Unbalance Response Research Articles

Dynamic characteristics analysis of a dual-rotor system with inter-shaft bearing

The dual-rotor structure is susceptible to vibration, causing the malfunction of the entire operating system. In order to avoid the resonance during operation, it is significant and necessary to conduct modal analysis of such rotors. The dynamic analysis of the full dual-rotor system under operating conditions is also necessary to study dynamic characteristics of the rotating system. In this paper, one-dimension Timoshenko beam-type model, including the effects of gyroscopic moments, rotary inertias, bending and shear deformations, and three-dimension model for dual-rotor system with inter-shaft bearing are developed. Critical speed tests of dual-rotor are carried out to verify the analytical results. Based on the finite element models, the first critical speed excited by inner rotor and the first two critical speeds excited by outer rotor are calculated. The comparisons between both finite element models indicate that 1D model costs less time, which can be used to predict the critical speeds. Good agreement between the theoretical and experimental results shows the accuracy of the FE models. The Campbell diagram, critical speeds, operational deflection shapes and unbalance response of the dual-rotor are obtained to fully study the dynamic characteristics of the dual-rotor system.

New Active Online Balancing Method for Grinding Wheel Using Liquid Injection and Free Dripping

Grinding is a vital method in machining techniques and an effective way to process materials such as hardened steels and silicon wafers. However, as the running time increases, the unbalance of grinding wheels produce a severe vibration and noise of grinding machines because of the uneven shedding of abrasive particles and the uneven adsorption of coolant, which has a severe and direct impact on the accuracy and quality of parts. Online balancing is an important and necessary technique to reduce the unbalance causing by these factors and adjust the time-varying balance condition of the grinding wheel. A new active online balancing method using liquid injection and free dripping is proposed in this paper. The proposed online balancing method possesses a continuous balancing ability and the problem of losing balancing ability for the active online balancing method using liquid injection is solved effectively because some chambers are full of liquid. The residual liquid contained in the balancing chambers is utilized as a compensation mass for reducing rotor unbalance, where the rotor phase is proposed herein as a target for determining the machine unbalance. A new balancing device with a controllable injection and free dripping structure is successfully designed. The relationship between the mass of liquid in the balancing chamber and the centrifugal force produced by liquid is identified. The performance of the proposed method is verified by the balancing experiments and the results of these experiments show that the vibration of unbalance response is reduced by 87.3% at 2700 r/min.

Identification of dynamic parameters of active magnetic bearings in a flexible rotor system considering residual unbalances

Active magnetic bearings (AMBs) support rotors using electromagnetic forces rather than mechanical forces. It is necessary to identify the AMB force coefficients (equivalent stiffness and damping) since they play key roles in the rotordynamic analysis. The identification is usually performed by analyzing the unbalance response. However, the presence of unknown residual unbalances reduces the identification accuracy and a rigid rotor model is only valid when the rotating speed is far below the first bending critical speed. Therefore, this paper proposes an identification algorithm to estimate the stiffness and damping parameters for a flexible rotor AMB system in the presence of unknown residual unbalances by using two independent unbalance response data sets. The proposed algorithm is first evaluated by numerical calculation for accuracy and then applied experimentally in the identification of a flexible rotor AMB system operating at speeds ranging from 3,000 rpm (50 Hz) to 30,000 rpm (500 Hz). The identification results are verified in the end.

Rubbing dynamics behavior of a flywheel shafting with a single point flexible support

The flywheel energy storage system is a new kind conversion device which realizes electric energy and kinetic energy transform into each other. The dynamic characteristics of flywheel energy storage system have been studied extensively in recent years. A single point flexible support is suitable for the small flywheel system, because the friction loss is very low. The flywheel spin test system with a single point flexible support was built. The dynamic model of the flywheel shafting was established to calculate the critical speeds, modal shape and modal damping ratio at different speeds. The results show that the dynamic characteristics of the flywheel shaft are stable, and its structure is simple and efficient. The comparison between the calculated unbalance response and the experimental response indicates that the dynamic model is appropriate. When the flywheel started up and rotated at different speeds, the rubbing dynamics behavior was obtained by the experiment. Full rubbing occurred at high speed would damage the flywheel and stop, which should be tried to avoid.

Rotordynamics of a Highly Flexible Hub for Inside-Out Ceramic Turbine Application: Finite Element Modeling and Experimental Validation

The inside-out ceramic turbine (ICT) is a promising concept to increase turbine inlet temperatures in microturbines by integrating individual monolithic ceramic. This architecture uses a carbon–polymer composite rim to support the blades mainly in compression. High tangential velocities lead to elevated radial displacement of the rim, and therefore, the rotor hub needs to have sufficient compliance to follow this radial displacement. However, the rotordynamics of a flexible hub is not widely understood. This paper presents the rotordynamic analysis of a highly flexible hub for an ICT architecture. Finite element modeling (FEM) is used to design a simplified turbine prototype that maximizes the hub flexibility to explore the limits of the concept. The rotordynamics behavior of the highly flexible hub is measured by spinning a 171-mm diameter prototype up to 49 krpm. This paper highlights three principal challenges of this particular rotordynamics. First, critical speeds mode shape becomes highly coupled with bearings displacement, shaft bending, and hub deformation. At high-speed, the hub deforms out of phase with the shaft, which can cause high stresses in the hub. Second, the angular position between unbalance masses of the flexible hub and the composite rim changes the unbalance response significantly. Finally, vibration causes high stresses in the hub, due to the relative displacement between the composite rim and the shaft, which could lead to failure of the hub. Nevertheless, the rotordynamics of an ICT configuration is manageable as long as the vibration-induced stress in the hub is kept under its limit.

Bearing dynamic parameters identification for a sliding bearing-rotor system with uncertainty

Bearing dynamic parameters of a sliding bearing-rotor system are important factors to the vibration absorbing characteristics. It is a valuable method to identify bearing dynamic parameters based on the unbalance response. Nevertheless, in Engineer, the unbalance parameters are uncertain due to the structural complexity and manufacturing or measuring error. Thus, developing an efficient method to estimate the bearing dynamic parameters for the uncertain unbalance parameters seems more important and necessary. This paper presented an inverse method for identifying stably the bounds of bearing dynamic parameters with uncertain unbalance parameters based on dynamic load identification method and the interval analysis .In the method, bearing dynamic parameters identification problem is formulated as the oil film force reconstruction by considering the oil film supports as rotor load boundary conditions; the midpoint oil film force and the first derivative to each uncertain unbalance parameter need be calculated with the interval analysis; the bounds of bearing dynamic parameters can be finally identified based on the interval mathematics. Finally, the efficiency and robustness of the proposed method are verified by a numerical example.

Dynamics of Flywheel Energy Storage System With Permanent Magnetic Bearing and Spiral Groove Bearing

Developing a flywheel energy storage system (FESS) with permanent magnetic bearing (PMB) and spiral groove bearing (SGB) brings a great challenge to dynamic control for the rotor system. In this paper, a pendulum-tuned mass damper is developed for 100 kg-class FESS to suppress low-frequency vibration of the system; the dynamic model with four degrees-of-freedom is built for the FESS using Lagrange's theorem; mode characteristics, critical speeds, and unbalance responses of the system are analyzed via theory and experiment. A comparison between the theoretical results and the experiment ones shows that the pendulum-tuned mass damper is effective, the dynamic model is appropriate, and the FESS can run smoothly within the working speed range.

Bending fault evaluation for the HP-IP rotor system of the nuclear steam turbine based on the dynamic model

With considering the unbalance mass-fluid film bearings-rotor elements, a dynamics model for the nuclear half-speed 1000 MW saturated steam turbine with No. Dongfang HN1089 is constructed. By solving of the Reynolds Equation and the dynamics model, the oil pressure distribution and dynamic coefficients of the fluid film bearings, and the unbalance response of the rotor, are obtained. The method for evaluating the bending fault based on the dynamics model is proposed, in which the bending parameter is transformed as the unbalance mass. A case on the bending fault evaluation for HN1089 is carried out. The results show that the response sensitivity of HN1089 on the unbalance mass is about 1/6 that of the thermal power units with the same capacity (1000 MW); and it is difficult to decrease the excited response from the bending fault even to add the maximum unbalance mass. In actual, the removing stress in the partial zone and turning method are applied to deal with the HP-IP rotor bending fault, and the response of the repaired rotor is 0.033 m by the actual field test. The results show the model and the method for evaluating the bending fault are accurate and reasonable, which will provide the important theoretical guide for fast and accurately dealing with such bending fault in the steam turbine rotor system.

The Trapezoid Counterweight Method in Dynamic Balance of Symmetric Flexible Rotor

Steam turbine generator unit, water pump and other high speed revolution symmetric flexible rotor were regarded as research objects in this paper. According to variation characteristic of rotor shaft in rigid and flexible working mode, nine-reel high pressure water pump rotor was analyzed. The former four-order intrinsic frequency of flexible rotor was obtained by modal analysis and harmonic response analysis. The methods of reaction force response and unbalance response were been studied after first order and second order resonance region eliminating in different modes of simple harmonic exciting force. Based on above theoretical research results, trapezoid counterweight method was proposed for dynamic balance of flexible rotor. This method solved problem that rigid dynamic balance of low speed rotor was destroyed after first order and second order resonance region counter weight in dynamic balance of flexible rotor. The dynamic balancing techniques of flexible rotor could be improved the qualities of rotor and its relative products by this method, eliminating the vibration of unbalance mass of products radically.

A Combined EFEM–Discrete Element Method Dynamic Model of Rotor–Bearing–Housing System

In this paper, a model was developed to study the effects of rotor and support flexibilities on the performance of rotor–bearing–housing system. The system is composed of a flexible rotor and two supporting deep-groove ball bearings mounted in flexible bearing housings. The dynamics of the ball bearings were simulated using an existing dynamic bearing model, which was developed using the discrete element method (DEM). The explicit finite element method (EFEM) was used to model the flexibilities of the rotor and bearing support. In order to combine the dynamic bearing model with finite element rotor and support system, new contact algorithms were developed for the interactions between the various components in the system. The total Lagrangian formulation approach was applied to decrease the computational effort needed for modeling the rotor–bearing–housing system. The combined model was then used to investigate the effects of bearing clearances and housing clearances. And it was found that, as the rotor is deformed due to external loading, the clearances have a significant impact on the bearing varying compliance motion and reaction moments. Results also show that deformation of the flexible housing depends on the total force and moment generated within the bearing due to rotor deformation. The first critical speed of rotor was simulated to investigate the unbalance response of the rotor–bearing system. It was demonstrated that rotor critical speed has a significant effect on inner race displacement and reaction moment generated at bearing location.

Nonlinear Effects of Surface Texturing on the Performance of Journal Bearings in Flexible Rotordynamic Systems

A dynamic model of a rotating shaft on two textured hydrodynamic journal bearings is presented. The hydrodynamic mean pressure is computed using multiscale periodic homogenization and is projected on a flexible shaft with internal damping. Harmonic balance method (HBM) is used to study the limit cycles of unbalance response of the coupled system discretized by finite element method (FEM). Stability is analyzed with Floquet multipliers computation. An example of an isotropic texturing pattern representing laser dimples on a lightweight rotor is analyzed. Vibration amplitude and stability zone are compared with plain bearing lubrication. It is shown in an example that full surface texturing leads to relatively higher vibration amplitude compared to plain bearings.

A fully coupled air foil bearing model considering friction – Theory & experiment

The dynamics of air foil bearings (AFBs) are not yet fully captured by any model. The recent years have, however, seen promising results from nonlinear time domain models, and simultaneously coupled formulations are now available, avoiding the previous requirements for undesirably small time steps and temporal convergence studies.In the present work, an alternative foil structure model is substituted for the simple elastic foundation model to avoid its inherent limitations. The new foil model is based on a truss representation from the literature, but incorporates the foil mass and a dynamic friction model. As a consequence of the friction model's velocity dependency, the foil mass is included to obtain a set of differential equations that can be coupled to the rotor and fluid domains while allowing a simultaneous solution.Considerations leading to a practically applicable implementation are discussed and numerical results are compared with experimental data. The model predicts natural frequencies and mode shapes well, but it is not yet capturing the unbalance response when friction is considered. Possible causes for this discrepancy are discussed and it is suggested that sticking is a more prevalent state than previously assumed.

Uncertainty quantification techniques applied to rotating systems: A comparative study

The modeling of mechanical systems involves different parameters that are susceptible to uncertainties. Commonly, the variations result from the mathematical difficulty of representing the peculiarities of the dynamic systems and the lack of knowledge about the physical properties of the materials used in a given application. In this context, the analysis of uncertainties that affect the performance of the system is an important design issue. Uncertainty analysis of dynamic systems has been studied by applying techniques based on stochastic and fuzzy logic approaches. The fuzzy logic technique seems to be more appropriate when the stochastic process that characterizes the uncertainties is unknown. Therefore, in the present contribution, the inherent uncertainties affecting the performance of a horizontal rotating machine are modeled by using both stochastic and fuzzy logic-based analysis. These methodologies have been compared through numerical simulations in terms of the dynamic behavior of the system as represented by rotor orbits, unbalance responses, and frequency response functions. The proposed uncertainty analysis provides additional information that can be useful for design and maintenance purposes.

Impact of system anisotropy on vibration reduction of rotating machinery and its evaluation method

The orbit shape responded from each concerned section of anisotropic rotating machinery varies along with the axial position of unbalance force, especially its parameters like the inclination angle and the major to minor axis ratio. Considering the axial position difference between the original unbalance mass existed and the balancing planes adopted,vibration reduction with balancing could be disturbed by the anisotropy of rotating machinery. Through in-depth analysis on these mechanisms, a method for anisotropy evaluation is presented based on the dispersion characteristics estimation of system difference coefficients. Balancing experiments under different degrees of system difference coefficients dispersion and different unbalance mass distribution are implemented to show the effectiveness of this method. Essentially, the unbalance response of each concerned section is a synthesis of system difference coefficients and unbalance mass. Therefore, as weight coefficients of unbalance mass, the dispersion evaluation indexes of system difference coefficients can be used in distributing the original unbalance mass to further reduce the disturbance of system anisotropy to vibration reduction.

Vibration Characteristics of Unbalance Response for Motorized Spindle System

Vibration characteristics of unbalance response are the research basis for active balancing control, which is the important method of vibration monitoring and control. For the motorized spindles system, due to its complex structures, the analysis of dynamic characteristics caused by unbalance is difficult. The dynamic model of the motorized spindle system was built in this paper, and then a mathematical solution of the vibration response caused by unbalance was derived. A finite element model of the motorized spindle system was constructed based on the structural characteristics of it. The dynamic response characteristics caused by unbalance were simulated, which revealed the vibration transmission characteristics of spindle system and the regularity of variation under the effect of different types of unbalance. The results of the theoretical solution and numerical simulation both showed that, when the speed and damping is constant, the steady-state unbalance response of the motorized spindle system undergoes harmonic vibration with the same frequency as the rotating speed, and the amplitude of the vibrations is proportional to the mass of the unbalance. The conclusion provided a necessary theoretical guidance to active balancing and vibration control research in motorized spindle systems.

Analysis of the Dynamic Behavior of a Rotating Composite Hollow Shaft

In the present paper, a simplified homogenized beam theory is used in the context of a numerical investigation regarding the dynamic behavior of a rotating composite hollow shaft. For this aim, a horizontal flexible composite shaft and a rigid disc form the considered simple supported rotating system. The mathematical model of the rotor is derived from the Lagrange’s equation and the Rayleigh-Ritz method, which is obtained from the strain and kinetic energies of the disc and shaft, and the mass unbalance. In this case, a convergence procedure is carried out in terms of the vibration modes to obtain a representative model for the rotor system. Therefore, the proposed analysis is performed in both frequency and time domains, in which the frequency response functions, the unbalance responses, the Campbell diagram, and the orbits are numerically determined. Additionally, the instability threshold of the rotor system is obtained. This study illustrates the convenience of the composite hollow shafts for rotor dynamics applications.

Influence of Varnish on Bearing Performance and Vibration of Rotating Machinery

Varnish is a kind of fouling adhered on bearing inner face near the load zone. The model to analyze its influence on bearing performance and rotor vibration was set up. Pressure and temperature distribution were solved on the basis of the Reynolds equation by the iteration method simultaneously. It is found that bearing performance is changed by the step flow effect at the leading edge of the varnish. Its influence is more obvious when the rotating speed is low. Bearing varnish results in a large decrease of minimum clearance and an increase in the oil film temperature and pressure. Loading capacity of bearing is also decreased. It is harmful to the bearing. With the varnish, the minimum oil film thickness decreases. This leads to an increase of bearing stiffness and damping coefficients. Its influence is larger in the horizontal direction than that in the vertical direction. The trend of unbalance response to rotating speed is similar. There is little influence of the varnish on the modal frequency. However, system stability is improved due to the increased bearing damping coefficients.

A Method for Dynamic Analysis of Three-Dimensional Solid Element Rotors With Uncertain Parameters

Three-dimensional solid element models often with a great number of degrees-of-freedom (DOFs) are now widely used for rotor dynamic analysis. While without reduction, it will cost considerable calculating resources and time to solve the equations of motion, especially when Monte Carlo simulation (MCS) is needed for stochastic analysis. To improve the analysis efficiency, the DOFs are partly reduced to modal spaces, and the stochastic results (critical speeds or unbalance response) are expanded to polynomial spaces. First, a reduced rotor model is got by component mode synthesis (CMS), and the stochastic results are expanded by polynomial chaos basis with unknown coefficients. Then, the reduced rotor model is used to calculate the sample results to obtain the coefficients. At last, the expressions of the result by polynomial chaos basis are used as surrogate models for MCS. An aero-engine rotor system with uncertain parameters is analyzed. The accuracy of the method is validated by direct MCS, and the high efficiency makes it possible for stochastic dynamic analysis of complex engine rotor systems modeled by 3D solid element.

Sensorless active magnetic dampers for the control of rotors

The aim of this paper is to present self-sensing Active Magnetic Dampers (AMDs) for the vibration control of rotating machines and evaluate their performance and advantages with respect to standard sensed solutions. The technique is implemented on a rotor reproducing the typical dynamic behaviour of an aero-engine gas turbine shaft. The proposed technique is based on a Luenberger observer that estimates the mechanical states of the system. The observed states are fed back in closed-loop to introduce damping into the system and to reduce the vibrations during critical speed crossing. The rotordynamic and electromechanical modeling is illustrated taking into account the anisotropy of rotor elastic supports. The control design is described along with a sensitivity analysis on the most critical model parameters and a study of electromagnet nonlinear effects on the closed loop behaviour. The importance of the inherent collocation in the self-sensing configuration during control design is discussed analysing modal shapes and sensor/actuator transfer functions.A phase of experimental identification of actuator parameters is performed on the open-loop system response to improve the reliability of the model. The effectiveness of the proposed method is evaluated experimentally by measuring unbalance response in open and closed-loop configuration showing a reduction of displacement during critical speed crossing from 0.35mm to 0.04mm. Furthermore, a classical AMD realized with the use of position sensors is implemented on the same rotor. The results obtained with sensed and self-sensing controls are compared to show the good quality of the damping performance reached with the proposed self-sensing technique.

Dynamic analysis for the energy storage flywheel system

A subcritical or supercritical rotor is often employed to improve the energy storage efficiency of flywheel systems. Consequently, it is necessary to introduce Squeeze film dampers (SFD) in the rotor-bearing system to suppress the lateral vibration of the rotor. Although the dynamic behavior of the rotor-bearing system can be investigated in a timely manner with ANSYS software, it is difficult, if not impossible, to directly solve the unbalance responses by the Full method (FM) offered by ANSYS package. The reason is because the stiffness and the damping coefficients of the SFD, which are required in the computation, are in fact functions of eccentricity ratio determined by the unbalance responses. In this paper, the model of the flywheel system was firstly analyzed by QR damped method. Campbell diagram and critical speeds were then obtained from the results. Natural frequencies and their corresponding mode shapes at the rotational speed of 0.1rad·s-1 were also calculated. Then, the unbalance responses of rotor-bearing system with SFD support were solved through iteration and through the FM with ANSYS Parametric design language routine. The comparison between the calculated unbalance responses and the experimental responses indicates that the dynamic model is valid.