Vibration Characteristics and Simulation Verification of the Dual-Rotor System for Aeroengines with Rub-Impact Coupling Faults

To study the rub-impact fault between the dynamic and static parts of the rotor system of aeroengines, the dual-rotor system of a typical aeroengine is introduced and taken as the research object.,e analytical kinetic model is established based on the Lagrange equation considering the structural characteristics of the dual-rotor system, the coupling effect of the intermediate bearing, and the rub-impact fault between the high-pressure turbine disc and the casing. ,e dynamic characteristics of the dual-rotor system under the rub-impact fault are analyzed, and the change rule of the rub-impact shape is obtained. ,e vibration coupling and transfer among the high-pressure rotor and the low-pressure rotor are revealed. ,e influence of the unbalanced position and the speed of high and low rotors on the vibration response of the dual rotor is obtained.,e sensitivity of the vibration response of the dual rotor at different test points to rub-impact stiffness, clearance, and friction coefficient is compared. ,e simulation model is established based on the rigid-flexible coupling multibody dynamic simulation platform. ,e analytical results and simulation results are compared, which have a good consistency.,e theoretical research can deepen the understanding of the nature and law of aeroengine rotor operation, expose the possible faults and design defects, greatly improve the development efficiency and quality, reduce repeated physical tests, reduce the development risk and cost, and accelerate the development process. ,is study can provide a theoretical basis for the monitoring and diagnosis of engine rub-impact faults and provide theoretical and practical reference for the establishment of the vibration fault test and analysis method system.


Introduction
As the 'heart' of an aircraft, the aeroengine is the decisive factor of aircraft safety, reliability, and operational performance. With the increasing requirements of high speed and the high thrust-weight ratio of aeroengines, the clearance between the rotor and stator decreases, which increases the possibility of a rub-impact fault. e rub-impact fault has become one of the most common faults of the dual-rotor system in aeroengines. It is one of the causes of the complex nonlinear vibration of the dual-rotor system and an important reason for the instability of the rotor system. e rub-impact fault will not only lead to the increase of the rotor-stator clearance, bearing wear, and blade cracks but also may cause the rotor system motion instability and make the casing deform greatly, and the excessive vibration will seriously affect the working efficiency of the engine. e vibration of the unit will increase dramatically, which will affect the service life of the unit. In serious cases, it will cause permanent bending of the rotor and even cause fatal accidents. It is difficult to find out the cause of abnormal vibration before the machine stops for overhaul. erefore, it is of great significance to explore the vibration characteristics of the rotor rub-impact, especially the early rub-impact characteristics, and detect these characteristics for avoiding rub-impact faults and secondary faults.
Many theoretical research studies on the aeroengine rotor system have been carried out by scholars at home and abroad. Representative results include the long-term research achievements and contributions of Professor Yushu Chen and Huabiao Zhang [1][2][3] of Harbin Institute of Technology, Litang Yan [4] of Beijing University of Aeronautics and Astronautics, Mingfu Liao [5][6][7] of Northwest Polytechnic University, Qingkai Han [8][9][10] of Dalian University of Technology, Guihuo Luo [11], and Guo Chen [12] of Nanjing University of Aeronautics and Astronautics. Wang [13] took a dual rotor as the research object, established a dynamic model considering the friction between the rotor and the casing, studied the nonlinear problem of the rub-impact rotor, and used the nonlinear rotor dynamics theory to analyze the model of the rub-impact rotor system and its chaotic motion evolution law. Liu et al. [14] established the dynamic equation of an aeroengine dual-rotor system with a rubimpact fault by using the Lagrange equation, simulated the rub-impact fault through numerical calculation, and proposed the effectiveness and reliability of the method of combining spectrum analysis and wavelet transform to diagnose the rub-impact fault of the rotor and stator. Considering the elastic deformation, contact penetration, and elastic damping support during the collision between the casing and the disc, Wang et al. [15] established the dynamic model of the dynamic and static rub-impact of the dual-rotor system by applying Hertz contact theory and Coulomb model and solved the dynamic response of the dual-rotor system under the rub-impact fault. e dual-rotor system testbed is established to carry out the dynamic and static rub-impact test, and it is proposed that the double-frequency and combined frequency components of the two excitation sources can be taken as the typical characteristics of the aeroengine dynamic and static rub-impact fault. Zhang et al. [16] took the dualrotor system of an aeroengine as the research object, established the coupled bending-torsion dynamic equation with rub-impact force by considering the force of the intermediate bearing, and calculated the vibration response of the dual-rotor under the rub-impact fault by using numerical methods. e frequency spectrum and bifurcation characteristics of the bending and torsional vibration are analyzed, and experimental research on the bending and torsional vibration is carried out based on the rotor test bench. e results show that the bending and torsional vibration have a similar characteristic frequency, but the torsional vibration characteristic frequency is more obvious, and the torsional vibration signal can be better used for rub-impact fault diagnosis. Ouyang and Yang [17] established the dynamic model of the dual-rotor system of the aeroengine without the intermediate bearing by using a lumped-mass method. e rotor rub-impact fault was simulated, and the vibration response of the rotor system under different rub-impact conditions was obtained. Zhang [18] established the dynamic model of the aeroengine dual-rotor-casing coupling system, solved the critical speed and vibration mode of the system, discussed the influence of support parameters and speed ratio on the critical speed and vibration mode, calculated the rub-impact response of the dual-rotor-casing coupling system, and studied the influence of different rub-impact degrees and unbalance on the dual-rotor rub-impact fault.
Liu [19] established the dynamic model of the dual-rotor system with a rub-impact fault and studied the vibration response of the dual-rotor system under the rub-impact fault. Compared with the unbalanced dynamic characteristics of the dual-rotor system, he found that the rubimpact fault makes the rotor system vibration response appear the combined frequency of rotation frequency, which makes the rotor system vibration appear nonlinear. e influence of the parameters such as the rub-impact clearance on the dynamic characteristics of the dual-rotor system was also studied, and the severity of the rub-impact fault can be judged according to it. e dual-rotor system of aeroengines has a special structure. For example, the low-pressure rotor is supported by three fulcrums, and the high-pressure rotor and the lowpressure rotor are connected by an intermediate bearing.
Although there have been some results on the dynamics of the dual-rotor system, the characteristics of dynamic coupling and vibration transmission of the dual-rotor system for aeroengines have not been studied in detail. According to the engineering observation, the sensitivity of the low-pressure rotor and the high-pressure rotor to the rub-impact is different, and the sensitivity of the rub-impact at different locations is analyzed in [20]. In this paper, the vibration sensitivity of different positions of the rotor with a rubimpact fault is studied by using the method of analysis and multibody dynamics simulation verification. e influence characteristics of rub-impact stiffness, clearance, and friction coefficient on the vibration response of the dual rotor are compared.

Establishment of the Dynamic Model for the Dual-Rotor System
Taking a typical aeroengine shown in Figure 1 in [20] as a prototype, a simplified model of the dual-rotor system as shown in Figure 2 is obtained according to the principle of similarity design. e main parts of the main structure of the dual-rotor system are the fan rotor, the low-pressure turbine rotor, the high-pressure rotor, turntable, support, and coupling. e low-pressure rotor is composed of a fan disc and one turbine disc. e total length of the low-pressure rotor is about 1261 mm. It adopts the supporting form of three fulcrums, namely, a 1-1-1 support form. e front fulcrum of the fan and the rear fulcrum of the low-pressure turbine are elastic supports. e low-pressure turbine shaft is slender, and the fan rotor and the low-pressure turbine rotor are connected by a sleeve gear coupling which can transmit axial force and torque. e high-pressure rotor is composed of the compressor and one turbine, in which the support span is 580 mm. e high-pressure compressor and the high-pressure turbine are rigidly connected through the hollow shaft, and the 1-0-1 two-point support mode is adopted. e front support of the high-pressure compressor is the elastic support, and the rear support is the intermediate bearing. e stiffness of each fulcrum is shown in Table 1. In order to simplify the structure, reduce the quality of the rotor system, and reduce the dynamic influence between the high-and low-pressure rotors, the rotor system adopts the intermediate bearing design with the highpressure rotor rear fulcrum as close as possible to the lowpressure turbine rear fulcrum. e high-and low-pressure rotors are coupled through the intermediate bearing. e rotor transmits the load through the fulcrum of another rotor. erefore, the dynamic characteristics of the dualrotor system are not only affected by the high-and lowpressure rotors but also have some unique vibration characteristics.

Dynamic Model of the Dual Rotor with the
Rub-Impact Fault e analytical equations of multisupport motion of the dualrotor system are derived utilizing the Lagrange method, and the governing differential equations of the dual-rotor system considering the axial and bending vibration but not torsional vibration are obtained. In the model, the four discs, the fan shaft, and the high-pressure shaft are considered to be rigid, while the slender shaft of the low-pressure turbine is considered as elastic. e support of the rotor system is considered to be elastic, and the speed of the rotating shaft is considered to be constant. e rubbing fault often occurs between the high-pressure rotor and the casing [21]. In this study, only the rub-impact between the high-pressure turbine disc and the stator casing is considered. e fixed coordinate system of the system is oxy, and the dynamic equation of the whole system is as follows: where M , C , G , K, and F are the mass matrix, damping matrix, gyro force matrix, stiffness matrix, and generalized force matrix, respectively.q is the generalized coordinate vector. Among them, q � y 1 z 1 θ y 1 θ z 1 y 2 z 2 θ y 2 θ z 2 y 3 z 3 θ y 3 θ z 3 y 4 z 4 θ y 4 θ z 4 , where F iy , F iz (i � 1 ∼ 4) are the component of unbalanced excitation force in the y-direction and z-direction by four discs and F Ry , F Rz are the component of rub-impact force in the y-direction and z-direction.

Unbalanced Model
e unbalance of the dual-rotor system mainly includes the fan disc unbalance, the low-pressure turbine disc unbalance, the high-pressure compressor disc unbalance, and the highpressure turbine disc unbalance. e components of the centrifugal force produced by the unbalanced mass of each disc in the y-direction and z-direction are as follows: where m ei is the unbalanced mass, and the unit is Kg · m. ϕ i is the initial phase angle of the disc centroid, and the unit is rad. Ω i is the rotational angular velocity of the low-and high-pressure rotors, and the unit is rad/s.

Rub-Impact Model
e schematic diagram of the local rub-impact between the rotor and stator is shown in Figure 3. F y and F z stand for the normal force and tangential force exerted on the disc by the rubbing plate, respectively. φ denotes the angle of the rubbing plate normal direction and the x-axis, and e is the moving distance of the rotor axis. e deformation of the rubbing plate caused by the rub-impact between the disc and rubbing plate is supposed to be linear. k c is the radial stiffness of the rubbing plate. f r and δ are the friction coefficient at the rubbing point and the clearance between the rubbing plate and the disc, respectively. Function H means that when (z − δ) is less than 0, it is equal to 0, and otherwise, it is equal to 1. e concrete expression is as follows: Rayleigh damping is adopted in the damping model, and the structure is as follows: e Rayleigh damping matrix is a linear combination of the mass matrix and the stiffness matrix, where α and β are damping coefficients, which are related to the modal damping ratio ξ of the structure. e calculation formula is as follows: After derivation, other matrices can be easily obtained.

Inherent Characteristics of the Dual-Rotor System
According to matrices M, G, and K in formula (1), the modal frequency and modal shape of the rotor can be obtained. e displacement of the rotor system is written as follows: where ω n is the whirl frequency of the rotor system; then, equation (3) can be written as When calculating the critical speed, the whirl frequency and rotation frequency of the rotor are equal; then, the above formula can be written as e square and eigenvector of the eigenvalue are the modal frequency and mode shape of the rotor system. e natural frequencies and vibration modes of the dual-rotor system are shown in Figure 4. e model parameters of the simplified dual-rotor system are shown in Tables 2-4, in which four equivalent discs are shown in Table 2, the equivalent parameters of the rotating shaft are shown in Table 3, and the distance parameters are shown in Table 4.
It can be seen from Figure 4 that the first and second modes of the low-pressure rotor are mainly the first bending mode of the low-pressure rotor turbine section, the first mode of the high-pressure rotor is the translation mode, and the second mode is the pitching vibration.

Method of Calculation.
In this paper, the Newmark-β method is used to solve the vibration response of the dualrotor system under the rub-impact fault. Newmark-β method is an integral dynamic numerical analysis method. Different from the analytical method and numerical integration method, it gives the complex calculation task to the computer through simple programming, which is convenient and can achieve good accuracy. e Newmark-β integration method is a kind of step-by-step integration method. It can set the time interval between every two calculation substeps and calculate the response result of the next calculation substep according to the previous calculation results. As long as the parameters are set reasonably, good convergence can be achieved. 4 Shock and Vibration     Table 4: Dimension parameters of the simplified dual-rotor system. Shock and Vibration 5 To study the vibration response of the dual-rotor system under the rub-impact fault, four measuring points 1-4 are selected on the low-pressure rotor, among which No. 1 measuring point is 1# fulcrum, No. 2 measuring point is the center of mass of the LPC (the fan disc), No. 3 measuring point is the center of mass of the LPT (the low-pressure turbine disc), and No. 4 measuring point is 6# fulcrum. Four measuring points 5-8 are selected on the outer rotor, among which No. 5 measuring point is 4# fulcrum, No. 6 measuring point is the center of mass of the HPC (the high-pressure compressor), No. 7 measuring point is the center of mass of the HPT (the high-pressure turbine disc), and No. 8 measuring point is 5# intermediary support. e arrangement of vibration measuring points of the dual-rotor system is shown in Figure 5.

Influence of Rub-Impact Stiffness on the Vibration
Response. Based on the analysis method, the vibration response of the dual-rotor system under the rub-impact fault is analyzed by the Newmark-β method. Speed setting: lowpressure speed N1 � 170 Hz; high-pressure speed N2 � 221.67 Hz. As shown in Table 5, the vibration characteristics of the dual-rotor system under four different parameter settings are analyzed, and the vibration time domain, frequency spectrum, and axis orbit of eight measuring points are obtained. e vibration response of the dual-rotor system under three different rub-impact parameter settings is shown in Figures 6-8.
Based on the analysis of the unbalance vibration characteristics of the dual-rotor system in [22], it can be seen that only high-and low-pressure rotating frequencies N1 and N2 appear in the unbalanced vibration response of the dual-rotor system. In this paper, the vibration trajectories of the low-pressure and high-pressure rotors are obtained as shown in Figure 9, under condition IV in Table 5.
Comparing the vibration results in Figures 6-9 of each measuring point with or without rub-impact, the following can be seen: (1) Rub-impact fault makes the vibration response of the dual-rotor system have nonlinear characteristics. e dynamic response of the rotor also contains the combined and division components of the speed frequency, and the occurrence of the rub-impact fault makes the axis track no longer a regular circle. (2) It can be seen from the time-domain diagram that the occurrence of the rub-impact fault increases the amplitude of the rotational frequency of the dualrotor system. (3) Compared with Figures 7-9, it can be seen that, with the increase of rub-impact stiffness, the amplitude of rub-impact spectrum components increases, and the component of the spectrum becomes more complex.
In the case of the slight rub-impact, there are no other components in the vibration spectrum of each measuring point except the rotational frequency and N2-N1. With the increase of rub-impact degree, (2N2-N1), 1/2N2, 2N1, N1 + N2, 2N2, etc., appear in the frequency components.

Shock and Vibration
Under the condition of no rub-impact and three different rub-impact degrees, the amplitude of speed frequency in each measuring point of the dual-rotor system is compared and analyzed, as shown in Figure 10. It can be seen that the vibration amplitude of every test point with the rubimpact fault is greater than that with an unbalanced condition, and with the increase of the rub-impact degree, the vibration amplitude of each measuring point increases. e No. 5 (4# fulcrum) and No. 6 (HPC) measuring points on the high-pressure rotor are the least affected by the highpressure turbine disc rub-impact and are mainly affected by the high-pressure compressor disc unbalance. Especially, the position of the No. 6 measuring point is the unbalanced position of the high-pressure rotor, and its axis orbit is relatively regular. Compared with Figures 10(a) and 10(b), it can be seen that the vibration of the low-pressure turbine    Shock and Vibration disc position is least affected by the high-pressure turbine disc rubbing. e transfer law of speed frequency of the dualrotor vibration on high-and low-pressure rotors remains unchanged. e vibration magnitude ordering of N1 was 8 > 4 > 7 > 3 > 5 > 1 > 2 > 6, and that of N2 was 5 > 6 > 4 > 8 > 3 > 1 > 2 > 7.

Influence of Rub-Impact Parameters on the Vibration
Response of the Dual-Rotor System. Rub-impact stiffness, rub-impact clearance, and friction coefficient are three important parameters in the rub-impact fault model. In this section, the influence of the three typical rub-impact parameters on the vibration response of the dual-rotor system is studied with three cases shown in Table 6. e vibration amplitude of fundamental frequency (N1 and N2) and 2 times of the high-pressure rotational frequency (2N2) are obtained in three cases. e influence of different rub-impact stiffness, rub-impact clearances, and rub-impact friction coefficients is compared. e representative results are shown in Figures 11-13     From Figure 11, we can see that under the three different parameter settings, the vibration amplitude of N1 at each measuring point has a small change, among which the variation of measuring points 2 and 6 is the smallest.
From Figure 12, we can see that under the three different parameter settings, the vibration amplitude of N 2 at each measuring point changes little, among which the variation of measuring points 5 and 6 of the high-pressure rotor is the largest.
It can be seen from Figure 13 that the amplitude of 2N2 at each measuring point changes slightly under the setting of I and III rubbing parameters, while the amplitude of 2N2 at each measuring point increases under the setting of the rubbing parameter in case II.
From Figures 11-13, it can be seen that the amplitude changes of N1 and N2 are less affected by friction coefficient   and rub-impact clearance and mainly affected by the unbalance of high and low rotors. e influence of friction coefficient on the amplitude of 2N2 is greater than that of rub-impact clearance. Among the three rub-impact parameters, the rub-impact stiffness has the greatest influence on the vibration response of each measuring point of the dual-rotor system, while the friction coefficient and rub-impact clearance have little influence on the vibration response of each measuring point of the dual-rotor system.

Influence of Rotating Speed on the Vibration Response of the Dual-Rotor System.
To study the influence of rotating speed on the vibration of the dual-rotor system under the rub-impact fault, in this section, without changing the unbalance of the rotor system, the vibration response of the dual-rotor system with the low-pressure speed N1 � 50 Hz, high-pressure speed N2 � 60 Hz, and rubimpact stiffness 7 × 10 6 N/m is studied. e vibration time domain and frequency spectrum axis trajectory of each measuring point are obtained, as shown in Figure 13.
In view of the influence of rotating speed on the vibration characteristics of the double-rotor system under the rub-impact fault, the vibration response of the double-rotor system with low-pressure speed, highpressure speed N2 � 60 Hz, and rub-impact stiffness 7 × 10 6 N/m is studied without changing the rotor system unbalance.
e vibration time domain and frequency spectrum of each measuring point are obtained, as shown in Figure 14.
By comparing the results of Figure 14 with Figure 8, it is found that the vibration response characteristics of the dualrotor system caused by the rub-impact fault are not completely identical at two speeds. e frequency components N1, N2, and N2-N1 appear in the vibration spectrum in both speed conditions. In Figure 13, in addition to the above frequency components, there are 2N2-N1, 2N2, and 3N2 in the spectrum of each measuring point. Under the case of rotating speed N1 � 50 Hz and N2 � 60 Hz, high-voltage frequency conversion N2 is dominant in the vibration spectrum of each measuring point, and there is no obvious peak in the time-domain diagram. e orbit of the shaft center is enveloped ellipse shape, which is more regular than the results in Figure 8.

Establishment of a Rigid-Flexible Coupling Multibody Dynamic Model for the Dual-Rotor System. ADAMS (automatic dynamic analysis of mechanical systems) is a professional product with rich industry application experience.
It is the only dynamic simulation software verified by a large number of practical projects [23][24][25][26][27][28]. e dynamic modeling, analysis, and vibration prediction of the aeroengine rotor system based on rigid-flexible coupling multibody dynamic system simulation technology can meet the requirements of characteristics' analysis of the hierarchical system and rigid-flexible coupling structure and vibration prediction of the rotor system in the process of new rotor design. In particular, the simulation analysis of typical vibration problems such as unbalance and rub-impact of the rotor system can be realized effectively.
e 'impact' is used to calculate the rub-impact force in ADAMS, which is based on the impact function to calculate the contact force between the two objects. e contact force is composed of two parts: the first part is the elastic force due to the mutual penetration between the two objects, and the other part is the damping force produced by relative speed. e rub-impact mechanics expression is 10) Among them, k is the stiffness coefficient, δ 0 is the initial distance between the two contact objects, x is the actual distance between the two contact objects in the rubbing process, C max is the maximum damping coefficient used to characterize the collision energy loss, N is the rotating shaft speed (high-and low-pressure rotor speeds are N2 and N1, respectively), e is the rub-impact index used to represent the nonlinear degree of the material, and d is the penetration depth. e low-pressure turbine shaft is considered as a flexible shaft, and the elastic support is simulated by a squirrel-cage elastic structure, and other parts are assumed to be rigid. When modeling the dual-rotor system, in order to truly reflect the connection state between various parts of the model, the parts originally fixed by bolts are connected with fixed pairs. e bearing is defined by stiffness and damping, simulated by the "bushing" element, and the coupling is   simplified as a short shaft structure. In order to ensure the steady increase of the speed, the step function is usually used to set the speed. e dual-rotor system unbalance is simulated by adding a mass block on the low-pressure compressor disc and the high-pressure compressor disc. A rub-impact block is set at a certain clearance from the high-pressure turbine disc (HPT). e fixed pair is used to define the rub-impact block as the stator. e contact adjustment clearance and rubbing parameters are set between the high-pressure turbine disc and the rubbing block to simulate different rubbing conditions. Finally, the rigid-flexible coupling multibody dynamic model of the dual-rotor system with rub-impact is shown in Figure 15. Low-pressure speed N1 � 50 Hz and high-pressure speed N2 � 60 Hz. e rigid-flexible coupling simulation model of the dual-rotor system is shown in Figure 15.
To verify the correctness of the model and the simulation accuracy, the first two natural frequencies of the dual-rotor system are obtained by ADAMS in Figure 16. And the results are compared with the analytical results based on the dynamic equation. e results show that the first two modes are consistent. e first and second modes of the lowpressure rotor are mainly the first-order bending of the lowpressure turbine shaft. e first mode of the high-pressure rotor is translational, and the second is the pitching mode. e first natural frequency difference ratio is 5%, and the second natural frequency difference ratio is 4.5%. e rationality of the simulation model is verified.

Parameter Setting of the Simulation.
Based on the multibody dynamics model of the dual-rotor system with the rub-impact fault in Figure 15, the vibration response of the dual-rotor system is simulated with five different rub-impact states as shown in Table 7 Figure 14: e time-domain diagram, spectrum, and axle center orbit of the dual-rotor system.
Analyzing the results shown in Figures 17-19, through the vibration time-domain diagram of each measuring point of the dual-rotor system, it is found that, with the increase of the rub-impact stiffness, the vibration amplitude of each measuring point increases.
rough the frequency spectrum, it can be seen that, with the increase of the rub-impact stiffness, the vibration spectrum components of each measuring point become more complex, and there are multiple combination and division frequency components, such as (2N2-N1)/2, 2N2-N1, (4N1 + N2)/2, and (2N/1-N2)/2, and N2 and 2N1-N2 are the main frequencies.
rough the analysis of the axis trajectory diagram, it is found that, as the degree of rubimpact increases, the axis trajectory of each measuring point becomes messy, no longer a regular circle or ellipse, and sharp corners appear in the rubbing direction. e simulation results are consistent with the theoretical analysis results.

Influence of Unbalance of the Dual-Rotor System on the Rub-Impact Vibration.
e rub-impact vibration characteristics of the dual-rotor system with 4 and 5 parameters in Table 4 are analyzed, and the influence of unbalance on the rub-impact vibration is studied. e vibration response of the dual-rotor system is obtained, as shown in Figures 20  and 21, respectively.
Comparing Figure 20 with Figure 21, it can be found that the influence of the fan disc unbalance on the rub-impact response of the dual-rotor system is greater than that of the high-pressure compressor disc unbalance. e increase of fan disc unbalance has a great influence on the vibration     response of the low-pressure rotor, but has little influence on the vibration response of the high-pressure rotor. e amplitude of frequency N2 in the spectrum of each measuring point of the low-pressure rotor increases with the increase of unbalance, and the impact of LPC unbalance is more obvious than that of HPC. It can be seen from the analysis that rotor unbalance will aggravate the vibration of the dual-rotor system caused by the rub-impact fault, and the rub-impact fault should be avoided as far as possible in design, assembly, and processing. e application of simulation technology in the aviation field can improve the vibration prediction and analysis      Shock and Vibration technology of a complex aeroengine rotor system. It can improve the stability and vibration control ability of the aeroengine rotor system, as well as the ability of dynamic analysis and design of the aeroengine rotor system. Comparing the vibration response of the dual-rotor system under the rub-impact fault in this paper with the results in [29][30][31][32], it can be seen that the double frequency and combined frequency of the high-and low-pressure rotors appear in the rub-impact vibration response of the dual-rotor system, such as 2N2-N1, 2N1-N2, N2-N1, 2N1, 2N2, N1 N2, and N2-N1. Moreover, with the difference in rotational speed, rub-impact stiffness, and rub-impact position, the performance of each component is obviously different. In addition, the dual-rotor system model applied in this paper also has the frequency division N2/2 of the fundamental frequency and the frequency division components of the combined frequency, such as (2N2-N1)/2, (2N1-N2)/2, and (4N1 N2)/2.

Conclusions
e dynamic modeling, analysis, and vibration prediction of the aeroengine rotor system based on the rigid-flexible coupling multibody dynamic system technology can meet the requirements of characteristics' analysis of the hierarchical system and rigid-flexible coupling structure and vibration prediction of the rotor system in the process of new rotor design. In particular, the simulation analysis of typical vibration problems such as unbalance and rub-impact of the rotor system can be realized effectively. In this paper, the vibration of the dual rotor with the rub-impact fault is studied by using the method of analysis and multibody dynamics simulation verification, and conclusions are obtained as follows: (1) e low-pressure rotor rotation frequency (N1) and the high-pressure rotor rotation frequency (N2) are the only frequencies of the unbalanced response of the dual-rotor system. e axis orbit of each measuring point is a regular circle.
(2) e rub-impact between the high-pressure turbine disc and the stator makes the vibration response of the dual-rotor system have nonlinear characteristics. e dynamic response of the rotor also contains the combined and division components of the speed frequency, and the occurrence of the rub-impact fault makes the axis track no longer a regular circle. e occurrence of the rub-impact fault increases the amplitude of the rotational frequency of the dualrotor system.
(3) With the increase of the rub-impact stiffness, the amplitude of the rub-impact spectrum components increases, and the component of the spectrum becomes more complex. (4) e transfer law of rotational frequencies (N1 and N2) of the dual-rotor vibration on high-and lowpressure rotors remains unchanged. (5) In the dual-rotor vibration caused by unbalance and rub-impact faults, the amplitude of N1 decreases along the transmission paths of low-pressure rotor 4-3-1-2 and high-pressure rotor 8-7-5-6. e amplitude of N2 decreases along the transmission paths of low-pressure rotor 4-3-1-2 and high-pressure rotor 5-6-8-7. (6) e vibration response characteristics of the dualrotor system caused by the fault are not completely identical at two speeds. e frequency components N1, N2, and N2-N1 appear in the vibration spectrum in both speed conditions. (7) Among the three parameters of the rub-impact fault, the stiffness has the greatest influence on the vibration response of each measuring point of the dual-rotor system, while the friction coefficient and clearance have little influence on the vibration response of each measuring point of the dual-rotor system. (8) e influence of the fan disc unbalance on the rubimpact response of the dual-rotor system is greater than that of the high-pressure compressor disc unbalance. e increase of fan disc unbalance has a great influence on the vibration response of the lowpressure rotor, but has little influence on the vibration response of the high-pressure rotor. e No. 5 (4# fulcrum) and No. 6 (HPC) measuring points on the high-pressure rotor are the least affected by the high-pressure turbine disc rub-impact and are mainly affected by the high-pressure compressor disc unbalance.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest.