CN111159871A

CN111159871A - Random multi-axis cycle counting method based on path curve integration

Info

Publication number: CN111159871A
Application number: CN201911338574.9A
Authority: CN
Inventors: 尚德广; 尹翔; 夏禹; 王松光; 王海潮; 常东帅; 陈烽; 张辉; 张佳林
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2019-12-23
Filing date: 2019-12-23
Publication date: 2020-05-15
Anticipated expiration: 2039-12-23
Also published as: CN111159871B

Abstract

The invention discloses a multi-axis cycle counting method based on path curve integration, which comprises the following steps of

Defining a curve integral Y in the strain space relative to the starting point_tFirst, find the corresponding maximum Y in the original load block_tPoints of values, reordering the load with the point as a boundary point, and then calculating Y for each point_tValue, starting point and Y_tThe history between the points with the largest value is a repetition, for the history and Y not counted_tThe process of the value breakover performs a similar step, using a recursive algorithm to calculate all half cycles. The method does not depend on a fatigue damage model, and overcomes the problem that an equivalent strain counting method omits a valley symbolThe method can be degraded to single-axis rain flow counting, the counting process does not involve material constants, the algorithm is simple, computer programming is easy, and the engineering practicability is high.

Description

Random multi-axis cycle counting method based on path curve integration

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

Many machines bear complex load states in service, such as aerospace vehicles, high-speed trains and large-scale carrying machines, critical part dangerous points of parts of the machines are in a multi-axis stress state, stress components generally randomly change along with time and have large amplitude, fatigue cracks are easy to generate and expand, service life is rapidly reduced, and therefore the significance of accurately predicting the amplitude-variable random multi-axis fatigue life is great.

Over the past decades, the uniaxial fatigue strength theory has been developed to be perfect, but the uniaxial fatigue strength theory needs to be supplemented and optimized. Predicting random multiaxial fatigue life may be simply divided into three steps: 1) by means of counting method, the random amplitude load course is decomposed into several constant amplitude load courses, i.e. several half cycles. 2) And calculating each repeated damage parameter by using a proper damage model so as to obtain the damage. 3) Fatigue life is estimated by accumulating each repeated damage as a total damage by means of a damage accumulation criterion. The counting method is a pretreatment process of variable amplitude random multi-axis life prediction, and the reasonability of the counting method directly influences the fatigue life evaluation precision. The existing counting method has many disadvantages, such as the multi-axis rain flow counting method may lose the peak-valley value of the auxiliary counting channel, the rain flow counting method based on equivalent strain may miss the valley value symbol, and the counting method relying on the damage model has no universality. Therefore, it is of great significance to provide a counting method which does not depend on the damage model and comprehensively considers component channel information.

Disclosure of Invention

Aiming at the development of variable amplitude multi-axial fatigue life prediction, the invention considers the influence of a loading path on the fatigue life, overcomes the defects of the dependence of a counting method on a fatigue damage model and the coincidence of missing counting channel valleys, and provides a random multi-axial 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): marking epsilon as positive strain and gamma as shear strain, projecting epsilon (t) -t and gamma (t) -t history under random multi-axis loading of pulling-twisting amplitude to

In space, the projection point corresponding to the time t is A_tThe start time is denoted as start, and the end time is denoted as end.

Step 2): to search for the start and end points of a half cycle, the effect of the loading path length on fatigue damage is taken into account

Defining an integral in strain space reflecting the change in the length of the loading path as follows

Wherein

Is the loading path between the proxel at starting time 1 and the proxel at time t,

is the vector of the projection point of the start time start pointing to the projection point of the time 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 infinitesimal of the loading path in space, sign (x) is a symbolic function, and the expression is as follows

Where x is any real number.

Step 3): calculating integral value Y of all points_tFind out the corresponding Y_tAbsolute value abs (Y) of_t) Maximum projection point A_mA is_mThe sequences of the courses before and after the point are exchanged, A is_mIs set as a starting point A_start。

Step 4): calculating Y of time points of new sequence_tFind out the corresponding Y_tMaximum projection point A_mStarting point A_startAnd point A_mThe history in between is recorded as a half cycle (iteration).

Step 5): for point A_mAnd an end point A_endThe course between A and A_mSetting a starting point, and then processing according to the step 4).

Step 6): if Y appears in step 4)_tThe sub-histories whose values are not monotonically increasing are processed according to steps 4) and 5) until all half-cycles (iterations) are counted.

Compared with the prior art, the invention has the following beneficial effects:

the invention provides a random multi-axis cycle counting method based on path curve integration, which is implemented by calculating

Curve integral value Y of each point in strain space relative to reference starting point_tFinding the projection point A with the maximum integral value_mA is₀And A_mThe history between is an iteration and is compared with the unprocessed historyRange and integral value Y_tThe process of the turning is recurred according to the steps until all the iterations are counted. The material constant does not need to be considered in the counting process, the damage model has no dependence, the problem that the equivalent strain-based counting method loses a load valley symbol is solved, the equivalent strain-based counting method can be degraded to a rain flow counting method in a single-axis state, the program is easy to realize, and the engineering calculation is convenient.

Drawings

Fig. 1 is a flow chart of a random multi-axis counting method based on path curve integration.

Fig. 2 is a graph of the pull-torsion load time history for a random multi-axial fatigue test to be counted.

FIG. 3 is a view of FIG. 2

The map is projected in space.

FIG. 4 shows the counting result and Y of the relative counting of the repetition start point for each repetition_t-t-graph.

Detailed Description

The embodiments of the present invention will be described with reference to the accompanying drawings.

The invention is further explained by a pull-torsion amplitude-change random multi-axial fatigue test, the test piece is made of En15R alloy steel, controlled strain loading is adopted, the loading waveform is oblique wave, the axial strain amplitude is 0.80%, the torsion strain amplitude is 1.37%, and 341 data points are acquired in the test.

In space, the projection point corresponding to time t is denoted as A_tThe start time is set to 1, and the end time is set to 341.

Step 2): to search for the start and end points of a half cycle, consider the effect of the load path length on fatigue damageSound at

Wherein

is the vector of the proxel at starting instant 1 pointing to the proxel at instant t,

Where x is any real number.

Step 3): numbering the projection points A according to the time sequence₁,A₁,…,A₃₄₀,A₃₄₁Calculating Y of all points_tValue, find the corresponding Y_tAbsolute value abs (Y) of_t) At the maximum time 300, the load is arranged as A₃₀₀,…A₃₄₁,A₁,…,A₂₉₉A is₃₀₀Is set to be A₁To obtain a new sequence A₁,A₁,…,A₃₄₀,A₃₄₁。

Step 4): for the new sequence, the integral value Y of each time point is calculated_tFind out the corresponding Y_tMaximum projection point A_m(m is 68 when this step is performed for the first time), A is added₁And A_mThe history in between is one and a half cycles. Where the value of m is updated with the number of recursions.

Step 5): a is to be_mAnd A_endRenumbering the history between A₁,…,A_end(341-68-274 at the first execution of this step), as per step 3). The value of end here is updated with the number of recursions.

Step 6): if the integral value Y in step 3) is_tThe turning point T appears over time₁(first execution of this step T₁41), corresponding to the integral value

Find and

equal time points T₂(first execution of this step T₂43), mixing T with₁And T₂With a sub-payload renumbering in between₁,…,A_end(end is 3 when the step is executed for the first time) and processing is carried out according to 3) and 4) until all half cycles are found. Here T₁、T₂The value of end is updated with the number of recursions.

Claims

1. A random multi-axis cycle counting method based on path curve integration is characterized in that: the implementation steps of the method are as follows,

In space, the projection point corresponding to the time t is A_tThe starting time is marked as start, and the ending time is marked as end;

step 2): to search for the start and end points of a half cycle, the loading path length is considered for fatigue lossThe influence of injury in

Wherein

Wherein x is any real number;

step 3): calculating integral value Y of all points_tFind out the corresponding Y_tAbsolute value abs (Y) of_t) Maximum projection point A_mA is_mThe sequences of the courses before and after the point are exchanged, A is_mIs set as a starting point A_start；

Step 4): calculating Y of time points of new sequence_tFind out the corresponding Y_tMaximum projection point A_mStarting point A_startAnd point A_mBetweenThe history of (a) is recorded as a half cycle;

step 5): for point A_mAnd an end point A_endThe course between A and A_mSetting a starting point, and then processing according to the step 4);

step 6): if Y appears in step 4)_tThe sub-histories whose values are not monotonically increasing are processed according to steps 4) and 5) until all half cycles are counted.

2. The random multi-axis cycle counting method based on path curve integration according to claim 1, characterized in that: said step 2) defines

Integral Y of the curve of strain space with respect to road stiffness_tThen by judging Y_tThe starting point and the ending point of the half cycle are judged according to the turning point.