A method for improving the aeroelastic stability of a blisk

Abstract

The present invention discloses a method for improving the aeroelastic stability of a bladed disk, comprising the following steps: Step S1: Measure the failure strain of a piezoelectric ceramic sheet when it is simultaneously subjected to a tensile load and a bending load; Step S2: Obtain the area where piezoelectric materials cannot be arranged in the blade part and the strain distribution of each unit in the blade part under the target mode, and calculate the equivalent electric field strength; Step S3: Arrange and paste piezoelectric materials with a specified amount of piezoelectric materials; Step S4: Adjust the coordinate system of the piezoelectric material unit and couple the electrodes; Step S5: Use the cyclic symmetric boundary condition to perform a static strength check on the bladed disk after the piezoelectric material has been pasted and arranged; Step S6: Connect the piezoelectric material electrodes on each blade to an external capacitor, adjust the value of the capacitor connected to each blade, realize the adjustment of the target mode frequency of the blade, complete the mistuning design of the bladed disk, and finally improve the aeroelastic stability of the bladed disk; The present invention provides a reliable and easy-to-use means for improving the aeroelastic stability of a bladed disk.

Description

Technical Field

[0001] The present invention relates to the field of blisks, and particularly to a method for improving the aeroelastic stability of blisks. Background Technique

[0002] Prior art one, "An optimized design method for embedded piezoelectric shunt damping for a general blisk structure". In this invention, its technical flow chart is as Figure 1 shown. The inventor arranges piezoelectric materials in an inlaid manner. Its optimal arrangement criterion is that the position with the maximum electric field intensity of the piezoelectric material is the optimal arrangement area, and the limiting condition is the amount of piezoelectric material used. Its arrangement is as follows: establish a single-sector finite element model of the target blisk structure, and divide the model into components to facilitate the selection of areas during the subsequent piezoelectric material arrangement process, as Figure 2 shown.

[0003] Set the relevant material parameters of the arranged piezoelectric materials, set parameters such as the target position of piezoelectric material arrangement, the amount of piezoelectric material used, and optimize parameters such as the target mode;

[0004] Conduct a cyclic modal analysis on the blisk structure, extract the unit principal strain data of the blisk in the target area of piezoelectric material arrangement under the target mode, and modify the coordinate system of the structural units in the target area of the blisk so that the z direction of its unit coordinate system points to the outer surface of the structure. This is because the piezoelectric ceramic material is transversely isotropic, so the x and y directions of the unit coordinate system do not need to be specified separately;

[0005] Using the unit principal strain data of the target area of the blisk, combined with the piezoelectric parameters of the piezoelectric material, calculate the electric field intensity of each unit, and sort the units according to the absolute value of the electric field intensity, with the units with larger absolute values of the electric field intensity ranked in the front;

[0006] In the order of the electric field intensity of the units, replace the original structural units with piezoelectric units one by one until the mass ratio of the piezoelectric material to the mass of the target structure of the blisk reaches the set value;

[0007] For piezoelectric units with a negative electric field intensity, it is necessary to reverse the z direction of its unit coordinate system to make its electric field intensity positive;

[0008] Couple the voltage degrees of freedom on the inner surface of the piezoelectric units on the single sector of the blisk as the negative electrode of the piezoelectric material, and couple the voltage degrees of freedom on the outer surface of the piezoelectric units as the positive electrode of the piezoelectric material;

[0009] Expand the single-sector model of the bladed disk with the piezoelectric material layout completed to the entire sector, set open-circuit and short-circuit conditions for the piezoelectric materials in the full-circle model of the bladed disk, calculate the corresponding modal frequencies, and obtain the electromechanical coupling coefficients for the target mode under the set amount of piezoelectric material used to determine the damping effect of the optimized layout scheme on the target mode.

[0010] Disadvantages of the prior art I:

[0011] 1. The piezoelectric material layout method is inlay layout, which damages the original structure. When the target working condition changes, the optimal layout position of the piezoelectric material changes accordingly, and the already processed structure cannot be repaired for the re-layout of the piezoelectric material, which results in that the piezoelectric material layout scheme for a specific working condition cannot adapt to the change of the working condition.

[0012] 2. The reliability factor is not considered during the layout of the piezoelectric materials in this patent. However, the bladed disk rotates at a high speed during operation, and the blade part bears a large centrifugal load. Compared with metal materials, the strength of piezoelectric ceramic materials is lower. And there is a large overlap between the optimal layout position of the piezoelectric material and the area with a high stress level on the blade, which requires considering the reliability problem of the piezoelectric material layout on the blade part under the service state.

[0013] 3. The inlay layout of the piezoelectric material causes damage to the original structure, which leads to a decrease in the strength of the original structure, and there is a risk of structural failure of the bladed disk under the design working condition.

[0014] Prior art II

[0015] Groth et al. achieved the change of the stiffness of each sector of the bladed disk by machining grooves in each sector of the bladed disk, adjusted the natural frequencies of different blades by changing the geometric dimensions of the machined grooves, and finally achieved the mistuning design to improve the aeroelastic stability of the bladed disk.

[0016] Figaschewsky et al. achieved the required adjustment of the blade natural frequencies by applying heavy paint on the blades. According to the required frequency change, different thicknesses of heavy paint were applied to each blade to change the mass of each blade, and the required frequency change of each blade in the circumferential direction was achieved to realize the mistuning design, thereby improving the aeroelastic stability of the blade row.

[0017] Roque et al. adjusted the modal frequencies of each blade by adding mass blocks on the blades. According to the different added mass blocks, the natural frequencies of different blades changed differently, so as to achieve the change of the blade modal frequencies along the circumferential direction according to a certain rule, that is, to realize the mistuning design, and finally improve the aeroelastic stability of the bladed disk.

[0018] Disadvantages of the prior art II:

[0019] The detuning design is achieved by modifying the structural parameters, which requires machining and has high requirements for machining accuracy.

[0020] Machining is irreversible. Each specimen can only be used for specific working conditions and is difficult to modify, which increases the cost of experiments and tests.

[0021] It is difficult to precisely control the strength of the detuning design, and it is difficult to quantify the relationship between the size of the added mass or the machined groove and the change in the blade modal frequency.

[0022] The aeroelastic stability of bladed disks is a key concern for researchers and designers. Piezoelectric materials, with their superior electromechanical coupling performance and ease of use, combined with external circuits to form piezoelectric technology, have become a new method to improve the aeroelastic stability of bladed disks. Currently, the effective means to improve the aeroelastic stability of bladed disks is the artificial detuning design. By machining, the mass or stiffness of each blade in the bladed disk changes circumferentially according to a certain law. Its essence is to adjust the natural vibration frequency of each blade. However, the machining method is irreversible, has high requirements for machining accuracy, and it is difficult to quantify the precise relationship between the machining amount and the change in the blade natural frequency.

[0023] The invention aims at the aeroelastic stability problem of the bladed disk structure and proposes to paste piezoelectric materials on the surface of the blades of the bladed disk. By adjusting the numerical value of the capacitance circuit connected to the electrodes of the piezoelectric materials, the natural vibration frequency of the blades is adjusted. The electrodes of the piezoelectric materials pasted on each blade are respectively connected to the capacitance circuit, and the circumferential change law of the connected capacitance value is adjusted to realize the circumferential change of the blade natural frequency in the target manner, equivalently realizing the artificial detuning design, thereby improving the aeroelastic stability of the bladed disk. To ensure the reliability of the piezoelectric coupling structure during operation, the invention also proposes a method for measuring the strength limit of piezoelectric ceramic materials under simulated service conditions.

[0024] When pasting piezoelectric materials, the position where the electric field strength of the piezoelectric material is the largest under the specified working conditions is used as the best pasting position of the piezoelectric material. However, the position where the electric field strength of the piezoelectric material is the largest coincides greatly with the position where the blade strain is the largest. At the same time, during the operation of the bladed disk, it is in a high-speed rotation state, and the blades bear a large centrifugal load. The strength of the piezoelectric material is much lower than that of metal materials. Therefore, its reliability has an important impact on the overall safety of the bladed disk. When pasting piezoelectric materials, it is necessary not only to maximize the electromechanical coupling ability of the piezoelectric materials but also to ensure the reliability of the structure during operation. Summary of the Invention

[0025] To solve the problems existing in the prior art, the invention provides a method for improving the aeroelastic stability of bladed disks, which provides a reliable and easy-to-use method for maximizing the aeroelastic stability of bladed disks.

[0026] The specific technical solution is as follows:

[0027] A method for improving the aeroelastic stability of a blisk, comprising the following steps:

[0028] Step S1: Measure the failure strain of a piezoelectric ceramic sheet when it is simultaneously subjected to tensile load and bending load;

[0029] Step S2: Obtain the areas where piezoelectric materials cannot be arranged in the blade part and the strain distribution of each element in the blade part under the target mode, and calculate the equivalent electric field strength;

[0030] Step S3: Paste and arrange piezoelectric materials with a specified amount of piezoelectric materials;

[0031] Step S4: Adjust the coordinate system of the piezoelectric material unit and perform electrode coupling;

[0032] Step S5: Use cyclic symmetric boundary conditions to check the strength of the blisk after the piezoelectric material is pasted and arranged;

[0033] Step S6: Connect the piezoelectric material electrodes on each blade to an external capacitor, adjust the values of the capacitors connected to each blade, adjust the target modal frequency of the blade, realize the detuning design of the blisk, and finally improve the aeroelastic stability of the blisk.

[0034] Preferably, step S1 includes the following sub-steps:

[0035] Sub-step S11: Fabricate a tensile test specimen and build an experimental system;

[0036] Sub-step S12: Measure the elastic modulus of the metal base material using the test specimen. The strain gauges are symmetrically pasted, the loading speed of the tensile load is 0.5 mm / min, the strain measurement method adopts the 1 / 2 bridge measurement method, record the surface strain of the tensile piece under different loads, and calculate the elastic modulus of the metal base;

[0037] Sub-step S13: Measure the elastic modulus of the piezoelectric ceramic sheet using the specimen, and symmetrically paste the piezoelectric ceramic sheet at the middle position of the metal base specimen;

[0038] Sub-step S14: The paste uses aviation epoxy resin glue and is consolidated by means of vacuum pumping. After completion, strain gauges are respectively pasted at the middle position of the piezoelectric ceramic sheet;

[0039] Sub-step S15: Measure the surface strain of the piezoelectric ceramic sheet under different tensile loads using the 1 / 2 bridge method, the loading speed of the tensile load is 0.5 mm / min, and calculate the elastic modulus of the piezoelectric ceramic sheet using the elastic modulus of the metal base;

[0040] Sub-step S16: Obtain the failure strain of the piezoelectric ceramic sheet;

[0041] Sub-step S17: Take another piezoelectric ceramic sheet and paste a single piezoelectric ceramic sheet at the middle position of the metal substrate specimen;

[0042] Sub-step S18: Obtain the strain level corresponding to the failure of the piezoelectric ceramic sheet by using the specimen in sub-step S17. During the experiment, the loading speed of the tensile load is set to 0.5 mm / min. Measure the surface strain of the piezoelectric ceramic sheet under different tensile loads by using the 1 / 4 bridge method, and obtain the load-strain curve.

[0043] Sub-step S19: Extract and process the load-strain data of the specimen obtained in sub-step S18 to obtain the strain level corresponding to the sudden increase in the surface strain of the piezoelectric ceramic. This strain level is the failure strain εmax of the piezoelectric ceramic when it simultaneously bears tensile load and bending load under the simulated service state.

[0044] Preferably, step S2 includes the following sub-steps:

[0045] Sub-step S21: First, use the mesh generation tool to generate a mesh for the single-sector model of the bladed disk. Use structured meshes for mesh generation, and establish the blade surface suction side element and pressure side element components. Divide and establish the periodic boundary mesh for subsequent analysis preparation;

[0046] Sub-step S22: Conduct a mesh independence verification for the mesh. The standard is to calculate the modal frequency of the structure by using ANSYS software. When the modal frequency no longer changes significantly with the increase of the mesh density, the mesh independence detection is completed;

[0047] Sub-step S23: Import the finite element model that has completed the mesh independence detection into Ansys software for static analysis. Use the periodic boundary conditions to expand the single-sector finite element model of the bladed disk into a complete bladed disk, set the rotational speed to the designed rotational speed of the bladed disk, and obtain the maximum principal strain of each element at the blade part under the designed rotational speed;

[0048] Sub-step S24: Compare the maximum principal strain of each element at the blade part with the failure strain of the piezoelectric ceramic obtained in step S1. When the maximum principal strain of the element exceeds the failure strain εmax, set this element as an element where piezoelectric material cannot be arranged. Traverse all the blade surface elements, mark the elements that exceed the failure strain of the piezoelectric ceramic as failed elements, and do not arrange piezoelectric materials at these positions subsequently;

[0049] Sub-step S25: Use the periodic cyclic boundary conditions to conduct a modal analysis on the bladed disk, extract the principal strain of each element on the blade surface under the target mode, and calculate the electric field strength that can be generated by the element strain by using the constitutive characteristics of the piezoelectric material Sort the absolute values of the element electric field strengths, and subsequently arrange and paste the piezoelectric materials in the order of the absolute values of the electric field strengths.

[0050] Preferably, step S3 includes the following sub-steps:

[0051] Sub-step S31: Set the amount of piezoelectric material used, Rm, which is the ratio of the mass of the piezoelectric material to the mass of the blade;

[0052] Sub-step S32: Set the unit coordinate system for each unit on the blade surface;

[0053] The piezoelectric material is a transversely isotropic material. For the piezoelectric material arranged by pasting, it is necessary to adjust the z direction of its unit coordinate system to the outer normal direction of the pasting surface. The unit coordinate system of the blade base unit prepares for the subsequent adjustment of the unit coordinate system of the piezoelectric unit;

[0054] Sub-step S34: Establish birth and death elements on the blade surface of the disk;

[0055] Sub-step S35: According to the electric field intensity calculated for each unit on the blade surface in the target mode, activate the corresponding birth and death elements of the blade surface units in sequence, modify the birth and death elements into piezoelectric units, and modify the piezoelectric unit coordinate system into the unit coordinate system of the corresponding blade surface unit;

[0056] Sub-step S36: Activate the birth and death elements in sequence according to the magnitude of the electric field intensity of the blade surface units and perform the above operations until the amount of piezoelectric material used reaches the required amount Rm, and delete the unused birth and death elements.

[0057] Preferably, sub-step S34 includes the following sub-steps:

[0058] Sub-step S341: Establish an array Nb of the node numbers on the blade surface;

[0059] Sub-step S342: Traverse each node in a loop. For each node Nb[i], obtain the element it belongs to and find the element Emin with the smallest number among them;

[0060] Sub-step S343: Convert the current working coordinate system to the unit coordinate system corresponding to the element Emin. Using the coordinates of the element Emin in the current working coordinate system, establish a new node Nb[i]+n, where n is a value greater than the largest node number in the current model. The x and y coordinates of the node Nb[i]+n in the current coordinate system are the same as the x and y of the node Nb[i], and the z coordinate is the z coordinate of the node Nb[i] plus the thickness value of the piezoelectric material used, and complete the operation on all the blade surface nodes;

[0061] Sub-step S344: Use the newly established nodes and the existing blade surface nodes to establish pasting elements and establish an array Eb of the blade surface unit numbers;

[0062] Sub-step S345: Obtain the array of node numbers Enb of the nodes belonging to the blade surface in element Eb[i], sort them according to the node number size, and establish a new element using the finite element node labeling rule. The order of the node numbers used is Enb[1], Enb[2], Enb[3], Enb[4], Enb[1]+n, Enb[2]+n, Enb[3]+n, Enb[4]+n;

[0063] Sub-step S346: Complete the establishment of the elements pasted on the blade surface, and set the newly established elements as birth-death elements without activation.

[0064] Preferably, step S4 includes the following sub-steps:

[0065] Sub-step S41: According to the electric field strength calculated for the blade surface elements in the target mode, when the electric field strength corresponding to the blade element is negative, reverse the z direction of the unit coordinate system of the piezoelectric element corresponding to the blade element to ensure that the piezoelectric elements in contact with the blade have the same electric potential, and complete the bladed disk with piezoelectric material arrangement;

[0066] Sub-step S42: Couple the voltage degrees of freedom of the piezoelectric elements on a single blade, and set the electrode on the side connected to the blade of the piezoelectric element as the negative electrode and the electrode on the outer surface of the piezoelectric element as the positive electrode.

[0067] Preferably, step S5 includes the following sub-steps:

[0068] Sub-step S51: Expand the single-sector bladed disk to a full circle, perform a static analysis at the designed rotational speed of the bladed disk, and obtain the maximum strain of each element in the blade part of the bladed disk at the designed rotational speed;

[0069] Sub-step S52: Ensure that under the piezoelectric material arrangement area, its maximum strain is lower than the failure strain of the piezoelectric material.

[0070] The beneficial effects of a method for improving the aeroelastic stability of a bladed disk according to the present invention are as follows:

[0071] 1. Aiming at the irreversibility and non-adjustability of the inlaid arrangement of piezoelectric materials and the problem of damage to the original structural strength, the present invention proposes to paste and arrange the piezoelectric materials on the blade surface. According to the change of the target working condition, the original piezoelectric materials can be removed and re-arranged according to the new target working condition, minimizing the impact on the original structure and ensuring the strength of the original bladed disk structure;

[0072] 2. When piezoelectric materials are inlaid and arranged, the reliability of piezoelectric materials under the design conditions of the blisk is not considered. The present invention proposes a measurement scheme for the strength limit of piezoelectric ceramic materials under service conditions, and considers its strength limit when arranging piezoelectric materials, so that the distribution area of piezoelectric materials meets the requirements of the strength limit of piezoelectric materials, ensuring the structural integrity of the blisk with piezoelectric materials under the design conditions;

[0073] 3. Aiming at the current deficiency of realizing detuning design through machining to improve the aeroelastic stability of the blisk: machining is irreversible and requires high precision. The present invention proposes to connect the electrodes of the piezoelectric materials arranged on the surfaces of the blades with a capacitance circuit, and adjust the aeroelastic stability of the blisk by adjusting the value of the capacitance, so as to realize the change of the modal frequencies of the blades. Moreover, this method can accurately establish the relationship between the change amount of the blade modal frequency and the value of the external capacitance, with higher precision, so as to maximize the aeroelastic stability of the blisk under the condition of limited piezoelectric material usage. Brief Description of the Drawings

[0074] Figure 1 It is a flowchart of the prior art I of the present invention.

[0075] Figure 2 It is a single-sector finite element model diagram of the prior art I of the present invention.

[0076] Figure 3 It is a design diagram of the base specimen of the present invention.

[0077] Figure 4 It is a diagram of each geometric parameter of the base tensile specimen of the present invention.

[0078] Figure 5 It is a diagram of the metal base specimen for measuring the elastic modulus of the base of the present invention.

[0079] Figure 6 It is a diagram of the specimen with double-sided pasted piezoelectric ceramic sheets for measuring the tensile elastic modulus of piezoelectric ceramics of the present invention.

[0080] Figure 7 It is a diagram of the specimen with single-sided pasted piezoelectric ceramic sheets for measuring the strength limit of piezoelectric ceramic materials under asymmetric installation conditions of the present invention.

[0081] Figure 8 It is a diagram of the experimental system for testing the strength limit of piezoelectric ceramic sheets of the present invention.

[0082] Figure 9 It is a diagram of the maximum strain distribution on the blade surface of the blisk of the present invention at the design rotational speed.

[0083] Figure 10 It is a schematic diagram of the direction of the unit coordinate system on the blade surface of the present invention.

[0084] Figure 11The nodal diameter diagram of the blade disk modal frequency of the present invention

[0085] Figure 12 The blade disk modal vibration mode diagram shown by the circles in the above figure of the invention.

[0086] Figure 13 The failure unit identification method diagram of the present invention

[0087] Figure 14 The flowchart of the piezoelectric material paste layout optimization considering strength factors of the present invention

[0088] Figure 15 The flowchart of generating surface birth and death elements of the present invention

[0089] Figure 16 The diagram of the static strength check of the blade disk at the designed rotational speed after pasting piezoelectric materials according to the present invention

[0090] Figure 17 The external capacitor diagram of the piezoelectric material electrode of the present invention

[0091] Figure 18 The relationship diagram between the blade modal frequency and the external capacitance value of the present invention

[0092] Figure 19 The diagram of adjusting the target modal frequency of the blade according to the present invention Specific implementation manners

[0093] The following illustrates the implementation manners of the present invention through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following examples only illustrate the basic concept of the present invention in a schematic manner.

[0094] A method for improving the aeroelastic stability of a blade disk, the specific steps are as follows:

[0095] 1. Measurement of the failure strain of piezoelectric ceramic sheets under tensile and bending loads

[0096] Fabricate tensile test specimens as Figure 5 , Figure 6 and Figure 7 . Paste strain gauges at the middle position of the specimens. The geometric shapes and related geometric parameters of the tensile specimens are as Figure 3 and Figure 4 shown. Build the experimental system as Figure 8 shown;

[0097] Utilize Figure 5The experimental specimen shown measures the elastic modulus of the metal base material. The strain gauges are symmetrically pasted, the tensile load loading speed is 0.5 mm / min, and the strain measurement method adopts the 1 / 2 bridge measurement method. The surface strain of the tensile part under different loads is recorded, and the elastic modulus of the metal base is calculated;

[0098] use Figure 6 The elastic modulus of the piezoelectric ceramic piece is measured by the specimen shown. The piezoelectric ceramic piece is symmetrically pasted in the middle of the metal base specimen. The pasting adopts aviation epoxy resin glue and is consolidated by vacuuming. After completion, strain gauges are pasted in the middle of the piezoelectric ceramic piece. The surface strain of the piezoelectric ceramic piece under different tensile loads is measured by the 1 / 2 bridge method. The tensile load loading speed is 0.5mm / min. The elastic modulus of the piezoelectric ceramic piece is calculated by using the elastic modulus of the metal base.

[0099] use Figure 7 The specimen shown obtains the strain level corresponding to the failure of the piezoelectric ceramic piece. The tensile load loading speed is set to 0.5mm / min. The surface strain of the piezoelectric ceramic piece under different tensile loads is measured using the 1 / 4 bridge method. During the experiment, the load-displacement curve is monitored. When the curve jumps, it indicates that the specimen has failed. At the same time, the voltage-controlled current source, oscilloscope, and signal generator are used to monitor the voltage change of the piezoelectric electrode. When the voltage amplitude suddenly increases, it indicates that the piezoelectric ceramic electrode has failed.

[0100] The specimen load-strain data obtained in the previous step are extracted and processed to obtain the strain level corresponding to the sudden increase in the surface strain of the piezoelectric ceramic. This strain level is the failure strain εmax of the piezoelectric ceramic when it is subjected to both tensile load and bending load under simulated service conditions.

[0101] 2. Obtain the electric field strength of each unit in the area where piezoelectric materials cannot be arranged and the blade part under the target mode. The specific steps are as follows:

[0102] I. First, use a meshing tool (such as ICEM) to mesh the single sector model of the blade disk, use structured meshing to mesh, and establish blade surface blade basin unit and blade back unit components, divide and establish periodic boundary meshes, and prepare for subsequent analysis;

[0103] II. Verify the mesh independence of the mesh. The standard is to use commercial software (such as Ansys) to calculate the modal frequency of the structure. When the modal frequency no longer changes significantly with the increase of mesh density, the mesh independence monitoring is completed;

[0104] III. Import the finite element model that has completed grid independence detection into a commercial calculation software (such as Ansys) for static analysis. Use periodic boundary conditions to expand the single-sector finite element model of the blisk into a complete blisk, set the rotational speed to the designed rotational speed of the blisk, and obtain the maximum principal strain of each element at the blade part under the designed rotational speed;

[0105] IV. Compare the maximum principal strain of each element at the blade part with the failure strain of the piezoelectric ceramics obtained from the first-step experiment measurement. When the maximum principal strain of the element exceeds the failure strain ε max , set this element as an element where no piezoelectric material can be arranged. Traverse all the surface elements of the blades, and mark the elements that exceed the failure strain of the piezoelectric ceramics as failed elements (the identification result is as shown in Figure 9 , and mark the failed elements with a black frame), and do not arrange piezoelectric materials at these parts in the follow-up. The specific process is as shown in Figure 13 ;

[0106] V. Use periodic cyclic boundary conditions to perform modal analysis on the blisk (such as the blisk modal information shown in Figure 11 and Figure 12 ), extract the principal strain of each element on the blade surface under the target mode, and use the constitutive characteristics of the piezoelectric material to calculate the electric field strength that can be generated by the element strain Sort the absolute values of the element electric field strengths, and then arrange the piezoelectric materials in the order of the absolute values of the electric field strengths. III. Arrange the piezoelectric materials under the specified piezoelectric material usage, and the specific steps are as follows: I. Set the piezoelectric material usage R m , and this usage is the ratio of the mass of the piezoelectric material to the mass of the blade;

[0107] II. Set the element coordinate system of each element on the blade surface. Since the blade base material is an isotropic metal material,

[0108] changing the element coordinate system has no effect on its characteristics. While the piezoelectric material belongs to a transversely isotropic material, for the piezoelectric materials arranged by pasting, it is necessary to adjust the z direction of its element coordinate system to the outer normal direction of the pasting surface, as shown in Figure 10 , and the element coordinate system of the blade base unit prepares for adjusting the element coordinate system of the piezoelectric unit in the follow-up;

[0109] III. Establish birth-death elements on the blade surface of the blisk. The specific process is as shown in Figure 15 :

[0110] 1) Establish an array Nb of the node numbers on the blade surface;

[0111] 2) Traverse each node in a loop. For each node Nb[i], obtain the element it belongs to, and then find the element E with the smallest number among them min ;

[0112] 3) Convert the current working coordinate system to element E min to the corresponding element coordinate system, and use the coordinates of element E min in the current working coordinate system to establish a new node Nb[i]+n, where n is a value greater than the largest node number in the current model. The x and y coordinates of node Nb[i]+n in the current coordinate system are the same as those of node Nb[i], and the z coordinate is the z coordinate of node Nb[i] plus the thickness value of the piezoelectric material used, and complete the operation on all the nodes on the blade surface;

[0113] 4) Use the newly created nodes and the existing nodes on the blade surface to establish bonding elements and establish an array Eb of the element numbers on the blade surface;

[0114] 5) Obtain the array Enb of the numbers of the nodes belonging to the blade surface in element Eb[i], sort them according to the node number size, and use the finite element node numbering rule to establish new elements. The order of the node numbers used is Enb[1], Enb[2], Enb[3], Enb[4], Enb[1]+n, Enb[2]+n, Enb[3]+n, Enb[4]+n;

[0115] 6) Complete the establishment of the bonding elements on the blade surface and set the newly created elements as birth-death elements without activation.

[0116] IV. According to the electric field intensity calculated for the elements on the blade surface in the target mode, activate the birth-death elements corresponding to the elements on the blade surface in sequence, modify the elements to piezoelectric elements, and modify the element coordinate system to the element coordinate system of the corresponding element on the blade surface;

[0117] V. Activate the birth-death elements in sequence according to the magnitude of the electric field intensity of the elements on the blade surface and perform the above operations until the amount of piezoelectric material used reaches the required amount R m , and delete the unused birth-death elements;

[0118] IV. Conduct adjustment of the element coordinate system and electrode coupling of the piezoelectric elements

[0119] I. According to the electric field intensity calculated for the elements on the blade surface in the target mode, when the electric field intensity corresponding to the blade element is negative, reverse the z direction of the element coordinate system of the corresponding piezoelectric element to ensure that the piezoelectric elements in contact with the blade have the same electric potential, and the bladed disk with the piezoelectric material arranged is as Figure 16 shown;

[0120] II. Couple the voltage degrees of freedom of the piezoelectric elements on a single blade, and set the electrode on the side connected to the blade of the piezoelectric element as the negative electrode and the electrode on the outer surface of the piezoelectric element as the positive electrode;

[0121] V. Perform strength verification on the bladed disk with the piezoelectric materials pasted and arranged. The specific method is to use the cyclic symmetric boundary to expand a single-sector bladed disk into a full circle and conduct a static analysis at the designed rotational speed of the bladed disk to obtain the maximum strain of each element at the blade part in the bladed disk at the designed rotational speed. As Figure 17 shown, ensure that in the area where the piezoelectric materials are arranged, the maximum strain is lower than the failure strain of the piezoelectric materials;

[0122] VI. Connect the electrodes of the piezoelectric materials on each blade to an external capacitor (as Figure 18 shown), adjust the values of the capacitors connected to each blade, and adjust the target modal frequency of the blade (as Figure 19 shown) to achieve the mistuning design of the bladed disk and ultimately improve the aeroelastic stability of the bladed disk.

[0123] VII. The material parameters used in the demonstration example are listed in Table 1, and the overall technical solution is as Figure 14 shown.

Claims

1. A method for improving the aeroelastic stability of a blisk, characterized in that Including the following steps: Step S1: Measure the failure strain of the piezoelectric ceramic sheet when it is simultaneously subjected to tensile load and bending load; Step S2: Obtain the area where piezoelectric materials cannot be arranged in the blade part and the strain distribution of each unit in the blade part under the target mode, and calculate the equivalent electric field strength; Step S3: Conduct the pasting and arrangement of piezoelectric materials with a specified amount of piezoelectric materials; Step S4: Adjust the coordinate system of the piezoelectric material unit and couple the electrodes; Step S5: Use the cyclic symmetric boundary condition to check the strength of the bladed disk after the pasting and arrangement of piezoelectric materials are completed; Step S6: Connect the piezoelectric material electrodes on each blade to an external capacitor, adjust the values of the capacitors connected to each blade, realize the adjustment of the target mode frequency of the blade, complete the mistuning design of the bladed disk, and finally improve the aeroelastic stability of the bladed disk; The said Step S1 includes the following sub-steps: Sub-step S11: Manufacture a tensile test specimen, paste strain gauges at the middle position of the specimen, and build an experimental system; Sub-step S12: Measure the elastic modulus of the metal base material using the experimental specimen. The strain gauges are symmetrically pasted. The loading speed of the tensile load is 0.5 mm / min. The strain measurement method adopts the 1 / 2 bridge measurement method. Record the surface strain of the tensile piece under different loads, and calculate to obtain the elastic modulus of the metal base; Sub-step S13: Measure the elastic modulus of the piezoelectric ceramic sheet using the specimen, and symmetrically paste the piezoelectric ceramic sheet at the middle position of the metal base specimen; Sub-step S14: The pasting uses aviation epoxy resin glue and is consolidated by means of vacuum pumping. After completion, paste strain gauges at the middle position of the piezoelectric ceramic sheet respectively; Sub-step S15: Measure the surface strain of the piezoelectric ceramic sheet under different tensile loads using the 1 / 2 bridge method. The loading speed of the tensile load is 0.5 mm / min. Use the elastic modulus of the metal base to calculate the elastic modulus of the piezoelectric ceramic sheet; Sub-step S16: Obtain the failure strain of the piezoelectric ceramic sheet; Sub-step S17: Take another piezoelectric ceramic sheet and paste a single piezoelectric ceramic sheet at the middle position of the metal base specimen; Sub-step S18: Use the specimen in Sub-step S17 to obtain the strain level corresponding to the failure of the piezoelectric ceramic sheet. During the experiment, the loading speed of the tensile load is set to 0.5 mm / min. Use the 1 / 4 bridge method to measure the surface strain of the piezoelectric ceramic sheet under different tensile loads and obtain the load-displacement curve; Sub-step S19: Extract and process the load-strain data of the specimen obtained in Sub-step S18 to obtain the strain level corresponding to the sudden increase in the surface strain of the piezoelectric ceramic. This strain level is the failure strain εmax of the piezoelectric ceramic when it simultaneously bears tensile load and bending load under the simulated service state; The said Step S2 includes the following sub-steps: Sub-step S21: First, use a mesh generation tool to generate a mesh for the single-sector model of the bladed disk. Use structured meshes for mesh generation, and establish the blade surface basin unit and back unit components, and divide and establish the periodic boundary mesh for subsequent analysis preparation; Sub-step S22: The grid is verified for grid independence. The criterion is to calculate the modal frequency of the structure using ANSYS software. When the modal frequency no longer changes significantly with the increase in grid density, the grid independence monitoring is completed. Sub-step S23: Import the finite element model that has completed the grid independence detection into Ansys software for static analysis. Use the periodic boundary condition to expand the single-sector finite element model of the blisk into a complete blisk, set the rotational speed to the designed rotational speed of the blisk, and obtain the maximum principal strain of each surface element at the blade part under the designed rotational speed. Sub-step S24: Compare the maximum principal strain of each surface element at the blade part with the failure strain of the piezoelectric ceramic measured in step S1. When the maximum principal strain of the element exceeds the failure strain εmax, set the area of this element as the non-arrangement area. Traverse all the surface elements of the blade, mark the elements that exceed the failure strain of the piezoelectric ceramic as failed elements, and do not arrange piezoelectric materials at these parts subsequently. Sub-step S25: Using the periodic cyclic boundary condition, perform modal analysis on the bladed disk, extract the principal strain of each element on the blade surface in the target mode, and calculate the electric field strength that can be generated by the element strain using the constitutive characteristics of the piezoelectric material , sort the absolute values of the element electric field strengths, and subsequently arrange the piezoelectric material paste according to the order of the absolute values of the electric field strengths The said step S3 includes the following sub-steps: Sub-step S31: Set the piezoelectric material usage amount Rm, which is the ratio of the mass of the used piezoelectric material to the mass of the blade. Sub-step S32: Set the element coordinate system of each element on the blade surface. Sub-step S33: The piezoelectric material belongs to a transversely isotropic material. For the piezoelectric material arranged by pasting, it is necessary to adjust the z direction of its element coordinate system to the outer normal direction of the pasted surface. The element coordinate system of the blade base unit prepares for the subsequent adjustment of the element coordinate system of the piezoelectric unit. Sub-step S34: Establish birth-death elements on the blade surface of the blisk. Sub-step S35: According to the electric field intensity calculated for each surface element of the blade in the target mode, activate the corresponding birth-death elements of each surface element of the blade in sequence, and modify the birth-death elements into piezoelectric elements. Modify the piezoelectric element coordinate system to the element coordinate system of the corresponding blade surface element. Sub-step S36: Activate the birth-death elements in sequence according to the magnitude of the electric field intensity of each surface element of the blade and perform the operation of sub-step S35 until the usage amount of the piezoelectric material used reaches the required amount Rm, and delete the unused birth-death elements. The said sub-step S34 includes the following sub-steps: Sub-step S341: Establish an array Nb of the node numbers on the blade surface. Sub-step S342: Traverse each node in a loop. For each node Nb[i], obtain the element it belongs to and find the element Emin with the smallest number among them. Sub-step S343: Convert the current working coordinate system to the element coordinate system corresponding to the element Emin. Use the coordinates of the element Emin in the current working coordinate system to establish a new node Nb[i]+n, where n is a value greater than the maximum node number in the current model. The x and y coordinates of the node Nb[i]+n in the current coordinate system are the same as the x and y coordinates of the node Nb[i], and the z coordinate is the z coordinate of the node Nb[i] plus the thickness value of the used piezoelectric material. Complete the operation for all the nodes on the blade surface. Sub-step S344: Use the newly established nodes and the existing nodes on the blade surface to establish pasting elements and establish an array Eb of the element numbers on the blade surface. Sub-step S345: Obtain the array Enb of the numbers of the nodes belonging to the blade surface in the element Eb[i], sort them according to the node number size, and use the finite element node labeling rule to establish a new element. The order of the node numbers used is Enb[1], Enb[2], Enb[3], Enb[4], Enb[1]+n, Enb[2]+n, Enb[3]+n, Enb[4]+n; Sub-step S346: Complete the establishment of the elements pasted on the blade surface, and set the newly established elements as birth-death elements without activation; The said step S4 includes the following sub-steps: Sub-step S41: According to the electric field intensity calculated for the blade surface elements in the target mode, when the electric field intensity corresponding to the blade element is negative, reverse the z direction of the unit coordinate system of the piezoelectric element corresponding to the blade element to ensure that the surfaces of the piezoelectric elements in contact with the blade have the same electric potential, and complete the arrangement of the piezoelectric materials on the bladed disk; Sub-step S42: Couple the voltage degrees of freedom of the piezoelectric elements on a single blade, and set the electrode on the side connected to the blade of the piezoelectric element as the negative electrode and the electrode on the outer surface of the piezoelectric element as the positive electrode; The said step S5 includes the following sub-steps: Sub-step S51: Expand the single-sector bladed disk to a full circle, conduct a static analysis at the designed rotational speed of the bladed disk, and obtain the maximum strain of each element in the blade part of the bladed disk at the designed rotational speed; Sub-step S52: Ensure that under the piezoelectric material arrangement area, its maximum strain is lower than the failure strain of the piezoelectric material.

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