Rotor Bearing Research Articles

Diagnosing the Machine Set Rotor Using Its Relative Vibrations

The efficiency and dependability of machine set depends on the quality of maintenance of functional units of the machine set rotor. Diagnosing the functional units of the machine set can significantly increase the effectiveness and efficiency of the maintenance of the machine set. The purpose of the study was to substantiate the separation of the machine set rotor and demonstrate the possibility of diagnosing such a functional unit using non-contact measurements of its relative vibrations. The measure of the wear margin of the machine set rotor was analyzed, and the symptoms of this measure were examined. Finally, the configuration of the relative vibration sensors of the machine set rotor was investigated. Three models of the relationship between the wear margin measures and the measures of the machine set rotor symptoms were developed for the machine set rotor with a crankshaft supported in slide bearings. One new sensors head (shaft position sensors head) of the relative vibration of the machine set rotor was designed. In each machine set, the rotor of the machine set can be distinguished. The developed models of relationships and designed sensors head can be used as parts of the diagnostic system of the supported slide bearings rotor of the machine set with the crankshaft.

Online Unbalance Detection and Diagnosis on Large Flexible Rotors by SVR and ANN trained by Dynamic Multibody Simulations

Multiple-stage steam turbine generators, like those found in nuclear power plants, pose special challenges with regards to mechanical unbalance diagnosis. Several factors contribute to a complex vibrational response, which can lead to incorrect assessments if traditional condition monitoring strategies are used without considering the mechanical system as a whole. This, in turn, can lead to prolonged machinery downtime. Several machine learning techniques can be used to integrally correlate mechanical unbalance along the shaft with transducer signals from rotor bearings. Unfortunately, this type of machinery has scarce data regarding faulty behavior. However, a variety of fault conditions can be simulated in order to generate these data using computational models to simulate the dynamic response of individual machines. In the present work, a multibody model of a 640 MW steam turbine flexible rotor is employed to simulate mechanical unbalance in several positions along the shaft. Synchronous components of the resulting vibration signals at each bearing are obtained and utilized as training data for two regression models designed for mechanical unbalance diagnosis. The first approach uses an artificial neural network and the second one utilizes a support vector regression algorithm. In order to test their performance, the stiffness of each bearing in the multibody simulation was altered between 50% and 150% of the training model values, random noise was added to the signal and several dynamic unbalance conditions were simulated. Results show that both approaches can reliably diagnose dynamic rotor unbalance even when there is a typical degree of uncertainty in bearing stiffness values.

Simultaneous Identification of Free and Supported Frequency Response Functions of a Rotor in Active Magnetic Bearings

Frequency response functions (FRFs) of rotor systems can be used as indicator functions for condition monitoring. Component-wise FRFs are of high interest to locate errors in the case of defects. To enable continuous monitoring, measurements should be taken during operation. This contribution shows methods of using active magnetic bearings (AMBs) for simultaneously determining different FRFs of a rotor system. The AMBs, in addition to supporting the rotor, are used simultaneously as sensors and actuators. Two different types of FRFs, namely, the one associated with the free rotor and with the supported rotor can be determined from a single experiment. This procedure does not need any change in the assembly because the AMBs are simultaneously used as bearing and excitation device. Considering as excitation the total bearing force of the AMBs results in the FRF of the free rotor. The FRF of the supported system is determined by considering a perturbation force only, which is applied on top of the controlled AMB force. As a showcase, an academic rotor test rig is used with and without rotation to verify the applicability of the method. To evaluate and interpret the results of the experiments, a numerical model of the rotor using finite-element formulations is used.

Experimental and Numerical Investigation of Static and Dynamic Characteristics of Bio-Oils and SAE40 in Fluid Film Journal Bearing.

Mineral-based oils are the market leaders when it comes to their consumption in different types of rotating machines. Recently, a lot of attention has been given to the bio-oils and lubricants due to their better thermophysical, tribological, and environmental characteristics for use in journal bearing and other rotating machines. The superior physical properties of bio-oils have instigated this research in order to evaluate their dynamic characteristics that can cause the harmful dynamic instabilities in rotating machinery. The dynamic characteristics of the fluid film are influenced by temperature, eccentricity ratio, and rotational speed. In this work, the effect of temperature is experimentally measured on the dynamic viscosity of bio-oils and mineral-based oil. The dynamic viscosity measured is then computationally used to estimate the hydrodynamic pressure response of three bio-oils (rapeseed, palm olein, and soybean) and SAE40, a mineral-based oil, to check their performance in the rotor bearing system. It is found that at 40 °C, the hydrodynamic pressure for SAE40 is observed to be 2.53, 2.72, and 3.32 times greater than those of rapeseed, palm olein, and soybean oil, respectively, whereas, at 125 °C, the hydrodynamic pressure for SAE40 is observed to be 8% and 4.3% less than those of rapeseed and palm olein, respectively, but 14% greater than that of soybean oil. Hence, the increasing temperature has less effect on the viscosity and hydrodynamic pressure of bio-oils compared to SAE40. Therefore, for high-temperature applications, the bio-oils can be used with further processing. The superior response of bio-oils is also an indication for better dynamic characteristics.

Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment

The nonlinear dynamic effects of the misalignment between inner disks in a flawed–machining rod–disk rotor is studied. Non–uniform stress distribution due to inner misalignment is obtained based on 3D static solution. The concomitant unbalances, including constant mass eccentricity and speed–variant rotor bending, are taken into account in the nonlinear dynamics. The dynamic results show that rotor bending leads to stability reduction and vibration growth. There is a distinctive feature in that the rotor’s vibration goes up again after critical speed. The maximum allowable inner misalignment is obtained according to its stability boundaries. An uneven tightening method is also presented to reduce adverse effects when the inner misalignment exists. Moreover, an experiment is designed to measure the vibration characteristics for the rod–disk rotor bearing system with inner misalignment. The results show that the theoretical result of vibration amplitude of the flawed rod–rotor bearing system is basically consistent with the experimental value. It is also found that the precise rotor performs the periodic motion, but the flawed rod–disk rotor exhibits the period–doubling orbit. This phenomenon proves that the flawed rod–disk rotor loses stability more easily than the precise rotor due to inner misalignment. However, the amplitude of harmonic frequency components for the precise rod–disk rotor system is obviously larger than the flawed rod–disk rotor system with inner misalignment. The peak value of the vibration amplitude increases when the inner misalignment becomes larger. On the whole, this work presents numerical and experimental analysis to study the dynamics of flawed-machining rod–disk rotor with inner misalignment. It also establishes the relationship between centration precision and dynamic features.

Vibration control of a bi-disk rotor using electro-rheological elastomers

Smart materials are widely used for vibration control of rotating machines. This paper considers the control of vibration of a bi-disk rotor bearing system using electro-rheological elastomer (ERE) rings inserted in the bearings. The bi-disk rotor is selected so that vibration response can be studied in a rotating speed range which includes the first two critical speeds. The rotor bearing system is modelled using the finite element method taking into account the gyroscopic effect of the rotor and the internal damping of the shaft. The influence of the active elastomer when it is subjected to different levels of the electric field on the critical speeds is first investigated. Then, the vibration response is determined for both steady-state and transient running up and running down conditions. Simulation results show the potentials of the ERE when used in passive mode for vibration reduction in the steady-state and transient running up and down conditions of the rotor system. In the active mode, the application of an electric field to the EREs shifts slightly the resonant speeds to higher frequencies due to the increase of the stiffness of the bearings while increasing the vibration amplitudes in the steady-state and transient running up and down conditions in the vicinity of the resonant speeds. Nevertheless, it has been shown that the rotor steady-state vibration response can be reduced at other rotating speed range when an electric field is applied.

An Improved Resonant Controller for AMB-Rotor System Subject to Displacement Harmonic Disturbance

The controller contains harmonic components due to the detection error of the displacement sensor. The harmonic component acts on the magnetic bearing coil in the form of harmonic current, resulting in undesirable harmonic vibration force, which is not conducive to the microvibration control of active magnetic bearing (AMB) rotor system. In order to solve the problems of slow response speed and limited harmonic frequency range in series mode, an improved resonant controller in parallel mode is proposed in this article, which greatly improves the response speed of the system and the suppression effect at harmonic frequency. In addition, the gain and phase angle at each harmonic frequency can be adjusted, so the robustness of each harmonic frequency can be independently controlled, and the system stability can be guaranteed in a wide range of operating speeds. Finally, the effectiveness of the proposed algorithm is verified by simulation and experiment, which has important significance and application value for harmonic current suppression of AMB-rotor system.

Acoustic Fault Diagnosis of Rotor Bearing System

Early diagnosis of failures can prevent financial losses and industry downtime. In this article, the author proposes an early fault diagnosis technique for rotor-bearing faults. The proposed technique is based on the recognition of sound signals. The author measured and analyzed the three states of the rotor-bearing system: the rotor-bearing system under normal operating conditions, the rotor-bearing system with faulty bearings, and the rotor-bearing system with rotor friction. In this article, an original feature extraction method is described, namely, the 1/3 doubling method (a method of selecting the amplitude of the frequency ratio that is a multiple of 30% of the maximum amplitude). This method is used to form feature vectors. A classification of the obtained vectors was performed by the KNN (K-nearest neighbor classifier), the SVM (support vector machine), and the decision tree. The method is also compared with the Fourier synchrosqueezed transform. The experimental results show that the method can diagnose early faults of rotor-bearing systems simply and quickly and can be used to protect the safe operation of mechanical equipment.

Suppression of Harmonic Current in Magnetic Bearing–Rotor System with Redundant Structure

The magnetic bearing–rotor system has the advantages of no mechanical friction and active vibration control. A magnetic bearing with redundant structures provides an effective method to apply fault-tolerant control to the magnetic bearing–rotor system. In this paper, in order to improve the robustness of a rotor suspended by a magnetic bearing with redundant structures, the harmonic current suppression approach is proposed. Firstly, the generation mechanism of harmonic current in the magnetic bearing–rotor system is analyzed. Secondly, on the basis of the current distribution theory of magnetic bearing with redundant structures, the linearization model of electromagnetic force is established. Then, the eight-pole symmetrical radial magnetic bearing is taken as the research object, and the control system model with a multi-excitation disturbance source is established under the condition of no coil failure. Lastly, considering the periodicity of disturbance signals, a repetitive controller that is suitable for magnetic bearing with redundant structures is proposed in this paper, Moreover, in order to verify the effectiveness of the proposed control strategy, we inserted the repetitive controller into the original controller applied to the magnetically levitated rotor with redundant structures, and the corresponding simulation was carried out. The results demonstrate that the repetitive control method proposed in this paper can effectively suppress the harmonic current and improve the suspension accuracy of the rotor supported by the magnetic bearing with redundant structures.

A deep learning framework for adaptive compressive sensing of high‐speed train vibration responses

Onboard monitoring plays an important role in real-time condition assessment of rail systems. However, the data amount is typically tremendous due to the high sampling rate needed and long traveling distance, especially for vibration data collected from high-speed trains (HSTs). As for fault diagnosis of mechanical systems, compressive sensing (CS) has been increasingly adopted to reduce the data amount. In comparison to rotary bearings and bolted joints in machinery that operate in relatively steady working environments, HSTs run in an open and varying environment throughout the traveling mileage, and the data amount is normally much larger, making it tricky to directly apply the classical CS methods. This study aims to bridge the gap by investigating the sparsity of HST vibration signals and CS approaches. Considering the lack of sparsity and long reconstruction time, we propose an efficient adaptive CS approach for dynamic responses of HSTs. More specifically, we unroll the iterative soft thresholding algorithm (ISTA) in a deep learning (DL) framework and configure it into a data reconstruction machine. Compared to the conventional CS methods, our approach exhibits two advantages: (i) The dictionary learning and signal reconstruction are integrated into one neural network and can be conducted in an end-to-end manner; (ii) the process is highly efficient since encapsulating ISTA in a DL framework can naturally leverage the capability of GPU. The proposed approach is validated using data collected from an in-service HST, and results show that our approach achieves superior reconstruction performance over fixed bases and redundant dictionaries.

Active Disturbance Rejection Control in Magnetic Bearing Rotor Systems with Redundant Structures.

At present, magnetic bearings are a better energy-saving choice than mechanical bearings in industrial applications. However, there are strongly coupled characteristics in magnetic bearing–rotor systems with redundant structures, and uncertain disturbances in the electrical system as well as external disturbances, and these unfavorable factors degrade the performance of the system. To improve the anti-interference performance of magnetic bearing systems, this paper proposes the inverse of the current distribution matrix W−1 meaning that the active disturbance rejection control simulation model can be carried out without neglecting the current of each coil. Firstly, based on the working mechanism of magnetic bearings with redundant structures and the nonlinear electromagnetic force model, the current and displacement stiffness models of magnetic bearings are established, and a dynamic model of the rotor is constructed. Then, according to the dynamic model of the rotor and the mapping relationship between the current of each coil and the electromagnetic force of the magnetic bearing, we established the equivalent control loop of the magnetic bearing–rotor system with redundant structures. Finally, on the basis of the active disturbance rejection control (ADRC) strategy, we designed a linear active disturbance rejection controller (LADRC) for magnetic bearings with redundant structures under the condition of no coil failure, and a corresponding simulation was carried out. The results demonstrate that compared to PID+current distribution control strategy, the LADRC+current distribution control strategy proposed in this paper is able to effectively improve the anti-interference performance of the rotors supported by magnetic bearings with redundant structures.

Experimental and theoretical investigations of unbalance flexible rotor in active magnetic bearings considering backup bearings contacts

This paper describes the experimental verification of an unbalance flexible rotor model in active magnetic bearings. The dynamic modeling takes into account the gyroscopic moments of the disk, geometric coupling of the magnetic actuators, and contact forces of the backup bearings. The Rung–Kutta method is used to integrate the equations of motion. The nonlinear dynamic response is analyzed using bifurcation plots, disc center trajectories, Fast Fourier Transforms, Poincaré maps, and maximum Lyapunov exponent. The analysis is carried out for different values of rotating speed and unbalance eccentricity. In the unbalance test, a concentrated mass of 5 gr is attached in three radial position of the disk. The numerical simulations and experiments prove that a variety of nonlinear dynamical phenomena such as period -3, -4, -8, periodic, quasi-periodic, and chaotic motions occur in the system. The results indicate that the response of the rotor returns back to a regular motion by increasing the rotational speed. Also, by increasing the unbalance eccentricity, the first irregular motion initiates at much higher rotational speeds. Therefore, sufficient attention should be paid to these factors in design of a flexible rotor system equipped with both active magnetic bearings and backup bearings in order to ensure system reliability.

The effect of lubricating oil temperature on the stability of rubbing rotor-bearing system

Based on the interaction between oil film force and rub impact force of fault rotor bearing system, the nonlinear dynamic equation of rotor bearing system is established to explore the influence of lubricating oil temperature on system stability. The Runge-Kutta method was used to solve the dynamic equations to analyze the steady-state characteristics of the system. The bifurcation diagrams, frequency-waterfall diagrams, time-series diagrams, axis orbit diagrams, poincare map diagrams, frequency spectra dia-grams of the system at oil temperatures of 0 ° C, 40 ° C, 80 ° C were used to reveal the nonlinear behavior of the system. The results show that the temperature mainly affects the speed and amplitude of the oil whirl. When the speed increases to oil whirl, the vibration of the system is mainly oil whirl.

Crack detection methodology in rotor bearing system by DWT based adaptive neuro-fuzzy inference systems

Data-based machine learning methods in condition monitoring of high-speed rotors are gaining more importance due to the increase in computational speeds of computers in recent years. Machine learning methods can analyze and predict the behaviour of the system more accurately based on the methodology and truthfulness of trained data. The proposed research is a data-based crack detection technique in rotors based on Discrete Wavelet Transforms (DWT) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS). DWT based ANFIS is used to de-noise the response of rotor with open cracks. A methodology is proposed to effectively train and validate ANFIS to de-noise the signal with DWT noise information. Detail-1 of DWT on ANFIS de-noised response is used to identify the location and severity of the crack in the overhung rotor. Two separate ANFIS are proposed to identify crack location and crack depth from DWT detail-1 coefficients of ANFIS de-noised response. It is found that proposed DWT Based ANFIS de-noise the signal with Root Mean Square Error (RMSE) of 3.96 × 10−8, detects the crack location with RMSE of 0.1656 and depth of crack with the RMSE of 1.321.

Application of dimension analysis and soft competitive tool to predict compound faults present in rotor-bearing systems

Localized and distributed faults in machinery may lead to catastrophic failures of the high-speed rotor bearings. Unbalance and misalignment present generate massive vibrations in the rotor-bearing system. This paper demonstrates duo of the matrix method of dimensional analysis (MMDA) and support vector machine (SVM) to investigate unbalance and misalignment present in the rotor-bearing system. Experimentation with different conditions is performed and compared with numerical results to reveal the effectiveness of the approach. The SVM algorithm is used to classify multiple fault classes based on vibration characteristics predicted by the MMDA model. The results comparison shows that the present duo predicts and classifies the misalignment and unbalance with acceptable error and can be useful for industrial high-speed machine diagnosis.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ТЕПЛОВОЙ НАГРУЗКИ И КАВИТАЦИИ НА НЕСУЩУЮ СПОСОБНОСТЬ ПОДШИПНИКА ТУРБОКОМПРЕССОРА

The aim of the study is to research the thermal and high-speed operating conditions for the tendency of the formation and distribution of fields of the volume fraction of vapor, pressure and temperature in the lubricating layer of a radial bearing. In this work, the numerical simulation of hydrodynamic processes in the lubricant layer of a real design of a radial bearing of a turbocharger. To solve the problem, authors used numerical methods of calculation: the method of finite differences and the method of finite dimensions. The novelty of the work lies in determining the parameters of the cavitation model for oil and carrying out calculations on a real design of a journal bearing, taking into account the experimental results of thermometry. As a result, studies were obtained of the dependence of the change in the bearing capacity and volumetric vapor in the lubricating layer depending on the thermal state and the rotor speed. An assessment of the influence of thermal and speed modes on the bearing capacity of a turbocharger rotor bearing is carried out. The results obtained indicate an increase in the volume fraction of vapor with the rotor speed. In this case, the thermal state of the bearing affects the shape of the vapor distribution and the value of the bearing capacity in the lubricating layer.

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients.

The dynamic stiffness matrix (DSM) method, an analytical method that provides exact solutions, has been used for the first time for the free vibration analysis of a functionally graded (FG) rotor bearing system subjected to temperature gradients and to investigate its application to FG rotors. The material gradation occurs based on the power law between the inner metal core and the outer ceramic rich layer of the FG rotor. The temperature gradation follows the Fourier law of heat conduction which leads to non-linear temperature distribution (NLTD) in the radial direction of the FG rotor. The development of the DSM formulations for Timoshenko FG rotor elements using the governing equations derived from translational and rotational equilibrium conditions is the novelty of the present work. The DSM of the FG rotor elements, rigid disk and linear isotropic bearings are assembled to obtain the global dynamic stiffness matrix of the FG rotor bearing system. The natural whirl frequencies are computed from the global DSM using the Wittrick–William algorithm as a root searching technique. The natural and whirl frequencies are validated with the results available in the literature and the exactness of the DSM method has been exemplified.

Modeling and stability characteristics of bump-type gas foil bearing rotor systems considering stick–slip friction

Frictional energy dissipation inside the foil structure is considered as a key factor in improving the stability of the gas foil bearing (GFB) rotor system. However, the effect and mechanism of friction on the stability of bump-type GFB rotor systems have remained partially addressed. This study aims to develop a novel comprehensive model to investigate the stability and frictional dissipation mechanism of the GFB rotor system. The LuGre dynamic friction model is adopted to capture accurate stick–slip states. The model order reduction technique and simultaneous solution framework are applied to improve the computational efficiency. The effect of friction on linear and nonlinear stability is investigated based on the proposed model, and an analysis of frictional dissipation is performed to explain the mechanism. The results reveal that the dissipation capacity of the foil structure is directly governed by the stick–slip states that are affected by the friction coefficient and disturbance magnitude, so the optimal friction coefficient for nonlinear stability is higher than the one for linear stability of the GFB rotor system. A further comparison between different friction models greatly highlights the necessity of the ability of the friction model to capture accurate stick–slip states.

Control technology and development status of flywheel energy storage system

Flywheel energy storage technology has attracted more and more attention in the energy storage industry due to its high energy density, fast charge and discharge speed, long service life, clean and pollution-free characteristics. It is wwidely used in uninterruptible power system, grid frequency modulation, energy recovery and reuse and other fields. With the development of flywheel rotor materials, motors, bearings and control technology, flywheel energy storage technology has been greatly developed. Introducing the basic structure of the flywheel energy storage system in the above three applications. Typical charge-discharge control strategies are given for the three sensor-less algorithms of model reference adaptive control, sliding mode observer andextended Kalman filter, which are suitable for flywheel energy storage devices.

Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.