PSI - Issue 22

Carlos D.S. Souto et al. / Procedia Structural Integrity 22 (2019) 376–385 Author name / Structural Integrity Procedia 00 (2018) 000–000

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3. Rainflow cycle counting

The rainflow counting algorithm was first introduced by Matsuishi and Endo (1968) and it is used in the analysis of fatigue data. The algorithm reduces a spectrum of varying stress into an equivalent set of simple stress reversals. Reversals are the local minima and maxima where the stress slope changes sign, also known as peaks and valleys. After this simplification has been made, the fatigue life of a constructional detail can be estimated using the Palmgren Miner rule to calculate the fatigue damage.

3.1. Traditional Method

The rainflow counting algorithm is named after the analogy with the flow of a raindrop that falls down a Pagoda’s roof (traditional Japanese tower), where a raindrop starts from the top of a roof, falling to subsequent roofs and possibly meeting with other raindrop trails. To achieve this, a stress vs. time graph must be rotated by 90 o , so the stress axis is horizontal (left to right) and the time axis is vertical (top to bottom). In this configuration, the graph looks like a series of Pagoda’s roofs. To actually do the counting, one shall start at either side of the graph (peak’s side or valley’s side). Starting on the peak’s side, an imaginary raindrop is placed on the topmost roof (a valley) and it starts to flow down the roofs. An half cycle is then counted when the raindrop falls o ff a roof and it passes through a valley that is smaller than the current valley from where the raindrop fell. An half cycle is also counted when the current raindrop meets the trail of a previous raindrop. The range of the counted half cycle is equal to the absolute value of the di ff erence between the values of stress where the raindrop started and ended. This process is then repeated to the valley’s side. When done, matching cycles can be added together. An application of the tradition method is shown in Fig. 2.

Fig. 2: Traditional rainflow counting method (Ribeiro et al., 2012). a) stress history; b) equivalent stress history in terms of reverse cycles.

3.2. Algorithm based on the ASTM E1049-85 standard

The rainflow counting algorithm is standardized in the ASTM E1049-85 (2017) standard. The algorithm counts cycles by considering a moving reference point of the data sequence, Z, and a moving ordered three-point subset with the following characteristics: • The first and second points are collectively called Y. • The second and third points are collectively called X. • In both X and Y, the points are sorted from earlier to later in time, but are not necessarily consecutive.