# A Novel Measurement Standard for Surface Roughness on Involute Gears
## 1 Introduction  
The relevance of the quality of surfaces of gears has increased dramatically over the last decade. Its texture has big impacts on the efficiency of gear boxes, which is why a precise description of profile properties is required. The mechanical power density, running behaviour, noise and the wear of a gear are influenced by the roughness properties of gear flanks [1]. In order to decrease noise [2], wear and power dissipation [3; 4; 5], gear flanks with roughness values of \(R_{\mathrm{z}}\leq 0.5\,\mathrm{\SIUnitSymbolMicro m}\) are achieved and used in production. This is made possible by using modern manufacturing processes such as slide grinding or polishing grinding [6]. This is why the surface quality of gears has grown more important over the last ten years. Manufacturers of coordinate measurement systems and gear measurement systems have developed probes specially designed to enable end-of-line-monitoring of the roughness properties of gears [7; 8]. Manufacturers of such instruments request national institutes and standardisation committees to meet their demand for traceability and comparability with established roughness metrology. Their customers typically are those in machine building and automotive industries. However, the roughness measurements on gear flanks still lack traceability with respect to standardised SI-units. Physical Measurement Standards (PMS), also denoted as material measure, for conventional roughness profile measurements represent planar surfaces only. In addition, most of them do not represent the functionality of surfaces regarding their tribological properties. The big challenge of roughness evaluations on gear flanks lies in the involute shape of the surface [9]. There still is a gap in dimensional metrology between measurement technologies for inspecting surface textures and for inspecting 3D geometries [10; 11]. Surface texture measurement strategies consider a surface as a plane with the topographic features perpendicular to the plane and being around three orders of magnitude smaller than thelateral sizes. Objects mounted on conventional roughness measurements instruments are required to be flat and often required to be sufficiently small. Calibration procedures for maintaining traceability of roughness instruments have been established for many decades. However, in the case of roughness metrology on involute geometries, the planarity assumption no longer holds. As a consequence, specific involute measurement devices have been developed and are already commercially available. For the specific involute roughness measurement systems, no calibration strategies currently exist. As those measurement systems are capable of mounting larger gear systems and can scan single teeth on an entire gear, it is a challenge to inspect such a system and to retrace its roughness data to the SI. Physical Measurement Standards (in short, PMS, and also referred to as material measure) are a common means to represent physical quantities used for calibration. Despite new and innovative approaches to the manufacture of PMS [12; 13], there is still no PMS allowing for the traceability of roughness measurements on an involute shape. Such a Physical Measurement Standard has been developed at the Physikalisch-Technische Bundesanstalt (PTB). It yields the following unique features of a PMS employed as the calibration standard for the inspection and calibration of involute roughness measurement systems:  
* First roughness measurement standard on a non-planar (but involute) surface;
* Modular layout of the artefact for both types of measurement systems on gear measuring machines and classical profilometers. This publication on the development of a PMS is structured as follows. In Section 2, the processes of measurement, analysis and calibration of the standard are explained. Different methods of separating form from form deviation and surface texture are presented. The two differing coordinate systems of profilometer data and of gear measuring machine data are explained.