Effect of manufacturing error in fillet radii on the reliability of stepped shafts

Abstract

Stress concentration has been recognized as a major factor in the fatigue life of machine elements. Stress concentration plots for a variety of cases are widely available in machine design books. In this paper the stress concentration curve K t = ψ(α,η,β,r/d) is modelled as an equilateral hyperbola, where parameters α, η, β are constants of the equation, d is a deterministic variable defining the characteristic dimension of the component determining its overall strength, and r is the random variable defining the radius of the surface of an angular junction. The randomness in the fillet radius r is due to the machining error introduced while manufacturing the shaft. The variability in r is modelled by a normal distribution. Using these mathematical models of K t and r, in conjunction with the Weibull equation of stress versus number of cycles to failure (S-N) curve, probability model f(N) to characterize the fatigue life of the stepped shaft is developed. This probability model can be used to calculate (1) the reliability, (2) the mean life, and (3) the scatter in the fatigue life of the shaft. The results are presented in a set of plots which illustrate the effect of the variability of the fillet radius, on the mean life and the scatter in the life. The results can also be used to assess the fatigue life when the stress concentration is caused by notches, holes or keyways in shafts and plates.