# Cycle Counting

Cycle counting is used to summarize lengthy, irregular load-versus-time histories by providing the number of times cycles of various amplitudes occur. The definition of a cycle varies with the method of cycle counting. In fatigue analysis, a cycle is the load variation from the minimum to the maximum and then to the minimum load. Cycle counts can be made for time histories of force, stress, strain, torque, acceleration, deflection or other loading parameters of interest.

Cycle counting yields the amplitude distribution. There is no frequency information contained in a cycle counting analysis. The result is the given distribution of amplitude cycles without regard to frequency.

Level Cross Counting
One count is recorded each time the positive sloped portion of the load exceeds a present level above the reference load, and each time the negative sloped portion of the load exceeds a present level below the reference load.

Reference load crossings are counted on the positive sloped portion of the loading history. Restrictions on the level-crossing counts are often specified to eliminate small amplitude variations which can give rise to a large number of counts. To do this, filter small load excursions prior to cycle counting. Or, make no counts at the reference load and specify that only one count be made between successive crossings of a secondary lower level associated with each level above the reference load.

Peak Counting
This method identifies the occurrence of a relative maximum or minimum load value.

Count the peaks above the reference load level and the valleys below the reference load level. Use mean-crossing peak counting to eliminate small amplitude loadings. The most damaging cycle count for fatigue analysis is derived from the peak count by first constructing the largest possible cycle, using the highest peak and lowest valley, followed by the second largest cycle, etc, until all peak counts are used.

Simple-Range Counting
Range is the difference between two successive reversals. The range is positive when a valley is followed by a peak. The range is negative when a peak is followed by a valley.

Count positive or negative ranges as one cycle if only one or the other is counted. Count each as one-half cycle if both are counted. Eliminate ranges smaller than a chosen number before counting.

Rainflow Counting and Related Methods
The previously mentioned counting methods are called one-parameter methods. Rainflow and related counting methods are two-parameter methods. Typically they preserve information about the mean value as well as the amplitude of each cycle. There are several two-parameter methods. If the load history begins and ends with its maximum peak, or with its minimum valley, all of these give identical counts. In other cases, the counts are similar, but not identical.

The following methods are similar to the rainflow methods:
• Range-pair counting
• Hayes method
• Original rainflow method
• Range-pair-range counting
• Ordered overall range counting
• Racetrack counting
• Hysteresis loop counting

Subjects: Durability Noise & Vibration