Reliability of gears - Determination of statistically validated material strength numbers

One of the most important goals when designing a gearbox is to ensure a sufficient reliability in operation. Depending on the field of application the acceptable probability of failure may be different, typical values commonly are in the range of 0.01% to 10%. Material strength values regarding main failure modes like pitting or tooth root breakage that are used for designing a gear stage are often obtained from testing. Because of the high effort for such experimental investigations the usual scope of testing is limited and typically allows for a reliable estimation of the determined strength values for a failure probability of 50% only. A conversion to other failure probabilities is possible if sufficient data or literature references for the considered material are available. Furthermore, common standardized methods for rating the load carrying capacity of gears like ISO 6336 or AGMA 2001 use strength values and S/N-curves specified for a failure probability of 1%. Consequently, the calculated safety factors, which are often used as main design criteria, are strictly correlated to this probability of failure. This paper is intended to give a review on the statistical reliability behavior of cylindrical gears with regard to pitting and tooth root breakage failures. Initially, the results of different relevant literature references were gathered and compared. It is shown that several previous investigations are not based on extensive research, insufficiently statistically validated or outdated. Therefore, general applicable distribution parameters for case hardened gears were determined based on a statistical analysis of current and former experimental test data available at FZG. Hence, a mathematical reliability approach was developed and drafted to expand standardized load capacity calculation methods such as ISO 6336. The deduced models and procedures allow for the consideration and conversion of different reliability levels in the design process of cylindrical gears. Finally, the relevance of the approach for industrial applications and the need for further investigations are discussed.