A methodology for dealing with irregular loading profiles

Simple Tools … Faster Solutions

Rainflow Cycle Counting

How do we identify cycles in a random variable amplitude loading sequence?

Rainflow Cycle Counting – Original Definition

[1]. Extract peaks and troughs from the time signal so that all points between adjacent peaks and troughs are discarded.

 

[2]. Make the beginning, and end, of the sequence have the same level. This can be done in a number of ways but the simplest is to add an additional point at the end of the signal to match the beginning.

 

[3]. Find the highest peak and reorder the signal so that this becomes the beginning and the end. The beginning and end of the original signal have to be joined together.

 

[4]. Start at the beginning of the sequence and pick consecutive sets of 4 peaks and troughs. Apply a rule that states,

Rainflow Cycle Counting – Practical Definition Long-Short-Long Rule

If the second segment is shorter (vertically) than the first, and the third is longer then the second, the middle segment can be extracted and recorded as a Rainflow cycle. In this case, B and C are completely enclosed by A and D.

[5]. If no cycle is counted then a check is made on the next set of 4 peaks, ie peaks 2 to 5, and so on until a Rainflow cycle is counted. Every time a Rainflow cycle is counted the procedure is started from the beginning of the sequence again.

Eventually all segments will be counted as cycles and so for every peak in the original sequence there should be a corresponding Rainflow cycle counted. There will be 5 cycles obtained from 10 peaks and troughs.

Rainflow Cycle Counting – Practical Definition (cont)

A

B C

D

or

A

B C

D

Peak

1

2

3

4

5

6

7

8

9 Value

0

135

67.5

112.5

22.5

112.5

45

90

0

Example: Rainflow Cycle Counting

Cycles

Range 45 90 135

Mean = 67.5 1 1 1

Mean = 90 1

0

22.5 45

67.5 90

112.5 135

As an example of this let us extract Rainflow cycles from the following sequence.

Variable Amplitude Loading

• SN tests are conducted under constant amplitude sinusoidal loading

• Real loading is usually fairly random

• The question is how do we break down real loads into equivalent cycle ranges so we can use the same SN curves?

• The is done using Rainflow Cycle Counting

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Complete rainflow Process

Figure 4. Rainflow Cycle Counting (RCC) Process – initial time history at constant delta T

Figure 5. Rainflow Cycle Counting (RCC) Process – extracted peaks and troughs

9

Complete rainflow Process

Figure 6. Rainflow Cycle Counting (RCC) Process – beginning and end joined

Figure 7. Rainflow Cycle Counting (RCC) Process – reordered so maximum is at beginning and end

10

Complete rainflow Process

Figure 8. Rainflow Cycle Counting (RCC) Process – 1st iteration to remove RCC loops

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Figure 9. Rainflow Cycle Counting (RCC) Process – 2nd iteration to remove RCC loops

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Complete rainflow Process

Figure 10. Rainflow Cycle Counting (RCC) Process – 3rd iteration to remove RCC loops

Figure 11. Rainflow Cycle Counting (RCC) Process – 4th iteration to remove RCC loops

12

Complete rainflow Process

Figure 12. Rainflow Cycle Counting (RCC) Process – 5th iteration to remove RCC loops

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Connection With Closed Stress Strain Hysteresis Loops There is a direct connection between Rainflow Cycles counted using the above method and closed stress-strain hysteresis loops that can be identified if the local stress and strain are monitored as a function of time. Eg, with B-C, E-F or G-H there is a separately identifiable rainflow cycle, and when these are counted and extracted there remains one final loop which is made from the largest cycle from the maximum and minimum peaks A-D.