To make sense of these values, they need to be converted to a “common currency,” and within this study, it was decided to convert to Weibull shape parameter. The approach taken by Hexagon contained several assumptions, and whilst alternative assumptions could have been made, Hexagon does not believe that they would affect the overall outcome of the study.

First, the data for the standard deviation in strength was converted to an equivalent Weibull shape parameter. A graphical representation can be seen in Figure 2. The S-N curve from the standards (ISO and AGMA) refers to the 1 percent failure rate. Assuming a normal distribution and using the standard deviation in strength, a distribution in strength can be implied.

A hypothetical population of gears with this distribution in strength was generated numerically, and their resulting failure points were calculated. The limited life part of the S-N curve for contact for case-carburized gears was used. This was because case carburized gears are most common, contact failures are more common than bending failures and the greatest number of gear fatigue tests have focused on this part of the S-N curve, owing to the greater ease in achieving failures.

Figure 3 shows the data arising from the FZG data for the full set of data. This shows that a normal distribution in strength, projected onto the time axis using the S-N curve of ISO 6336, does not give a perfect Weibull distribution. This pattern was also seen for all the other values used.

It was decided to concentrate on the earlier sections of the population, since it is unlikely that a complete population of gears would be allowed to fail in service. By concentrating on the first 50 percent of failures, a closer match to Weibull could be achieved and a clearer value for