中英文翻译版本：雨流计数法

1、Designation: E 1049 - 85 (Reapproved 2005)名称：E1049至85年(己重新审核批准2005年)Standard Practices forCycle Counting in Fatigue Analysis These practices are under the jurisdiction of ASTM Committee E0-8 on Fatigue and Fracture and are the direct responsibility of Subcommittee E08.04 on Structural Applications.疲

2、劳与断裂中的这些规程属于ASTM委员会E0-8管辖范围内，E08.04委员会对结构应用程序负直接责任。Current edition approved June 1, 2005. Published June 2005. Originally approved in 1985. Last previous edition approved in 1997 as E1049 - 85(1997).当前版本在2005年6月1日批准。发布时间：2005年6月。在1985年最初批准。最新上一版本在1997 年批准为 E1049-85 (1997)。 Withdrawn.撤回在疲劳分析中循环计数的标准规

3、程This standard is issued under the fixed designation E 1049; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (e) indic

4、ates an editorial change since the last revision or reapproval.该标准发行时命名为E 1049；紧随其后的数字表示最初采用或者修订年份，括号内的 数字表示最近一次重新审批的年份。上标表明自上次修订或重新审批后又做了一次编辑修 改。Scope适用范围These practices are a compilation of acceptable procedures for cycle-counting methods employed in fatigue analysis. This standard does not intend

5、 to recommend a particular method.本规定针对疲劳分析中循环计数方法只给出了可汇编的程序步骤。本标准不会指定一个 特定的方法。This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determi

6、ne the applicability of regulatory limitations prior to use.本标准不旨在解决所有的安全问题，如果有的话，也仅限于与其使用有关的。本标准的 责任是在满足确定规章限制的前提下，优先使用其建立适当的安全和健康措施。Referenced DocumentsASTM Standards:2 ASTM 标准：E 912 Definitions of Terms Relating to Fatigue LoadingE912中与疲劳载荷有关的条款的定义Terminology 术语Definitions:定义constant amplitude lo

7、adingin fatigue loading, a loading in which all of the peak loads are equal and all of the valley loads are equal.恒定幅值加载一一在疲劳载荷中，其所有的所有峰值载荷和峰谷载荷是相等的。cyclein fatigue loading, under constant amplitude loading, the load variation from the minimum to the maximum and then to the minimum load.NOTE 1一In sp

8、ectrum loading, definition of cycle varies with the counting method used.循环一一疲劳载荷中，在恒定幅值加载下，载荷变动从最小值到最大值，然后到最小负 载的。注1：在载荷谱中，该定义是用来对循环变化时计数使用的。mean crossingsin fatigue loading, the number of times that the load-time history crosses the mean-load level with a positive slope （or a negative slope, or bo

9、th, as specified） during a given length of the history （see Fig. 1）.平均交叉（横跨参考载荷的交叉）一一疲劳载荷中，在给定一段载荷-时间历程，该载 荷时间曲线以正的斜率（或者负的斜率，或者指定同时存在）穿过平均载荷水平的次数（请 参阅图1）。DiscussionFor purposes related to cycle counting, a mean crossing may be defined as a crossing of the reference load level.讨论一一与循环计数目的相关的，一个平均交叉可以

10、定义为一次穿越参考载荷水平。mean load, Pm 一in fatigue loading, the algebraic average of the maximum and minimum loads in constant amplitude loading, or of individual cycles in spectrum loading,Pm=(Pmax+Pmin ”2or the integral average of the instantaneous load values or the algebraic average of the peak and valley

11、loads of a spectrum loading history.平均载荷一一疲劳载荷中，在恒定幅值加载时最大和最小载荷的代数平均，或载荷谱中 各个循环的代数平均，或瞬时载荷值的积分平均，或者载荷谱历程中的峰值和谷值载荷的代 数平均。peakin fatigue loading, the point at which the first derivative of the load-time history changes from a positive to a negative sign; the point of maximum load in constant amplitude

12、 loading (see Fig. 1).峰值在疲劳载荷，载荷时间历程一阶导数从正变为负时的那个点；恒定幅值加载时 则为载荷最大的点(参照图1)。rangein fatigue loading, the algebraic difference between successive valley and peak loads (positive range or increasing load range), or between successive peak and valley loads (negative range or decreasing load range); see F

13、ig. 1.NOTE 2In spectrum loading, range may have a different definition, depending on the counting method used; for example, “overall range” is defined by the algebraic difference between the largest peak and the smallest valley of a given load-time history.范围一一在疲劳载荷，连续的山谷和峰值载荷(正的范围或增加的载荷范围)，或连续 的峰值和

14、谷值载荷(负的范围或减少负载范围)之间的代数差，请参阅图1。注2：载荷谱中，范围可以有不同的定义，这取决于所使用的计数方法，例如，“整体 范围”所定义的是在一个给定的载荷-时间历程中最大峰值和最小峰谷代数差。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 necessarily successive events. In these

15、 practices, the definition of the word “range” is broadened so that events of this type are also included.讨论一一在各种方法的循环计数中，一般采用峰谷和峰值载荷之间的范围，或峰值和谷 值载荷，这里的峰值和谷值不一定是连续的。在这些用法中，“范围”这个词的定义被扩大， 不连续的这种情形也包括在内。reversalin fatigue loading, the point at which the first derivative of the load-time history change

16、s sign (see Fig. 1).NOTE 3In constant amplitude loading, a cycle is equal to two reversals.反转一一疲劳载荷中，该点的载荷-时间历程一阶导数改变符号(参照图1)。注3：在常幅载荷中，一个周期等于两次逆转。spectrum loading in fatigue loading, a loading in which all of the peak loads are not equal or all of the valley loads are not equal, or both, (Also know

17、n as variable amplitude loading or irregular loading.)载荷谱一一在疲劳载荷中，一次加载中所有的峰值载荷是不相等的或所有的峰谷载荷是 不相等的，或两者兼有。(也称为变幅载荷或随机载荷)。valleyin fatigue loading, the point at which the first derivative of the load-time history changes from a negative to a positive sign (also known as trough); the point of minimum lo

18、ad in constant amplitude loading (see Fig. 1).峰谷一一疲劳载荷中，该点的载荷-时间历史一阶导数从负变化为正(也被称为波谷)； 恒定幅值载荷中的最小负载点的(参照图1)。Definitions of Terms Specific to This Standard:定义本标准的特殊条款loadused in these practices to denote force, stress, strain, torque, acceleration, deflection, or other parameters of interest.载荷一一在这些做法

19、表示力，应力，应变，扭矩，加速度，挠度或其它感兴趣的参数。reference loadfor spectrum loading , used in these practices 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 the history, but this is not required.Fo

20、r other definitions of terms used in these practices refer to Definitions E 912.参考(基准)载荷对于载荷谱加载，用于表示的加载水平，它表示一个稳定状态并 且载荷变化是可以叠加的。参考载荷与历程中的平均载荷可以是相同的，但是这不是必需的。对于其他的这些规定中使用的术语的定义，请参阅定义E912。Significance and Use 意义和使用Cycle counting is used to summarize (often lengthy)irregular load-versus-time histories

21、 by providing the number of times cycles of various sizes occur. The definition of a cycle varies with the method of cycle counting. These practices cover the procedures used to obtain cycle counts by various methods, including level-crossing counting, peak counting, simple-range counting, range-pai

22、r counting, and rainflow counting. Cycle counts can be made for time histories of force, stress, strain, torque, acceleration, deflection, or other loading parameters of interest.循环计数用于汇总(通常是冗长的)不规则的负载与时间历程，通过提供循环的各种尺 寸发生的数目。随循环计数的方法的变化一个循环有不同的定义。这些规程涉及的程序，用 了不同方法来获取循环计数，包括交叉计数，峰值计数，简单的范围计数，范围-对计数以

23、及雨流计数。循环计数随时间历程的参数有力，应力，应变，扭矩，加速度，挠度或其它感 兴趣的负载参数。Procedures for Cycle Counting 循环计数的程序Level-Crossing Counting :水平交叉计数：Results of a level-crossing count are shown in Fig. 2(a). One count is recorded each time the positive sloped portion of the load exceeds a preset level above the reference load, and

24、 each time the negative sloped portion of the load exceeds a preset level below the reference load. Reference load crossings are counted on the positive sloped portion of the loading history. It makes no difference whether positive or negative slope crossings are counted. The distinction is made onl

25、y to reduce the total number of events by a factor of two.一个水平交叉的计数结果显示于图2(a)。每一次正斜率部分的载荷超过预先设定的高于 参考载荷的水平，以及每一次的负斜率部分的载荷超过预先设定的低于参考载荷的水平，记 录一次计数。载荷历程中横穿参考载荷的正斜率部分会被计数。无论是正或负斜率横穿进行 计数，这都没有区别。区别仅仅是减少总的事件数为一半。In practice, restrictions on the level-crossing counts are often specified to eliminate small

26、 amplitude variations which can give rise to a large number of counts. This may be accomplished by filtering small load excursions prior to cycle counting. A second method is to make no counts at the reference load and to specify that only one count be made between successive crossings of a secondar

27、y lower level associated with each level above the reference load, or a secondary higher level associated with each level below the reference load. Fig.2(b) illustrates this second method. A variation of the second method is to use the same secondary level for all counting levels above the reference

28、 load, and another for all levels below the reference load. In this case the levels are generally not evenly spaced.在这种方法中，水平交叉计数通常用来消除小幅度变化，这可能会引起大量的计数。它 可以在循环计数之前通过过滤小载荷振幅来完成。第二种方法是在参考载荷水平没有计数， 并指定连续的横穿高于参考载荷的水平且与该水平相关的二次较低水平只能计数一次，或低 于于参考载荷的水平且与该水平相关的二次较高水平。图2(b)阐释了第二方法。第二种方法 的一个变体是使用相同的二级水平可用于所有

29、参考载荷以上的水平的计数，和另一些所有低 于参考载荷的水平计数。在这种情况下，载荷水平一般不会均匀地间隔开。The most damaging cycle count for fatigue analysis is derived from the level-crossing count by first constructing the largest possible cycle, followed by the second largest, etc.,until all level crossings are used. Reversal points are assumed to

30、occur halfway between levels. This process is illustrated by Fig. 2(c). Note that once this most damaging cycle count is obtained, the cycles could be applied in any desired order, and this order could have a secondary effect on the amount of damage. Other methods of deriving a cycle count from the

31、level-crossings count could be used.疲劳分析中最具破坏性的循环计数首先来自构造最大循环水平穿越计数，其次是第二 大，等等，直到所有的水平交叉被计数。假设逆转点发生在(相邻)水平间的半路。此过程 如图2(c)所示。注意，一旦得到这个最具破坏性的循环计数，循环可以以任何所需要的顺序 来应用，该顺序可能有一个伤害量的二次效应。也可使用其他方法从水平交叉计数得到另一 个循环计数。5.2 Peak Counting:波峰计数Peak counting identifies the occurrence of a relative maximum or minimum

32、load value. Peaks above the reference load level are counted, and valleys below the reference load level are counted, as shown in Fig. 3(a). Results for peaks and valleys are usually reported separately. A variation of this method is to count all peaks and valleys without regard to the reference loa

33、d.峰值计数标识产生的相对最大或最小载荷值。计数包括高于参考载荷水平的峰值以及低 于参考载荷水平的峰谷，如图3(a)所示。波峰和波谷的结果通常是单独记录的。这种方法的 一个变体是计数所有波峰和波谷时不用考虑参考载荷。To eliminate small amplitude loadings, mean-crossing peak counting is often used. Instead of counting all peaks and valleys, only the largest peak or valley between two successive mean crossin

34、gs is counted as shown in Fig. 3(b).为了消除小幅度载荷，平均交叉峰值计数经常被使用。代替计数所有的峰值和峰谷，只 在两个连续的平均交叉间的峰值或峰谷才被计数，如图3(b)所示。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, crossings are counte

35、d on the positive sloped portion of the followed by the second largest cycle, etc., until all peak counts are used. This process is illustrated by Fig. 3(c). Note that once this most damaging cycle count is obtained, Alternate methods of deriving a cycle count, such as randomly selecting pairs of pe

36、aks and valleys, are sometimes used.疲劳分析中最具破坏性的循环计数首先来自使用最高峰值和最低峰谷构造最大循环峰 值计数，计数斜率为正的交叉，其次是第二大循环，等等，直到所有的峰值计数使用。此过 程是如图3(c)所示。注意，一旦这个最具破坏性的循环得以计数，其后循环的计数有时采用 随机地选择成对峰值和谷谷。Simple-Range Counting:简单-范围计数For this method, a range is defined as the difference between two successive reversals, the range be

37、ing positive when a valley is followed by a peak and negative when a peak is followed by a valley. The method is illustrated in Fig. 4. Positive ranges, negative ranges, or both, may be counted with this method. If only positive or only negative ranges are counted, then each is counted as one cycle.

38、 If both positive and negative ranges are counted, then each is counted as one-half cycle. Ranges smaller than a chosen value are usually eliminated before counting.对于这种方法，一个范围被定义为两个连续的逆转，不同之处在于，范围为正则是一个 峰谷后着一个峰值，为负则是一个峰值后着一个峰谷。方法如图4中所示。正范围，负范围， 或两者，都可以用这种方法计数。如果只对正或负的范围计数，那么每个计数为一个循环。 如果正和面的范围都进行计数

39、，那每个当作半个循环进行计数。通常在计数之前小于设定值 的范围会被排除。When the mean value of each range is also counted, the method is called simple range-mean counting. For the example of Fig. 4, the result of a simple range-mean count is given in X1.1 in the form of a range-mean matrix.当每个范围的平均值也被计数，该方法被称为简单范围-均值计数。对于图4的例子中， 在X1.1

40、表中给出的是一个简单范围均值计数以矩阵的形式给出的结果。Rainflow Counting and Related Methods:雨流计数和相关的方法A number of different terms have been employed in the literature to designate cycle-counting methods which are similar to the rainflow method. These include range-pair counting (1, 2), The boldface numbers in parentheses ref

41、er to the list of references appended to these practices.黑体括号中的数字是指这些方法依附的参考文献列表 the Hayes method (3), the original rainflow method (4-6), range-pair-range counting (7), ordered overall range counting (8), racetrack counting (9), and hysteresis loop counting (10). If the load history begins and ends

42、 with its maximum peak, or with its minimum valley, all of these give identical counts. In other cases, the counts are similar, but not generally identical. Three methods in this class are defined here: range-pair counting, rainflow counting, and a simplified method for repeating histories.许多文献中已经指定

43、类似雨流方法的循环计数法采用了一些不同的术语。这些方法包 括范围-对计数(1, 2),海耶斯方法(3),原来的雨流计数法(4-6),范围-对-范围计数(7), 命令整体范围计数(8),赛马场计数(9),和滞回环计数(10)。如果载荷历程以其最大峰 值，或者最小峰谷开始和结束，所有这些方法有完全相同的计数。在其他情况下，计数是相 似的，但通常不相同。这类计数中三种方法被定义：范围-对计数，雨流计数以及对重复历 程简化方法。The various methods similar to the rainflow method may be used to obtain cycles and the

44、mean value of each cycle; they are referred to as two-parameter methods. When the mean value is ignored, they are one-parameter methods, as are simple-range counting, peak counting, etc.各种方法类似雨流方法可以用来获得循环和每个循环的平均值；它们被称为两参数方 法。当平均值被忽略时，他们是单参数的方法，例如简单-范围计数，峰值计数等。Range-Pair Counting The range-paired me

45、thod counts a range as a cycle if it can be paired with a subsequent loading in the opposite direction. Rules for this method are as follows:范围-对计数法一一如果一个范围与后续的载荷在相反的方向上可以配对，范围配对方 法将该范围计数为一个循环。此方法的规则如下：Let X denote range under consideration; and Y, previous range adjacent to X .设X表示正在考虑的范围，Y表示与X相邻且在

46、其之前范围。Read next peak or valley. If out of data, go to Step 5.读取下一个峰值或谷值。如果没有数据，则转到步骤5。If there are less than three points, go to Step 1. Form ranges X and Y using the three most recent peaks and valleys that have not been discarded.如果少于三个点，则转到步骤1。使用最近的三个没有被舍弃峰值和谷值，组成X和Y 范围。Compare the absolute value

47、s of ranges X and Y 比较 X 和 Y 范围的绝对值If X Y, go to Step 1.若 X Y, go to Step 4.若 X3Y，则转到步骤 4。Count range Y as one cycle and discard the peak and valley of Y; go to Step 2.计数Y范围为一个循环，舍弃Y的峰值和谷值；转到步骤2。The remaining cycles, if any, are counted by starting at the end of the sequence and counting backwards.

48、If a single range remains, it may be counted as a half or full cycle.如果还剩余循环，则从序列末尾开始倒回来计数。如果一个单一的范围仍然存在，它可 以被算做半个或一个循环。The load history in Fig. 4 is replotted as Fig. 5(a) and is used to illustrate the process.Details of the cycle counting are as follows:图4中的载荷历程重绘为图5 (a),用来说明这个过程。循环计数的细节如下：Y = IA-

49、B I; X = IB-CI; and X Y. Count IA-B I as one cycle and discard points A and B.(See Fig. 5(b). Note that a cycle is formed by pairing range A-B and a portion of range B-C.)Y= I A-B I, X=I B-C I;和 X Y。计数I A-B作为一个循环并舍弃点A和B (参见图5 (b), 注意，一个循环由配对范围AB和一部分BC范围来形成。)Y = IC-DI; X = ID-E I; and X YY =I C-D I；

50、X =I D-EI；和 XY。Y = ID-EI; X = IE-F I; and X YY =I D-E I； X =I E-F I；和 X Y. Count IE-FI as one cycle and discard points E and F. (See Fig. 5(c).)Y =I E-FI ； X =I F-GI；和X Y。计数IE-F I作为一个周期并丢弃点E和F。(参见图5(c)。)Y = IC-DI; X = ID-G I; and X Y . Count IC-DI as one cycle and discard points C and D. (See Fig. 5

51、(d).)=I C-D I； X =I D-GI； 和 X Y。计数IC-DI作为一个循环并丢弃点C和D(参见图5(d)。)Y = IG-HI; X = IH-I I; and X Y. Go to the end and count backwards.Y=I G-H I X =I H-II；和X Y. Count H-II as one cycle and discard points H and I. (See Fig. 5(e).)=I H-II； X =I GHI；和X Y计数IH-II作为一个循环并舍弃点H和I。(参见图5(e)End of counting. See the ta

52、ble in Fig. 5 for a summary of the cycles counted in this example, and see Appendix X1.2 for this cycle count in the form of a range-mean matrix.结束的计数。本例中的循环计数见图5中的表汇总，此循环计数组成的一个范围均值矩 阵见附录X1.2。Rainflow Counting :雨流计数Rules for this method are as follows: let X denote range under consideration; Y, pre

53、vious range adjacent to X ; and S, starting point in the history.方法规则如下：设X表示正在考虑的范围；Y相邻于X且在其以前的范围；和历程的 起点S。Read next peak or valley. If out of data, go to Step 6.读取下一个峰值或谷值。如果没有数据，请转至步骤6。If there are less than three points, go to Step 1. Form ranges X and Y using the three most recent peaks and vall

54、eys that have not been discarded.如果少于三个点，则转到步骤1。使用最近的三个没有被舍弃峰值和谷值，组成X和Y 范围。Compare the absolute values of ranges X and Y 比较 X 和 Y 范围的绝对值If X Y , go to Step 1.若 X Y, go to Step 4.若 X NY，则转到步骤 4。If range Y contains the starting point S, go to Step 5; otherwise, count range Y as one cycle; discard the

55、peak and valley of Y; and go to Step 2.如果范围Y包含的起始点S，则转到步骤5；否则，计数范围Y为一循环;舍弃Y的峰 值和谷值;转到步骤2。Count range Y as one-half cycle; discard the first point (peak or valley) in range Y; move the starting point to the second point in range Y; and go to Step 2.计数范围Y为半个周期，舍弃范围Y的第一个(峰值或谷值)点，移动出发点至范围 Y中的第二点；转到步骤2。C

56、ount each range that has not been previously counted as one-half cycle.之前未计数的每个范围均按半个循环计数。The load history of Fig. 4 is replotted as Fig. 6(a) and is used to illustrate the process. Details of the cycle counting are as follows:图4载荷历程被重绘于图6(a)，用来说明该过程。循环计数的详细节如下：S = A; Y = IA-BI; X = IB-C I; X Y . Y

57、contains S, that is, point A . Count IA-B I as one-half cycle and discard point A ; S = B. (See Fig. 6(b).)S= A，Y =I A-B I； X=I B-C I ； X Y。Y包含S，即A点。I A-B计数半个循环，舍弃点 A，S = B。(参见图 6(b)Y = IB-CI; X = IC-D I; X Y. Y contains S, that is, point B. CountI B-CI as one-half cycle and discard point B ; S = C.

58、 (See Fig. 6(c).)Y=l B-C|, X= | C-D |； X Y。Y包含S,即B点。计数| B-C |半个循环，并舍弃的点B, S= C。(参见图 6 (c)Y = |C-D|; X = |D-E |; X Y .Y = |D-E|; X = |E-F |; X Y Count |E-F|as one cycle and discard points E and F, (See Fig.6(d). Note that a cycle is formed by pairing rangeE-F andaportionof rangeF-G.)Y=| E-F|，X= | F-G

59、 |； X Y。计数| E-F|为一个循环和舍弃点E和F (参见图6(d)。注 意：一个循环是由范围EF和范围FG的一部分组成的。)Y = |C-D|; X = |D-G |; X Y ; Y contains S, that is, point C. Count |C-D| as one-half cycle and discard point C. S = D. (See Fig. 6(e).)Y =| C-D|，X= | D-G |； X Y； Y包含S，即C点。计数C-D |作为半个循环，并舍弃点 C。S = D。(参见图第6(e)Y = |D-G|; X = |G-H |; X Y

60、.Y = |G-H|; X = |H-I |; X Y . End of data.Count |D-G| as one-half cycle, |G-H| as one-half cycle, and| H-I| as one-half cycle. (See Fig. 6(f ).)计数| D-G|半个循环，| G-H作为半个循环，和| H-I |半个循环。(参见图6(f)End of counting. See the table in Fig. 6 for a summary of the cycles counted in this example, and see Appendix