Simulation method for rotating inertial excitation response of multi-row bolted rotors in aero-engines

Abstract

The present invention belongs to the technical field of aero-engine vibration control and rotor dynamics simulation, and specifically relates to a method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine, which mainly includes: establishing a nonlinear contact model of the rotor; defining mass eccentricity and inertia principal axis tilt in key rotor components, thereby simultaneously applying lateral unbalanced forces and angular inertia moments; using time-domain integration and Newton-Raphson iteration to determine and update the interface conversion between static friction and dynamic friction and the amount of irreversible slip; and finally accurately predicting the dynamic response of the rotor at high speeds, especially in the supercritical range. By coupling the discontinuous characteristics of the interface with the rotational inertia excitation, the present invention can capture the phenomenon of the rotor vibration amplitude continuously increasing, reveal the additional imbalance accumulation mechanism caused by interface looseness or wear, and improve the evaluation accuracy of the aero-engine rotor safety margin and vibration control strategy.

Description

Technical Field

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

[0002] As requirements for aircraft engine thrust-to-weight ratios and efficiency continue to increase, rotor systems are becoming increasingly complex, and operating speeds are constantly climbing. At high speeds, manufacturing and assembly errors inevitably lead to eccentricity between the rotor's center of mass and the rotor's axis of rotation, as well as tilt between the principal axis of inertia and the axis of rotation. These two deviations are collectively referred to as sources of "local rotational inertial excitation" of the rotor. Traditional methods typically only consider the unbalanced forces caused by mass eccentricity, while ignoring the angular moment of inertia resulting from the tilt of the principal axis of inertia. This results in an inability to accurately predict the continuous increase in rotor vibration amplitude with speed within the supercritical speed range.

[0003] On the other hand, modern aircraft engines often utilize multi-stage rotor structures composed of multiple discs, drums, and shaft segments connected by bolts or flanges with interference fits. Such connections inevitably exhibit interfacial discontinuities. In particular, at high speeds, nonlinear effects such as friction, slip, and local relaxation between the flange end faces and mating surfaces cause the rotor's dynamic response to exhibit complex segmented stiffness, hysteresis, and potentially irreversible deformation. The stiffness attenuation and frictional nonlinearity at these interfaces often further exacerbate the rotor's dynamic response. Furthermore, localized friction and slip can lead to the accumulation of additional imbalance, making the vibration characteristics difficult to explain with simple models.

[0004] In recent years, research on the dynamic behavior of flexible rotors at high speeds has shown that ignoring the local rotational inertia moment of the rotor and interface nonlinear factors can easily lead to 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 experience a continuously increasing vibration amplitude, and irreversible loosening, angular deformation, or eccentricity changes will be measured at connections such as flanges. These phenomena all indicate that a more complete and higher-precision simulation analysis method is needed for rotor systems with interface discontinuities to evaluate 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 inertia principal axis tilt, 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 the aircraft engine and provide a basis for rotor vibration control, structural optimization and balance correction strategy. Summary of the Invention

[0006] To address the aforementioned technical issues, the present invention provides a method for simulating the rotational inertial excitation response of a multi-row bolted rotor in an aeroengine. This method addresses the multi-stage disk / drum / shaft segment connection structure commonly found in aeroengine rotor systems. It comprehensively considers the local rotational inertial excitations generated by center of mass eccentricity and inclination of the principal axis of inertia, as well as the nonlinear friction and slip characteristics at interfaces such as flanges, bolts, and flange interference fits. During the numerical simulation process, the present invention discretizes the rotor's dynamic equations into the time domain. At each time step, modeling, application of local rotational inertial loads, determination of interface friction, and iterative correction are sequentially performed. Ultimately, the dynamic response of the rotor can be determined at high speeds, particularly within the supercritical range.

[0007] The present invention is implemented by providing a method for simulating the rotational inertia excitation response of a multi-row bolted rotor of an aero-engine, which specifically includes the following steps:

[0008] S1: Before starting the simulation, first divide the entire analysis process 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. The multi-row bolted rotor parameters include rotor geometry and material properties, interface normal preload, number of bolts, and friction coefficient, providing necessary input for subsequent steps;

[0009] S2: Establish a rotor dynamics model with multi-stage disks / shaft segments, divide the mass structure unit in the rotor dynamics model, and define the mass eccentricity, mass eccentricity phase, inertia principal axis tilt angle, and inertia principal axis tilt angle phase for the mass structure unit to apply local rotational inertia excitation; considering that flanges, bolts and other connection parts are prone to exhibit nonlinearity under high speed loads, a nonlinear friction unit is established at the rotor connection structure interface during model construction. The nonlinear friction unit contains normal contact stiffness and tangential friction or angular friction, allowing switching between static friction and dynamic friction; if the lumped 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 the Penalty or Augmented Lagrange method) with the friction model;

[0010] In this step, the thin-walled, high-moment-of-inertia disks in the multi-row bolted rotor are divided into mass structural units, and the four aforementioned inertia deviation parameters are defined. This allows for the application of lateral unbalanced forces and angular moments of inertia during the simulation. Furthermore, elastic degrees of freedom are retained for slender shaft segments or components prone to significant bending deformation, allowing for the capture of rotor bending modes at supercritical speeds.

[0011] S3: At the current time step, according to the rotor angular velocity Calculate the lateral unbalanced force of each mass structural unit and 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;

[0012] S4: The initial slip of each rotor connection structure interface is set to zero, indicating that the rotor connection structure interface is in close contact and has no pre-looseness;

[0013] S5: To solve the dynamic equations including local rotating inertia loads and interface nonlinear forces, the Newmark-β method is used to perform time-domain integration on the rotor dynamics model including nonlinear friction elements to obtain the predicted values of displacement, velocity, and acceleration;

[0014] S6: Calculate the relative displacement or angular displacement and relative velocity of the rotor connection structure interface based on the displacement, velocity, and acceleration prediction values;

[0015] 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;

[0016] 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;

[0017] 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, dynamic adjustment is performed until convergence is achieved.

[0018] In this step, when using Newton-Raphson iteration, 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 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 that the sudden change of the rotor connection structure interface state is captured in real time.

[0019] 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.

[0020] 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 shortened or the rotor connection structure interface parameters are modified before restarting the iteration;

[0021] 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.

[0022] 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.

[0023] Compared with the prior art, the advantages of the present invention are:

[0024] (1) Taking into account both lateral unbalanced forces and angular moments of inertia. The present invention applies two types of loads simultaneously during simulation: mass eccentricity and inertia axis tilt. This allows for accurate capture of the potential continuous increase in rotor dynamic response at high speeds (especially in the supercritical region), rather than being limited to the "rapid decrease after peak" pattern of conventional methods.

[0025] (2) Considering interface nonlinearity and slip effects. By establishing friction units at connections such as flange bolts and allowing for 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 using linear or ideal fixed models.

[0026] (3) Adaptable to the design and analysis of multi-stage and complex rotors. This invention adopts differentiated modeling strategies for different parts such as large masses, thin-walled disks, and long shaft segments. It can capture the rotor bending modes in the elastic unit and apply local rotational inertial excitation in the mass structure unit. It is applicable to various types of aircraft engine rotor systems and can be implemented in any commercial finite element software or self-written program, showing strong versatility and engineering value.

[0027] (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 mechanistic explanation for certain irreversible deformations and vibration increases observed in actual test runs. It also provides theoretical support for subsequent measures such as improving the assembly process, enhancing the reliability of bolt preload, and correcting the balance correction surface.

[0028] 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 loads, which has important application value for aircraft engine dynamics design and vibration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. 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 any creative work.

[0030] Figure 1 This is a simplified diagram of a typical multi-row bolt-connected rotor structure in one embodiment;

[0031] Figure 2 This is the simulation method and analysis process of the rotational inertial excitation response of the multi-row bolted rotor of an aero-engine;

[0032] Figure 3 Yes Figure 1 A simplified lumped unit model schematic diagram of an embodiment;

[0033] Figure 4 Yes Figure 1 The multi-row bolted rotor model of the embodiment is used to develop amplitude-speed curves under different angular excitation conditions. DETAILED DESCRIPTION

[0034] To more clearly illustrate the technical solutions of the specific embodiments of the present invention, the present invention is further described below with reference to the accompanying drawings and examples. It is obvious that the described embodiment is only one parameter setting of the present invention, and all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0035] The present invention provides a method for simulating the rotational inertia 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 present invention considers the lateral force and angular moment generated by mass eccentricity and inclination of the principal axis of inertia, and introduces the nonlinear friction and slip effects of the interface.

[0036] To further verify and illustrate the simulation method of the present invention for the inertial excitation response of the non-continuous rotor rotation of an 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 comparative analysis of the results. The structure of the multi-disc rotor is shown in the figure below. Figure 1As shown, the rotor structure comprises a bearing 1, a compressor assembly 2, and a turbine assembly 4. The front compressor assembly 2 is relatively heavy and thick, while the rear turbine assembly 4 is comparable in mass to the compressor disk assembly 2 but thinner. Each assembly is connected to the shaft segment by a connecting structure 3 with a discontinuous contact interface. The turbine disk has significant inertial characteristics. If the principal axis of inertia deflects, it will exert a significant angular moment of inertia on the surrounding connecting structure at high speeds, potentially causing interface slip and localized relaxation.

[0037] 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, namely , and perform the time domain iterative solution described in the present invention within each step. Figure 3 , by Figure 1 The engine rotor shown is simplified into a lumped mass unit, with the compressor assembly 2 simplified into a compressor unit 5, the turbine assembly 4 simplified into a turbine unit 7, and the bolt connection structures 3 at both ends of the turbine assembly 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 .

[0038] Table 1

[0039]

[0040] S2: Establish a dynamic model with multiple disk and interface elements, 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 connecting structure unit 6 and the second connecting structure unit 8 between the turbine disk and the shaft segment introduce nonlinear connecting 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 under compression and tension. To facilitate the description of angular deformation, this embodiment records the equivalent angular stiffness of the first connecting structure unit 6 as , the second connecting structure unit 8 is recorded as , and combined with its cylindrical friction characteristics, it appears as an interface nonlinear force in the rotor dynamics equation.

[0041] S3: Apply local rotational inertial excitation. At each time step, the lateral force and angular moment generated by the mass eccentricity and the 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 inertial axis tilt . Then at the current angular velocity Under this condition, the local rotational inertia load of the rotor can be written as:

[0042]

[0043] 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.

[0044] S4: Set the initial interface slip to zero. Before calculation, set the initial slip of the flange / flange cylindrical interface of the first connecting structure unit 6 and the second connecting structure unit 8 to zero, assuming that the interface fits well after assembly, without any looseness or pre-deformation. This helps determine in subsequent steps when the static friction threshold is exceeded and the dynamic friction or slip zone is entered.

[0045] S5: Newmark-β method is used for time domain integration. In this embodiment, the dynamic equation of the rotor system is written as

[0046]

[0047] Where, \left [ {M} \right ] 、\left [ {C} \right ] 、\left [ {G} \right ] 、\left [ {K} \right ] are the mass matrix, damping matrix, gyroscopic torque 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 tilt of the principal axis of inertia, is the nonlinear interface 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 this equation, and the rotor displacement, velocity, and acceleration values are predicted at each time step.

[0048] S6: Calculate the relative displacement and velocity of the connection structure, based on the predicted and , the angular deformation of the first connecting structural unit 6 and the second connecting structural unit 8 and If the normal compressive force of the connection structure is large, slip is unlikely to occur in the low-speed range, and the interface exhibits a linear elastic response. However, near a certain threshold speed, if the angular moment of inertia continues to increase, interface slip may occur.

[0049] S7: Determine whether the static friction threshold is exceeded. If the tangential / angular resistance requirements of the first connecting structure unit 6 or the second connecting structure unit 8 are within the range, the static friction state is maintained; if the threshold is exceeded, 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 is , dynamic friction coefficient .

[0050] 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:

[0051]

[0052] in, is the relative slip velocity, It can be a function that changes monotonically with the speed or a constant value. N is the coefficient of the dynamic friction model. If static friction is still present, a linear spring-like force-displacement relationship is used. Furthermore, if the connection experiences varying degrees of tension / compression due to bending, segmented stiffness must be used to compensate.

[0053] 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 / kinetic 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.

[0054] S10: Record and update interface slip. At the end of this time step iteration, if irreversible slip occurs in the first connecting structure unit 6 or the second connecting structure unit 8, the slip amount and the corresponding angular deformation must be stored, and statistics must be calculated to see whether there is any additional impact on the overall rotor mass eccentricity or inertia axis tilt. If the slip is significant or reaches the permanent deformation threshold, the imbalance can be corrected in subsequent time steps to simulate loose bolts or local wear on the flange end face.

[0055] S11: Determine whether convergence conditions are 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 usually converges within a few iterations. At higher speeds, flange slip is more likely to occur, causing a sudden change in the mechanical properties of the interface.

[0056] 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 value of the next step. If the speed increase analysis is performed, Repeat steps S5 to S11 and continuously record the rotor displacement response and connection structure deformation. This process repeats until the full range of 0 to 16,000 r / min is covered.

[0057] 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 spindle tilt): When tilt exists, the rotor typically exhibits a "continuously increasing" response with increasing speed in the supercritical range. If the normal force of the connection structure is insufficient or the friction threshold is not high, 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 points. Typical results of the bearing vibration amplitude and turbine disk angular displacement as a function of speed at different tilt angles show that the supercritical response growth rate increases significantly when the tilt angle is large. If the effect of interfacial dynamic friction is considered, sudden slip and resonance peaks may occur within a certain speed range, showing a significantly different shape compared to the curve without friction considerations.

[0058] 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 forces and angular inertia moments in a 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 and the irreversible loosening 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 made based on the specific engine model, number of bolts, flange size, and eccentricity measurement data.

[0059] By serially executing 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 and slip process, thereby significantly enhancing the depth of research on aircraft engine rotors and their interface nonlinearities, which is of great significance for improving the safety and durability of the entire machine.

[0060] The above specific embodiments are only used to illustrate the principles and effects of the present invention. Any equivalent replacements 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 in an aero-engine, characterized by: The specific steps include: S1: Set 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 rotor dynamics model into mass structural units, and define the mass eccentricity, mass eccentricity phase, inertia principal axis tilt angle, and inertia principal axis tilt angle phase for the mass structural 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 and 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: The initial slip of each rotor connection structure interface is set to zero, indicating that the rotor connection structure interface is in close contact and has no pre-looseness; S5: The Newmark-β method is used to perform time-domain integration on the rotor dynamics model containing nonlinear friction elements 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 based on the displacement, velocity, and acceleration prediction values; S7: judging whether the rotor connection structure interface exceeds the static friction threshold 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, dynamic adjustment is performed until convergence is achieved. S10: Record and update the irreversible slip of the rotor connection structure interface. If the slip is significant, it will be 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 shortened or the rotor connection structure interface parameters are modified before restarting the iteration; 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 multi-row bolted rotor 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 the above-mentioned 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 said S9, when Newton-Raphson iteration is used, the contact state of the rotor connection structure interface 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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