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

Authors: Pingping Ma; Mingxin Shan; Jingyu Zhai; Hao Zhang; Qingkai Han
Journal: Shock and Vibration
 (2021)

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## Abstract

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. The 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. The 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. The vibration coupling and transfer among the high-pressure rotor and the low-pressure rotor are revealed. The influence of the unbalanced position and the speed of high and low rotors on the vibration response of the dual rotor is obtained. The sensitivity of the vibration response of the dual rotor at different test points to rub-impact stiffness, clearance, and friction coefficient is compared. The simulation model is established based on the rigid-flexible coupling multibody dynamic simulation platform. The analytical results and simulation results are compared, which have a good consistency. The 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. This 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.


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## Body

## 1. 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. The 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. The 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. The 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. Therefore, 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 [1–3] of Harbin Institute of Technology, Litang Yan [4] of Beijing University of Aeronautics and Astronautics, Mingfu Liao [5–7] of Northwest Polytechnic University, Qingkai Han [8–10] 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 rub-impact 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. The 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 dual-rotor 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. The 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. The 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. The 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 rub-impact fault makes the rotor system vibration response appear the combined frequency of rotation frequency, which makes the rotor system vibration appear nonlinear. The 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.The 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 low-pressure 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 rub-impact fault is studied by using the method of analysis and multibody dynamics simulation verification. The influence characteristics of rub-impact stiffness, clearance, and friction coefficient on the vibration response of the dual rotor are compared.


## 2. Establishment of the Dynamic Model for the Dual-Rotor System

Taking a typical aeroengine shown in Figure1 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. The 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. The low-pressure rotor is composed of a fan disc and one turbine disc. The 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. The front fulcrum of the fan and the rear fulcrum of the low-pressure turbine are elastic supports. The 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. The high-pressure rotor is composed of the compressor and one turbine, in which the support span is 580 mm. The 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. The front support of the high-pressure compressor is the elastic support, and the rear support is the intermediate bearing. The 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 high-pressure rotor rear fulcrum as close as possible to the low-pressure turbine rear fulcrum. The high- and low-pressure rotors are coupled through the intermediate bearing. The rotor transmits the load through the fulcrum of another rotor. Therefore, the dynamic characteristics of the dual-rotor system are not only affected by the high- and low-pressure rotors but also have some unique vibration characteristics.Figure 1
Structural sketch of a dual-rotor system for a typical aeroengine.Figure 2
The diagram of the simplified dual-rotor model.Table 1
Stiffness of the supports.
Kb1Kb2Kb3Kb4Kb59 × 106 N/m2.5 × 108 N/m3 × 106 N/m2.5 × 108 N/m3 × 106 N/m


## 3. Dynamic Model of the Dual Rotor with the Rub-Impact Fault

The analytical equations of multisupport motion of the dual-rotor 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. The support of the rotor system is considered to be elastic, and the speed of the rotating shaft is considered to be constant. The 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.The fixed coordinate system of the system isoxy, and the dynamic equation of the whole system is as follows:(1)Mq¨+Cq˙+Gq˙+Kq=F,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,(2)q=y1z1θy1θz1y2z2θy2θz2y3z3θy3θz3y4z4θy4θz4,F=F1yF1z00F2yF2z00F3yF3z00F4y+FRyF4z+FRz00,where Fiy, Fiz (i=1∼4) are the component of unbalanced excitation force in the y-direction and z-direction by four discs and FRy, FRz are the component of rub-impact force in the y-direction and z-direction.


## 4. Unbalanced Model

The 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 high-pressure turbine disc unbalance. The components of the centrifugal force produced by the unbalanced mass of each disc in they-direction and z-direction are as follows:(3)Fiy=meiΩi2cosΩit+ϕiFiz=meiΩi2sinΩit+ϕi,i=1−4,where mei is the unbalanced mass, and the unit is Kg⋅m. ϕi is the initial phase angle of the disc centroid, and the unit is rad. Ωi is the rotational angular velocity of the low- and high-pressure rotors, and the unit is rad/s.


## 5. Rub-Impact Model

The schematic diagram of the local rub-impact between the rotor and stator is shown in Figure3. Fy and Fz 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. The deformation of the rubbing plate caused by the rub-impact between the disc and rubbing plate is supposed to be linear. kc is the radial stiffness of the rubbing plate. fr 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. The concrete expression is as follows:(4)FRz=−krz−δHFRy=FRzfr=−krz−δHfr.Figure 3
The dynamic model of fixed-point rubbing. (a) Schematic diagram of rubbing between the casing and blisk. (b) Mechanical model of fixed-point rub-impact.
(a)(b)Rayleigh damping is adopted in the damping model, and the structure is as follows:(5)C=αM+βK.The Rayleigh damping matrix is a linear combination of the mass matrix and the stiffness matrix, whereα and β are damping coefficients, which are related to the modal damping ratio ξ of the structure. The calculation formula is as follows:(6)α=2ω1ω2ξ1ω2−ξ2ω1ω22−ω12,β=2ξ2ω2−ξ1ω1ω22−ω12.After derivation, other matrices can be easily obtained.


## 6. Inherent Characteristics of the Dual-Rotor System

According to matricesM, G, and K in formula (1), the modal frequency and modal shape of the rotor can be obtained. The displacement of the rotor system is written as follows:(7)q=q0eiωnt,where ωn is the whirl frequency of the rotor system; then, equation (3) can be written as(8)−ωn2Mq0+iωnΩGq0+Kq0=0.When calculating the critical speed, the whirl frequency and rotation frequency of the rotor are equal; then, the above formula can be written as(9)M−iG−1Kq0=ωn2q0.ωn2 is the eigenvalue of matrix M−iG−1K. The eigenvalue and eigenvector of matrix M−iG−1K are obtained by MATLAB programming. The square and eigenvector of the eigenvalue are the modal frequency and mode shape of the rotor system. The natural frequencies and vibration modes of the dual-rotor system are shown in Figure 4.Figure 4
Vibration modes’ diagram of the dual-rotor system. (a) First-order vibration (58.8 Hz). (b) Second-order vibration (75.4 Hz).
(a)(b)The model parameters of the simplified dual-rotor system are shown in Tables2–4, 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.Table 2
Parameters of four equivalent discs.
Disch (mm)D (mm)d (mm)m (Kg)J (Kg·m^2)D1183303514.0Jp = 0.164, Jd = 0.101D2103164811.3Jp = 0.059, Jd = 0.060D3353057320Jp = 0.230, Jd = 0.120D4143046210Jp = 0.102, Jd = 0.050Table 3
Parameters of the equivalent rotation shaft.
Shaft numberD (mm)d (mm)L (mm)The shaft of the low-pressure compressor300381The shaft of the low-pressure turbine300923The shaft of the high-pressure rotor6540680Table 4
Dimension parameters of the simplified dual-rotor system.
Parameter nameOD1B2D2B3D3D3B4D4B4C1C2D1C1OB3B4B5B2B5Numerical value (mm)12773711645969701381186581814It can be seen from Figure4 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.


## 7. Analysis Results

### 7.1. Method of Calculation

In this paper, the Newmark-β method is used to solve the vibration response of the dual-rotor 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. The 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.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. The arrangement of vibration measuring points of the dual-rotor system is shown in Figure5.Figure 5
The arrangement of vibration measuring points of the dual-rotor system.


### 7.2. Vibration Characteristics of the Dual Rotor with HPT Rubbing

#### 7.2.1. 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: low-pressure 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. The vibration response of the dual-rotor system under three different rub-impact parameter settings is shown in Figures 6–8.Table 5
Parameter setting of the rub-impact model.
ParameterIIIIIIIVRub-impact stiffness1 × 106 N/m7 × 106 N/m3 × 107 N/m0Friction coefficient0.40.40.60Rub-impact clearance1×10−7 m1×10−6 m1×10−7 m0LPC unbalance500 g mm500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mm500 g mmBased 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.Figure 6
The time-domain diagram, spectrum, and axle center obit of the test point under the Case I.
(a)(b)Comparing the vibration results in Figures6–9 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. The 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 dual-rotor system.(3)
Compared with Figures7–9, 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.Figure 7
The time-domain diagram, spectrum, and axle center obit of the test point under Case II.
(a)(b)Figure 8
The time-domain diagram, spectrum, and axle center obit of the test point under Case III.
(a)(b)Figure 9
Axis orbit diagram of the high- and low-pressure rotors. (a) The low-pressure rotor axis orbit diagram. (b) The high-pressure rotor axis orbit diagram.
(a)(b)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 Figure10. It can be seen that the vibration amplitude of every test point with the rub-impact 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. The 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. 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 disc position is least affected by the high-pressure turbine disc rubbing. The transfer law of speed frequency of the dual-rotor vibration on high- and low-pressure rotors remains unchanged. The 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.Figure 10
The amplitude of vibration frequenciesN1 and N2 at each measuring point of the dual rotor is affected by rub-impact. (a) N1. (b) N2.
(a)(b)


#### 7.2.2. 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 Table6. The vibration amplitude of fundamental frequency (N1 and N2) and 2 times of the high-pressure rotational frequency (2N2) are obtained in three cases. The influence of different rub-impact stiffness, rub-impact clearances, and rub-impact friction coefficients is compared. The representative results are shown in Figures 11–13 which are the amplitudes of N1, N2, and 2N2 of each measuring point with the change of the rub-impact parameters.Table 6
Parameter setting of the rub-impact model.
ParameterIIIIIIRub-impact stiffness3 × 106 N/m3 × 106 N/m3 × 106 N/mFriction coefficient0.40.40.6Rubbing clearance1×10−7 m1×10−6 m1×10−7 mLPC unbalance1500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mmFigure 11
The vibration amplitude ofN1 with different rub-impact parameters.
(a)(b)From Figure11, 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 Figure12, we can see that under the three different parameter settings, the vibration amplitude of N2 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 Figure13 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.Figure 12
The vibration amplitude ofN2 with different rub-impact parameters.
(a)(b)From Figures11–13, 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. The influence of friction coefficient on the amplitude of 2N2 is greater than that of rub-impact clearance.Figure 13
The vibration amplitude of 2N2 with different rub-impact parameters.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.


### 7.3. 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 speedN1 = 50 Hz, high-pressure speed N2 = 60 Hz, and rub-impact stiffness 7 × 106 N/m is studied. The 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, high-pressure speedN2 = 60 Hz, and rub-impact stiffness 7 × 106 N/m is studied without changing the rotor system unbalance. The vibration time domain and frequency spectrum of each measuring point are obtained, as shown in Figure 14.Figure 14
The time-domain diagram, spectrum, and axle center orbit of the dual-rotor system.
(a)(b)By comparing the results of Figure14 with Figure 8, it is found that the vibration response characteristics of the dual-rotor system caused by the rub-impact fault are not completely identical at two speeds. The 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. The orbit of the shaft center is enveloped ellipse shape, which is more regular than the results in Figure 8.


## 7.1. Method of Calculation

In this paper, the Newmark-β method is used to solve the vibration response of the dual-rotor 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. The 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.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. The arrangement of vibration measuring points of the dual-rotor system is shown in Figure5.Figure 5
The arrangement of vibration measuring points of the dual-rotor system.


## 7.2. Vibration Characteristics of the Dual Rotor with HPT Rubbing

### 7.2.1. 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: low-pressure 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. The vibration response of the dual-rotor system under three different rub-impact parameter settings is shown in Figures 6–8.Table 5
Parameter setting of the rub-impact model.
ParameterIIIIIIIVRub-impact stiffness1 × 106 N/m7 × 106 N/m3 × 107 N/m0Friction coefficient0.40.40.60Rub-impact clearance1×10−7 m1×10−6 m1×10−7 m0LPC unbalance500 g mm500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mm500 g mmBased 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.Figure 6
The time-domain diagram, spectrum, and axle center obit of the test point under the Case I.
(a)(b)Comparing the vibration results in Figures6–9 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. The 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 dual-rotor system.(3)
Compared with Figures7–9, 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.Figure 7
The time-domain diagram, spectrum, and axle center obit of the test point under Case II.
(a)(b)Figure 8
The time-domain diagram, spectrum, and axle center obit of the test point under Case III.
(a)(b)Figure 9
Axis orbit diagram of the high- and low-pressure rotors. (a) The low-pressure rotor axis orbit diagram. (b) The high-pressure rotor axis orbit diagram.
(a)(b)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 Figure10. It can be seen that the vibration amplitude of every test point with the rub-impact 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. The 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. 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 disc position is least affected by the high-pressure turbine disc rubbing. The transfer law of speed frequency of the dual-rotor vibration on high- and low-pressure rotors remains unchanged. The 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.Figure 10
The amplitude of vibration frequenciesN1 and N2 at each measuring point of the dual rotor is affected by rub-impact. (a) N1. (b) N2.
(a)(b)


### 7.2.2. 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 Table6. The vibration amplitude of fundamental frequency (N1 and N2) and 2 times of the high-pressure rotational frequency (2N2) are obtained in three cases. The influence of different rub-impact stiffness, rub-impact clearances, and rub-impact friction coefficients is compared. The representative results are shown in Figures 11–13 which are the amplitudes of N1, N2, and 2N2 of each measuring point with the change of the rub-impact parameters.Table 6
Parameter setting of the rub-impact model.
ParameterIIIIIIRub-impact stiffness3 × 106 N/m3 × 106 N/m3 × 106 N/mFriction coefficient0.40.40.6Rubbing clearance1×10−7 m1×10−6 m1×10−7 mLPC unbalance1500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mmFigure 11
The vibration amplitude ofN1 with different rub-impact parameters.
(a)(b)From Figure11, 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 Figure12, we can see that under the three different parameter settings, the vibration amplitude of N2 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 Figure13 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.Figure 12
The vibration amplitude ofN2 with different rub-impact parameters.
(a)(b)From Figures11–13, 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. The influence of friction coefficient on the amplitude of 2N2 is greater than that of rub-impact clearance.Figure 13
The vibration amplitude of 2N2 with different rub-impact parameters.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.


## 7.2.1. 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: low-pressure 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. The vibration response of the dual-rotor system under three different rub-impact parameter settings is shown in Figures 6–8.Table 5
Parameter setting of the rub-impact model.
ParameterIIIIIIIVRub-impact stiffness1 × 106 N/m7 × 106 N/m3 × 107 N/m0Friction coefficient0.40.40.60Rub-impact clearance1×10−7 m1×10−6 m1×10−7 m0LPC unbalance500 g mm500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mm500 g mmBased 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.Figure 6
The time-domain diagram, spectrum, and axle center obit of the test point under the Case I.
(a)(b)Comparing the vibration results in Figures6–9 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. The 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 dual-rotor system.(3)
Compared with Figures7–9, 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.Figure 7
The time-domain diagram, spectrum, and axle center obit of the test point under Case II.
(a)(b)Figure 8
The time-domain diagram, spectrum, and axle center obit of the test point under Case III.
(a)(b)Figure 9
Axis orbit diagram of the high- and low-pressure rotors. (a) The low-pressure rotor axis orbit diagram. (b) The high-pressure rotor axis orbit diagram.
(a)(b)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 Figure10. It can be seen that the vibration amplitude of every test point with the rub-impact 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. The 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. 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 disc position is least affected by the high-pressure turbine disc rubbing. The transfer law of speed frequency of the dual-rotor vibration on high- and low-pressure rotors remains unchanged. The 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.Figure 10
The amplitude of vibration frequenciesN1 and N2 at each measuring point of the dual rotor is affected by rub-impact. (a) N1. (b) N2.
(a)(b)


## 7.2.2. 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 Table6. The vibration amplitude of fundamental frequency (N1 and N2) and 2 times of the high-pressure rotational frequency (2N2) are obtained in three cases. The influence of different rub-impact stiffness, rub-impact clearances, and rub-impact friction coefficients is compared. The representative results are shown in Figures 11–13 which are the amplitudes of N1, N2, and 2N2 of each measuring point with the change of the rub-impact parameters.Table 6
Parameter setting of the rub-impact model.
ParameterIIIIIIRub-impact stiffness3 × 106 N/m3 × 106 N/m3 × 106 N/mFriction coefficient0.40.40.6Rubbing clearance1×10−7 m1×10−6 m1×10−7 mLPC unbalance1500 g mm500 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mmFigure 11
The vibration amplitude ofN1 with different rub-impact parameters.
(a)(b)From Figure11, 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 Figure12, we can see that under the three different parameter settings, the vibration amplitude of N2 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 Figure13 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.Figure 12
The vibration amplitude ofN2 with different rub-impact parameters.
(a)(b)From Figures11–13, 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. The influence of friction coefficient on the amplitude of 2N2 is greater than that of rub-impact clearance.Figure 13
The vibration amplitude of 2N2 with different rub-impact parameters.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.


## 7.3. 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 speedN1 = 50 Hz, high-pressure speed N2 = 60 Hz, and rub-impact stiffness 7 × 106 N/m is studied. The 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, high-pressure speedN2 = 60 Hz, and rub-impact stiffness 7 × 106 N/m is studied without changing the rotor system unbalance. The vibration time domain and frequency spectrum of each measuring point are obtained, as shown in Figure 14.Figure 14
The time-domain diagram, spectrum, and axle center orbit of the dual-rotor system.
(a)(b)By comparing the results of Figure14 with Figure 8, it is found that the vibration response characteristics of the dual-rotor system caused by the rub-impact fault are not completely identical at two speeds. The 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. The orbit of the shaft center is enveloped ellipse shape, which is more regular than the results in Figure 8.


## 8. Simulation Verification

### 8.1. 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 [23–28]. The 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.The ‘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. The 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.The rub-impact mechanics expression is(10)F=0,x≥δ0kδ0−xe−NCmaxstepx,δ0−d,1,δ0,0x≪δ0.Among them,k is the stiffness coefficient, δ0 is the initial distance between the two contact objects, x is the actual distance between the two contact objects in the rubbing process, Cmax 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.The 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. The 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.The 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). The fixed pair is used to define the rub-impact block as the stator. The 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 Figure15. Low-pressure speed N1 = 50 Hz and high-pressure speed N2 = 60 Hz. The rigid-flexible coupling simulation model of the dual-rotor system is shown in Figure 15.Figure 15
The multibody dynamic model of the dual-rotor system based on ADAMS.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 Figure16. And the results are compared with the analytical results based on the dynamic equation. The results show that the first two modes are consistent. The first and second modes of the low-pressure rotor are mainly the first-order bending of the low-pressure turbine shaft. The first mode of the high-pressure rotor is translational, and the second is the pitching mode. The first natural frequency difference ratio is 5%, and the second natural frequency difference ratio is 4.5%. The rationality of the simulation model is verified.Figure 16
The first two modes and natural frequencies of the dual-rotor system based on ADAMS. (a) The first mode shape (53 Hz). (b) The second mode shape (79 Hz).
(a)(b)


### 8.2. Parameter Setting of the Simulation

Based on the multibody dynamics model of the dual-rotor system with the rub-impact fault in Figure15, the vibration response of the dual-rotor system is simulated with five different rub-impact states as shown in Table 7.Table 7
Parameter setting of the simulation model based on ADAMS.
ParameterCase 1Case 2Case 3Case 4Case 5Rub-impact stiffness1 × 106 N/m1 × 107 N/m1 × 108 N/m1 × 107 N/m1 × 107 N/mRub-impact damping100 Ns/m1000 Ns/m10000 Ns/m1000 Ns/m1000 Ns/mForce exponent1.51.51.51.51.5Penetration depth0.1 mm0.1 mm0.1 mm0.1 mm0.1 mmRubbing clearance1×10−7m1×10−7m1×10−6m1×10−7m1×10−7mLPC unbalance500 g mm500 g mm500 g mm1000 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mm500 g mm1000 g mm


### 8.3. Simulation Results

#### 8.3.1. Influence of Different Rubbing Stiffness on the Vibration

As shown in Table4, the vibration of the dual-rotor system under three different impact stiffness (1–3) is simulated and analyzed, and the vibration time domain, frequency spectrum, and high- and low-pressure rotor center orbit of each measuring point under three conditions are obtained, as shown in Figures 17–19.Figure 17
The vibration of the dual-rotor system with slight rubbing (case 1). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 18
The vibration of the dual-rotor system with less severe rubbing (case 2). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 19
The vibration of the dual-rotor system with severe rubbing (case 3). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Analyzing the results shown in Figures17–19, 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. Through 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. Through the analysis of the axis trajectory diagram, it is found that, as the degree of rub-impact 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. The simulation results are consistent with the theoretical analysis results.


#### 8.3.2. Influence of Unbalance of the Dual-Rotor System on the Rub-Impact Vibration

The rub-impact vibration characteristics of the dual-rotor system with 4 and 5 parameters in Table4 are analyzed, and the influence of unbalance on the rub-impact vibration is studied. The vibration response of the dual-rotor system is obtained, as shown in Figures 20 and 21, respectively.Figure 20
The influence of LPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 4). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Figure 21
The influence of HPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 5). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Comparing Figure20 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. The 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.The amplitude of frequencyN2 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.The application of simulation technology in the aviation field can improve the vibration prediction and analysis 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 [29–32], 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.


## 8.1. 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 [23–28]. The 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.The ‘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. The 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.The rub-impact mechanics expression is(10)F=0,x≥δ0kδ0−xe−NCmaxstepx,δ0−d,1,δ0,0x≪δ0.Among them,k is the stiffness coefficient, δ0 is the initial distance between the two contact objects, x is the actual distance between the two contact objects in the rubbing process, Cmax 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.The 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. The 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.The 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). The fixed pair is used to define the rub-impact block as the stator. The 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 Figure15. Low-pressure speed N1 = 50 Hz and high-pressure speed N2 = 60 Hz. The rigid-flexible coupling simulation model of the dual-rotor system is shown in Figure 15.Figure 15
The multibody dynamic model of the dual-rotor system based on ADAMS.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 Figure16. And the results are compared with the analytical results based on the dynamic equation. The results show that the first two modes are consistent. The first and second modes of the low-pressure rotor are mainly the first-order bending of the low-pressure turbine shaft. The first mode of the high-pressure rotor is translational, and the second is the pitching mode. The first natural frequency difference ratio is 5%, and the second natural frequency difference ratio is 4.5%. The rationality of the simulation model is verified.Figure 16
The first two modes and natural frequencies of the dual-rotor system based on ADAMS. (a) The first mode shape (53 Hz). (b) The second mode shape (79 Hz).
(a)(b)


## 8.2. Parameter Setting of the Simulation

Based on the multibody dynamics model of the dual-rotor system with the rub-impact fault in Figure15, the vibration response of the dual-rotor system is simulated with five different rub-impact states as shown in Table 7.Table 7
Parameter setting of the simulation model based on ADAMS.
ParameterCase 1Case 2Case 3Case 4Case 5Rub-impact stiffness1 × 106 N/m1 × 107 N/m1 × 108 N/m1 × 107 N/m1 × 107 N/mRub-impact damping100 Ns/m1000 Ns/m10000 Ns/m1000 Ns/m1000 Ns/mForce exponent1.51.51.51.51.5Penetration depth0.1 mm0.1 mm0.1 mm0.1 mm0.1 mmRubbing clearance1×10−7m1×10−7m1×10−6m1×10−7m1×10−7mLPC unbalance500 g mm500 g mm500 g mm1000 g mm500 g mmHPC unbalance500 g mm500 g mm500 g mm500 g mm1000 g mm


## 8.3. Simulation Results

### 8.3.1. Influence of Different Rubbing Stiffness on the Vibration

As shown in Table4, the vibration of the dual-rotor system under three different impact stiffness (1–3) is simulated and analyzed, and the vibration time domain, frequency spectrum, and high- and low-pressure rotor center orbit of each measuring point under three conditions are obtained, as shown in Figures 17–19.Figure 17
The vibration of the dual-rotor system with slight rubbing (case 1). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 18
The vibration of the dual-rotor system with less severe rubbing (case 2). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 19
The vibration of the dual-rotor system with severe rubbing (case 3). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Analyzing the results shown in Figures17–19, 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. Through 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. Through the analysis of the axis trajectory diagram, it is found that, as the degree of rub-impact 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. The simulation results are consistent with the theoretical analysis results.


### 8.3.2. Influence of Unbalance of the Dual-Rotor System on the Rub-Impact Vibration

The rub-impact vibration characteristics of the dual-rotor system with 4 and 5 parameters in Table4 are analyzed, and the influence of unbalance on the rub-impact vibration is studied. The vibration response of the dual-rotor system is obtained, as shown in Figures 20 and 21, respectively.Figure 20
The influence of LPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 4). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Figure 21
The influence of HPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 5). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Comparing Figure20 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. The 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.The amplitude of frequencyN2 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.The application of simulation technology in the aviation field can improve the vibration prediction and analysis 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 [29–32], 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.


## 8.3.1. Influence of Different Rubbing Stiffness on the Vibration

As shown in Table4, the vibration of the dual-rotor system under three different impact stiffness (1–3) is simulated and analyzed, and the vibration time domain, frequency spectrum, and high- and low-pressure rotor center orbit of each measuring point under three conditions are obtained, as shown in Figures 17–19.Figure 17
The vibration of the dual-rotor system with slight rubbing (case 1). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 18
The vibration of the dual-rotor system with less severe rubbing (case 2). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Figure 19
The vibration of the dual-rotor system with severe rubbing (case 3). (a) Time-domain diagram of each measuring point. (b) Spectrum of each measuring point. (c) Axis orbit of the low-pressure rotor. (d) Axis orbit of the high-pressure rotor.
(a)(b)(c)(d)Analyzing the results shown in Figures17–19, 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. Through 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. Through the analysis of the axis trajectory diagram, it is found that, as the degree of rub-impact 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. The simulation results are consistent with the theoretical analysis results.


## 8.3.2. Influence of Unbalance of the Dual-Rotor System on the Rub-Impact Vibration

The rub-impact vibration characteristics of the dual-rotor system with 4 and 5 parameters in Table4 are analyzed, and the influence of unbalance on the rub-impact vibration is studied. The vibration response of the dual-rotor system is obtained, as shown in Figures 20 and 21, respectively.Figure 20
The influence of LPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 4). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Figure 21
The influence of HPC unbalance on the vibration response of the dual-rotor system with the rub-impact fault (Case 5). (a) Time-domain and frequency spectrum of the low-pressure rotor at measuring points 1–4. (b) Time-domain and frequency spectrum of the high-pressure rotor at measuring points 5–8.
(a)(b)(c)(d)Comparing Figure20 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. The 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.The amplitude of frequencyN2 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.The application of simulation technology in the aviation field can improve the vibration prediction and analysis 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 [29–32], 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.


## 9. Conclusions

The 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)
The 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. The axis orbit of each measuring point is a regular circle.(2)
The rub-impact between the high-pressure turbine disc and the stator makes the vibration response of the dual-rotor system have nonlinear characteristics. The 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. The occurrence of the rub-impact fault increases the amplitude of the rotational frequency of the dual-rotor 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)
The transfer law of rotational frequencies (N1 and N2) of the dual-rotor vibration on high- and low-pressure rotors remains unchanged.(5)
In the dual-rotor vibration caused by unbalance and rub-impact faults, the amplitude ofN1 decreases along the transmission paths of low-pressure rotor 4-3-1-2 and high-pressure rotor 8-7-5-6. The 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)
The vibration response characteristics of the dual-rotor system caused by the fault are not completely identical at two speeds. The frequency componentsN1, 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)
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. The 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. The 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.



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*Source: 6622065-2021-04-27.xml*