## 2 Overall Methodology
### Film Thickness Measurements  
The film thickness measurements were performed in the same test rig as the friction measurements, as described in Section 2.4, but modified to allow for optical measurements of the film thickness, as shown in Figure 2. The lubricant is situated in a container in which the ball is rotating, and a pump system is used to keep this container filled with lubricant to ensure fully flooded conditions. Heaters are placed in both the smaller oil container where the ball is placed, but also in the bigger lubricant supply below to enable heating of the lubricants. The steel disc is substituted by a Pyrex glass disk with a chromium semi-reflecting coating acting as a beam splitter, and an optical microscope is attached on top to allow study of the film formed between the steel ball and the glass disk. A beam of white light is directed through the glass disc into the contact where a part is reflected back by the chromium layer, while the rest passes through the lubricant film before being reflected back by the steel ball. There will be a phase shift of the light due to the difference in optical path length for the light reflected in the beam splitter, and the light reflected at the ball surface. This can be used to calculate the film thickness. See for instance refs [29; 30] for more information on optical interferometry and its use for lubricant and grease film thickness measurements. Several different methods have been proposes for the translation of optical phase differences into film thickness [31; 32; 33], where the method described by [PERSON] et al. [33] is used in the present work.  
The ball on disk test device was used to measure film thickness of the two lubricants at two different temperatures; 25 and 60 \({}^{\circ}\)C. All measurements were conducted at a condition as close as possible to pure rolling. Before starting the experiments for each lubricant, the test device was warmed up to the desired operating temperature for approximately 60 min with lubricant circulating over both ball and disk to ensure thermal stability. At the start of each test cycle the entrainment speed is set to a reasonably high value to ensure a condition of full film lubrication when a load of 27 N, which corresponds to a maximum Hertzian pressure of 0.5 GPa is applied. The entrainment speed is then reduced to a limit where the film thickness is around 100 nm, and the measurement series is started. The speed is gradually increased to the point where the intensity of the interference is too low to get an estimation of the film thickness, or to the point where oil splash is so great that the loss of lubricant is too high.  
Figure 2: Wedeven Associates Machines ball on disc test apparatus with optical interferometry setup.  
An approximation of the pressure-viscosity coefficient, alpha of each lubricant at both 25 and 60 \({}^{\circ}\)C was calculated by the use of the Hamrock and Dowson equation for central film thickness [26]:  
\[H_{c}=2.69U^{0.67}G^{0.53}W^{-0.067}(1-0.61e^{-0.73k}) \tag{7}\]  
where \(H_{c}\) is the central film thickness, \(U\) the dimensionless speed parameter, \(G\) the dimensionless material parameter, \(W\) the dimensionless load parameter and \(k\) the ellipticity parameter. Since all of these are known except the pressure-viscosity coefficient, an approximation of this parameter can be computed by use of a least square fit to match each film thickness in a measurement series as close as possible. A thorough description in the use of optical interferometry and film thickness equation to assess pressure-viscosity coefficients is given elsewhere [34].