Method for simulating rotation inertia excitation response of multi-row bolted rotor of aero-engine

Abstract

The invention belongs to the technical field of aero-engine vibration control and rotor dynamics simulation, and particularly relates to an aero-engine multi-row bolt connection rotor rotation inertia excitation response simulation method which mainly comprises the steps that a rotor nonlinear contact model is established; mass eccentricity and inertia main shaft inclination are defined on key components of the rotor, so that transverse unbalanced force and angular inertia moment are applied at the same time; time domain integration and Newton-Raphson iteration means are utilized to judge and update conversion between static friction and dynamic friction and irreversible slippage of the interface; and finally, accurately predicting the dynamic response of the rotor at a high rotating speed, especially in a supercritical range. According to the method, the phenomenon that the vibration amplitude of the rotor is continuously increased can be captured by coupling the discontinuous characteristics of the interface and rotational inertia excitation, an additional unbalanced accumulation mechanism caused by interface loosening or abrasion is disclosed, and the evaluation precision of the safety margin and the vibration control strategy of the aero-engine rotor is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of aviation engine vibration control and rotor dynamics simulation, and in particular relates to a method for simulating the rotational inertia excitation response of an aviation engine multi-row bolt-connected rotor. Background Art

[0002] As the thrust-to-weight ratio and efficiency requirements of aircraft engines continue to increase, the structure of the rotor system becomes more and more complex, and the operating speed continues to rise. At high speeds, the rotor inevitably has eccentricity between the rotor center of mass and the rotor rotation axis, and inclination between the inertia axis and the rotation axis due to manufacturing and assembly errors. These two deviations are generally collectively referred to as the source of "local rotational inertia excitation" of the rotor. Traditional methods usually only consider the unbalanced force caused by mass eccentricity, while ignoring the angular inertia moment caused by the inclination of the inertia axis, resulting in the inability to accurately predict the phenomenon that the rotor vibration amplitude continues to increase with the speed within the supercritical speed range.

[0003] On the other hand, modern aircraft engines mostly use a multi-stage rotor structure composed of multiple discs, drums, shaft segments, etc. connected by bolts or flanges with interference fit. This type of connection structure inevitably has interface discontinuity characteristics, especially at high speeds, due to nonlinear effects such as interface friction, slip, and local relaxation between the flange end face and the mating surface, the dynamic response of the rotor will show complex segmented stiffness, hysteresis characteristics, and possible irreversible deformation. The stiffness attenuation and friction nonlinearity at these interfaces often further aggravate the dynamic response of the rotor, and due to local friction slip, additional unbalance accumulation will occur, making the vibration characteristics difficult to explain with a simple model.

[0004] In recent years, studies on the dynamic behavior of flexible rotors at high speeds have shown that if the local rotational inertia moment of the rotor and the interface nonlinear factors are ignored, it is easy to cause deviations between simulation predictions and measured data. Some experimental and test results also show that when the speed exceeds the critical speed, some rotors with thinner disks / blades will have a continuously increasing vibration amplitude, and irreversible looseness, angular deformation or eccentricity changes will be measured at the flange and other joints. These phenomena all indicate that it is necessary to apply a more complete and more accurate simulation analysis method to the rotor system with interface discontinuity characteristics to evaluate the impact of the combined effects of local rotational inertial excitation, interface friction, slip, etc. on the rotor dynamic characteristics.

[0005] Therefore, there is an urgent need for a dynamic simulation method that can not only consider the rotational inertial excitation caused by mass eccentricity and inclination of the inertial principal axis, but also characterize the friction nonlinearity and slip characteristics of the multi-stage rotor flange / bolt connection interface at high speed, so as to improve the prediction accuracy of the complex rotor dynamic response of aero-engines and provide a basis for rotor vibration control, structural optimization and balance correction strategies. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for simulating the response of the rotating inertial excitation of a multi-row bolted rotor of an aero-engine. The method comprehensively considers the local rotating inertial excitation generated by the eccentricity of the center of mass and the inclination of the main axis of inertia, as well as the nonlinear friction and slip characteristics at the interfaces of the flange, bolt, flange interference fit, etc., for the multi-stage disk / drum / shaft segment connection structure commonly found in the rotor system of an aero-engine. In the numerical simulation process, the present invention discretizes the dynamic equations of the rotor into the time domain, and completes modeling, application of local rotating inertial loads, interface friction determination and iterative correction in each time step, and finally obtains the dynamic response of the rotor at high speed, especially in the supercritical range.

[0007] The present invention is implemented by providing a method for simulating the rotational inertia excitation response of a multi-row bolt-connected rotor of an aero-engine, which specifically comprises the following steps: S1: Before starting the simulation, the entire analysis process is divided into several time steps or speed steps according to the research purpose or test conditions, recorded as , and initialize the parameters of the multi-row bolted rotor, which include rotor geometry and material properties, interface normal preload, number of bolts and friction coefficient, to provide necessary input for subsequent steps; S2: Establish a rotor dynamics model with multi-stage disks / shaft segments, divide the mass structure unit in the rotor dynamics model, define the mass eccentricity, mass eccentricity phase, inertia principal axis tilt angle and inertia principal axis tilt angle phase for the mass structure unit, so as to apply local rotational inertia excitation; considering that flanges, bolts and other connection parts are prone to show nonlinearity under high speed loads, a nonlinear friction unit is established at the rotor connection structure interface while the model is being constructed. The nonlinear friction unit includes normal contact stiffness and tangential friction or angular friction, allowing static friction and dynamic friction to switch; if the concentrated parameter method is used, the bolts, flange cylindrical surfaces, etc. can be discretized in the circumferential direction and then the angular nonlinear model can be established in a segmented parallel / series manner; if the finite element method is used, the interface slip can be described by combining nonlinear contact units (such as Penalty or Augmented Lagrange method) with the friction model; In this step, the thin-walled and large moment of inertia wheels in the multi-row bolted rotor are divided into mass structural units, and the four inertia deviation parameters mentioned above are defined, so that the lateral unbalanced force and angular moment of inertia can be applied during the simulation process; on the other hand, the elastic degrees of freedom are retained for the slender shaft segments or components that are prone to significant bending deformation, so as to capture the bending mode of the rotor at supercritical speed; S3: At the current time step, according to the rotor angular velocity Calculate the lateral unbalanced force of each mass structural unit Angular moment of inertia ,in and The polar moment of inertia and diametric moment of inertia of the mass structural unit, respectively, represents the tilt angle, and the lateral unbalanced force and angular inertia moment are applied to the center of mass node of each mass structural unit; S4: setting the initial slip amount of each rotor connection structure interface to zero, indicating that the rotor connection structure interface fits tightly and has no pre-looseness; S5: To solve the dynamic equations including local rotational inertia loads and interface nonlinear forces, the Newmark-β method is used to integrate the rotor dynamics model including nonlinear friction elements in the time domain to obtain the predicted values ​​of displacement, velocity, and acceleration; S6: Calculate the relative displacement or angular displacement and relative velocity of the rotor connection structure interface according to the displacement, velocity and acceleration prediction values; S7: Determine whether the rotor connection structure interface exceeds the static friction threshold based on the calculation results of S6. If it does not exceed, maintain static friction. If it exceeds, switch to dynamic friction and adjust the dynamic friction coefficient according to the actual working conditions. and relative slip velocity to calculate friction; S8: Based on the judgment result of S7, the friction force of the rotor connection structure interface is updated and assembled into the rotor dynamics model; S9: Correct the rotor connection structure interface friction and rotor displacement through Newton-Raphson iteration. If static friction and dynamic friction switch during the iteration, adjust dynamically until convergence is achieved. In this step, when Newton-Raphson iteration is used, the interface contact state of the rotor connection structure is checked in real time and the friction force is updated in each time step; if the static friction threshold is detected to be exceeded during the iteration process, it is immediately switched to dynamic friction and the rotor dynamics model is reassembled to ensure real-time capture of sudden changes in the interface state of the rotor connection structure.

[0008] S10: Once the interface slips, the irreversible slip amount of the rotor connection structure interface is recorded and updated. If the slip is significant, it is regarded as the accumulation of additional unbalance amount; S11: For the rotor connection structure interface whose iteration results satisfy convergence, the next time step is entered; for the rotor connection structure interface whose iteration results do not satisfy convergence, the time step is reduced or the rotor connection structure interface parameters are modified and then the iteration is restarted; S12: Repeat S5 to S11, and gradually advance in the entire operating speed and supercritical speed range, and finally obtain the rotational inertia excitation response of the multi-row bolted rotor at each speed and the interface slip distribution of the rotor connection structure.

[0009] The present invention is not limited to any specific commercial finite element software or self-written program, as long as it can realize time domain integration and nonlinear iteration.

[0010] Compared with the prior art, the advantages of the present invention are: (1) Taking into account both the lateral unbalanced force and the angular inertia moment. The present invention applies two types of loads generated by mass eccentricity and inertia axis tilt at the same time during simulation, which can accurately capture the continuous increase phenomenon of the rotor dynamic response at high speed (especially in the supercritical region), rather than being limited to the "rapid decrease after peak" mode in traditional methods.

[0011] (2) Considering interface nonlinearity and slip effects. By establishing friction units at flange bolts and other joints and allowing slip or irreversible deformation, the present invention can reflect the dynamic effects of factors such as bolt loosening and contact surface wear on rotor vibration and imbalance, overcoming the limitations of existing methods that only describe interfaces with linear or ideal fixed models.

[0012] (3) Adapt to the design and analysis of multi-stage and complex rotors. The present invention adopts differentiated modeling strategies for different parts such as large mass, thin-walled disks, and long shaft segments. It can capture the rotor bending mode in the elastic unit and apply local rotational inertial excitation in the mass structure unit. It is suitable for various types of aircraft engine rotor systems. It can be implemented on any commercial finite element software or self-compiled program, and has strong versatility and engineering value.

[0013] (4) Effective explanation of supercritical vibration and additional imbalance accumulation. By coupling the interface slip process, the present invention can simulate the dynamic evolution process of "slip-relaxation-additional eccentricity" that the multi-stage rotor interface may experience at high speed, providing a mechanism explanation for certain irreversible deformations and vibration increases observed in actual test runs, and also providing theoretical support for subsequent measures such as improving assembly processes, enhancing bolt preload reliability, and correcting balance correction surfaces.

[0014] In summary, the present invention can accurately predict the dynamic response characteristics of the rotor under high-speed conditions and analyze the complex vibration phenomena caused by the coupling of interface nonlinearity and local rotational inertia load, which has important application value for aircraft engine dynamics design and vibration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0016] Figure 1is a schematic diagram of a typical multi-row bolt-connected rotor structure in an embodiment; Figure 2 It is the simulation method and analysis process of the rotating inertial excitation response of the multi-row bolted rotor of an aero-engine; Figure 3 Yes Figure 1 A simplified lumped unit model schematic diagram of an embodiment; Figure 4 Yes Figure 1 The multi-row bolted rotor model of the embodiment develops amplitude-speed curves under different angular excitation conditions. DETAILED DESCRIPTION

[0017] In order to more clearly illustrate the technical solution of the specific implementation of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments. It is obvious that the described embodiment is one parameter setting of the present invention, and all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] The present invention provides a method for simulating the rotational inertial excitation response of a multi-row bolted rotor of an aero-engine. Aiming at the discontinuous interface of the connection structure in the multi-row bolted rotor, the lateral force and angular moment generated by the mass eccentricity and the inclination of the inertia principal axis are considered, and the interface friction nonlinearity and slip effect are introduced.

[0019] In order to further verify and illustrate the simulation method of the present invention for the rotational inertial excitation response of the non-continuous rotor of the aircraft engine interface, a high-pressure rotor with a compressor disk and a thin-walled turbine disk and multiple connection structures is used as a representative example to carry out dynamic numerical solution and result comparison analysis. The structure of the multi-disc rotor is shown in the figure below. Figure 1 As shown, the rotor structure includes bearings 1, compressor components 2 and turbine components 4. The front compressor component 2 is relatively large and thick, and the rear turbine component 4 is comparable in mass to the compressor disk component 2 but thinner in shape. Each component is connected to the shaft section by a connection structure 3 with a discontinuous contact interface. The inertial characteristics of the turbine disk are relatively prominent. If there is a deviation in the inertial main axis, a significant angular inertial moment will be applied to the surrounding connection structure at high speed, which may cause interface slip and local relaxation.

[0020] S1: Time step setting and initial parameter reading, such as Figure 2 At the beginning of the numerical analysis, the rotor speed is discretized into several steps from 0 to 16000 r / min, that is, , and perform the time domain iterative solution described in the present invention within each step. Figure 3 , by Figure 1The engine rotor shown is simplified into a lumped mass unit, and the compressor assembly 2 is simplified into a compressor unit 5, the turbine assembly 4 is simplified into a turbine unit 7, and the bolt connection structures 3 at both ends of the turbine assembly are simplified into a first connection structure unit 6 and a second connection structure unit 8. The specific parameter settings of the mass, moment of inertia, normal and tangential (or angular) stiffness, number of bolts and friction coefficient of the main components such as the disk and the connection structure are shown in Table 1. Among them, the mass of the compressor disk is 120 kg, and the polar moment of inertia is 5.4 kg·m^2; the mass of the turbine disk is 140 kg, and the polar moment of inertia is 6.1 kg·m^2; the first connection structure unit 6 and the second connection structure unit 8 have different numbers of bolts and circumferential stiffness distributions, and show piecewise nonlinear characteristics in the compression and tension directions. In addition, to simplify the analysis, the lateral support stiffness of the front support and the rear support can be taken as and .

[0021] Table 1

[0022] S2: Establish a dynamic model with multiple disks and interface units, such as Figure 3 As shown, according to the present invention, a combination of concentrated mass and elastic beam units is used to describe the multi-disc rotor in the modeling stage: the compressor disk can be regarded as a "thick disk" unit, and the turbine disk is a "thin disk" unit. The first connection structure unit 6 and the second connection structure unit 8 between the turbine disk and the shaft segment introduce nonlinear connection structure units to simulate the tangential friction stiffness of the flange end face and the interference fit cylindrical surface; if circumferential discreteness is considered, a piecewise nonlinear model can be further set at each bolt to distinguish the difference in stiffness of the flange when it is under compression and tension. To facilitate the description of angular deformation, this embodiment records the equivalent angular stiffness of the first connection structure unit 6 as , the second connecting structural unit 8 is recorded as , combined with its cylindrical friction characteristics, it appears as an interface nonlinear force in the rotor dynamics equations.

[0023] S3: Apply local rotational inertial excitation. At each time step, the lateral force and angular moment generated by mass eccentricity and inclination of the principal axis of inertia are applied to the compressor and turbine disk. Assume that the compressor and turbine disk each have an unbalanced , and the inclination of the principal axis of inertia . Then at the current angular velocity Under this condition, the local rotation inertia load of the rotor can be written as:

[0024] The superscripts "C" and "T" represent the compressor and turbine units, respectively. These loads are applied to the center of mass nodes of the corresponding units. In this embodiment, as the speed changes in the range of 0 to 16000 r / min, the inclination angle The value range is 0~0.3rad.

[0025] S4: The initial slip of the interface is set to zero. Before calculation, the initial slip of the flange / flange cylindrical surface interface of the first connection structure unit 6 and the second connection structure unit 8 is uniformly set to 0, assuming that the interface fits well after assembly without any looseness or pre-deformation. This will help to determine when the static friction threshold is exceeded and the dynamic friction or slip zone is entered in the subsequent steps.

[0026] S5: Newmark-β method is used for time domain integration. In this embodiment, the dynamic equation of the rotor system is written as

[0027] Where, \left [ {M} \right ] , \left [ {C} \right ] , \left [ {G} \right ] , \left [ {K} \right ] They are the mass matrix, damping matrix, gyroscopic moment matrix and stiffness matrix of the rotor system respectively. are generalized coordinates, and are the acceleration and velocity in generalized coordinates, is the nonlinear stiffness matrix, represents the unbalanced force caused by mass eccentricity, represents the equivalent effect of the angular moment of inertia caused by the inclination of the principal axis of inertia, is the interface nonlinear force (including the compression / tension segment stiffness of the bolt and the friction force of the cylindrical surface). The Newmark-β method is used to time discretize the equation and predict the rotor displacement, velocity and acceleration values ​​at each time step.

[0028] S6: Calculate the relative displacement and velocity of the connection structure according to the predicted and , the angular deformation of the first connecting structure unit 6 and the second connecting structure unit 8 and If the normal compression force of the connection structure is large, slip is not likely to occur in the low speed zone, and the interface shows a linear elastic response; however, when the speed approaches a certain threshold, if the angular inertia moment continues to increase, interface slip may occur.

[0029] S7: Determine whether the static friction threshold is exceeded. If the tangential / angular resistance requirement of the first connection structure unit 6 or the second connection structure unit 8 does not exceed the range, the static friction state is maintained; if it exceeds the threshold, the dynamic friction zone is entered. In this embodiment, the number of bolts, flange radius, and preload jointly determine the magnitude of the interface normal force and friction force. In this embodiment, the static friction coefficient , dynamic friction coefficient .

[0030] S8: Update of the interface force of the connection structure. Once the dynamic friction is confirmed, the interface force term in the rotor equation will be switched to the speed-dependent or constant dynamic friction model, for example:

[0031] in, is the relative slip velocity, It can be a function or a constant value that changes monotonically with the speed. N is the coefficient of the dynamic friction model; if it is still static friction, the linear spring force-displacement relationship is used. In addition, if the degree of stretching / compression caused by bending of the connection structure is different, the segmented stiffness needs to be called for compensation.

[0032] S9: Newton-Raphson iteration. In order to obtain an accurate solution for the above nonlinear factors in each time step, this embodiment performs Newton-Raphson iteration: first assemble the remaining vectors according to the interface state (static friction / dynamic friction) , and then solve for the correction increment After each iteration, if the interface state switches, the friction and stiffness of the connection structure need to be updated, and the residuals are recalculated until convergence is determined.

[0033] S10: Record and update the interface slip. At the end of the iteration of this time step, if the first connection structure unit 6 or the second connection structure unit 8 has irreversible slip, the slip amount and the corresponding angular deformation need to be stored, and statistics are performed to see whether there is an additional impact on the overall mass eccentricity of the rotor or the inclination of the main axis of inertia. If the slip is significant or reaches the permanent deformation threshold, the unbalance amount can be corrected in the subsequent time step to simulate the situation of loose bolts or local wear of the flange end face.

[0034] S11: Determine whether the convergence condition is met. If the Newton-Raphson iteration converges within a given accuracy, proceed to the next step; if the iteration does not converge, the time step can be reduced or the connection structure parameters can be adjusted. In actual calculations, this embodiment can usually converge within several iterations, and flange slip is more likely to occur at higher speeds, thereby causing a sudden change in the mechanical properties of the interface.

[0035] S12: Enter the next time step and sweep the speed. After the time step is determined, the displacement, speed, interface slip and other results are used as the initial values ​​of the next step. If the speed increase analysis is performed, , repeat S5~S11 and continuously record the displacement response of the rotor and the deformation of the connection structure. This process repeats and finally covers the full range of 0~16000 r / min.

[0036] After completing the above steps, key results such as the vibration amplitude, interface slip and irreversible deformation of the multi-disc rotor at supercritical high speed in this embodiment can be obtained, such as Figure 4 To verify the influence of angular inertia moment on vibration characteristics, we can compare (no inertia spindle tilt) and Simulation results (with main shaft tilt): When there is tilt, the rotor usually shows a "continuous increase" response with increasing speed in the supercritical range, and if the normal force of the connection structure is insufficient or the friction threshold is not high, the flange / bolt slip may be triggered at a certain critical speed point, resulting in resonance peaks or even irreversible deformation at the bearing or disk surface measurement point. The typical results of the bearing vibration amplitude and turbine disk angular displacement changing with speed at different tilt angles show that when the tilt angle is large, the supercritical response growth rate increases significantly; if the interface dynamic friction is considered, a sudden slip and resonance peak may occur in a certain speed range, which is significantly different from the curve without considering friction.

[0037] Through the calculation and comparative analysis of the examples in this embodiment, it can be clearly seen that the present invention simultaneously applies lateral unbalanced force and angular inertia moment in the multi-disc rotor model, and accurately characterizes the friction and slip behavior of the connection structure interface, which can better explain the mechanism of the continuous increase in vibration amplitude at supercritical speeds, as well as the irreversible looseness or deformation characteristics that may occur at the flange connection structure; it also provides strong simulation support for evaluating the rotor dynamics safety margin under high speed conditions and formulating corresponding assembly balance strategies during the actual aircraft engine design and test process. The above examples are only illustrative. Without departing from the principles of the present invention, parameter correction or expanded application can be performed according to the specific engine model, number of bolts, flange size, and eccentricity measurement data.

[0038] Through the serial execution of the above steps, the present invention can accurately predict the dynamic response characteristics of the rotor at high speeds, and analyze the additional imbalance accumulation that may be generated by the rotor in combination with the interface friction slip process, thereby significantly enhancing the depth of research on aircraft engine rotors and their interface nonlinearities, which is of great significance to improving the safety and durability of the entire machine.

[0039] The above specific embodiments are only used to illustrate the principles and effects of the present invention. Any equivalent substitutions or modifications made within the scope of the present invention should be deemed to fall within the protection scope of the present invention.

Claims

1. A simulation method for the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine, characterized in that: The specific steps include: S1: Set the time step And initialize the parameters of the multi-row bolted rotor; S2: Establish a rotor dynamics model with multi-stage disk / shaft segments, divide the mass structure unit in the rotor dynamics model, define the mass eccentricity, mass eccentricity phase, inertia principal axis inclination angle and inertia principal axis inclination angle phase for the mass structure unit; at the same time, establish a nonlinear friction unit at the rotor connection structure interface to allow switching between static friction and dynamic friction; S3: At the current time step, according to the rotor angular velocity Calculate the lateral unbalanced force of each mass structural unit Angular moment of inertia ,in and The polar moment of inertia and diametric moment of inertia of the mass structural unit, respectively, represents the tilt angle, and the lateral unbalanced force and angular inertia moment are applied to the center of mass node of each mass structural unit; S4: setting the initial slip amount of each rotor connection structure interface to zero, indicating that the rotor connection structure interface fits tightly and has no pre-looseness; S5: The Newmark-β method is used to integrate the rotor dynamics model including nonlinear friction elements in the time domain to obtain the predicted values ​​of displacement, velocity, and acceleration; S6: Calculate the relative displacement or angular displacement and relative velocity of the rotor connection structure interface according to the displacement, velocity and acceleration prediction values; S7: judging whether the rotor connection structure interface exceeds the static friction threshold value according to the calculation result of S6, if not, maintaining static friction, if exceeded, switching to dynamic friction; S8: Based on the judgment result of S7, the friction force of the rotor connection structure interface is updated and assembled into the rotor dynamics model; S9: Correct the rotor connection structure interface friction and rotor displacement through Newton-Raphson iteration. If static friction and dynamic friction switch during the iteration, adjust dynamically until convergence is achieved. S10: Record and update the irreversible slip amount of the rotor connection structure interface. If the slip is significant, it is regarded as additional unbalance accumulation; S11: For the rotor connection structure interface whose iteration results satisfy convergence, the next time step is entered; for the rotor connection structure interface whose iteration results do not satisfy convergence, the time step is reduced or the rotor connection structure interface parameters are modified and then the iteration is restarted; S12: Repeat S5 to S11, and gradually advance in the entire operating speed and supercritical speed range, and finally obtain the rotational inertia excitation response of the multi-row bolted rotor at each speed and the interface slip distribution of the rotor connection structure.

2. The method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine according to claim 1, characterized in that: In S1, the parameters of the rotor connected by multiple rows of bolts include rotor geometry and material properties, interface normal preload, number of bolts and friction coefficient.

3. The method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine according to claim 1, characterized in that: In S2, the wheels in the rotor connected by multiple rows of bolts are divided into mass structural units.

4. The method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine according to claim 1, characterized in that: In S2, the nonlinear friction unit includes normal contact stiffness and tangential friction force or angular friction force.

5. The method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine according to claim 1, characterized in that: In S9, when Newton-Raphson iteration is used, the interface contact state of the rotor connection structure is checked in real time at each time step and the friction force is updated; If it is detected that the static friction threshold is exceeded during the iteration process, it will immediately switch to dynamic friction and reassemble the rotor dynamics model to ensure real-time capture of sudden changes in the interface state of the rotor connection structure.

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