RELATIVE RANKING OF FATIGUE LIVES OF ROTATING ALUMINUM SHAFTS USING L_(10) WEIBULL-JOHNSON CONFIDENCE NUMBERS

摘要

Leonard Johnson [1964] first proposed a Weibull-based methodology to quantitatively compare or rank two sets of probabilistic data, such as fatigue life of rotating shafts. Using his methodology, confidence numbers (the likelihood that the respective order of two repeated measurement will be observed) at the mean and L_(10) life are graphically determined knowing the fatigue life ratio, Weibull slopes, and total degrees of freedom of the two data sets being compared or ranked. In this work, simple algebraic equations were fitted to the figures of Leonard Johnson, allowing for the calculation of confidence numbers not only at the combination of parameters used by Johnson to create his figures, but also at those interpolated between and reasonably extrapolated beyond. At the 99% confidence number for L_(10) Life Ratio, the simplified algebraic equation was found to differ from those obtained graphically by less than 1.0- percent. The methodology was then used to rank the fatigue lives of rotating aluminum 6061 shafts with two different surface finishes (unpolished and anodized). The anodized shafts demonstrated a decrease in fatigue mean life with an associated confidence number of 0.9989; however, at the L_(10) life, there was no statistical difference between the two materials. This example illustrates the complexity of ranking fatigue life of rotating shafts.