Behavior Of Rotor System Research Articles

Numerical theory and method on the modal behavior of a pump-turbine rotor system considering gyro-effect and added mass effect

The pump-turbine unit is the core equipment of pumped storage power station, and the rotor system is the key component of the pump-turbine unit. In this paper, the numerical method considering the gyro-effect and added mass effect is proposed, the effect of the added mass, gyro-effect and bearing stiffness are discussed, respectively, and a “transfer” phenomenon of the mode shape is found. A coupling influence coefficient is proposed to analyze the coupling influence of gyro-effect and added mass effect on the rotor system mode, and the nodal diameter (ND) mode of runner is discussed. For the forward whirling ND mode, the coupling influence coefficient increases with the increase of the rotational speed, while for the reverse whirling ND mode, the coupling influence coefficient decreases with the increase of the rotational speed. The results in this paper can provide a theoretical basis for revealing the complex dynamic behaviors of the rotor system, and provide scientific guidance for the research and development, design, and safe and stable operation of pump-turbine units.

Coupling dynamics of pedestal looseness and impact-rub for rotor system with nonlinear support

It is easy for the rotor system to produce the plastic deformation at the support after a long-term operation, this change will cause looseness of the bolt. Due to the particularity of the material and the structure for the bearing base and foundation, the elastic force of the support is nonlinear. Larger vibration of the loosening rotor under the nonlinear support will occur, resulting in the impact-rub between the rotor and stator. In order to study the dynamic behaviors of the loosening-rubbing coupling rotor system under the nonlinear support, the model is established to analyze the influencing mechanism of the key parameters such as the eccentricity, the disk offset, the looseness gap, the rubbing gap, and the nonlinear parameters on the vibrational responses of the system. The piecewise cubic nonlinear expression is applied to describe the nonlinear support with the loosing bolt; Coulomb friction is employed to characterize the rubbing of the impact-rub. The research results show that the nonlinear support will stimulate and amplify the nonlinear dynamic behaviors of the rotor system; there exists a threshold for the effect of the loosening gap on the vibrational characteristics of the system; increasing nonlinear parameters to a certain degree will cause the increase of the proportion of quasi-period and chaos. The research focus and conclusions are certain innovative in this paper. The work is of great value for fault diagnosis and structural design.

Analysis of the approaches used for calculating involute splined couplings and the methods of considering their influence on the dynamic behavior of systems

Spline couplings, due to their high reliability and strength parameters, are widespread not only in mechanical engineering. The ability to transmit high torque with a sufficiently long service life has led to the extensive use of these couplings in the aircraft industry. Since this unit is under heavy loads in aircraft gas turbine engines, much attention is paid not only to strength characteristics, but also to the influence on the dynamic parameters of the rotor system. To mitigate the risks of destruction and the occurrence of defects, a large number of studies are carried out allowing us to evaluate the rotor system operation with splines and make a forecast of its behavior in the event of various factors leading to a change in the operation of splines. This paper provides a review of various methods, techniques and models of involute spline couplings used in the analysis of the dynamic behavior of rotor systems. The analytical models that allow us to take into account the coupling in various systems as well as finite element models that demonstrate the description of various processes in splines. The publications, devoted to the comparison of finite element models with analytical ones confirming the results associated with the dynamic characteristics of systems with an increase in radial and angular swashes, have been considered. The results of comparing the above models and their results with experimental research to verify and confirm various effects are also presented. The given research of rotor systems with swash allows for a conclusion about a significant spline influence, since they can cause a change in the coupling rigidity, redistribution of contact, increased loads in meshing, increased vibration amplitudes, change in the spectrum of excited frequencies and self-oscillatory processes due to various factors.

Nonlinear vibration analysis and stability analysis of rotor systems supported on SFD by combining DQFEM, CMS and IHB methods

In this paper, the differential quadrature finite element method (DQFEM), component mode synthesis (CMS) method and incremental harmonic balance (IHB) method are combined to propose a methodology to perform vibration analysis and stability analysis of rotor systems supported on fluid-film bearings that exhibit localized nonlinearities such as squeeze-film damper (SFD). In multi-degree of freedom systems with SFD, a method for dynamic analysis of the system by reducing the degrees of freedom is first suggested in this paper. DQFEM are used to create the mass matrix, stiffness matrix, and gyroscopic matrix of the system. Then, the system is divided into linear system and nonlinear system, and the motion equation of the linear system reduces the degrees of freedom using the free interface CMS method, and the motion equation of the nonlinear system is written without reducing the degrees of freedom. By synthesizing the equations of motion of each component, the motion equation of the entire system is created. That is, the motion equation of the whole system uses hybrid coordinates. The motion equation of the system is solved using the modified IHB method. To evaluate the effectiveness of the suggested method, the computed solutions are compared with the results presented in the previous literature, and the results are very consistent. Also, stability analysis of the obtained solutions is performed by the Floquet theory. The method suggested in the paper can be effectively used to analyze the dynamic behavior of rotor systems exhibiting localized nonlinearities such as SFD.

Experimental investigation of dynamic behavior of rotor system with a novel double layers flexible support tilting pad bearing

Among all kinds of journal bearings, the tilting pad bearing has the characteristics of high stability. In order to further reduce the vibration and improve the stability of rotor-bearing systems, a novel double layers flexible support tilting pad bearing (DL-FSTPB) is presented in this paper. The bearing utilizes two layers of springs, which have different functions. The offset springs control the swing angle of the tilting pad to ensure the formation of a convergent oil film, and the symmetrical springs are used to change the bearing stiffness coefficient, increase the bearing elasticity, and improve the ability to accommodate misalignment. Experiments were carried out to study the vibration characteristics of the rotor system. The results were analyzed using wavelet analysis of acceleration and displacement, waterfall plots, a wavelet analysis, a run-up process and shaft center orbits areas. The results show that the DL-FSTPB exhibits excellent vibration attenuation characteristics, which can effectively reduce the amplitude and the system vibration level.

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.

Balancing of Flexible Rotors Supported on Fluid Film Bearings by Means of Influence Coefficients Calculated by the Numerical Assembly Technique

In this paper, a new method for the balancing of rotor-bearing systems supported on fluid film bearings is proposed. The influence coefficients necessary for balancing are calculated using a novel simulation method called the Numerical Assembly Technique. The advantages of this approach are quasi-analytical solutions for the equations of motion of complex rotor-bearing systems and very low computation times. The Numerical Assembly Technique is extended by speed-dependent stiffness and damping coefficients approximated by the short-bearing theory to model the behavior of rotor systems supported on fluid film bearings. The rotating circular shaft is modeled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, influence coefficients, eigenvalues, and the Campbell diagram of the rotor. These values are compared to simulations with the Finite Element Method to show the accuracy of the procedure. Two numerical examples of rotor-bearing systems are successfully balanced by the proposed balancing method.

Analysis of nonlinear vibration and stability of Jeffcott rotor supported on squeeze-film damper by IHB method

In this paper, a methodology to analyze the nonlinear vibration of a Jeffcott rotor supported on a squeeze-film damper (SFD) with centering springs, which is widely used in high-speed rotating machines, is proposed using the incremental harmonic balance (IHB) method. In this paper, the IHB method is modified to analyze the dynamic behavior of rotor systems supported on fluid-film bearings, such as SFDs. The processing of the mass matrix, stiffness matrix, and linear force matrix proceeds in exactly the same way as in classical IHB. The nonlinear force generated in the oil film of the SFD is calculated using the alternating frequency/time method and the transformation matrix and incorporated into the computational processing of the classical IHB method. This calculation method is first proposed in this paper. Solutions computed using the proposed method are compared with solutions computed using numerical integration. The results are very close. The stability of the calculated solutions is determined using the Floquet theory. Based on this, frequency–response curves according to the change in various parameters are constructed. The proposed method can be effectively used to analyze the nonlinear vibration characteristics of rotor systems supported on fluid-film bearings, such as SFDs.

Nonlinear vibration behaviors of marine rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion

To study the nonlinear vibration behaviors of rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion, the dynamic model is established considering the effect of heaving motion, its steady-state responses are numerically obtained using Runge-Kutta method and the results are surveyed by tools such as the spectrum waterfall diagram, time-domain response, frequency-domain response, axis orbit, and Poincaré map. The effects of rotating speed, ship heaving amplitude, and its frequency on the nonlinear dynamic behavior of the system are mainly studied. The results show that the responses of the rotor and raft are of obvious nonlinear behaviors such as amplitude jumping, bifurcation, and chaos due to the effects of nonlinear oil film force and ship heaving motion. With the increase of rotating speed, the motion of rotor and raft presents quasi-periodic and chaotic vibrations. Ship heaving amplitude and its frequency all have great effect on the vibration of rotor and raft; as heaving amplitude or frequency increases, the motion state of rotor and raft changes, and the amplitude of raft increases significantly. The displacement restrictor can effectively limit the vibrating displacements of the raft when ship heaving amplitude or its frequency is large.

Coupling dynamic behavior of aero-engine rotor system caused by rolling, pitching and yawing maneuver loads

It is an important embodiment of fighter's comprehensive ability to have high maneuverability. Therefore, it is necessary to study the coupling dynamic behavior of rotor system in typical maneuvering flight. Based on the finite element method, a 6-node rotor-bearing-disk system model with three kinds of maneuvering loads, nonlinear contact force of rolling bearing, eccentric unbalanced force of disk and gravity field is established in this paper, and the dynamic responses of the system under rolling, pitching and yawing maneuvering is analyzed in detail. The Newmark-β method is used to solve the system model. The system responses under different rotation speeds and two given rotation speeds are mainly analyzed. The system responses under three kinds of maneuvering loads are compared and analyzed. Finally, the 7-node stepped shaft system model is used to verify the universality of the analysis results in this paper. It is found that, under the same maneuvering load value, the possibility of rub-impact and frequency division components caused by different flight modes are different. The research in this paper can provide a cognitive basis for the mechanism of system rubbing fault under different maneuvers.

Investigation on dynamic behaviors of rotor system with looseness and nonlinear supporting

Pedestal looseness and supporting stiffness nonlinearities usually occur in rotating machines. To enhance the robustness and accurately forecast the nonlinear behaviors of rotor systems, these two kinds of common nonlinearities should be considered so that to meet the requirements of the dynamical design of a multi-disk rotor system. In this paper, the rotor system model with cubic supporting stiffness and looseness fault is established by the Lagrange method. The harmonic balance (HB) and Runge–Kutta (RK) methods are used to solve the dynamic response of the double disk rotor system, and the accuracy of the HB method is justified in comparison to the RK method. The bifurcation diagram, time history, frequency spectrum, phase portrait and Poincaré map are provided to discuss the individual and coupling effects of these two nonlinearities on the transient and steady-state response. The obtained experimental results indicate that the proposed model can capture the main nonlinear behaviors of looseness fault and nonlinear supporting stiffness, verifying the accuracy of theoretical and numerical results.

Nonlinear behaviors analysis of high-speed rotor system supported by aerostatic bearings

In the paper, the dynamic model of aerostatic bearing-rotor system combining rotor motion equation and transient Reynolds equation is established to study influences of rotational speed, unbalance, rotor mass and supply pressure on the nonlinear behaviors of rotor system. The results reveal abundant nonlinear phenomenon consisting of 3 T-periodic, 5 T-periodic and quasi-periodic motions. Furthermore, chosen proper unbalance, smaller rotor mass and larger supple pressure can control the nonlinear vibration and improve the system stability. The results provide a theoretical basis for a simple and feasible method to control the nonlinear vibration of rotor system by adjusting supply pressure.

Scaled boundary finite element method for hydrodynamic bearings in rotordynamic simulations

The behavior of rotor systems with hydrodynamic bearings can be affected crucially by the nonlinear bearing forces. These forces are incorporated in rotordynamic simulations by solving the Reynolds equation in every step of a time integration scheme. Since closed-form analytical solutions of the Reynolds equation are known only for simplified boundary conditions, numerical methods and look-up table approaches are applied. To obtain accurate and convergent results, numerical solutions require a fine discretization, while the look-up tables require a fine grid of interpolation points. In both cases, the numerical effort of the rotordynamic simulation is dominated by the computation of the bearing forces.In this study, a semi-analytical solution of the Reynolds equation based on the Scaled Boundary Finite Element Method (SBFEM) is developed to reduce the numerical effort of the overall simulation. In contrast to a purely numerical solution, the two-dimensional pressure field is discretized in only one coordinate direction, whereas in the other direction, an analytical formulation is used. This results in a system of non-homogeneous ordinary differential equations, which is solved under consideration of the boundary conditions. Since the complexity of the SBFEM model and the resulting numerical effort depend on the modeling of the oil supply groove, three different models are analyzed in this paper. The equations are derived, the solutions are verified, and their numerical efficiency is investigated in comparison to an FEM solution, which is one of the standard numerical approaches.

Method and device to investigate the behavior of large rotors under continuously adjustable foundation stiffness

Vibration problems have been observed after the installation of large rotating machines, such as electric machines and generators and paper machine rolls. One possible cause can be differences between the foundation stiffness of the installation location and the testing platform where the machine is balanced and optimized. Foundation stiffness exerts a significant effect on the behavior of a rotating system, and the above-mentioned differences can cause major unexpected changes at natural frequencies, and thus resonance. The problem is typical for large machines due to their large mass, which leads to low natural frequencies. This induces situations where these natural frequencies coincide with rotor excitations and cause excessive vibration. This study presents a novel method and a device for adjusting the foundation stiffness of a large rotor system, consequently enabling the investigation of the effect of foundation stiffness on rotor behavior. However, this investigation is restricted to the horizontal axis. The characteristics of the device were analyzed together with a rotor behavior measurement that consisted of versatile measurements of acceleration, force and displacement in different locations inside the rotating system. The device in the presented form is best applied in R&D laboratories and factory acceptance test cells, in which it can be used to predict the behavior of various rotors on different foundations. With the dynamic rotor behavior measurement performed with the device, the natural frequencies and their harmonic components can be presented as a function of foundation stiffness. This information can be used both to optimize rotor behavior in an installation location and also to improve the rotor system behavior in the design phase. The method and device presented in this study can be considered effective and successful, since the natural frequencies of the first two rotor modes could be manipulated freely at a range of 50-100 % by changing the stiffness.

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.

Nonlinear dynamic behavior of a flexible asymmetric aero-engine rotor system in maneuvering flight

Aero-engine rotor systems installed in aircraft are considered to have a base motion. In this paper, a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers (SFDs), and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied. Effects of the translational accelerative motions, the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated. The results show that, due to the nonlinear coupled effects among the rotor, ball bearings and SFDs, within the first bending resonance region, responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon, amplitude jumping phenomenon and non-synchronous vibration. Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region. The pitching angular motion mainly affects rotational vibration of the rotor system, and thus further induces their transverse vibrations. For the pitching flight with combined translational and angular motions, a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system, in which one response displays small amplitude and synchronous vibration, and the other shows large amplitude and non-synchronous vibration.

Influence of Fluid Film Boundary Migration on Dynamic Coefficients of Journal Bearings and Behavior of Rotor System

Abstract The position of fluid film in journal bearing will change while the journal moving in bearing, which can be named fluid film boundary migration (FFBM). It is usually ignored in the calculation of linear dynamic coefficients. While, the errors brought by this neglection was not ever investigated in detail. In this paper, the influence of FFBM on bearing dynamic coefficients and rotor system dynamic behaviors are investigated. A new perturbation-based model is proposed to take the FFBM into account by modifying the boundary conditions of governing equations. It is then verified by the experimental results and analytical results from previous research. Furthermore, the effects of FFBM on stiffness and damping in two typical journal bearings are investigated. The result indicates that the FFBM has a significant influence on dynamic coefficients of full circular journal bearing but little impact on journal bearing with axial grooves. Moreover, it affects the stiffness and damping more significantly in the cases of large length-to-diameter ratios or small eccentricity ratios in full circle bearing. Finally, the dynamical behavior of a rotor-bearing system with considering the FFBM is also investigated. The result shows that the FFBM of oil film has remarkable influences on the instability threshold and imbalance responses of the rotor system, which should not be ignored. The conclusions obtained in this research are expected to be helpful for the design of full circular journal bearings or rotor-bearing systems.

Study on Coupling Fault Dynamics of Sliding Bearing-Rotor System

The phenomenon of oil film oscillation and frequency locked may occur in a healthy rotor system which is supported by sliding bearing. The dynamic behavior of the rotor system with misalignment and rubbing coupling fault supported by sliding bearing is also very complex. To solve the problem of fault diagnosis in this case, a dynamical model of rotor system is proposed in this paper. The short bearing oil film force, the equivalent misalignment moment, and Hertz contact theory are applied to establish the model. For rubbing faults, the Augmented Lagrange method is used to deal with the contact constraints to ensure that the boundary penetration depth is within the specified tolerance range. Furthermore, the dynamic behavior of the faulty rotor system under different rubbing stiffness conditions is analyzed in this paper. Meanwhile, the fault signal is divided into equal-band by the wavelet basis functions to find out the fault frequency band of the rotor system. Finally, the accuracy of the simulation study is verified by measurements obtained from the faulty rotor test platform. The following findings are made in this paper. The rubbing fault is dominant in the coupling fault. With the increasing of the speed, the frequency components of the system are dominated by high frequency. The double frequency is the main fault feature frequency band. It can be seen that the rotor system moves gradually from a quasi-periodic state into chaos due to the Lyapunov exponent. At the same time, due to the effects of misalignment moment and friction force, the phenomenon of oil film instability is partially suppressed. The lagging of the first and second-order oil film oscillations occurs.

The Oscillation Attenuation of an Accelerating Jeffcott Rotor Damped by Magnetorheological Dampers Affected by the Delayed Yielding Phenomenon in the Lubricating Oil

Adding damping devices to the rotor supports is a frequently used technological solution for reducing vibrations of rotating machines. To achieve their optimum performance, their damping effect must be adaptable to the current operating speed. This is offered by magnetorheological squeeze film dampers. The magnetorheological oils are liquids sensitive to magnetic induction and belong to the class of fluids with a yielding shear stress. Their response to the change of a magnetic field is not instantaneous, but it is a process called the delayed yielding. The developed mathematical model of the magnetorheological squeeze film damper is based on the assumptions of the classical theory of lubrication. The lubricant is represented by a bilinear material, the yielding shear stress of which depends on magnetic induction. The delayed yielding process is described by a convolution integral with an exponential kernel. The developed mathematical model of the damper was implemented in the computational procedures for transient analysis of rotors working at variable operating speed. The carried-out simulations showed that the delayed yielding effect could have a significant influence on performance of magnetorheological damping devices. The development of a novel mathematical model of a magnetorheological squeeze film damper, the representation of the magnetorheological oil by bilinear material, taking the delayed yielding phenomenon into consideration, increased numerical stability of the computational procedures for transient analysis of flexible rotors, and extension of knowledge on behavior of rotor systems damped by magnetorheological squeeze film dampers are the principal contributions of this paper.

Dynamic Analysis of Rotor-Ball Bearing System of Air Conditioning Motor of Electric Vehicle

Nowadays, electric vehicles (EV) present a promising solution to reduce greenhouse gas emissions. They are considered zero emission vehicles. Rotor bearing system is important part of air conditioning motor of EV. The aim of this research is to develop a numerical model to investigate the structural dynamic response of the rigid rotor supported on deep groove ball bearings. The numerical model considers rotor imbalance that varies with speed, as well as sources of nonlinearity such as Hertzian contact force, ball clearance and varying compliance vibration. This is very important on the design point of view. The 4th order Runge-Kutta numerical integration technique has been applied. The results are presented in form of time displacement response, frequency spectra, and Poincare map. The analysis demonstrates that the number of balls is one of the key factors affecting on the dynamic characteristics of rotor bearing system. The model can also be used as a tool for predicting nonlinear dynamic behavior of rotor system of air conditioning motor of electric vehicle under different operating conditions. Moreover, the study may contribute to a further understanding of the nonlinear dynamics of rotor bearing system.