PSI - Issue 57

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Karthik Krishnasamy et al. / Procedia Structural Integrity 57 (2024) 793–798 Karthik KRISHNASAMY/ Structural Integrity Procedia 00 (2019) 000 – 000

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The material strength of the component at 92% reliability is higher than the reliability at 99%. If the design is developed for 92%, its safety factor is much higher and consequently the service life of the component increases. This overestimates the design and it increases its cost. In addition, the damage calculated with the method suggesting different reliabilities cannot compare directly. A shaft may fail because of a part that breaks prematurely which is not expected and this happens in real life. To overcome this problem, the reliability concept used in VALEO and the results are presented in a curve that shows the reliability of a component or system over the lifetime. Since the reliability calculation considers the inherent failure probability as in table-1, it is now compared with each other parts and the smallest achievable life is the critical component of the system. 3. Weibull distributions Weibull distributions has a unique characteristic to adapt to different situation, which is why it is primarily used in reliability and life data analysis. Parameter values affect the distribution, which is used to model the different behaviors for a particular function. The two parametric Weibull distribution leads to reliability function ( ) =exp⁡ (−( ) ) (1) Where, n c is the required number of cycles, T and β are the scale and shape parameters. This two parametric Weibull distribution always describes failures starting from time n c = 0. Three-parameter Weibull distribution has an additional parameter, where the failure begins after a certain time ( t o ) and it can be derived from 2-parameter distribution with a time transformation. Bertsche recommends it in his book (ref: 2) ( ) = ⁡ (− ( − 0 − 0 ) ) (2) The β chosen based on the table-2, to adapt the T parameter. Therefore, the distribution meets the required reliability target.

Table 2. Factor of Weibull distribution.

Components

β

f tb

Shafts

1.1 to 1.9

0.7 to 0.9 0.1 to 0.3 0.1 to 0.3 0.8 to 0.95 0.4 to 0.8

Ball Bearing Roller Bearing

1.1

1.35

Gear tooth bending Gear tooth contact

1.2 to 2.2 1.1 to 1.5

The parameters T determined by a lifetime calculation or operational fatigue strength calculation. Both T and t 0 calculated from the achievable life of the component (B). For example, for the calculation of roll bearings one yields by defining the B10 lifetime (R(n c ) = 90%) and for the calculation of gears the B1 lifetime (R(n c ) = 99%). With these data, a point for each lifetime identified in the probability net. The complete statistical failure behavior can be determined with the additional knowledge of the shape parameter β and by the potential failure free time t 0 . According to Bertsche the lifetime T can be calculated with the below equations (3 & 4). = B −f .B 10 √− ⁡( ( ) ) + . 10 (3)