# A Novel Measurement Standard for Surface Roughness on Involute Gears
## 4 Physical Measurement Standard (PMS) Representing Roughness on Involutes  
### Design of the PMS  
The goal is to realize an artefact as PMS for calibrating measurement instruments that determine roughness on gear teeth. The requirements are that the roughness parameters represented by the PMS should adhere to the following:  
* Are reproducible and have to be insensitive to the positioning of the evaluation interval;
* Can be traced back to the international unit meter of the dimension length. To facilitate calibration procedures using calibrated profilometers, a modular object resembling a gear with shaft and gear piece has been designed. This ensures that the gear piece, representing a tooth, can be removed from the shaft such that it can be measured with a profilometer separately. When combined, the entire standard can be examined by using a gear measurement system and its roughness probes. The gear shaft then provides the reference to the entire gear geometry with shaft axis direction and position and with base radius \(r_{\text{b}}\). The modular structure of the standard is shown in Figure 8.  
The axis of the gear shaft has to be coaxial to the axis of the involute on the gear piece when the two modules are assembled. The measurement processes of the gear shaft and the gear piece are independent in the case of this object and require sufficiently high precision. Furthermore, consistency requires an exact adjustment of the gear piece when mounting it on the shaft. **The gear shaft** of the PMS ensures that the profile can be measured similarly to a common gear on a gear measuring system. This mainly means that the measurement can be performed by using rolling movements. It consists of an axis with two reference bands that enable determining the axis precisely and of a central cylinder with four eroded deepenings that are precisely manufactured and hold the gear piece. The gear piece is positioned by using a skew screw and a steel ball to ensure three-point contact of the gear piece within the gear shaft. Using this technique, the surface centre of all three surfaces of the gear piece can be positioned with a reproducibility of \(\Delta x<10\,\upmu\)m.  
The gear shaft can be used for gear pieces that embody \(r_{\text{b}}\geq 29\) mm. Smaller base radii cause the correct position of the root of the involute to be located within the body of the gear shaft. Such profiles can, therefore, not be realised, including the root area of the involute. Figure 8: Components of the PMS: (**a**) gear shaft to enable measurements as a gear and (**b**) gear piece with calibrated roughness profile. For **the gear piece**, a manufacturing method is needed that meets both requirements concerning the design of the texture following an involute geometry and, furthermore, has to be applicable on hardened steel such that diamond turning is not an option. The most appropriate process that can be realized at PTB, therefore, is Electrical Discharge Machining (EDM). The gear piece is manufactured from a hardened steel similar to the materials used in actual gears in production. This ensures that the PMS resembles gears from production also in its material properties and provides necessary robustness. Super fine roughness standards are commonly manufactured from a copper substrate with a layer hardened by nickel phosphorus that is thick enough to be usable for structuring. This allows surfaces to be manufactured via turning with a highly determined diamond tip. It enables the roughness profile to be configured before production on a \(\upmu\)m level. The PMS, however, faces additional requirements and is, therefore, not manufactured via diamond turning. While high performance profilometers impose small contact forces in the mN range, gear measurement systems often use much higher forces. To withstand these contact forces, the gear piece of the PMS is made of hardened steel. PMS's made of this material are commonly used in gear metrology and maintenance procedures to prevent rust and to keep the artefact clean are well established.