| Summary: | In this paper, a Weibull probabilistic methodology is proposed with an approach to model vibration fatigue damage accumulation using two parameters: Weibull distribution and a nonlinear fatigue damage accumulation model. The damage is cumulated based on the application of a vibration stress profile and is used to determine both the Weibull <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi></mrow></semantics></math></inline-formula> parameters, and the corresponding component reliability R(t). The vibration fatigue damage is analyzed to accumulate the damage as a stress function for a fatigue life exponent derived with the assistance of the acceleration’s force response. The steps to determine the Weibull <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi></mrow></semantics></math></inline-formula> parameters are estimated based only on the principal vibration stresses <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> that allow the reproduction of the vibration fatigue damage. The method’s efficiency is based on the probabilistic approach by using the vibration fatigue damage as the <i>Y<sub>i</sub></i> vector that covers the arithmetic mean as well as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi></mrow></semantics></math></inline-formula> parameter. Finally, the procedure proposed is applied in a practical case where a mechanical component is used as a support for telecommunication connections and is submitted to vibration stress. The results show that using the damage accumulated as the <i>Y<sub>i</sub></i> vector to estimate the parameters allows for the analysis of dynamic and individual applications.
|
|---|