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Analyzing the nonlinear characteristics of dual-rotor systems under thermo-mechanical (TM) coupling situations is critical, as operational conditions should be accurately determined, to avoid potential thermally-induced failures. This paper proposes the coupled TM model of a dual-rotor system, which considers multiple nonlinearities and heat generation of four bearings that couple the mechanical and thermal fields. Heat dissipation controlled by lubricant flow rates is introduced into the model to simulate different TM coupling degrees. Nonlinear phenomena and stability evolution are analyzed by the modified incremental harmonic balance method (IHB) at primary resonance regions. An increase in TM coupling degrees can lead to more bifurcation points, resonance regions with lower frequencies, larger vibration responses, and unstable regions. It can also transform resonance hysteresis phenomena into more complex nonlinear phenomena and some saddle-node bifurcation points into Neimark–Sacker bifurcation points. The reason for these transformations is that the effective radial clearance (RC) of bearings changes with rotation speed and thermal expansion. Temperature nonlinearities are induced by the radial bearing loads and the lubricant viscosity, which are investigated by various generalized nonlinear thermal forces. These findings can help further understand nonlinear coupled TM problems of complex dual-rotor systems. [ABSTRACT FROM AUTHOR]

Rub-impact is one of the common failures in dual-rotor systems, and seriously affects the machine's operation cost. Currently, research about this fault mainly focuses on models that gain initial excitation through rotor unbalance. Whereas, this excitation source is rarely aggravated during rotating machinery's full life period. Aiming at this issue, a Hertz impact-contact model of casing-disc-shaft dual-rotor system with rubbing fault caused by disc looseness is developed to simulate a deteriorating failure. Thus, the system vibration variation during the fault deterioration can be analyzed, and the necessary basis for prediction of the coupling faults are provided. In this model, slight unbalance provides the initial excitation amplified by disc looseness, from which the rub-impact defect is induced between the loose disc and the outer casing. Further, motion equations for this coupling fault system are derived to simulate the vibration signals. Result shows that the critical parameters significantly affect the system's vibration, and the deterioration of coupling faults takes the system from steady-state to chaotic-state. The study of this paper provides theoretical bases for the rub-impact fault tracing of dual-rotor systems, and proposes different scales to indicate the fault severity degree qualitatively and quantitatively. [ABSTRACT FROM AUTHOR]

To enhance the static and dynamic performance of the grinding wheel spindle system, with the gear grinding machine (YKF2060) as the research object, a static mechanics model of the spindle system was established based on Castigliano's theorem, taking into account the equivalent effect of the triple-point contact ball bearing at the front end of the spindle. Meanwhile, based on the overall transfer matrix method, a dynamic model of the main spindle–eccentric shaft dual-rotor system was established, taking into account the effects of shear deformation and gyroscopic moments. On this basis, the effect of the spindle span, the front and rear overhang of the eccentric shaft, and the bearing stiffness on the static stiffness and first-order critical speed of the system was analyzed. Finally, static stiffness experiments, modal tests, and finite element simulation models were conducted to verify the static and dynamic models. The results show that the stiffness of the front outer bearing has the greatest influence on the static and dynamic performance of the system, while the stiffness of the rear inner bearing has the least influence. The relative errors of the static stiffness and the first two natural frequencies between static stiffness experiments, modal tests, and finite element simulation models are less than 10%, and the mode shapes match well. The established static and dynamic model can effectively reflect both the static and dynamic characteristics of the spindle system. [ABSTRACT FROM AUTHOR]

Previous studies on rub-impact faults have mainly focused on the rub-impact between rotors and stators, with less research on inter-rotor rub impact. The impact of inter-rotor rub impact on rotor nonlinear vibration is particularly significant. This study investigates the effects of inter-shaft rub impact on the vibration characteristics and whirl behavior of dual-rotor systems. Initially, a dual-rotor model with inter-shaft bearings is established using the finite element method, and inter-shaft rub-impact forces are derived based on contact mechanics. Next, the system response is solved using the Newmark method. Vibration characteristics are analyzed through Campbell diagrams, 3D waterfall plots, time-frequency domain plots, and steady-state rub-impact force plots. Finally, the influence of inter-shaft rub impact on the whirl behavior of the dual-rotor system is studied based on the theory of full-spectrum analysis. The study concludes that inter-shaft rub-impact faults shift the system's resonance points backward, increase harmonic and combination frequency components, and significantly affect the system response under dual-rotor co-rotation. Excessive friction can lead to self-excited vibrations and sudden amplitude increases, particularly in the LP rotor frequency. Additionally, inter-shaft rub impact primarily affects the whirl behavior of the LP-compressor disk1, showing multiple cycles of forward and backward whirl alternation during acceleration due to combined unbalanced and rub-impact excitations. [ABSTRACT FROM AUTHOR]

To enhance the static and dynamic performance of the grinding wheel spindle system, with the gear grinding machine (YKF2060) as the research object, a static mechanics model of the spindle system was established based on Castigliano’s theorem, taking into account the equivalent effect of the triple-point contact ball bearing at the front end of the spindle. Meanwhile, based on the overall transfer matrix method, a dynamic model of the main spindle–eccentric shaft dual-rotor system was established, taking into account the effects of shear deformation and gyroscopic moments. On this basis, the effect of the spindle span, the front and rear overhang of the eccentric shaft, and the bearing stiffness on the static stiffness and first-order critical speed of the system was analyzed. Finally, static stiffness experiments, modal tests, and finite element simulation models were conducted to verify the static and dynamic models. The results show that the stiffness of the front outer bearing has the greatest influence on the static and dynamic performance of the system, while the stiffness of the rear inner bearing has the least influence. The relative errors of the static stiffness and the first two natural frequencies between static stiffness experiments, modal tests, and finite element simulation models are less than 10%, and the mode shapes match well. The established static and dynamic model can effectively reflect both the static and dynamic characteristics of the spindle system.

The dual-rotor system is the core component of advanced aero-engine. Establishing a reasonable, accurate, and efficient dynamics model is the key to studying the dynamics and vibration of the rotor system for aero-engine. This manuscript takes a representative aircraft engine dual-rotor system as a prototype, considers the rig-id-flexible coupling characteristics of different stiffness elastic supports and rotor structures, and establishes an analytical dynamic model of the dual-rotor system. Based on the established dynamic model, the natural char-acteristics of the dual-rotor system are analyzed. The model was validated using two different research methods: the rigid-flexible coupling multi-body system dynamics simulation platform ADAMS, and finite element analy-sis. The dynamic model of the dual-rotor system established in this paper can meet the requirements of hierar-chical rigid-flexible coupling of system and structure, overall mass distribution, and stiffness distribution. In particular, it can also effectively realize the simulation of multi-facet and multi-phase unbalanced vibration of the rotor system. The research methods of this paper can further enrich the basic theory of dynamics and vibration of the aero-engine rotor system. [ABSTRACT FROM AUTHOR]

In order to study the effects of maneuvering overload on the main shaft bearing (abbreviation: bearing) reaction force in an aero-engine, a bending-torsion coupling dynamic model of the dual rotor system under maneuvering overload was established. Combined with the output parameters of the system model, the bearing reaction force analysis model was established. The maneuvering overload parameters are input into system model. Newmark-ß and Newton-raphson methods are used to obtain the bearing reaction force response, and the change laws of bearing reaction force under the different maneuvering overloads are analyzed. The results show that gravity will make the transient response of bearing reaction force offset, and maneuvering overload will make the offset shift. Maneuvering overload will cause bearing to produce a circumferential asymmetric reaction force. For bearing 1, the additional gyroscopic torque in maneuvering overload has a significant effect on the dynamic eccentricity, resulting in a larger offset of reaction force of ʸ direction. For bearings 3 and 4, reaction force of ˣ direction has a larger offset. Under the influence of bent-torsional coupling, the combined frequencies of base frequencies of rotational speed appear in the reaction force spectrum diagram. [ABSTRACT FROM AUTHOR]

The nonlinear thermo-mechanic coupling effect refers to the interaction between the nonlinear dynamic characteristics of a dual-rotor system and the thermal effect of an intershaft bearing. In this paper, the nonlinear thermo-mechanic coupling effect of the dual-rotor system is proposed and studied by the operating radial clearance and dynamic load of the intershaft bearing. A nonlinear dynamic model of the dual-rotor system under the thermal effect of the intershaft bearing is established by considering nonlinear factors such as the Hertzian contact force and the operating radial clearance of the intershaft bearing. The dynamic load of the intershaft bearing is obtained based on the dynamic responses of the system. Based on this, a thermal effect model of the intershaft bearing considering the nonlinear dynamic characteristics of the system is proposed. The operating radial clearance of the intershaft bearing is attained according to the temperature field of the intershaft bearing. The thermo-mechanic coupling model of the dual-rotor system is presented by connecting the dynamic model and the thermal effect model. The results solved by numerical iteration show that the nonlinear dynamic characteristics of the dual-rotor system are deeply coupled with the thermal effect of the intershaft bearing, and become weaker. In turn, a complex nonlinear thermal effect affects the bearing due to the nonlinear dynamic characteristics of the system. Furthermore, the operating radial clearance of the intershaft bearing is closely related to the thermo-mechanic coupling effect of the system. The operating radial clearance decreases with increasing temperature, decreases with decreasing initial radial clearance, and decreases sharply in the resonance regions. Thus, the "negative clearance" may affect the operating radial clearance of the intershaft bearing, which endangers the operation of the rotor system. Moreover, the nonlinear characteristics of the thermo-mechanic coupling effect become stronger as the ambient temperature increases. The results presented in this paper provide insight into the mechanism of the nonlinear thermo-mechanic coupling effect and new theoretical guidances for the dynamic and thermodynamic design of the intershaft bearing in the dual-rotor system. [ABSTRACT FROM AUTHOR]

Previous studies on rub-impact faults have mainly focused on the rub-impact between rotors and stators, with less research on inter-rotor rub impact. The impact of inter-rotor rub impact on rotor nonlinear vibration is particularly significant. This study investigates the effects of inter-shaft rub impact on the vibration characteristics and whirl behavior of dual-rotor systems. Initially, a dual-rotor model with inter-shaft bearings is established using the finite element method, and inter-shaft rub-impact forces are derived based on contact mechanics. Next, the system response is solved using the Newmark method. Vibration characteristics are analyzed through Campbell diagrams, 3D waterfall plots, time-frequency domain plots, and steady-state rub-impact force plots. Finally, the influence of inter-shaft rub impact on the whirl behavior of the dual-rotor system is studied based on the theory of full-spectrum analysis. The study concludes that inter-shaft rub-impact faults shift the system’s resonance points backward, increase harmonic and combination frequency components, and significantly affect the system response under dual-rotor co-rotation. Excessive friction can lead to self-excited vibrations and sudden amplitude increases, particularly in the LP rotor frequency. Additionally, inter-shaft rub impact primarily affects the whirl behavior of the LP-compressor disk1, showing multiple cycles of forward and backward whirl alternation during acceleration due to combined unbalanced and rub-impact excitations.

This paper focuses on the combination resonances of a dual-rotor system with inter-shaft bearing. The motion equations of the dual-rotor system are formulated by the Lagrange equation, in which the unbalanced excitations of the two rotors and the clearance of the inter-shaft bearing are taken into consideration. The HB-AFT method (harmonic balance-alternating frequency/time domain method) is employed to obtain all the periodic solutions including the unstable solutions of the system. The combination resonance characteristics of the system are analyzed in detail by using the frequency response curves and separated frequency responses of the dual-rotor system. Besides the two primary resonance peaks, three more combination resonance regions in the frequency response curves of the system are found, in which the jump and bi-stable phenomena are observed. The primary resonance is mainly dominated by the excitation frequency ω 1 and ω 2 , the combination resonance of the system is mainly dominated by the combined frequency component of 2 ω 2 - ω 1 , 4 ω 2 - 3 ω 1 , 3 ω 2 - 2 ω 1 and is almost independent of other frequency components. Furthermore, the effect of inter-shaft bearing clearance on the combination resonance regions is obtained, it is indicated that increasing the inter-shaft bearing clearance will not only affect the response amplitudes of the combination resonance and change the "softening and hardening characteristic" of the frequency response curves, but also show a certain "stiffness weakening effect" on the rotor system. The study in this paper is of great significance to select the parameters of the dual-rotor system reasonably so as to avoid harmful combination resonance. [ABSTRACT FROM AUTHOR]

In this paper, an analytical model of a rotor-bearing-rotor coupling system is established for aero-engine from the Lagrange equation, based on the dynamics theory of the dual-rotor system and combined with its stiffness, damping, and misalignment characteristics. In the model, the misalignment fault simulation method is introduced. The coupling effect between the low-pressure rotor and high-pressure rotor and the influence of misalignment of the support on low-pressure coupling are considered. The vibration characteristics of the dual-rotor system with the misalignment fault of the low-pressure turbine rear support are studied. The time-domain responses, the frequency spectra, and the shaft-center trajectory of the dual-rotor system with different misalignments are obtained. The influence of unbalance on the vibration characteristics of the low-pressure rotor and the high-pressure rotor with misalignment fault is analyzed. Finally, test verification is carried out by the designed dual-rotor test rig. The experimental results are consistent with the analytical results, confirming the established model's feasibility and simulation method in this paper. The results may provide a theoretical basis for research on the misalignment fault in aero-engine dual-rotor systems.

The magnetic suspended dual-rotor system (MSDS) has the advantage of a high power density. The system can be used in high-speed rotating machinery. The major purpose of this study is to predict the unbalance response of the MSDS considering the nonlinear bearing characteristics of active magnetic bearings (AMBs). Firstly, the nonlinear bearing model was established by a non-linear magnetic circuit method (NMCM). The model considers magnetic flux leakage, magnetic saturation, and working position flotation accurately. Then, the dynamic model of the system was established by using the finite element method and solved by the Newmark-β method. Finally, the effects of external load, rotational speeds, and control parameters were studied. Axial trajectory diagrams, stability zone diagrams, and waterfall diagrams were employed to analyze the dynamic behaviors of the MSDS. The results indicate that the external load, rotational speeds, and control parameters have a significant impact on the unbalance response of the system. Super harmonics of rotational frequencies and their combined frequencies may be excited by heavy load conditions. Appropriate control parameters can suppress the nonlinear phenomena. The obtained results of this research will contribute to the design and fault diagnosis of MSDSs. [ABSTRACT FROM AUTHOR]

This article presents a nonlinear vibration characteristics study of a bolted joint dual-rotor system. The motion equations are derived through the lumped mass modeling method and a two-node bolted joint element. Nonlinear time-varying bending stiffness at the joint interface is considered in the numerical integration. Qualitative analysis of the effect of preload on system responses is conducted through changing the value of the transition point of bending stiffness of the bolted joint. Moreover, the transfer path of vibration in the dual-rotor system through inner-shaft bearing was discussed in the present work. The nonlinear differential equations are solved using the Newmark integration method to predict the dynamic characteristics of the dual-rotor system. The results show that the maximum vibration displacement of LP rotor is positively correlated with that of HP rotor as preload changes. Moreover, the maximum amplitude of the time-domain responses of the HP rotor will decrease and the minimum amplitude will increase with the increase of preload. The difference between the maximum and minimum values of the time-domain response will decrease with the increase of preload. This can be explained by the "stiffness hardening" phenomenon of the bolted joint. The research results can help understanding the dynamic properties of the bolted joint dual-rotor system and the vibration transfer path of the rotor system through inner-shaft bearing. [ABSTRACT FROM AUTHOR]

The dimension reduction incremental harmonic balance (DRIHB) method is developed to study the dynamic behavior of dual-rotor system with multi-frequency excitations and nonlinear rubbing faults. On the basis of consideration of an aero-engine, a dynamic model of rotor system is built and the piecewise-nonlinear model of rubbing force is used to investigate the nonlinear behavior of system. Considering the features of multi-frequency excitation, high dimension and strong nonlinearity of dual-rotor system, the dimension reduction approach combined with the incremental harmonic balance (IHB) method is derived for theoretically studying the dynamic response of system with nonlinear rubbing fault. The accuracy and efficiency of the method are proved through comparison with the numerical simulation result solved by the Newmark- β method and the IHB method. Then, the influences of rubbing stiffness, contact gap, rotational speed and speed ratio on dynamic response are studied and discussed. It is shown that the dual-rotor system with nonlinear rubbing fault will cause the system to generate rich combination frequency components in addition to excitation frequency. All the works indicate that the DRIHB method is an effective tool for studying the nonlinear behavior of dual-rotor systems with multi-frequency excitation, high dimensions and strong nonlinearities. [ABSTRACT FROM AUTHOR]

The cantilever dual-rotor system is a typical structure of the blade output end of the open rotor engine and the coaxial output turboshaft engine. The excessive unbalanced vibration of a coupled cantilever dual-rotor system is one of the main factors limiting the application of the above engine type. In order to accurately describe the vibration coupling effect between the dual-rotor-intermediate bearings, the unbalanced response of the cantilever dual-rotor system is analyzed, and the self-sensitivity coefficient is proposed to guide the selection of measuring points and vibration suppression experiments for the dual-rotor system. On this basis, a new online automatic balance actuator applicable to this dual-rotor system is designed, and a feasibility experiment is carried out. The experimental results indicate that: (1) The self-sensitivity coefficient can be used as the basis for the actual vibration measuring point arrangement and unbalanced vibration suppression strategy of the dual-rotor system, and the proposed step-by-step vibration suppression strategy can reduce the vibration of the dual-rotor system by more than 80%. (2) The designed online automatic balance actuator can reduce the unbalanced vibration by 53% in 3.52 s. The proposed method in this study can provide guidance for the vibration suppression of the dual-rotor system. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic dynamic analysis of a dual-rotor system with a local defect on the inner raceway of the inter-shaft bearing is presented. The dynamic model of the dual-rotor system is also proposed. The defect size and its uncertainty are considered. The non-intrusive polynomial chaos expansion model is utilized to deal with the uncertainty of the defect size, and the validity of the model is verified. The probability density distribution of vibration displacements for the dual-rotor system is obtained. Results indicate that the mean value (MV) and standard deviation (SD) of the defect edge length have extremely significant effects on the displacement distribution of high-pressure rotor. The coefficients of variation of the displacements along x2 and ϕx directions for high-pressure rotor increase by 6.56 and 7.06 times, respectively. When the MV of the defect edge length increases by three times, 3.46 times, and 3.69 times, its SD increases by five times. The increase of eccentricity has opposite effects on the vibration displacements of high- and low-pressure rotors. The variation of the radial clearance of the inter-shaft bearing has a complex influence on the dual-rotor system. As the radial clearance increases, the displacement dispersion of the low-pressure rotor along θx direction is almost unchanged. However, that along x1 direction is increased. [ABSTRACT FROM AUTHOR]

In order to improve the thrust-weight ratio, modern aeroengines generally adopt a coaxial dual-rotor system. Factors such as manufacturing errors, assembly errors, bearing wear, and structural deformation can cause misalignment failures in a dual-rotor system. Supporting misalignment is one of the common types of misalignments in a dual-rotor system. To analyze the vibration characteristics of misalignment faults, in this study, we aim to build a finite element model of a dual-rotor system with supporting misalignment. The bearing loads caused by supporting misalignment are calculated using the three-bending moment equation method. Bearing loads are introduced into the dynamic model of the dual-rotor system. The influence of supporting misalignment at different bearings on the dynamic characteristics of the rotor system is investigated based on the supporting misalignment model. Studies have shown that supporting misalignment at different bearings has similar effects on the dynamic characteristics of the dual-rotor system. The proposed supporting misalignment model is more adaptable than the coupling misalignment model. It indicates that the damping of a rolling bearing should be considered in the dynamic analysis of a dual-rotor system although the value of the damping is not large. An experimental analysis is carried out. The simulation results are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The magnetic suspended dual-rotor system (MSDS) has the advantage of a high power density. The system can be used in high-speed rotating machinery. The major purpose of this study is to predict the unbalance response of the MSDS considering the nonlinear bearing characteristics of active magnetic bearings (AMBs). Firstly, the nonlinear bearing model was established by a non-linear magnetic circuit method (NMCM). The model considers magnetic flux leakage, magnetic saturation, and working position flotation accurately. Then, the dynamic model of the system was established by using the finite element method and solved by the Newmark-β method. Finally, the effects of external load, rotational speeds, and control parameters were studied. Axial trajectory diagrams, stability zone diagrams, and waterfall diagrams were employed to analyze the dynamic behaviors of the MSDS. The results indicate that the external load, rotational speeds, and control parameters have a significant impact on the unbalance response of the system. Super harmonics of rotational frequencies and their combined frequencies may be excited by heavy load conditions. Appropriate control parameters can suppress the nonlinear phenomena. The obtained results of this research will contribute to the design and fault diagnosis of MSDSs.

Dual-rotor systems are widely used in aero-engines, in which rubbing–misalignment mixed faults are essential, as both are frequently observed and can occur simultaneously due to the harsh working conditions of high temperature, high pressure, and high speed. To analyze the vibration characteristics of such faults, a dual-rotor system model is established and dynamic responses under varying parameters of the dual-rotor system with rubbing–misalignment mixed fault are investigated. Through numerical simulation, the effects of speed ratio, rubbing clearance, and rubbing stiffness on the dual-rotor system with rubbing–misalignment fault are revealed. Meanwhile, experimental tests are conducted for validation, the main findings of which are that the characteristic frequency components could benefit the diagnosis of mixed faults in dual-rotor systems. [ABSTRACT FROM AUTHOR]

The cantilever dual-rotor system is a typical structure of the blade output end of the open rotor engine and the coaxial output turboshaft engine. The excessive unbalanced vibration of a coupled cantilever dual-rotor system is one of the main factors limiting the application of the above engine type. In order to accurately describe the vibration coupling effect between the dual-rotor-intermediate bearings, the unbalanced response of the cantilever dual-rotor system is analyzed, and the self-sensitivity coefficient is proposed to guide the selection of measuring points and vibration suppression experiments for the dual-rotor system. On this basis, a new online automatic balance actuator applicable to this dual-rotor system is designed, and a feasibility experiment is carried out. The experimental results indicate that: (1) The self-sensitivity coefficient can be used as the basis for the actual vibration measuring point arrangement and unbalanced vibration suppression strategy of the dual-rotor system, and the proposed step-by-step vibration suppression strategy can reduce the vibration of the dual-rotor system by more than 80%. (2) The designed online automatic balance actuator can reduce the unbalanced vibration by 53% in 3.52 s. The proposed method in this study can provide guidance for the vibration suppression of the dual-rotor system.

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The aim of this paper is to gain insight into dynamic characteristics of a dual-rotor system in the absence and presence of a nonlinear energy sink. Firstly, the governing equations of motion of the dual-rotor system are derived by the Lagrange's equation. Then the dynamic characteristics of the system in the different conditions of rotational speed ratio are investigated. On this basis, a nonlinear energy sink is introduced in the LP rotor, where the effects of rotational speed ratio on the optimization of control parameters are taken into account. At last, the vibration suppression of the dual-rotor system is carried out. Moreover, the parameters analysis of the system is accomplished as well. [ABSTRACT FROM AUTHOR]

• A novel CMS method is proposed for the non-proportionally damped nonlinear systems. • Regarding the nonlinear interface forces as additional unknowns simplifies the synthesis procedure. • This method can preserve the intrinsic properties of nonlinear interface forces as much as possible. Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs. [ABSTRACT FROM AUTHOR]

[Display omitted] • A bolted joint dual-rotor system was established by considering bolted joint bending stiffness and rubbing fault. • The effect of the HP rotor and LP rotor subjected to the rubbing fault on rotor dynamics are evaluated. • The relationship between the soften effect of bolted joint bending stiffness and system responses are investigated. • The dynamic features of the bolted joint dual-rotor with rubbing fault are discussed through experimental and numerical studies. Large gas turbines often utilize dual-rotor structures to improve efficiency. To facilitate manufacture and maintenance, the large rotor systems are typically constructed by connecting components made from different materials together through the bolted joint. In this work, a dynamic model of a dual-rotor system with bolted joint included in the high-pressure (HP) rotor is established based upon the finite element theory of Timoshenko beam element, as well as taking into account the bearing forces and fixed-point rubbing fault. To evaluate the influence of rubbing faults on the dynamic behavior of a dual-rotor system, this study analyzed the response characteristics of the rotor under the cases of the LP rotor and the HP rotor subjected to the rubbing fault, respectively. In order to further reveal the effect of bolted joint structure on the system response while rubbing fault occurs, piecewise linear bending stiffness is also considered in this study. The nonlinear vibration responses of the bolted joint dual rotor-bearing system are studied through numerical simulation. Effect of rotor–stator contact stiffness and the occurrence of rubbing faults at the low-pressure (LP) rotor and the HP rotor are investigated through frequency-amplitude curves, waterfall diagrams, time-domain responses, and bending stiffness of the bolted joint. The results indicate that the presence of rubbing faults, whether occurring at the LP rotor or the HP rotor, leads to a decrease in the critical speed. Furthermore, under a rubbing fault, the bending stiffness of the bolted joint enters the stiffness softening region earlier and exhibits a wider range, which is exacerbated with increased contact stiffness. This phenomenon is considered one of the main causes of system response instability. Finally, the experimental studies are carried out on a bolted joint dual-rotor test rig to validate the numerical simulation results. [ABSTRACT FROM AUTHOR]

The unbalance of the rotor system is the main factor causing the vibration of aeroengines. Research on unbalancing vibration coupling, vibration transmission, and vibration sensitivity of inner and outer dual rotors is the key link of the whole machine vibration and dynamic balance research. In this paper, the motion differential equation and dynamic model of the inner-outer dual-rotor system are established, and the unbalanced vibration of the dual-rotor system considering the coupling effect of the intermediate bearing is studied by combining theoretical analysis and simulation methods. The influence of unbalanced position, the magnitude and phase of unbalance, and the stiffness of the intermediate bearing on the vibration response of dual rotors are obtained. Aiming at the randomness of the unbalance vector distribution in the rotor system, the unbalance vector is extracted based on the Monte Carlo sampling principle. The multidisk and multiplane unbalanced vibration response law of the dual-rotor system is obtained, and the vibration transmission law and vibration sensitivity of the rotor under an unbalanced state caused by the coupling action of the inner-outer rotors are revealed. Finally, an experiment is carried out based on a self-designed test bed; the measured results are consistent with the analytical and simulation results. [ABSTRACT FROM AUTHOR]

The dual-rotor system has been widely used in aero-engines and has the characteristics of large axial size, the interaction between the high-pressure rotor and low-pressure rotor, and stiffness nonlinearity of bolted joints. However, the testing of a full-scale dual-rotor system is expensive and time-consuming. In this paper, the scaling relationships for the dual-rotor system with bolted joints are proposed for predicting the responses of full-scale structure, which are developed by generalized and fundamental equations of substructures (shaft, disk, and bolted joints). Different materials between prototype and model are considered in the derived scaling relationships. Moreover, the effects of bolted joints on the dual-rotor system are analyzed to demonstrate the necessity for considering bolted joints in the similitude procedure. Furthermore, the dynamic characteristics for different working conditions (low-pressure rotor excitation, high-pressure rotor excitation, two frequency excitations, and counter-rotation) are predicted by the scaled model made of a relatively cheap material. The results show that the critical speeds, vibration responses, and frequency components can be predicted with good accuracy, even though the scaled model is made of different materials.

In order to improve the thrust-weight ratio, modern aeroengines generally adopt a coaxial dual-rotor system. Factors such as manufacturing errors, assembly errors, bearing wear, and structural deformation can cause misalignment failures in a dual-rotor system. Supporting misalignment is one of the common types of misalignments in a dual-rotor system. To analyze the vibration characteristics of misalignment faults, in this study, we aim to build a finite element model of a dual-rotor system with supporting misalignment. The bearing loads caused by supporting misalignment are calculated using the three-bending moment equation method. Bearing loads are introduced into the dynamic model of the dual-rotor system. The influence of supporting misalignment at different bearings on the dynamic characteristics of the rotor system is investigated based on the supporting misalignment model. Studies have shown that supporting misalignment at different bearings has similar effects on the dynamic characteristics of the dual-rotor system. The proposed supporting misalignment model is more adaptable than the coupling misalignment model. It indicates that the damping of a rolling bearing should be considered in the dynamic analysis of a dual-rotor system although the value of the damping is not large. An experimental analysis is carried out. The simulation results are in good agreement with the experimental results.

A finite element model of an aero-engine dual-rotor system with intermediate bearing supported by six bearings is set up. Three modes of non-concentricity caused by the assembly process are defined, namely parallel non-concentricity, front deflection angle non-concentricity and rear deflection angle non-concentricity. The influence of the non-concentricity on the vibration characteristics of the dual-rotor system is investigated in detail. The results show that the parallel non-concentricity and the front deflection angle non-concentricity have a significant influence on the bending vibration modals of the high-pressure rotor and the low-pressure rotor, but have little influence on the local vibration modals of the rotors. With the increase in the magnitude of the non-concentricity, the natural frequencies of the bending modals decrease continuously, and the mode shapes of bending modals and that of local modals may be interchanged, leading to the emergence of bending modals in advance. Therefore, the key parameters to be controlled in the assembly process are the parallel non-concentricity and the front deflection angle non-concentricity. In order to prevent the bending modal of the dual-rotor system from appearing in advance, it is necessary to control the parallel non-concentricity within 2 mm and the front deflection angle non-concentricity amount within 0.18°.

This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system. [ABSTRACT FROM AUTHOR]

Misalignment fault is the main factor that affects the normal running of dual-rotor system. Quantitative identification the misalignment fault is an important way to ensure the safe and stable service of the dual-rotor system, while the identification accuracy of traditional methods is low. Aiming at the above problems, this paper proposed a dual-rotor misalignment fault quantitative identification method based on DBN and D-S evidence theory improved by mutual information measure (MIMD-S). Seven groups experiments were conducted and several vibration signals were collected. By comparing it with the traditional methods D-S, and Pignistic improved D-S (PD-S) evidence theory, the results show that the method proposed in this paper improves the accuracy of the misalignment fault quantitative identification of the dual-rotor, the identification error rate was only 0.36%.

In order to improve energy efficiency and compact structure, the dual-rotor structure, with low-pressure rotor and high-pressure rotor, has been widely used in aero-engines. In severe operation conditions, the high rotating speed dual-rotor structure is vulnerable to some faults, such as misalignment, which may cause strong vibration and even catastrophic accidents. Perfect balance of the dual-rotor system cannot be obtained in practice, and some amount of unbalance is almost always present. The rotors’ centrelines are not co-linear in the couplings and the rotors run in improper axial positions in a dual-rotor system. The differential equations of rotor system is derived by using modern nonlinear dynamics and dual-rotor dynamics principles. The governing equations of the dual-rotor system with unbalance-misalignment coupling faults are solved numerically by the Runge–Kutta method. The complicated vibration responses influenced by different rotational angular speeds, mass eccentricity, misalignment angle and parallel misalignment are analyzed by the cascade plot, time waveform and frequency spectrum. Second harmonic frequency and rotational frequency components of dual rotors are observed. To verify the validity of the dual-rotor system dynamic model, the unbalance-misalignment coupling faults are carried out on a dual-rotor test rig by adjusting the height and quantity of gaskets and installing a screw on the disk of the inner rotor. The simulation results are found to agree with the experimental results. These results provide important theoretical and engineering references for the safe operation of dual-rotor system and the exact identification of coupling faults. [ABSTRACT FROM AUTHOR]

• A Lagrangian energy equation containing kinetic energy, potential energy, Rayleigh dissipation energy and generalized force virtual work is derived from the dynamics universal equation, based on which a fault dynamics model of an 8-degree-of-freedom dual-rotor inter-shaft bearing system is developed. • Validate the model to be accurate in simulating local defects. • Accurately simulated the time-frequency characteristics of the dual-rotor inter-shaft bearing system when failures occur. • Based on the discrete characteristics of Lagrange's equation, the analysis of different structural vibration characteristics in the same system increases the efficiency of work. • It is found that the rotor vibration signal is accompanied by high harmonic vibration signal when there is a fault in the system, and this conclusion provides theoretical support for aero-engine fault vibration analysis. In order to study the vibration characteristics of inter-shaft bearing failures of a dual-rotor system, an eight-degree-of-freedom dynamic model of dual-rotor system containing inter-shaft bearings is established. The Newmark-β method is used to solve the proposed model equations. The dynamic characteristics of the rotor system when the inner ring and outer ring of the inter-shaft bearing has single-point failures or composite failures are analyzed. The comparison results show that the fault frequency distribution pattern in the envelope spectrum of the dynamic simulation results is consistent with that of the test results, which proves the effectiveness of the proposed dynamic model. It is found that when the inter-shaft bearing fails, a combination of rotor rotation frequency, multi-frequency, and fault frequency modulation frequency occurs in the fault characteristic frequency of the dual-rotor system. In addition to the speed-synchronized vibration components caused by the eccentricity, the rotor vibration signal is usually accompanied by a high-order harmonic vibration signal. [ABSTRACT FROM AUTHOR]

In order to study the dual-rotor system's rubbing fault, a new dynamic model is established. The unbalance and the rubbing faults are modeled, respectively. Considering the softening characteristics of casing, the Lankarani-Nikravesh model is utilized to describe the impact force between the disk and fixed limiter. The numerical integral method is applied to obtain system's dynamic behavior, and the characteristics of the rubbing faults are analyzed by time-domain waveform, 3D waterfall plot and spectrum cascades. The influences of rotational speed ratio, initial clearance, mass eccentricity and inter-shaft bearing stiffness on the dynamic characteristics are investigated. The vibration displacement of the low-pressure rotor is collected from the impact experiment performed on a dual-rotor test rig. The analysis result of simulation is identical with the experiment result. Consequently, this method can be used to study characteristics of rubbing faults of dual-rotor bearing system efficiently. [ABSTRACT FROM AUTHOR]

In this paper, the steady-state responses and their stability of a dual-rotor system with rub-impact are investigated. The nonlinear equations of motion in eight d.o.f.s are obtained with the consideration of the gyroscopic effect. The multi-harmonic balance combined with the alternating frequency/time domain technique (MHB-AFT) is utilized to calculate the accurate amplitude of each harmonic component. Arc-length continuation is embedded in the MHB-AFT procedure to trace the branch of the periodic solutions, and the Floquet theory is used to discuss the stability of the obtained solutions. Through the numerical calculation, complicated nonlinear phenomena, such as combined harmonic vibrations, hysteresis and resonant peak shifting are obtained when the rub-impact occurs. The result also shows that the control parameters such as mass eccentricity, inter-shaft stiffness and rotational speed ratio make significant but different influences on the dynamic characteristics of the two rotors. Therefore, the contribution of this study is to provide a further understanding of the steady-state response characteristics of the dual-rotor system with rub-impact. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear response characteristics of a dual-rotor system with a breathing transverse crack in the hollow shaft of the high-pressure rotor (rotor 1). A finite element model of the system is set up, and the motion equations of the system are formulated, in which the unbalance excitations of the rotor 1 and rotor 2 (low-pressure rotor) and the time-varying stiffness of the cracked shaft are considered. By using the harmonic balance method, the motion equations are analytically solved to obtain the dynamic responses of the two rotors. Accordingly, the effects of the crack depth and location on the vibration amplitudes are discussed in detail. The results indicate that when a transverse crack appears, it may bring super-harmonic responses to the rotor system, and the resonance peaks at the second, third and even fourth subcritical whirling speeds of the two rotors can be observed. The deeper the crack is, the larger the resonances amplitudes are, especially when the crack is located in the middle of the shaft or around the disks. In addition, the super-harmonic responses of rotor 1 where the crack located, can also be observed in rotor 2, which means that the crack signals can be detected in the entire system. Moreover, the numerical computations are carried out by using the Newmark- $$\beta $$ method, which shows great agreement with the previous analytical results. The results obtained in this paper will contribute to the modeling and the fault diagnosis of dual-rotor systems with hollow-shaft crack. [ABSTRACT FROM AUTHOR]

• Backward whirling motion of dual-rotor systems caused by unbalanced excitation. • The effects of rotation direction, unbalanced excitation, speed ratio, etc. on the whirling characteristics. • Experimental verification of backward whirling characteristics of dual-rotor systems. In this paper, a dual-rotor system with five-point support is established, considering the nonlinearity of the inter-shaft bearing. Based on the full-spectrum analysis theory, the whirling characteristics of the dual-rotor system are analyzed. In a counter-rotating dual-rotor system, the backward whirling phenomenon caused by the unbalanced excitation is found, and the effects of rotation direction, unbalanced excitation, speed ratio, and inter-shaft bearing on this phenomenon are discussed. Finally, the simulation results are verified based on the dual-rotor test rig. The results show that a negative speed ratio is a necessary condition to generate the backward whirling of the rotor; in the counter-rotating dual-rotor, a large unbalance of one rotor is an important factor causing the backward whirling of the other rotor. The larger the unbalance is, the more likely the backward whirl will occur; changing the speed ratio will mainly affect the initial speed and speed range at which backward whirl occurs; The radial clearance and stiffness of the intermediate bearing mainly affect the coupling degree of the inner and outer rotors, thereby affecting the whirl characteristics of the dual-rotor. The above research helps understand the whirl characteristics of the counter-rotating dual-rotor deeply. [ABSTRACT FROM AUTHOR]

• Rub-impact fault and model interval uncertainties are considered in a dual-rotor system using the non-probabilistic representations. • The nonlinear dynamical response with turning points, which is characterized as having multi-solution regions, is dealt with the polar angle interpolation method. • Performances of the polar angle interpolation method and the non-intrusive uncertainty analysis method are validated through deep comparisons. • Complicated uncertain behaviours are observed in the steady-state dynamical responses of the nonlinear system for various numerical cases under different conditions. This paper aims to study the nonlinear steady-state response of a dual-rotor system with rub-impact fault subject to unknown-but-bounded (UBB) uncertainties. Mathematical modelling of the non-linear dynamical system is carried out based on the Lagrangian formulation. The nonlinear dynamic response of the rubbing dual-rotor system without uncertainty is solved by using the multi-dimensional harmonic balance method coupled with the alternating frequency/time technique. The arc-length continuation is used to track the solution branches. To predict the response range subject to uncertainty, a non-intrusive surrogate model in conjunction with the polar angle interpolation (PAI) with efficiency enhancement is developed to track the propagations of parametric variabilities. The PAI is dedicated to dealing with collocations where the responses have multiple solutions. Effects of UBB variables in the physical model and fault-related parameters are investigated comprehensively. Different features of the variabilities in the steady-state responses are found under the typical uncertain degrees. The interval scanning method is used to validate the computation accuracy of the whole procedure. Moreover, the working mechanism of the PAI method is demonstrated via examples in detail. The results obtained in simulations can provide useful guidance for the nonlinear dynamic investigations and rub-impact fault diagnosis of dual-rotor systems under the UBB uncertainties. The proposed non-intrusive uncertainty quantification framework based on the PAI will also be beneficial to other nonlinear vibration problems where multiple solutions are involved. [ABSTRACT FROM AUTHOR]

Because of the use of seals between two rotors in aero-engines, inter-shaft rub-impact becomes a possibility in dual-rotor systems. Most studies have focused on the rotordynamics of rotor–stator rub-impacts, but there are few studies about inter-shaft rub-impacts in dual-rotor systems, and the corresponding nonlinear behaviors are not well understood. This paper aims to reveal the nonlinear behaviors of a dual-rotor system with inter-shaft rub-impact. In particular, two types of operation conditions, i.e., co-rotation and counter-rotation, are considered in the analysis of rubbing dynamics. First, a dynamic model of the dual-rotor system with inter-shaft rub-impact is established based on the finite element method. Then, the modal characteristics and vibration responses are analyzed in detail through the Campbell diagram, 3D waterfall plots, time and frequency domain waveforms, etc. The results show that inter-shaft rub-impact can lead to vibration coupling of the two rotors, and consequently, the number of critical speeds is increased. Three types of rubbing motions can be observed in the dual-rotor system: continuous inter-shaft rub-impact, intermittent inter-shaft rub-impact and self-excited rubbing motion. Among them, the self-excited rubbing motion is dominated by system natural modes and usually has high amplitude, which is very dangerous to the dual-rotor system. Moreover, the rotation direction significantly affects the rotordynamics, and the dynamic characteristics under the counter-rotation condition seem more complicated. • A dynamic model of the dual-rotor system with inter-shaft rub-impact is developed. • Three kinds of inter-shaft rubbing motions are clarified. • The influence of rotation direction on the nonlinear dynamics is discussed comprehensively. [ABSTRACT FROM AUTHOR]

• Dynamic model of aeroengine dual-rotor system with inter-shaft rub-impact is built. • Nonlinear dynamics of dual-rotor system with inter-shaft rub-impact are studied. • Experiment results conducted in a real aeroengine dual-rotor system are discussed. Inter-shaft rub-impact, i.e., the rub-impact between two rotors, may occur in an aeroengine dual-rotor system. This paper represents the first attempt to investigate the nonlinear dynamics of a dual-rotor system with inter-shaft rub-impact. The dynamic model of a complex dual-rotor system is built using the 3D finite solid element method by considering the inter-shaft rubbing forces. An analysis strategy combining the component mode synthesis method and numerical integration method is developed to overcome the problem of solving the large-DOF model. The modes and vibration responses of the dual-rotor system under the effect of inter-shaft rub-impact are clarified. The results show that the inter-shaft rub-impact leads to vibration coupling between LP and HP rotors, leading to the appearance of novel resonance peaks in the vibration response. Three kinds of rubbing types, i.e., continuous rub-impact, intermittent rub-impact and self-excited vibration may be excited when inter-shaft rub-impact occurs in a dual-rotor system. The characteristics and mechanisms of these rubbing motions are examined using the orbit, time and frequency curves as well as the rubbing force and relative velocity curves. By reducing the rubbing stiffness and friction coefficient, the dangerous self-excited rubbing vibrations can be eliminated. Moreover, by comparing the rubbing responses under constant and variable speeds, the key effects of the initial conditions on the inter-shaft rubbing responses are highlighted. Finally, the results of inter-shaft rubbing experiments conducted using a real aeroengine dual-rotor system are discussed and used to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: The efficient identification of the unbalanced responses in the inner and outer rotors from the beat vibration is the key step in the dynamic balancing of a dual-rotor system with a slight rotating speed difference. This paper proposes a non-whole beat correlation method to identify the unbalance responses whose integral time is shorter than the whole beat correlation method. The principle, algorithm and parameter selection of the proposed method is emphatically demonstrated in this paper. From the numerical simulation and balancing experiment conducted on horizontal decanter centrifuge, conclusions can be drawn that the proposed approach is feasible and practicable. This method makes important sense in developing the field balancing equipment based on portable Single Chip Microcomputer (SCMC) with low expense. [Copyright &y& Elsevier]

The dynamical equation for the nonlinear vibration of the counter-rotating dual-rotor systems is deduced, basing on the simplified model of non-linear stiffness of inter-shaft bearings. The influences of the rotor speeds, the amount of unbalance, and the radial clearance of inter-shaft bearings to the system response characteristics are studied. The results indicate that the nonlinear vibration can be reduced by selecting the parameters, including the rotor speed and the amount of unbalance and the non-periodic vibration can be avoided by decreasing the radial clearance of inter-shaft bearings. [ABSTRACT FROM AUTHOR]

The dual-rotor system has been widely used in aero-engines and has the characteristics of large axial size, the interaction between the high-pressure rotor and low-pressure rotor, and stiffness nonlinearity of bolted joints. However, the testing of a full-scale dual-rotor system is expensive and time-consuming. In this paper, the scaling relationships for the dual-rotor system with bolted joints are proposed for predicting the responses of full-scale structure, which are developed by generalized and fundamental equations of substructures (shaft, disk, and bolted joints). Different materials between prototype and model are considered in the derived scaling relationships. Moreover, the effects of bolted joints on the dual-rotor system are analyzed to demonstrate the necessity for considering bolted joints in the similitude procedure. Furthermore, the dynamic characteristics for different working conditions (low-pressure rotor excitation, high-pressure rotor excitation, two frequency excitations, and counter-rotation) are predicted by the scaled model made of a relatively cheap material. The results show that the critical speeds, vibration responses, and frequency components can be predicted with good accuracy, even though the scaled model is made of different materials. [ABSTRACT FROM AUTHOR]