Mechanical Components Example: Difference between revisions

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The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:
The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:


::<math>\beta =1.771460,\text{  }B=86.183591,\text{  }C=1170.423770.</math>
::<math>\begin{align}
\beta =1.771460,\text{  }B=86.183591,\text{  }C=1170.423770.
\end{align}</math>


A small value for  <math>B</math>  was estimated. The following observations can then be made:
A small value for  <math>B</math>  was estimated. The following observations can then be made:

Revision as of 06:48, 9 August 2012

Mechanical Components Example

A mechanical component was put into an accelerated test with temperature as the accelerated stress. The following times-to-failure were observed.

343 K 363 K 383 K
266.66 618.54 351.12
430.09 666.72 355.1
570.45 724.4 672.69
890.42 950.89 923.35
1046.65 1148.4 948.22
1158.14 1202.94 1277.04
1396.01 1492.56 1538.81
1918.38 1619.59 2020.34
2028.86 2592.29 2099.03
2785.58 3596.85 2173.04

1) Determine the parameters of the Arrhenius-Weibull model.

2) What is your observation?

Solution

The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:

[math]\displaystyle{ \begin{align} \beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770. \end{align} }[/math]

A small value for [math]\displaystyle{ B }[/math] was estimated. The following observations can then be made:

  • Life is not accelerated with temperature, or
  • the stress increments were not sufficient, or
  • the test stresses were well within the "specification limits" for the product (see discussion here).

A small value for [math]\displaystyle{ B }[/math] is not the only indication for this behavior. One can also observe from the data that at all three stress levels, the times-to-failure are within the same range. Another way to observe this is by looking at the Arrhenius plot. The scale parameter, [math]\displaystyle{ \eta }[/math] , and the mean life are plotted next.

Eta and Mean Life vs. Stress.

It can be seen that life ( [math]\displaystyle{ \eta }[/math] , and the mean life) is almost invariant with stress.