CN111159871B - Random multi-axis cycle counting method based on path curve integration - Google Patents
Random multi-axis cycle counting method based on path curve integration Download PDFInfo
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Abstract
The invention discloses a multi-axis circulation counting method based on path curve integration, which comprises the following steps ofDefining a curve integral Y relative to the origin in the strain space t First, find out the corresponding maximum Y in the original load block t The point of the value, reorder the load with the point as the demarcation point, and then calculate Y for each point t Value, sum of start point and Y t The history between the points with the maximum values is counted as one iteration, and the history without counting and Y t The history of the value occurrences of the turns performs a similar step, and all half-cycles are calculated using a recursive algorithm. The method is independent of a fatigue damage model, solves the problem that valley symbols are omitted in an equivalent strain counting method, can be degenerated to uniaxial rain flow counting, does not involve material constants in the counting process, is simple in algorithm, easy to program a computer and high in engineering practicability.
Description
Technical Field
The invention relates to the field of fatigue strength, in particular to a random multi-axis cycle counting method based on path curve integration.
Background
When many machines are in service, the machines bear complex load states, such as aerospace aircrafts, high-speed trains and large-scale carrying machines, critical part dangerous points of parts are in multi-axis stress states, stress components generally change randomly along with time, the amplitude is large, fatigue cracks are easy to initiate and expand, service life is greatly reduced, and therefore the accurate prediction of the amplitude-variable random multi-axis fatigue life is significant.
The uniaxial fatigue strength theory developed gradually over the past several decades, but the multiaxial fatigue strength theory also requires supplementation and optimization. Predicting random multiaxial fatigue life can be simply divided into three steps: 1) The random luffing load history is decomposed into a plurality of constant amplitude load histories, namely a plurality of half cycles (repetitions) by a counting method. 2) And calculating the damage parameters of each iteration by using a proper damage model, so as to obtain damage. 3) Each repeated lesion is accumulated as a total lesion by means of a lesion accumulation criterion, and fatigue life is estimated. The counting method is a preprocessing flow of amplitude random multi-axis life prediction, and the rationality of the preprocessing flow directly influences the fatigue life assessment precision. Existing counting methods have a plurality of defects, such as that the multi-axis rain flow counting method can lose peaks and valleys of an auxiliary counting channel, the rain flow counting method based on equivalent strain can miss valley symbols, and the counting method depending on a damage model has no universality. Therefore, the counting method which does not depend on the damage model and comprehensively considers the component channel information is of great significance.
Disclosure of Invention
Aiming at the development of amplitude-variable multiaxial fatigue life prediction, the invention considers the influence of a loading path on fatigue life, overcomes the defects of dependence of a counting method on a fatigue damage model and missing of coincidence of a counting channel valley value, and provides a random multiaxial fatigue cycle counting method based on path curve integration.
The invention provides a random multiaxial fatigue cycle counting method based on path curve integration, which comprises the following steps:
step 1): recording epsilon as positive strain, gamma as tangential strain, projecting epsilon (t) -t and gamma (t) -t histories under random multiaxial loading of a pull-torsion amplitude toSpace, recording the projection point corresponding to the time t as A t The start time is denoted as start and the end time is denoted as end.
Step 2): in order to search the starting point and the ending point of the half cycle, the influence of the loading path length on fatigue damage is considered, inThe integral of the load path length change is defined in the strain space as follows
Wherein the method comprises the steps ofIs the loading path between the projection point at the starting time 1 and the projection point at the time t, +.>Is the vector of the projection point of the start moment start to the projection point of the moment t +.>Is the vector of the projection point at time t-1 pointing to the projection point at time t, ds is +.>The arc length of the loading path in space is a trace element, sign (x) is a sign function, and the expression is as follows
Where x is any real number.
Step 3): calculating the integral value Y of all time points t Find out the corresponding Y t Absolute value abs (Y t ) Maximum projection point A m Will A m The sequence of the strokes before and after the point is changed, and A is as follows m Set as a starting point A start 。
Step 4): calculating Y of all time points of new sequence t Find out the corresponding Y t Maximum projection point A m Will start point A start And point A m The history between them is recorded as one half cycle (iteration).
Step 5): for point A m And end point A end The history between them is that A is firstly m Set as a starting point and then processed according to step 4).
Step 6): if Y occurs in step 4) t The sub-histories with non-monotonically increasing values are processed according to steps 4) and 5) until all half cycles (iterations) are calculated.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a random multiaxial cycle counting method based on path curve integration, which comprises the following steps of calculatingCurve integral value Y of each point in strain space relative to reference starting point t Finding the projection point A with the largest integral value m Will A 0 And A is a m The course between them is repeated, and the untreated course and integral value Y t The course of the turn is recursively processed according to the steps until all iterations are calculated. The counting process does not need to consider material constants, has no dependence on a damage model, solves the problem that the counting method based on equivalent strain loses load valley symbols, can be degenerated to a rain flow counting method in a single-axis state, is easy to realize programs and is convenient for engineering calculation.
Drawings
FIG. 1 is a flow chart of a random multi-axis counting method based on path curve integration.
FIG. 2 is a graph showing the tensile-torsional load time history of a random multiaxial fatigue test to be counted.
FIG. 3 is the view of FIG. 2And projecting the map in space.
FIG. 4 is a graph showing the result of the counting and the Y of the repetition start point calculated for each repetition t -t plot.
Detailed Description
Specific embodiments of the present invention will be described with reference to the accompanying drawings.
The invention is further explained by a random multiaxial fatigue test of tensile-torsional amplitude, wherein the test piece is made of En15R alloy steel, strain loading is controlled, loading waveform is oblique wave, axial strain amplitude is 0.80%, torsional strain amplitude is 1.37%, and 341 data points are collected in the test.
The invention provides a random multiaxial fatigue cycle counting method based on path curve integration, which comprises the following steps:
step 1): recording epsilon as positive strain, gamma as tangential strain, projecting epsilon (t) -t and gamma (t) -t histories under random multiaxial loading of a pull-torsion amplitude toSpace, the projection point corresponding to the time t is marked as A t The start time is 1 and the end time is 341.
Step 2): in order to search the starting point and the ending point of the half cycle, the influence of the loading path length on fatigue damage is considered, inThe integral of the load path length change is defined in the strain space as follows
Wherein the method comprises the steps ofIs the loading path between the projection point at the starting time 1 and the projection point at the time t, +.>Is the vector of the projection point of the starting moment 1 pointing to the projection point of the moment t, +.>Is the vector of the projection point at time t-1 pointing to the projection point at time t, ds is +.>The arc length of the loading path in space is a trace element, sign (x) is a sign function, and the expression is as follows
Where x is any real number.
Step 3): numbering the projection points as A according to the time sequence 1 ,A 1 ,…,A 340 ,A 341 Calculating Y of all time points t Value, find out the corresponding Y t Absolute value abs (Y t ) At maximum time 300, the load is arranged as A 300 ,…A 341 ,A 1 ,…,A 299 Will A 300 Put as A 1 Obtaining a new sequence A 1 ,A 1 ,…,A 340 ,A 341 。
Step 4): for the new sequence, the integrated value Y of each time point is calculated t Find out the corresponding Y t Maximum projection point A m (m=68 when this step is first performed), will a 1 And A m The history between them is one half cycle. Where the value of m is updated with the number of recursions.
Step 5): will A m And A end The history between them is renumbered as A 1 ,…,A end (end=341-68=274 when this step is first performed), according to step 3). Here the end value will be updated with the number of recursions.
Step 6): if the integrated value Y in step 3) t Occurrence of turning point T over time 1 (T when this step is performed for the first time) 1 =41), corresponding to the integrated valueFind and->Equal time point T 2 (T when this step is performed for the first time) 2 =43), will T 1 And T 2 The subload between is renumbered as A 1 ,…,A end (end=3 when this step is first performed) and processing is performed as per 3), 4) until all half cycles are found. Here T 1 、T 2 The end value is updated with the number of recursions.
Claims (2)
1. A random multiaxial cycle counting method based on path curve integration is characterized in that: the method is implemented as follows,
step 1): recording epsilon as positive strain, gamma as tangential strain, projecting epsilon (t) -t and gamma (t) -t histories under random multiaxial loading of a pull-torsion amplitude toSpace, recording the projection point corresponding to the time t as A t The starting time is recorded as start, and the ending time is recorded as end;
step 2): in order to search the starting point and the ending point of the half cycle, the influence of the loading path length on fatigue damage is considered, inThe integral of the load path length change is defined in the strain space as follows
Wherein the method comprises the steps ofIs the loading path between the projection point at start time start and the projection point at time t +.>Is the vector of the projection point of the start moment start to the projection point of the moment t +.>Is the vector of the projection point at time t-1 pointing to the projection point at time t, ds is +.>The arc length of the loading path in space is a trace element, sign (x) is a sign function, and the expression is as follows
Wherein x is any real number;
step 3): calculating the integral value Y of all time points t Find out the corresponding Y t Absolute value abs (Y t ) Maximum projection point A m Will A m The sequence of the strokes before and after the point is changed, and A is as follows m Set as a starting point A start ；
Step 4): calculating Y of all time points of new sequence t Find out the corresponding Y t Maximum projection point A m Will start point A start And point A m The history between the two is recorded as a half cycle;
step 5): for point A m And end point A end The history between them is that A is firstly m Setting the starting point as the starting point, and then processing according to the step 4);
step 6): if Y occurs in step 4) t And (3) processing the sub-histories with non-monotonically increasing values according to the steps 4) and 5) until all half cycles are calculated.
2. A random multiaxial cycle counting method based on path curve integration according to claim 1, wherein: said step 2) definingCurve integral Y of strain space with respect to path t Then by judging Y t And determining the starting point and the ending point of the half cycle.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| JP2013044667A (en) * | 2011-08-25 | 2013-03-04 | Ihi Corp | Multiaxial fatigue life evaluation method |
| CN106600066A (en) * | 2016-12-19 | 2017-04-26 | 南京理工大学 | SCADA data-based wind driven generator gearbox fatigue life estimation method |
| CN109883709A (en) * | 2019-03-08 | 2019-06-14 | 北京工业大学 | A kind of random multiaxis heat engine method of counting based on relative equivalent strain |
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| JP2013044667A (en) * | 2011-08-25 | 2013-03-04 | Ihi Corp | Multiaxial fatigue life evaluation method |
| CN106600066A (en) * | 2016-12-19 | 2017-04-26 | 南京理工大学 | SCADA data-based wind driven generator gearbox fatigue life estimation method |
| CN109883709A (en) * | 2019-03-08 | 2019-06-14 | 北京工业大学 | A kind of random multiaxis heat engine method of counting based on relative equivalent strain |
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| 一个新的多轴疲劳循环计数法;孙斌斌;王英玉;;江苏航空(S1);全文 * |
| 多轴非比例加载下疲劳短裂纹扩展速率的探讨;于强;;机械强度(01);全文 * |
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