Applying Goodman, Gerber, Soderberg and Elliptical failure theories does not make it possible to determine the span of failure times (cycles to failure-Ni) of a mechanical element, and so in this paper a fatigue-life/Weibull method to predict the span of the Ni values is formulated. The input’s method are: (1) the equivalent stress (σeq) value given by the used failure theory; (2) the expected Neq value determined by the Basquin equation; and (3) the Weibull shape β and scale η parameters that are fitted directly from the applied principal stress σ1 and σ2 values. The efficiency of the proposed method is based on the following facts: (1) the β and η parameters completely reproduce the applied σ1 and σ2 values. (2) The method allows us to determine the reliability index R(t), that corresponds to any applied σ1i value or observed Ni value. (3) The method can be applied to any mechanical element’s analysis where the corresponding σ1 and σ2, σeq and Neq values are known. In the performed application, the σ1 and σ2 values were determined by finite element analysis (FEA) and from the static stress analysis. Results of both approaches are compared. The steps to determine the expected Ni values by using the Weibull distribution are given.
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.
Since the designed bearing’s reliability of 90% was determined in a lab environment, it does not represent the actual used environment. In this paper, a new methodology to determine the actual reliability that corresponds to the use conditions is offered. This new method is based on the standard method used to select the ball bearing. The proposed method is based on the two parameters of Weibull distribution, where the shape (β) and scale (η) parameters are both determined from the Hertz contact stresses values, which are generated under the surface of the motionless outer race, and by the forces transmitted between the ball and the outer race. Therefore, the derived reliability is different from the 90% index offered by manufacturers.
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.
In this paper a Weibull methodology to determine the probabilistic percentiles for the S-N curve of the A572 Gr. 50 steel is formulated. The given Weibull/S-N formulation is based on the true stress and true strain values, which are both determined from the stress-strain analysis. For the analysis, the Weibull β and η parameters are both determined directly from the maximum and minimum addressed stresses values. The S-N curve parameters are determined for 103 and 106 cycles. In the application, published experimental data for the CSA G40.21 Gr. 350W steel is used to derive the true stress and true strain parameters of the A572 Gr. 50 steel. Additionally, the application of the S-N curve, its probabilistic percentiles and the Weibull parameters that represent these percentiles are all determined step by step. Since the proposed method is flexible, then it can be applied to determine the probabilistic percentiles of any other material.
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