Home > Theory > Fatigue Analysis > Rain- flow Counting Method
RFC method
In the case of a wide banded vibration, the method used is the rainflow counting.
The rainflow counting (RFC) is a well-known method, which has been widely improved and validated. This method consists in determining the amplitude of each peak and crest of a stress time series and to take it for half of a cycle for the counting of the total cycles submitted by a structure. The mean stress is directly given for each cycle. This method is strongly recommended in case of wide banded vibrations. The algorithm is for instance presented in "C. Lalanne, « Vibrations et chocs mecaniques », tome 4, pp 201-211, 1999" .
The calculation is split in three phases:
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Peaks and valley determination,
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Ranges and associated number of cycles determination,
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Damage calculation.
The method is illustrated in the sketch below :
Peaks and valleys: The peaks and valleys are determined as it is defined in the figure below.
These values are included in a P&V table.
Ranges and associated number of cycles determination: The RFC method allows determining the effective ranges and associates number of cycles experienced by the structure. The algorithm uses a table including the peaks and valleys. This P&V table is updated at each step of the calculation.
Begenning of the loop
Case1 : One unique value in the P&V table
No fatigue => end of the loop
Case2 : Two Values in the P&V table
1/2 fatigue for the stress range $|X_2-X_1|$ => end of the loop
Case3 : More than two values in the P&V table $(X_1,...,X_n)$
Case 3.1 :
1 fatigue cycle for the stress range $|X_2-X_1|$. $X_2$ is erased from the P&V table. The first point stays unchanged and the others are renumbered. Return to the beginning of the loop.
Case 3.2 :
1 fatigue cycle for the stress range $|X_6-X_5|$. $X_6$ and $X_5$ are erased from the P&V table. The first four points stays unchanged and the others are renumbered. Return to the beginning of the loop.
Case 3.3 :
1/2 fatigue cycle for the stress range $|X_2-X_1|$.
1/2 fatigue cycle for the stress range $|X_3-X_2|$.
...
1/2 fatigue cycle for the stress range $|X_9-X_8|$.
End of the loop.
Damage calculation:
When the P&V table is empty, the ranges and their associated number of cycle (1/2 or 1) are sorted in blocks. The maximum range is determined and defines the lower and upper bound of each block.
The number of cycle of each block is determined and the associated damage is calculated with the stress range \(\Delta\sigma_i\) where :
The total damage is the sum of the damages associated to each block.
