Device and Method for Identifying Contact Stiffness and Damping of Tenon Connection Structure

Abstract

The present invention belongs to the field of aerospace mechanical design, and proposes a contact stiffness and damping identification device and identification method for a tenon connection structure. The device includes a blade disk, a blade disk bracket, a base plate and a vibration table; the integral structure composed of the blade disk and the blade disk bracket is provided with a through hole, and the through hole includes a tenon structure and a long strip; the root of the blade is a tenon, which is engaged with the tenon structure; the force transmission pad is removably inserted into the through hole; the hydraulic cylinder contacts the force transmission pad through a pressure sensor; the pressure sensor and the acceleration sensor are used to measure the centrifugal tensile stress and vibration acceleration of the structure. The present invention realizes the accurate identification of the contact stiffness and contact damping of the tenon connection structure of the complex non-continuous interface. The contact stiffness and damping identification device for the tenon connection structure of the present invention has a sophisticated design and a simple structure, and is universal and has high identification accuracy for the identification of contact stiffness and damping of multiple pairs of non-continuous tooth surfaces.

Description

Technical Field

[0001] The present invention relates to the field of aerospace machinery design, and particularly to a device and method for identifying the contact stiffness and damping of a tenon connection structure. Background Art

[0002] The tenon connection structure is widely used in the blade-disk connection structure of turbomachinery represented by aeroengines and is the main connection form between turbine blades and disks. Under different working conditions and loads, the stiffness and damping of the tenon connection structure may change non-linearly, which has a significant impact on the dynamic characteristics of the blade-disk structure. Since the tenon connection structure is generally in an environment of high temperature, high speed, and complex loads, accurate prediction of the structural strength, contact characteristics, and dynamic characteristics of the tenon head / groove is the guarantee for the safe and stable operation of aeroengines. The coordinated contact stiffness and damping characteristics of multiple curved surfaces in the tenon connection structure are affected by many factors such as the surface roughness of machining, initial assembly deviation, operating speed frequency, and centrifugal force caused by the speed, resulting in difficulties in directly modeling the contact finite element of the tenon connection structure and testing the connection stiffness and damping.

[0003] Currently, due to the large magnitude of the surface contact stiffness, directly measuring the contact stiffness of the tenon connection structure will introduce large sensor measurement errors, etc.; there is little research on the indirect identification method for the contact damping of the tenon connection structure with a complex discontinuous interface. The contact damping identification method for a simple mechanical joint surface (such as a pair of rough planes connected by bolts) is still difficult to be directly applied to the contact damping modeling of a complex multi-tooth surface. Therefore, a suitable test experimental device and identification method for the contact stiffness and damping of the tenon connection structure are needed to provide a basis for the design, manufacture, and assembly of the tenon connection structure. Summary of the Invention

[0004] In view of the deficiencies of the existing experimental devices and methods for measuring the performance of the tenon connection structure, the present invention proposes a device and method for identifying the contact stiffness and damping of the tenon connection structure.

[0005] The technical solution of the present invention: A device for identifying the contact stiffness and damping of a tenon connection structure includes a blade-disk 1, a force-transmitting spacer 2, a blade 3, an acceleration sensor 4, a vibration table 5, a bottom plate 6, a blade-disk support 7, a hydraulic cylinder 8, a pressure sensor 9, a bolt 10, a digital display 11, a charge amplifier for retention 12, a dynamic data acquisition instrument 13, and an industrial control computer 14;

[0006] The blisk 1, the blisk support 7, the bottom plate 6 and the vibration table 5 are fixedly connected in sequence from top to bottom; a hollow box structure is arranged inside the blisk support 7; in the overall structure composed of the blisk 1 and the blisk support 7, a through hole is opened at the geometric shape center and communicated to the hollow box structure. The upper half of the through hole is a tenon groove structure with multiple pairs of symmetric tooth surfaces, and the lower half is strip-shaped; the root of the blade 3 is a toothed tenon, which meshes with the tenon groove structure; the force transmission cushion block 2 contacts the root of the blade 3 and can be detachably inserted into the strip-shaped through hole part; one end of the hydraulic cylinder 8 located inside the hollow box structure contacts the force transmission cushion block 2 through a pressure sensor 9, and the other end is fixed;

[0007] The pressure sensor 9 is connected to the holding charge amplifier 12, and the pressure signal is amplified by the holding charge amplifier 12 and displayed on the digital display 11 in real time, which is used to measure the centrifugal tensile stress F provided by the hydraulic cylinder 8 to the blade 3; the acceleration sensor 4 is located on the surface of the blade 3 and is connected to the holding amplifier charge 12, the dynamic data acquisition instrument 13 and the industrial control computer 14 in sequence, which is used to measure the vibration acceleration of the structure.

[0008] The shape of the bottom plate 6 is I-shaped.

[0009] The blisk 1, the blisk support 7, the bottom plate 6 and the vibration table 5 are fixedly connected in sequence from top to bottom by screwing with bolts 10.

[0010] A method for identifying the contact stiffness and damping of a tenon connection structure includes the following steps:

[0011] Step 1: Assemble a device for identifying the contact stiffness and damping of a tenon connection structure;

[0012] Step 2: Apply a centrifugal tensile stress F to the root of the blade 3 by using the hydraulic cylinder 8;

[0013] Step 3: After the centrifugal tensile stress F is loaded, wait until the state of the entire tenon connection structure is stable, and hammer different positions of the blade 3;

[0014] Step 4: Obtain the frequency value of the tenon connection structure corresponding to the centrifugal tensile stress F according to the acceleration sensor 4 and the industrial control computer 14;

[0015] Step 5: Use the hydraulic cylinder 8 to apply a gradually increasing centrifugal tensile stress until all stress load conditions are tested, and obtain the relationship between different centrifugal tensile stresses and natural frequencies;

[0016] Step 6: Repeat the above Step 5 no less than 5 times;

[0017] Step 7: Endow the tenon connection structure model with a thin layer element of a certain thickness by using the thin layer element method, and perform finite element modal analysis on the tenon connection structure model by changing the elastic modulus of the thin layer element, so as to obtain the relationship between the elastic modulus and the natural frequency;

[0018] Step 8. Method for identifying the contact stiffness of the mortise connection structure:

[0019] S8.1 Define the squared error function of the test results and the modal results of the simulation model:

[0020]

[0021] Where, represent the first and third natural frequencies under the action of a specific centrifugal tensile stress in the test of the inherent characteristics of the mortise connection structure; represent the first and third order frequency fitting functions obtained by simulation calculation using the thin layer element method; η i represents the weight ratio of each order of natural frequency measured in the test, indicating the sensitivity of each order of natural frequency to the change of centrifugal tensile stress, and is defined as:

[0022]

[0023] S8.2 Use Matlab software to obtain the elastic modulus value that minimizes R(F), through the formula: Where, h is the thickness of the thin layer element; identify the unit contact stiffness value of the mortise joint contact surface corresponding to different centrifugal tensile stresses;

[0024] Step 9. Method for identifying the contact damping of the mortise connection structure:

[0025] S9.1 Re - assemble the device for identifying the contact stiffness and damping of the mortise connection structure, and turn on the vibration table 5;

[0026] S9.2 Repeat the operation processes of Steps 2, 3, 4, and 5 above 3 times to obtain the relationship between different centrifugal tensile stresses and vibration responses;

[0027] S9.3 Use the thin layer element method to endow the mortise joint model with thin layer elements of a certain thickness, and on the basis of identifying the contact stiffness of the contact surface, change the damping ratio of the thin layer elements, and conduct a finite element harmonic response analysis on the mortise connection structure model to obtain the relationship between the damping ratio and the vibration response;

[0028] S9.4 Select a first - order acceleration response obtained from the harmonic response analysis under the centrifugal tensile stress, and perform an octic polynomial fitting on it according to the following formula to obtain M1:

[0029] A1 = [M1][ξ b ;

[0030] [M1] = [M1(1), M1(2), M1(3), M1(4), M1(5), M1(6), M1(7), M1(8), M1(9)]

[0031]

[0032] Among them, A1 is the amplitude of the first-order acceleration response; ξ b is the material damping ratio of the thin-layer element; M1(1)-M1(9) are the correlation coefficients of the eighth-order fitting polynomial;

[0033] S9.5 Substitute the average amplitude A1 of the three vibration responses corresponding to the centrifugal tensile stress in the test results into the above fitting formula to obtain the damping ratio corresponding to the centrifugal tensile stress F;

[0034] S9.6 Select other centrifugal tensile stresses F and repeat the above calculation processes of S9.4 and S9.5 to identify the contact damping values of the tenon joint contact surfaces corresponding to different centrifugal tensile stresses.

[0035] For the device and method for identifying the contact stiffness and damping of the tenon joint structure of the present invention, the measuring principle of the contact pressure distribution on the tooth surface of the tenon joint structure is as follows: First, select a pressure-sensitive paper with an appropriate range and cut it slightly larger than the contact surface size of the tenon head and tenon groove; Second, place the pressure-sensitive paper on the first pair of maximum tooth contact surfaces of the tenon head and tenon groove while ensuring that the cross-sections on both sides of the tenon head and tenon groove are aligned, and ensure that the contact surface and the pressure-sensitive paper are in a completely contact state; Apply a vertically upward force to the bottom of the blade 3 through the hydraulic cylinder 8 located in the disk carrier 7 to complete the application of the centrifugal tensile stress F to the tenon joint structure, and obtain the pressure-sensitive paper with surface coloring; By changing the centrifugal tensile stress F and repeating the above operations, obtain the influence law of different centrifugal tensile stresses F on the coloring degree of the pressure-sensitive paper, and further determine the implementation method of the pressure at the root of the blade 3.

[0036] For the device and method for identifying the contact stiffness and damping of the tenon joint structure of the present invention, the measuring and identifying principle of the contact stiffness of the tenon joint structure is as follows: Apply a vertically upward force to the root of the blade 3 through the hydraulic cylinder 8 located in the disk carrier 7 to complete the application of the centrifugal tensile stress F to the tenon joint structure; Knock on the surface of the blade 3 with an impact force hammer, and use the acceleration sensor 4 to measure the vibration characteristics of the tenon joint structure; Then, through the comprehensive post-processing analysis of the acceleration sensor signals, obtain the change laws of the natural frequencies of each order and the change laws of the vibration characteristics of the tenon joint structure at different centrifugal tensile stresses F. According to the relationship between the centrifugal tensile stress F and the vibration frequency, combined with finite element analysis, inversely deduce the contact stiffness of the tenon joint structure.

[0037] Device and method for identifying contact stiffness and damping of tenon connection structure of the present invention. The principle of measuring and identifying contact damping of tenon connection structure is as follows: First, start the vibration table 5 to conduct a vibration response test on the tenon connection structure. Apply a vertically upward force to the root of the blade 3 through the hydraulic cylinder 8 located in the disk support 7 to complete the application of the centrifugal tensile stress F on the tenon connection structure. Tap the surface of the blade 3 with an impact hammer, and use the acceleration sensor 4 to measure the vibration characteristics of the tenon connection structure. Then, through the comprehensive post-processing and analysis of the acceleration sensor signals, obtain the variation law of the vibration responses of each order of the tenon connection structure under different centrifugal tensile stresses F. According to the relationship between the centrifugal tensile stress F and the vibration response, combined with finite element analysis, inversely deduce the contact damping of the tenon connection structure.

[0038] Advantages of the present invention:

[0039] (1) By characterizing the tenon connection contact surface as an elastic thin layer to simulate the contact effect of multiple pairs of rough surfaces, establishing a finite element model, and combining the inherent characteristics and vibration response tests, the non-linear contact stiffness and damping of the tenon connection structure can be effectively identified with high identification accuracy.

[0040] (2) The present identification device and method can avoid the limitations of the pure experimental measurement of the contact surface object and the randomness of the data results.

[0041] (3) The present identification device and method are more reliable, universal, and traversable for the identification of the contact stiffness and contact damping of such multiple pairs of discontinuous curved surfaces. Description of the drawings

[0042] Figure 1 is the front view of the device for identifying contact stiffness and damping of tenon connection structure;

[0043] Figure 2 is the contact stiffness diagram per unit area of the tenon connection structure identified under different mean stresses;

[0044] Figure 3 is the curve of contact damping varying with mean stress.

[0045] In the figure: 1 disk, 2 force transfer pads, 3 blade, 4 acceleration sensor, 5 vibration table, 6 bottom plate, 7 disk support, 8 hydraulic cylinder, 9 pressure sensor, 10 bolt, 11 digital display, 12 charge for maintaining amplification, 13 dynamic data acquisition instrument, 14 industrial control computer. Specific implementation manners

[0046] The following further describes the specific implementation manners of the present invention in combination with the drawings and technical solutions.

[0047] As Figure 1As shown in the figure, the device and method for identifying the contact stiffness and damping of the tenon connection structure of the present invention. The device includes a bladed disk 1, a force-transmitting spacer 2, a blade 3, an acceleration sensor 4, a vibration table 5, a bottom plate 6, a bladed disk support 7, a hydraulic cylinder 8, a pressure sensor 9, a bolt 10, a digital display 11, a charge amplifier for retention 12, a dynamic data acquisition instrument 13, and an industrial control computer 14;

[0048] The specific implementation steps are as follows:

[0049] 1). Assemble the device for identifying the contact stiffness and damping of the tenon connection structure;

[0050] 2). Apply a centrifugal tensile stress F to the root of the blade 3 using the hydraulic cylinder 8;

[0051] 3). After the centrifugal tensile stress F is applied, wait for the state of the entire tenon connection structure to be stable, and then hammer different positions of the blade 3;

[0052] 4). Obtain the frequency value of the tenon connection structure corresponding to the centrifugal tensile stress F according to the acceleration sensor 4 and the industrial control computer 14;

[0053] 5). Use the hydraulic cylinder 8 to apply a gradually increasing centrifugal tensile stress until all stress load conditions are tested, and obtain the relationship between different centrifugal tensile stresses and natural frequencies;

[0054] 6). Repeat step 5) no less than 5 times;

[0055] 7). Endow the tenon connection structure model with thin-layer elements of a certain thickness using the thin-layer element method, and perform finite element modal analysis on the tenon connection structure model by changing the elastic modulus of the thin-layer elements, thereby obtaining the relationship between the elastic modulus and the natural frequency;

[0056] 8). Method for identifying the contact stiffness of the tenon connection structure:

[0057] S8.1. Define the square error function of the test results and the modal results of the simulation model:

[0058]

[0059] Among them, represents the first and third natural frequencies under the action of a specific centrifugal tensile stress in the tenon connection structure natural characteristic test; represents the first and third order frequency fitting functions obtained by simulation calculation using the thin-layer element method; η i represents the weight ratio of each order of natural frequency measured in the test, indicating the sensitivity of each order of natural frequency to the change of centrifugal tensile stress, and is defined as:

[0060]

[0061] S8.2. Obtain the elastic modulus value that minimizes R(F) using Matlab software through the formula: h is the thickness of the thin layer element, and the contact stiffness value per unit area of the mortise joint contact surface corresponding to different centrifugal tensile stresses F can be identified.

[0062] 9). Method for identifying the contact damping of the mortise joint structure:

[0063] ①. Reassemble the device for identifying the contact stiffness and damping of the mortise joint structure, and turn on the shaking table 5;

[0064] ②. Repeat the operation processes of steps 2), 3), 4), and 5) above 3 times to obtain the relationship between different centrifugal tensile stresses F and the vibration response;

[0065] ③. Endow the mortise joint model with thin layer elements of a certain thickness using the thin layer element method. Based on the identification of the contact stiffness on the contact surface, change the damping ratio of the thin layer elements, and conduct a finite element harmonic response analysis on the mortise joint structure model to obtain the relationship between the damping ratio and the vibration response;

[0066] ④. Select a first-order acceleration response obtained from the harmonic response analysis under the centrifugal tensile stress F and perform an octic polynomial fitting on it according to the following formula to obtain M1:

[0067] A1 = [M1][ξ b ;

[0068] [M1] = [M1(1), M1(2), M1(3), M1(4), M1(5), M1(6), M1(7), M1(8), M1(9)]

[0069]

[0070] where A1 is the amplitude of the first-order acceleration response; ξ b is the material damping ratio of the thin layer element; M1(1)-M1(9) are the correlation coefficients of the octic fitting polynomial;

[0071] ⑤. Substitute the average amplitude A1 of the 3 vibration responses corresponding to the centrifugal tensile stress in the test results into the above fitting formula to obtain the damping ratio corresponding to the centrifugal tensile stress F;

[0072] ⑥. Select other centrifugal tensile stresses F and repeat the calculation processes of ④ and ⑤ in step 9) above to identify the contact damping values of the mortise joint contact surface corresponding to different centrifugal tensile stresses F.

[0073] Taking the identification of the contact stiffness and damping of a certain mortise joint structure as an example, the specific implementation steps are as follows:

[0074] (1). Test on the inherent characteristics of a certain mortise joint structure:

[0075] ①. Assemble a contact stiffness and damping identification device for the tenon connection structure;

[0076] ②. Apply a centrifugal tensile stress F to the root of the blade 3 using the hydraulic cylinder 8, and the centrifugal tensile stress F is loaded from 2000 N to 48000 N in sequence;

[0077] ③. After the centrifugal tensile stress F is loaded, wait for the state of the entire tenon connection structure to be stable, and then hammer different positions of the blade 3;

[0078] ④. Obtain the frequency value of the tenon connection structure corresponding to the centrifugal tensile stress F according to the acceleration sensor 4 and the industrial control computer 14;

[0079] ⑤. Use the hydraulic cylinder 8 to apply a gradually increasing centrifugal tensile stress F until all stress load conditions are tested, and repeat this step no less than 5 times;

[0080] ⑥. Calculate the average value of the first and third-order natural frequencies corresponding to the five test loadings under the same centrifugal tensile stress F, so as to obtain the relationship between the first and third-order natural frequencies corresponding to different centrifugal tensile stresses under the test conditions;

[0081] (2) Simulation of the natural characteristics of a tenon connection structure based on the thin layer element method:

[0082] ①. According to Figure 1 Establish a finite element model of the tenon connection structure and reasonably simplify part of the model;

[0083] ②. Simplify the key tooth structure where the tenon groove structure of the disk 1 contacts the tenon of the blade 3 into a rectangular thin layer element. The thickness of the thin layer element is designed to be 0.1 mm, the density of the thin layer element is designed to be 8.5 g / cm3, and the Poisson's ratio of the thin layer element is designed to be 0.3;

[0084] ③. Import the finite element model of the tenon connection structure containing the thin layer element into the simulation software, set the contact mode and boundary conditions, and the boundary conditions are set to be consistent with the test conditions;

[0085] ④. Conduct a modal analysis on the tenon connection structure. By modifying the elastic modulus of the thin layer element, the simulation results are continuously approximated to the natural frequencies of the tenon connection structure measured in the experiment. When the difference between the simulation results and the experimental results is minimized, the correct elastic modulus of the thin layer element and the corresponding first and third-order natural frequencies are obtained, and then the relationship between different elastic moduli and natural frequencies is obtained;

[0086] (3) Identification of the contact stiffness of a tenon connection structure:

[0087] ①. For a given centrifugal tensile stress F, considering the weight influence of the natural frequencies of each order of the tenon connection structure, define the square error function of the test results and the modal results of the simulation model based on the thin layer element as follows:

[0088]

[0089] Among them, represent the first and third natural frequencies under the action of specific centrifugal tensile stress in the test of the inherent characteristics of the tenon connection structure; represents the first and third order frequency fitting functions obtained by simulation calculation using the thin layer element method; η i represents the weight ratio of the natural frequencies measured in the test, indicating the sensitivity of each natural frequency to the change of centrifugal tensile stress, and is defined as:

[0090]

[0091] ②. Use Matlab software to obtain the elastic modulus value that minimizes R(F). Through the formula: h is the thickness of the thin layer element, and the contact stiffness value per unit area of the contact surface of the tenon connection structure corresponding to different centrifugal tensile stresses can be identified, as shown in Table 1;

[0092] ③. Table 1 shows the elastic modulus values, relative error values, and the corresponding contact stiffness per unit area obtained based on the thin layer element method under some working conditions of different centrifugal tensile stresses F;

[0093] Table 1 Parameters under different centrifugal tensile stress conditions

[0094]

[0095] Among them, the average stress is the centrifugal tensile stress divided by the contact area of the tenon connection structure; the relative error R' between the natural frequencies calculated by the optimal thin layer element elastic modulus and the experimental test results is defined as:

[0096] i = 1~n, where n is the order of the natural frequency

[0097] ④. Draw the contact stiffness diagram per unit area of the tenon connection structure identified under different average stresses, as Figure 2 shown.

[0098] (4). Identification of the contact damping of a tenon connection structure:

[0099] ①. Reassemble the device for identifying the contact stiffness and damping of the tenon connection structure, and turn on the vibration table 5;

[0100] ②. Repeat the above step (1): The test process of the inherent characteristics of a tenon connection structure is carried out 3 times to obtain the relationship between different centrifugal tensile stresses / average stresses and the vibration response;

[0101] ③. Repeat the above step (2): For the simulation of the inherent characteristics of a certain tenon connection structure based on the thin layer element method, by changing the damping ratio of the thin layer element on the basis of the contact stiffness identification of the contact surface, perform a finite element harmonic response analysis on the tenon connection structure model to obtain the relationship between the damping ratio and the vibration response;

[0102] ④. Select a first-order acceleration response obtained from the harmonic response analysis under the centrifugal tensile stress, and perform an octic fitting on it according to the following formula to obtain M1:

[0103] A1 = [M1][ξ b ;

[0104] [M1] = [M1(1), M1(2), M1(3), M1(4), M1(5), M1(6), M1(7), M1(8), M1(9)]

[0105]

[0106] where, A1 is the amplitude of the first-order acceleration response; ξ b is the material damping ratio of the thin layer element; M1(1)-M1(9) are the correlation coefficients of the octic fitting polynomial;

[0107] ⑤. Substitute the average amplitude A1 of the three vibration responses under the corresponding centrifugal tensile stress in the test results into the above fitting formula to obtain the damping ratio corresponding to the centrifugal tensile stress F;

[0108] ⑥. Select other centrifugal tensile stresses F and repeat the calculation processes in ④ and ⑤ of (4) above, so as to identify the contact damping values of the tenon joint contact surface corresponding to different centrifugal tensile stresses / mean stresses, as Figure 3 shown.

Claims

1. A device for identifying the contact stiffness and damping of a tenon connection structure, characterized in that The device for identifying the contact stiffness and damping of the tenon connection structure includes a blisk (1), a force - transmitting spacer (2), a blade (3), an acceleration sensor (4), a vibration table (5), a base plate (6), a blisk support (7), a hydraulic cylinder (8), a pressure sensor (9), bolts (10), a digital display (11), a charge amplifier for retention (12), a dynamic data acquisition instrument (13), and an industrial control computer (14); The blisk (1), the blisk support (7), the base plate (6), and the vibration table (5) are fixedly connected in sequence from top to bottom; the blisk support (7) has a hollow box - body structure inside; in the overall structure composed of the blisk (1) and the blisk support (7), a through - hole is opened at the geometric center and communicated with the hollow box - body structure. The upper half of the through - hole is a tenon - groove structure with multiple pairs of symmetric tooth surfaces, and the lower half is strip - shaped; the root of the blade (3) is a toothed tenon, which meshes with the tenon - groove structure; the force - transmitting spacer (2) contacts the root of the blade (3) and is detachably inserted into the strip - shaped part of the through - hole; One end of the hydraulic cylinder (8) located inside the hollow box - body structure contacts the force - transmitting spacer (2) through the pressure sensor (9), and the other end is fixed; The pressure sensor (9) is connected to the charge amplifier for retention (12). The pressure signal is amplified by the charge amplifier for retention (12) and displayed on the digital display (11) in real time, which is used to measure the centrifugal tensile stress F provided by the hydraulic cylinder (8) to the blade (3); the acceleration sensor (4) is located on the surface of the blade (3) and is sequentially connected to the charge amplifier for retention (12), the dynamic data acquisition instrument (13), and the industrial control computer (14), which is used to measure the vibration acceleration of the structure.

2. The device for identifying the contact stiffness and damping of a tenon connection structure according to claim 1, characterized in that The shape of the base plate (6) is I - shaped.

3. The device for identifying the contact stiffness and damping of a tenon connection structure according to claim 1 or 2, characterized in that The blisk (1), the blisk support (7), the base plate (6), and the vibration table (5) are fixedly connected in sequence from top to bottom by screwing with bolts (10).

4. A method for identifying the contact stiffness and damping of a tenon connection structure, characterized in that Based on the device for identifying the contact stiffness and damping of the tenon connection structure described in claim 1, the steps are as follows: Step 1: Assemble the device for identifying the contact stiffness and damping of the tenon connection structure; Step 2: Apply a centrifugal tensile stress F to the root of the blade (3) using the hydraulic cylinder (8); Step 3: After the centrifugal tensile stress F is applied and the state of the entire tenon connection structure is stable, hammer different positions of the blade (3); Step 4: Obtain the frequency value of the tenon connection structure corresponding to the centrifugal tensile stress F according to the acceleration sensor (4) and the industrial control computer (14); Step 5: Use the hydraulic cylinder (8) to apply gradually increasing centrifugal tensile stress until all stress - load conditions are tested, and obtain the relationship between different centrifugal tensile stresses and natural frequencies; Step 6: Repeat step 5 no less than 5 times; Step 7: Endow the tenon connection structure model with thin - layer elements of a certain thickness using the thin - layer element method, and perform finite - element modal analysis on the tenon connection structure model by changing the elastic modulus of the thin - layer elements to obtain the relationship between the elastic modulus and the natural frequency; Step 8: Method for identifying the contact stiffness of the tenon connection structure: S8.1 Define the square - error function of the test results and the modal results of the simulation model; Among them, represent the first and third natural frequencies under the action of specific centrifugal tensile stress in the test of the inherent characteristics of the tenon connection structure; represent the first and third order frequency fitting functions obtained by simulation calculation through the thin layer element method; η i represent the weight ratios of the natural frequencies measured in the test, indicating the sensitivity of each order of natural frequency to the change of centrifugal tensile stress, and are defined as: S8.2 Use Matlab software to obtain the elastic modulus value that minimizes R(F) through the formula: where h is the thickness of the thin layer element; identify the unit contact stiffness values of the tenon joint contact surface corresponding to different centrifugal tensile stresses; Step 9: Method for identifying the contact damping of the tenon connection structure: S9.1 Re - assemble the contact stiffness and damping identification device of the tenon connection structure, and turn on the shaking table (5); S9.2 Repeat the operation processes of Steps Two, Three, Four, and Five above 3 times to obtain the relationship between different centrifugal tensile stresses and vibration responses; S9.3 Endow the tenon joint model with thin - layer elements of a certain thickness using the thin - layer element method. By changing the damping ratio of the thin - layer elements on the basis of identifying the contact stiffness of the contact surface, conduct a finite - element harmonic response analysis on the tenon connection structure model to obtain the relationship between the damping ratio and the vibration response; S9.4 Select a first - order acceleration response obtained from the harmonic response analysis under centrifugal tensile stress, and perform an octic polynomial fitting on it according to the following formula to obtain M1: A1 = [M1][ξ b ; [M1] = [M1(1), M1(2), M1(3), M1(4), M1(5), M1(6), M1(7), M1(8), M1(9)] Among them, A1 is the amplitude of the first-order acceleration response; ξ b is the material damping ratio of the thin-layer element; M1(1)-M1(9) are the correlation coefficients of the eighth-order fitting polynomial; S9.5 Substitute the average amplitude A1 of the 3 - time vibration responses under the corresponding centrifugal tensile stress in the test results into the above fitting formula to obtain the damping ratio corresponding to the centrifugal tensile stress F; S9.6 Select other centrifugal tensile stresses F and repeat the calculation processes of Steps S9.4 and S9.5 to identify the contact damping values of the tenon joint contact surfaces corresponding to different centrifugal tensile stresses.

Images