Rotor Mass Research Articles

Investigation of nonlinear dynamic behaviors of vertical rotor system supported by aerostatic bearings

Abstract A common issue associated with gas bearing-rotor systems is the tendency to generate self-excited vibrations, leading to instability. To address this problem, the fluid-structure coupling model of an aerostatic bearing-rotor system is established in this paper. Then a hybrid method combining the finite difference method and direct integration method, is employed to solve the bearing lubrication equation and rotor motion equation simultaneously. Furthermore, based on the orbit of rotor center,frequency spectrum diagram, Poincaré map, waterfall diagram and bifurcation diagram, the effects of rotational speed, rotor mass, orifice diameter and nominal clearance on the nonlinear dynamic behaviors of the bearing-rotor system are investigated. The results indicate that the system exhibits rich nonlinear behaviors with increasing rotational speed and rotor mass, including the occurrence of typical half-speed whirl. However, the nonlinear vibrations of the system can be restricted by selecting appropriate bearing structural parameters, providing theoretical guidance for the design of aerostatic bearing-rotor systems.

Effect of shaft deflection on the dynamic behaviors of the ceramic bearing rotor system within wide temperature ranges

The shaft deflection has great impact on the dynamic characteristics of the ceramic bearing rotor system, which cannot be ignored within wide temperature ranges. This paper establishes a model considering the shaft deflection, and the impact of shaft deflection appears along with changes in bearing attitude. The interaction between the various components of the bearing is recalculated, and the dynamic behavior of the full ceramic bearing rotor system in wide temperature ranges is obtained based on the thermal deformation difference. The trends of dynamic behaviors with rotor mass, rotation speed and shaft length-diameter ratio are investigated, and comparisons between simulation and experimental results are conducted for verification. It is found that the shaft deflection makes impact by bringing in extra centrifugal force, and the effects are reflected in frequency components and trajectories. The simulation results with shaft deflection fit well with the experimental results, which proves that the dynamic model considering the shaft deflection better illustrates the dynamic behavior of the ceramic outer ring when the contact situations change with working temperature. The research carries out deep insight into the running of ceramic bearing rotor system, and provides guidance for the improvement of dynamic behaviors in wide temperature ranges.

A SSA-based CFFOPID drop deloaded tidal turbine controller using HVDC-link

In contemporary scenario, electric power companies have observed upsurge in penetration level of tidal power plants (TPPs) in the traditional electric power system framework. However, the tidal turbines offer less frequency assistance due to their lesser rotor mass. Hence, TPPs may be collaborated with conventional units like diesel engine generator (DEG) to confirm system frequency stability in multi-area micro-grid system. The DEG comprises of primary and proportional integral derivative (PID) secondary frequency controls. However, in TPPs, to advance the system frequency regulation, deloading control approach is suggested and a cascade fuzzy fractional order PID-ID with derivative filter (CFFOPID-IDF) droop controller is suggested in place of the conventional non-cascade controller droop in the deloaded region. The suggested controller gains are fetched exploiting Salps swarm algorithm. For further enhancement of the dynamic responses, a precise high voltage direct current (AHVDC) link with the inertia emulation-based control (INEC) scheme is adopted, which allows the utilization of the gathered energy from the capacitance of the HVDC interface for frequency regulation. It provides better results compared to conventional AC tie line interface having less undershoot (34 %/20.63 %/43.75 %) and settling time (20.45 %/59.09 %/16.83 %) for variation in area-1 frequency/area-2 frequency/tie line power, respectively. The recommended control scheme is evidenced superior over numerous existing control techniques and provides least cost function in contrast to other control techniques. Additionally, it offers a highly stable performance under variable load conditions.

Genetically optimised SMOTE-based adversarial discriminative domain adaptation for rotor fault diagnosis at variable operating conditions

Abstract For safety, reliability, and uninterrupted output of gas turbines, aviation engines, power-generating equipment, pumps, gears, compressors etc., rotor mass imbalance must be detected and diagnosed to avoid catastrophic failure. Industry 4.0 relies on predictive digital maintenance and deep learning-based convolutional neural network (CNN), which predicts defects but fails if the operating conditions change. Research studies in various fields indicate that the domain shift issue occurs due to source and target samples being from different domains, which reduces prediction capability. Moreover, research studies are scarce in examining prediction capability under varying operating speeds for rotor mass imbalance. Hence, this research proposes the adversarial discriminative domain adaptation (ADDA) technique which predicts machine failures under various operational conditions. The efficacy of ADDA has been explored by introducing 1D-CNN as a source and a target encoder inside ADDA's architecture to take advantage of CNN's feature extraction capability. Further, this research effectively tackles CNN's inherent issues of overfitting and hyperparameters value selection. Furthermore, The real-world scenario has more healthy samples than fault condition samples, causing a multiclass imbalance in sample data, which affects the classification decision boundary and causes biased prediction. Hence, the proposed methodology first addresses the class imbalance through synthetic minority oversampling (SMOTE), then genetic algorithm optimizes 1D-CNN's hyperparameters, and the effective dropout layer positioning solves the overfitting. Finally, the deep learning-based SMOTE_ADDA_GO-1D-CNN decreases domain discrepancy with adversarial discriminative domain adaptation. The proposed methodology's efficacy has been explored through F1-Score, which is used as multiclass evaluation metrics, and it has been benchmarked against standard machine learning and deep learning algorithms. The test results of the proposed methodology surpassed all of them with maximum prediction accuracy. Thus, this study contributes to rotor mass imbalance detection and diagnosis for multiclass imbalanced data under varying operational conditions by successfully overcoming potential challenges during fault prediction.

Dynamic investigation of the electromechanical coupling system in a permanent magnet direct-drive locomotive under rotor eccentricity faults

In the traction system of a direct-drive locomotive, the gearbox design is eliminated, enabling the direct transmission of output torque from the traction motor to the wheelset. Due to this unique structure, rotor eccentricity, which is a common fault in traction motors, can have a direct impact on the dynamic performance of key components such as the motor, bogie, and wheelset in locomotives. In order to investigate the dynamic response of the direct drive locomotive under rotor eccentricity faults, a comprehensive electromechanical coupling model that considers the dynamic motion of the rotor is established in this paper. The coupling effect between the mechanical system and the electrical system, as well as the dynamic forces induced by rotor eccentricity, are taken into account in the model. The simulation results reveal that ripple torque has an obvious effect on rotor dynamics behaviour, while rotor air-gap eccentricity and mass eccentricity exhibit varying degrees of influence on the dynamic performance of the vehicle system. Furthermore, the influence laws of rotor eccentric distance on the vibration responses of critical locomotive components are revealed. These findings provide valuable theoretical guidance for the operational maintenance and fault diagnosis of traction motors in direct-drive locomotives.

Design of a Floating Vertical Axis Wind Turbine for Wind-Wave Basin Experiments

This paper presents the design and manufacturing of two novel small floating Darrieus vertical axis wind turbines (VAWT) developed for a wind-wave basin test campaign. As with typical designs, the rotor design needed to satisfy the traditional structural safety requirements (such as strain, deflection, resonant-free dynamics) from design standards along with other manufacturing and assembly constraints. In addition, for this particular design, some special conditions are present as the facility (the wind-wave basin itself) and use of existing Floating Offshore-wind and Controls Advanced Laboratory (FOCAL) semi-submersible floating platform (originally designed for HAWT test) imposed an additional set of design requirements including wind speed and size constraints, and specific, target overturning moments and rotor mass. Addressing all these constraints (facility, existing hull, structural safety, and manufacturing) presented a challenging design task in this case, thus the focus of this paper is presenting the design approach and results leading to final designs satisfying all these competing requirements. Using the presented design process, two Darrieus troposkein-shaped vertical axis wind turbines (two-bladed and three-bladed versions) were designed and manufactured, after ensuring compliance with all the design requirements. The presented study can aid researchers interested in developing similar floating turbine test campaigns.

Voting model prediction of nonlinear behavior for double-circumferential-slot air bearing system

Double-circumferential-slot air bearing (DCSAB) systems provide multidirectional supporting forces and have high stiffness, increasing the stability of instruments at high rotational speeds. However, DCSAB systems may exhibit chaotic motion because of a nonlinear pressure distribution within the gas film, supplied gas imbalances, or an inappropriate design. This study investigated the occurrence of nonperiodic motion in a DCSAB system by analyzing the dynamic response of systems with different rotor masses and bearing numbers. The dynamic trajectory, spectral response, bifurcation, Poincaré map, and maximum Lyapunov exponent were analyzed to identify chaotic behavior. Behavior was found to be highly sensitive to rotor mass and bearing number; the system exhibits chaotic behavior when the rotor mass has values in three intervals within 0.1–6.0 kg given a fixed bearing number of Λ = 3.8. To reduce the computational cost of predicting chaotic behavior, the maximum Lyapunov exponent was predicted using various machine learning models; a voting model combining random forest with XGBoost has the highest performance. The results can be used as a guideline for designing of DCASB systems for use in industrial applications.

Investigation of Lateral Vibrations in Turbine-generator Unit 5 of the Inga 2 Hydroelectric Power Plant

The article presents a case study on the Investigation of lateral vibrations in the turbine-generator unit 5 of the Inga 2 hydroelectric power plant in the Democratic Republic of the Congo. Lateral vibrations were experimentally determined using twelve proximity and eddy-current probes, positioned on each measurement plane. The results were analyzed using the Dasylab and R software. Hence, it was observed that the vibration amplitudes of the upper guide bearing, lower guide bearing, and pivot/rotor exceeded acceptable or critical limit values of the international vibration standard for a rotating speed between 100-250 rpm. These excesses can lead to rotor mass imbalances, the eccentricity of the rotor axis relative to the rotation axis of the shaft, and the deformation of the coupling shaft between the upper rotor shaft and the turbine rotor shaft. Subsequently, the means and the variances of the vibration amplitudes were evaluated and compared to the reference values of the international standard. The results of the compliance analysis revealed statistically significant differences between the measured amplitudes and the reference values. Thus, it indicates deviations from international specifications.

Nonlinear Dynamic Analysis and Forecasting of Symmetric Aerostatic Cavities Bearing Systems

Symmetric Aerostatic Cavities Bearing (SACB) systems have attracted increasing attention in the field of high-precision machinery, particularly rotational mechanisms applied at ultra-high speeds. In an air bearing system, the air bearing serves as the main support, and the load-carrying capacity is not as high as that of oil film bearings. However, the aero-spindle can operate at considerably high rotational speeds with relatively lower heat generated from rotation compared with that of oil film bearings. In addition, the operating environment of air bearings does not easily cause the rotor to deform. Hence, through adequate design, air pressure systems exhibit a certain level of stability. In general, the pressure distribution function of air bearings exhibits strong nonlinearity when there are changes in the rotor mass or rotational speed, or when the bearing system is inadequately designed. These issues may lead to instabilities in the rotor, such as unpredictable nonperiodic movements, rotor collisions, or even chaotic movements under certain parameters. In this study, rotor oscillation was analyzed using the maximum Lyapunov exponent to identify whether chaotic behavior occurred. Machine learning methods were then used to establish models and predict the rotor behavior. Especially, random forest and extreme gradient boosting were combined to develop a new model and confirm whether this model offered higher prediction performance and more accurate results in predicting tendencies with considerable changes compared with other models. The results can be effectively used to predict the SACB system and prevent nonlinear behavior from occurring.

Performance analysis of genetically optimized 1D-convolutional neural network architecture for rotor system fault detection and diagnosis

Rotor mass imbalance is a critical problem in industries, which can lead to a breakdown or a catastrophic failure if unattended. Hence, Industry 4.0 uses deep learning approaches like convolutional neural network (CNN) for rotor fault detection and diagnosis of Industrial machines and turbomachinery where multifunctional structures are used. In machinery fault diagnosis, manual tuning of CNN hyperparameters is widely used, which is a tedious, time-consuming, and challenging task to achieve effective feature extraction. Additionally, overfitting of CNN during its training is an obstacle to achieving higher prediction accuracy. Hence, to address these issues, this research focuses on multi-class mass imbalance fault diagnosis using genetically optimized deep learning architecture of 1D-CNN to achieve higher diagnosis capability. The performance of the proposed methodology is evaluated through various case studies using experimental data from the in-house developed test rig. The test results are compared against various 1D-CNN architectures in which the hyperparameters and effective dropout layer positioning are genetically optimized. Also, the performance is benchmarked against standard machine learning algorithms. The results show that genetic algorithm (GA)-optimized 1D-CNN with dropout achieves highest fault prediction accuracy of 97.47% with reduced depth of CNN (with three convolution layers) compared to 84.16% of manually tunned CNN architecture (with seven convolutional layers) and outperformed standard machine learning algorithms. Best drop positioning (end of feature extraction part) reduced the learnable parameters to 95.9% with the highest prediction accuracy of 97.47% compared to adding dropout at all the CNN layers. The proposed GA-optimized 1D-CNN with effective dropout positioning eliminates human intervention and reduces the depth of CNN architecture; this, in turn, reduces computational load and time by reducing learnable parameters of CNN (network weights) with the highest prediction accuracy. Hence, the proposed approach shows promise in enhancing the performance and contributing to the advancement of 1D-CNN for rotor system fault detection and diagnosis.

Nonlinear vibration control of magnetic bearing system considering positive and negative stiffness

The nonlinear dynamics are studied for an active magnetic bearing (AMB) system under the low-frequency sinusoidal excitation, which can affect the operational stability of a high-speed magnetic bearing. A single-degree-of-freedom nonlinear dynamics model of magnetic bearing was developed with a c-type active magnetic bearing as the research target. The characteristics of the magnetic bearing system show positive and negative stiffness for different feedback gains. The amplitude–frequency response curves of the vibration characteristics of the positive stiffness magnetic bearing system were obtained by using the method of multiple scales. The influence of each parameter on the resonance amplitude and nonlinearity of the magnetic bearing system is understood by analyzing the amplitude–frequency response curve. The bifurcation diagram for the rotor with rotor mass, and control parameters is derived from the numerical simulation of the negative stiffness magnetic bearing system. The parameter intervals that cause single-cycle vibration, double-cycle vibration, and chaotic state of the magnetic bearing rotor are discovered by analyzing the bifurcation diagrams of each parameter. The simulation results show that the magnetic bearing system exhibits complex nonlinear dynamic characteristics when it is a negative stiffness system.

Design and Analysis of a Novel Electromagnetic-Propulsion Rotary Machine With External Blending-Shaped Tessellation Magnet Pattern

One major challenge for the design of rotary machine of electric propulsion aircraft is how to improve its torque output and power density. The objective of this paper is to propose a novel external blending-shaped tessellation (EBT) magnet pattern for electromagnetic rotary machine. It can offer several advantages. First, it helps to increase the magnetic flux density in the airgap, and thus the torque output of the rotary machine is increased. Second, it enhances the self-shielding effect greatly, and thus the back iron can be removed completely and replaced with low-density materials. As a result, the rotor mass can be reduced and the system dynamics could be improved. Third, the improved torque and the reduced mass may contribute to the high power density as well. The design concept and operating principle of the proposed external blending-shaped tessellation magnet pattern are presented. Following that, the magnetic field distribution is formulated analytically through Laplace's and Poisson's equations. Then the torque generation of the rotary machine is modeled mathematically. Subsequently, the numerical simulation is conducted to validate the analytical models of the magnetic field distribution and torque output. The magnetic flux density and torque output of the proposed magnet pattern are compared with those of conventional magnet arrays. A research prototype of the electric rotary machine with the EBT magnet pattern is developed, and an experimental test platform is constructed. Experiments are conducted on the magnetic flux density and torque output to verify the proposed design and analytical models. The experimental results validate the derived analytical model of magnetic field and the output torque, and the effectiveness of the magnet array in improving the output characteristic. It shows that the output torque generated by the proposed design is larger than that of conventional Halbach array by 27 percent.

LSTM Neural Networks Using the SMOTE Algorithm for Wind Turbine Fault Prediction

Abstract This work proposes a method using a long short-term memory neural network as a diagnostic tool to detect wind turbine rotor mass imbalance. The method uses the synthetic minority oversampling technique for data augmentation in an unbalanced dataset. For this purpose, a 1.5 MW three-bladed wind turbine model was simulated at Turbsim, FAST, and Matlab Simulink to generate rotor speed data for different scenarios, simulating different wind speeds and creating a mass imbalance by changing the density of the blades in the software. Features extraction and power spectral density were also used to improve the Neural Network results. The results were compared to nine different classifiers with four different combinations of datasets and demonstrated that the technique is promising for mass imbalance detection.

An Efficient Computational Analysis and Modelling of Transferred Aerodynamic Loading on Direct-Drive System of 5 MW Wind Turbine and Results Driven Optimisation for a Sustainable Generator Structure

The study presents an efficient computational investigation on the behaviour of the direct-drive system integrated into the offshore 5 MW NREL wind turbine model under demanding aerodynamic loading conditions with the aim of optimising and developing more sustainable key structural components. The research was based on computational simulation packages in order to verify the use of real-world wind data and the loading conditions on the blade structures through aero-elastic simulation studies as well as analyse the behaviour of the drive system. Through the application of validated aerodynamic loading conditions, resulting normal forces on the blades structure were obtained and applied to a dedicated simplified model that was also previously validated to estimate the transferred loads into the powertrain. The adopted methodology allowed for the identification of shaft misalignment induced air gap eccentricity. The impact of shaft deflections on resulting magnetomotive force was considered by making use of the Maxwell stress distribution expression. By taking into account the resulting loading cases on the generator structure, as well as the inherent typical loads generated by the electrical machine, a procedure including structural parametric and topology optimisation was developed and performed, achieving a rotor mass reduction between 8.5 and 9.6% compared to the original model.

Induction Motor Vibrations Caused by Mechanical and Magnetic Rotor Eccentricity

Vibration reduction of induction motors is a significant problem that requires effective models for the effects of mechanical and electromagnetic unbalanced forces. This article presents a mathematical model of dynamics for induction motors with rotor mass eccentricity and static and dynamic magnetic eccentricity. The model allows for the influence of the gyroscopic torque of the rotor and considers the elastic-damping characteristics of each of the stator supports and their location. The model has eight degrees of freedom, which makes it possible to simulate transverse and axial vibrations of various designs’ rotors and housings of induction motors. The results of modeling the dynamics for a three-phase squirrel cage induction motor with 11 kW capacity agreed with those obtained by other authors. Simultaneously, new results were also obtained within the research. The simulation results showed that the static magnetic eccentricity causes the appearance of additional critical speed of the motor, and its value decreases in proportion to the growth of the number of pole pairs. The change of the moment of inertia of the motor at a mismatch of the main axis of symmetry of the stator and the rotor axis of rotation allowed for obtaining an actual frequency spectrum of free oscillations, including the rotational motion of the stator. Since the actual static magnetic eccentricity can additionally increase at operating frequencies due to the increase of bearing clearance caused by dynamic unbalanced load, it should be considered in the analysis of unbalanced magnetic pull. The angle of static magnetic eccentricity significantly affects the magnitude of radial vibrations. This feature should also be considered when selecting the locations of balancing weights during the rotor balancing procedure.

Nonlinear Dynamic Analysis on Dual‐Rotor‐Bearing‐Casing System for Marine Gas Turbine

Taking the marine gas turbine as a research background, a dual‐rotor‐bearing‐casing system model was established considering the bearing nonlinearities and unbalanced excitation. Based on Lagrange’s equation of motion and rotor dynamics theory, the effects of key parameters such as radial clearance of intershaft bearing, rotor mass eccentricity, and rotational speed on the nonlinear characteristics of the system are investigated. The results indicate that the typical parameters have a significant effect on the system’s nonlinearities. To alleviate the vibration jump phenomenon, the radial clearance should be reduced to improve the coupling between the high‐ and low‐pressure rotors. Reducing the mass eccentricity can effectively degrade the resonance peaks, but it will highlight the hard resonance characteristics. The work process should pass through the resonant‐speed regions and the low‐speed regions of start‐stop phase as soon as possible. The research findings contribute to understanding the nonlinear dynamic characteristics of dual‐rotor systems, providing a theoretical basis for their stable operation and the optimal design of working speeds.

Synchronous disturbance suppression of active magnetic bearing rotor systems using variable period adaptive control algorithm

This paper aims to investigate the issue of suppressing synchronous vibration in active magnetic bearing (AMB) systems. The rotor mass imbalance is a challenging problem for the AMB system, which will cause synchronous vibration and severely affect the system stability and safety. However, existing algorithms based on the iterative feed-forward control strategy find it difficult to simultaneously ensure system’s stability and competent convergence performance. They struggle to maintain tolerable robustness within the system operating bandwidth. This paper proposes a variable period adaptive control algorithm to address these challenges. The overall control scheme can achieve current and displacement elimination separately by switching control structures and is applicable to variable speed conditions. This algorithm can adaptively adjust the iteration period based on rotational speed to ensure both splendid convergence performance and system dynamic performance. Furthermore, this work employs the Lyapunov method to analyze the algorithm’s asymptotic stability and provides a lookup table for algorithm parameters. This could significantly enhance the robustness and stability of the algorithm within the system operating bandwidth. Finally, this methodology has proven to be effective and superior in simulations and experiments.

Aerodynamic rotor design for a 25 MW offshore downwind turbine

Continuously increasing offshore wind turbine scales require rotor designs that maximize power and performance. Downwind rotors offer advantages in lower mass due to reduced potential for tower strike, and is especially true at large scales, e.g., for a 25 MW turbine. In this study, three 25 MW downwind rotors, each with different prescribed lift coefficient distributions were designed (chord, geometry, and twist) and compared to maximize power production at unprecedented scales and Reynolds numbers, including a new approach to optimize rotor tilt and coning based on aeroelastic effects. To achieve this objective the design process was focused on achieving high power coefficients, while maximizing swept area and minimizing blade mass. Maximizing swept area was achieved by prescribing pre-cone and shaft tilt angles to ensure the aeroelastic orientation when the blades point upwards was nearly vertical at nearly rated conditions. Maximizing the power coefficient was achieved by prescribing axial induction factor and lift coefficient distributions which were then used as inputs for an inverse rotor design tool. The resulting rotors were then simulated to compare performance and subsequently optimized for minimum rotor mass. To achieve these goals, a high Reynolds number design space was developed using computational predictions as well as new empirical correlations for flatback airfoil drag and maximum lift. Within this design space, three rotors of small, medium and large chords were considered for clean airfoil conditions (effects of premature transition were also considered but did not significantly modify the design space). The results indicated that the medium chord design provided the best performance, producing the highest power in Region 2 from simulations while resulting in the lowest rotor mass, both of which support minimum LCOE. The methodology developed herein can be used for the design of other extreme-scale (upwind and downwind) turbines.

Modeling of a Digital Twin for Magnetic Bearings

As an essential enabling technology to realize advanced concepts such as digitization, intelligence, and service, information technology plays a critical role in shaping modern society and driving innovation across various industries and domains. The concept of the digital twin is attracting attention from academics and industry, and how to apply it in various fields. In this paper, the performance of the magnetic bearing system may be simulated in real-time using a digital twin, especially the resulting vibration from the unbalanced rotor mass, which caused a drop in performance and a high risk of system instability and potential safety accidents. It is suggested to use a model-data combination driven digital twin model to examine its dynamic characteristics and vibration mechanism. The vibration data of the magnetic bearing was collected through experiments and compared with the data derived from the simulation results. The efficiency of the suggested strategy is demonstrated by confirming that digitally anticipated vibration signals are consistent with physical space measurements. The result shows that the fine digital twin geometric model of magnetic bearing is more consistent with the actual operation. By allowing the identification of problems before they become critical, using a digital twin may increase the dependability of magnetic bearings while reducing the possibility of unexpected downtime or failures.

ГИДРОДИНАМИКА РОТОРНОГО ДИСКОВОГО АБСОРБЕРА

The hydrodynamics of a new rotary mass transfer apparatus is considered. It is shown that the most important hydrodynamic characteristics of the apparatus operation are: the average drop diameter, the initial drop velocity, the drop rise time, the drop rise height