A virtual-real fusion-based compressor blisk burst speed prediction method

By integrating virtual and real elements, using digital twin models and real-time data correction technology, the problem of accurately predicting the rupture speed of the integral blade disc of an aircraft engine compressor was solved, ensuring flight safety.

CN120579291BActive Publication Date: 2025-10-21TAIHANG LABORATORY
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Patent Information

Application Number
CN202511072845.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-08-01
Publication Date
2025-10-21
Estimated Expiration
2045-08-01

AI Technical Summary

Technical Problem

Existing technologies make it difficult to accurately predict the rupture speed of the integral blade disk of an aircraft engine compressor, resulting in an inability to effectively prevent the blade disk from rupturing and failing at high speeds, posing a risk of non-contained accidents.

Method used

A method based on virtual-reality fusion is adopted to establish a digital twin model of the integral blade disk of the aircraft engine compressor. Combined with neural network and parallel computing technology, the failure criteria are corrected using real-time data to predict the rupture speed.

Benefits of technology

The high-precision rupture speed prediction of the integral blade disk of the aircraft engine compressor is achieved, which avoids the blade disk rupture, improves flight safety and reduces the occurrence of non-containment accidents.

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Abstract

The application provides a virtual-real fusion-based compressor blisk burst speed prediction method, and belongs to the technical field of an aero-engine. Specifically, a digital twin model of the aero-engine compressor blisk oriented to the burst speed is established, the model itself and the failure criterion are double-corrected by using test real-time data, and parallel computing technology is used for acceleration in the simulation process, so that a high-precision burst speed prediction value for a single aero-engine compressor blisk body and meeting the physical law and test measurement can be quickly obtained.
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Description

Technical Field

[0001] The present application relates to the field of aero engines, and in particular to a method for predicting the rupture speed of a compressor integral blade disk based on virtual-real fusion. Background Art

[0002] The compressor blisk is a critical component in aircraft engines, operating under harsh conditions for extended periods, facing challenges such as high speeds, high temperatures, high pressures, and alternating loads. Especially at high speeds, excessive centrifugal forces can exceed the allowable stress of the compressor blisk material, leading to rupture and failure. Preventing rupture and failure of compressor blisks at high speeds requires predicting the rupture speed of the compressor blisk.

[0003] There are two main methods for determining the breakaway speed in the past: experimental and physics-based. The experimental method simulates the failure process of an aircraft engine compressor blisk through a disk overspeed test. However, the disk overspeed test is a destructive test, and after the breakaway speed is determined, the compressor blisk is unusable.

[0004] Physics-based methods, specifically physical analysis methods based on failure criteria, explain the disk failure process from a physical mechanistic perspective by summarizing failure criteria. Currently, a variety of failure criteria have been developed. Although the specific parameters and calculation methods vary, they fundamentally compare the internal stress or strain of a material with its calibration value. Specifically, failure occurs when the internal stress or strain exceeds its calibration value. However, since calibration values ​​for stress and strain are mostly measured using standard specimens, real materials exhibit anisotropy. Even single-crystal and directionally crystallized materials cannot be completely isotropic. This leads to discrepancies between the calibration values ​​for a single aeroengine compressor blisk and the standard specimen. Furthermore, real aeroengine compressor blisks exhibit errors in processing technology and operating conditions, and their internal stress and strain also exhibit a degree of randomness. These errors in stress and strain and their calibration values ​​lead to limitations in physical analysis methods based on failure criteria, making it difficult to accurately predict the rupture speed of a single aeroengine compressor blisk.

[0005] In recent years, some prediction schemes based on digital twin models of aircraft engines have emerged, theoretically capable of predicting aircraft engine lifespan. However, these approaches often focus solely on macro-performance prediction and the development of twin theory, lacking methods for predicting compressor blisk rupture speed and practical engineering approaches. Summary of the Invention

[0006] In view of this, the present application provides a method for predicting the rupture speed of an integral blade of a compressor based on virtual-real fusion, which solves the problems in the prior art and can quickly obtain a high-precision rupture speed prediction value for a single individual integral blade of an aircraft engine compressor that conforms to physical laws and experimental measurements.

[0007] The present application provides a method for predicting the rupture speed of a compressor blade disk based on virtual-real fusion, which adopts the following technical solutions:

[0008] A method for predicting compressor blade rupture speed based on virtual-real fusion, including:

[0009] S1, establishing a digital twin model of an aero-engine compressor blade disk based on neural network technology for burst speed;

[0010] S2, gives the initial conditions for the digital twin model of the aero-engine compressor blade;

[0011] S3, simulates the digital twin model of an aero-engine compressor blade using parallel computing technology;

[0012] S4, collects real-time data of the compressor blade during operation and makes real-time corrections to the digital twin model and failure criteria of the aircraft engine compressor blade;

[0013] S5, based on the revised failure criteria, the simulation results of the revised digital twin model of the aero-engine compressor blade are judged and the predicted rupture speed is given.

[0014] Optionally, S1 specifically includes:

[0015] S11, conduct multi-dimensional error analysis on multi-source data of aircraft engine compressor blades during operation, conduct sensitivity analysis at different speeds, and identify key parameters affecting the model;

[0016] S12, setting upper and lower limits for each key parameter, performing random sampling, performing finite element calculations, obtaining sample data under different working conditions, and constructing a sample set;

[0017] S13, constructing a reduced-order model of stress and strain based on a neural network method, improving the accuracy of the reduced-order model by adjusting parameters, and using the sample set to train a maximum strain proxy model;

[0018] S14, keeping all key parameters except the rotational speed unchanged, changing the rotational speed, and using the dichotomy method to minimize the difference between the maximum fracture strain predicted value output by the maximum strain proxy model and the true value of the maximum fracture strain. The rotational speed with the smallest difference is the fracture speed.

[0019] Optionally, S3 specifically includes:

[0020] S31, creating a heterogeneous parallel pool;

[0021] S32, based on the solution process of the digital twin model simulation calculation of the aircraft engine compressor integral blade disk, decompose the task into several subtasks;

[0022] S33, assigning each subtask in S32 to a worker in the parallel pool;

[0023] S34, tracking the working status of each subtask in S33 and managing each subtask;

[0024] S35, obtaining the asynchronous execution results of each subtask in S34;

[0025] S36: After all tasks are completed, the parallel pool is closed and resources are released.

[0026] Optionally, S4 specifically includes:

[0027] S41: A compressor blisk physical model is manufactured and pre-tested. By destroying the compressor blisk physical model, the actual maximum stress and strain of the compressor blisk physical object are measured;

[0028] S42, obtain multiple maximum stress and strain values ​​through batch pre-test, then remove data noise to obtain stress and strain calibration values ;

[0029] S43, collecting real-time data of the compressor blade during operation, and modifying the digital twin model of the aircraft engine compressor blade in combination with pre-test data;

[0030] S44, using real-time data collected by S43 to predict the maximum stress and strain of the digital twin model of the aircraft engine compressor blade Make corrections to obtain the maximum stress-strain correction value ,in, is a parameter related to the material properties. 、 、 These are parameters related to the material properties, geometry, and test operation status. 、 、 is the correction coefficient, respectively 、 、 and change;

[0031] S45, when the maximum stress-strain correction value is obtained Greater than the stress-strain calibration value in S42 When the compressor blade fails, the failure criterion is corrected in real time.

[0032] Optionally, in step S44, determine 、 、 The method is:

[0033] S441: Keep the multi-source data unchanged, and change only one parameter except the speed each time. Carry out several sets of corresponding digital twin model simulations and pre-tests to obtain the maximum stress and strain prediction value output by the digital twin model and the maximum stress and strain measurement value collected by the pre-test, respectively. and ;

[0034] S442, from several groups and Take any three groups and substitute them into the formula Solve to get a set of 、 、 ;

[0035] S443, for several groups of S441 and Repeat the combination and solve to get several groups 、 、 , remove data noise, and then weighted average to obtain a set of 、 、 The weighted average is the final correction factor.

[0036] Optionally, S5 specifically includes:

[0037] S51, using the modified digital twin model of the aero-engine compressor blade to predict the stress and strain fields at different subsequent speeds;

[0038] S52, using the modified failure criterion to judge the stress-strain field predicted in S51, and judging the rotation speed when the failure criterion condition is met as the rupture rotation speed.

[0039] Optionally, the compressor integral blade disk rupture speed prediction method also includes S6, building a virtual experiment visualization platform to interactively display the digital twin model of the aircraft engine compressor integral blade disk.

[0040] Optionally, S6 specifically includes:

[0041] S61, design and build the naked-eye 3D holographic display system, optical tracking system, and operating handle hardware environment;

[0042] S62, visualization of aircraft engine compressor blades based on digital software;

[0043] S63, designs the interaction mode and interface, input and feedback between users and systems in virtual scenes, and realizes the interactive display of the digital twin model of the integral blade disk of the aircraft engine compressor.

[0044] In summary, this application has the following beneficial technical effects:

[0045] Compared to experimental methods that can damage the compressor blisk and physics-based methods that can only provide general, static analysis, the virtual-real fusion-based compressor blisk rupture speed prediction method described in this application neither damages the compressor blisk itself nor, in combination with real-time operating conditions, predicts the rupture speed for a single aircraft engine compressor blisk. This application can effectively prevent excessive speeds in aircraft engine compressor blisks, thereby preventing blisk rupture failures caused by excessive speeds, reducing the occurrence of non-containment accidents in aircraft engines and ensuring flight safety.

[0046] The present application's compressor integral blade rupture speed prediction method based on virtual-real fusion utilizes pre-test data and real-time test data to dynamically correct failure criteria and digital twin models, ensuring the accuracy of the prediction. In addition, it utilizes parallel technology to accelerate the simulation speed of the digital twin model and improve computational efficiency. A special rupture speed prediction method based on virtual-real fusion is proposed for integral blades of aircraft engines, providing an engineered digital twin technology path. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0048] Figure 1 This is a flow chart of the compressor blade rupture speed prediction method based on virtual-real fusion in this application;

[0049] Figure 2 The predicted range of rupture speed before correction in the embodiment of the present application;

[0050] Figure 3 This is the revised rupture speed prediction range in the embodiment of the present application. DETAILED DESCRIPTION

[0051] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0052] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the features in the following embodiments and embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative work are within the scope of protection of this application.

[0053] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this application, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0054] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show components related to the present application and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0055] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0056] The embodiment of the present application provides a method for predicting the rupture speed of a compressor integral blade disk based on virtual-real fusion.

[0057] like Figure 1 As shown in FIG, a method for predicting the rupture speed of a compressor blade disk based on virtual-real fusion includes:

[0058] S1, establishes a digital twin model of the integral blade disk of an aircraft engine compressor based on the burst speed based on neural network technology.

[0059] S2, gives the initial conditions for the digital twin model of the aero-engine compressor blade.

[0060] S3, simulates the digital twin model of the integral blade disk of an aero-engine compressor based on parallel computing technology.

[0061] S4 collects real-time data of the compressor blade during operation and makes real-time corrections to the digital twin model and failure criteria of the aircraft engine compressor blade.

[0062] S5, based on the revised failure criteria, the simulation results of the revised aero-engine compressor blisk digital twin model are judged and the predicted rupture speed is given;

[0063] S6, build a virtual experiment visualization platform to interactively display the digital twin model of the aircraft engine compressor integral blade disk.

[0064] By establishing a digital twin model of an aero-engine compressor blade for rupture speed, using real-time experimental data to double-correct the model itself and the failure criteria, and using parallel computing technology to accelerate the simulation process, it is possible to quickly obtain a high-precision rupture speed prediction value for a single aero-engine compressor blade that conforms to physical laws and experimental measurements.

[0065] In the embodiment of the present application, the specific method of the compressor blade disk rupture speed prediction method based on virtual-real fusion includes:

[0066] S1, based on neural network technology, establishes a digital twin model of an aircraft engine compressor blade disk for burst speed, specifically including:

[0067] S11. Perform multi-dimensional error analysis on multi-source data in the operation of the integral blade disk of the aircraft engine compressor, carry out sensitivity analysis at different speeds, and determine the key parameters affecting the model; wherein, the multi-source data of the integral blade disk of the aircraft engine compressor include but are not limited to the geometry, material, operating conditions, and performance parameters of the integral blade disk of the aircraft engine compressor; the geometric parameters include but are not limited to the inner thickness, outer thickness, inner diameter, and outer diameter of the integral blade disk of the aircraft engine compressor, which can be obtained from the drawing file of the integral blade disk of the aircraft engine compressor; the material parameters of the integral blade disk of the aircraft engine compressor include but are not limited to the elastic modulus, Poisson's ratio, and yield strength of the integral blade disk of the aircraft engine compressor; the operating parameters of the integral blade disk of the aircraft engine compressor should include speed, temperature, constraints, and loads; the performance parameters of the integral blade disk of the aircraft engine compressor include but are not limited to strain, stress, and vibration.

[0068] S12, setting upper and lower limits for each key parameter, performing random sampling, performing finite element calculations, obtaining sample data under different working conditions, and constructing a sample set;

[0069] S13, constructing a reduced-order model of stress and strain based on neural network methods including but not limited to RBF, MLP, CNN, etc., improving the accuracy of the reduced-order model by adjusting parameters, and training the maximum strain proxy model using a sample set. RBF stands for Radial Basis Function Networks, which means radial basis function network in Chinese; MLP stands for Multilayer Perceptrons, which means multilayer perceptron in Chinese; CNN stands for Convolutional Neural Networks, which means convolutional neural network in Chinese;

[0070] S14, keeping all key parameters except the speed unchanged, changing the speed, and using the dichotomy method to minimize the difference between the maximum fracture strain prediction value output by the maximum strain proxy model and the actual maximum fracture strain value. The speed with the smallest difference is the fracture speed; this proxy model is the digital twin model of the integral blade of the aircraft engine compressor for the fracture speed. When the upper and lower limits of the parameters affecting the model except the speed are set and randomly sampled, the proxy model can be used to output a series of fracture speed discrete points to obtain the fracture speed prediction range, such as Figure 2 shown.

[0071] S2, gives the initial conditions for the digital twin model of the aircraft engine compressor blade, including but not limited to the initial values ​​of all parameters of the S11 influencing model that conform to the operating state.

[0072] S3, based on parallel computing technology, conducts simulation of the digital twin model of the aero-engine compressor blade. Specifically, it includes:

[0073] S31, integrates GPU and CPU resources to create a heterogeneous parallel pool;

[0074] S32, based on the solution process of the digital twin model simulation calculation of the aircraft engine compressor integral blade disk, decompose the task into several subtasks;

[0075] S33, assigning each subtask in S32 to a worker in the parallel pool;

[0076] S34, tracking the working status of each subtask in S33 and managing each subtask;

[0077] S35, obtaining the asynchronous execution results of each subtask in S34;

[0078] S36, after all tasks are completed, the parallel pool is closed and resources are released. The simulation results include fracture speed and stress-strain field.

[0079] S4 collects real-time data from the compressor blade during operation and makes real-time corrections to the digital twin model and failure criteria of the aircraft engine compressor blade. Specifically, it includes:

[0080] S41: A compressor blisk mockup was manufactured and pre-tested. By destroying the compressor blisk mockup, its true maximum stress and strain were measured.

[0081] S42, obtain multiple maximum stress and strain values ​​through batch pre-test, then remove data noise to obtain stress and strain calibration values ,in It is a parameter related to the properties of the material itself. is the elastic modulus;

[0082] S43, collecting real-time data of the compressor blade during operation, and modifying the digital twin model of the aircraft engine compressor blade in combination with pre-test data to ensure consistency between the digital twin model and the physical model;

[0083] S44, using real-time data collected by S43 to predict the maximum stress and strain of the digital twin model of the aircraft engine compressor blade Make corrections to obtain the maximum stress-strain correction value ,in, is a parameter related to the material properties. 、 、 These are parameters related to the material properties, geometry, test operation status, etc. 、 、 is the correction coefficient, respectively 、 、 And change; In the embodiment of the present application is the temperature, For the outer diameter, is Poisson's ratio.

[0084] S45, when the maximum stress-strain correction value is obtained Greater than the stress-strain calibration value in S42 When the compressor blade fails, the failure criterion is corrected in real time.

[0085] In step S44, determine 、 、 The method is:

[0086] S441: Keep the S11 multi-source data unchanged, and change only one parameter except the speed each time. Carry out several sets of corresponding digital twin model simulations and pre-tests to obtain the maximum stress and strain prediction value output by the digital twin model and the maximum stress and strain measurement value collected by the pre-test, respectively. and ;

[0087] S442, from several groups and Take any three groups and substitute them into the S44 formula Solving the problem can yield a set of 、 、 ,in 、 、 Only represents 、 、 It is related to the material properties, geometric shape, test operation status, etc., and does not need to be solved;

[0088] S443, for several groups of S441 and Repeated combination and solution can get several groups 、 、 , remove the data noise, and then perform weighted averaging to obtain a set of 、 、 The weighted average is the final correction factor.

[0089] S5: Based on the revised failure criteria, the simulation results of the revised aero-engine compressor blisk digital twin model are judged and the predicted rupture speed is given, including:

[0090] S51, the modified digital twin model of the aero-engine compressor blade is used to predict the stress and strain fields at different subsequent speeds. When the upper and lower limits of the parameters affecting the model except the speed are set and randomly sampled, the modified rupture speed prediction interval can be obtained, such as Figure 3 As shown in the figure, the prediction interval of the rupture speed after correction is obviously narrower than that before correction, so the prediction value of the rupture speed after correction has higher credibility.

[0091] S52, using the modified failure criterion to judge the stress-strain field predicted in S51, and judging the rotation speed when the failure criterion condition is met as the rupture rotation speed.

[0092] S6: Build a virtual experiment visualization platform to interactively display the digital twin model of the aircraft engine compressor blade. Specifically, it includes:

[0093] S61, design and build the naked-eye 3D holographic display system, optical tracking system, and operating handle hardware environment;

[0094] S62, Visualization of an aircraft engine compressor blade using digital software including but not limited to Unreal Engine;

[0095] S63, designs the interaction mode and interface, input and feedback between users and systems in virtual scenes, and realizes the interactive display of the digital twin model of the integral blade disk of the aircraft engine compressor.

[0096] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for predicting the rupture speed of a compressor blade based on virtual-real fusion, characterized in that: include: S1, establishing a digital twin model of an aero-engine compressor blade disk based on neural network technology for burst speed; S2, gives the initial conditions for the digital twin model of the aero-engine compressor blade; S3, simulates the digital twin model of an aero-engine compressor blade using parallel computing technology; S4, collects real-time data of the compressor blade during operation and makes real-time corrections to the digital twin model and failure criteria of the aircraft engine compressor blade; S5, based on the revised failure criteria, the simulation results of the revised aero-engine compressor blisk digital twin model are judged and the predicted rupture speed is given; S1 specifically includes: S11, conduct multi-dimensional error analysis on multi-source data of aircraft engine compressor blades during operation, conduct sensitivity analysis at different speeds, and identify key parameters affecting the model; S12, setting upper and lower limits for each key parameter, performing random sampling, performing finite element calculations, obtaining sample data under different working conditions, and constructing a sample set; S13, constructing a reduced-order model of stress and strain based on a neural network method, improving the accuracy of the reduced-order model by adjusting parameters, and using the sample set to train a maximum strain proxy model; S14, keeping all key parameters except the rotational speed unchanged, changing the rotational speed, and using the dichotomy method to minimize the difference between the maximum fracture strain predicted value output by the maximum strain proxy model and the true value of the maximum fracture strain. The rotational speed with the smallest difference is the fracture speed; S4 specifically includes: S41: A compressor blisk physical model is manufactured and pre-tested. By destroying the compressor blisk physical model, the actual maximum stress and strain of the compressor blisk physical object are measured; S42, obtain multiple maximum stress and strain values ​​through batch pre-test, then remove data noise to obtain stress and strain calibration values ; S43, collecting real-time data of the compressor blade during operation, and modifying the digital twin model of the aircraft engine compressor blade in combination with pre-test data; S44, using real-time data collected by S43 to predict the maximum stress and strain of the digital twin model of the aircraft engine compressor blade Make corrections to obtain the maximum stress-strain correction value ,in, is a parameter related to the material properties. 、 、 These are parameters related to the material properties, geometry, and test operation status. 、 、 is the correction coefficient, respectively 、 、 and change; S45, when the maximum stress-strain correction value is obtained Greater than the stress-strain calibration value in S42 When the compressor blade fails, the failure criterion is corrected in real time.

2. The method for predicting compressor blade rupture speed based on virtual-real fusion according to claim 1 is characterized in that: S3 specifically includes: S31, creating a heterogeneous parallel pool; S32, based on the solution process of the digital twin model simulation calculation of the aircraft engine compressor integral blade disk, decompose the task into several subtasks; S33, assigning each subtask in S32 to a worker in the parallel pool; S34, tracking the working status of each subtask in S33 and managing each subtask; S35, obtaining the asynchronous execution results of each subtask in S34; S36: After all tasks are completed, the parallel pool is closed and resources are released.

3. The method for predicting compressor blade rupture speed based on virtual-real fusion according to claim 1 is characterized in that: In step S44, determine 、 、 The method is: S441: Keep the multi-source data unchanged, and change only one parameter except the speed each time. Carry out several sets of corresponding digital twin model simulations and pre-tests to obtain the maximum stress and strain prediction value output by the digital twin model and the maximum stress and strain measurement value collected by the pre-test, respectively. and ; S442, from several groups and Take any three groups and substitute them into the formula Solve to get a set of 、 、 ; S443, for several groups of S441 and Repeat the combination and solve to get several groups 、 、 , remove data noise, and then weighted average to obtain a set of 、 、 The weighted average is the final correction factor.

4. The method for predicting compressor blade rupture speed based on virtual-real fusion according to claim 1 is characterized in that: S5 specifically includes: S51, using the modified digital twin model of the aero-engine compressor blade to predict the stress and strain fields at different subsequent speeds; S52, using the modified failure criterion to judge the stress-strain field predicted in S51, and judging the rotation speed when the failure criterion condition is met as the rupture rotation speed.

5. The compressor blade rupture speed prediction method based on virtual-real fusion according to claim 1 is characterized in that: The compressor blade rupture speed prediction method also includes S6, which builds a virtual experiment visualization platform to interactively display the digital twin model of the aircraft engine compressor blade.

6. The method for predicting compressor blade rupture speed based on virtual-real fusion according to claim 5 is characterized in that: S6 specifically includes: S61, design and build the naked-eye 3D holographic display system, optical tracking system, and operating handle hardware environment; S62, visualization of aircraft engine compressor blades based on digital software; S63, designs the interaction mode and interface, input and feedback between users and systems in virtual scenes, and realizes the interactive display of the digital twin model of the integral blade disk of the aircraft engine compressor.

Citation Information

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