Dynamic Characteristics Of Rotor System Research Articles

Experimental Research on Dynamic Characteristics of a Multi-Disc Rotor System Supported by Aerostatic Bearings

Gas bearings have the advantages of small friction loss, wide applicable speed range, no pollution, etc., and have important application prospects in micro and small high-speed rotating machinery. However, due to its compressibility and low viscosity, its dynamic stability in high-speed rotating machinery is the key to constraining its development. The experimental study of shaft system dynamics is the main means to explore the mechanism of rotor behavior. On the test platform of dynamic characteristics of multi-disc rotor system supported by aerostatic bearings, experimental research on the nonlinear dynamic characteristics of a rotor system was carried out, and nonlinear vibration test and analysis methods, such as axial orbits, bifurcation diagrams, and spectral characteristics, were adopted, and vibration phenomena, including the critical rotational speed accumulating energy and low-frequency accumulating energy, were presented and the vibration characteristics of bearing fracture faults were presented. The bearing supply pressure and rubber damping pad were introduced as a method to suppress the low-frequency vibration of the aerostatic bearing rotor system, and its vibration-reduction effect was verified by experiments. The above results can provide technical support for vibration control and fault diagnosis of rotor systems supported by aerostatic bearings.

A parametric study of a bolted joint rotor-bearing system with an unbalanced offset disk

The turbine disk is the core component of an aero-engine whose position and unbalanced force seriously affect the vibration stability of the rotor system. Ignoring the influence of the offset disk may result in discrepancies between real-world scenarios and numerical simulation results. The present work aims to explore the nonlinear dynamic characteristics of rotor systems under the coupling of bolted joint and offset disk effect, as well as the influence of offset disk position and its unbalanced force on the system dynamic behavior and bending stiffness of bolted joint also investigated. The governing equations of a bolted joint rotor-bearing system with an offset disk were established based on the finite element method and derived as a dimensionless expression in the first. Then, the Newmark method was employed for the numerical solution of the motion equations, and then a bifurcation analysis of the rotor system and the evolution of bending stiffness for the bolted joint was studied. Next, by comparing the frequency-amplitude diagrams, bifurcation diagrams, time history, shaft obits, and bending stiffness diagrams of the bolted joint, the effect of the offset disk position and its unbalanced force on the nonlinear system dynamic was revealed. Finally, an experimental study was carried out to verify the numerical result using the bolted joint rotor test rig with an offset disk. The analysis result of the present work can provide theoretical guidance for structure design and stability analysis on the aero-engine.

Influence of brush seal hysteresis effect on the nonlinear characteristics of rotor system

The hysteresis effect of brush seal is a key factor affecting the sealing performance of the rotor system, so it is particularly important to study the nonlinear behaviors of the rotor-bearing-brush seal system under the hysteresis effect. First, the entire circle of bristle pack is classified according to the position angle and contact condition of single bristle, and the rotor support force, the interaction force between the bristles, the air pressure and the friction of back plate are considered. It is proposed to use the loss rate to calculate the uniform load of the back plate, according to the linear beam theory, the bending force model of bristle under different rotor eccentricity is established. Second, the hysteresis angle is proposed to represent the degree of hysteresis effect of the whole circle of bristle pack, and the seal force model under hysteresis effect is established. Third, considering the interaction of seal force and oil-film force, the dynamic model of Jeffcott rotor-bearing-brush seal system is established. The influence of hysteresis effect on the dynamic characteristics of rotor system is studied by using bifurcation diagram, axis orbit, Poincaré map, spectrum diagram and time history. It is found that the hysteresis effect has different degrees of influence on the nonlinear dynamic characteristics of the rotor system in different rotational velocity intervals. In addition, the influence of seal interference on the motion state of rotor system cannot be ignored.

A state-of-the-art review on uncertainty analysis of rotor systems

Uncertainty handling and analysis of rotor systems have been active research areas during the last two decades. This paper provides a state-of-the-art review on the research progress of uncertainty treatment in rotor systems. Firstly, sources of uncertainties are identified and then classified according to their nature. Secondly, the most popular uncertainty analysis methods are summarized based on different types of uncertainties, including their basic principles, strengths and limitations. Thirdly, the dynamic characteristics of rotor systems under various uncertainties are described in detail, i.e., the natural characteristics and unbalanced responses, faulted rotor dynamics, stability problems and parameter identifications. Then, the reliability analysis, optimizations and vibration control for uncertain rotor systems are reviewed. Finally, comments on the latest research progress are made and outlooks on future research directions are highlighted. It is expected that this review will provide useful guidelines for designers and researchers towards the more efficient handling of uncertainty and robust dynamic analysis for rotor systems as well as insightful prospects, showing where extra efforts are needed.

Nonlinear modal analysis of rotor systems considering gyroscopic and dry friction effects

Part looseness is a common fault in rotor systems, which may lead to serious dynamic problems. Rotor system with part looseness turns to be a complicated nonlinear problem, with gyroscopic and dry friction effects occurring simultaneously. The analysis of nonlinear systems is in general confronted with two key challenges: complicated calculation method and long calculation time. This work has developed a fast and efficient numerical scheme based on nonlinear modal analysis. By employing the proposed nonlinear modal analysis strategy, the essential gyroscopic effect, as well as the dry friction influence caused by part looseness, are both taken into account when analyzing the dynamic behavior of rotor systems. First, the theoretical aspects and the analysis approach considering the nonlinear force and the gyroscopic effect are proposed for a general rotor system. Second, by employing the proposed nonlinear modal strategy, simulations are conducted on a general rotor system considering the gyroscopic effect and dry friction caused by part looseness. Third, modal parameters such as resonance frequencies and modal damping ratios are carefully investigated as functions of rotation speed and modal amplitude. In the realization of a nonlinear modal analysis of a rotor system, the key point is to establish the relationship between modal parameters with both modal amplitude and rotation velocity. The proposed strategy can help better analyzing and interpreting the dynamic characteristics of rotor systems from the modal overview.

Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

The traditional modeling method of rotor system with a slant crack considers only integer-order calculus. However, the model of rotor system based on integer-order calculus can merely describe local characteristics, not historical dependent process. The occur of fractional order calculus just makes up for the deficiency in integer-order calculus. Therefore, a new dynamic model with a slant crack based on fractional damping is proposed. Here, the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method. The proposed model is simulated by Runge-Kutta method and continued fraction Euler method. The influence of the fractional order, rotating speed, and crack depth on the dynamic characteristics of rotor system is discussed. The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order. With the increase of the rotating speed, the amplitude of first harmonic component becomes gradually larger, the amplitude of the second harmonic becomes smaller, while the amplitude of the other frequency components is almost invariant. The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping. With the increase of the slant crack depth, the amplitude of the transverse response frequency in the rotor system with a slant crack increases, and the amplitude in the second harmonic component also increases significantly. In addition, the torsional excitation frequency and other coupling frequency components also occur. The proposed model is further verified by the experiment. The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Effect of ball bearing misalignment on dynamic characteristics of rotor system

A theoretical model with 5 degrees of freedom (DOF) is derived for a rigid rotor system supported by two ball bearings considering the changes of the bearing stiffness due to misalignment. And then radial and axial vibrations of the rotor system and its bearing reactions under different misaligned offsets are investigated with theoretical and numerical analysis. Then, the effects of misalignment on the vibrations of rotor and the bearing, the variation of stiffness and reaction characteristics of the misaligned ball bearing are predicted theoretically. It is concluded that angular misalignment may cause axial vibration and parallel misalignment can bring out extra moment loads for misaligned bearing.

Partial similitude for dynamic characteristics of rotor systems considering gravitational acceleration

In practical engineering, gravitational acceleration cannot be scaled (λg = 1), which is not considered in the existing similitude studies of rotor systems. In this paper, a restriction in scaling procedure caused by λg = 1 is first demonstrated analytically. Aiming at this issue, a method to derive the scaling laws of rotor systems is proposed based on the generalized equations of subsystems, where gravitational acceleration, geometric and material distortion are considered. The derived scaling law for the vibration response is different from that of previous literatures because λg = 1 is considered. On this basis, this paper presents a method for designing scaled models that can reduce the difficulty and costs of the model test. The accuracy and effectiveness of the proposed methods are verified by predicting the dynamic characteristics of a rotor system. Moreover, the effect of gravitational acceleration is discussed and the predicted results are compared with the previous literature. The results show that neglecting the gravitational acceleration leads to a certain error when predicting the vibration responses in the vertical direction.

Dynamic modeling and nonlinear analysis of a rotor system supported by squeeze film damper with variable static eccentricity under aircraft turning maneuver

A high-speed rotating rotor system mounted on an aircraft is inevitably induced by parametric excitations, inertial forces and gyroscopic moments caused by maneuvering flights. With the increase of maneuverability, this effect becomes more significant, which may lead to severe vibrations and even abnormal operation. Using Lagrange's principle, equations of motion for a squeeze film damped rotor system relative to a maneuvering aircraft are derived, considering additional inertial forces and variable static eccentricity of journal, of which the mechanism and computation procedure under turning maneuver are analyzed and proposed. The effects of flight status, structural parameters, and operating conditions on transient responses are discussed, including forward velocity, turning radius, rotating speed, mass unbalance, and elastic support stiffness. The results indicate that when an aircraft negotiates a turn, the offset direction of whirl orbit is determined by centrifugal acceleration and gyroscopic moment. The journal whirls around variable static eccentricity, of which the magnitude is related to maneuvering loads and supporting stiffness. Increasing forward velocity or decreasing turning radius, the rotor vibration will enter earlier into or withdraw later from the relatively large eccentricity. During maneuvering flight, rotating near critical speeds and excessive mass unbalances should be prevented. The elastic support stiffness has a great impact on vibration behavior of rotor system in maneuvering flights. Using finite element modeling combined with mechanism analysis, dynamic characteristics of rotor system supported by squeeze film damper (SFD) under aircraft maneuver can be predicted, which provides theoretical and technical support for dynamic design of engine's rotor system mounted on aircraft with high maneuverability and agility.

Dynamic Characteristics Analysis of Rotor-Bearing System and Experimental Validation

As for the vibration problem of rotor system for large rotating machinery such as aero engines, a finite element model for dynamic similarity experiment system of rotor is established based on finite element theory. The effect of support stiffness and support position on the dynamic characteristics of the rotor system have been emphatically analyzed. Moreover, the effect of support stiffness on the dynamic characteristics of rotor system have been verified on the designed test rig. The results show that, under different support stiffness intervals, each order natural frequency of the rotor system has a different variation tendency with the support stiffness or position. In addition, the variation of the mode shapes with the support stiffness or position are closely related to the variation of the natural frequencies with the support stiffness and position. Combining with the practice, the natural frequencies of the rotor system can be reasonably designed and the harmful mode shapes can be avoided by adjusting the supporting characteristics of the rotor system.

Parametric Modeling and Dynamic Characteristics Analysis of a Power Turbine Rotor System

Abstract With the increasing requirements of aeroengine performance and working stability, the primary research task of the rotor system dynamics is to build a rotor system model that can reflect the actual situation and obtain the calculation results which can reflect the real dynamic characteristics of the rotor system. In this paper, the finite element analysis model of a power turbine rotor was established, and the dynamic model and dynamic characteristics of the complex rotor system were studied. The results indicated that the finite element model could reflect the real dynamic characteristics of the power turbine rotor. For the given design rotational speed, the critical speed had enough margin and the rotor system worked safely and smoothly. This research provided a reference and theoretical basis for the calculation of the dynamic characteristics of the similar rotor system.

Dynamic characteristics of aero-engine’s rotor under large maneuvering flight

In view of the large maneuvering overload of the rotor system in Unmanned Aerial Vehicle (UAV), the dynamic characteristics of rotor system under large maneuvering overload conditions were analyzed in this paper. The finite element model of rotor system under large maneuvering overload was first established by Timoshenko beam element theory and finite element method. The motion differential equations of the rotor system were derived by Lagrange equation, and the additional damping matrix, stiffness matrix and excitation force were obtained. Critical speeds and unbalance response were calculated by characteristic equation method and Newmark-β numerical integration method respectively. The calculation results showed that the additional damping and stiffness leaded the critical speeds of the rotor system to change under large maneuvering flight, and the additional excitation force resulted in a certain static displacement of the whirling orbits.

Study on the Effect of Temperature on Dynamic Characteristics of Rotor System with Straight Crack

The effect of temperature on the dynamic characteristics of cracked rotor is studied in this paper. The crack is simulated by the extended finite element method (XFEM). Based on the theory of fracture mechanics, appropriate fracture criteria are selected, and the damage and failure criteria of materials are set up, and the finite element simulation analysis is carried out. The results show that with the increase of temperature, the amplitude of 3X in frequency domain increases most obviously, and the deformation degree of axis trajectory is high. The research results have important reference value and scientific significance for the study of dynamic characteristics of cracked rotor system under high temperature environment.

Analysis of the rotor dynamics characteristics of multi-degree-of-freedom permanent magnet synchronous motor

The spherical shell rotor is contained in the multi-degree-of-freedom permanent magnet synchronous motor. When the rated speed of motor is close to the critical speed, the motor will generate multiple resonances, which will affect the normal operation of the motor. The motor rotor must pass through the first-order critical speed and work at the safety range between 1-order and 2-order critical speed. According to the dynamic characteristics of rotor system, a mathematical model of rotor under free state is established, and the result between finite element and analytical methods is comparison. The influence of rotor gyroscope effect on critical speed is analyzed, and the finite element analysis of whether the rigidity of rotor material affects the critical speed is also carried out. The relationship between bending modal and deformation displacement is tested under different rigidity conditions and the stator deformation caused by rotor rotation is analyzed when the stator is filled with different liquids. The relationship between the rotational speed and the amplitude of the spherical rotor is verified by experiments, and the corresponding rules are summarized. The results of the simulation and analysis are referenced by the optimal design of motor.

Dynamics of a rotor system coupled with water-lubricated rubber bearings

Dynamic behaviour is significantly important in the design of large rotor systems supported on water-lubricated rubber bearings. In this study, the mathematical model of elastohydrodynamic lubrication of the bearing is established based on the theory of hydrodynamic lubrication after considering the elastic deformation of rubber, and the dynamic characteristics of water-lubricated rubber bearings are analysed under small perturbation conditions according to the load increment method and the finite difference method. Next, the differential equation of rotor systems coupled with the water-lubricated rubber bearing is deduced using Lagrange’s approach, and its critical speeds, stability, and unbalanced responses are analysed in detail. The numerical results show that several parameters, such as the eccentricity, length–diameter ratio, and clearance of bearing and the rotating speed of the rotor, have a great impact on the dynamic performance of water-lubricated rubber bearings, and this influence cannot be ignored, especially in the case of large eccentricity ratios. The dynamic characteristics of rotor systems guided by water-lubricated rubber bearings reveal that the critical speeds are much lower than the ones under the rigid supports because of the elastic deformation, and they also indicate that the rotor system supported on water-lubricated rubber bearings has a weaker stability. In addition, the steady-state responses of the rotor system are analysed when the mass unbalance of the propeller exists, and the effect of the thickness of the rubber liner is also considered.

Research on modeling and dynamic characteristics of complex coaxial rotor system

To make up deficiency of the finite element method in predicting nonlinear dynamic characteristics of coaxial rotor systems, nonlinear dynamic model of a coaxial rotor system was established with a method combining the finite element method and the fixed interface modal synthesis method. Then an implicit time domain method was presented to solve the nonlinear equations of motion thus dynamic characteristics of the rotor system can be obtained. The computational efficiency of this method largely depends on the number of degrees of freedom with nonlinear forces acting on. With nonlinear forces of squeeze film damper and intermediate bearing considered, nonlinear dynamic response characteristics of the coaxial rotor system under multiple unbalance forces were studied in this work. The results showed that the unbalance excitation frequencies are dominant in the responses of the rotor system. Besides, due to coupling effect of the intermediate bearing some combinations of the unbalance excitation frequencies were also observed in the spectrogram. Stability and periodicity of the rotor system was investigated with bifurcation diagram, Poincare map and phase diagram. It was found that the rotor system executes multiple periods orbital motion under relatively low rotational speeds. With the increasing of rotational speed, the rotor system would execute quasi-periodic motion, chaotic motion and periodic motion again. The quasi-periodic motion and chaotic motion are closely related with the SFD. Finally, under relatively low speed, the nonlinear model was validated by comparing the simulation results with the experimental data. The proposed modeling and solving method is expected to provide theoretical and engineering basis for improving prediction of nonlinear dynamic characteristics of complex rotor systems.

Dynamic characteristics of rotor system and rub-impact fault feature research based on casing acceleration

Aimed at the vibration of whole aero-engine, a coupled dynamic model of rotor-ball bearing-stator of aero-engine is built. By means of the lumped mass method, taking into account the nonlinear rub-impact, bearing failure force and deformation of the casing, the dynamic equation of the system containing typical rub-impact is derived. The response of the system under different conditions is obtained by using the fourth order Runge-Kutta numerical integration algorithm. By adopting the finite element analysis software ANSYS, the finite element model of the rotor shaft is established and the first six-order natural frequencies of the rotor system are acquired. Taking advantage of the parameters of the signal in time domain and frequency domain, frequency characteristics are extracted as the fault features. The single-point rubbing experiment is carried out in the test rig, and the working speed is higher than the first critical speed, so the rotor shaft is flexible rotor. By the methods of spectrum and cepstrum analysis, the rub-impact characteristics of the casing vibration acceleration time series data are analyzed. The results show that the casing vibration acceleration has obvious impact characteristics; the impact frequency is equal to the product of rotating frequency and number of the blades; the impact frequency component and its multiple-frequencies are demonstrated in the frequency spectrum; the strength of impact is modulated by the rotating frequency, so that there are families of side bands on impact frequency and both sides of frequency doubling, and the interval of sideband equals the rotating frequency. The frequency components of the rotating frequency and its frequency doubling are clearly shown in the cepstrum. By comparing the simulation and experiment, the rubbing characteristics found out in this paper has enough accuracy.

Analysis of Dynamic Characteristics of Key Parts of Centrifugal Atomizer in Waste to Energy

Uneven distribution of mass and temperature usually have important effects on the dynamic characteristics of rotary mechanism. Based on thermal-structural coupling theory, dynamic response analyses of the flexible rotor of centrifugal atomizer can be done by FEM. Considering eccentric quantity is caused by nozzle clogging and axial non-uniform distribution of temperature, the dynamic characteristics of the is studied; the response of mass unbalance and thermal bending or coupled the both is researched and compared. It is shown from the calculation that all of the three conditions have affected the dynamic characteristics of rotor system and the design can basically meet the stable operation requirement of the atomizer. The results can be applied to improve the design of the centrifugal atomizer. Developing more detail analysis to optimize the design in the future research.

Determination of Damage Severity on Rotor Shaft Due to Crack Using Damage Index Derived from Experimental Modal Data

After long duration of an operation, a shaft under high spin speeds and heavy loadings may develop fatigue cracks. This could lead to catastrophic failure and could be difficult to detect. An accurate prediction of dynamic characteristics of rotor system is fundamentally important. Hence, a practical method to nondestructively locate and estimate the severity of a crack in terms of its damage index by measuring the changes in natural frequencies of the rotor shaft is presented. In this study, experimental modal analysis (EMA) data were utilized. A crack detection algorithm to locate and identify cracks in the rotor system using the first and second natural frequencies was outlined. Subsequently, a crack-locating model was formulated by relating the fractional changes in modal energy to the changes in natural frequencies as a result of cracks based on the experimentally obtained natural frequencies and mode shapes’ functions. The feasibility and practicality of the crack detection scheme were evaluated for several damage scenarios by locating and sizing cracks in test rotor shafts for which the first two natural frequencies were available. It was observed that crack could be confidently located with a relatively small localization error. It was also observed that crack severity could be estimated in terms of its damage index.

Modal Testing Theory of Rotor-Bearing Systems

Since all dynamic characteristics of rotor systems are closely related with rotor rotations, the directivity of modes is very important in rotor dynamics. But the classical modal testing theories which have been applied to nonrotating structures were often applied to rotor systems. Whereas the dynamic characteristics in negative frequency region have no meanings in nonrotating stuctures, the dynamic characteristics of rotor systems in the negative frequency region which are different from those in the positive frequency region have significant physical meanings. Here a new modal testing theory is proposed to separate the rotor vibration into positive and negative frequency regions. In particular, the amplitude and directivity variations of frequency response functions in positive and negative frequency regions are discussed when using complex modal displacement. And a method to identify the directivity of modes such as forward and backward is suggested using the frequency response function obtained by the proposed modal testing theory. The whirl directions of forced responses related with the directivity of modes are also discussed. In addition, even if the anisotropy in bearings and the effects of gyroscopic moments are permitted, the relations between the right and left eigenvectors of general damped anisotropic rotor systems are evaluated under some practical conditions. If the relations between the right and left eigenvectors are given, the necessity of additional modal testing to identify the adjoint modal parameters is relaxed.