PROBABILISTIC FATIGUE DESIGN OF SHAFT FOR BENDING AND TORSION

Abstract

The ever increasing demand for better and reliable mechanical systems necessitates the explicit consideration of reliability in the modeling and design of these systems. Design for reliability (DFR) has been receiving a great deal of attention for several years and companies are deploying resources to the design for reliability process because of the need to satisfy customers and reduce warranty costs. In traditional or deterministic design, safety or design factors are usually subjectively assigned in product design so as to assure reliability. But this method of design does not provide a logical basis for addressing uncertainties, so the level of reliability cannot be assessed quantitatively. This paper presents a probabilistic design approach for shafts under combined bending and torsional loads using the generalized Gerber fatigue failure rule. The design model parameters are considered as random variables characterized by mean values and coefficients of variation (covs). The coefficient of variation of the shaft design model is obtained by using first order Taylor series expansion for strength and stress in a stress-life fatigue design. A reliability factor is defined and related to the covs of design parameters and a failure probability. The design model assumes a lognormal probability density distribution for the parameters. This approach thus accounts for variability of design model parameters and provides quantitative assessment of product reliability. The approach is flow-charted for ease of application. This study shows that deterministic engineering models can be transformed into probabilistic models that can predict the risk in a design situation. From the design examples considered, it is shown that the popular modified Goodman model (MGM) for stresslife fatigue design is slightly on the conservative side. The study indicates possible reduction in component size and hence savings in product cost can be obtained through probabilistic design. Probabilistic design seems to be the most practical approach in product design due to the inherent variability associated with service loads, material properties, geometrical attributes, and mathematical design models. The computations in the present model were done using Microsoft Excel. This demonstrates that probabilistic design can be simplified so that specialized software and skills may not be required, especially at the preliminary design phase. Very often, available probabilistic models are intensive in numerical computation, requiring custom software and skilled personnel. The model approach presented needs to be explored for other design applications, so as to the make probabilistic design a common practice.