Fatigue Load Equivalent to Distribution of Loads From the US Population

Abstract

In seeking to simplify fatigue life calculations for components of fitness equipment, this paper develops a general expression for the user weight Le which, in NT cycles, generates the same fatigue damage as a set of user weights {Li} described by a probability density function fi = Ni/NT, where each Li gets applied for Ni cycles and Σ Ni = NT. The derivation of the method goes beyond the textbook development of equivalent load by retaining geometric, material, and loading parameters throughout the derivation. The expression allows exploration of the effect of the geometry of the mechanical component, material properties, and loading on the value of the user weight Le which simulates the set of user weights {Li}. The paper explores a range of stress-life exponent b typical of common steels. The paper explores the complete range of stress ratio R ∈ (-1, 1). The paper explores the combined effect of the component’s ultimate tensile strength and the ratio between applied load and stress. These last two parameters determine the user weight Lb which causes single-cycle fracture of the component. The results indicate a strong dependence of Le on stress ratio R, stress-life exponent b, and on breaking weight Lb. The paper proposes guidelines for assignment of Le in the special case where the {Li} arise from body weights of the US population.