Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage
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...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/18/10291 |
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| author | Jesús M. Barraza-Contreras Manuel R. Piña-Monarrez Roberto C. Torres-Villaseñor |
| author_facet | Jesús M. Barraza-Contreras Manuel R. Piña-Monarrez Roberto C. Torres-Villaseñor |
| author_sort | Jesús M. Barraza-Contreras |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:04:19Z |
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| language | English |
| last_indexed | 2024-03-10T23:04:19Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-4e19fa67088e406ea0bfee64464507492023-11-19T09:25:41ZengMDPI AGApplied Sciences2076-34172023-09-0113181029110.3390/app131810291Reliability by Using Weibull Distribution Based on Vibration Fatigue DamageJesús M. Barraza-Contreras0Manuel R. Piña-Monarrez1Roberto C. Torres-Villaseñor2Industrial and Manufacturing Department, Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, MexicoIndustrial and Manufacturing Department, Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, MexicoIndustrial and Manufacturing Department, Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, MexicoIn 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.https://www.mdpi.com/2076-3417/13/18/10291random vibrationmechanical fatiguedamageWeibull distributionreliability |
| spellingShingle | Jesús M. Barraza-Contreras Manuel R. Piña-Monarrez Roberto C. Torres-Villaseñor Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage Applied Sciences random vibration mechanical fatigue damage Weibull distribution reliability |
| title | Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage |
| title_full | Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage |
| title_fullStr | Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage |
| title_full_unstemmed | Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage |
| title_short | Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage |
| title_sort | reliability by using weibull distribution based on vibration fatigue damage |
| topic | random vibration mechanical fatigue damage Weibull distribution reliability |
| url | https://www.mdpi.com/2076-3417/13/18/10291 |
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