CN109374450B - Method for determining usable limit of blade leaf basin leaf back crack type hard object damage considering high and low cycle fatigue - Google Patents
Method for determining usable limit of blade leaf basin leaf back crack type hard object damage considering high and low cycle fatigue Download PDFInfo
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Abstract
The invention discloses a method for determining the usable limit of damage to a crack type hard object on the back of a blade basin blade in consideration of high and low cycle fatigue, which comprises the steps of firstly extracting a high cycle fatigue load and a low cycle fatigue load from a high/low cycle composite load borne by the blade, respectively establishing a series of equivalent curves with the stress ratio related to the crack/crack type hard object damage crack non-expansion under the high cycle fatigue load and the low cycle fatigue load, then determining the static stress and the dynamic stress at each point of the leaf basin blade back by a finite element numerical analysis method, and finally determining the crack size corresponding to the equivalent curves by comparing the positions of the static stress and the dynamic stress in the equivalent curves with the crack non-expansion, namely the usable limit of the damage to the crack/crack type hard object at the point of the leaf basin blade back. The invention not only provides a simple and effective method for determining the usable limit of the hard object damage, but also forms a normalized usable limit making process aiming at the tearing/cracking type hard object damage of the blade back of the blade basin.
Description
Technical Field
The invention relates to a method for determining the usable limit of blade basin blade back crack type hard object damage considering high and low cycle fatigue, and belongs to the field of design and maintenance of hard object damage tolerance of aeroengine blades.
Background
Impact damage caused by the collision of hard objects such as metal, debris, gravel, stones and the like with the air flow entering the engine air flow passage and the blades rotating at high speed is one of the important reasons for aggravating fatigue failure of the blades. Although foreign object damage prevention measures such as aircraft runway foreign object cleaning, ground crew service tool inspection and control have been proposed, hard object damage is always inevitable.
For the problem of inevitable hard object damage, although the engine designer provides the blade with a certain hard object damage tolerance capability, it is also necessary to provide a service manual with the hard object damaged blade at the later stage of engine development, and provide necessary suggestions for the user when using and maintaining the engine blade, for example, how to judge whether the hard object damaged blade is usable (repair-free) after the hard object damage occurs to the blade. At present, the main size for judging the damage severity of hard objects is damage depth, the allowed maximum damage depth is often adopted as the available limit of the blade after the hard objects are damaged in an engine maintenance manual, and the reasonable available limit is determined so as to reduce the times of detaching, repairing and replacing the blade after the blade is damaged by foreign objects to a certain degree on the premise of ensuring safety and performance, and improve the economy and the readiness integrity.
At present, engine companies do not make a standardized program of blade usable limits after hard object damage, the usable limits of engine blades newly designed in the past are usually based on the use and maintenance experience of old engines, however, with the continuous development of blade design technologies, a novel blade structure (such as a blisk, a hollow blade and the like) enables the empirical extrapolation mode to face a huge challenge.
The invention provides a method for determining the usable limit of crack type hard object damage of a blade basin leaf back considering high and low cycle fatigue, which aims to provide a reasonable and standard usable limit making flow for the hard object damage.
Disclosure of Invention
The invention aims to provide a method for determining the usable limit of damage to a leaf and a basin leaf back crack type hard object in consideration of high and low cycle fatigue, so as to solve the problem that a reasonable and normative usable limit formulation flow is not available for the damage to the tear/crack type hard object at present.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for determining the usable limit of damage of a crack type hard object on the back of a blade basin blade considering high and low cycle fatigue comprises the following steps:
(1) extracting high cycle fatigue load and low cycle fatigue load which may occur from the high/low cycle composite fatigue load borne on each point of a blade basin and a blade back of the blade;
(2) establishing a crack propagation threshold value model related to the stress ratio according to the crack propagation threshold value data of the blade material under different stress ratios;
(3) setting the tearing/cracking type damage in the leaf basin and the leaf back of the leaf as an I-type semielliptical surface crack, wherein the semiaxis length a of the depth of the elliptical crack is the maximum depth d of the tearing/cracking type damage, and the semiaxis length b of the surface of the elliptical crack is 1.5 times of the semielliptical surface crack, and establishing a stress intensity factor calculation method of the semielliptical surface crack;
(4) respectively establishing crack non-expansion models of high cycle fatigue load and low cycle fatigue load under different stress ratio conditions, and drawing crack non-expansion equivalent curve graphs under different crack depths a;
(5) obtaining static stress and dynamic stress of each point of a blade basin blade back through a finite element numerical analysis method;
(6) and determining the crack size a corresponding to the equivalent curve by comparing the positions of the static stress and the dynamic stress in the equivalent curve of crack non-propagation, namely determining the available limit of the crack/tear type hard object damage at the point of the blade back of the blade.
In the step (1), the high/low cycle composite load of the blade refers to interaction of low-frequency centrifugal force cyclic load and high-frequency vibration load of the blade when the engine normally works, the low-frequency centrifugal force cyclic load in the blade is recorded as low-cycle fatigue load, the medium-high frequency vibration load in the blade is recorded as high-cycle fatigue load, and the high-cycle fatigue load and low-cycle fatigue load forms which may appear at each point of a blade basin and a blade back of the blade are determined through load spectrum analysis.
In the step (2), the crack propagation threshold value is expressed by a stress intensity factor range delta K, wherein when the stress ratio R is>When 0,. DELTA.K ═ Kmax-KminAnd K isminNot equal to 0, when the stress ratio R is less than or equal to 0, delta K is equal to Kmax-KminAnd K ismin0; crack propagation threshold Δ KthExpressed as a function of the stress ratio R.
In the step (3), the blade with the I-shaped hemielliptic surface crack is regarded as a hemielliptic crack body model with limited thickness, infinite width and infinite length, and the load borne on the crack surface adopts a power function distribution stress expression, namely:
wherein, sigma (x) is stress distribution on a crack surface, a is the crack length, x is a coordinate along the crack propagation direction, the origin of the coordinate is the intersection point of the unilateral crack and the leading edge point, and sigma (x) is the stress distribution on the crack surfaceiIs a polynomial coefficient, i is a polynomial index, and n is less than or equal to 7; the stress distribution of the crack surface born by the large plate with the I-shaped semielliptical surface cracks equivalent to the tearing/cracking type blade is uniform distribution, namely n is 0, and the stress intensity factor calculation method adopts a universal weight function method;
the calculation expression of the stress intensity factor when the crack surface of the semi-elliptic surface is subjected to the stress distributed by the power function is as follows:
wherein m (x, a) is a weight function of the crack body, and the maximum point of the stress intensity factor for the semielliptical surface crack is usually the deepest point A of the crack front edge or the surface point B of the crack front edge;
the general weight function of the deepest point A of the crack front edge of the semiellipse surface is as follows:
the general weight function of the point B on the surface of the semiellipse surface crack front edge is as follows:
when σ (x) is σ0And when the stress intensity factors of the point A and the point B are implicitly expressed as follows:
wherein K is the stress intensity factor, M1A、M2A、M3A、M1B、M2B、M3BIs a coefficient of a general weight function, pi is a circumferential ratio, sigma0The stress is uniformly distributed on the crack surface.
In the step (4), the criterion of crack non-propagation of high cycle fatigue load under the condition of different stress ratios is delta KHCF＝ΔKth(RHCF) The crack non-propagation equivalent curve model is as follows:
when stress ratio is-1<R<At the time of 0, the number of the first,
when the stress ratio is 0 to R<When the pressure of the mixture is 1, the pressure is lower,
the criterion of crack non-propagation under low cycle fatigue load is delta KLCF＝ΔKth(RLCF) Stress ratio R ofLCFThe crack propagation-free iso-curve model is then:
wherein, Δ KHCFIs the stress intensity factor range, Δ K, under HCF load cyclesLCFIs the stress intensity factor range under low cycle fatigue load; rHCFStress ratio, R, for HCF loadingLCFStress ratio for LCF loading; fnIs a geometric correction coefficient; sigmadynFor dynamic stress, σstaFor static stress, Δ σth(RHCF) And Δ σth(RLCF) Is threshold stress;
the abscissa of the crack non-propagation equivalent curve graph is static stress and the ordinate is dynamic stress.
In the step (5), the static stress and the dynamic stress of each point of the blade basin and the blade back of the blade are expressed by the effective stress of a unit Von-mises and the like, and the unit size representing the blade back point of the blade basin is 1 mm.
And (6) taking the minimum value of the crack size determined by the crack non-propagation equivalent curve corresponding to the high-cycle fatigue load and the crack size determined by the low-cycle fatigue load as the available limit of the tearing/cracking type hard object damage at the point of the blade and the blade back.
Has the advantages that: the invention provides a reasonable and standard available limit determination method and a reasonable and standard available limit determination process for the tearing/cracking type hard object damage to the blade and the basin blade in the using process of the blade of the aero-engine. The invention considers the typical failure mode of the blade after being damaged by hard objects: the method is characterized in that high cycle fatigue and low cycle fatigue are achieved, a simple and efficient crack non-propagation principle is adopted to establish a crack non-propagation equivalent curve graph of the blade, and a standard step for establishing the usable limit of the tearing/crack type damage in the blade basin back of the blade is provided.
Drawings
FIG. 1 is a schematic diagram of high/low cycle composite fatigue;
FIG. 2 is a schematic of low cycle fatigue and high cycle fatigue;
3 a-3 e are schematic views of HCF and LCF loading patterns that may occur at various points on the bucket back of the bucket blade;
FIG. 4 is crack propagation threshold data and model for a titanium alloy TC4 commonly used for blades;
FIG. 5 is an equivalent simplification of a leaf blade bilge tear/crack type damage to an I-type semi-elliptical surface crack;
FIG. 6 is a schematic view of a crack propagation-free iso-curve under HCF load;
FIG. 7 is a crack non-propagation iso-curve under HCF load of a TC4 titanium alloy material;
FIG. 8 is a schematic view of a crack propagation-free iso-curve under LCF load;
FIG. 9 is a crack non-propagation iso-curve under HCF load of the TC4 titanium alloy material;
FIG. 10 is an aircraft engine blade and meshing formation;
FIG. 11 is a steady state stress distribution as indicated by the Von-mises stress;
FIG. 12 is a first order modal vibrational stress as represented by Von-mises stress;
FIG. 13 is a second order modal vibrational stress as represented by Von-mises stress;
FIG. 14 is a schematic illustration of the determination of the usable limits of the bucket back of a bucket blade by a crack propagation free contour plot;
FIG. 15 is a graph of the usable limit distribution of blade bucket backface tear/crack type hard object damage under first order modal vibration;
FIG. 16 is a graph of the usable limit distribution of blade bucket back tear/crack type damage under second order modal vibration.
Detailed Description
The invention is further explained below with reference to the drawings and the examples.
Examples
A method for determining the usable limit of damage of a crack type hard object on the back of a blade basin blade considering high and low cycle fatigue comprises the following steps:
(1) the high and low cycle fatigue loads that may occur are extracted from the high/low cycle composite fatigue loads experienced at each point of the bucket and the back of the blade. Among them, the High cycle fatigue load, i.e., the High cycle fatigue load, is abbreviated as HCF, and the low cycle fatigue load, i.e., the low cycle fatigue load, is abbreviated as LCF.
The high/low cycle composite load of the blade refers to the interaction of the low frequency centrifugal force cyclic load and the high frequency vibration load of the blade when the engine works normally, as shown in FIG. 1. According to the invention, the centrifugal force cyclic load in the blade is recorded as low cyclic fatigue load, namely low cycle fatigue load, and the high-frequency vibration load exceeding 1KHz in the blade is recorded as high cyclic fatigue load, namely high cycle fatigue load, as shown in figure 2. The HCF load and the LCF load which possibly occur at each point of the blade back of the blade are determined by the load spectrum analysis and are shown in the figure 3.
(2) And establishing a crack propagation threshold value model related to the stress ratio according to the crack propagation threshold value data of the blade material under different stress ratios. The crack propagation threshold value of the blade material is expressed by a stress intensity factor range delta K, wherein the stress ratio R is>When 0,. DELTA.K ═ Kmax-KminAnd K isminNot equal to 0, when the stress ratio R is less than or equal to 0, delta K is equal to Kmax-KminAnd K ismin0. Crack propagation threshold Δ KthExpressed as a function of the stress ratio R. In the embodiment, the titanium alloy material TC4 commonly used for the engine fan/compressor blade is taken as an example, and the crack propagation model value data and the curve thereof are shown in figure 4. The crack propagation threshold model for the TC4 titanium alloy is:
when 0 ≦ R < 1:
when-1. ltoreq. R < 0:
wherein,
the range of effective stress intensity factors when the stress ratio R is 0,
A0＝0.00729、A1＝1.0108、A2＝-0.3959、A3-0.10356 is a coefficient of the coefficient,
the stress intensity factor range when the stress ratio R is 0,
(3) assuming the tearing/cracking type damage in the blade basin blade back as an I-shaped semielliptical surface crack, wherein the semiaxis length a of the depth of the elliptical crack is the maximum depth d of the tearing/cracking type damage, and the semiaxis length b of the surface of the elliptical crack is 1.5 times of a, and establishing a stress intensity factor calculation method of the semielliptical surface crack; the blade with the I-type semielliptical surface crack is regarded as a semielliptical crack body model with finite thickness, infinite width and infinite length as shown in FIG. 5, and the load borne on the crack surface adopts a power function distribution stress expression, namely:
wherein σ (x) is a stress distribution on a crack surfaceWhere a is the crack length, x is the coordinate along the crack propagation direction, with the origin of the coordinate being the intersection of the single-sided crack with the leading edge point, σiIs a polynomial coefficient, i is a polynomial index, and n is less than or equal to 7. The stress distribution of the crack surface born by the large plate with the I-shaped semielliptical surface cracks equivalent to the tearing/cracking type blade is uniform distribution, namely n is 0, and the stress intensity factor calculation method adopts a universal weight function method.
The calculation expression of the stress intensity factor when the crack surface of the semi-elliptic surface is subjected to the stress distributed by the power function is as follows:
wherein m (x, a) is a weight function of the crack body, and the maximum point of the stress intensity factor for the semielliptical surface crack is usually the deepest point A of the crack front edge or the surface point B of the crack front edge;
the general weight function of the deepest point A of the crack front edge of the semiellipse surface is as follows:
the general weight function of the point B on the surface of the semiellipse surface crack front edge is as follows:
when σ (x) is σ0And when the stress intensity factors of the point A and the point B are implicitly expressed as follows:
wherein K is the stress intensity factor, M1A、M2A、M3A、M1B、M2B、M3BIs a coefficient of a general weight function, pi is a circumferential ratio, sigma0The stress is uniformly distributed on the crack surface.
(4) Respectively establishing crack non-expansion models of high cycle fatigue load and low cycle fatigue load under different stress ratio conditions, and drawing a crack non-expansion equivalent curve chart under different crack lengths. The criterion of crack non-propagation of high cycle fatigue load under different stress ratios is delta KHCF＝ΔKth(RHCF) The crack non-propagation equivalent curve model is as follows:
when stress ratio is-1<R<At the time of 0, the number of the first,
when the stress ratio is 0 to R<When the pressure of the mixture is 1, the pressure is lower,
when the stress ratio R is large, a range of stress intensity factors may occur in which cracks do not propagate, but the maximum stress intensity factor KmaxThe fracture toughness of the material is reached causing the transient crack to propagate to fracture. The crack propagation-free contour should then be supplemented by the boundary condition, i.e. Kmax＝KIC. Thus, a graphical representation of the crack propagation free iso-curve under HCF loading is shown in FIG. 6. The contour plot of crack propagation under HCF load for the TC4 titanium alloy material is shown in FIG. 7.
The criterion of crack non-propagation under low cycle fatigue load is delta KLCF＝ΔKth(RLCF) Stress ratio R ofLCFThe crack propagation-free iso-curve model is then:
wherein, Δ KHCFIs the stress intensity factor range, Δ K, under HCF load cyclesLCFIs the stress intensity factor range under low cycle fatigue load; rHCFStress ratio, R, for HCF loadingLCFStress ratio for LCF loading; fnAs a geometric correction factor；σdynFor dynamic stress, σstaFor static stress, Δ σth(RHCF) And Δ σth(RLCF) Is the threshold stress. The schematic diagram of the crack non-propagation isocurve under the LCF load is shown in FIG. 8, and the crack non-propagation isocurve under the LCF load of the TC4 titanium alloy material is shown in FIG. 9.
The abscissa of the crack non-propagation equivalent curve graph is static stress and the ordinate is dynamic stress.
(5) And obtaining the static stress and the dynamic stress of each point of the blade back of the blade basin through a finite element numerical analysis method. The static stress and the dynamic stress of each point of the blade basin back are expressed by the equivalent stress of a unit Von-mises, and the unit size representing the blade basin back point is 1 mm. In this embodiment, a certain type of aircraft engine blade and its meshing pattern are shown in fig. 10. The static stress of the engine blade is determined by the working rotating speed in the actual working process, so that the static stress can be quickly and accurately obtained by a finite element analysis method. However, the calculation process of the actual vibration stress in the blade is not only very complicated but also difficult to ensure the calculation accuracy. Therefore, in order to illustrate the calculation flow of the method of the present invention, the vibration load of the blade in this embodiment is represented by Von-mises effective stress when the blade generates 1 st order modal vibration and 2 nd order modal vibration respectively and the blade tip vibration displacement is 5 mm. The static stress distribution of the blade in this embodiment is shown in fig. 11. The blade first order modal vibration stress distribution expressed by the Von-mises stress is shown in FIG. 12, and the blade second order modal stress distribution expressed by the Von-mises stress is shown in FIG. 13.
(6) And determining the crack size corresponding to the equivalence curve by comparing the positions of the static stress and the dynamic stress in the crack non-propagation equivalence curve, and taking the minimum value of the crack size determined by the crack non-propagation equivalence curve corresponding to the high-cycle fatigue load and the crack size determined by the low-cycle fatigue load as the available limit of the crack/tear type hard object damage at the point of the blade basin blade back. Wherein, the usable limit process of the blade and the bucket back of the blade is determined by a crack non-propagation iso-curve chart under the HCF load as shown in FIG. 14.
The usable limit distribution of the blade back tearing/crack type hard object damage under the first-order modal vibration in the embodiment is shown in fig. 15, and the usable limit distribution of the blade back tearing/crack type hard object damage under the second-order modal vibration is shown in fig. 16.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto, and those skilled in the art can make various modifications and alterations without departing from the spirit and scope of the present invention.
Claims (5)
1. A method for determining the usable limit of damage of a crack type hard object on the back of a blade basin blade considering high and low cycle fatigue is characterized by comprising the following steps: the method comprises the following steps:
(1) extracting high cycle fatigue load and low cycle fatigue load which may occur from the high/low cycle composite fatigue load borne on each point of a blade basin and a blade back of the blade;
(2) establishing a crack propagation threshold value model related to the stress ratio according to the crack propagation threshold value data of the blade material under different stress ratios;
(3) setting the tearing/cracking type damage in the leaf basin and the leaf back of the leaf as an I-type semielliptical surface crack, wherein the semiaxis length a of the depth of the elliptical crack is the maximum depth d of the tearing/cracking type damage, and the semiaxis length b of the surface of the elliptical crack is 1.5 times of the semielliptical surface crack, and establishing a stress intensity factor calculation method of the semielliptical surface crack;
the blade with the I-shaped semielliptical surface crack is regarded as a semielliptical crack body model with limited thickness, infinite width and infinite length, and the load borne on the crack surface adopts a power function distribution stress expression, namely:
wherein, sigma (x) is stress distribution on a crack surface, a is the crack length, x is a coordinate along the crack propagation direction, the origin of the coordinate is the intersection point of the unilateral crack and the leading edge point, and sigma (x) is the stress distribution on the crack surfaceiIs a polynomial coefficient, i is a polynomial index, and n is less than or equal to 7;the stress distribution of the crack surface born by the large plate with the I-shaped semielliptical surface cracks equivalent to the tearing/cracking type blade is uniform distribution, namely n is 0, and the stress intensity factor calculation method adopts a universal weight function method;
the calculation expression of the stress intensity factor when the crack surface of the semi-elliptic surface is subjected to the stress distributed by the power function is as follows:
wherein m (x, a) is a weight function of the crack body, and the maximum point of the stress intensity factor for the semielliptical surface crack is usually the deepest point A of the crack front edge or the surface point B of the crack front edge;
the general weight function of the deepest point A of the crack front edge of the semiellipse surface is as follows:
the general weight function of the point B on the surface of the semiellipse surface crack front edge is as follows:
when σ (x) is σ0And when the stress intensity factors of the point A and the point B are implicitly expressed as follows:
wherein K is the stress intensity factor, M1A、M2A、M3A、M1B、M2B、M3BIs a coefficient of a general weight function, pi is a circumferential ratio, sigma0The stress is uniformly distributed on the crack surface;
(4) respectively establishing a crack non-expansion equivalent curve model of a high cycle fatigue load and a low cycle fatigue load under different stress ratio conditions, and drawing a crack non-expansion equivalent curve graph under different crack depths a;
wherein the criterion of crack non-propagation of high cycle fatigue load under different stress ratio conditions is delta KHCF＝ΔKth(RHCF) The crack non-propagation equivalent curve model is as follows:
when stress ratio is-1<R<At the time of 0, the number of the first,
when the stress ratio is 0 to R<When the pressure of the mixture is 1, the pressure is lower,
the criterion of crack non-propagation under low cycle fatigue load is delta KLCF＝ΔKth(RLCF) Stress ratio R ofLCFThe crack propagation-free iso-curve model is then:
wherein, Δ KHCFIs the stress intensity factor range, Δ K, under HCF load cyclesLCFIs the stress intensity factor range under low cycle fatigue load; rHCFStress ratio, R, for HCF loadingLCFStress ratio for LCF loading; fnIs a geometric correction coefficient; sigmadynFor dynamic stress, σstaFor static stress, Δ σth(RHCF) And Δ σth(RLCF) Is threshold stress;
the abscissa of the crack non-expansion equivalent curve graph is static stress and the ordinate is dynamic stress;
(5) obtaining static stress and dynamic stress of each point of a blade basin blade back through a finite element numerical analysis method;
(6) and determining the crack size a corresponding to the equivalent curve by comparing the positions of the static stress and the dynamic stress in the equivalent curve of crack non-propagation, namely determining the available limit of the crack/tear type hard object damage at the point of the blade back of the blade.
2. The method for determining the usable limit of damage of hard objects in the form of cracks on the back of a blade or a bucket considering high and low cycle fatigue, according to claim 1, wherein: in the step (1), the high/low cycle composite load of the blade refers to interaction of low-frequency centrifugal force cyclic load and high-frequency vibration load of the blade when the engine normally works, the low-frequency centrifugal force cyclic load in the blade is recorded as low-cycle fatigue load, the medium-high frequency vibration load in the blade is recorded as high-cycle fatigue load, and the high-cycle fatigue load and low-cycle fatigue load forms which may appear at each point of a blade basin and a blade back of the blade are determined through load spectrum analysis.
3. The method for determining the usable limit of damage of hard objects in the form of cracks on the back of a blade or a bucket considering high and low cycle fatigue, according to claim 1, wherein: in the step (2), the crack propagation threshold value is expressed by a stress intensity factor range delta K, wherein when the stress ratio R is>When 0,. DELTA.K ═ Kmax-KminAnd K isminNot equal to 0, when the stress ratio R is less than or equal to 0, delta K is equal to Kmax-KminAnd K ismin0; crack propagation threshold Δ KthExpressed as a function of the stress ratio R.
4. The method for determining the usable limit of damage of hard objects in the form of cracks on the back of a blade or a bucket considering high and low cycle fatigue, according to claim 1, wherein: in the step (5), the static stress and the dynamic stress of each point of the blade basin and the blade back of the blade are expressed by the effective stress of a unit Von-mises and the like, and the unit size representing the blade back point of the blade basin is 1 mm.
5. The method for determining the usable limit of damage of hard objects in the form of cracks on the back of a blade or a bucket considering high and low cycle fatigue, according to claim 1, wherein: and (6) taking the minimum value of the crack size determined by the crack non-propagation equivalent curve corresponding to the high-cycle fatigue load and the crack size determined by the low-cycle fatigue load as the available limit of the tearing/cracking type hard object damage at the point of the blade and the blade back.
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