Vibration Properties of Dual-Rotor Systems under Base Excitation, Mass Unbalance and Gravity

Taking the dual-rotor system in an aero-engine as a research object, the vibration behaviors of a dual-rotor bearing system that is fault-free or has misalignment, rub-impact or misalignment rub-impact coupling faults are studied, respectively. First, the three-dimensional model of the dual rotor bearing system is established, and then the first six modes and critical speeds of the dual rotor bearing system are obtained by the finite element method. Then, the dynamic equations of the dual rotor bearing system with and without faults are derived based on the Lagrange method. The Runge–Kutta method is used to solve the dynamic equation, and the nonlinear dynamic response of the system is obtained. The vibrational behaviors of the dual rotor system with misalignment, rub-impact and misalignment rub-impact coupling faults are analyzed and discussed through the time history, phase diagram and frequency spectrum of the rotor. The vibrational behaviors of the first six modes of the dual rotor system with and without faults are analyzed, respectively. The results provide theoretical guidance for the structural optimization design of an aero-engine rotor system and the prior decision information for misalignment and rub-impact coupling fault diagnosis.

In this paper, an investigation regarding the dynamic behavior of a rotating machine subjected to a base excitation is presented numerically. Regarding aeronautical applications, the aircraft engine is considered a typical onboard rotor that has its dynamic behavior influenced by base excitations. The mathematical model of the machine is derived from the finite element method, which is obtained by considering the strain and kinetic energies of the rotor subsystems (shaft, discs, bearings, mass unbalance, etc.). The resulting differential equations are used to provide information about the vibration responses of the rotor under base and unbalance excitations, simultaneously. The rotating machine used in this work is represented by a horizontal flexible shaft containing two rigid discs and supported by two ball bearings. In this case, the base of the rotor system is considered as being rigid. Therefore, the proposed analysis is performed both in the time and frequency domains, as generated by the orbits, unbalance response, and Campbell diagram of the rotor. This study illustrates the differences between fixed and onboard rotors, focusing on the dynamic behavior of the system.

PurposeAs a core rotating component of power machinery and working machinery, the rotor system is widely used in the fields of machinery, electric power and aviation. When the system operates at high speed, the system stability is of great importance. To enhance the system stability, squeeze film damper (SFD) is being installed in the rotor system to alleviate vibration. The purpose of this paper is to first classify the rotor system into two types, the dual rotor system and the single rotor system, and to comprehensively and specifically mention the method of generating the dynamic model. Next, based on the establishment of a dynamic model with and without SFD in the rotor system, the optimization design of the rotor system with SFD was carried out using a genetic algorithm. Through sensitivity analysis, SFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system, and the objective function was the minimization of the maximum amplitude of the rotor system with SFD within the operation speed range.Design/methodology/approachIn this paper, first, the rotor system was classified into two types, namely, the dual rotor system and the single rotor system, and the method of creating a dynamic model was comprehensively and specifically mentioned. Here, the dynamic model of the rotor system was derived in detail for the single rotor system and the dual rotor system with and without SFD. Next, based on the establishment of a dynamic model with and without SFD in the rotor system, the optimization design of the rotor system with SFD was carried out using a genetic algorithm. The sensitivity analysis of the unbalanced response was carried out to determine the design variables of the optimization design. Through sensitivity analysis, SFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system, and the objective function was the minimization of the maximum amplitude of the rotor system with SFD within the operation speed range.FindingsSFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system through sensitivity analysis of the unbalanced response. These three variables are basic factors affecting the amplitude of the rotor system with SFD.Originality/valueIn the existing studies, only a dynamic model of a single rotor system with SFD was created, and the characteristic values of pure SFD were selected as optimization variables and optimization design was carried out. But in this study, the rotor system was classified into two types, namely, the dual rotor system and the single rotor system, and the method of creating a dynamic model was comprehensively and specifically mentioned. In addition, optimization design variables were selected and optimized design was performed through sensitivity analysis on the unbalanced response of factors affecting the vibration characteristics of the rotor system.

The dual-rotor structure is the primary excitation source of aero-engine vibration. It is essential to study the dynamical model and analyse the dynamic characteristics such as critical speed and the unbalanced response for rotor system dynamics. The coaxial dual-rotor support scheme of an aero-engine was introduced in the previous work, and the physical model with a high-speed flexible inner rotor of a sizeable length-diameter ratio has been designed. Then a finite element dynamic model based on the Timoshenko beam elements and rigid body kinematics of the dual-rotor system is modelled, with the Newmark-β method and Newton-Raphson method used for the numerical calculation to study the dynamic characteristics of the system. Three different simulation models, including beam-based FE (1D finite element) model, solid-based FE (3D finite element) model, and TM (transfer matrix) model, were designed to study the characteristics of mode and the critical speed characteristic of the dual-rotor system. The unbalanced response of the dual-rotor system was analysed to study the influence of mass unbalance on the rotor system. The effect of different disc unbalance phases and different speed ratios on the dynamic characteristics of the dual-rotor system were investigated in detail. The experimental result shows that the beam-based FE model is effective and suitable for studying the dual-rotor system. Conflict of Interest Statement The authors declare no conflicts of interest.

The finite element model of a dual-rotor system was established by Timoshenko beam element. The dual-rotor system is a coaxial rotor whose supporting structure is similar to that of an aero-engine rotor system. The inner rotor is supported by three bearings, which makes it a redundantly supported rotor. The outer rotor connects the inner rotor by an intershaft bearing. The spectrum characteristics of the dual-rotor system under unbalanced excitation and misalignment excitation were analysed in order to study the influence of coupling misalignment of the inner rotor on the spectral characteristics of the rotor system. The results indicate that the vibration caused by the misaligned coupling of the inner rotor will be transmitted to the outer rotor through the intershaft bearing. Multiple harmonic frequency components, mainly 1x and 2x, will be excited by the coupling misalignment. The amplitudes of all harmonic frequencies increase with the misalignment in both the inner and outer rotors. The vibration level of the outer rotor affected by the misalignment is lower than that of the inner rotor because it is far from the misaligned coupling. Harmonic resonance occurs when any harmonic frequencies of the misalignment response coincide with a natural frequency of the system. In order to verify the theoretical model, experiments are performed on a test rig. Both the experimental and simulation results are in good accordance with each other.

A sliding bearing system performs a critical function in a rotating machinery system and provides support for the rotating components. In this paper, a single-rotor experimental rig and a dual-rotor sliding bearing experimental rig were independently established, and the dynamic response of the test systems are investigated. To study the effect of oil pressure levels on the dynamic response of the test systems under the single-rotor system and the dual-rotor system, the vibration response of single-rotor and dual-rotor systems ware analyzed by different oil inlet pressures to study the effect of oil pressure levels on the dynamic response of the test systems under the single-rotor system and the dual-rotor system. Among them, the single rotor system under a large oil pressure system is mostly periodic and more stable. While under different inlet oil pressure conditions applied in the experiments, the dynamic motion of the dual-rotor bearing system is relatively stable in both the subcritical and supercritical speed regions. However, the oil whirl and oil whip of the dual-rotor system were observed at the critical speed, which causes the system into unstable multiperiodic motions. In general, this paper can give some insight into the dynamic response of the sliding bearing system influenced by different oil pressure levels.

Intershaft bearing is widely adopted in dual rotor turbofan aircraft engines. Since this kind of dual rotor system has two different rotor speeds and the intershaft bearing leads to the coupling between HP rotor and LP rotor, the calculation of the critical speeds is much more complicated than that of the rotor systems without intershaft bearing. Compared to a single rotor system, the dual rotor system has more critical speeds which can be classified as critical speeds excited by HP rotor and that by LP rotor. In the paper, a finite element rotor model of a high-bypass turbofan jet engine with intershaft bearing is established for the study of critical speeds analysis. The general axisymmetric element is used to model the shafts and disks, and the blades are simplified to mass points. The main bearings including the intershaft bearing are set up with spring element. Assuming that the rotational speed ratio of the two rotors for the dual rotor system is a fixed number, the critical speeds are calculated using three methods based on the finite element rotor model. For the first method, the system critical speeds are obtained directly by Campbell diagram based on QR damped solution method. Then the synchronous unbalance response analyses are carried out and the rotor critical speeds are derived from the amplitude-frequency curves. For the last method, multiple group Campbell diagram analyses are conducted. With one rotor speed fixed at constant rpm N, we can change the speed of the other rotor to obtain one group of critical speeds. By varying speed N of the two rotors, a critical speeds data set can be obtained and plotted as a dual rotor critical speed map. The critical speeds can be easily extracted from the critical speed map according to the rotational speed curve of the engine. The study shows that the dual rotor system critical speeds calculated from above three methods are identical. For the first two methods, the rotational speed ratio of two rotors must be a known and fixed number, which is impossible in reality. The third proposal has no rotation speed relation restriction for rotors, and therefore is recommended for analyzing the critical speeds of aircraft engines with intershaft bearing.

The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems; however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of this method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems, however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of this method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

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.

We are building an efficient and smart wind turbine system. The significant features of this turbine are its dual rotor blade system which is positioned horizontally at upwind and downwind locations, its drive train which is installed horizontally inside the tower with a new efficient induction generator, and its control and safety systems. The project focuses mainly on the methodology to analyze the power flow performance. The scientific literature indicates that a dual-rotor system could extract additional 20–30% power compared to a single rotor system from the same wind stream. Our wind tunnel test indicates that a scaled-down version of the dual-rotor turbine system may produce up to 60% more power than a single-rotor system. Designed for on-site power generation by commercial, industrial, and residential electric users in remote locations, our model uses wind tunnel effect to capture and amplify wind for optimized production of energy. It is intended that this turbine system will be available in tower-mounted design and can capture wind in regions where it has low speed wind. The successful design should allow an economical transition to a utility scale.

Multi-electrification is an important development direction of aero-engine. Spindle direct-drive startup generator (SDSG) is the key technology, and it introduces electromagnetic excitations to aero-engine dual-rotor system (DRS). With the pursuit of high efficiency, clearances between components become smaller and smaller and it makes the rub-impact more easily to happen. Because of the SDSG and small seal clearance between rotors, dynamic characteristics of DRS considering electromagnetic excitation and rub-impact deserve attention. This paper researches the dynamic characteristics of DRS coupling electromagnetic excitation and inter-shaft rub-impact (ISRI) at different rotation speeds, initial static eccentricities, and mass eccentricities. The dynamic model of spindle direct-drive DRS with electromagnetic excitation and ISRI is established. Results show that electromagnetic excitation increases the speed range of intermittent rub-impact in DRS by 141% and reduces the speed range of continuous rub-impact in DRS by 21%. At certain rotation speeds, specific fraction multiple frequencies (e.g., A + B → f l , C + D → f l , E + F → f l ) conforming to a particular rule occur in rotor system. 0.5 f h leads to the subharmonic resonance when initial static eccentricity falls within a certain range. The mass eccentricity of magnetic steel increases the intermittent rub-impact threshold in DRS by 149%, while reducing the continuous rub-impact tolerance by only 5%. This indicates that electromagnetic excitation can suppress the vibration of DRS during ISRI. The researches can offer guidance for the vibration identification and control of aero-engine spindle direct-drive DRS.

A dual-rotor system with an intershaft bearing subjected to mass unbalance and base motions is established. Using Lagrange’s principle, equations of motion for dual-rotor system relative to moving base are derived. Rotary inertia, gyroscopic inertia, transverse shear deformation, mass unbalance, and six components of deterministic base motions are taken into account. Using state-space vector, steady-state characteristics of dual-rotor system are analyzed through dual-rotor critical speed map, mode shapes, unbalance responses considering base rotations, frequency responses due to base motions, and shaft orbits. The results show that base translations just add external force vectors, while base rotations bring on parametric system matrices and additional force vectors. Base rotations not only change natural frequencies of dual-rotor system, but also break the symmetry of dynamic characteristics in the case of base lateral rotation. Excited by base harmonic translation, resonant frequencies correspond to whirl frequencies. The orbit remains circular under base axial rotation, while it becomes elliptical with a static offset under lateral rotation and then a complicated curve due to harmonic translation. When harmonic frequency of base translation gets close to dual-rotor excitation frequencies, obvious beat vibration appears. Overrall, this flexible approach can ensure calculation accuracy with high efficiency and good expandability.

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. The objective of this paper is to develop a general model for flexible rotor systems subjected to time-varying base excitations and study the direct effects of angular base motions on the dynamic behaviors of a simple rotor. The model is developed based upon finite element method and Lagrange’s equation. Two groups of Euler angles are introduced to describe the rotation of the rotor and the base, respectively. Six types of base motions are considered in the model. In the numerical simulations, three types of angular base motions (pitching, rolling and yawing) are considered and assumed to be sinusoidal varying with time. The effects of base angular amplitudes, base frequency and rotation speed on the system dynamic behaviors are discussed in detail. It is shown that pitching and yawing have a great influence on the response amplitudes and the shape of the rotor orbits. Especially, resonances occur when the base frequency meets the natural frequencies. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency.

Unbalanced force produced by the unbalanced mass will affect vibrations of rotor systems, which probably results in the components failures of rotating machinery. To study the effects of unbalanced mass on the vibration characteristics of rotor systems, a flexible rotor system model considering the unbalanced mass is proposed. The time-varying bearing force is considered. The developed model is verified by the experimental and theoretical frequency spectrums. The displacements and axis orbits of flexible and rigid rotor systems are compared. The results show that the unbalanced mass will affect the vibration characteristics of rotor system. This model can be more suitable and effective to calculate vibration characteristics of rotor system with the flexible deformation and unbalanced mass. This paper provides a new reference and research method for predicting the vibrations of flexible rotor system considering the unbalanced mass.