# A Novel Measurement Standard for Surface Roughness on Involute Gears
## 4 Physical Measurement Standard (PMS) Representing Roughness on Involutes
### Calibration of the PMS  
The measurements for the calibration of the PMS are performed by using the HRTS described in Section 2.6. Showing the profile obtained via the fitting algorithm not only shows the structure of the roughness profile but also the two distinct valleys of the markers at the root and tip part of the profile. These simplify the orientation on the profile but are excluded from the filtered roughness profile to prevent distortions. The roughness profile of the PMS, shown in Figure 10, consists of peaks and valleys within the range of \(\pm 1\) um. There is no noticeable change in the characteristics along the arc length. In contrast to the results of the measurements on the master work piece shown in Figure 5), the roughness parameters remain almost constant for all positions of the evaluation intervals (see Figure 11). By manufacturing a much more homogeneous profile, the sensitivity of the evaluation towards the position of the evaluation subprofile is reduced and the metrological applicability is improved. Figure 11: Roughness parameters as function of the position \(x_{\mathrm{m}}\) of the evaluation interval; PMS shows that roughness is _constant_ along the profile. Figure 10: Roughness profile of Physical Measurement Standard (PMS) after form elimination and filtration. (**a**) Complete roughness profile. (**b**) Zoomed in part of roughness profile. Measurement uncertainties are influenced by the instrument, the measurement object and the environment. The contributions due to the instrument and its environment are small compared to the characteristics of the object. Previous investigations have already shown how the sensitivity of roughness parameters to the heterogeneity of textures can be determined [27]. For the industrial gear surface, it has been shown that texture varies along the tooth and, therefore, causes a dependency of the roughness parameters on the location of the evaluation region (see Section 3). The gear piece of the PMS has been manufactured, aiming at a high degree of homogeneity of the texture. Still, there is a small residual influence of the randomness of the texture features that needs to be accounted for as an uncertain contribution. It has been observed that the contribution is significantly larger than the uncertainty contribution of the HTRS measurement process. The relocalization of the evaluation region and whether the evaluation length is that on the arc of the involute or on its chord determine which texture features are included. Therefore, the following parameters influence the uncertainty of the roughness parameters:  
Position of the evaluated partial profile in tooth width direction;  
Position \(x_{\text{m}}\) of the evaluation region in involute direction;  
Length \(l_{\text{e}}\) of the evaluation region;  
Form operator: removal of fitted involute and removal of a smoothing spline with or without scaling correction with respect to chord vs. arc bow size. According to the \"Guide to Measurement Uncertainty\" and its supplementary documents [28], uncertainty has been estimated by varying the relevant parameters of the evaluation. Roughness evaluation for the calibration values is performed by following the relevant ISO standards ([21; 23; 24] and their successors [16; 22]), with an evaluation length of \(l_{\text{e}}=5\cdot 0.8\,\text{mm}=4\,\text{mm}\). The specific values of the roughness parameters will not be published to ensure the possibility of future round robin tests but their magnitude and the determined measurement uncertainties are presented in Table 2.  
The values of the roughness and material ratio parameters are in the order of magnitude of common gears in production. The profile does not show the typical asymmetry of deep valleys and small peaks but shows a normally distributed profile. This is demonstrated in the symmetry of \(R_{\text{pk}}\) and \(R_{\text{vk}}\).