A method for predicting the rotating unbalance of a blisk type part

Abstract

This invention discloses a method for predicting the rotational imbalance of bladed disk components, comprising: Step 1: obtaining the volume and centroid radius of the thickened geometry of the blade; Step 2: calculating the imbalance sensitivity coefficient; Step 3: obtaining the contour lines of multiple detection sections along the blade height direction, and discretizing each contour line into several small line segments; Step 4: calculating the theoretical area and theoretical perimeter of each detection section of the theoretical blade; Step 5: obtaining the actual area of ​​each detection section of each processed blade; Step 6: calculating the thickness deviation of each detection section of each processed blade; Step 7: calculating the average thickness of the entire blade, thereby obtaining the overall imbalance of the bladed disk. This invention, based on existing measurement data from the production site, can quickly and accurately predict the rotational imbalance of bladed disk components, thus solving the problems of long cycle time, high cost, low accuracy, and poor adaptability to the production site in existing technologies.

Description

Technical Field

[0001] This invention belongs to the field of blade detection, and in particular relates to a method for predicting the rotational imbalance of bladed disk-type parts. Background Technology

[0002] In power equipment such as aero engines and gas turbines, integral bladed disks and integral blade rings are core rotating components, and their rotational balance performance directly determines the operational stability, reliability, and service life of the equipment. Compared to traditional bladed disk structures with tenon-groove connections, integral bladed disks / blade rings eliminate the tenon structure through integrated molding technology. This not only significantly reduces the weight of the parts and the number of assembly steps but also improves structural strength and aerodynamic efficiency, leading to their widespread application in modern high-end power equipment. However, the manufacturing of such parts faces many technical challenges: the blade profile is usually a complex free-form surface with characteristics such as large overhang length, thin wall thickness, and low stiffness. Furthermore, the materials used, such as titanium alloys and high-temperature alloys, are difficult to machine and have poor machinability. During machining, factors such as tool wear, cutting vibration, and clamping deformation can easily cause deviations between the actual machined dimensions and the theoretical design dimensions of the blade, leading to uneven mass distribution and ultimately resulting in excessive rotational imbalance after assembly.

[0003] Existing technical solutions for addressing imbalance in bladed disk components primarily employ a multi-cycle iterative approach: machining → deburring → low-speed balancing machine trial weighing → repeated milling / grinding to remove weight → re-balancing. This approach has significant drawbacks: Firstly, the process is cumbersome and time-consuming. Each round of balancing test and deduplication process requires a lot of equipment resources and man-hours, resulting in low production efficiency and a significant increase in manufacturing costs. Secondly, repeated manual milling or grinding to remove weight can damage the surface integrity of the blades, generate residual stress, reduce the fatigue strength and corrosion resistance of the blades, and pose potential structural safety hazards. Third, there is a difference between low-speed balance testing and the high-speed rotation conditions of the parts in actual working conditions. The weight reduction compensation based on the low-speed test results is difficult to fully meet the dynamic balance requirements under high-speed conditions, and the problem of "passing low-speed balance but being unbalanced at high speed" is likely to occur.

[0004] To improve the above situation, existing technologies attempt to predict the unbalanced response of parts through numerical simulation methods, such as finite element modal analysis or computational fluid dynamics (CFD). However, these methods have significant limitations: on the one hand, they rely on complete and high-precision three-dimensional geometric models, accurate material density distribution data, and complex boundary condition settings, requiring extremely high levels of preliminary data preparation; on the other hand, the calculation process is complex and computationally intensive, often requiring professional simulation analysts, and the calculation results lag behind the production schedule, making it difficult to directly apply to real-time decision-making and process adjustments on the production site. In addition, existing technologies have proposed methods to estimate the unbalance based on the integral of blade thickness deviation to solve for the mass moment, but this type of method has key technical defects: it does not establish an explicit mathematical mapping relationship of "unit area deviation - unit perimeter - unbalance", and cannot directly and quickly convert the measured geometric deviation into the unbalance; at the same time, it ignores the influence of the difference in lever arms in the radial direction of different blade cross sections on the unbalance, resulting in a large deviation between the predicted results and the actual unbalance, insufficient accuracy, and difficulty in meeting the accuracy requirements for unbalance prediction on the production site. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the rotational imbalance of bladed disk parts, so as to solve the problems of long cycle, high cost, low accuracy and poor adaptability to the production site in the prior art.

[0006] This invention employs the following technical solution: a method for predicting the rotational imbalance of bladed disk-type parts, comprising: Step 1: Extract the profile of any blade using the geometric model of the theoretical bladed disk; thicken the profile of the blade to obtain a thickened geometry, and obtain the volume and centroid radius of the thickened blade geometry; Step 2: Calculate the unbalance sensitivity coefficient using the volume and centroid radius of the thickened geometry; Step 3: Using the geometric model of the theoretical bladed disk, obtain the contour lines of multiple detection sections in the blade height direction, and discretize each contour line into several small line segments; Step 4: Calculate the theoretical area and theoretical perimeter of each test section of the theoretical blade using the numerical integration method; Step 5: Scan and measure the actual profile of all processed blades, and then process the data to obtain the actual area of ​​each detection section of each processed blade; Step 6: Calculate the thickness deviation of each detection section of each processed blade based on the actual area, theoretical area, and theoretical perimeter of each detection section; Step 7: Based on the thickness deviation of each detection section of each processed blade, calculate the average thickness increase of the entire blade, and then obtain the overall imbalance of the bladed disk.

[0007] The beneficial effects of this invention are: This invention is based on existing measurement data from the production site and can quickly and accurately predict the rotational imbalance of bladed disk parts, thus solving the problems of long cycle time, high cost, low accuracy and poor adaptability to the production site in the existing technology. This invention utilizes only the point cloud data of the blade cross-sectional profile already collected by a coordinate measuring machine at the production site. Without requiring additional specialized testing equipment or complex simulation calculations, it can quickly and accurately calculate the initial imbalance of the entire disc (ring) part on the processing site, enabling early prediction of the part's imbalance state. Simultaneously, based on the prediction results, it provides a quantitative compensation scheme, offering a scientific basis for subsequent selective weight reduction or adaptive adjustment of processing parameters. This significantly reduces the number of iterations in the balancing process, shortens the production cycle, lowers manufacturing costs, and avoids the adverse effects of repeated weight reduction on blade performance, ensuring the structural integrity and reliability of the part.

[0008] This invention offers high prediction efficiency, is well-suited to production site requirements, and requires no additional specialized testing equipment or complex simulation calculations. It can quickly calculate imbalance using only the point cloud data already collected by the coordinate measuring machine on the production site. The entire prediction process can be completed within one hour after the part is finished, achieving "measurement equals prediction." This provides support for real-time decision-making on the production site and significantly shortens the cycle of traditional balance testing and iterative deduplication.

[0009] This invention establishes an explicit mapping relationship of "unit area deviation - unit perimeter - unbalance" while considering the differences in radial lever arms at different blade cross-sections. This allows for precise correction of the sensitivity coefficient, effectively improving the prediction accuracy of the unbalance. The prediction error can be controlled within ±5%, far superior to existing methods based on thickness deviation integration. The quantitative compensation scheme generated based on the accurate prediction results enables targeted deduplication, avoiding performance damage to parts caused by indiscriminate deduplication.

[0010] This invention significantly reduces the number of iterations in the balancing process, typically reducing the traditional 3-5 iteration cycles to 1-2, greatly reducing equipment downtime and labor costs. At the same time, it avoids the damage to the surface integrity and fatigue strength of the blades caused by repeated de-weighting, reduces rework and scrap rates due to defective parts, and improves product qualification rate and production efficiency.

[0011] This invention does not depend on specific part structures or material types, and can be applied to integral bladed disks and integral blade rings with different blade profiles and different size specifications. It also has no special requirements for the model of coordinate measuring machine and can be directly adapted to the existing testing equipment in the production site without the need for large-scale equipment modification. It has good versatility and engineering practicality. Detailed Implementation

[0012] The present invention will now be described in detail with reference to specific embodiments.

[0013] This invention discloses a method for predicting the rotational imbalance of bladed disk-type parts, comprising: steps 1-7.

[0014] Step 1: Extract the profile of any blade using the geometric model of the theoretical bladed disk; thicken the profile of the blade to obtain a thickened geometry, and obtain the volume and centroid radius of the thickened blade geometry.

[0015] The geometric model of the theoretical bladed disk can be a high-precision CAD theoretical model of the entire bladed disk. This model must contain complete geometric information of the blades and the disk, including key dimensional parameters such as blade profile curves, cross-sectional contours, and the inner diameter, outer diameter, and thickness of the disk. The model accuracy must meet the requirements of coordinate measuring machine (CMM) measurement and subsequent calculations (geometric tolerance no greater than ±0.001mm). Based on the theoretical CAD model, the rotation center axis of the part (i.e., the dynamic balancing reference axis) is determined. This reference axis must be consistent with the rotation axis of the part during actual installation and use, serving as the benchmark for subsequent unbalance calculations.

[0016] Step 2: Calculate the unbalance sensitivity coefficient using the volume and centroid radius of the thickened geometry.

[0017] The unbalance sensitivity coefficient is defined as the change in unbalance of the component around its rotational axis caused by a unit change in the overall thickness of the blade (e.g., 0.01 mm), expressed in g·mm / mm. Therefore, the formula for calculating the unbalance sensitivity coefficient per unit thickness is: ; In the formula; The density of the material (can be found in a handbook or by actual measurement), the unit is: g / cm³; This represents the increase in blade volume per unit volume for every 0.01 mm increase in blade profile thickness, expressed in mm. 3 / mm;L f The distance from the center of gravity of the thickened portion to the axis of rotation after the blade thickness is increased by 0.01 mm is expressed in mm.

[0018] Step 3: Using the geometric model of the theoretical bladed disk, obtain the contour lines of multiple detection sections in the blade height direction, and discretize each contour line into several small line segments.

[0019] The steps for extracting the theoretical closed curves of each cross-section to obtain the theoretical area of ​​each test cross-section are as follows: Based on the machining process requirements and quality inspection standards of the part, clarify the height distribution of the test cross-sections of the blade profile. The test cross-sections need to be arranged uniformly along the blade height direction or according to key feature points, and the number of cross-sections needs to meet the calculation accuracy requirements (usually no less than 5, and for complex blade profiles, this can be increased to 8-12) to ensure that the overall deviation of the blade profile can be fully reflected.

[0020] Based on a defined rotation center axis, the theoretical contour line of each detection section is extracted from the theoretical CAD model using a section cutting method at a preset detection section height. During extraction, it is essential to ensure that the section is perpendicular to the rotation center axis, and the extraction accuracy of the contour line is no less than the original accuracy of the CAD model.

[0021] For irregular free-form surface sections, the point set is distributed using a chord tolerance method, and the contour line is discretized into several small line segments. The point set density is consistent with the density collected by the coordinate measuring machine.

[0022] Step 4: Calculate the theoretical area and theoretical perimeter of each test section of the theoretical blade using the numerical integration method.

[0023] Numerical integration methods (Simpson's integral method and trapezoidal integral method) are used to calculate the area of ​​the region enclosed by the contour line of each theoretical cross-section, thus obtaining the theoretical area S of each test cross-section. 0m (m is the section number, m=1, 2, ..., p; p is the total number of sections), specifically: In the formula, n is the total number of discrete points on the cross section, where , (Closed point set) Calculate the theoretical perimeter of each test section. The expression is: Step 5: Scan and measure the actual surface of all processed blades, and then process the data to obtain the actual area of ​​each detection section of each processed blade.

[0024] A coordinate measuring machine (CMM) with an accuracy class of not less than 0.002 mm / m was selected as the inspection equipment. The equipment was calibrated before measurement to ensure that the measurement accuracy met the requirements. At the same time, the parts were properly clamped, and special tooling fixtures were used to ensure the clamping and positioning accuracy of the parts. Deformation of the parts was avoided during the clamping process, and the positioning datum was consistent with the design datum of the CAD model.

[0025] According to the preset detection section height and measurement path, the probe of the coordinate measuring machine is controlled to scan and measure the actual surface of the blade, collecting the contour point cloud data of each detection section. During the measurement process, the sampling density of the point cloud data needs to be reasonably set according to the complexity of the blade surface, ensuring that the distance between adjacent sampling points is no greater than 0.01mm, so as to completely restore the actual surface contour of the blade. The collected raw point cloud data is preprocessed: first, abnormal points (noise points) caused by measurement interference, probe contact error, etc. are removed by using distance threshold or statistical filtering methods to screen abnormal points; then, the effective point cloud after screening is smoothed to eliminate the influence of measurement fluctuations; finally, the preprocessed point cloud data is converted into a coordinate system consistent with the theoretical CAD model to ensure the comparability of the measured data and theoretical data and the point cloud file (.RPT format file) is output.

[0026] Step 6: Calculate the thickness deviation of each detection section of each processed blade based on the actual area, theoretical area, and theoretical perimeter of each detection section.

[0027] Calculate the actual area of ​​the blade inspection section and the average blade thickness: For each inspection section, based on the preprocessed actual point cloud data, use the same numerical integration method to calculate the actual measured area S of all measured sections of each blade. im (i=1, 2,...,k; m=1, 2,...,p).

[0028] The expression for calculating the area deviation at the corresponding cross-sectional height of each blade is as follows: ; In the formula, ΔS im A positive value indicates that the actual area of ​​the cross-section is greater than the theoretical area (i.e., the blade is thickened), ΔS im A negative value indicates that the actual area of ​​the cross-section is smaller than the theoretical area (i.e., the blade is thinned); S im S represents the actual area of ​​the m-th cross section of the i-th blade; 0m Let m be the theoretical area of ​​the m-th cross section of any blade in the geometric model of the theoretical bladed disk; Calculate the thickness deviation Δt for each measurement section of each blade. im The expression is: In the formula, L m Let m be the theoretical perimeter of the m-th cross section of any blade in the geometric model of the theoretical bladed disk.

[0029] Step 7: Based on the thickness deviation of each detection section of each processed blade, calculate the average thickness increase of the entire blade, and then obtain the overall imbalance of the bladed disk.

[0030] Step 701: Based on the thickness deviation of each detection section of each processed blade, calculate the average thickness increase of the entire blade using the weighted average method. Based on the thickness deviation Δt of each section im The weighted average method was used to calculate the average thickness increase of the entire blade. The weighting coefficients are determined based on the proportion of each section in the blade's mass distribution. For example, the root section has a larger mass proportion and is given a higher weighting coefficient, while the tip section is given a lower weighting coefficient, to ensure that the average thickness increase can truly reflect the overall thickness deviation of the blade.

[0031] Step 702: Calculate the contribution of each blade to the overall imbalance of the bladed disk. Average thickness calculated per blade Sensitivity coefficient of unit thickness imbalance Calculate the contribution of each blade to the overall imbalance of the bladed disk. : in, This is a vector parameter containing magnitude and direction information (the direction is determined by the azimuth angle of the blade distribution position relative to the rotation center axis). This represents the contribution of the i-th leaf to the overall imbalance of the bladed disk.

[0032] Complete the acquisition of actual profile point cloud, thickness deviation calculation, and individual blade imbalance of all k blades on the bladed disk. Solve for it.

[0033] Step 703: Calculate the overall imbalance of the impeller disk. The vector synthesis algorithm (orthogonal decomposition) is used to superimpose the unbalance vectors of all blades to obtain the total unbalance U of the entire bladed disk (ring). total This includes the magnitude and phase angle of the unbalance. The phase angle indicates the distribution of the unbalanced mass, providing a precise location basis for subsequent weight reduction and compensation.

[0034] Calculate the overall imbalance U total The expression is: In the formula, θ i To calculate the phase angle between the blade and the first blade.

[0035] Calculate the distribution azimuth θ of the indicated unbalance quantity total The expression is: The steps to generate a quantitative compensation plan and guide on-site de-duplication are as follows: The calculated total imbalance U...total The unbalanced threshold U of the parts limit (Determined according to product technical requirements) Compare and determine the imbalance state of the parts.

[0036] If U total ≤U limit Once the dynamic balance of the parts is deemed satisfactory, no weight reduction compensation is required, and the parts can proceed directly to the next process. If U total >U limit If the dynamic balance of a part is deemed unqualified, quantitative compensation is required.

[0037] Based on the magnitude and phase angle of the overall imbalance, combined with the blade profile tolerance, the optimal weight reduction scheme, weight reduction area (prioritizing non-critical stress areas and non-aerodynamically sensitive areas of the blade), weight reduction thickness, and weight reduction range are determined. This ensures that the overall imbalance after weight reduction is reduced to within the acceptable threshold, while minimizing the impact of weight reduction on the blade's structural strength and aerodynamic performance. Finally, an imbalance prediction report and a detailed compensation scheme are output, including key information such as the imbalance distribution of the bladed disk (ring), the magnitude of the overall imbalance, the weight reduction area, and the weight reduction thickness, providing clear guidance for subsequent processing.

[0038] Example Taking a certain aero-engine's first-stage integral bladed disk as an example, this integral bladed disk is made of titanium alloy material (density ρ=4.51g / cm³). 3 It contains 20 blades, and the dynamic balance qualification threshold U limit =2700g・mm.

[0039] The profile of any blade is extracted using the geometric model of the theoretical bladed disk, and then the blade body is thickened by 0.01 mm to obtain the volume of a thickened geometric body. Obtain its volume and centroid coordinates. The sensitivity coefficient of unit thickness unbalance was calculated. =778.716172 g·mm / mm.

[0040] The geometric tolerance of the theoretical bladed disk geometric model is ±0.001mm. Its rotation center axis is defined as the Z-axis, and the rotation center is the origin of the absolute coordinate system (0,0). The blades are uniformly distributed circumferentially along the Z-axis. Six inspection sections are selected along the blade height direction according to process requirements (with the rotation center as the reference height): blade root section (height 200mm), blade root upper section (height 230mm), blade middle section (height 260mm), blade upper middle section (height 290mm), blade tip lower section (height 320mm), and blade tip section (height 350mm).

[0041] The extracted cross-sectional contours are discretized into numerous small line segments according to chordal tolerance, with the point set density consistent with that acquired by the coordinate measuring machine. The area enclosed by each theoretical cross-sectional contour is calculated using a numerical integration method (Simpson's integral method) to obtain the theoretical area of ​​each detected cross-section: S 01 = 835.2, S 02 = 754.6, S 03 = 685.1, S 04 = 614.8, S 05 = 555.7, S 06 = 523.3. The corresponding theoretical perimeter of each cross-section is: L 01 = 687.3, L 02 =634.6, L 03 = 558.6, L 04 = 504.1, L 05 = 450.7, L 06 = 412.3.

[0042] A coordinate measuring machine (CMM) with an accuracy class of not less than 0.002 mm / m was selected as the inspection equipment. The equipment was calibrated before measurement to ensure that the measurement accuracy met the requirements. Simultaneously, the parts were properly clamped using specialized tooling fixtures to ensure the clamping and positioning accuracy of the parts. Deformation of the parts was avoided during clamping, and the positioning datum was kept consistent with the design datum of the CAD model.

[0043] According to the preset detection section height and measurement path, the probe of the coordinate measuring machine is controlled to scan and measure the actual surface of the blade, collecting the contour point cloud data of each detection section. During the measurement process, the sampling density of the point cloud data needs to be reasonably set according to the complexity of the blade surface, ensuring that the distance between adjacent sampling points is no greater than 0.01mm, so as to completely restore the actual surface contour of the blade. The collected raw point cloud data is preprocessed: first, abnormal points (noise points) caused by measurement interference, probe contact error, etc. are removed by using distance threshold or statistical filtering methods to screen abnormal points; then, the effective point cloud after screening is smoothed to eliminate the influence of measurement fluctuations; finally, the preprocessed point cloud data is converted into a coordinate system consistent with the theoretical CAD model to ensure the comparability of the measured data and theoretical data and the point cloud file (.RPT format file) is output.

[0044] For each detection section, based on the preprocessed actual point cloud data, the actual area of ​​the measurement section of the 20 blades was calculated using the Simpson numerical integration method, and the thickness deviation of each section was further calculated as shown in Table 1.

[0045] Table 1. Thickness deviation of each blade section (mm) Based on the thickness deviation Δt of each section im The weighted average method was used to calculate the average thickness Δt of the entire blade. ave The weighting coefficients are determined based on the proportion of each section in the blade mass distribution: ω1=0.3, ω2=0.25, ω3=0.2, ω4=0.15, ω5=0.025, ω6=0.025.

[0046] Average thickness Δt calculated for each blade ave Sensitivity coefficient of unit thickness imbalance Calculate the contribution value ΔU of each cross section to the unbalance of the blade. i Further calculate the overall imbalance. and θ total After calculation, 3022.39918 g·mm, θ total =289.3685°.

[0047] Comparison U total =3022.39918 g·mm and U limit =2700g・mm, because U total >U limit The overall dynamic balance of the impeller was determined to be unqualified, requiring weight reduction compensation. Based on the calculated phase angle, the overall unbalanced area of ​​the impeller was determined to be between blades 16 and 17. Therefore, blades 15, 16, 17, and 18 of the impeller were polished, with the polishing area extending from 10 mm from the blade tip to 20 mm from the blade root, and a removal amount of 0.01 mm on each side.

[0048] After the integral bladed disk was deweighted according to the above compensation scheme, it was measured and verified by YYQ-50 dynamic balancing machine. The actual imbalance was measured to be 2430.246 g·mm, which is only 6.67% different from the imbalance after polishing and compensation predicted by this invention (2592.377 g·mm). The prediction accuracy meets the engineering requirements. Compared to traditional multi-iteration balancing processes, this embodiment pre-estimates the initial imbalance using numerical calculations and achieves the required standard with a single de-weighting process. Furthermore, measuring the impeller imbalance using a dynamic balancing machine costs approximately 1000 yuan per measurement, taking about 40 minutes per unit. Using the method of this invention, the impeller imbalance can be obtained in just 5 minutes. Based on an annual production of 200 impellers, this can save 200,000 yuan in production costs and reduce the time cycle by more than 85%, significantly improving production efficiency.

[0049] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting rotational imbalance in bladed disk-type parts, characterized in that, include: Step 1: Extract the profile of any blade using the geometric model of the theoretical bladed disk; The blade profile is thickened to obtain a thickened geometry, and the volume and centroid radius of the thickened blade geometry are obtained. Step 2: Calculate the unbalance sensitivity coefficient using the volume and centroid radius of the thickened geometry; Step 3: Using the geometric model of the theoretical bladed disk, obtain the contour lines of multiple detection sections in the blade height direction, and discretize each contour line into several small line segments; Step 4: Calculate the theoretical area and theoretical perimeter of each test section of the theoretical blade using the numerical integration method; Step 5: Scan and measure the actual profile of all processed blades, and then process the data to obtain the actual area of ​​each detection section of each processed blade; Step 6: Calculate the thickness deviation of each detection section of each processed blade based on the actual area, theoretical area, and theoretical perimeter of each detection section; Step 7: Based on the thickness deviation of each detection section of each processed blade, calculate the average thickness increase of the entire blade, and then obtain the overall imbalance of the bladed disk.

2. The method for predicting rotational imbalance of bladed disk-type parts according to claim 1, characterized in that, The formula for calculating the unbalance sensitivity coefficient in step 2 is as follows: ； in, The unbalance sensitivity coefficient; The density of the material used in the impeller; To increase the volume of the geometry; To increase the centroid radius of the geometric solid.

3. The method for predicting rotational imbalance of bladed disk-type parts according to claim 1, characterized in that, The formula for calculating the thickness deviation of each detection section of each processed blade in step 6 is as follows: ； in, Let be the thickness deviation of the m-th section of the i-th blade; S im S represents the actual area of ​​the m-th cross section of the i-th blade; 0m L is the theoretical area of ​​the m-th cross-section of any blade in the geometric model of the theoretical bladed disk; m Let m be the theoretical perimeter of the m-th cross section of any blade in the geometric model of the theoretical bladed disk.

4. The method for predicting rotational imbalance of bladed disk-type parts according to claim 1, characterized in that, Step 7 specifically includes: Step 701: Based on the thickness deviation of each detection section of each processed blade, calculate the average thickness increase of the entire blade using the weighted average method; Step 702: Calculate the contribution of each blade to the overall imbalance of the bladed disk; Step 703: Calculate the total imbalance of the impeller.

5. The method for predicting rotational imbalance of bladed disk-type parts according to claim 4, characterized in that, Step 702: The formula for calculating the contribution of each blade to the overall imbalance of the bladed disk is as follows: ； in, This represents the contribution of the i-th leaf to the overall imbalance of the bladed disk. The unbalance sensitivity coefficient; Let be the thickness deviation of the i-th blade.

6. The method for predicting rotational imbalance of bladed disk-type parts according to claim 4, characterized in that, Step 703 The formula for calculating the total imbalance of the impeller is: ； in, This represents the overall imbalance of the bladed disk; This represents the contribution of the i-th leaf to the overall imbalance of the bladed disk. is the phase angle between the i-th blade and the first defined blade; k is the total number of blades.

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