Blisk forced response analysis method

Abstract

This application provides a method for forced response analysis of an integral bladed disk (IBD), comprising: constructing a finite element model of an IBD sector; conducting disk-coupled resonance analysis of the finite element model to obtain the frequency, mode shape, and relative vibration stress of the IBD blades under one to multiple node diameters, and plotting disk-coupled resonance diagrams; determining the critical node diameter related to the number of rotor and stator blades; determining the frequency order and corresponding critical resonance speed by combining the plotted disk-coupled resonance diagrams and the critical node diameter; performing damping tests on the IBD blades to obtain the frequency order and corresponding modal damping ratios; establishing a full-ring model of the IBD rotor blades and the stator blades before and after them; conducting steady flow field analysis of the full-ring model to obtain steady results as the initial field conditions for unsteady flow field analysis; conducting unsteady flow field analysis to obtain the actual vibration stress of the IBD; and conducting dynamic strength reserve analysis to evaluate the dynamic strength reserve of the high-load IBD under the analysis conditions.

Description

Technical Field

[0001] This application belongs to the field of aero-engine technology, and specifically relates to a method for analyzing the forced response of an integral bladed disk. Background Technology

[0002] The integral bladed disk structure is one of the development directions of aero engines with a thrust-to-weight ratio between 15 and 20. Its design feature is to eliminate the conventional disk tenon connection structure and integrate the blade and the disk into one structure. This can reduce the weight of the blade rotor, reduce the number of parts, and eliminate flow losses in the gap between the tenon root and the tenon groove. The integral bladed disk structure is now widely used in aero engine fans, compressors and turbines.

[0003] However, due to the thinness of the integral bladed disk and the stronger coupling of the blades, vibrational energy cannot be dissipated during the transmission between the blade tenon and the disk, nor can it be reduced by conventional friction damping structures such as edge dampers, shoulders, blade crowns, and reinforcing ribs. Therefore, flow-induced motion (FIM) is more prominent in the integral bladed disk structure, which greatly reduces the high-cycle fatigue life of the bladed disk.

[0004] Currently, in engineering, Campbell diagrams are often drawn based on vibration characteristic analysis results to assess the resonant speed margin of blades and take measures to avoid resonant speeds. However, since it is impossible to accurately predict the actual vibration stress, only the possible resonant speeds and mode shapes can be predicted. This method has significant limitations and is only suitable for a preliminary understanding of the blade's resonance situation in the early stages of design. It cannot meet the evaluation of flow-induced vibration and high-cycle fatigue capabilities of complex integral bladed disk structures under high loads. Summary of the Invention

[0005] The purpose of this application is to provide a method for analyzing the forced response of an overall bladed disk, in order to solve or mitigate at least one of the problems in the background art.

[0006] The technical solution of this application is: a method for analyzing the forced response of an integral bladed disk, the method comprising:

[0007] Construct a finite element model of the integral bladed disk sector at a predetermined angle, and apply periodic symmetric boundary conditions to the cutting surface of the integral bladed disk sector finite element model.

[0008] Disc coupling resonance analysis of integral blade sector was carried out to obtain the frequency, mode shape and relative vibration stress of integral blade disk blades from one-node diameter to multiple-node diameter, and the disc coupling resonance diagram was plotted.

[0009] Based on the principle that resonance will be induced at the corresponding nodal diameter when the excitation order equals the nodal diameter number, and the relationship between the nodal diameter number and the excitation factor, the critical nodal diameter number related to the number of rotor and stator blades is determined:

[0010] The frequency order and the corresponding critical resonance speed are determined by combining the drawn disk coupling resonance diagram and the critical node diameter.

[0011] Damping tests were performed on several blades of the integral bladed disk to obtain the frequency order and the corresponding modal damping ratio.

[0012] Establish a full-ring model of the integral bladed disk rotor blades and the stator blades before and after them;

[0013] A steady flow field analysis of the full-ring model is carried out to obtain steady results, which are then used as the initial field conditions for the unsteady flow field analysis.

[0014] Based on the determination of the critical resonance speed and the analysis of the whole-ring steady flow field, the unsteady flow field analysis is carried out to obtain the true vibration stress of the integral bladed disk.

[0015] Combining the vibration fatigue limit and static stress level of the integral bladed disk, dynamic strength reserve analysis is carried out using Goodman diagrams to evaluate the dynamic strength reserve of the high-load integral bladed disk under the analysis conditions. If the reserve meets the requirements, the analysis is completed; otherwise, the analysis is restarted after the vibration reduction design is carried out.

[0016] Furthermore, the cutting surface of the finite element model of the integral bladed disk sector is established using the four-point surface method, and the integral bladed disk is cut.

[0017] Furthermore, the predetermined angle is θ = 360 / N, where N is the number of blades in the entire bladed disk.

[0018] Furthermore, the number of multi-section diameters does not exceed N / 2 or (N-1) / 2, where N is the number of blades in the entire bladed disk.

[0019] Furthermore, the number of nodal diameters and the excitation factors satisfy the following:

[0020] ND = |A1×EO - A2×N|

[0021] In the formula, ND is the number of pitch diameters, EO is the excitation factor, and A1 and A2 are natural numbers.

[0022] Furthermore, when testing the entire blade, the tapping method is used, and the number of blades tested is 3 to 6 evenly distributed blades.

[0023] Furthermore, the damping ratio is calculated as follows:

[0024]

[0025] In the formula: ζ is the damping ratio, i is the number of waves involved in the calculation, A1 is the peak value of the first wave involved in the calculation, and A i+1 The peak value of the wake wave used in the calculation.

[0026] Furthermore, the damping ratio used in the unsteady analysis is the average damping ratio of several blades.

[0027] Furthermore, when conducting unsteady flow field analysis, the static pressure on the surface of the integral bladed disk that varies with time is first calculated, and the unsteady aerodynamic force of the static pressure on the surface of the integral bladed disk is converted into nodal pressure that varies with time and applied to the finite element model of the integral bladed disk.

[0028] Furthermore, when conducting unsteady flow field analysis, the obtained damping ratio is used to perform transient response analysis on the integral bladed disk. The analysis part is selected as the monitoring point at the root of the integral bladed disk with the maximum vibration stress. After iteration, the vibration stress at the monitoring point on the surface of the integral bladed disk tends to converge. At this time, the vibration stress obtained is the true vibration stress of the integral bladed disk.

[0029] The fluid-structure interaction-based forced response analysis method for integral bladed disks provided in this application considers the effects of unsteady flow field across the entire ring, damping effects, and dangerous vibration mode identification. It can effectively evaluate the vibration of the integral bladed disk across the entire speed range, ensuring that the bladed disk will not suffer high-cycle fatigue failure and improving engine safety and reliability. Attached Figure Description

[0030] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.

[0031] Figure 1 This is a flowchart of the overall bladed disk forced response analysis method of this application.

[0032] Figure 2 This is a coupled resonance diagram of the first 10 frequencies of an embodiment of this application. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings.

[0034] This application provides a forced response analysis method for an integral bladed disk based on fluid-structure interaction. It identifies critical resonance modes through coupled resonance Campbell diagram analysis. Unsteady aerodynamic forces on the bladed disk surface in the time domain are obtained through unsteady flow field analysis. Based on the measured damping, vibration response analysis is performed to obtain vibration stress and deformation analysis, thereby effectively evaluating the vibration of the bladed disk at critical resonance speeds.

[0035] like Figure 1 As shown, the forced response analysis method for high-load integral bladed disks based on fluid-structure interaction provided in this application includes the following steps:

[0036] 1) Finite element modeling of the integral bladed disk

[0037] Since the integral bladed disk lacks a tenon-and-disc connection structure, and the blades and disk are integrated, conducting vibration characteristic analysis on the entire bladed disk would be time-consuming. Therefore, this application uses the four-point surface method in modeling software to create a cutting surface, cuts the integral bladed disk, and applies periodically symmetric boundary conditions to the cutting surface.

[0038] In the finite element modeling of the integral bladed disk, only one sector is selected, with the corresponding angle being θ = 360 / N, where N is the number of blades in the integral bladed disk. This sector must contain a complete blade of the integral bladed disk. For example, in one embodiment of this application, the integral bladed disk has 20 blades, so only an 18° sector containing the blades needs to be created during modeling.

[0039] 2) Disk-coupled resonance analysis

[0040] Finite element software was used to conduct disk coupling resonance analysis on the sector of the finite element model established in the above process. The frequency, mode shape and relative vibration stress of the overall bladed disk were obtained from 1 section diameter to N / 2 or (N-1) / 2 section diameter, and the disk coupling resonance diagram was plotted.

[0041] like Figure 2 The figure shown is a coupled resonance diagram drawn using the resonance analysis of the first 10 frequencies as an example in one embodiment of this application. In this diagram, 2E to 10E, 23E, and 45E are the ellipticity of the casing and the excitation factors of the stator blades, f1 to f10 are the first 10 frequencies of the integral bladed disk, and n1 to n3 are the operating speeds.

[0042] 3) Identify the critical pitch diameter

[0043] To determine the potential dangerous resonance patterns of an integral bladed disk, the number of dangerous nodal diameters must first be determined. The process includes:

[0044] 3.1) When the excitation order equals the number of nodal diameters, resonance will be induced in the corresponding nodal diameter;

[0045] 3.2) The critical nodal diameter related to the number of rotor-stator blades, determined by the following formula:

[0046] ND = |A1×EO - A2×N|

[0047] In the formula, ND is the number of pitch diameters, EO is the excitation factor, and A1 and A2 are natural numbers.

[0048] For example, in one embodiment of this application, the number of leaves N is 20, and EO includes 2E to 10E, 23E, and 45E. By traversing the above formula A1 = 1, 2, 3, ... ∞ and A2 = 1, 2, 3, ... ∞, multiple node diameter numbers ND can be obtained. Considering the restriction that the node diameter number ND must be less than N / 2 = 10, the possible dangerous node diameter numbers are 3 and 5.

[0049] 4) Determine the critical resonance speed

[0050] Based on the disk coupling resonance diagram drawn in step 2 and the critical node diameter determined in step 3, the resonance speed is determined.

[0051] For example, in this embodiment, based on the disk coupling resonance diagram drawn in step 2 and the number of dangerous nodal diameters determined in step 3, the dangerous vibration mode can be determined to be the second-order resonance excited by the 5-nodal diameter excited by the excitation factor 5E, with a resonance rotation speed of n2.

[0052] 5) Determine the damping

[0053] The integral bladed disk structure mainly has structural damping and material damping. The selection of damping has a significant impact on the response calculation results. The damping determination method in this application is to use the tapping method to uniformly select 3 to 6 blades around the circumference for damping test, obtain the second-order frequency and the corresponding modal damping ratio, and take the average value in the calculation.

[0054] The blades of the integral bladed disk are struck with a rubber mallet, and the damping ratio is calculated using the following formula. The measured signal containing multiple frequencies is separated into single-frequency vibration signals of each target order frequency through digital bandpass filtering, and the time-domain damping ratio is calculated to obtain the damping ratio corresponding to each vibration frequency:

[0055]

[0056] In the formula: ζ is the damping ratio, i is the number of waves involved in the calculation, A1 is the peak value of the first wave involved in the calculation, and A i+1 The peak value of the wake wave used in the calculation.

[0057] The same procedure was then performed on several other blades to calculate their damping ratios. Finally, the average damping ratio of the tested blades was calculated using an arithmetic mean.

[0058] 6) Consider flow field modeling for the front and rear rows of stator blades.

[0059] Because the front and rear rows of stator blades have a significant impact on the vibration of the rotor blades of the overall bladed disk, the wake excitation and separation flow of the stator blades will directly affect the vibration response of the overall bladed disk. Therefore, the front and rear rows of stator blades must be considered when modeling the flow field.

[0060] To capture flow field characteristics more accurately, this application performs full-ring modeling of the rotor and stator blades.

[0061] 7) Whole-ring steady flow field analysis

[0062] In unsteady flow field analysis, the calculation may fail to converge due to oscillations in the flow field parameters. Therefore, this application first conducts a steady flow field analysis of the entire ring, using the steady results as the initial field conditions for the unsteady flow field analysis.

[0063] 8) Fluid-structure interaction forced response analysis

[0064] Based on the dangerous resonance speed determined in step 4 and the steady flow field analysis of the entire annular rotor in step 7, an unsteady flow field analysis is conducted. Fluid simulation software is used to perform unsteady flow field analysis on the entire annular rotor and stator blade models. The values ​​2E to 6E are analyzed by setting the harmonic numbers in the program.

[0065] Taking the second-order resonance of the 5-nodal diameter induced by 5E as an example, the static pressure on the surface of the integral bladed disk as a function of time is first calculated. The unsteady aerodynamic force of the static pressure on the surface of the integral bladed disk is then converted into a nodal pressure that varies with time and applied to the finite element model of the integral bladed disk.

[0066] Using the damping ratio (mean) determined in step 5, the transient response analysis of the entire bladed disk is performed using the modal superposition method. The maximum vibration stress point at the root of the entire bladed disk is selected as the monitoring point for analysis.

[0067] After several cycles of calculation and iteration, the vibration stress at the monitoring points on the surface of the overall bladed disk tends to converge, and the calculated vibration stress at this time is the true vibration stress of the overall bladed disk.

[0068] 9) Vibration stress evaluation

[0069] Based on the vibration stress calculated in step 8, and combined with the vibration fatigue limit and static stress level of the integral bladed disk, a dynamic strength reserve analysis is carried out using a Goodman diagram to evaluate the dynamic strength reserve of the high-load integral bladed disk under the analysis conditions. If the reserve meets the requirements, the analysis is completed; otherwise, the analysis is restarted after the vibration reduction design is carried out.

[0070] The fluid-structure interaction-based forced response analysis method for integral bladed disks provided in this application considers the effects of unsteady flow field across the entire ring, damping effects, and dangerous vibration mode identification. It can effectively evaluate the vibration of the integral bladed disk across the entire speed range, ensuring that the bladed disk will not suffer high-cycle fatigue failure and improving engine safety and reliability.

[0071] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for analyzing the forced response of an integral bladed disk, characterized in that, The method includes: Construct a finite element model of the integral bladed disk sector at a predetermined angle, and apply periodic symmetric boundary conditions to the cutting surface of the integral bladed disk sector finite element model. Disc coupling resonance analysis of integral blade sector was carried out to obtain the frequency, mode shape and relative vibration stress of integral blade disk blades from one-node diameter to multiple-node diameter, and the disc coupling resonance diagram was plotted. Based on the principle that resonance will be induced at the corresponding nodal diameter when the excitation order equals the nodal diameter number, and the relationship between the nodal diameter number and the excitation factor, the critical nodal diameter number related to the number of rotor and stator blades is determined: The frequency order and the corresponding critical resonance speed are determined by combining the drawn disk coupling resonance diagram and the critical node diameter. Damping tests were performed on several blades of the integral bladed disk to obtain the frequency order and the corresponding modal damping ratio. Establish a full-ring model of the integral bladed disk rotor blades and the stator blades before and after them; A steady flow field analysis of the full-ring model is carried out to obtain steady results, which are then used as the initial field conditions for the unsteady flow field analysis. Based on the determination of the critical resonance speed and the analysis of the whole-ring steady flow field, the unsteady flow field analysis is carried out to obtain the true vibration stress of the integral bladed disk. Combining the vibration fatigue limit and static stress level of the integral bladed disk, dynamic strength reserve analysis is carried out using Goodman diagrams to evaluate the dynamic strength reserve of the high-load integral bladed disk under the analysis conditions. If the reserve meets the requirements, the analysis is completed; otherwise, the analysis is restarted after the vibration reduction design is carried out.

2. The method for analyzing the forced response of an integral bladed disk as described in claim 1, characterized in that, The cutting surface of the finite element model of the integral bladed disk sector is established by the four-point surface method, and the integral bladed disk is cut.

3. The method for analyzing the forced response of an integral bladed disk as described in claim 2, characterized in that, The predetermined angle is θ = 360 / N, where N is the number of blades in the entire bladed disk.

4. The method for analyzing the forced response of an integral bladed disk as described in any one of claims 1 to 3, characterized in that, The number of multi-section diameters shall not exceed N / 2 or (N-1) / 2, where N is the total number of blades in the entire bladed disk.

5. The method for analyzing the forced response of an integral bladed disk as described in claim 4, characterized in that, The number of nodal diameters and the excitation factors satisfy the following: ND = |A1×EO - A2×N| In the formula, ND is the number of pitch diameters, EO is the excitation factor, and A1 and A2 are natural numbers.

6. The method for analyzing the forced response of an integral bladed disk as described in claim 5, characterized in that, When testing the entire blade, the tapping method is used, and the number of blades tested is 3 to 6 evenly distributed blades.

7. The method for analyzing the forced response of an integral bladed disk as described in claim 6, characterized in that, The damping ratio is calculated as follows: In the formula: ζ is the damping ratio, i is the number of waves involved in the calculation, A1 is the peak value of the first wave involved in the calculation, and A i+1 The peak value of the wake wave used in the calculation.

8. The method for analyzing the forced response of an integral bladed disk as described in claim 7, characterized in that, The damping ratio used in the unsteady analysis is the average damping ratio of several blades.

9. The method for analyzing the forced response of an integral bladed disk as described in claim 8, characterized in that, When conducting unsteady flow field analysis, the static pressure on the surface of the integral bladed disk that varies with time is first calculated. The unsteady aerodynamic force of the static pressure on the surface of the integral bladed disk is then converted into nodal pressure that varies with time and applied to the finite element model of the integral bladed disk.

10. The method for analyzing the forced response of an integral bladed disk as described in claim 9, characterized in that, When conducting unsteady flow field analysis, the obtained damping ratio is used to perform transient response analysis on the integral bladed disk. The analysis part is selected as the monitoring point at the root of the integral bladed disk with the maximum vibration stress. After iteration, the vibration stress at the monitoring point on the surface of the integral bladed disk tends to converge. At this time, the vibration stress obtained is the true vibration stress of the integral bladed disk.

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