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Rotating systems are essential components and play a critical role in many industrial sectors. Unbalance is a very common and serious fault that can cause machine downtime, unplanned maintenance, and potential damage to vital rotating machines. Accurately estimating unbalance in rotor–bearing systems is crucial for ensuring the reliable and efficient operation of machinery. This research paper presents a novel approach utilizing artificial neural networks (ANNs) to estimate the unbalance masses in a multidisk system based on simulation data from a nonlinear rotor–bearing system. Additionally, this study explores the effect of various operating parameters on oil film stability and vibration response through a combination of bifurcation diagrams, spectrum cascades, Poincare maps, and orbit and FFT plots. This study demonstrates the effectiveness of ANNs for unbalance estimation in a fast and accurate way and discusses the potential of ANNs in smart online condition monitoring systems. [ABSTRACT FROM AUTHOR]

Rotor dynamics plays a crucial role in the performance and safety of rotating machinery, with disk position and unbalance significantly impacting system behavior. This study investigates the dynamic characteristics of two rotor configurations: a centrally mounted unbalanced disk (Rotor05un) and an off-center unbalanced disk (Rotor025un). Using numerical simulations and Monte Carlo analysis, we examined critical speeds and orbital patterns for both configurations. Probability distributions of shaft orbital positions revealed distinct patterns for each configuration. Quantile analysis revealed approximate linear trends for Rotor025un, suggesting higher system stiffness and more predictable behavior near critical speeds. Cross-sectional analyses of the orbits provided insights into the complex interactions between disk position, gyroscopic effects, and system natural frequencies. These findings provide valuable insights for rotor system design, particularly for applications with non-ideal mass distributions. The study goes beyond traditional critical speed analysis to examine orbital patterns and point on orbit occurrence from a probabilistic perspective. Based on the simulation of the orbits, an orbital is determined that allows the probability of the shaft occurring at the analyzed distance from the origin to be determined. The paper also offers insights into the complex interaction behavior of chosen rotor configurations and highlights the importance of considering disk position in predicting and optimizing rotor dynamic behavior, contributing to the development of more robust and efficient rotating machinery. [ABSTRACT FROM AUTHOR]

A comprehensive theoretical investigation on the occurrence of secondary resonances in parametrically excited unbalanced spinning composite beams under the stretching effects is conducted numerically and analytically. Based on an optimal stacking sequence and Rayleigh’s beam theory, the governing equations of the system are derived using extended Hamilton’s principle. The system’s partial differential equations are then discretized using the Galerkin method. Numerical (Runge–Kutta technique) and analytical (multiple scales method) approaches are exploited to solve the reduced-order equations, and their results are compared and verified accordingly. Comparison and convergence investigations are performed to guarantee the validity of the outcomes. Stability and bifurcation analyses are accomplished, and resonance effects are thoroughly studied utilizing frequency-response diagrams, phase portraits, Poincaré maps and time-history responses. It is observed that among the various types of secondary resonance, only a combination resonance can be observed in the system dynamics. The outputs reveal that, in this resonance, the gyroscopic coupling results in the steady-state time response consisting of three main frequencies. By examining the effects of damping, eccentricity, and beam length, it is exhibited that this resonance does not occur in the system’s dynamics for any combination of these parameters. Therefore, these parameters can be adjusted in the design of asymmetric beams to prevent this type of resonance. [ABSTRACT FROM AUTHOR]

This paper reports the preliminary experimental studies carried out on an innovative sliding bearing made of polycrystalline diamond, a material with excellent mechanical and chemical characteristics, used mainly in the drilling industry. Bearings crafted from this material do not necessitate lubrication due to their extremely low coefficient of friction and high resistance to wear. For this reason, they are prime candidates for replacing traditional oil bearings, eliminating the need for auxiliary systems and thereby reducing environmental risks. In this regard, an innovative test rig was designed, capable of reaching speeds up to 6000 rpm both in vertical and horizontal configurations thanks to a novel tilting frame. Moreover, with a high modularity it was possible to test three different kinds of radial PCD bearings. Dynamic data were acquired and elaborated to evaluate orbits, acceleration and absorbed torque, to finally compare these different configurations to better understand how dynamic behavior is influenced by bearings' geometrical characteristics. [ABSTRACT FROM AUTHOR]

This paper reports the preliminary experimental studies carried out on an innovative sliding bearing made of polycrystalline diamond, a material with excellent mechanical and chemical characteristics, used mainly in the drilling industry. Bearings crafted from this material do not necessitate lubrication due to their extremely low coefficient of friction and high resistance to wear. For this reason, they are prime candidates for replacing traditional oil bearings, eliminating the need for auxiliary systems and thereby reducing environmental risks. In this regard, an innovative test rig was designed, capable of reaching speeds up to 6000 rpm both in vertical and horizontal configurations thanks to a novel tilting frame. Moreover, with a high modularity it was possible to test three different kinds of radial PCD bearings. Dynamic data were acquired and elaborated to evaluate orbits, acceleration and absorbed torque, to finally compare these different configurations to better understand how dynamic behavior is influenced by bearings’ geometrical characteristics.

Real-world rotordynamic systems exhibit inherent uncertainties in manufacturing tolerances, material properties, and operating conditions. This study presents a Monte Carlo simulation approach using MSC Adams View and Adams Insight to investigate the impact of these uncertainties on the performance of a Laval/Jeffcott rotor model. Key uncertainties in bearing damping, bearing clearance, and mass imbalance were modeled with probabilistic distributions. The Monte Carlo analysis revealed the probabilistic nature of critical speeds, vibration amplitudes, and overall system stability. The findings highlight the importance of probabilistic methods in robust rotordynamic design and provide insights for establishing manufacturing tolerances and operational limits. [ABSTRACT FROM AUTHOR]

Gas foil bearings are particularly suitable for supporting rotors of hydrogen fuel cell air compressors. Based on Reynolds equation and elastic mechanics theory, a fluid-structure interaction model of gas foil bearings is introduced. A series of perturbation equations are developed and solved to obtain stiffness and damping coefficients of the foil bearings at different rotational speeds. A lumped model of the bearing-rotor system is developed and the rotor stability is analysed by innovatively applying Riccati transfer matrix method. The natural frequencies of the rotor are calculated and then the Campbell diagram is plotted. Subsequently, the critical speeds and the corresponding vibration modes are obtained. The predicted values of the proposed model are highly consistent with the reported experimental results and finite element results, indicating the accuracy of the model. Based on the calculation of rotor unbalance response, further investigation on the effects of unbalance parameters on unbalance response is conducted. The results obtained in this paper could provide theoretical reference for the design of foil bearing supported rotors. [ABSTRACT FROM AUTHOR]

Hydropower generators withstand multiple forces from diverse sources during operation. To ensure their stability and safe performance, numerical tools are developed to characterize their dynamic properties. Traditionally, generators are assumed to be rigid in rotordynamic analyses. However, the measurements in power stations challenge this assumption. This article proposes a novel approach to modeling hydropower generators with floating rotor rims using a three-dimensional (3-D) Finite Element Method, aiming to study their dynamic performance and properties, including natural frequencies, the modes of vibrations, and expansion due to centrifugal and electromagnetic forces, with the goal of improving the reliability of modern designs. Both this approach and employing a two-dimensional (2-D) model using curved beams result in similar in-plane natural frequencies and the expansion of the rotor rim due to centrifugal forces. However, the 3-D model can be used to calculate the out-of-plane natural frequencies and modes, to model the dynamics of complex geometries, and to perform stress evaluation and fatigue analysis. [ABSTRACT FROM AUTHOR]

Rotating systems are essential components and play a critical role in many industrial sectors. Unbalance is a very common and serious fault that can cause machine downtime, unplanned maintenance, and potential damage to vital rotating machines. Accurately estimating unbalance in rotor–bearing systems is crucial for ensuring the reliable and efficient operation of machinery. This research paper presents a novel approach utilizing artificial neural networks (ANNs) to estimate the unbalance masses in a multidisk system based on simulation data from a nonlinear rotor–bearing system. Additionally, this study explores the effect of various operating parameters on oil film stability and vibration response through a combination of bifurcation diagrams, spectrum cascades, Poincare maps, and orbit and FFT plots. This study demonstrates the effectiveness of ANNs for unbalance estimation in a fast and accurate way and discusses the potential of ANNs in smart online condition monitoring systems.

Rotor dynamics plays a crucial role in the performance and safety of rotating machinery, with disk position and unbalance significantly impacting system behavior. This study investigates the dynamic characteristics of two rotor configurations: a centrally mounted unbalanced disk (Rotor05un) and an off-center unbalanced disk (Rotor025un). Using numerical simulations and Monte Carlo analysis, we examined critical speeds and orbital patterns for both configurations. Probability distributions of shaft orbital positions revealed distinct patterns for each configuration. Quantile analysis revealed approximate linear trends for Rotor025un, suggesting higher system stiffness and more predictable behavior near critical speeds. Cross-sectional analyses of the orbits provided insights into the complex interactions between disk position, gyroscopic effects, and system natural frequencies. These findings provide valuable insights for rotor system design, particularly for applications with non-ideal mass distributions. The study goes beyond traditional critical speed analysis to examine orbital patterns and point on orbit occurrence from a probabilistic perspective. Based on the simulation of the orbits, an orbital is determined that allows the probability of the shaft occurring at the analyzed distance from the origin to be determined. The paper also offers insights into the complex interaction behavior of chosen rotor configurations and highlights the importance of considering disk position in predicting and optimizing rotor dynamic behavior, contributing to the development of more robust and efficient rotating machinery.

In this paper, the design of a large-scale axial turbine operating with supercritical carbon dioxide (sCO2) blended with sulfur dioxide (SO2) is presented considering aerodynamic and mechanical design aspects as well as the integration of the whole turbine assembly. The turbine shaft power is 130 MW, designed for a 100 MWe concentrated-solar power plant with turbine inlet conditions of 239.1 bar and 700 °C, total-to-static pressure ratio of 2.94, and mass-flow rate of 822 kg/s. The aerodynamic flow path, obtained in a previous study, is first summarized before the aerodynamic performance of the turbine is evaluated using both steady-state and unsteady three-dimensional numerical models. Whole-annulus unsteady simulations are performed for the last turbine stage and the exhaust section to assess the unsteady loads on the rotor due to downstream pressure field distortion and to assess the aerodynamic losses within the diffuser and exhaust section. The potential low engine order excitation at the last rotor stage natural frequency modes due to downstream pressure distortion is assessed. The design of the turbine assembly is constrained by current manufacturing capabilities and the properties of the proposed working fluid. High-level flow-path design parameters, such as pitch diameter and number of stages, are established considering a trade-off between weight and footprint, turbine efficiency, and rotordynamics. Rotordynamic stability is assessed considering the high fluid density and related cross coupling effects. Finally, shaft end sizing, cooling system design, and the integration of dry gas seals are discussed. [ABSTRACT FROM AUTHOR]

In 2015, a 45 MW vertical hydropower machine exhibited excessive vibration after refurbishment. Measurements revealed a substantial bearing clearance at the lower generator guide bearing. Consequently, the bearing was unable to generate sufficient opposing force to drive the rotor toward the bearing center, resulting in more pronounced overall system vibration. Addressing this challenge required a cost-effective and feasible solution for mitigating the vibration problem. To this end, a design modification was implemented wherein the lower generator guide bearing (originally a sleeve bearing) was modified to a four-lobe bearing by offsetting the two halves of the bearing twice in two axes. Numerical simulations and experimentations were conducted, and the dynamics of the machine before and after the design modification were investigated. Both the simulation and experimental results showed that the machine with the four-lobe bearing improved the system stability and reduced the vibration amplitudes. The numerical simulation result demonstrated that, due to the design modification, the first and second critical speeds were effectively eliminated for a speed range of up to three times the nominal speed. Furthermore, for nominal operation with unbalanced magnetic pull, the four-lobe bearing provided a stability advantage in terms of the modal parameters relative to the original sleeve bearing. [ABSTRACT FROM AUTHOR]

AbstractThe dynamic response of various rotating stiffened cylindrical and disk structures has been performed using low- and high-fidelity two-dimensional finite element models. The methodology is based on the Carrera Unified Formulation, in which the shell models are obtained hierarchically and automatically. These theories are formulated by expanding the unknown variables over the shell thickness. Various shell models can be implemented depending on the choice of the polynomial employed in the expansion. Lagrange polynomials are considered for developing different kinematic models and for easily modeling the stiffeners. The stiffener deformation is precisely captured through higher-order models, and the mechanical continuity between the stiffeners and skin is automatically guaranteed at the Lagrange points. The linearized equations of motion include the Coriolis and initial stress contributions. Stiffened cylinders and disks with different boundary conditions are considered. The results are compared with the three-dimensional finite element solutions from the literature or obtained using commercial software. [ABSTRACT FROM AUTHOR]

This work investigates the dynamic response of various rotating cylindrical structures using low- and high-fidelity one-dimensional (1D) and two-dimensional (2D) finite element models. The adopted mathematical formalism is based on the Carrera Unified Formulation (CUF). CUF offers a procedure to obtain higher-order beam and shell models hierarchically and automatically. These theories are formulated by expanding the unknown variables over the beam cross-section or along the shell thickness. Various beam and shell models can be implemented depending on the choice of the polynomial employed in the expansion. Both Taylor-like and Lagrange polynomials are considered for developing different kinematic models. The linearized equations of motion include the Coriolis and initial stress contributions. Various thick and thin cylinders and disk structures with different boundary conditions are considered. The beam and shell results are compared with analytical and three-dimensional (3D) finite element (FE) solutions from the literature. [ABSTRACT FROM AUTHOR]

Gas foil bearings are gaining popularity for their compliance properties in various high-speed turbomachinery applications such as air cycle machine, turbocompressor, turbocharger, turboexpander etc. A modest attempt is made in the current research to study the feasibility of gas foil bearing for a turboexpander rotating at 1,75,000 rpm. The turboexpander rotor with 16 mm diameter and 91 mm length used for experimentation is supported by a pair of gas foil journal bearings and mounted with turbine and compressor wheels at both ends of the rotor. The feasibility study was performed based on comparison of rotodynamic analysis and experimental data for the critical speed of the rotor and unbalance response at bearing locations. The critical speeds and the unbalance response are predicted using the finite element analysis, which takes into account the gyroscopic effect, shear deformation, internal damping, inertia of the rotor and the dynamic coefficients of the gas foil bearing. The predicted and experimental variation of critical speed is found to be within a relative error of 3–6%; similarly, the variation of unbalance response was found with a relative error of 2–9%. The low relative errors suggest that the experiment and prediction methodology are credible. The author believes that the rotodynamic analysis methodology will be quite valuable for researchers working in the area of high-speed rotors supported with gas foil bearings. [ABSTRACT FROM AUTHOR]

Foil air bearings (FABs) are the mainstay of oil-free turbomachinery technology which is undergoing rapid expansion. A rotor system using such bearings is a nonlinear multi-domain dynamical system comprising the rotor, the air films and the foil structures. Multi-pad (segmented) FABs offer opportunity for enhanced stability performance but are naturally more computationally challenging than single (360°) pad FABs. Their analysis has been limited to a simple model that ignores the detachment of the top foil from the underlying foil. Although a correction can be applied for the rotor vibration, the actual top foil deflection cannot be predicted. Additionally, reduced order modelling techniques have so far not been applied to such bearings. This paper presents the nonlinear and linearised dynamic analyses of three-pad FAB rotor systems considering foil detachment and using both Galerkin Reduction (GR) and Finite Difference (FD) to model the air film. Various models for the force distribution on the top foil are considered for use within a bilinear foil model, focusing on the ability to achieve numerical convergence. GR halved the computation time for a waterfall graph, without compromising the accuracy of the prediction of the nonlinear response. The results are validated against results from the literature. [ABSTRACT FROM AUTHOR]

Real-world rotordynamic systems exhibit inherent uncertainties in manufacturing tolerances, material properties, and operating conditions. This study presents a Monte Carlo simulation approach using MSC Adams View and Adams Insight to investigate the impact of these uncertainties on the performance of a Laval/Jeffcott rotor model. Key uncertainties in bearing damping, bearing clearance, and mass imbalance were modeled with probabilistic distributions. The Monte Carlo analysis revealed the probabilistic nature of critical speeds, vibration amplitudes, and overall system stability. The findings highlight the importance of probabilistic methods in robust rotordynamic design and provide insights for establishing manufacturing tolerances and operational limits.

A common problem in transient rotordynamic simulations is the numerical effort necessary for the computation of hydrodynamic bearing forces. Due to the nonlinear interaction between the rotordynamic and hydrodynamic systems, an adequate prediction of shaft oscillations requires a solution of the Reynolds equation at every time step. Since closed-form analytical solutions are only known for highly simplified models, numerical methods or look-up table techniques are usually employed. Numerical solutions provide excellent accuracy and allow a consideration of various physical influences that may affect the pressure generation in the bearing (e.g., cavitation or shaft tilting), but they are computationally expensive. Look-up tables are less universal because the interpolation effort and the database size increase significantly with every considered physical effect that introduces additional independent variables. In recent studies, the Reynolds equation was solved semianalytically by means of the scaled boundary finite element method (SBFEM). Compared to the finite element method (FEM), this solution is relatively fast if a small discretization error is desired or if the slenderness ratio of the bearing is large. The accuracy and efficiency of this approach, which have already been investigated for single calls of the Reynolds equation, are now examined in the context of rotordynamic simulations. For comparison of the simulation results and the computational effort, two numerical reference solutions based on the FEM and the finite volume method (FVM) are also analyzed.

A common problem in transient rotordynamic simulations is the numerical effort necessary for the computation of hydrodynamic bearing forces. Due to the nonlinear interaction between the rotordynamic and hydrodynamic systems, an adequate prediction of shaft oscillations requires a solution of the Reynolds equation at every time step. Since closed-form analytical solutions are only known for highly simplified models, numerical methods or look-up table techniques are usually employed. Numerical solutions provide excellent accuracy and allow a consideration of various physical influences that may affect the pressure generation in the bearing (e.g., cavitation or shaft tilting), but they are computationally expensive. Look-up tables are less universal because the interpolation effort and the database size increase significantly with every considered physical effect that introduces additional independent variables. In recent studies, the Reynolds equation was solved semianalytically by means of the scaled boundary finite element method (SBFEM). Compared to the finite element method (FEM), this solution is relatively fast if a small discretization error is desired or if the slenderness ratio of the bearing is large. The accuracy and efficiency of this approach, which have already been investigated for single calls of the Reynolds equation, are now examined in the context of rotordynamic simulations. For comparison of the simulation results and the computational effort, two numerical reference solutions based on the FEM and the finite volume method (FVM) are also analyzed. [ABSTRACT FROM AUTHOR]

Many rotating machines utilize a fluid-type bearing. Despite their reliability and high load capacity, these bearings often show instabilities due to the interaction between the fluid media and the rotating shaft. These instabilities, known as oil-whirl and oil-whip, occur due to a Hopf bifurcation; being the parameter the shaft speed. Identifying the type of bifurcation, either sub-critical or super-critical, is an important task to determine the safety of the machines near the instability speed, and it tells whether one experiences oil-whip or oil-whirl. This work presents an approach, based on the center manifold reduction (CMR) method, to obtain limit cycles near Hopf bifurcations of rotors supported on fluid-film bearings. The basis of the method is the obtention of the center manifold of the system, which allows one to assess the type of bifurcation at hand. To obtain the center manifold, the parameterization method for invariant manifolds is used, which is a powerful tool to obtain invariant manifolds of high-dimensional dynamical systems. The proposed method is evaluated by comparing its results with an open-source numerical continuation package (MATCONT) in two systems: a simple and a realistic rotor system. The results show that the CMR, together with the parameterization method, can be used reliably to learn if the rotor system presents sub- or super-critical bifurcations, to perform parametric studies with different bearing properties, and also to predict the amplitude of the limit cycles. [ABSTRACT FROM AUTHOR]

Vibration is an essential subject for the design of rotordynamic systems, being responsible for compromising the integrity and causing risks to operational functioning. This work deals with an experimental investigation of the semi-active vibration controller for a rotordynamic system using shape memory alloy (SMA) elements. SMAs are smart materials that present thermomechanical coupling represented by solid phase transformations that promote either stiffness change or hysteretic dissipation. In this regard, they are useful in controllers employing thermal actuation from electric current through the Joule effect. This paper presents a proof of concept of a controller using SMA elements. An experimental apparatus is proposed considering a typical rotor system using SMA wires at the bearings. In this regard, proper temperature variations allow the system to cross critical resonant conditions. [ABSTRACT FROM AUTHOR]

Hydropower generators withstand multiple forces from diverse sources during operation. To ensure their stability and safe performance, numerical tools are developed to characterize their dynamic properties. Traditionally, generators are assumed to be rigid in rotordynamic analyses. However, the measurements in power stations challenge this assumption. This article proposes a novel approach to modeling hydropower generators with floating rotor rims using a three-dimensional (3-D) Finite Element Method, aiming to study their dynamic performance and properties, including natural frequencies, the modes of vibrations, and expansion due to centrifugal and electromagnetic forces, with the goal of improving the reliability of modern designs. Both this approach and employing a two-dimensional (2-D) model using curved beams result in similar in-plane natural frequencies and the expansion of the rotor rim due to centrifugal forces. However, the 3-D model can be used to calculate the out-of-plane natural frequencies and modes, to model the dynamics of complex geometries, and to perform stress evaluation and fatigue analysis.

Rotodynamic simulation of complex or/and large systems, for instance hydropower machines, may consist of models with many degrees of freedom and require multidisciplinary computations such as fluid-thermal-structure interactions or rotor-stator interactions due to electromagnetic forces. Simulating such systems is often computationally heavy and impractical, especially in the case of optimization or parametric study, where many iterations are required. This has, therefore, created a need for simplified dynamic models to improve computational efficiency without significantly affecting the accuracy of the simulation result. The purpose of this paper is to present simplified coordinate transformation matrices for journal bearings in vertical rotors, which require less computational effort. Matrix multiplications, which appear during coordinate transformation, were eliminated, and the bearing stiffness and damping matrices in the fixed reference frame were represented by local coefficients instead. The dynamic response of a vertical rotor with eight-shoe Tilting pad journal bearings was simulated using the proposed model for two operational conditions, i.e., when the rotor was spinning at constant and variable speeds. The results from the proposed model were compared to those from the original model and validated through experiments. The conclusion was that the presented simulation model is time efficient and can effectively be used in rotordynamic simulations and analyses.

Active magnetic bearings are complex mechatronic systems that consist of mechanical, electrical, and software parts, unlike classical rolling bearings. Given the complexity of this type of system, fault detection is a critical process. This paper presents a new and easy way to detect faults based on the use of a fault dictionary and machine learning. The dictionary was built starting from fault signatures consisting of images obtained from the signals available in the system. Subsequently, a convolutional neural network was trained to recognize such fault signature images. The objective of this study was to develop a fault dictionary and a classifier to recognize the most frequent soft electrical faults that affect position sensors and actuators. The proposed method permits, in a computationally convenient way that can be implemented in real time, the determination of which component has failed and what kind of failure has occurred. Therefore, this fault identification system allows determining which countermeasure to adopt in order to enhance the reliability of the system. The performance of this method was assessed by means of a case study concerning a real turbomachine supported by two active magnetic bearings for the oil and gas field. Seventeen fault classes were considered, and the neural network fault classifier reached an accuracy of 93% on the test dataset. [ABSTRACT FROM AUTHOR]