Rotordynamic System Research Articles

Numerical investigation of cracked rotor

The aim of this paper is investigating the cracked Jeffcott with an offset disk rotor system. The finite element method (FEM) used in ANSYS gives an attractive approach for modeling the rotor dynamic system. The effect of changing speeds has been analyzed on the dynamic parameters of journal bearings (stiffness and damping) and then on Sommerfeld number. The relation of the dynamic bending stress with the static stress of rotor with cracks (dynamic load factor (DLF)) and with the ratio of depth crack to radius rotor has been established. The results have been obtained numerically by using ANSYS. The results show when crack’s depths increase the DLF increases and reach to maximum when a/R = 0.8.

Passive vibration absorbers for vibration reduction in the multi-bladed rotor with rotor and stator contact

Contact phenomena are among the most undesirable incidences in a rotor dynamic system where its emergence could be due to the centrifugal force generated by an unbalance disk. In this work, a Jeffcott rotor supported by oil film journal bearings and with rigid blades is taken into account. The long oil film lubrication is considered where the axial flow is negligible. The rotational speed is taken as a control parameter, and the analysis is performed for two different clearances considering the rotor with three, four, and five blades. To reduce the vibrations of the system with the purpose of contact elimination, a tuned mass damper and a nonlinear energy sink as passive absorbers are utilized. Then, by an optimization process applying a complex averaging method, the optimum parameters for each absorber are calculated. Due to the critical behavior of the system in the lower clearance values, double coupling of the absorbers is suggested. The results demonstrate that single coupling of the absorbers can considerably reduce the vibration of the system. On the other hand, for the lower clearance value single coupling is not efficient, and double coupling could be utilized to mitigate the unwanted vibrations of the 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.

A mixed variational‐based dynamic simulation method for fiber‐reinforced continua in non‐isothermal rotordynamical systems

AbstractThree‐dimensional woven carbon‐fiber reinforced polymers (3D‐CFRP) are being increasingly used for blades in rotordynamical systems as turbine fans, shafts as well as disc brake rotors. By using dynamic mixed finite‐element methods, these materials can be simulated as anisotropic continua with non‐isothermal behaviour in the matrix as well as the fiber material. Therefore, we present a novel dynamic mixed finite‐element method which is variational‐based and capable to simulate these materials. This dynamic mixed finite‐element method preserves each basic balance law emanating from the variational principle exact in a discrete setting. We demonstrate this physically‐consistent simulation behaviour by using dynamic simulations of a disc brake rotor and a rotating pipe subject to thermal and mechanical loads.

On bifurcation trees of period-1 to period-2 motions in a nonlinear Jeffcott rotor system

In this paper, periodic motions in a nonlinear rotor system are predicted through an implicit mapping method. The bifurcation trees of different period-1 to period-2 motion are presented, and there are many segments for different period-1 and period-2 motions. Harmonic frequency-amplitude characteristics of periodic motions are discussed for analysis and design of nonlinear rotor systems. Numerical simulations of periodic motions are completed for comparison of predicted and numerical results. The predictions of periodic motions in the nonlinear rotor system can provide guides for practical measurements of rotor systems, and one can have a better understanding of nonlinear rotor dynamics compared to the traditional perturbation analysis. Such studies presented in this paper just throw out some guides and ideas to predict complex motions in nonlinear rotor systems. The authors hope one can follow what presented in this paper to do further studies in nonlinear rotor dynamical systems and to improve design and control of nonlinear rotor systems.

Active vibration control of rotor-bearing system by virtual dynamic absorber

The main sources of the vibration in rotor dynamic systems are unbalanced masses and manufacturing defects of bearings used in the rotor system. In this study, magnetic absorber as a new method brings the rotor system out of resonance state by applying a dynamic absorber system force and creating two new natural frequencies. This study virtually reconstructed magnetic absorber controller software as a combined active and passive dynamic absorber to reduce vibration amplitude, efficiently. In this approach, combined routes are defined for the rotor frequency response, so that the optimal values of the parameters of dynamic absorber system are calculated using H∞ method and maximum damping for frequencies lower and higher than resonance frequencies, respectively. The results confirm that transient response overshoot is less, and transient response attenuation is more in maximum damping method. Hence, the controller system easily recognizes initial overshoots and determines the parameters of the dynamic absorber system in accordance with maximum damping state if it is struck at any rotor frequency and any rotation angle. It is also observed that for all rotor rotation frequencies, the system overshoot reduces in comparison with H∞ method by using this control method.

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

Abstract Campbell diagrams describe the variation with speed of the modes of low amplitude (linear) free vibration of a rotordynamic system about its static equilibrium condition, and are an important tool that aids the interpretation of the nonlinear response. However, Campbell diagrams for foil-air bearing (FAB) rotor systems are currently derived using the linear force coefficients (FC) method and individual modes have not been verified by transient nonlinear dynamic analysis (TNDA) at low amplitudes. In fact, significant discrepancies between FC and TNDA predictions for the stability of the leading (i.e. least damped) mode have been reported. This paper establishes for the first time a method for deriving Campbell diagrams of a generic FAB-rotor model that avoids the FC method. It is based on an eigenvalue analysis of the Jacobian matrix of the dynamical system. Through suitable scaling and the application of appropriate criteria, the multitude of eigenvectors of the Jacobian can be filtered to extract the relevant modes. Each mode is verified using TNDA with mode-specific initial conditions derived from the Campbell diagram analysis. The methodology is successfully tested on three cases in the literature, which respectively illustrate its applicability to complex bearing types (3-pad), complex foil models, and flexible rotors.

Numerical and Experimental Research on the Fluid-Induced Forces of Clearance Flow in Canned Motor Reactor Coolant Pump

Reactor coolant pump (RCP) is one of the most important equipment of the coolant loop in a pressurized water reactor system. Its safety relies on the characteristics of the rotordynamic system. For a canned motor RCP, the liquid coolant fills up the clearance between the metal shields of the rotor and stator inside the canned motor, forming a long clearance flow. The fluid-induced forces of the clearance flow in canned motor RCP and their effects on the rotordynamic characteristics of the pump are numerically and experimentally analyzed in this work. A transient computational fluid dynamics (CFD) method has been used to investigate the fluid-induced force of the clearance. A vertical experiment rig has also been established for the purpose of measuring the fluid-induced forces. Fluid-induced forces of clearance flow with various whirl frequencies and various boundary conditions are obtained through the CFD method and the experiment. Results show that clearance flow brings large mass coefficient into the rotordynamic system and the direct stiffness coefficient is negative under the normal operating condition. The rotordynamic stability of canned motor RCP does not deteriorate despite the existence of significant cross-coupled stiffness coefficient from the fluid-induced forces of the clearance flow.

Analysis of a rotordynamic system with anisotropy and nonlinearity using the Floquet theory and the method of normal forms

The system under analysis is composed of an asymmetric rotor, two asymmetric bearings and a nonlinear spring-damper system representing an annular gas seal. The anisotropy in the rotor stiffness introduces time-periodic coefficients in the equations of motion which lead to parametric excitation with the typical resonance effects. As the additional anisotropy in the bearings may increase the area of unsafe operation conditions, the impact of these two different sources of anisotropy on the stability of the trivial solution is investigated in detail by a numerical approach based on the Floquet theory. Further insight into the stability behavior in case of an unstable trivial solution is obtained by accounting for stiffness and damping nonlinearities due to the gas seal. In this nonlinear case, the stability of the periodic solutions is analyzed by the semi-analytical method of normal forms revealing the influence of individual system parameters. The results of the semi-analytical approximation are verified by numerical calculations showing good agreement.

Development and Experimental Validation of Auxiliary Rolling Bearing Models for Active Magnetic Bearings (AMBs) Applications

Nowadays, the search for increasing performances in turbomachinery applications has led to a growing utilization of active magnetic bearings (AMBs), which can bring a series of advantages thanks to their features: AMBs allow the machine components to reach higher peripheral speeds; in fact there are no wear and lubrication problems as the contact between bearing surfaces is absent. Furthermore, AMBs characteristic parameters can be controlled via software, optimizing machine dynamics performances. However, active magnetic bearings present some peculiarities, as they have lower load capacity than the most commonly used rolling and hydrodynamic bearings, and they need an energy source; for these reasons, in case of AMBs overload or breakdown, an auxiliary bearing system is required to support the rotor during such landing events. During the turbomachine design process, it is fundamental to appropriately choose the auxiliary bearing type and characteristics, because such components have to resist to the rotor impact; so, a supporting design tool based on accurate and efficient models of auxiliary bearings is very useful for the design integration of the Active Magnetic Bearing System into the machine. This paper presents an innovative model to accurately describe the mechanical behavior of a complete rotor-dynamic system composed of a rotor equipped with two auxiliary rolling bearings. The model, developed and experimentally validated in collaboration with Baker Hughes a GE company (providing the test case and the experimental data), is able to reproduce the key physical phenomena experimentally observed; in particular, the most critical phenomenon noted during repeated experimental combined landing tests is the rotor forward whirl, which occurs in case of high friction conditions and greatly influences the whole system behavior. In order to carefully study some special phenomena like rotor coast down on landing bearings (which requires long period of time to evolve and involves many bodies and degrees of freedom) or other particular events like impacts (which occur in a short period of time), a compromise between accuracy of the results and numerical efficiency has been pursued. Some of the elements of the proposed model have been previously introduced in literature; however the present work proposes some new features of interest. For example, the lateral and the axial models have been properly coupled in order to correctly reproduce the effects observed during the experimental tests and a very important system element, the landing bearing compliant suspension, has been properly modelled to more accurately describe its elastic and damping effects on the system. Furthermore, the model is also useful to characterize the frequencies related to the rotor forward whirl motion.

Vibration Suppression of a Flexible-Joint Robot Based on Parameter Identification and Fuzzy PID Control

In order to eliminate the influence of the joint torsional vibration on the system operation accuracy, the parameter identification and the elastic torsional vibration control of a flexible-joint robot are studied. Firstly, the flexible-joint robot system is equivalent to a rotor dynamic system, in which the mass block and the torsion spring are used to simulate the system inertia link and elasticity link, for establishing the system dynamic model, and the experimental prototype is constructed. Then, based on the mechanism method, the global electromechanical-coupling dynamic model of the flexible-joint robot system is constructed to clear and define the mapping relationship between the driving voltage of the DC motor and the rotational speed of joint I and joint II. Furthermore, in view of the contradiction between the system response speed and the system overshoot in the vibration suppression effect of the conventional PID controller, a fuzzy PID controller, whose parameters are determined by the different requirements in the vibration control process, is designed to adjust the driving voltage of the DC motor for attenuating the system torsional vibration. Finally, simulation and control experiments are carried out and the results show that the designed fuzzy PID controller can effectively suppress the elastic torsional vibration of the flexible-joint robot system with synchronization optimization of control accuracy and dynamic quality.

A Performance Study of Controlled Impact Timing on Harmonics Reduction in Operational Modal Testing

As an alternative to operational modal analysis and classical experimental modal analysis (EMA), a novel method was introduced previously, namely impact-synchronous modal analysis (ISMA). The effectiveness ISMA on rotor and structural dynamic systems has been proven in previous literature. More recently, an automated impact device (AID) was introduced which utilized tachometer pulse as initiation signal and its effectiveness on ISMA was proven. An attempt to further enhance this device in term of equipment and cost is then proposed by replacing the tachometer with the in-use tri-axial accelerometer through utilizing the filtered response of cyclic load component as an initiation signal to control the impact device, which is also the primary aim for this study. Prior to modal testing, accuracy of this device is illustrated at desired phase angles of 0 deg, 90 deg, 180 deg, and 270 deg. Subsequently, frequency response function (FRF) estimations obtained for ISMA using enhanced AID has demonstrated the suppression capabilities of this device on disturbances, i.e., reduction of 93.58% at 30 Hz and 57.78% at 60 Hz, resulting in a high correlation for signature assurance criterion (SAC) and cross signature assurance criterion (CSAC). Modal parameters extracted from the EMA and ISMA using impact device are presented and compared, for the first three natural modes of the test rig. It is found that natural frequencies are deviating by less than 6%, whereas modal assurance criterion (MAC) values between the mode shapes of the two tests are found to be above 0.9.

Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports

A rotor dynamic system requires high power/torque to accelerate through its resonance conditions or critical speeds to operate at a super-critical speed. Most practical drive sources are non-ideal in nature, i.e. they can only provide a limited amount of power to the rotor system. Thus, if there is insufficient power to overcome a resonance then the rotor speed may get arrested at that resonance or take a long time to escape from the resonance; and thereby damage the system. For the present analysis, a Direct Current (DC) motor is considered as the non-ideal prime mover for a rigid rotor shaft with unbalanced disk which is supported by flexible anisotropic supports/bearings. Due to the anisotropy in the supports, both forward and backward whirl motions of the rotor get excited. This causes a multi-Sommerfeld effect where two non-linear jump phenomena are manifested at the first forward and backward critical speeds during rotor coast up and coast down. When the two critical speeds are close to each other, a complex speed capture and jump phenomena occurs. Accordingly, the transitions through both resonance conditions are examined. At first, the analytical solutions are obtained under steady state assumption and then transient simulations are performed with the help of a bond graph (BG) model.

Determination of Random Matrices Dispersion Parameters for Nonparametric Modeling of Stochastic Dynamic Systems with Experimental Verification

Extraction of random behavior of dynamic systems under the influence of the uncertainty associated with modeling error is a major challenge. In the present study, Random Matrix Theory (RMT) is applied to simulate this type of uncertainty in rotor shafts of high-speed rotordynamic systems. For this purpose, simulation of a random matrix is carried out based on the nonparametric approach followed by the determination of the mean model and dispersion parameters. The mean model is determined by extracting the mechanical and dimensional parameters of 15 rotor shaft samples via exact dimensional measurements and Experimental Modal Analysis (EMA). In this study, presenting the Difference Measure (DM) value, the dispersion parameters of the mass and stiffness of the rotor shafts are exploited. In this research, by minimizing the DM value as an objective function, domain variations and probability density distribution of the uncertain response (rotor shaft natural frequencies in this paper) obtained from the EMA and RMT are coincided simultaneously. The simulation process of a random matrix is fulfilled using the direct Monte Carlo simulation and minimization of the DM parameter is performed using Bee’s Algorithm (BA). It is demonstrated that this swarm intelligence-based algorithm provides an approach to extract optimal and accurate dispersion parameters in RMT implementation. The results show that the calculated dispersion parameters are in good agreement with the experimental data and the BA-based method is effective.

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non-linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincaré maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system.

Vibration mitigation of a flexible bladed rotor dynamic system with passive dynamic absorbers

The main objective of this paper is to study the application of tuned mass damper (TMD) and nonlinear energy sink (NES) on vibration mitigation of a flexible bladed rotor system. TMD tunes to a specific frequency of the main system and reduces its amplitude only in a vicinity of that frequency. NES is another well-known passive dynamic absorber comprises a mass, nonlinear spring, and linear or nonlinear damper. The nonlinearity of this absorber allows it to reduce the vibrations of the main system in a wider frequency range. In this study to reduce the contact of flexible bladed rotor system, the mentioned passive absorbers are attached both to the disk and to the tips of the blades, such that to deactivate the effect of disk's eccentricity force and stabilizing the behavior of the system. The optimum parameters of the absorbers are obtained through optimization. The bifurcation diagrams, and Lyapunov exponent of the system are obtained with respect to different parameter and rotational speed are obtained and consequently, the efficiency of the absorbers are investigated. The obtained results show how these passive absorbers can decrease the vibration of the rotor system and remove the contact at higher clearance values between the blades and the stator; although, there are limitations in their performances at lower values of clearance.

Improved non-invasive inverse problem method for the balancing of nonlinear squeeze-film damped rotordynamic systems

Abstract A non-invasive inverse problem method for rotor balancing relies on casing vibration readings and prior knowledge of the structure. Such a method is important for rotors that are inaccessible under operating conditions. This paper introduces a method for solving the quasi-implicit inverse problem that arises when identifying the required balancing correction for a rotor with only one weak linear connection to the casing, apart from the nonlinear connections. This is typical of aero-engine designs that use a retainer spring with only one of the nonlinear squeeze-film damper (SFD) bearings that support the rotor within the casing. The SFD journal displacements are estimated from casing vibration readings using identified inverse SFD models based on Recurrent Neural Networks (RNNs). The information from these is then used to enhance the condition of the explicit inverse problem set up in previous research for simpler configurations. The methodology is validated using simulated casing vibration readings. The reliability of the RNN inverse SFD models is first demonstrated. The second part of the validation shows that the novel enhanced explicit inverse problem method is essential for effective balancing of this previously unconsidered system. Repeatability and robustness to noise/model uncertainty are satisfactorily demonstrated and limitations discussed.

Active rotordynamic stability control by use of a combined active magnetic bearing and hole pattern seal component for back-to-back centrifugal compressors

Active control methods of rotordynamic stability for rotordynamic systems have been developed for many years, however effectively implementing these methods in real machines remains a significant challenge. With the goal of improving the performance of a back-to-back centrifugal compressor, a new integral electromagnetic actuator that combines the functions of an active magnetic bearing with a hole pattern seal is designed and used to replace the original balance piston of the machine. The structure design and assembly in the compressor are presented and an investigation on the seal performance and magnetic bearing forces is carried out. The results show that this innovative integral actuator can provide both sealing and vibration control, with two vibration feedback control methods experimentally validated for the elimination of oil whip, improving the rotordynamic stability of the machine.

Design of Active Magnetic Bearing Controllers for Rotors Subjected to Gas Seal Forces

Proper design of feedback controllers is crucial for ensuring high performance of active magnetic bearing (AMB) supported rotor dynamic systems. Annular seals in those systems can contribute significant forces, which, in many cases, are hard to model in advance due to complex geometries of the seal and multiphase fluids. Hence, it can be challenging to design AMB controllers that will guarantee robust performance for these kinds of systems. This paper demonstrates the design, simulation, and experimental results of model-based controllers for AMB systems, subjected to dynamic seal forces. The controllers are found using H∞ and μ synthesis and are based on a global rotor dynamic model in which the seal coefficients are identified in situ. The controllers are implemented in a rotor-dynamic test facility with two radial AMBs and one annular seal with an adjustable inlet pressure. The seal is a smooth annular type, with large clearance (worn seal) and with high preswirl, which generates significant cross-coupled forces. The H∞ controller is designed to compensate for the seal forces and the μ controller is furthermore designed to be robust against a range of pressures across the seal. In this study, the rotor is nonrotating. Experimental and simulation results show that significant performance can be achieved using the model-based controllers compared to a reference decentralized proportional-integral-derivative (PID) controller and robustness against large variations of pressure across the seal can be improved by the use of robust synthesized controllers.

On-Site Identification of Dynamic Annular Seal Forces in Turbo Machinery Using Active Magnetic Bearings: An Experimental Investigation

Significant dynamic forces can be generated by annular seals in rotordynamics and can under certain conditions destabilize the system leading to a machine failure. Mathematical modeling of dynamic seal forces are still challenging, especially for multiphase fluids and for seals with complex geometries. This results in much uncertainty in the estimation of the dynamic seal forces, which often leads to unexpected system behavior. This paper presents the results of a method suitable for on-site identification of uncertain dynamic annular seal forces in rotordynamic systems supported by active magnetic bearings (AMB). An excitation current is applied through the AMBs to obtain perturbation forces and a system response, from which the seal coefficients are extracted by utilizing optimization and a priori information about the mathematical model structure and its known system dynamics. As a study case, the method is applied to a full-scale test facility supported by two radial AMBs interacting with one annular center-mounted test seal. Specifically, the dynamic behavior of a smooth annular seal with high preswirl and large clearance (worn seal) is investigated in this study for different excitation frequencies and differential pressures across the seal. The seal coefficients are extracted and a global model on reduced state-space modal form is obtained using the identification process. The global model can be used to update the model-based controller to improve the performance of the overall system. This could potentially be implemented in all rotordynamic systems supported by AMBs and subjected to seal forces or other fluid film forces.