CN106844958A - Based on the thin-wall construction thermoacoustic Fatigue Life Prediction method for improving rain flow method - Google Patents

Abstract

The present invention proposes that, based on the thin-wall construction thermoacoustic Fatigue Life Prediction method for improving rain flow method, the method is：Obtain Aero-Space thin-wall construction T under the effect of thermoacoustic load_rStress response time history in response time, obtains the extreme value sequence of thin-wall construction stress response time history；The maximum of thin-wall construction stress response time history and the pairing of minimum are set up using rainflow ranges counting method, all rainflow ranges for obtaining thin-wall construction stress response time history count right；Rainflow ranges according to thin-wall construction stress response time history count the rainflow ranges matrix to setting up thin-wall construction stress response；Rainflow ranges matrix according to thin-wall construction stress response is based on the fatigue life T that Morrow average stress models determine thin-wall construction；Traditional rain flow method be the method overcome in Cyclic Stress counting process, the shortage of data that a little constituted diverging wave causes is left by existing, it is ensured that the correctness of result of calculation.

Description

thin-wall structure thermoacoustic fatigue life estimation method based on improved rain flow counting method

Technical Field

The invention belongs to the technical field of aerospace engineering, and particularly relates to a thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method.

Background

Aerospace thin-walled structures, such as hypersonic aircraft skins, thermal protection systems, ram engine tail nozzles, aero-engine flame tubes, heat-insulating vibration-proof screens and other high-specific-strength, high-specific-stiffness and high-temperature-resistant material structures, can bear complex load conditions under working conditions. The structure surface bears the high-amplitude heat load condition caused by working mechanisms such as pneumatic heating, high-temperature combustion and the like, and the high-amplitude heat load condition is represented by high heat flow density and non-uniform temperature field, so that the complex heat effect is brought to the structure. On the other hand, due to the action mechanism of a turbulent boundary layer on the surface of the structure and the action of unsteady flow, unsteady combustion and the like, the aeroacoustic effect around the structure is caused, so that the surface of the structure acts on a complex sound field, and strong dynamic response is brought to the structure. The thin-wall structure can generate complex large-deflection nonlinear response under the action of high-temperature strong noise load, so that rapid alternating stress appears in the structure, the structure is subjected to fatigue fracture failure, the fatigue life of the structure is seriously influenced, and the problem is called as thermoacoustic fatigue in engineering. Therefore, the analysis and the service life estimation of the thermo-acoustic fatigue failure of the aerospace thin-wall structure become the key of structural strength design, and the research and establishment of an effective estimation method of the random fatigue life has important engineering application value.

The fatigue life estimation problem of the thin-wall structure under the action of the thermoacoustic load is very complex, and the establishment of an effective random fatigue life estimation method based on different failure modes is very difficult. As the aerospace engineering needs to be towed, research institutions at home and abroad have already carried out a plurality of works, and research establishes a plurality of estimation methods, mainly comprising an estimation method based on stress power spectral density, an estimation method based on stress probability density and an estimation method based on local stress strain field intensity. Research shows that the stress power spectral density method is one of the earlier methods, and has certain applicability to the structural dynamics problem which mainly takes fundamental frequency response as the main point; the stress probability density method is an estimation method established by combining a random fatigue theory and engineering experience based on the amplitude domain statistics of structural dynamics stress response as main parameters, and has certain applicability to a simple structure in engineering; the local stress-strain field intensity method is an estimation method established by combining a random fatigue theory based on stress-strain field intensity parameters of the structure at an internal dangerous position under the action of thermoacoustic load, and is mainly suitable for positions with sudden changes of geometric dimensions such as hole opening, reinforcement and the like on the structure in engineering and has certain applicability. In general, no effective engineering estimation method is available for complex thin-wall structural components. Considering that dynamic stress response of a thin-wall structure under the action of thermoacoustic load in engineering practice is represented as a random time history, the dynamic stress response is essentially a stress/strain response parameter random process, and the time sequence influence of loading is fully considered in failure analysis and fatigue life estimation, so that the rain flow counting method has certain superiority. On the basis of the traditional rain flow counting method, the time sequence of load loading and dynamic stress-strain response is fully considered, and the random fatigue theory is combined to establish the improved rain flow counting method, so that the method is suitable for the estimation of the thermo-acoustic fatigue life of the complex thin-wall structure in engineering.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method.

The technical scheme of the invention is as follows:

a thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method comprises the following steps:

step 1: obtaining T of aerospace thin-wall structure under action of thermoacoustic load_rEliminating useless points in the stress response time history to obtain an extreme value sequence of the stress response time history of the thin-wall structure;

step 2: establishing pairing of a maximum value and a minimum value of the stress response time history of the thin-wall structure by adopting a rain flow cycle counting method to obtain all rain flow cycle counting pairs of the stress response time history of the thin-wall structure;

step 2.1: determining each maximum M in a sequence of maxima X (t) of the stress response time history of the thin-walled structure_kAnd each minimum value m in the sequence of minimum values x (t)_kN, wherein k is 1.. n, and the number of n maximum values or the number of n minimum values;

step 2.2: determining a maximum value M_kLeft side search boundary ofAnd right search boundary

Maximum value M_kMaximum on leftSatisfy the requirement ofThen maximum valueThe corresponding time is a left side searching boundary, otherwise, the starting point of the time history is the left side searching boundary;

maximum value M_kMaximum on the rightSatisfy the requirement ofThen maximum valueThe corresponding time is the right side searching boundary, otherwise, the end point T of the time course_rSearch for the border for the right side;

step 2.3: determining a maximum value M_kLeft side search boundaryAnd right search boundaryLeft minimum of intervalAnd right minimum

The maximum value M_kLeft minimum ofAnd right minimumThe determination formula of (a) is as follows:

wherein inf is a small exact bound;

step 2.4: according to the maximum value M_kLeft minimum ofAnd right minimumDetermining the minimum value of its corresponding rain flow cycleObtain a rain flow circulation counting pair

The maximum value M_kMinimum value of rain flow circulationThe determination formula of (a) is as follows:

step 2.5: removing the determined rain flow cycle count pairs from the sequence of extrema of the stress response time history of the thin-walled structureRepeating steps 2.2 to 2.4 until T is determined_rAll rain flow cycle count pairs of the stress response time history of the thin-walled structure over the response time period.

And step 3: establishing a rain flow circulation matrix of the stress response of the thin-wall structure according to the rain flow circulation counting pair of the stress response time history of the thin-wall structure;

and 4, step 4: determining the fatigue life T of the thin-wall structure based on a Morrow average stress model according to a rain flow cyclic matrix of the stress response of the thin-wall structure;

the calculation formula for determining the fatigue life T of the thin-wall structure based on the Morrow average stress model according to the rain flow cyclic matrix of the stress response of the thin-wall structure is as follows:

wherein,rain flow cyclic damage matrix, RFM (sigma) for thin-walled structures_min，σ_max) Rain flow circulation matrix of thin-walled structure, N_f(σ_min，σ_max) Number of cycles, σ, for fatigue failure of thin-walled structures under the current thermoacoustic loading_minIs the minimum value of stress cycle, σ_maxIs the maximum stress cycle.

The invention has the beneficial effects that:

the invention provides a thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method. The method overcomes the problem that the effective cyclic counting accuracy is influenced due to data loss caused by the existence of a divergent wave formed by the remaining points in the stress cyclic counting process of the traditional rain flow counting method, so that the accuracy of a calculation result is ensured; on the basis of the traditional rain flow counting method, the time sequence of load loading and dynamic stress-strain response is fully considered, and the random fatigue theory is combined to establish the improved rain flow counting method, so that the method is suitable for the estimation of the thermo-acoustic fatigue life of the complex thin-wall structure in engineering, and has important engineering application value.

Drawings

FIG. 1 is a flow chart of a thin-wall structure thermo-acoustic fatigue life estimation method based on an improved rain flow counting method according to an embodiment of the present invention;

FIG. 2 is an extreme sequence of stress response time histories of an aerospace thin-wall structure in accordance with an embodiment of the present invention;

FIG. 3 is a schematic diagram of a counting process in a rain flow cycle counting process according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of an exemplary rain flow circulation matrix in accordance with an embodiment of the present invention;

fig. 5 is a schematic diagram of a rain flow cycle matrix for establishing a stress response of a thin-wall structure according to a rain flow cycle count of a stress response time history of the thin-wall structure in an embodiment of the present invention.

Detailed Description

The following detailed description of embodiments of the invention refers to the accompanying drawings.

The invention provides a thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method, which comprises the following steps as shown in figure 1:

step 1: obtaining T of aerospace thin-wall structure under action of thermoacoustic load_rAnd eliminating useless points in the stress response time history to obtain an extreme value sequence of the stress response time history of the thin-wall structure.

In the embodiment, T of the aerospace thin-wall structure obtained based on numerical calculation or experimental test under the action of thermoacoustic load_rStress response time history over a response time period. Eliminating useless points in the stress response time course to obtain an extreme value sequence of the stress response time course of the thin-wall structure as shown in figure 2, wherein a maximum value sequence X (t) and a minimum value sequence x (t) are formed, and the maximum value is M_kIt is shown that,minimum value of m_kN, n is the maximum or minimum number.

Step 2: and establishing the pairing of the maximum value and the minimum value of the stress response time course of the thin-wall structure by adopting a rain flow cycle counting method to obtain all rain flow cycle counting pairs of the stress response time course of the thin-wall structure.

Step 2.1: determining each maximum M in a sequence of maxima X (t) of the stress response time history of the thin-walled structure_kAnd each minimum value m in the sequence of minimum values x (t)_k。

Step 2.2: determining a maximum value M_kLeft side search boundary ofAnd right search boundary

In the present embodiment, the maximum value M_kThere may be a minimum value on both sides, so it is necessary to determine the search intervals on both sides of the maximum value, wherein the left search boundary isThe right search boundary is

Maximum value M_kMaximum on leftSatisfy the requirement ofThen maximum valueThe corresponding time is the left side search boundary, otherwise, the starting point of the time course isLeft search boundary, as shown in equation (1):

maximum value M_kMaximum on the rightSatisfy the requirement ofThen maximum valueThe corresponding time is the right side searching boundary, otherwise, the end point T of the time course_rSearch boundary on the right side, as shown in equation (2):

wherein sup { } is the supremum.

Step 2.3: determining a maximum value M_kLeft side search boundaryAnd right search boundaryLeft minimum of intervalAnd right minimumAs shown in formulas (3) and (4):

wherein inf is a small exact bound.

Step 2.4: according to the maximum value M_kLeft minimum ofAnd right minimumDetermining the minimum value of its corresponding rain flow cycleObtain a rain flow circulation counting pair

In the present embodiment, if the current maximum value M is large_kRight side search boundary ofLess than T_rThen maximum value M is added_kLeft minimum ofAnd right minimumThe maximum value of M is the maximum value_kMinimum value of rain flow circulationIf the current maximum value M_kRight side search boundary ofIs equal to T_rThen maximum value M is added_kLeft minimum ofAs a maximum value M_kMinimum value of rain flow circulationRain flow circulation counting pair for obtaining stress response time history of thin-wall structureMaximum value M_kMinimum value of rain flow circulationIs represented by formula (5):

step 2.5: removing the determined rain flow cycle count pairs from the sequence of extrema of the stress response time history of the thin-walled structureRepeating steps 2.2 to 2.4 until T is determined_rAll rain flow cycle count pairs of the stress response time history of the thin-walled structure over the response time period.

In the present embodiment, as shown in fig. 3, one counting process in the rain flow circulation counting process is a maximum value M₅For example, the maximum value M₅Left side search boundaryIs maximum value M₃Corresponding time, maximum value M₅Right side search boundary ofIs T_rLeft minimum value thereofFor example, as₅Right minimum valueFor example, as₇In the present embodiment, the maximum value M is used₅Right side search boundaryIs T_rSo maximum value M₅Minimum value of rain flow circulationAfter a cycle is counted, two extreme points of the cycle are deleted from the extreme value sequence, and the new extreme value sequence is repeatedly counted until an effective cycle cannot be obtained, T_rAll rain flow cycles of stress response time history over the response time period are shown in table 1.

TABLE 1T_rAll rain flow cycles of stress response time history over response time duration

And step 3: and establishing a rain flow circulation matrix of the stress response of the thin-wall structure according to the rain flow circulation counting pair of the stress response time history of the thin-wall structure.

In this embodiment, the stress cycle characteristics in the engineering can be represented by a rain flow cycle matrix. A typical rain flow circulation matrix is shown in fig. 4. The X axis of the rain flow circulation matrix is a rain flow circulation counting pairMinimum value of (2)Y-axis being maximum value M of cycle_k. Any active cycle corresponds to one of the cyclic matrix mapsAnd (4) point. Due to effective circulation must satisfyTherefore, there is necessarily no circulation point to the right of the direct diagonal of the rain flow circulation matrix.

As can be seen from fig. 4, R ═ σ_min/σ_max＝0、R＝σ_min/σ_max1 and R σ_min/σ_maxThe opposite diagonal left side is divided into three regions by infinity three rays. When maximum value of stress cycle σ_maxAnd minimum value of stress cycle σ_minWhen the same sign is positive, the cycle point is located between two rays, R0 and R1. When maximum value of stress cycle σ_maxAnd minimum value of stress cycle σ_minWhen the same sign is negative, the cycle point is located between the two rays, R ═ 1 and R ∞. When maximum value of stress cycle σ_maxAnd minimum value of stress cycle σ_minWhen of opposite sign, the cycle point is located between the two rays, R ═ 0 and R ∞. Mean value of stress cycleThe zero cycle point is on the R-1 ray, the mean value of the stress cycle σ_aThe larger the cycle point, the further away from R ═ 1; amplitude of stress cycleThe zero cycle point is on the R-1 ray, the stress cycle amplitude σ_mThe larger the distance between the cycle point and R1. The rain flow cycle count from the stress response time history of the thin-walled structure versus the rain flow cycle matrix for establishing the stress response of the thin-walled structure is shown in fig. 5, where 1 and 2 represent 1 rain flow cycle and 2 rain flow cycles, respectively.

And 4, step 4: and determining the fatigue life T of the thin-wall structure based on a Morrow average stress model according to the rain flow cyclic matrix of the stress response of the thin-wall structure.

In this embodiment, the Morrow mean stress model is directed to determining a zero-mean equivalent stress magnitude that is the same as the current non-zero-mean cycle life.

The current non-zero mean cycle is known as (σ)_a，σ_m) And the experimental result shows that the cyclic number N of the fatigue failure of the thin-wall structure under the action of the current thermoacoustic load_f(σ_min，σ_max) Is a reaction of N_fThe equivalent zero mean stress amplitude sigma which is the same as the current non-zero mean cyclic fatigue life can be obtained by being substituted into the Basquin formula_arAs shown in formula (6):

σ_ar＝σ′_f(2N_f)^b(6)

wherein, σ'_fB is a constant, which is the fatigue strength coefficient.

By stress cycle amplitude σ_mOr dimensionless quantity σ_m/σ_arIs the horizontal axis, in dimensionless quantity σ_a/σ_arFor the vertical axis, different mean stress models can be obtained by fitting the data points using different equations.

Using fatigue strength σ_bReplacing the fatigue strength coefficient to obtain a Morrow average stress model shown in the formula (7):

when the accumulated damage D reaches a certain value, the structure is subjected to fatigue damage, under the action of cyclic load, the fatigue damage is linearly accumulated, and the stresses are mutually independent and complementarily related to obtain a Miner linear fatigue accumulated damage theoretical formula, as shown in formula (8):

wherein σ_aiIs the ith stress amplitude, N_fFor corresponding fatigue life, n_iThe number of stress cycles for that magnitude.

Equation (8) applies to structures with deterministic responses, and when a structure exhibits a random response, equation (8) is rewritten to the mathematically expected form, as shown in equation (9):

wherein, E [ D ]]For the expectation of injury, E [ P ]]Is the peak expectation per unit time, T_rIs the response signal duration, p (σ)_min，σ_max) For a joint probability density function of the stress cycle minimum and the stress cycle maximum, equation (9) can be written as shown in equation (10) when using the stress cycle mean and magnitude representation:

N_f(σ_min，σ_max) Is (sigma)_a，σ_m) Is determined by the selected Morrow mean stress model. When the rain flow cycle counting method is used, p (σ) in the formula (9) and the formula (10)_a，σ_m) Can be estimated from the rain flow circulant matrix, as shown in equation (11):

wherein N is_RFThe RFM is a rain circulation matrix. RFM (sigma)_a，σ_m) Is a rain flow circulation matrix represented by a stress cycle mean and a stress cycle amplitude, N_RFFatigue life at various stress levels in the rain flow cycle matrix.

For response signals T of finite duration_rPeak expectation E [ P ]]≈N_RF/T_rInjury expectation E [ D]Can be written as shown in equation (12):

wherein RFD (σ)_min，σ_max) Is a rain flow cyclic damage matrix.

When the damage expectation E [ D ] is 1, the fatigue life T of the thin-walled structure can be obtained as shown in equation (13):

Claims (2)

1. A thin-wall structure thermoacoustic fatigue life estimation method based on an improved rain flow counting method is characterized by comprising the following steps:

step 1: obtaining T of aerospace thin-wall structure under action of thermoacoustic load_rEliminating useless points in the stress response time history to obtain an extreme value sequence of the stress response time history of the thin-wall structure;

step 2: establishing pairing of a maximum value and a minimum value of the stress response time history of the thin-wall structure by adopting a rain flow cycle counting method to obtain all rain flow cycle counting pairs of the stress response time history of the thin-wall structure;

and step 3: establishing a rain flow circulation matrix of the stress response of the thin-wall structure according to the rain flow circulation counting pair of the stress response time history of the thin-wall structure;

and 4, step 4: determining the fatigue life T of the thin-wall structure based on a Morrow average stress model according to a rain flow cyclic matrix of the stress response of the thin-wall structure;

the calculation formula for determining the fatigue life T of the thin-wall structure based on the Morrow average stress model according to the rain flow cyclic matrix of the stress response of the thin-wall structure is as follows:

$T=T_r/\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}RFD({\mathrm{\σ}}_{min},{\mathrm{\σ}}_{max});$

wherein,rain flow cyclic damage matrix, RFM (sigma) for thin-walled structures_min,σ_max) Rain flow circulation matrix of thin-walled structure, N_f(σ_min,σ_max) Number of cycles, σ, for fatigue failure of thin-walled structures under the current thermoacoustic loading_minIs the minimum value of stress cycle, σ_maxIs stressThe maximum value of the cycle.

2. The method for estimating the thermo-acoustic fatigue life of the thin-wall structure based on the improved rain flow counting method according to claim 1, wherein the step 2 comprises the following steps:

step 2.1: determining each maximum M in a sequence of maxima X (t) of the stress response time history of the thin-walled structure_kAnd each minimum value m in the sequence of minimum values x (t)_kN, wherein k is 1.. n, and the number of n maximum values or the number of n minimum values;

step 2.2 determining the maximum M_kLeft side search boundary ofAnd right search boundary

Maximum value M_kMaximum on leftSatisfy the requirement ofThen maximum valueThe corresponding time is a left side searching boundary, otherwise, the starting point of the time history is the left side searching boundary;

maximum value M_kMaximum on the rightSatisfy the requirement ofThen maximum valueThe corresponding time is the right side searching boundary, otherwise, the end point T of the time course_rSearch for the border for the right side;

step 2.3: determining a maximum value M_kLeft side search boundaryAnd right search boundaryLeft minimum of intervalAnd right minimum

The maximum value M_kLeft minimum ofAnd right minimumThe determination formula of (a) is as follows:

$m_k^{-}=inf\{x\left(t\right):t_k^{-}<t<t_k\};$

$m_k^{+}=inf\{x\left(t\right):t_k<t<t_k^{+}\};$

wherein inf is a small exact bound;

step 2.4; according to the maximum value M_kLeft minimum ofAnd right minimumDetermining the minimum value of its corresponding rain flow cycleObtain a rain flow circulation counting pair

The maximum value M_kMinimum value of rain flow circulationThe determination formula of (2) is as follows;

$m_k^{RFC}=\left\{\begin{array}{cc}max(m_k^{-},m_k^{+}),& if{t}_k^{+}<T_r\\ m_k^{-},& if{t}_k^{+}=T_r\end{array}\right.;$

step 2.5: removing the determined rain flow cycle count pairs from the sequence of extrema of the stress response time history of the thin-walled structureRepeating steps 2.2 to 2.4 until T is determined_rAll rain flow cycle count pairs of the stress response time history of the thin-walled structure over the response time period.