Blade crack identification method for mistuned blisk

Abstract

The patent application discloses a blade crack identification method for mistuned bladed disk, which comprises the following processes: geometric model establishment for complete bladed disk and bladed disk with crack under random mistuned condition; simplification of bladed disk model, construction of bladed disk lumped parameter model, response analysis of mistuned bladed disk system with crack based on nonlinear contact force, calculation of steady-state response of each blade and analysis; three-dimensional geometry of complete blade and blade with crack for finite element model establishment; resonance state and non-resonance state vibration response of intact bladed disk and bladed disk with breathing crack under mistuned condition, analysis of corresponding frequency domain response; definition of bladed disk harmonic index and bladed disk blade harmonic index based on bladed disk vibration response characteristics, and utilization of harmonic index for effective crack positioning and identification of bladed disk with crack, which provides basis and guidance for crack identification in bladed disk.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical fault diagnosis, and in particular relates to a method for identifying blade cracks of a detuned integral blade disk. Background Art

[0002] As a key component of advanced aircraft engine compressors and turbines, the blisk, with its unique integrated design and manufacturing technology, has significantly improved aeroengine performance and reliability. However, blisks operate in a harsh environment and are susceptible to multiple loads, including aerodynamic, centrifugal, and friction loads. These loads generate significant alternating stresses in the blades, particularly in stress concentration areas such as the blade root, where fatigue cracks are highly likely to develop. Once a crack develops in a blade, its vibration characteristics will undergo significant changes. These changes involve not only alterations in modal characteristics but also more complex nonlinear phenomena. Under the influence of a crack, the blade's stiffness will be locally reduced, affecting its natural frequency and mode shape. This nonlinear response can manifest as an increase in vibration amplitude, frequency shifts, and harmonic responses, making the blisk more susceptible to resonance and failure.

[0003] Current research focuses less on the vibration mechanism of blade cracks. This means that when the cracks are not obvious in the early stages, the vibration characteristics generated by the cracks are not obvious enough, making it difficult to identify them effectively. However, when the cracks develop significantly, they often lead to more serious consequences. In addition, during the actual processing of the integral blade disc, processing errors, material unevenness, and other factors often occur, which can lead to detuning. The results of this detuning are very similar to cracks, and can also cause localized vibrations. Often, they occur during the processing of the integral blade disc and are difficult to avoid. Current research often finds it difficult to effectively distinguish between cracks and detuning, so detuning often causes more serious interference in crack identification. Therefore, inventing a method for identifying blade cracks in detuned integral blade discs is of great significance for ensuring the operational safety and reliability of aircraft engines. Summary of the Invention

[0004] In order to solve the above problems, the present invention proposes a method for identifying cracks in a detuned blisk, which is used to solve the problem of identifying cracks in a blisk.

[0005] The present invention includes the following technical solutions:

[0006] A method for identifying blade cracks of a detuned blisk comprises the following steps:

[0007] Step 1: Establish a 3D geometric model of the intact blade disk, and then establish a 3D geometric model of the cracked integral blade disk based on the 3D geometric model of the intact blade disk.

[0008] Step 2: Based on the intact blade three-dimensional geometric model, a dynamic model of the intact blade is constructed from the mechanism. Under actual operating conditions, the first-order mode of the intact blade is most likely to be excited and cause resonance, so the dynamic model of the intact blade is simplified to obtain the lumped parameter model of the intact blade.

[0009] Step 3: Nonlinear contact force is applied to the lumped parameter model of the intact blade to simulate breathing cracks, and the mistuning strength is given. The steady-state response analysis of the overall blade with breathing cracks is performed, and the steady-state response results of each blade are calculated. The steady-state response results of each blade are analyzed to provide theoretical guidance for the index determination of step 6.

[0010] Step 4: Based on the three-dimensional geometric models of the intact blade and the blade with breathing cracks, finite element models of the intact blade and the overall blade with breathing cracks are established to meet the subsequent vibration characteristic analysis.

[0011] Step 5: The same mistuning strength as step 3 is given to the finite element model, and the resonance state and non-resonance state vibration response of the intact blade and the overall blade with breathing cracks is performed to obtain the corresponding frequency domain response results.

[0012] Step 6: According to the analysis of the steady-state response results of the blades in step 3 and the resonance state and non-resonance state vibration response of the blade with breathing cracks in step 5, the overall blade harmonic index and the blade harmonic index for the overall blade are defined.

[0013] Step 7: The overall blade harmonic index is calculated by the defined harmonic index formula. According to whether the overall blade harmonic index is greater than 0, it is judged whether the overall blade contains breathing cracks. If there are breathing cracks, the blade harmonic index for the overall blade is calculated to locate the breathing cracks.

[0014] Further, in step 1, the geometric characteristics corresponding to the three-dimensional geometric model include blade length l, blade width b, blade height h, elastic modulus of blade material E, mass density p, Poisson's ratio μ, and blade installation angle.

[0015] Further, in step 2, the lumped parameter model is constructed by the following parameters: the equivalent mass of the i-th blade Equivalent stiffness Equivalent damping The effect of the wheel disc on the blade is equivalent to a massless spring damping model, and the coupling stiffness and coupling damping are k R and c R .

[0016] Further, in step 3: the applied nonlinear contact force formula is:

[0017]

[0018] Where k nl is the contact stiffness, y is the displacement of the crack blade, and φ is the smoothing coefficient. As long as the value of φ is large enough, the normal relationship between the nonlinear force and displacement is smooth enough, and the breathing behavior of the crack can be simulated more accurately.

[0019] k nl Here, the solution is obtained by finite element calculation, which is expressed as follows:

[0020]

[0021] A unit force F is applied to the blade tip of the finite element model, where p is the contact pressure at each node of the contact surface, and x is p Displacement of each node on the contact surface, S p is the contact surface area.

[0022] This invention simulates the differences in natural frequency between blades by assuming the slight differences between blades are differences in elastic modulus. Given a given detuning intensity, each simulation requires only generating random numbers from a normal distribution and assigning them to each blade tip. This can be expressed as:

[0023] k i =(1+δ i )k0

[0024] Where k0 is the ideal stiffness of each blade, k i is the stiffness of the i-th blade, v i is the stiffness detuning amount.

[0025] The above nonlinear contact force and given detuning strength are used to perform steady-state response analysis on the integral blade disk containing breathing cracks, and the steady-state response of each blade is calculated.

[0026] The overall vibration equation of the integral blade disk with breathing crack is:

[0027]

[0028] Where M, C, and K represent the mass, viscous damping, and stiffness matrix of the integral blade disk with breathing cracks, respectively; X represents the displacement response vector of the integral blade disk with breathing cracks. represents the velocity response vector of the integral blade with breathing crack, represents the acceleration response vector of the integral blade with breathing crack, F ext is the exciting force vector, which is described as:

[0029] F ext =F+[0 0 0 F nl … 0]T

[0030] where F is the harmonic breathing crack whole bladed disk row wave excitation matrix, and the nonlinear contact force F is added at the breathing crack blade nl The equivalent breathing characteristics are expressed. The equation is solved by using the fourth-order variable step Runge-Kutta method, and the steady-state response of each blade can be obtained.

[0031] The steady-state response of each blade is analyzed, and the harmonic response and other nonlinear phenomena of the blade are obtained when the bladed disk only has mistuning and when the mistuned bladed disk has a breathing crack. Specifically, when the bladed disk only has mistuning, there is no harmonic response and other nonlinear phenomena in the steady-state response diagram of each blade. When the mistuned bladed disk has a breathing crack, the blade has a harmonic response, and the components are mostly even orders, such as the 2nd order and the 4th order. These specific harmonic response components can be used as key indicators to identify the existence of a breathing crack.

[0032] Further, the step 4 is specifically: in the process of establishing the finite element model, hexahedral mesh is used for division, and a contact pair is created to make the crack have a "breathing" feature. In the process of expansion, the shape of the breathing crack is a semi-ellipse. In order to facilitate discussion and calculation, the width-height ratio of the blade section is set as the initial value d0, and different expansion coefficients s are defined to define the shape of the breathing crack and describe the nonlinear characteristics.

[0033] d=sd0

[0034] In the formula, d is the length-depth ratio of the breathing crack, which is used to define the actual shape of the breathing crack. In the finite element calculation, the specific value of the set expansion factor s is 1 / 12, 1 / 6, 1 / 4, 1 / 3, 1 / 2, and 2 / 3. When s is 1 / 3, it is the initial breathing crack length. With the initial breathing crack as the boundary, more calculation points are selected to help identify the breathing crack in the early stage of expansion. When the breathing crack expands to a certain extent, the blade will often directly lead to fracture, and there is no need to identify.

[0035] Further, in the step 5, the corresponding frequency domain response result is specifically: whether in the resonance state or the non-resonance state, the blade without a breathing crack in the mistuned state does not have nonlinear characteristics, and the blade with a breathing crack in the mistuned state has obvious nonlinear characteristics such as harmonic response, which is 2nd order and 4th order harmonic response. The results obtained in step 3 are verified with each other.

[0036] Further, in the step 6: the harmonic index H of the bladed disk is:

[0037]

[0038] Where H imax is the harmonic response with the highest amplitude of each blade on the blade disk, H i3 is the third-order harmonic response of each blade on the blade disk, H i0 is the fundamental component of the vibration response of each blade on the blisk, the subscript i represents the blade number, and N is the number of blades.

[0039] Definition of the harmonic index H for the blade of the blisk i ′, after confirming the presence of respiratory cracks in the blade disk, this index is used to locate the blade containing respiratory cracks, which is defined as

[0040]

[0041] Where H i2 is the second-order harmonic response component of each blade on the blisk, H i3 is the third-order harmonic response component of each blade on the blisk, H i0 is the fundamental component of the vibration response of each blade on the blisk, where the subscript i represents the blade number. Using harmonic indices to quantitatively describe the nonlinear characteristics of a blade with a breathing crack can specifically quantify the vibration changes caused by the breathing crack. These two harmonic indices can effectively identify and locate the crack.

[0042] Furthermore, the step 7 is specifically as follows: using the harmonic index, different crack stages of the breathing crack blade can be judged, and the existence of multiple cracks can be accurately identified.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1. After obtaining the harmonic response corresponding to the blade disk, the present invention can effectively identify and locate the cracks in the blade disk including breathing cracks by using harmonic indicators.

[0045] 2. This invention utilizes harmonic indicators to identify the different crack stages of a breathing crack blade. Specifically, during the initial crack initiation phase, especially when the shape index is less than 1 / 6, the harmonic indicator grows slowly. However, once the crack exceeds this threshold, nonlinear growth becomes apparent and accelerates.

[0046] 3. The present invention can identify cracks in an integral blade disk with detuned blade stiffness and multiple breathing cracks, and can accurately identify the presence of multiple cracks. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 : Flow chart of the present invention.

[0049] Figure 2 : Three-dimensional modeling of the overall blade disk model.

[0050] Figure 3 : Diagram of the equivalent multi-blade coupled lumped parameter model.

[0051] Figure 4 : Vibration responses of each blade in the first-order bending mode of the detuned integral blade disk and the detuned integral blade disk with breathing cracks, where (a) detuned integral blade disk; (b) detuned integral blade disk with breathing cracks.

[0052] Figure 5 : Finite element model of the integral bladed disk.

[0053] Figure 6 : Finite element model of breathing crack blade.

[0054] Figure 7 : Vibration response of each blade of a first-order bending detuned blisk with breathing crack, including (a) detuned blisk, (b) detuned blisk with crack.

[0055] Figure 8 : Vibration response of each blade of a detuned blisk with a breathing crack under non-resonant excitation (n=1 / 2), including (a) detuned blisk, (b) detuned blisk with cracks.

[0056] Figure 9 : Harmonic indicators of the integral blade disk with breathing cracks under different states, including (a) non-resonant state, (b) resonant state (one bend).

[0057] Figure 10 : Variation trend of harmonic indicators in different expansion stages of integral blade containing breathing crack.

[0058] Figure 11 : Harmonic index of detuned integral blade disk with multiple breathing cracks. DETAILED DESCRIPTION

[0059] The specific embodiments of the invention will be described below with reference to the accompanying drawings.

[0060] like Figure 1As shown, the present invention provides a method for identifying blade cracks of a detuned blisk, comprising the following steps:

[0061] Step 1: Build a 3D geometric model with the intact blade as the object, and then build a 3D geometric model of the cracked blade based on the 3D geometric model of the intact blade. The obtained 3D geometric model contains all the corresponding geometric features. Specifically: the blade length is l = 60 × 10 -3 m, blade width b = 28.28 × 10 -3 m, blade height h=2×10 -3 m, and the elastic modulus of the blade material is E = 2.1 × 10 11 Pa, mass density is ρ = 7800 kg / m 3 , Poisson's ratio μ is 0.3, the blade installation angle is 45°, and there are 12 blades in total. The three-dimensional modeling of the entire blade disk is as follows Figure 2 shown.

[0062] Step 2: Based on the intact blade's 3D geometric model, a dynamic model of the intact blade is constructed from the mechanism. Under actual operating conditions, the first-order mode of the intact blade is most likely to be excited and cause resonance. Therefore, the dynamic model of the intact blade is simplified to obtain a lumped parameter model of the intact blade. The equivalent multi-blade coupled lumped parameter model is shown in the figure below. Figure 3 shown.

[0063] The lumped parameter model is constructed by the following parameters: the equivalent mass of the i-th blade Equivalent stiffness Equivalent damping The effect of the wheel on the blade is equivalent to a massless spring and damping, and the coupling stiffness and coupling damping are k R and c R .

[0064] Step 3: Apply nonlinear contact force to the lumped parameter model of the intact blade to simulate the breathing crack, and given the detuning strength, perform steady-state response analysis on the entire blade with the breathing crack, calculate the steady-state response of each blade and analyze it. The formula for the applied nonlinear contact force is:

[0065]

[0066] Where k nl is the contact stiffness, y is the displacement of the crack blade, and φ is the smoothing coefficient. As long as the value of φ is large enough, the normal relationship between the nonlinear force and displacement is smooth enough, and the breathing behavior of the crack can be simulated more accurately.

[0067] k nl Here, the solution is obtained by finite element calculation, which is expressed as follows:

[0068]

[0069] A unit force F is applied to the blade tip of the finite element model, where p is the contact pressure at each node of the contact surface, and x is p Displacement of each node on the contact surface, S p The contact surface area is .The No. 4 blade in the present invention is a blade containing respiratory cracks.

[0070] This invention simulates the differences in natural frequency between blades by assuming that the slight differences between blades are differences in their elastic moduli. If the detuning intensity is given, in each simulation, it is sufficient to simply generate a random number according to a normal distribution and assign it to each blade tip. This can be expressed as:

[0071] k i =(1+δ i )k0

[0072] Where k0 is the ideal stiffness of each blade, k i is the stiffness of the i-th blade, and is the stiffness detuning amount. Using the above nonlinear contact force and given detuning strength, the steady-state response analysis of the integral blade with breathing crack is carried out, and the steady-state response of each blade is calculated.

[0073] The overall vibration equation of the integral blade disk with breathing crack is:

[0074]

[0075] Where M, C, and K represent the mass, viscous damping, and stiffness matrix of the integral blade disk with breathing cracks, respectively; X represents the displacement response vector of the integral blade disk with breathing cracks. represents the velocity response vector of the integral blade with breathing crack, represents the acceleration response vector of the integral blade with breathing crack, F ext is the exciting force vector, which is described as:

[0076] F ext =F+[0 0 0 F nl … 0] T

[0077] Where F is the traveling wave excitation matrix of the harmonic blade, and the nonlinear contact force F is added at the breathing crack blade. nl The fourth-order variable-step Runge-Kutta method is used to solve the overall vibration equation of the equation, and the steady-state response of each blade can be obtained.

[0078] When the excitation order EO=1 times the resonance frequency is applied to the integral blade disk with a detuning strength of 2%, the calculated steady-state response of each blade is as follows: Figure 4 As shown. Figure 4It can be seen from the figure that when the integral blade only has detuning, there is no nonlinear phenomenon such as harmonic response in the steady-state response diagram of each blade; when there is a phenomenon such as breathing crack in the detuned integral blade, a harmonic response will appear on the blade, and its components are mostly even-order, such as 2nd order, 4th order, etc. These specific harmonic response components can be used as key signs to identify the presence of cracks.

[0079] Step 4: Establish a finite element model of the three-dimensional geometry of the intact blade and the blade with breathing crack to meet the needs of subsequent vibration characteristic analysis. The mesh is divided into hexahedral meshes with a mesh size of 1 mm. The final number of meshes is 19080 and the number of nodes is 99392. The three-dimensional solid element SOLID186 is used. The finite element model of the harmonic solid blade is as follows: Figure 5 As shown, the 12 sectors of the integral blade disk are numbered in reverse order, 1 to 12.

[0080] During the expansion of the breathing crack, the crack shape is semi-elliptical. To facilitate discussion and calculation, the aspect ratio of the blade section is set to the initial value d0, and different expansion coefficients s are defined to define the crack shape and describe the nonlinear characteristics.

[0081] d=sd0

[0082] Where d is the crack's length-to-depth ratio, which defines the crack's actual shape. During finite element calculations, the expansion factor s is set to 1 / 12, 1 / 6, 1 / 4, 1 / 3, 1 / 2, and 2 / 3. When s is 1 / 3, it represents the initial crack length. Using the initial crack as a boundary, selecting more calculation points in the early stages of crack development can help achieve earlier crack identification. However, once the crack reaches a certain size, the blade often fractures, eliminating the need for identification.

[0083] The establishment of the finite element model of the crack needs to show the "breathing" characteristics of the crack. On the No. 4 blade, 1mm away from the blade root, a crack surface is set, and the crack is drawn separately. The shape is set to semi-elliptical, the crack length is 9.43mm, and the crack width is 0.67mm. The non-crack part on the interface realizes the "bonding" of the two parts through the degree of freedom of the coupling node. The actual position and shape of the crack are as follows: Figure 6 shown.

[0084] Step 5: Considering the integral blade disk with breathing cracks and a detuning intensity of 2%, the vibration response analysis of the finite element model in the first-order bending resonance state is performed. The frequency domain response of the intact blade disk and the blade disk with breathing cracks in the detuning state is analyzed. The frequency domain response results are as follows: Figure 7 As shown. Figure 7It can be seen that the breathing crack blade in mistuned state shows obvious nonlinear characteristics, which are 2nd and 4th order harmonic responses, and the results are verified by the results of step 3.

[0085] The n times of the resonance frequency of the blisk is used as the excitation frequency to analyze the non-resonance state vibration response of the blisk, and the mistuning strength is 2%. The frequency domain response results are shown in FIG. 6. Figure 8 It can be found from the analysis of the vibration response diagram that the harmonic order of the breathing crack blade is basically consistent, which is 2nd, 3rd and 4th order harmonic, while the other blades show different results from the 1st order resonance vibration response.

[0086] Step 6: According to the steady-state response analysis of the blade in step 3 and the resonance state and non-resonance state vibration response of the blisk with breathing crack in step 5, the harmonic index of the blisk and the harmonic index of the blade of the blisk are defined as H, which is defined as

[0087]

[0088] In the formula, H imax is the highest harmonic response of the response amplitude of each blade of the blisk, H i3 is the 3rd order harmonic response of each blade of the blisk, H i0 is the fundamental component in the vibration response of each blade of the blisk, and the subscript i represents the blade number.

[0089] The harmonic index calculated from the resonance state and non-resonance state vibration response in step 5 is shown in Table 1. In the actual application of blisk crack identification, the excitation frequency of the 1st order bending mode family is preferred to be used for vibration response analysis.

[0090] Table 1

[0091]

[0092] The harmonic index of the blade of the blisk H i ′ is defined for positioning the breathing crack blade after the breathing crack is determined in the blisk, which is defined as

[0093]

[0094] In the formula, H i2 is the 2nd order harmonic response component of each blade of the blisk, H i3 is the 3rd order harmonic response component of each blade of the blisk, and H i0is the fundamental component of the vibration response of each blade on the blisk, with the subscript i representing the blade number. To locate blades with breathing cracks in blisks, the second-order harmonic component of the blade is primarily used. Harmonic indices are used to quantitatively describe the nonlinear characteristics of blades with breathing cracks, specifically quantifying the vibration changes caused by the breathing cracks. These two harmonic indices can effectively identify and locate cracks.

[0095] Step 7: Calculate the harmonic index of the integral blade using the defined harmonic index formula. Determine whether the integral blade contains a breathing crack based on whether the harmonic index is greater than 0. If a breathing crack exists, calculate the harmonic index for the blade of the integral blade to identify and locate the breathing crack.

[0096] Figure 9 is the harmonic index of the blade of the integral blisk with breathing cracks in different states, Figure 9 As can be seen from the figure, the harmonic index of the blade with breathing crack is higher than that of the intact blade, whether in resonant or non-resonant state. Therefore, when cracks are confirmed in the integral blade, this method can be used to effectively identify and locate the cracks.

[0097] In addition, the harmonic index can also be used to identify breathing cracks in detuned integral blades at different expansion stages. Figure 10 The harmonic index variation trend of the integral blade with breathing crack at different expansion stages. Figure 10 The harmonic index trend shows that in the initial crack initiation stage, especially when the shape index is less than 1 / 6, the harmonic index grows slowly. However, once the crack exceeds this threshold, nonlinear growth becomes apparent and the growth rate accelerates, which can be used as a criterion for judging crack initiation.

[0098] At the same time, the detuned integral blade disk with multiple cracks is analyzed and the blade harmonic index is calculated as shown in the figure below: Figure 11 As shown in Figure 2, it can be seen that the blade harmonic index in the detuned blade disk is effectively used to identify cracks. Compared with the blade without cracks, the blade with breathing crack shows more significant harmonic index.

[0099] Combining the above-mentioned integral blisk harmonic indicators and blade harmonic indicators, it is possible to identify and locate cracks with a shape index s ≥ 1 / 6. At this time, the crack size is approximately 4.75 mm long and 0.3 mm wide. This method is sufficient to promptly detect newly initiated cracks under detuned conditions and can accurately identify the presence of multiple cracks, thereby preventing possible serious consequences.

Claims

1. A method for identifying blade cracks in a detuned blisk, characterized in that: The following steps are involved: Step 1: Establish a 3D geometric model of the intact blade disk, and then establish a 3D geometric model of the cracked integral blade disk based on the 3D geometric model of the intact blade disk; Step 2: Based on the intact blade's 3D geometric model, a dynamic model is constructed for the intact blade from the mechanism. Under actual operating conditions, the first-order mode of the intact blade is most likely to be excited and cause resonance. Therefore, the dynamic model of the intact blade is simplified to obtain a lumped parameter model of the intact blade. Step 3: Apply nonlinear contact force to the lumped parameter model of the intact blade to simulate the breathing crack. Given the detuning strength, perform steady-state response analysis on the entire blade containing the breathing crack. Calculate the steady-state response results of each blade and analyze the steady-state response results of each blade to provide theoretical guidance for determining the indicators in step 6. Step 4: Based on the three-dimensional geometric models of the intact blade and the blade with breathing crack, a finite element model is established to obtain the finite element models of the intact blade and the integral blade with breathing crack to meet the needs of subsequent vibration characteristics analysis; Step 5: The finite element model is given the same detuning intensity as in step 3, and the intact blade disk and the integral blade disk with breathing cracks in the detuned state are subjected to resonant and non-resonant vibration responses to obtain the corresponding frequency domain response results. Specifically, no matter in the resonant or non-resonant vibration state, there is no nonlinear feature on the blade without breathing cracks in the detuned state, while the blade with breathing cracks in the detuned state has obvious nonlinear features such as harmonic response, which are manifested as 2nd and 4th order harmonic responses, which are mutually verified with the results obtained in step 3; Step 6: Based on the analysis of the steady-state response results of the blade in step 3 and the resonant and non-resonant vibration responses of the blade disk with breathing cracks in step 5, the harmonic index of the integral blade disk and the harmonic index for the integral blade disk are defined. The harmonic index H of the integral blade disk is: ； Where H imax is the harmonic response with the highest amplitude of each blade on the blade disk, H i3 is the third-order harmonic response of each blade on the blade disk, H i0 is the fundamental component of the vibration response of each blade on the blisk, the subscript i represents the blade number, and N is the number of blades; Definition of the harmonic index H for the blade of the blisk i ', after confirming the presence of respiratory cracks in the leaf disk, this indicator is used to locate the leaf with respiratory cracks, which is defined as ； Where H i2 is the second-order harmonic response component of each blade on the blisk, H i3 is the third-order harmonic response component of each blade on the blisk, H i0 is the fundamental component of the vibration response of each blade on the integral blade disk, and the subscript i represents the blade number. Harmonic indices are used to quantitatively describe the nonlinear characteristics generated by the breathing crack blade, which can specifically quantify the vibration changes caused by the breathing crack. The above two harmonic indices can effectively identify and locate the crack. Step 7: Calculate the harmonic index of the integral blade using the defined harmonic index formula. Determine whether the integral blade contains a breathing crack based on whether the harmonic index is greater than 0. If a breathing crack exists, calculate the harmonic index of the blade of the integral blade to locate the breathing crack.

2. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: In step 1, the geometric features corresponding to the three-dimensional geometric model include blade length l, blade width b, blade height h, elastic modulus E of blade material, mass density , Poisson's ratio μ and the installation angle of the blade.

3. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: In step 2, the lumped parameter model is constructed by the following parameters: Equivalent mass of blade , equivalent stiffness , equivalent damping , the effect of the wheel on the blade is equivalent to a massless spring damping model, and the coupling stiffness and coupling damping are and .

4. The method for identifying blade cracks of a detuned blisk according to claim 1, wherein: In step 3: the formula for the applied nonlinear contact force is: ； Where, is the contact stiffness, is the displacement of the cracked blade, is the smoothing coefficient, as long as If the value is large enough, the normal relationship between the nonlinear force and displacement will be smooth enough, and the breathing behavior of the crack can be simulated more accurately. Here, the solution is obtained by finite element calculation, which is expressed as follows: ； A unit force F is applied to the blade tip of the finite element model, where p is the contact pressure at each node of the contact surface, and x is p Displacement of each node on the contact surface, S p is the contact surface area; The slight differences between blades are set as the differences in elastic modulus of each blade to simulate the differences in natural frequency between blades. If the detuning intensity is given, in each simulation, it is only necessary to generate random numbers according to the normal distribution and assign them to each blade tip. This can be expressed as: ； Where k0 is the ideal stiffness of each blade, k i is the stiffness of the i-th blade, is the stiffness detuning amount; The steady-state response analysis of the integral blade with breathing crack is carried out using the above nonlinear contact force and a given detuned intensity, and the steady-state response of each blade is calculated. The overall vibration equation of the integral blade disk with breathing crack is: ； Where M, C, and K represent the mass, viscous damping, and stiffness matrix of the integral blade with breathing crack, respectively. represents the displacement response vector of the integral blade disk with breathing crack, represents the velocity response vector of the integral blade with breathing crack, represents the acceleration response vector of the integral blade with breathing crack, F ext is the exciting force vector, which is described as: ； Where F is the traveling wave excitation matrix of the integrated blade with breathing crack, and the nonlinear contact force F is added at the blade with breathing crack. nl The equivalent breathing characteristics expressed by the equation are solved by the fourth-order variable step-size Runge-Kutta method to obtain the steady-state response of each blade; The steady-state response of each blade was analyzed, and the nonlinear harmonic response of the blade was found when the blade disk was only detuned and when breathing cracks existed in the detuned integral blade disk. Specifically, when the integral blade disk was only detuned, there was no nonlinear harmonic response in the steady-state response diagram of each blade. However, when breathing cracks existed in the detuned integral blade disk, a harmonic response would appear on the blade, and its components were mostly even-order. These specific harmonic response components can serve as key signs for identifying the presence of breathing cracks.

5. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: The step 4 specifically includes: in the process of establishing the finite element model, using hexahedral mesh for division, creating contact pairs to make the crack show "breathing" characteristics; During the expansion process of the breathing crack, the shape of the breathing crack is always semi-elliptical. In order to facilitate discussion and calculation, the aspect ratio of the blade section is set to the initial value d0, and different expansion coefficients s are defined to define the shape of the breathing crack and describe the nonlinear characteristics. ； Where d is the length-to-depth ratio of the breathing crack, which is used to define the actual shape of the breathing crack; When performing finite element calculations, the specific values ​​of the expansion factor s are set as 1 / 12, 1 / 6, 1 / 4, 1 / 3, 1 / 2, and 2 / 3. When the value of s is 1 / 3, it is the initial breathing crack length. Taking the initial breathing crack as the boundary, in the early stage of breathing crack expansion, selecting more calculation points can help achieve earlier breathing crack identification. When the breathing crack expands to a certain extent, the blade will often directly break, and there is no need for identification.

6. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: The step 7 is specifically as follows: using the harmonic index, different crack stages of the breathing crack blade can be judged, and the existence of multiple cracks can be accurately identified.

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