# A Novel Measurement Standard for Surface Roughness on Involute Gears
## 5 Conclusions  
A Physical Measurement Standard (PMS) for roughness measurements on involute gear flanks has been developed. It embodies calibrated roughness height parameters (\(R_{\mathrm{a}}\), \(R_{\mathrm{z}}\) and \(R_{\mathrm{q}}\)) and material ratio parameters (\(R_{\mathrm{k}}\), \(R_{\mathrm{pk}}\), \(R_{\mathrm{vk}}\), Mr1 and Mr2). It is possible to investigate the PMS both with classical profilometers as well as gear measurement systems using the gear shaft. Measurement uncertainties are comparable to those of other PMS, e.g., the \(R_{\mathrm{k}}\) material measure described in [30]. As described in Section 1, there are already established measurement systems capable of measuring not only the involute shape but the roughness on the teeth of gears as well. The demand for traceability of roughness  
Figure 12: Semideterministic periodic profiles that are an attempt to utilize periodic profiles on involute gear flanks as PMSs. (**a**) Entire semideterministic profile manufactured by repeating grinding processes and resulting in a periodic profile. (**b**) Peaks of different parts of the profile (start, centre and end) combined and aligned: the peaks are equal to the sub-μm level; thus, the profile can be considered to be periodic.  
measurements on gears by manufacturers of such instruments and their customers can now be fulfilled via the developed PMS.  
Necessary evaluation algorithms have been developed. The developed optimisation algorithm (fit) has shown to be capable of directly determining the primary profile as the normal deviation from the ideal involute with respect to the unwrapped arc length of the involute. This process uses more computing resources than when using a smoothing spline as the form filter. However, the fit delivers information about the absolute position of the profile on the involute and, therefore, enables the direct comparison of measurements on profilometers and gear measurement systems, closing the gap between these applications of roughness measurement.  
Furthermore, it has been shown that the values of roughness parameters of inhomogeneous surface textures are highly sensitive to variations of the position of the evaluation region. This positioning uncertainty further increased when the relevant reference systems are applied incorrectly.  
Next to the development of the semi-deterministically ground surface described in Section 4.3, further comparative measurements of the calibrated PMS, especially on gear measurement systems, are planned.  
Conceptualization, M.S.; methodology, F.S., D.H., R.M. and M.S.; software, F.S. and D.H.; validation, F.S. and D.H.; formal analysis, F.S. and D.H.; investigation, F.S., R.M. and D.H.; resources, R.M.; data curation, F.S. and D.H.; writing--original draft preparation, F.S. and D.H.; writing--review and editing, F.S., D.H., R.M. and M.S.; visualization, F.S.; supervision, M.S. and D.H.; project administration, M.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available to not influence comparative measurements.  
We acknowledge the fruitful discussions and the provision of the example gear by the following industrial project partners: Klingelnberg AG, Volkswagen AG and Magna PT B.V. & Co. KG.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} PMS & Physical Measurement Standard; \\ PTB & Physikalisch Technische Bundesanstalt; \\ HRTS & High Resolution Topo Scan; \\ EDM & Electrical Discharge Machining. \\ \end{tabular}