1、Designation: E 1049 85 (Reapproved 2005) 名称：E1049 至 85 年（己重新审核批准 2005 年）Standard Practices for Cycle Counting in Fatigue Analysis1在疲劳分析中循环计数的标准规程This standard is issued under the fixed designation E 1049; the number immediately following the designation indicates the year of original adoption or, in
2、 the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (e) indicates 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。1. Scope 适
3、用范围 1.1 These practices are a compilation of acceptable procedures for cycle-counting methods employed in fatigue analysis. This standard does not intend 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。1.2 This standard does not purport to address all of the safety conce
4、rns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine 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。2. Referenc
5、ed Documents 2.1 ASTM 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3. Terminology 术语3.1 Definitions: 定义1 These practices are under the jurisdiction of ASTM Committee E0-8 on Fatigue and Fracture and are the direct responsibility of Subcommittee E08.04
6、on Structural Applications. 疲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 E104985(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
7、E1049-85（1997） 。 2 Withdrawn. 撤回3.1.1 constant amplitude loadingin 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。3.1.2 cyclein fatigue loading, under constant amplitude loading, the load variation from the
8、minimum to the maximum and then to the minimum load. NOTE 1In spectrum loading, definition of cycle varies with the counting method used.循环疲劳载荷中，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。3.1.3 mean crossingsin fatigue loading, the number of times that the load-time history crosses t
9、he mean-load level with a positive slope (or a negative slope, or both, 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）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） 。3.1.3.1 DiscussionFor purposes related to cycle counting, a mean crossing may b
10、e defined as a crossing of the reference load level. 讨论与循环计数目的相关的，一个平均交叉可以定义为一次穿越参考载荷水平。3.1.4 mean load, Pm 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 )/2 (1)or the integral aver
11、age of the instantaneous load values or the algebraic average of the peak and valley loads of a spectrum loading history. 平均载荷疲劳载荷中，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。3.1.5 peakin fatigue loading, the point at which the first derivative of the load-time history cha
12、nges from a positive to a negative sign; the point of maximum load in constant amplitude 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） 。3.1.6 rangein fatigue loading, the algebraic difference between successive valley and peak loads (positive range or increasing load rang
13、e), or between successive peak and valley loads (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” is defined by the algebraic difference between the largest peak
14、 and the smallest valley of a given load-time history. 范围在疲劳载荷，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。3.1.6.1 DiscussionIn cycle counting by various methods, it is common to employ ranges between vall
15、ey and peak loads, or between peak and valley loads, which are not necessarily successive events. In these practices, the definition of the word “range” is broadened so that events of this type are also included.讨论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
16、括在内。3.1.7 reversalin fatigue loading, the point at which the first derivative of the load-time history changes sign (see Fig. 1). NOTE 3In constant amplitude loading, a cycle is equal to two reversals. 反转疲劳载荷中，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。3.1.8 spectrum loadingin fatigue loading,
17、 a loading in which all of the peak loads are not equal or all of the valley loads are not equal, or both. (Also known as variable amplitude loading or irregular loading.) 载荷谱在疲劳载荷中，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） 。3.1.9 valleyin fatigue loading, the point at which the first der
18、ivative of the load-time history changes from a negative to a positive sign (also known as trough); the point of minimum load in constant amplitude loading (see Fig. 1). 峰谷疲劳载荷中，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） 。3.2 Definitions of Terms Specific to This Standard: 定义本标准的特殊条款3.2.1 lo
19、adused in these practices to denote force, stress, strain, torque, acceleration, deflection, or other parameters of interest. 载荷在这些做法表示力，应力，应变，扭矩，加速度，挠度或其它感兴趣的参数。3.2.2 reference loadfor spectrum loading , used in these practices to denote the loading level that represents a steady-state condition up
20、on which load variations are superimposed. The reference load may be identical to the mean load of the history, but this is not required. 3.3 For 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
21、。对于其他的这些规定中使用的术语的定义，请参阅定义 E912。4. Significance and Use 意义和使用4.1 Cycle counting is used to summarize (often lengthy)irregular load-versus-time histories 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
22、cover the procedures used to obtain cycle counts by various methods, including level-crossing counting, peak counting, simple-range counting, range-pair counting, and rainflow counting. Cycle counts can be made for time histories of force, stress, strain, torque, acceleration, deflection, or other l
23、oading 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。5. Procedures for Cycle Counting 循环计数的程序5.1 Level-Crossing Counting : 水平交叉计数：5.1.1 Results of a level-cr
24、ossing 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 each time the negative sloped portion of the load exceeds a preset level below the reference load. Reference load crossings are counted on
25、 the positive sloped portion of the loading history. It makes no difference whether positive or negative slope crossings are counted. The distinction is made only 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
26、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。5.1.2 In practice, restrictions on the level-crossing counts are often specified to eliminate small amplitude variations which can give rise to a large number of counts. This may be accomplished by filtering small load excursions prio
27、r 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 secondary lower level associated with each level above the reference load, or a secondary higher level associated with each level below the ref
28、erence 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 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
29、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。5.1.3 The most damaging cycle count for fatigue analysis is derived from the level-c
30、rossing 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 occur halfway between levels. This process is illustrated by Fig. 2(c). Note that once this most damaging cycle count is obtained, t
31、he 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 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
32、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5.2.1 Peak counting identifies the occurrence of a relative maximum or minimum load value. Peaks above the reference load level are counted, and valleys below the reference load level are counted, as shown
33、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 load. 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。5.2.2 To eliminate
34、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 crossings 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。5.2.3 The most
35、 damaging cycle count for fatigue analysis is derived from the peak count by rst constructing the largest possible cycle, using the highest peak and lowest valley, crossings are counted on the positive sloped portion of the followed by the second largest cycle, etc., until all peak counts are used.
36、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 peaks 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
37、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。5.3 Simple-Range Counting: 简单-范围计数5.3.1 For this method, a range is dened as the difference between two successive reversals, the range being positive when a valley is followed by a peak and negative when a peak is followed by a valley. The metho
38、d 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. If both positive and negative ranges are counted, then each is counted as one-half cycle. Ranges smaller th
39、an 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，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。5.3.2 When the mean value of each range is also counted, the method is ca
40、lled 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 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。5.4 Rainflow Counting and Related Methods: 雨流计数和相关的方法5.4.1 A number of
41、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),3 the Hayes method (3), the original rainflow method (4-6), range-pair-range counting (7), ordered overall range counting (8), r
42、acetrack counting (9), and hysteresis loop counting (10). 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 generally identical. Three methods 3 The boldface numbers in parenthese
43、s refer 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 in this class are defined here: range-pair counting, rainow counting, and a simplified method for repeating histories. 许多文献中已经指定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） ，
44、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。5.4.2 The various methods similar to the rainow method may be used to obtain cycles and the mean value of each cycle; they are referred to as two-parameter methods. Whe
45、n 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。5.4.3 Range-Pair CountingThe range-paired method counts a range as a cycle if it can be paired with a subsequent lo
46、ading in the opposite direction. Rules for this method are as follows: 范围-对计数法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：5.4.3.1 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 相邻且在其之前范围。(1) Read next peak or valley. If out of data, go to
47、Step 5. 读取下一个峰值或谷值。如果没有数据，则转到步骤 5。(2) 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。(3) Compare the absolute values of ranges X and Y. 比较 X 和 Y 范围的绝对值 (a)
48、If X Y. Count |A-B | 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= | A-B |，X=| B-C |;和 X Y。计数| 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。 ）(2) Y = |C-D|; X = |D-E |; and X Y. Count |E-F| as
49、one cycle and discard points E and F. (See Fig. 5(c).) Y =| E-F| ；X =| F-G|；和 X Y。计数| E-F|作为一个周期并丢弃点 E 和 F。 （参见图5（c） 。 ）(5) Y = |C-D|; X = |D-G |; and X Y. Count |C-D| as one cycle and discard points C and D. (See Fig. 5(d).) Y =| C-D |；X =| D-G|；和 X Y。计数|C-D|作为一个循环并丢弃点 C 和 D（参见图5（d） 。 ）(6) Y = |G-H|; X = |H-I |; and X Y. Count H-I| as one cycle and discard points H and I. (See Fig. 5(e).) Y =| H-I|；X =| GH| ；和 X Y 计数|H-I|作为一个循环并舍弃点 H 和 I。 （参见图 5（e） ）(8) End of counting. See the table in Fig. 5 for a summary of the cycles counted in this e
