Blade crack identification method for mistuned blisk

Abstract

The invention provides a blade crack identification method for a mistuned blisk. The method comprises the following steps: carrying out geometric model modeling on a blisk and a blisk containing cracks under a random detuning condition; a blisk model is simplified, a blisk lumped parameter model is constructed, response analysis is conducted on the blisk system containing crack detuning on the basis of a non-linear contact force mode, and steady-state response of all blades is obtained through calculation and analyzed; finite element models are established for the three-dimensional geometry of the complete blade and the crack-containing blade; performing resonance state and non-resonance state vibration response on the intact bladed disc and the bladed disc containing the breathing crack in the detuning state, and analyzing corresponding frequency domain response; based on the vibration response characteristics of the blisk, the harmonic index of the blisk and the harmonic index of the blisk blade are defined, the positioning and identification of the crack of the blisk containing the crack can be effectively carried out by using the harmonic index, and a basis and guidance are provided for the identification of the crack in the blisk.

Description

Technical Field

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

[0002] As one of the key components of the compressor and turbine of advanced aircraft engines, the integral blade disk has greatly improved the performance and reliability of aircraft engines with its unique integrated design and manufacturing technology. However, the working environment of the integral blade disk is relatively harsh and is susceptible to various loads such as aerodynamic, centrifugal and friction loads, which leads to large alternating stresses on the blades, especially in stress concentration areas such as the root of the blade, where fatigue cracks are very likely to occur. Once cracks appear in the blade, its vibration characteristics will change significantly. These changes not only involve changes in modal characteristics, but also include some more complex nonlinear phenomena. Under the influence of cracks, the stiffness of the blade will be locally reduced, thereby affecting its natural frequency and vibration mode; this nonlinear response may be manifested as an increase in vibration amplitude, frequency shift, harmonic response, etc., which is more likely to cause resonance, failure and other risks for the integral blade disk.

[0003] There are few studies on the vibration mechanism of blade cracks at present, which means that when the cracks are not obvious at the beginning, the vibration characteristics generated by the cracks are not obvious enough and it is difficult to identify them effectively. However, when the cracks develop greatly, it often leads to more serious consequences. In addition, in the actual processing of the integral blade disk, processing errors, material unevenness and other effects often occur, which will cause detuning. The result of this detuning is very similar to that of cracks, and it will also cause localized vibration. It often occurs in the processing stage of the integral blade disk and is difficult to avoid. At present, it is often difficult to effectively distinguish between cracks and detuning. Therefore, in the identification of cracks, detuning often causes more serious interference. Therefore, it is of great significance to invent a method for identifying blade cracks of detuned integral blade disks to ensure the operating safety and reliability of aircraft engines. Summary of the invention

[0004] In order to solve the above-mentioned problem, the present invention proposes a method for identifying cracks in blades of a detuned integral blade disk, which is used to solve the problem of identifying cracks in an integral blade disk.

[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 with the intact blade disk as the object, 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 three-dimensional geometric model of the intact blade disk, a dynamic model of the intact blade disk is constructed from the mechanism. Under actual operating conditions, the first-order mode of the intact blade disk is most likely to be excited and cause resonance. Therefore, the dynamic model of the intact blade disk is simplified to obtain a lumped parameter model of the intact blade disk.

[0009] Step 3: Apply nonlinear contact force to the lumped parameter model of the intact blade disk to simulate the breathing crack, and give the detuning strength, perform steady-state response analysis on the entire blade disk 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.

[0010] Step 4: Based on the three-dimensional geometric model of the intact blade and the blade with breathing crack, a finite element model is established to obtain the finite element model of the intact blade and the integral blade with breathing crack to meet the subsequent vibration characteristics analysis.

[0011] Step 5: The finite element model is given the same detuning intensity as in step 3, and the resonant and non-resonant vibration responses of the intact blade disk and the integral blade disk with breathing crack in the detuned state are performed to obtain the corresponding frequency domain response results.

[0012] 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 containing breathing cracks in step 5, define the harmonic index of the entire blade disk and the harmonic index of the blade for the entire blade disk.

[0013] Step 7: Calculate the harmonic index of the entire blade disk through the defined harmonic index formula, and determine whether the entire blade disk contains a breathing crack based on whether the harmonic index of the entire blade disk is greater than 0. If a breathing crack exists, calculate the harmonic index of the blade of the entire blade disk to locate the breathing crack.

[0014] Furthermore, 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 ρ, Poisson's ratio μ and blade installation angle.

[0015] Furthermore, 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 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] Furthermore, in step 3: the formula of the applied nonlinear contact force is:

[0017]

[0018] In the formula, k nl is the contact stiffness, y is the crack blade displacement, and φ is the smoothing coefficient. As long as the value of φ is large enough, the normal relationship between the nonlinear force and the 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 blade finite element model, p is the contact pressure at each node of the contact surface, x is p Displacement of each node on the contact surface, S p is the contact surface area.

[0022] The present invention sets the slight difference between blades as the difference in elastic modulus of each blade to simulate the difference 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. It 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 ith blade, v i is the stiffness detuning amount.

[0025] The above nonlinear contact force and given detuning strength are used to carry out steady-state response analysis of 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 traveling wave excitation matrix of the integrated blade with breathing crack, and the nonlinear contact force F is added at the breathing crack blade. nl The equivalent breathing characteristics expressed by . The equation is solved by the fourth-order variable step-size Runge-Kutta method to obtain the steady-state response of each blade.

[0031] The steady-state response of each blade is analyzed to obtain nonlinear phenomena such as harmonic response of the blade when only detuning exists in the blade disk and when breathing cracks exist in the detuned integral blade disk. Specifically, when only detuning exists in the integral blade disk, there is no nonlinear phenomenon such as harmonic response in the steady-state response diagram of each blade; when breathing cracks exist in the detuned integral blade disk, 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 existence of breathing cracks.

[0032] Furthermore, step 4 is specifically as follows: in the process of establishing the finite element model, a hexahedral mesh is used for division, and a contact pair is created to make the crack show a "breathing" feature. During the expansion of the breathing crack, the shape of the breathing crack is a semi-ellipse. For the convenience of 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.

[0033] d=sd0

[0034] 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 to 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. 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 often directly breaks, and there is no need to identify it.

[0035] Furthermore, in step 5, the corresponding frequency domain response results are obtained as follows: no matter in the resonant or non-resonant vibration state, there are no nonlinear characteristics on the blades without breathing cracks in the detuned state, while on the blades with breathing cracks in the detuned state, relatively obvious nonlinear characteristics such as harmonic response appear, which are manifested as 2nd and 4th order harmonic responses, which verify each other with the results obtained in step 3.

[0036] Furthermore, in step 6: the overall blade disk harmonic index H is:

[0037]

[0038] In the formula, 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 in 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 breathing cracks in the blade disk, this index is used to locate the blade containing breathing cracks, which is defined as

[0040]

[0041] In the formula, H i2 is the second-order harmonic response component of each blade on the integral blade disk, H i3 is the third-order harmonic response component of each blade on the integral blade disk, 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. The harmonic index is used to quantitatively describe the nonlinear characteristics generated by the breathing crack blade, and the vibration changes caused by the breathing crack can be specifically quantified. The above two harmonic indicators can be used to 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 determined, 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 containing breathing cracks by using harmonic indicators.

[0045] 2. The present invention uses harmonic indicators to determine the different crack stages of breathing crack blades. Specifically, in the initial stage of crack initiation, especially when the shape index is less than 1 / 6, the growth rate of the harmonic index is relatively slow. However, once the crack exceeds this threshold, the nonlinear growth becomes obvious and the growth rate accelerates.

[0046] 3. The present invention can identify cracks in an integral blade disk with misaligned blade stiffness and containing 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 implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying 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 response of each blade in the first-order bending mode of the detuned integral blisk and the detuned integral blisk with breathing crack, where (a) detuned integral blisk; (b) detuned cracked integral blisk.

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

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

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

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

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

[0057] Fig.10 : Variation trend of harmonic indicators at different extension stages of integral blade containing breathing crack.

[0058] Fig.11 : Harmonic index of the detuned integral blade disk containing multiple breathing crack blades. DETAILED DESCRIPTION

[0059] The specific implementation 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 integral blade disk, comprising the following steps:

[0061] Step 1: Establish a 3D geometric model with the intact blade disk as the object, and then establish a 3D geometric model of the cracked integral blade disk based on the 3D geometric model of the intact blade disk. 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, 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 overall blade disk model is as follows Figure 2 shown.

[0062] Step 2: Based on the intact blade disk 3D geometric model, a dynamic model of the intact blade disk is constructed from the mechanism. Under actual operating conditions, the first-order mode of the intact blade disk is most likely to be excited and cause resonance. Therefore, the dynamic model of the intact blade disk is simplified to obtain the lumped parameter model of the intact blade disk. The equivalent multi-blade coupled lumped parameter model constructed 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 disk to simulate the breathing crack, and given the detuning strength, perform steady-state response analysis on the entire blade disk with breathing crack, calculate the steady-state response of each blade and analyze it. The formula for the applied nonlinear contact force is:

[0065]

[0066] In the formula, k nl is the contact stiffness, y is the crack blade displacement, and φ is the smoothing coefficient. As long as the value of φ is large enough, the normal relationship between the nonlinear force and the 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 blade finite element model, p is the contact pressure at each node of the contact surface, and x p Displacement of each node on the contact surface, S p The contact surface area is . The blade No. 4 in the present invention is a blade containing breathing cracks.

[0070] The present invention assumes that the slight differences between blades are differences in elastic modulus of blades to simulate the differences in natural frequencies between blades. If the detuning intensity is given, in each simulation, it is only necessary to generate random numbers according to normal distribution and assign them to each blade tip. It 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 ith 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 disk, and the nonlinear contact force F is added at the breathing crack blade. nl Equivalent breathing characteristics. The overall vibration equation is solved by the fourth-order variable step-size Runge-Kutta method to obtain the steady-state response of each blade.

[0078] When the excitation order EO=1 times the resonance frequency is applied to the integral blade disk with a detuning intensity 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 disk is only detuned, 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 cracks in the detuned integral blade disk, a harmonic response will appear on the blade, and its components are mostly even-order, such as the 2nd order, the 4th order, etc. These specific harmonic response components can be used as key signs to identify the existence 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 subsequent vibration characteristics analysis. The mesh is divided into hexahedral meshes, the mesh size is set to 1mm, the final number of meshes is 19080, the number of nodes is 99392, and the three-dimensional solid element SOLID186 is used. The finite element model of the harmonic solid blade disk is as follows: Figure 5 As shown, the 12 sectors of the integral blade disk are numbered in reverse order, 1 to 12 respectively.

[0080] During the expansion of the breathing crack, the crack shape is 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 crack shape and describe the nonlinear characteristics.

[0081] d=sd0

[0082] Where d is the length-to-depth ratio of the crack, which is used to define the actual shape of the crack. When performing finite element calculations, the specific values ​​of the expansion factor s are set to 1 / 12, 1 / 6, 1 / 4, 1 / 3, 1 / 2, and 2 / 3. When s is 1 / 3, it is the initial crack length. Taking the initial crack as the boundary, in the early stage of crack development, selecting more calculation points can help achieve earlier crack identification. When the crack reaches a certain extent, the blade often directly breaks, and there is no 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, 1 mm away from the blade root, a crack surface is set, and the crack is drawn separately. The shape is set to a semi-elliptical shape, with a crack length of 9.43 mm and a crack width of 0.67 mm. 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 shown in Figure 1. 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 to analyze the frequency domain response of the intact blade disk and the blade disk with breathing cracks in the detuning state. The frequency domain response results are shown in Figure 7 As shown. Figure 7It can be seen that in the detuned state, the breathing crack blade disk shows obvious nonlinear characteristics, which are manifested as 2nd and 4th order harmonic responses, which verify the results obtained in step 3.

[0085] The non-resonant vibration response analysis of the blade disk is performed by using n times the resonance frequency of the blade disk as the excitation frequency, and the detuning intensity is 2%. The frequency domain response results are shown in Figure 8 By analyzing the vibration response diagram, it can be found that the harmonic frequency orders generated by the blades with breathing cracks are basically the same, showing the 2nd, 3rd, and 4th order frequency, while the performance of other blades is different from the first-order resonant vibration response results.

[0086] Step 6: Based on the steady-state response analysis of the blade in step 3 and the resonant and non-resonant vibration responses of the blade disk with breathing cracks in step 5, define the overall blade disk harmonic index and the overall blade disk blade harmonic index H, which is defined as

[0087]

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

[0089] The harmonic indicators calculated from the resonant and non-resonant vibration responses in step 5 are shown in Table 1. In the practical application of integral blade crack identification, the excitation frequency of the first-order bending mode family is preferably used for vibration response analysis.

[0090] Table 1

[0091]

[0092] Definition of the harmonic index H for the blade of the blisk i ′, after confirming the presence of breathing cracks in the blade disk, this index is used to locate the blade with breathing cracks, which is defined as

[0093]

[0094] In the formula, H i2 is the second-order harmonic response component of each blade on the integral blade disk, H i3 is the third-order harmonic response component of each blade on the integral blade disk, H i0is the fundamental component in the vibration response of each blade on the integral blade disk, and the subscript i represents the blade number. In order to locate the blade with breathing crack in the integral blade disk, the second-order harmonic component of the blade is mainly used. The harmonic index is used to quantitatively describe the nonlinear characteristics generated by the breathing crack blade, and the vibration changes caused by the breathing crack can be specifically quantified. The above two harmonic indicators can effectively identify and locate the crack.

[0095] Step 7: Calculate the harmonic index of the entire blade disk through the defined harmonic index formula, and judge whether the entire blade disk contains breathing cracks based on whether the harmonic index is greater than 0. If breathing cracks exist, calculate the harmonic index of the blade of the entire blade disk to identify and locate the breathing cracks.

[0096] Fig. 9 is the harmonic index of the integral blade disk with breathing cracks in different states. Fig. 9 It can be seen that 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 it is confirmed that there is a crack in the integral blade disk, this method can be used to effectively identify and locate the crack.

[0097] In addition, the harmonic index can also be used to identify breathing cracks in detuned integral blades at different expansion stages. Fig.10 The variation trend of harmonic indexes in different expansion stages of the integral blade containing breathing cracks. Fig.10 It can be observed from the change trend of the harmonic index that in the initial stage of crack initiation, especially when the shape index is less than 1 / 6, the growth rate of the harmonic index is relatively slow. However, once the crack exceeds this threshold, the nonlinear growth becomes obvious and the growth rate accelerates, which can be used as a criterion for judging the occurrence of cracks.

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

[0099] Combining the above-mentioned overall blisk harmonic index and blade harmonic index, the crack with shape index s≥1 / 6 can be identified and located. At this time, the crack size is about 4.75 mm long and 0.3 mm wide. This method is sufficient to detect the newly initiated cracks in time under detuned conditions and can accurately identify the existence of multiple cracks, thereby preventing possible serious consequences.

Claims

1. A method for identifying blade cracks of a detuned integral blade disk, characterized in that: The following steps are involved: Step 1: Establish a 3D geometric model with the intact blade disk as the object, 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 3D geometric model of the intact blade disk, a dynamic model of the intact blade disk is constructed from the mechanism. Under actual operating conditions, the first-order mode of the intact blade disk is most likely to be excited and cause resonance. Therefore, the dynamic model of the intact blade disk is simplified to obtain a lumped parameter model of the intact blade disk. Step 3: Apply nonlinear contact force to the lumped parameter model of the intact blade disk to simulate the breathing crack, and give the detuning strength, perform steady-state response analysis on the entire blade disk with 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 the determination of the indicators in step 6; Step 4: Establish a finite element model based on the three-dimensional geometric model of the intact blade and the blade with breathing crack, and obtain the finite element model of the intact blade disk and the integral blade disk with breathing crack to meet the subsequent vibration characteristic analysis; Step 5: Given the same detuning intensity as in step 3, the finite element model is subjected to resonant and non-resonant vibration responses of the intact blade disk and the integral blade disk with breathing crack in the detuned state, and the corresponding frequency domain response results are obtained; 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, define the harmonic index of the entire blade disk and the harmonic index of the blade for the entire blade disk; Step 7: Calculate the harmonic index of the entire blade disk through the defined harmonic index formula, and determine whether the entire blade disk contains a breathing crack based on whether the harmonic index of the entire blade disk is greater than 0. If a breathing crack exists, calculate the harmonic index of the blade of the entire blade disk 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 ρ, Poisson's ratio μ and blade installation angle.

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: 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 damping model, and the coupling stiffness and coupling damping are k R and c R .

4. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: In step 3: the formula for the applied nonlinear contact force is: In the formula, 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 the displacement is smooth enough, and the breathing behavior of the crack can be simulated more accurately. k nl 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 blade finite element model, p is the contact pressure at each node of the contact surface, x is p Displacement of each node on the contact surface, S p is the contact surface area; The slight difference between the blades is set as the difference in elastic modulus of the blades to simulate the difference in natural frequency between the 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. It can be expressed as: k i =(1+δ i )k0 Where k0 is the ideal stiffness of each blade, k i is the stiffness of the i-th blade, δ i is the stiffness detuning amount; The above nonlinear contact force and given detuned strength are used to analyze the steady-state response of the integral blade with breathing crack, 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 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: F ext =F+[0 0 0 F nl … 0] T Where F is the traveling wave excitation matrix of the integrated blade disk with breathing crack, and the nonlinear contact force F is added at the breathing crack blade. 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 is analyzed, and it is found that the harmonic response nonlinearity of the blade occurs when only detuning exists in the blade disk and when breathing cracks exist in the detuned integral blade disk. Specifically, when only detuning exists in the integral blade disk, there is no harmonic response nonlinearity in the steady-state response diagram of each blade. When breathing cracks exist in the detuned integral blade disk, harmonic responses will appear on the blade, and most of their components are even-order. These specific harmonic response components can be used as key signs to identify the existence of breathing cracks.

5. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: The step 4 is specifically as follows: in the process of establishing the finite element model, hexahedral mesh is used for division, and contact pairs are created 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. d=sd0 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 to 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. 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: In step 5, the corresponding frequency domain response results are obtained as follows: no matter in the resonant or non-resonant vibration state, there are no nonlinear characteristics on the blades without breathing cracks in the detuned state, while on the blades with breathing cracks in the detuned state, relatively obvious nonlinear characteristics such as harmonic response appear, which are manifested as 2nd and 4th order harmonic responses, which verify each other with the results obtained in step 3.

7. The method for identifying blade cracks of a detuned blisk according to claim 1, characterized in that: In step 6: the blisk harmonic index H is: In the formula, 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 in the vibration response of each blade on the blade disk, 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 breathing cracks in the blade disk, this index is used to locate the blade containing breathing cracks, which is defined as In the formula, H i2 is the second-order harmonic response component of each blade on the integral blade disk, H i3 is the third-order harmonic response component of each blade on the integral blade disk, H i0 is the fundamental component in the vibration response of each blade on the integral blade disk, and the subscript i represents the blade number. The harmonic index is used to quantitatively describe the nonlinear characteristics caused by the breathing crack blade, and the vibration changes caused by the breathing crack can be specifically quantified. The above two harmonic indicators can be used to effectively identify and locate the crack.

8. 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 determined, and the existence of multiple cracks can be accurately identified.

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