1、Designation: E 1049 85 (Reapproved 2005)Standard Practices forCycle Counting in Fatigue Analysis1This standard is issued under the fixed designation E 1049; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision.
2、 A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 These practices are a compilation of acceptable proce-dures for cycle-counting methods employed in fatigue analysis.This standard d
3、oes not intend to recommend a particularmethod.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regu
4、latory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 912 Definitions of Terms Relating to Fatigue Loading3. Terminology3.1 Definitions:3.1.1 constant amplitude loadingin fatigue loading,aloading in which all of the peak loads are equal and all of thevalley loads are equal.3.1
5、.2 cyclein fatigue loading, under constant amplitudeloading, the load variation from the minimum to the maximumand then to the minimum load.NOTE 1In spectrum loading, definition of cycle varies with thecounting method used.3.1.3 mean crossingsin fatigue loading, the number oftimes that the load-time
6、 history crosses the mean-load levelwith a positive slope (or a negative slope, or both, as specified)during a given length of the history (see Fig. 1).3.1.3.1 DiscussionFor purposes related to cycle counting,a mean crossing may be defined as a crossing of the referenceload level.3.1.4 mean load, Pm
7、in fatigue loading, the algebraicaverage of the maximum and minimum loads in constantamplitude loading, or of individual cycles in spectrum loading,Pm5 Pmax1 Pmin!/2 (1)or the integral average of the instantaneous load values or thealgebraic average of the peak and valley loads of a spectrumloading
8、history.3.1.5 peakin fatigue loading, the point at which the firstderivative of the load-time history changes from a positive toa negative sign; the point of maximum load in constantamplitude loading (see Fig. 1).3.1.6 rangein fatigue loading, the algebraic differencebetween successive valley and pe
9、ak loads (positive range orincreasing load range), or between successive peak and valleyloads (negative range or decreasing load range); see Fig. 1.NOTE 2In spectrum loading, range may have a different definition,depending on the counting method used; for example, “overall range” isdefined by the al
10、gebraic difference between the largest peak and thesmallest valley of a given load-time history.3.1.6.1 DiscussionIn cycle counting by various methods,it is common to employ ranges between valley and peak loads,or between peak and valley loads, which are not necessarilysuccessive events. In these pr
11、actices, the definition of the word“range” is broadened so that events of this type are alsoincluded.3.1.7 reversalin fatigue loading, the point at which thefirst derivative of the load-time history changes sign (see Fig.1).NOTE 3In constant amplitude loading, a cycle is equal to tworeversals.3.1.8
12、spectrum loadingin fatigue loading, a loading inwhich all of the peak loads are not equal or all of the valleyloads are not equal, or both. (Also known as variable amplitudeloading or irregular loading.)3.1.9 valleyin fatigue loading, the point at which the firstderivative of the load-time history c
13、hanges from a negative toa positive sign (also known as trough); the point of minimumload in constant amplitude loading (see Fig. 1).3.2 Definitions of Terms Specific to This Standard:3.2.1 loadused in these practices to denote force, stress,strain, torque, acceleration, deflection, or other paramet
14、ers ofinterest.3.2.2 reference loadfor spectrum loading, used in thesepractices to denote the loading level that represents a steady-state condition upon which load variations are superimposed.The reference load may be identical to the mean load of thehistory, but this is not required.1These practic
15、es are under the jurisdiction ofASTM Committee E0-8 on Fatigueand Fracture and are the direct responsibility of Subcommittee E08.04 on StructuralApplications.Current edition approved June 1, 2005. Published June 2005. Originallyapproved in 1985. Last previous edition approved in 1997 as E104985(1997
16、).2Withdrawn.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.3 For other definitions of terms used in these practicesrefer to Definitions E 912.4. Significance and Use4.1 Cycle counting is used to summarize (often lengthy)irregular
17、 load-versus-time histories by providing the number oftimes cycles of various sizes occur. The definition of a cyclevaries with the method of cycle counting. These practices coverthe procedures used to obtain cycle counts by various methods,including level-crossing counting, peak counting, simple-ra
18、ngecounting, range-pair counting, and rainflow counting. Cyclecounts can be made for time histories of force, stress, strain,torque, acceleration, deflection, or other loading parameters ofinterest.5. Procedures for Cycle Counting5.1 Level-Crossing Counting:5.1.1 Results of a level-crossing count ar
19、e shown in Fig.2(a). One count is recorded each time the positive slopedportion of the load exceeds a preset level above the referenceload, and each time the negative sloped portion of the loadexceeds a preset level below the reference load. Reference loadcrossings are counted on the positive sloped
20、 portion of theloading history. It makes no difference whether positive ornegative slope crossings are counted. The distinction is madeonly to reduce the total number of events by a factor of two.5.1.2 In practice, restrictions on the level-crossing countsare often specified to eliminate small ampli
21、tude variationswhich can give rise to a large number of counts. This may beaccomplished by filtering small load excursions prior to cyclecounting. A second method is to make no counts at thereference load and to specify that only one count be madebetween successive crossings of a secondary lower lev
22、elassociated with each level above the reference load, or asecondary higher level associated with each level below thereference load. Fig. 2(b) illustrates this second method. Avariation of the second method is to use the same secondarylevel for all counting levels above the reference load, andanoth
23、er for all levels below the reference load. In this case thelevels are generally not evenly spaced.5.1.3 The most damaging cycle count for fatigue analysis isderived from the level-crossing count by first constructing thelargest possible cycle, followed by the second largest, etc.,until all level cr
24、ossings are used. Reversal points are assumedto occur halfway between levels. This process is illustrated byFig. 2(c). Note that once this most damaging cycle count isobtained, the cycles could be applied in any desired order, andthis order could have a secondary effect on the amount ofdamage. Other
25、 methods of deriving a cycle count from thelevel-crossings count could be used.5.2 Peak Counting:5.2.1 Peak counting identifies the occurrence of a relativemaximum or minimum load value. Peaks above the referenceload level are counted, and valleys below the reference loadlevel are counted, as shown
26、in Fig. 3(a). Results for peaks andvalleys are usually reported separately. A variation of thismethod is to count all peaks and valleys without regard to thereference load.5.2.2 To eliminate small amplitude loadings, mean-crossingpeak counting is often used. Instead of counting all peaks andvalleys,
27、 only the largest peak or valley between two successivemean crossings is counted as shown in Fig. 3(b).5.2.3 The most damaging cycle count for fatigue analysis isderived from the peak count by first constructing the largestpossible cycle, using the highest peak and lowest valley,followed by the seco
28、nd largest cycle, etc., until all peak countsare used. This process is illustrated by Fig. 3(c). Note that oncethis most damaging cycle count is obtained, the cycles could beapplied in any desired order, and this order could have asecondary effect on the amount of damage. Alternate methodsof derivin
29、g a cycle count, such as randomly selecting pairs ofpeaks and valleys, are sometimes used.5.3 Simple-Range Counting:5.3.1 For this method, a range is defined as the differencebetween two successive reversals, the range being positivewhen a valley is followed by a peak and negative when a peakis foll
30、owed by a valley. The method is illustrated in Fig. 4.Positive ranges, negative ranges, or both, may be counted withthis method. If only positive or only negative ranges arecounted, then each is counted as one cycle. If both positive andnegative ranges are counted, then each is counted as one-halfcy
31、cle. Ranges smaller than a chosen value are usually elimi-nated before counting.5.3.2 When the mean value of each range is also counted,the method is called simple range-mean counting. For theFIG. 1 Basic Fatigue Loading ParametersE 1049 85 (2005)2example of Fig. 4, the result of a simple range-mean
32、 count isgiven in X1.1 in the form of a range-mean matrix.5.4 Rainflow Counting and Related Methods:5.4.1 A number of different terms have been employed inthe literature to designate cycle-counting methods which aresimilar to the rainflow method. These include range-paircounting (1, 2),3the Hayes me
33、thod (3), the original rainflowmethod (4-6), range-pair-range counting (7), ordered overallrange counting (8), racetrack counting (9), and hysteresis loopcounting (10). If the load history begins and ends with itsmaximum peak, or with its minimum valley, all of these giveidentical counts. In other c
34、ases, the counts are similar, but notgenerally identical. Three methods in this class are definedhere: range-pair counting, rainflow counting, and a simplifiedmethod for repeating histories.5.4.2 The various methods similar to the rainflow methodmay be used to obtain cycles and the mean value of eac
35、h cycle;they are referred to as two-parameter methods. When the meanvalue is ignored, they are one-parameter methods, as aresimple-range counting, peak counting, etc.5.4.3 Range-Pair CountingThe range-paired methodcounts a range as a cycle if it can be paired with a subsequentloading in the opposite
36、 direction. Rules for this method are asfollows:5.4.3.1 Let X denote range under consideration; and Y,previous range adjacent to X.(1) Read next peak or valley. If out of data, go to Step 5.3The boldface numbers in parentheses refer to the list of references appended tothese practices.(a)Level Cross
37、ing Counting(b)Restricted Level Crossing CountingFIG. 2 Level-Crossing Counting ExampleE 1049 85 (2005)3(2) If there are less than three points, go to Step 1. Formranges X and Y using the three most recent peaks and valleysthat have not been discarded.(3) Compare the absolute values of ranges X and
38、Y.(a)IfX Y.Count |A-B|asonecycle and discard points A and B. (See Fig. 5(b). Note that acycle is formed by pairing range A-B and a portion of rangeB-C.)(2) Y = |C-D|; X = |D-E|; and XY.Count |E-F|asonecycle and discard points E and F. (See Fig. 5(c).)(5) Y = |C-D|; X = |D-G|; and XY.Count |C-D| as o
39、necycle and discard points C and D. (See Fig. 5(d).)(6) Y = |G-H|; X = |H-I|; and XY.Count |H-I|asonecycle and discard points H and I. (See Fig. 5(e).)(a)Peak Counting(b)Mean Crossing Peak Counting(c)Cycles Derived from Peak Count of (a)FIG. 3 Peak Counting ExampleE 1049 85 (2005)4(8) End of countin
40、g. See the table in Fig. 5 for a summaryof the cycles counted in this example, and see Appendix X1.2for this cycle count in the form of a range-mean matrix.5.4.4 Rainflow Counting:5.4.4.1 Rules for this method are as follows: let X denoterange under consideration; Y, previous range adjacent to X; an
41、dS, starting point in the history.(1) Read next peak or valley. If out of data, go to Step 6.(2) If there are less than three points, go to Step 1. Formranges X and Y using the three most recent peaks and valleysthat have not been discarded.(3) Compare the absolute values of ranges X and Y.(a)IfXY.Y
42、contains S, that is,point A. Count |A-B| as one-half cycle and discard point A;S=B.(See Fig. 6(b).)(2) Y = |B-C|; X = |C-D|; XY.Ycontains S, that is, pointB. Count| B-C| as one-half cycle and discard point B; S=C.(See Fig. 6(c).)(3) Y = |C-D|; X = |D-E|; XY.Count |E-F| as one cycleand discard points
43、 E and F. (See Fig. 6(d). Note that a cycle isformed by pairing range E-F and a portion of range F-G.)(6) Y = |C-D|; X = |D-G|; XY; Y contains S, that is, pointC. Count |C-D| as one-half cycle and discard point C. S=D.(See Fig. 6(e).)(7) Y = |D-G|; X = |G-H|; XY. Count | E-F| as one cycleand discard
44、 points E and F. (See Fig. 7(c).) Note that a cycleis formed by pairing range E-F and a portion of range F-G.(3) Y = |D-G|; X = |G-H|; XY. Count |A-B| as one cycleand discard points A and B. (See Fig. 7(d).)(7) Y = |G-H|; X = |H-C|; XY.Count |H-C| as one cycleand discard points H and C. (See Fig. 7(
45、e).)(9) Y = |D-G|; X = |G-D|; X=Y.Count| D-G| as one cycleand discard points D and G. (See Fig. 7(f).)(10) End of counting. See the table in Fig. 7 for a summaryof the cycles counted in this example, and see Appendix X1.4for this cycle count in the form of a range-mean matrix.(c)(d)(e)(f)FIG. 6 Rain
46、flow Counting ExampleE 1049 85 (2005)7APPENDIX(Nonmandatory Information)X1. RANGE-MEAN MATRIXES FOR CYCLE COUNTING EXAMPLESX1.1 The Tables X1.1-X1.4 which follow correspond to thecycle-counting examples of Figs. 4-7. In each case, the table isa matrix giving the number of cycles counted at the indic
47、atedcombinations of range and mean. Note that these examples arethe ones illustrating (1) simple-range counting, (2) range-paircounting, (3) rainflow counting, and (4) simplified rainflowcounting for repeating histories, which are the methods that canbe used as two-parameter methods.(a)(b)(c)(d)(e)(
48、f)FIG. 7 Example of Simplified Rainflow Counting for a Repeating HistoryTABLE X1.1 Simple Range-Mean Counting (Fig. 4)RangeUnitsMean Units2.0 1.5 1.0 0.5 0 + 0.5 + 1.0 + 1.5 + 2.010 . . . . . . . . .9 . . . . . . . . .8 . . . . 0.5 . 0.5 . .7 . . . 0.5 . . . . .6 . . . . . . 0.5 . 0.55 . . . . . . .
49、 . .4 . . 0.5 . . . 0.5 . .3 . . . 0.5 . . . . .2 . . . . . . . . .1 . . . . . . . . .E 1049 85 (2005)8REFERENCES(1) Anonymous, “The Strain Range Counter,” VTO/M/416, Vickers-Armstrongs Ltd. (now British Aircraft Corporation Ltd.), TechnicalOffice, Weybridge, Surrey, England, April 1955.(2) Burns, A., “Fatigue Loadings in Flight: Loads in the Tailpipe and Finof a Varsity,” Technical Report C.P. 256, Aeronautical ResearchCouncil, London, 1956.(3) Hayes, J. E., “Fatigue Analysis and Fail-Safe Design,” Analysis andDesign of Flight Vehicle Structures, E. F
