The paper’s content allowed us to determine the fatigue life of a component that is being subjected to a random vibration environment. Its estimation is performed in the frequency domain with loading frequencies being closer to the system’s natural frequency. From loads’ amplitude and their interaction effect, we derive a nonlinear damage model to cumulate the generated fatigue damage. The exponent value of 0.4 from the Manson–Halford curve damage model was replaced by a vibration bending stress relation that considers the effect and interaction of loads. The analysis is performed from a progressive accelerated vibration spectrum to predict the fatigue life estimation. From this accelerated scenario, the accelerated coefficients and cumulated damage are both determined. The proposed nonlinear model is based on the following facts: (1) vibration and bending stress σvb values are obtained from the response acceleration of power spectral density (PSD) applied and (2) the model can be applied to any mechanical component analysis where the corresponding acceleration responses Ares and the dynamic load factor σdynamic values are known. The steps to determine the expected fatigue damage accumulation D by using the curve damage are given.
In this paper, the formulation to incorporate the used vibration profile, the stress generated by the product’s application, mass, and the resonance frequency is given. After that, based on the vibration output data, the two-parameter Weibull distribution is used to predict the corresponding reliability indices. In the method, the mentioned stress is incorporated as acceleration response (Ares), and by using a dynamic stress factor (σdyn). In addition, the Weibull parameters are determined based on the generated maximum and minimum principal vibration stress values. In the paper we show the efficiency of the fitted Weibull distribution to predict the reliability indices, by using its Weibull shape and scale parameters, it is always possible to reproduce the principal vibration stress values. Additionally, from the numerical application, we show how to use the Weibull analysis to determine the reliability index for a desired stress or desired cycle value. Finally, we also present the guidelines to apply the proposed method to any vibration fatigue analysis where the Ares (used to determine the σ1 and σ2 values), and the σdyn value are both known.
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