Page 280 - Failure Analysis Case Studies II

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As expected, Table 2 shows that the higher weight levels require considerably fewer cycles to
failure than the lower weight levels.

2.8. Cumulatice damage

The final step in determining the total number of cycles to failure was to combine the various
weight levels and the user distribution for the three week period using Miner’s rule for block
loading. According to Palmgren and Miner, failure occurs when the cumulative damage caused by
each loading cycle equals one. The general form of the Palmgren-Miner rule [6] is given by,

where k = number of stress levels in the block loading spectrum, n, = number of cycles at each
stress level in the block loading spectrum and Ni = number of cycles to failure at each stress level.
Using equation (8) and the values from Table 2 the cumulative damage incurred by one three
week loading block was 0.057. Therefore, a total of 17.7 loading blocks would be required to cause
failure of the adjustment pin. This translates into approximately 53 weeks of typical use before
failure. According to the purchase records of the machine the actual failure occurred after 1; years
of operation.
It should be remembered that fatigue calculations are only an estimate and the calculated
lifetimes are very sensitive to small changes in geometry that affect stress levels. This analysis
ignores the presence of plastic deformation that occurs at the higher stress levels. In addition, the
standard notch sensitivity formulas are derived from data where the notch depth does not exceed
four times the notch radius. So, according to R.E. Peterson, “This means that caution should be
exercised in application to cases of deep sharp notches or very small fillets on stepped shafts . . .”.
However, the analysis does show the pin design to be inadequate.

3. Design implications

The analysis confirms that the pin failure was due to a poor design and lack of engineering. The
stress calculations indicate that the pin plastically deformed under the maximum load. The fatigue
analysis determined that the pin should fail after only approximately one year of typical service.
This is clearly unacceptable and the design should be altered to take the maximum load and fatigue
loading into account.
One way to improve the design to avoid fatigue failure would be to redesign the machine to add
support at the end of the pin. This would reduce the bending stresses by half since the pin could
be modeled as a simply supported beam instead of a cantilever beam. Another method of changing
the design would be to increase the pin diameter and/or use a stronger grade of steel. However,
this would probably increase material and manufacturing costs. It has also been shown that the
addition of a relief groove behind the shoulder causes a reduction in the stress concentration,
Figure 10.
The addition of relief grooves does require extra machining and may not be possible due to the
geometry of the machine. Since the localized stress concentration is dependent on the shoulder root