=0.02\ \upmu\text{m}.\end{array}  \tag{1}\]  
If we consider that the digital device and the measured quantities follow the uniform distribution law of random values, then we will consider the extended measurement uncertainty with a coverage coefficient with a value of \(\surd 3\) at the significance level of 0.95. Then we will consider the expanded uncertainties of the displacement measurement:  
\[ \begin{array}{c}u_{BX}=u_{BX}\cdot k_{\text{cov}}=2.6\ \upmu\text{m}\\ u_{BZ}=u_{BZ}\cdot k_{\text{cov}}=0.035\ \upmu\text{m}.\end{array}  \tag{2}\]  
It should be emphasized that this is only a very rough estimate, and for a more precise determination of the measurement uncertainty, it is also necessary to consider the uncertainty resulting from the geometry of the measuring tip, the uncertainty resulting from its elastic deformation during measurement, the uncertainty resulting from lateral movements during measurement, the uncertainty resulting from the noise of the device. It is very complicated to identify all components of measurement uncertainty when using such a complex device. The surface tester used has the function of automatic calibration using secondary surface roughness standards. Secondary surface roughness standards for surface roughness testers, which is a calibration etalon artifact with unidirectional irregular profile of type D1 (according to ISO 5436-1:2000) [36], is recommended for the calibration of the gauge. For this artifact, the value of \(Ra\) and \(Rz\) is defined.