# Rainflow Cycle Counting

Cycle counting is used to extract discrete simple "equivalent" constant amplitude cycles from a random loading sequence.

One way to understand "cycle counting" is as a changing stress-strain versus time signal. Cycle counting will count the number of stress-strain hysteresis loops and keep track of their range/mean or maximum/minimum values.

- Simple Load
History:Since this load history is continuous, it is converted into a load history consisting of peaks and valleys only.It is clear that point 4 is the peak stress in the load history, and it will be moved to the front during rearrangement (Figure 3). After rearrangement, the peaks and valleys are renumbered for convenience.
Next, pick the first three stress values (1, 2, and 3) and determine if a cycle is present.

If ${S}_{i}$ represents the stress value, point ${}_{i}$ then:

$$\text{\Delta}{S}_{12}=\left|{S}_{1}-{S}_{2}\right|$$$$\text{\Delta}{S}_{23}=\left|{S}_{2}-{S}_{3}\right|$$As you can see from Figure 3, $\text{\Delta}{S}_{12}\ge \text{\Delta}{S}_{23}$ ; therefore, no cycle is extracted from point 1 to 2. Now consider the next three points (2, 3, and 4).

$$\text{\Delta}{S}_{23}=\left|{S}_{2}-{S}_{3}\right|$$$$\text{\Delta}{S}_{34}=\left|{S}_{3}-{S}_{4}\right|$$$\text{\Delta}{S}_{23}\le \text{\Delta}{S}_{34}$ , hence a cycle is extracted from point 2 to 3. Now that a cycle has been extracted, the two points are deleted from the graph.The same process is applied to the remaining points:

$$\text{\Delta}{S}_{14}=\left|{S}_{1}-{S}_{4}\right|$$$$\text{\Delta}{S}_{45}=\left|{S}_{4}-{S}_{5}\right|$$In this case, $\text{\Delta}{S}_{14}=\text{\Delta}{S}_{45}$ , so another cycle is extracted from point 1 to 4. After these two points are also discarded, only point 5 remains; therefore, the rainflow counting process is completed.

Two cycles (2→3 and 1→4) have been extracted from this load history. One of the main reasons for choosing the highest peak/valley and rearranging the load history is to guarantee that the largest cycle is always extracted (in this case, it is 1→4). If you observe the load history prior to rearrangement, and conduct the same rainflow counting process on it, then clearly, the 1→4 cycle is not extracted.

- Complex Load
HistoryThe rainflow counting process is the same regardless of the number of load history points. However, depending on the location of the highest peak/valley used for rearrangement, it may not be obvious how the rearrangement process is conducted. Figure 7 shows just the rearrangement process for a more complex load history. The subsequent rainflow counting is just an extrapolation of the process mentioned in the simple example above, and is not repeated here.Since this load history is continuous, it is converted into a load history consisting of peaks and valleys only:Clearly, load point 11 is the highest valued load and therefore, the load history is now rearranged and renumbered.
The load history is rearranged such that all points including and after the highest load are moved to the beginning of the load history and are removed from the end of the load history.

Parameters affecting rainflow cycle counting may be defined on a FATPARM Bulk Data Entry. The appropriate FATPARM Bulk Data Entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information Entry.