An aero-engine fan rotor keyless phase virtual dynamic balancing method and system based on finite element method

Abstract

The application relates to the technical field of vibration active control and artificial intelligence, and discloses a keyless phase virtual dynamic balancing method and system for an aero-engine fan rotor based on a finite element method, which comprises the following modules: a modeling and simulation module configured to obtain a first-order critical rotating speed and a vibration mode of an initial rotor dynamics simulation model; a model calibration module configured to calibrate the initial rotor dynamics simulation model according to a first actual amplitude, and obtain a calibrated rotor dynamics simulation model; a model updating module configured to update the calibrated rotor dynamics simulation model, and obtain an updated rotor dynamics simulation model; a trial weight and counterweight module configured to substitute the second actual amplitude into a particle swarm optimization, calculate an actual rotor system total unbalance and a trial weight angle difference, finally add a counterweight and select a direction until vibration is reduced, and dynamic balancing is achieved. According to the application, the position of an unbalance can be accurately determined through amplitude analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of active vibration control and artificial intelligence, in particular to a fan rotor of an aero-engine keyless phase virtual dynamic balancing method and system based on finite element method. BACKGROUND

[0002] Under the harsh environment of high speed, high temperature and high load, the rotor system of the aero-engine may deform, wear and change in concentricity. These changes will cause the mass center of the rotor to deviate from the rotation center, thereby causing vibration and affecting the stability of the whole machine. Unbalance is the main cause of engine vibration, and the vibration fault caused by mass unbalance is particularly common and harmful. In actual dynamic balancing operation, the influence coefficient method is usually used, but this method requires at least one weight, and the size of the weight often depends on experience, which leads to high balancing cost. In addition, frequent start-stop operations also significantly increase the production cost. Therefore, it is crucial to reduce the start-stop times to improve the dynamic balancing efficiency while meeting the balancing requirements. At present, the influence coefficient method, modal balancing method, coordinate wheel optimization and its optimization method are relatively mature dynamic balancing technologies. The influence coefficient method and the modal balancing method both need to collect data through multiple trial runs to identify unbalance, which belongs to the steady-state balancing method. The coordinate wheel optimization method will perform trial adjustment before each balancing adjustment to determine the adjustment method and direction of the next step. Although this method is simple and practical, it is suitable for both steady-state and non-steady-state conditions, but the trial adjustment process has a certain blindness and may cause incorrect adjustment. Moreover, each optimization starts from zero and does not effectively utilize the beneficial data from the previous step, so the balancing efficiency is not high. Virtual dynamic balancing technology, as a new method, significantly improves the cost-effectiveness of balancing by adding virtual excitation to the simulation model for unbalance response analysis.

[0003] In actual field dynamic balancing operation, it is usually necessary to measure the phase of rotor vibration to determine the weight position, which requires the installation of a key phase sensor in advance to ensure the smooth progress of the rotor field dynamic balancing. However, due to the particularity of the structure of the aero-engine, sometimes it does not have the condition to output phase information, which brings great challenges to actual dynamic balancing.

[0004] Therefore, it is necessary to design a fan rotor of an aero-engine keyless phase virtual dynamic balancing method and system based on finite element method to solve the problems in the prior art. SUMMARY

[0005] In view of this, the present application provides a fan rotor of an aero-engine keyless phase virtual dynamic balancing method and system based on finite element method, which aims to solve the problem that due to the particularity of the structure of the aero-engine, sometimes it does not have the condition to output phase information, which brings great challenges to actual dynamic balancing.

[0006] In one aspect, the present application provides an aero-engine fan rotor keyless phase virtual dynamic balancing system based on finite element method, comprising:

[0007] A modeling and simulation module is configured to establish an initial rotor dynamics simulation model, perform modal analysis on the initial rotor dynamics simulation model by using finite element method, and obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model;

[0008] A model calibration module is configured to measure a critical speed of an actual rotor, compare the critical speed with the first-order critical speed, determine whether to calibrate the initial rotor dynamics simulation model according to a comparison result, measure a first actual amplitude of the actual rotor if the initial rotor dynamics simulation model is to be calibrated, calibrate the initial rotor dynamics simulation model according to the first actual amplitude, and obtain a calibrated rotor dynamics simulation model;

[0009] A model updating module is configured to calculate bearing stiffness and original unbalance by using the measured first actual amplitude through particle swarm optimization, update the calibrated rotor dynamics simulation model, and obtain an updated rotor dynamics simulation model;

[0010] A trial weight and counterweight module is configured to add a trial weight on the actual rotor according to a particle optimization result, measure a second actual amplitude, substitute the second actual amplitude into particle swarm optimization, calculate an actual rotor system total unbalance and a trial weight angle difference, finally add a counterweight and select a direction until vibration is reduced, and realize dynamic balancing.

[0011] Further, when the modeling and simulation module performs modal analysis on the initial rotor dynamics simulation model by using finite element method to obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model, the method comprises:

[0012] The actual rotor system is converted into a discretization model with a finite number of degrees of freedom by using finite element method;

[0013] The discretization model is simulated by using a finite element program, and a steady-state unbalance response is analyzed;

[0014] The initial rotor dynamics simulation model is modal analyzed to obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model.

[0015] Further, when the model calibration module compares the critical speed with the first-order critical speed, and determines whether to calibrate the initial rotor dynamics simulation model according to a comparison result, the method comprises:

[0016] Calculate the difference between the critical speed and the first-order critical speed, and record it as the critical speed deviation value;

[0017] The critical speed deviation value is compared with the critical speed deviation threshold, and the initial rotor dynamics simulation model is calibrated based on the comparison result.

[0018] When the critical speed deviation value is within the critical speed deviation threshold, it is determined that the initial rotor dynamics simulation model will not be calibrated.

[0019] When the critical speed deviation value is outside the critical speed deviation threshold, it is determined that the initial rotor dynamics simulation model needs to be calibrated.

[0020] Further, the model calibration module calibrates the initial rotor dynamics simulation model based on the first actual amplitude, and when obtaining the calibrated rotor dynamics simulation model, it includes:

[0021] The first actual amplitude is the amplitude measured at three different measuring points at the same rotational speed of the actual rotor, or the amplitude measured at three different rotational speeds at the same measuring point of the actual rotor.

[0022] Based on the first actual amplitude, adjust the bearing stiffness parameters of the initial rotor dynamics simulation model to obtain a calibrated rotor dynamics simulation model.

[0023] Furthermore, the model update module utilizes the measured first actual amplitude to calculate the bearing stiffness and original unbalance through particle swarm optimization, and updates the calibrated rotor dynamics simulation model. The updated rotor dynamics simulation model includes:

[0024] Based on the aforementioned calibrated rotor dynamics simulation model, the first actual amplitude is substituted into the particle swarm optimization algorithm for optimization.

[0025] Define a fitness function, using the bearing stiffness and the original unbalance as optimization variables, and calculate the fitness value based on finite element simulation;

[0026] Initialize the particle swarm parameters and calculate the initial fitness value; wherein, the particle swarm parameters include population size, number of iterations, velocity, maximum and minimum position values;

[0027] Calculate individual extreme values ​​and group extreme values, and continuously update the velocity and position of particles according to optimization rules. After multiple iterations, obtain the optimization result of the first particle swarm. The optimization rules are as follows: each particle calculates its velocity in the next generation based on the individual extreme value and group extreme value, and then calculates its position based on the velocity.

[0028] Based on the first particle swarm optimization results, the bearing stiffness and original unbalance parameters in the calibrated rotor dynamics simulation model are updated to obtain an updated rotor dynamics simulation model.

[0029] Furthermore, the fitness function is:

[0030] Function[fitness]=Fitness(x,y,z);

[0031] Here, Function is a defined function in MATLAB, that is, defining a fitness function; x and y represent bearing stiffness; and z represents the initial unbalance.

[0032] Furthermore, when the model update module initializes the particle swarm parameters and calculates the initial fitness value, it includes:

[0033] A population of random individuals is generated, where each individual's velocity and position are three-dimensional vectors. The fitness function (x, y, z) is called, and the fitness value is output using the individual's position information (x, y, z).

[0034] Furthermore, when the model update module calculates individual extreme values ​​and population extreme values, it includes:

[0035] By comparing the various fitness values, the individual extreme values ​​and the population extreme values ​​are obtained.

[0036] The individual extreme value refers to the best fitness value experienced by an individual, and the population extreme value refers to the maximum fitness value in a certain generation of the population.

[0037] Furthermore, the trial weight and counterweight module substitutes the second actual amplitude into particle swarm optimization, calculates the total imbalance of the actual rotor system and the trial weight angle difference, and finally adds counterweights and selects directions until the vibration is reduced and dynamic balance is achieved, including:

[0038] A trial weight is added to the actual rotor, the trial weight being equal to the original imbalance calculated by particle swarm optimization, and the second actual amplitude is measured.

[0039] The second actual amplitude is substituted into the particle swarm optimization algorithm again to obtain the second particle swarm optimization result, and the total imbalance and trial weight angle difference of the actual rotor system are calculated.

[0040] Based on the optimization results of the second particle swarm, add counterweights and select directions until the vibration is reduced and dynamic balance is achieved.

[0041] Compared with existing technologies, the advantages of this invention are that it eliminates the need for phase measurement. This invention is particularly suitable for rotor systems where key phase sensors cannot be installed, allowing for precise determination of the location of imbalance solely through amplitude analysis. It is especially applicable to the dynamic balancing of aero-engine rotors and demonstrates broad application potential.

[0042] By combining particle swarm optimization (PSO) algorithm with virtual dynamic balancing technology, this method significantly improves the accuracy of balancing results. Virtual dynamic balancing technology uses a simulation model to mimic the actual rotor and obtains unbalanced response analysis by applying virtual counterweights, effectively replacing the tedious process of repeatedly starting the engine and adding actual counterweights, thus greatly improving the efficiency of dynamic balancing. Furthermore, the introduction of the particle swarm optimization algorithm from machine learning allows for more accurate verification of the simulation model, ensuring a high degree of consistency with the actual rotor, resulting in a significantly improved accuracy compared to traditional virtual dynamic balancing techniques.

[0043] This technology can calculate the initial imbalance of the system through a single initial vibration measurement. When adding trial weights, the weights are adjusted according to the calculation results, and there is a 30% probability that balance will be achieved on the first trial weight. Even if the first trial weight fails to reduce vibration, there is a 50% probability that vibration will be completely reduced on the second weight addition; otherwise, vibration reduction will definitely be achieved on the third trial weight.

[0044] In another aspect, this invention also proposes a keyless virtual dynamic balancing method for aero-engine fan rotors based on the finite element method, comprising the following steps:

[0045] S100: Establish an initial rotor dynamics simulation model, and perform modal analysis on the initial rotor dynamics simulation model using the finite element method to obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model;

[0046] S200: Measure the critical speed of the actual rotor and compare the critical speed with the first-order critical speed. Based on the comparison result, determine whether to calibrate the initial rotor dynamics simulation model. If so, measure the first actual amplitude of the actual rotor and calibrate the initial rotor dynamics simulation model based on the first actual amplitude to obtain a calibrated rotor dynamics simulation model.

[0047] S300: Using the measured first actual amplitude, the bearing stiffness and original imbalance are calculated through particle swarm optimization, and the calibrated rotor dynamics simulation model is updated to obtain an updated rotor dynamics simulation model.

[0048] S400: Based on the particle optimization results, add trial weights to the actual rotor and measure the second actual amplitude; substitute the second actual amplitude into the particle swarm optimization, calculate the total imbalance of the actual rotor system and the angle difference of the trial weights, and finally add counterweights and select directions until the vibration is reduced and dynamic balance is achieved.

[0049] It is understandable that the above-mentioned virtual dynamic balancing method and system for keyless phase of aero-engine fan rotor based on the finite element method have the same beneficial effects, and will not be elaborated here. Attached Figure Description

[0050] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0051] Figure 1 A structural block diagram of a keyless phase virtual dynamic balancing system for an aero-engine fan rotor based on the finite element method, provided for an embodiment of the present invention;

[0052] Figure 2 A flowchart of a virtual dynamic balancing method for aero-engine fan rotors based on the finite element method, provided for an embodiment of the present invention. Detailed Implementation

[0053] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] See Figure 1 As shown in some embodiments of this application, this embodiment provides a keyless virtual dynamic balancing system for aero-engine fan rotor based on the finite element method, including:

[0055] The modeling and simulation module is configured to establish an initial rotor dynamics simulation model, perform modal analysis on the initial rotor dynamics simulation model using the finite element method, and obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model.

[0056] The model calibration module is configured to measure the critical speed of the actual rotor and compare the critical speed with the first-order critical speed. Based on the comparison result, it determines whether the initial rotor dynamics simulation model should be calibrated. If so, the first actual amplitude of the actual rotor is measured, and the initial rotor dynamics simulation model is calibrated based on the first actual amplitude to obtain a calibrated rotor dynamics simulation model.

[0057] The model update module is configured to use the measured first actual amplitude to calculate the bearing stiffness and original imbalance through particle swarm optimization, and update the calibrated rotor dynamics simulation model to obtain an updated rotor dynamics simulation model.

[0058] The trial weight and counterweight module is configured to add trial weights to the actual rotor according to the particle swarm optimization results and measure the second actual amplitude; substitute the second actual amplitude into the particle swarm optimization to calculate the total imbalance of the actual rotor system and the angle difference of the trial weights, and finally add counterweights and select directions until the vibration is reduced and dynamic balance is achieved.

[0059] It is understood that the keyless phase virtual dynamic balancing system for aero-engine fan rotors based on the finite element method provided in this embodiment can achieve precise dynamic balancing without phase measurement, greatly improving the convenience and efficiency of operation. In practical applications, the system first establishes an accurate initial rotor dynamics simulation model through the modeling and simulation module, and performs modal analysis using the finite element method to obtain key parameters such as the first-order critical speed and mode shape. Subsequently, the model calibration module measures the critical speed of the actual rotor and compares it with the first-order critical speed of the simulation model to ensure the accuracy of the simulation model. If there is a deviation, the simulation model is calibrated according to the first actual amplitude of the actual rotor to obtain a calibrated rotor dynamics simulation model that is closer to reality. After the model calibration is completed, the model update module further uses the first actual amplitude to calculate the bearing stiffness and the original imbalance through an advanced particle swarm optimization algorithm, and updates the calibrated simulation model to obtain an updated rotor dynamics simulation model. This process fully utilizes the global search capability and fast convergence characteristics of the particle swarm optimization algorithm, effectively improving the accuracy and reliability of the simulation model. Finally, the trial weight and counterweight module adds trial weights to the actual rotor based on the particle swarm optimization results and measures the second actual amplitude. Then, the second actual amplitude is again substituted into the particle swarm optimization algorithm to calculate the total imbalance of the actual rotor system and the trial weight angle difference. Based on this information, counterweights can be added precisely and in the correct direction until the vibration is reduced, achieving dynamic balance. This process not only avoids the tedious repeated start-up and addition of actual counterweights in traditional dynamic balancing methods but also significantly improves the efficiency and accuracy of dynamic balancing.

[0060] Specifically, when the modeling and simulation module uses the finite element method to perform modal analysis on the initial rotor dynamics simulation model to obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model, it includes:

[0061] The actual rotor system is transformed into a discretized model with a finite number of degrees of freedom using the finite element method;

[0062] The discretized model was subjected to dynamic simulation using a finite element method, and the steady-state unbalanced response was analyzed.

[0063] Modal analysis was performed on the initial rotor dynamics simulation model to obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model.

[0064] It is understandable that the stiffness of two bearings is randomly set to 10. 6 Based on the N / m, modal analysis was performed on the initial rotor simulation model, and the first critical speed of the model was obtained as 3469 r / min.

[0065] Specifically, when the model calibration module compares the critical speed with the first-order critical speed and determines whether to calibrate the initial rotor dynamics simulation model based on the comparison result, it includes:

[0066] Calculate the difference between the critical speed and the first-order critical speed, and record it as the critical speed deviation value;

[0067] The critical speed deviation value is compared with the critical speed deviation threshold, and the initial rotor dynamics simulation model is calibrated based on the comparison result.

[0068] When the critical speed deviation value is within the critical speed deviation threshold, it is determined that the initial rotor dynamics simulation model will not be calibrated.

[0069] When the critical speed deviation value is outside the critical speed deviation threshold, it is determined that the initial rotor dynamics simulation model needs to be calibrated.

[0070] In this embodiment, the critical speed deviation threshold is set based on empirical values ​​and industry standards, and is used to determine whether the deviation between the actual rotor's critical speed and the first-order critical speed of the simulation model is within an acceptable range.

[0071] Understandably, when calibrating the initial rotor dynamics simulation model, the system adjusts relevant parameters in the simulation model based on the first actual amplitude of the actual rotor to ensure that the simulation results are closer to reality. This calibration process not only improves the accuracy of the simulation model but also provides a more reliable basis for subsequent dynamic balancing operations.

[0072] Specifically, the model calibration module calibrates the initial rotor dynamics simulation model based on the first actual amplitude to obtain a calibrated rotor dynamics simulation model, including:

[0073] The first actual amplitude is the amplitude measured at three different measuring points at the same rotational speed of the actual rotor, or the amplitude measured at three different rotational speeds at the same measuring point of the actual rotor.

[0074] Based on the first actual amplitude, adjust the bearing stiffness parameters of the initial rotor dynamics simulation model to obtain a calibrated rotor dynamics simulation model.

[0075] Understandably, when adjusting bearing stiffness parameters, the system comprehensively considers the vibration characteristics of the actual rotor and the prediction results of the simulation model, gradually approximating the optimal parameter combination through iterative optimization algorithms. This process not only ensures that the calibrated simulation model accurately reflects the dynamic characteristics of the actual rotor, but also provides more precise guidance for subsequent dynamic balancing operations.

[0076] Specifically, the model update module uses the measured first actual amplitude to calculate the bearing stiffness and original imbalance through particle swarm optimization, and updates the calibrated rotor dynamics simulation model. The updated rotor dynamics simulation model includes:

[0077] Based on the aforementioned calibrated rotor dynamics simulation model, the first actual amplitude is substituted into the particle swarm optimization algorithm for optimization.

[0078] Define a fitness function, using the bearing stiffness and the original unbalance as optimization variables, and calculate the fitness value based on finite element simulation;

[0079] Initialize the particle swarm parameters and calculate the initial fitness value; wherein, the particle swarm parameters include population size, number of iterations, velocity, maximum and minimum position values;

[0080] Calculate individual extreme values ​​and group extreme values, and continuously update the velocity and position of particles according to optimization rules. After multiple iterations, obtain the optimization result of the first particle swarm. The optimization rules are as follows: each particle calculates its velocity in the next generation based on the individual extreme value and group extreme value, and then calculates its position based on the velocity.

[0081] Based on the first particle swarm optimization results, the bearing stiffness and original unbalance parameters in the calibrated rotor dynamics simulation model are updated to obtain an updated rotor dynamics simulation model.

[0082] In this embodiment, the formula for particle update velocity and position is as follows:

[0083]

[0084] Where w is the inertia weight (i nert i awe i ght), Let be the historical best solution found from the i-th particle up to the t-th generation. This is the optimal solution found so far for the entire particle swarm. Vi(t) represents the current position and velocity of the i-th particle, c1 and c2 are non-negative constants called acceleration factors, r1 and r2 are random numbers between [0,1], and g is the index of the optimal particle position.

[0085] In this embodiment, non-linearly decreasing dynamic weights are used to adjust particle velocity and position to balance the globality of the search and the convergence speed. The adjustment formula for the inertial weight w is as follows:

[0086]

[0087] Among them, W max W is the maximum weight set in the algorithm. min t is the minimum weight set in the algorithm. max This is the maximum number of iterations set.

[0088] In this embodiment, the three optimal particle positions are:

[0089] 1.054×10 6 N / m, 1.018×10 6 N / m, 6.226×10 -4 kg·m.

[0090] Comparing with the original settings, we can see that the optimization errors of the two bearings are 5.4% and 1.8% respectively, and the optimization error of the original imbalance is 3.8%. The errors are small and can be used.

[0091] Understandable

[0092] Specifically, the fitness function is:

[0093] Function[fitness]=Fitness(x,y,z);

[0094] Here, Function is a defined function in MATLAB, that is, defining a fitness function; x and y represent bearing stiffness; and z represents the initial unbalance.

[0095] Specifically, when the model update module initializes the particle swarm parameters and calculates the initial fitness value, it includes:

[0096] A population of random individuals is generated, where each individual's velocity and position are three-dimensional vectors. The fitness function (x, y, z) is called, and the fitness value is output using the individual's position information (x, y, z).

[0097] Specifically, when the model update module calculates individual extreme values ​​and population extreme values, it includes:

[0098] By comparing the various fitness values, the individual extreme values ​​and the population extreme values ​​are obtained.

[0099] The individual extreme value refers to the best fitness value experienced by an individual, and the population extreme value refers to the maximum fitness value in a certain generation of the population.

[0100] Understandably, in the particle swarm optimization process, the continuous updating of individual and swarm optima guides the particles toward the global optimum. The updating of individual optima depends on comparing the historical fitness of each particle, while the updating of swarm optima is based on the optimal fitness of the entire population in the current iteration. Through continuous iteration and optimization, the particle swarm gradually converges to the optimal solution, thereby accurately calculating the bearing stiffness and the initial imbalance. After obtaining the updated rotor dynamics simulation model, the trial weight and counterweight module begins to function. This module first adds trial weights to the actual rotor based on the particle swarm optimization results and measures the second actual amplitude after adding the trial weights. Subsequently, this amplitude value is substituted back into the particle swarm optimization algorithm to further accurately calculate the total imbalance of the actual rotor system and the trial weight angle difference. This process achieves accurate identification and location of the actual rotor imbalance, providing accurate guidance for the subsequent addition of counterweights. During the counterweight addition stage, the system accurately determines the mass and addition position of the counterweights based on the calculated total imbalance and trial weight angle difference. By gradually adding counterweights and measuring vibration, the system can continuously adjust the counterweight parameters until the vibration is reduced to a satisfactory level, thus achieving dynamic balance. This process not only avoids the tedious process of repeatedly starting the engine and adding actual counterweights in traditional dynamic balancing methods, but also significantly improves the efficiency and accuracy of dynamic balancing, providing a strong guarantee for the stable operation of aero-engine fan rotors.

[0101] Specifically, the trial weight and counterweight module substitutes the second actual amplitude into particle swarm optimization, calculates the total imbalance of the actual rotor system and the trial weight angle difference, and finally adds counterweights and selects directions until the vibration is reduced and dynamic balance is achieved, including:

[0102] A trial weight is added to the actual rotor, the trial weight being equal to the original imbalance calculated by particle swarm optimization, and the second actual amplitude is measured.

[0103] The second actual amplitude is substituted into the particle swarm optimization algorithm again to obtain the second particle swarm optimization result, and the total imbalance and trial weight angle difference of the actual rotor system are calculated.

[0104] Based on the optimization results of the second particle swarm, add counterweights and select directions until the vibration is reduced and dynamic balance is achieved.

[0105] In this embodiment, particle swarm optimization iteration is performed. The particle swarm is set to one dimension, and the calibrated rotor dynamics simulation model is repeatedly updated to obtain an updated rotor dynamics simulation model. Through this process, we obtain the original imbalance and the angle difference between the test weight and the initial imbalance, which is 60°. Dynamic balancing is achieved by adding a virtual counterweight. Given that the initial excitation occurs in the 0° direction, while the test weight is located in the 60° direction, the angle difference calculated by the particle swarm algorithm is exactly 60°, indicating that the calculated phase is correct. However, in actual operation, we are unsure whether the test weight is 60° in a clockwise or counterclockwise direction. Therefore, in the opposite direction of 0°, i.e., the 180° direction, a virtual counterweight of 6.226 × 10⁻⁶, obtained from the calculation steps, is added. -4 kg·m. Subsequently, we obtained a 7-node simulated response of 3.4 μm, which represents a vibration reduction effect of 96.3% compared to the original response. This proves that the simulation method is entirely feasible.

[0106] Understandably, in utilizing particle swarm optimization (PSO) algorithms for trial weighting and balancing, we fully considered the complexity and dynamic characteristics of the actual rotor. By precisely calculating the size and location of the trial weights, as well as the direction and mass of the balancing weights, we achieved effective control and adjustment of rotor imbalance. This process not only relies on advanced algorithms and techniques but also requires operators with extensive experience and expertise. In practical applications, operators will flexibly adjust and optimize based on the guidance and suggestions provided by the system, combined with the actual situation, to ensure the accuracy and effectiveness of dynamic balancing operations. Furthermore, the system possesses high scalability and flexibility, capable of adapting to the dynamic balancing needs of different models and specifications of aero-engine fan rotors. Through continuous optimization and upgrades to system functions and performance, we can further improve the efficiency and accuracy of dynamic balancing, providing more reliable support and assurance for the stable operation and performance improvement of aero-engines.

[0107] See Figure 2 As shown in some embodiments of this application, this embodiment provides a keyless phase virtual dynamic balancing method for aero-engine fan rotors based on the finite element method, including the following steps:

[0108] S100: Establish an initial rotor dynamics simulation model, and perform modal analysis on the initial rotor dynamics simulation model using the finite element method to obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model;

[0109] S200: Measure the critical speed of the actual rotor and compare the critical speed with the first-order critical speed. Based on the comparison result, determine whether to calibrate the initial rotor dynamics simulation model. If so, measure the first actual amplitude of the actual rotor and calibrate the initial rotor dynamics simulation model based on the first actual amplitude to obtain a calibrated rotor dynamics simulation model.

[0110] S300: Using the measured first actual amplitude, the bearing stiffness and original imbalance are calculated through particle swarm optimization, and the calibrated rotor dynamics simulation model is updated to obtain an updated rotor dynamics simulation model.

[0111] S400: Based on the particle optimization results, add trial weights to the actual rotor and measure the second actual amplitude; substitute the second actual amplitude into the particle swarm optimization, calculate the total imbalance of the actual rotor system and the angle difference of the trial weights, and finally add counterweights and select directions until the vibration is reduced and dynamic balance is achieved.

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program goods. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program goods embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program goods according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A finite element method based keyless phase virtual dynamic balancing system for aero-engine fan rotor, characterized in that, The method comprises the following steps: a modeling and simulation module configured to establish an initial rotor dynamics simulation model, perform modal analysis on the initial rotor dynamics simulation model by using a finite element method, and obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model; a model calibration module configured to measure a critical speed of an actual rotor, compare the critical speed with the first-order critical speed, determine whether to calibrate the initial rotor dynamics simulation model according to a comparison result, measure a first actual amplitude of the actual rotor if the initial rotor dynamics simulation model is to be calibrated, calibrate the initial rotor dynamics simulation model according to the first actual amplitude, and obtain a calibrated rotor dynamics simulation model; a model updating module configured to calculate bearing stiffness and an original unbalance amount by using the measured first actual amplitude through particle swarm optimization, update the calibrated rotor dynamics simulation model, and obtain an updated rotor dynamics simulation model; a trial weight and counterweight module configured to add a trial weight on the actual rotor according to a particle optimization result, measure a second actual amplitude, substitute the second actual amplitude into particle swarm optimization to calculate an actual rotor system total unbalance amount and a trial weight angle difference, finally add a counterweight and select a direction until vibration is reduced, and realize dynamic balancing. When the model calibration module compares the critical speed with the first-order critical speed and determines whether to calibrate the initial rotor dynamics simulation model according to a comparison result, the method comprises the following steps: calculating a difference between the critical speed and the first-order critical speed, and recording the difference as a critical speed deviation value; comparing the critical speed deviation value with a critical speed deviation threshold value, and determining whether to calibrate the initial rotor dynamics simulation model according to a comparison result; when the critical speed deviation value is within the critical speed deviation threshold value, determining not to calibrate the initial rotor dynamics simulation model; when the critical speed deviation value is outside the critical speed deviation threshold value, determining to calibrate the initial rotor dynamics simulation model. When the model calibration module calibrates the initial rotor dynamics simulation model according to the first actual amplitude to obtain a calibrated rotor dynamics simulation model, the method comprises the following steps: the first actual amplitude is an amplitude of the actual rotor at a same speed measured at three different measuring points or an amplitude of the actual rotor at a same measuring point measured at three different speeds; adjusting a bearing stiffness parameter of the initial rotor dynamics simulation model according to the first actual amplitude to obtain a calibrated rotor dynamics simulation model.

2. The finite element method based aero-engine fan rotor keyless phase virtual dynamic balancing system according to claim 1, characterized in that, When the modeling and simulation module performs modal analysis on the initial rotor dynamics simulation model by using a finite element method to obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model, the method comprises the following steps: transforming the actual rotor system into a discretization model with a finite number of degrees of freedom by using a finite element method; performing dynamic simulation on the discretization model by using a finite element program and analyzing a steady-state unbalance response; performing modal analysis on the initial rotor dynamics simulation model to obtain a first-order critical speed and a vibration mode of the initial rotor dynamics simulation model.

3. The finite element method based aero-engine fan blade off phasor virtual dynamic balancing system according to claim 1, characterized in that, The model updating module utilizes the measured first actual amplitude to calculate bearing stiffness and original unbalance through particle swarm optimization, and updates the calibration rotor dynamics simulation model, to obtain an updated rotor dynamics simulation model, comprising: Based on the calibration rotor dynamics simulation model, the first actual amplitude is substituted into a particle swarm optimization algorithm for optimization; A fitness function is defined, taking the bearing stiffness and original unbalance as optimization variables, and calculating a fitness value based on finite element simulation; Particle swarm parameters are initialized, and an initial fitness value is calculated; wherein the particle swarm parameters include population size, iteration number, velocity, maximum and minimum position; Individual extreme values and group extreme values are calculated, and the velocity and position of the particles are continuously updated according to the optimization rules, and the first particle swarm optimization result is obtained after multiple iterations; wherein the optimization rules are that each particle calculates the velocity in the next generation according to the individual extreme values and group extreme values, and then calculates the position according to the velocity; According to the first particle swarm optimization result, the bearing stiffness and original unbalance parameters in the calibration rotor dynamics simulation model are updated to obtain an updated rotor dynamics simulation model.

4. The finite element method based aero-engine fan blade off phasor virtual dynamic balancing system according to claim 3, characterized in that, The fitness function is: where, is the definition function of matlab, i.e. define a fitness function ; , denotes the bearing stiffness; denotes the original unbalance.

5. The finite element method based aero-engine fan blade off phasor virtual dynamic balancing system of claim 4, wherein, When the model updating module initializes the particle swarm parameters and calculates the initial fitness value, it includes: A population of several individuals is randomly generated, each with a three-dimensional vector for speed and position, and the fitness function is called with the individual position information as and the output is the fitness value.

6. The finite element method based aero-engine fan blade off phasor virtual dynamic balancing system of claim 5, wherein, When the model updating module calculates the individual extreme values and group extreme values, it includes: Each fitness value is compared to obtain the individual extreme values and group extreme values in the population; Wherein, the individual extreme value refers to the best fitness value experienced by the individual, and the group extreme value refers to the maximum fitness value in a generation of the population.

7. The finite element method based aero-engine fan blade off phasor virtual dynamic balancing system of claim 6, wherein, The trial weight and counterweight module substitutes the second actual amplitude into particle swarm optimization to calculate the total unbalance of the actual rotor system and the trial weight angle difference, and finally adds counterweights and selects directions until the vibration is reduced to achieve dynamic balancing, comprising: A trial weight is added to the actual rotor, and the size of the trial weight is equal to the original unbalance calculated by particle swarm optimization, and the second actual amplitude is measured; The second actual amplitude is substituted into the particle swarm optimization algorithm again to obtain a second particle swarm optimization result, and the total unbalance of the actual rotor system and the trial weight angle difference are calculated; According to the second particle swarm optimization result, counterweights are added and directions are selected until the vibration is reduced to achieve dynamic balancing.

8. A finite element method based aero-engine fan rotor non-key phasing virtual dynamic balancing method applied in the finite element method based aero-engine fan rotor non-key phasing virtual dynamic balancing system of any one of claims 1-7, characterized in that, Comprising: An initial rotor dynamics simulation model is established, and modal analysis is performed on the initial rotor dynamics simulation model using the finite element method to obtain the first-order critical speed and mode shape of the initial rotor dynamics simulation model; The critical speed of the actual rotor is measured, and the critical speed is compared with the first-order critical speed, and whether to calibrate the initial rotor dynamics simulation model is determined according to the comparison result; if yes, the first actual amplitude of the actual rotor is measured, and the initial rotor dynamics simulation model is calibrated according to the first actual amplitude to obtain a calibration rotor dynamics simulation model; The measured first actual amplitude is utilized to calculate bearing stiffness and original unbalance through particle swarm optimization, and the calibration rotor dynamics simulation model is updated to obtain an updated rotor dynamics simulation model; According to the particle optimization result, a trial weight is added on the actual rotor, and a second actual amplitude is measured; the second actual amplitude is substituted into particle swarm optimization to calculate the actual rotor system total unbalance and the trial weight angle difference, finally a counterweight is added and the direction is selected until the vibration is reduced, and dynamic balancing is realized.

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