ABSTRACT. Accurate modeling in rotor dynamics is usually constrained by simplifying assumptions that neglect nonlinear and secondary physical effects, leading to systematic discrepancies between physics-based predictions and experimental observations. Although data-driven approaches have been increasingly adopted to reduce these discrepancies, their black-box nature often compromises reliability and compliance with industrial V\&V standards. To address this limitation, this work proposes a physics-consistent discrepancy modeling framework for rotor dynamics that augments a calibrated finite-element model with an interpretable and explainable data-driven operator. First, experiments were conducted on a rotor subjected to varying levels of unbalance and a transversal crack. Next, a physics-based model was calibrated using the measured data. The residual errors between the model and the experimental results were then used to train a Bayesian Deep Operator Network enhanced by modes extracted using Proper Orthogonal Decomposition (POD). This approach enables the integration of an explainable and interpretable artificial intelligence model into the modeling process, improving the accuracy of the physics-based model while preserving its reliability and physical meaning.

ABSTRACT. Hybrid metal–composite shafts offer high load capacity and provide design parameters that enable tuning of their vibratory behavior. However, their dynamic prediction remains limited because classical homogenized beam models found in the literature often omit internal and interlayer damping. Due to limitations in ANSYS for capturing gyroscopic effects in multilayered structures, a shell finite element model is built by homogenizing multilayer configurations using Classical Laminate Theory (CLT) into equivalent single-layer shell elements. Experimental modal analysis is conducted on a fully composite multilayered shaft at rest to validate the numerical model and to estimate the modal damping ratio for each mode using the Modal Strain Energy (MSE) method. Subsequent dynamic analyses of the same shaft in rotation are performed numerically to evaluate the effect of gyroscopic forces on the first bending natural frequencies. Parametric studies using a design-of-experiments (DOE) approach are conducted on the composite stacking sequences of the hybrid metal–composite shaft to identify patterns and rules that minimize the maximum torsional angle, highlighting a promising stacking scenario for future optimization and fabrication of the hybrid shaft. This approach allows assessing the torsional stability of the rotor while also comparing the mass with metallic shafts. Approximately 23 % weight savings are observed compared with metallic shafts, while maintaining torsional performance, demonstrating the potential of this approach for high-performance laminated rotor design

ABSTRACT. This study integrates symbolic regression (SR) with rotor-bearing-impact dynamics for contact force identification. A hydrodynamic Jeffcott rotor is modeled using Kramer’s approximation and the Hunt & Crossley contact law with Coulomb friction. Using a physically-constrained loss function in PySR, the algorithm successfully recovers the exact Hunt & Crossley functional form and parameters (stiffness and restitution) from clean data. Under 1% Gaussian noise, the fundamental equation structure remains robust with minor parameter deviations. The results validate SR as an automated, interpretable approach for governing equation discovery in rotordynamics

ABSTRACT. Academic research on AI-based condition monitoring of rotating machines focuses largely on benchmark datasets measured on singular machines. However, real-world condition monitoring is often concerned with fleets of machines. In this paper, we investigate the benefits of having training data from additional fleet machines for anomaly detection in realistic scenarios. The most common methods for varying training dataset size are undersampling and decreasing the sample window overlap. However, in most industry scenarios the limiting factor is the number of fault events, not the amount of data obtained from each. We used five wind turbines from the Care to Compare wind farm dataset to construct different realistic fleet anomaly detection scenarios. The anomaly detection itself was performed with a combination of XGBoost and isolation forest. Our results show that prior fleet data is advantageous for performing anomaly detection on wind turbines within the fleet that have no previous recorded fault events.

ABSTRACT. Condition monitoring (CM) relies on accurate state information. While vibration analysis using accelerometers is key to monitoring rotating machines, the high cost often limits its continuous industrial application. Building monitoring systems upon readily available quantities, such as rotational speed (RPM), significantly enhances cost-efficiency by eliminating the need for additional hardware. We studied the use of high-resolution RPM measurements as a basis for classifying different normal operating states of an internal combustion engine (ICE). To ensure computational efficiency, we leveraged state-of-the-art time-series feature extraction libraries alongside logistic regression. We built and compared classifiers based on high-resolution RPM and acceleration measurements and studied the effect of feature reduction on model accuracy. We show that, regardless of the feature extraction method, basing the classification on RPM instead of acceleration yields significantly more accurate models. These results promote RPM as a promising base for CM of ICEs.

ABSTRACT. Online fault monitoring of high-speed rotating machines, particularly those suspended with active magnetic bearings (AMBs), is a critical topic due to safety requirements and the need for robust, uninterrupted operation in industrial applications. Conventional monitoring tools rely on sensor data and visualization dashboards; however, they generally lack mechanisms for simulating fault scenarios. To address these limitations, this paper proposes an online monitoring system that integrates a digital twin model capable of generating fault scenarios. The digital twin, a detailed rotor-AMB system, which has been updated based on grey-box parameter estimation, serves as a replica of the physical system, enabling fault detection and diagnosis. A Grafana-based dashboard is employed to visualize both time-domain and frequency-domain data, supporting real-time and offline analysis of measurements. The solution uses InfluxDB as a time-series database with a custom data processing pipeline, allowing efficient storage, retrieval, and analysis for condition monitoring. Faults in the electromechanical system are detected using wavelet analysis, while the digital twin assists in interpreting these signals for diagnostics. The implementation of the dashboard is demonstrated on a laboratory AMB rig, highlighting the main functionalities and software realization of the system. The fault diagnostic routine is validated through simulation studies conducted with the digital twin.

ABSTRACT. Typically, active magnetic bearings (AMB’s) are used to support passive rotors. In this paper, the rotor is also considered to be an active component. This is achieved by fitting a bend actuator inside the hollow section of the rotor. In this way, the bend is applied to the rotor in a synchronously rotating frame of refer-ence. Hence, static bend actuation may be used to apply the equivalence of syn-chronous excitation from an actuation component based in an inertial frame of ref-erence. In this way, the bend actuation may be used to relieve the synchronous demand from the AMB’s, which implies that low bandwidth AMB levitation can be combined with low bandwidth bend actuation for synchronous vibration con-trol. Thus, the overall system control need only be of low bandwidth for the con-trol of the rotor unbalance response. The conceptual bend actuator design and its principle of operation includes being commanded wirelessly. The power required to operate lead screw motors from an onboard battery is low. Performance is demonstrated experimentally in static tests in which rotor deformation under bend actuation is measured using a laser tracker. The rotor is then levitated on AMB’s and the synchronous vibration control achievable by static internal bending is demonstrated.

ABSTRACT. Coupled rotor systems are extensively utilized in modern industries such as aerospace propulsion, power generation, marine engineering, and high-speed manufacturing, where multi-stage rotating assemblies are essential for transmitting torque, enhancing load capacity, and improving system redundancy. However, these configurations are inherently prone to dynamic faults like misalignment and unbalance, which can induce complex vibrational responses, reduce operational efficiency, and compromise structural integrity. This study investigates the dynamic behavior of a coupled flexible rotor system supported by active magnetic bearings (AMBs) at both ends. The system comprises two interconnected flexible shafts, eccentric discs, and a coupling element, subjected to simultaneous misalignment and unbalance faults. The governing equations of motion are derived using Timoshenko Beam theory, which accounts for shear deformation and rotary inertia, critical for accurately modeling high-speed flexible rotors. The formulation is based on Hamilton’s principle and discretized using finite element methods to capture transverse vibrations and gyroscopic effects. A SIMULINK-based simulation framework is developed to analyze rotor displacement responses under different fault conditions. The results reveal fault signatures and their influence on system dynamics, offering insights into fault diagnosis, control optimization, and predictive maintenance. This work contributes to the development of intelligent monitoring systems and robust control, as well as fault identification strategies for coupled flexible rotor-AMB systems, ensuring safer, more efficient operation in advanced industrial applications.

ABSTRACT. Accurate linearized stiffness parameters of active magnetic bearings (AMBs) are essential for rotor-dynamics modelling, controller design and performance assessment. This paper presents a reproducible, physics-informed time-domain identification method to estimate the position and current stiffness of two radial AMBs supporting a rigid rotor. Open-loop tests without outer position feedback controller are performed using the inner current control, where step current excitations are applied separately to each AMB while the collocated position sensor records the radial displacement. A hyperbolic-cosine model is fitted to the transient displacement via non-linear least squares, and the fitted pole-like parameter is converted to stiffness using the effective mass. The method is validated on both linear and nonlinear actuator models using a detailed simulation model as well as on experimental data collected from a modular test rig. The findings indicate that the proposed method can accurately estimate stiffness parameters, demonstrating its suitability for system commissioning with limited knowledge.

ABSTRACT. This work investigates a specific type of torsional instability which occurs during the direct-on-line start-up of induction motor-driven systems. The phenomenon arises when the mechanical system features a large load-side inertia relative to the motor and a low-frequency first torsional mode. This configuration leads to a prolonged starting time, which allows the instability to develop and results in a first torsional mode shape characterized by significant relative motion in the motor rotor core, thereby making the mode highly sensitive to torsional excitation from the motor itself.

While this type of instability has been partially described in earlier literature, several aspects remain insufficiently explained or quantified. The goal of this study is to improve the current understanding of the torsional instability phenomenon by applying fully coupled electromechanical torsional models. This approach captures the interaction between the motor’s electromagnetic behavior and the mechanical dynamics of the shaft line, enabling a more complete analysis of the conditions which lead to instability. The findings contribute to a more accurate prediction and mitigation strategies for torsional issues in high-inertia industrial drive systems.

ABSTRACT. Torsional vibrations are a critical concern as they typically exhibit low damping compared to other forms of vibrations. Passive vibration control methods, such as isolators, can be used to attenuate these vibrations. However, there are currently few solutions available for torsional vibrations and their performance is often affected by environmental conditions, such as temperature. This study presents an experimental investigation of torsional wire rope isolators. A test bench, designed for evaluating their performance, was introduced. Three different prototypes were examined and compared to a rigid coupling. Two of the prototypes showed excellent isolation performance, while having sufficient damping at resonance. The isolators exhibited a strong nonlinear softening behavior dependent on the load amplitude. The used isolator design induced notable undesired axial forces to the system. Yet, the use of wire ropes for torsional vibration isolation shows great potential, especially if design modifications were to be considered in future research.

ABSTRACT. This contribution deals with dynamic instabilities in a decanter centrifuge due to a self-excitation mechanism and how the stability threshold can be increased by a dynamic vibration absorber.

Decanter centrifuges are a widely used type of centrifuges, that are employed in many industrial processes for solid-liquid separation within a continuous process. Such centrifuges consist of a horizontally rotating bowl that spins at high speed, thereby generating the high centrifugal forces required for solid-liquid separation. A spiral conveyor rotates inside the bowl at a specific dif-ferential speed. Both rotating parts are driven by an electric motor via a planetary gearbox and form the torsional vibration system under investiga-tion. In the dewatering zone, where the liquid phase is separated from the sol-id phase, a self-excitation mechanism occurs that limits the rotational speed and thus the performance of this machine.

To increase the operating speed the stability limit for self-excited torsional vi-brations needs to be increased first. Since the dewatering process, which is the main cause of self-excitation, cannot be influenced, more damping must be introduced to the system. For this purpose, a dynamic absorber is em-ployed that allows to shift the natural frequencies of the system and simulta-neously feed damping to the system. Since there are two possible installation locations for such an absorber, namely as an attachment to the bowl or to the screw conveyor, a feasibility study is carried out to determine the optimal ab-sorber design. The mathematical methods used and the resulting design are presented and discussed in this article.

ABSTRACT. Rotating elements are present in almost every machine across several applications. Such elements must meet product requirements in order to provide a satisfactory performance without failing, avoiding human and economical losses. Common tools, such as CAE softwares, or even most current tools such as digital twins, should work field-integrated within operating systems to ensure whether products can meet their performance requirements. Verification and Validation assessments are essential for credibility improvements of the machines virtual models that deals with physical quantities, which in turn will be able to perform precise calculations, satisfying the customer demand, assuring reliability and safety, and consequent competitiveness. This work aims to develop and apply a statistical validation – which identifies and takes into account different types of uncertainties in order to assess a software – and contribute to the improvement of the insight proposed in a ASME standard traditional validation. The statistical validation is detailed present-ed here as well as its advantages and contributions. The developed code analyzes the dynamics of rotating machines through finite element and finite volumes nu-merical methods for both shaft and hydrodynamic bearings, respectively. Both shaft and hydrodynamic bearing computational models are presented, along with the test rig to be virtually replicated. The obtained results identify the main oppor-tunities of computational model adjustments for motor coupling. The model can be considered as validated in shaft regions far from motor coupling.

ABSTRACT. This study presents an analytical solution for evaluating a V-shaped permanent magnet rotor’s mechanical behavior, emphasizing stress distribution and dynamic response. The rotor geometry introduces modeling challenges, particularly in the region between the shaft and the magnetic poles. Tangential and radial bridges are analyzed using classical beam deflection theory, producing results consistent with established for- mulations. A novel aspect of this work is a more detailed analysis of the region between the shaft and pole, where stress gradients are significant. The average stress near the shaft shows strong agreement with finite element method (FEM) simulations. The model assumes that the area outside the radius of the pole interface does not contribute to stiffness, with the exception of tangential bridge, and the applied inertial force is modeled as negative pressure. The tangential bridge is modeled as an equivalent thin-walled ring exerting pressure on a continuous ring. Tan- gential stress is derived from the normal stress of a tangential spring from the previous step. Defining stress concentration factors (SCFs) is crucial for obtaining the maximum values of localized stresses. The method also allows for more efficient optimization of the rest of the system, and a sensitivity analysis of the effect of different diameters on rotordynamics is conducted.

ABSTRACT. This study investigated the nonlinear dynamic behavior of a full-length equivalent rotor-LS system representing the actual shaft train of a heavy-duty gas turbine within its normal operational speed range of 20 to 3500 rpm. An equivalent mass approach, considering labyrinth seal forces modeled via an interpolation database method (IDM) and sliding bearing force formulated from short-bearing theory, is established. The results showcase that the system exhibits a clear progression from low-speed period-one motion to a broad quasi-periodic regime, approximately 1040 to 1840 rpm. The transfer into a complex motion forms above 2200 rpm. In the upper speed range, intermittent shifts between quasi-periodicity and weak chaos are observed, including broadband spectral features and isolated multi-period islands. Particularly in the final quasi-periodic domain, weak chaotic effect emerge, evidenced by local irregularities in Poincaré maps and positive excursions of the Lyapunov exponent, yet the rotor center remains constrained within a finite orbital envelope, effectively forming a stable limit cycle. This bounded behavior implies that even under nonlinear coupling with slight chaotic influence, the rotor system can sustain dynamically stable and confined motion within the designed operational range of the heavy-duty gas turbine.

ABSTRACT. Magnetic brakes are components used in rotating systems to create a resisting torque on the machine. The most common design involves the use of electromagnetic induction to generate eddy currents in a rotating element (usually a disk). By adjusting the electric current in the coils of the electromagnets, the resisting torque of the brake can be controlled, allowing for a smooth and controllable stop of the machine (active solution). In contrast, a brake that employs permanent magnets can only exert a constant resisting torque, which depends on the distance between the magnets and the rotating part (passive solution). As a result, permanent magnet brakes are typically used in experimental setups for component testing. Although there has been extensive research on modeling and experimental validation of electromagnetic brakes, there is relatively little focus on permanent magnet brakes. There are not many studies providing a mathematical model that accurately correlates with experimental results regarding the resultant applied torque on the rotating system. This work aims to contribute to this area. The NdFeB magnets are represented as an equivalent coil circuit, while the induction of eddy currents is described using electromagnetic theory. The model also ac-counts for torque saturation due to the cancellation of the magnetic field by the induced field in the rotating part at higher speeds. The numerical results for resisting torque are compared with measurements obtained from a test rig using a torque transducer. Tests are conducted at various rotating speeds and at different distances between the magnets and the rotating part. The results demonstrate a strong correlation between the model and the experimental data, indicating that this model is reliable and practical for such systems.

ABSTRACT. Hybrid Gas Foil Thrust Bearings (HGFTBs) are compliant self-acting hydrodynamic bearings using additional hydrostatic lubrication. Gas Foil Thrust Bearings (GFTBs) are used in high-speed, oil-free, low and high temperature environments to support axial loads in turbomachinery. Conventional GFTBs are typically limited to small, very high-speed, horizontal, rotor systems, where axial force balancing, often achieved via impeller thrust, is crucial for minimizing bearing loads. By including a hydrostatic injection, the operational range of GFTBs is significantly extended. This addition allows even vertical rotors to achieve lift-off at zero angular velocity, thereby avoiding initial contact friction and improves start-stop wear. However, the dynamic characteristics of rotors supported by HGFTBs remain poorly documented, even though such knowledge is crucial for understanding potential instabilities and failure modes. This study presents a strongly coupled multiphysical model of an HGFTB to analyze the axial rotor dynamics. The presented results comprise of linearized, as well as nonlinear frequency response functions under hydrostatic and hydrodynamic conditions. The fluid film introduces a softening nonlinearity, while hydrostatic injection increases nonlinear behavior under hydrostatic conditions. With careful selection of the foil oscillation frequency during linearization, relative errors remain below 3% across the full frequency range, except near resonance, where large external forces cause significant deviations. This analysis provides valuable insight for simplified industrial models based on linearized bearing coefficients.

ABSTRACT. Rotor dynamics analysis is essential for improving robustness in hydropower machine design. The generator is of particular interest due to its considerable size, small air gaps and strong dynamic influence. Generators comprise rotating and stationary parts that operate under substantial thermal, centrifugal and electromagnetic loads. Short-circuit faults produce severe magnitudes of electromagnetic torque, leading to excessive vibration. This paper investigates a 180 MW synchronous hydropower generator using finite element models of a floating-rim rotor and sliding-foot stator, with emphasis on torque transmission under short-circuit conditions. The results clarify load transfer mechanisms, identify critical structural points, and support improved generator design under fault loading.

ABSTRACT. In this research paper, the rotordynamic characteristics of a vertical rotor equipped with a squeeze-film damper were investigated. An impact test was simulated on a slender mid-span rotor supported by two structural assemblies located at the top and bottom ends of the shaft. Each assembly consisted of an eight-shoe tilting-pad journal bearing, a squeeze-film damper, and a bracket. The modal parameters were extracted using a continuous wavelet transform. Simulations were performed for two configurations, i.e., one with the squeeze-film damper and one without, to assess the influence of squeeze-film damper on the overall system’s dynamics. Additional factors, such as rotor speed and unbalance mass, were also varied in the simulations to evaluate their effects. The results showed that the squeeze-film damper significantly improved the damping characteristics of the vertical rotor. Experimental tests were conducted to validate the simulation results, yielding good agreement between the simulations and the experiments.

ABSTRACT. Bearings are a critical component in all rotordynamic systems, with journal bearings widely employed to separate the rotating journal from the stationary support structure. Their large load-carrying surface and use of a lubricating oil film make them especially suitable for heavily loaded machinery. Under such conditions, significant pressure build-up occurs within the lubricant film, and elastic deformation of the bearing surface allows the structure to adapt to the rotating journal. This elastohydrodynamic interaction enhances the bearing’s load-carrying capacity, and in some cases, bearings are purposefully designed to exploit this effect.

Accurately simulating heavily and dynamically loaded journal bearings with the finite element method is challenging, as it demands high model fidelity and thus substantial computational resources. This paper presents the application of an in-house engine simluation framework implemented in MATLAB to perform fully coupled elasto-hydrodynamic simulations of two-stroke marine engines in the time-domain. The framework employs the nodal-based Floating Frame of Reference Formulation to model the flexible crankshaft, rigid bodies to model the crank mechanism, and a linear finite element model to model the flexible housing. The main bearings are modeled as elasto-hydrodynamic bearings by solving the incompressible Reynolds equation using the finite element method. The results are validated against measurements from an actual two-stroke test engine situated at the Research Center Copenhagen in Denmark, showing good agreement between the measured and simulated journal orbit and journal misalignment inside the main bearing clearance.

ABSTRACT. Many large-scale industrial machines employ fluid-film journal bearings (JBs) to support rotating shafts. However, the design complexity and inherent modeling inaccuracies of such systems often lead to system-level instabilities, costly redesigns, and significant financial implications. With the growing demand for active control solutions directly integrated into bearings, particularly in the field of rotor dynamics, the development and experimental validation of an integrated Journal Bearing / Active Magnetic Bearing (AMB) system is presented herein. This novel concept referred to as a Smart Electro-Magnetic Actuator Journal Integrated Bearing (SEMAJIB), is implemented on a scaled-down test rig with a 5 cm shaft diameter to emulate industrial applications, with the objective of enhancing stability, performance, efficiency and overall system operation. The research objectives expand the capabilities of the SEMAJIB by designing and implementing control algorithms that mitigate vibrations caused by common machine faults such as mass unbalance, coupling misalignment, and uneven load sharing. Four main sub-objectives are pursued: 1- Instability control by using a derivative (D) controller to suppress oil-whip vibrations within the instability region. 2- Unbalance control by employing the influence coefficient method combined with a least-squares estimator to suppress synchronous (1X) vibrations across a range of rotor speeds, and 3- Multi-harmonic control by targeting super-synchronous (nX) vibrations and also using the influence coefficient method. This paper focuses on multi-harmonic control that complements the previously developed control algorithm. The numerical and experimental results show the successful implementation of the developed multi-harmonic control, and is quite successful in controlling such such super harmonics. The integration of the different control algorithms simultaneously, clearly show the superiority of the SEMAJIB due to the available control capacity in the electro-magnetic actuator.

ABSTRACT. Journal bearing (JB) is one of essential components of rotor systems and is widely used in marine propulsion, power generation equipment, compressors, pumps, and aerospace applications. Bearing wear during long-term operation can induce vibration, instability, and even failure, making effective maintenance indispensable. Traditional time-based maintenance (TBM) suffers from inefficiency and over-maintenance, and thus condition-based maintenance (CBM) has attracted increasing attention. Within CBM framework of the hybrid physics-based method (HPBM) for bearing wear estimation, vibration data is reproduced from physical and mathematical models, and characteristic features are extracted to construct an evaluation function against experimental measurements. Bearing wear is then inferred by minimizing this function. Previous studies have mainly relied on Fourier-based analysis to extract synchronous features such as forward whirl, backward whirl, maximum and minimum radius, roundness, and inclination. However, the sensitivity of these features and their effect on estimation accuracy remain insufficiently understood. In addition, our earlier work assumed monotonically increasing wear as a strict constraint in the optimization process. Such a strictly monotonic constraint can amplify estimation deviations, because a large error at previous step inevitably propagates into subsequent wear estimates. To address aforementioned issues, this study applies sensitivity analysis to evaluate the influence of extracted vibration features, and further investigates the estimation accuracy of the proposed method under relaxed monotonicity constraints. The results show that assessing the relative importance of different features can significantly improve both the reliability and accuracy of bearing wear estimation.

ABSTRACT. Accurate identification of bearing characteristics and unbalance in flexible rotor systems is essential for the reliable design and active control of turbomachinery. This work presents a physics-aware unscented Kalman filtering framework for the simultaneous estimation of bearing dynamic coefficients and rotor unbalance parameters in a complex realistic turbine rotor. The system dynamics are modeled using a finite element formulation, incorporating gyroscopic effects and structural flexibility, and the dynamic model is reduced via the Craig-Bampton method to retain accuracy of the dynamics. Bearing forces are generated using nonlinear short-bearing approximations, to obtain accurate stiffness and damping coefficients. Synthetic measurement data are generated from the reduced-order model under realistic operating conditions and used to evaluate the proposed estimation approach. Bearing stiffness and damping coefficients, along with the magnitude and phase of the residual unbalance, are jointly estimated by augmenting the system state with unknown parameters. To enhance robustness and statistical consistency in the presence of modeling uncertainty, the unscented Kalman filter is tuned using a physics-informed loss that exploits innovation statistics and model-based residuals. This optimization of the adaptive Unscented Kalman Filter parameters aims for the estimated states and parameters to be consistent with the state transition function. The results demonstrate recovery of a subset of the bearing coefficients and unbalance parameters, highlighting the effectiveness of the proposed framework for inverse identification in high-dimensional flexible rotor systems. The methodology provides a scalable and physics-consistent foundation for digital twin development, health monitoring, and model-based control of large turbomachinery.

ABSTRACT. This paper presents a data outlier insensitive method for estimation of unknown external excitations, and subsequent recon- struction of the complete torsional response of a powertrain by uti- lizing convex optimization. Shaft torque is measured using physical sensors, which are installed on the powertrain shaft line. Measuring external disturbances and determining the full torsional response of the powertrain with only physical sensors is often impractical, thus, methods for estimating shaft torque, also known as torque observers, have gained great interest. Torque observers allow more freedom in choosing sensor locations and can replace physical measurement equipment to a certain extent. Methods utilizing convex optimiza- tion provide good flexibility in designing the torque observer, i.e., enforcing desired structure in the estimates, such as smoothness or sparsity, to ensure that the estimates adhere to physical principles. In this paper, using simulations on a laboratory-scale system, the torque observer is designed to enforce smoothness and reject data outliers originating from malfunctions in physical sensors to gain an accurate estimate of the torsional response of a powertrain.

ABSTRACT. High‑speed energy conversion systems often use rotors supported by active magnetic bearings (AMBs). When operating in the overcritical range, AMB controllers can be designed using model‑based methods to provide enough damping to pass the first bending critical speed. However, predicting critical speeds and mode shapes remains difficult. This study examines the rotordynamics of an AMB‑supported gas turbine generator using both beam‑element and 3D solid finite‑element (FE) models. Beam models are computationally efficient but can be inaccurate for complex shafts with laminated or multilayer structures and impellers connected through geometric joints. In contrast, 3D solid FE models capture these effects more accurately but require substantially more computation. Using a supercritical gas turbine generator as a case study, the paper compares the two modeling approaches and shows that 3D solid FE modeling yields different natural frequencies and nodal locations due to increased flexibility, bearing influence, and prestress effects.

ABSTRACT. This paper analyses the nonlinear behaviour of Passive Magnetic Bearings (PMBs), overcoming the conventional assumption of constant stiffness commonly adopted in their modelling. In case of rotors equipped with PMBs, the magnetostatic interaction between permanent magnets results in nonlinear radial stiffness with a strong impact on the system dynamics, requiring accurate modelling. In this work, the bearing stiffness is investigated as a function of the relative axial and radial position between rotor and stator magnets. Particular attention is given to the influence of axial offset between magnetic rings, which alters the magnetic field distribution and consequently affects the nature of stiffness nonlinearity. Furthermore, the impact of topological variations in the bearing configuration, specifically, the stacking of multiple magnetic rings, is examined to assess their influence on the stiffness characteristics. A lumped-parameter rotor model with nonlinear supports is employed to simulate system dynamics under different PMB configurations. The resulting steady-state frequency responses are analysed to identify the onset of nonlinear phenomena, while Fast Fourier Transform analyses provide insight into the frequency content associated with these effects. The findings highlight the crucial role of PMB topology in determining the effective stiffness and overall dynamic behaviour of PMB-supported rotors.

ABSTRACT. This paper presents the segmentation and modelling of radial support magnets for a vertical rotor in a flywheel energy storage system (FESS) demonstrator, emphasizing the impact of magnetic configuration on the nonlinear rotordynamic response. A multiphysics-based model is developed to simulate the magneto-mechanical behaviour of the bearings, enabling high-fidelity prediction of stiffness and damping of supports under several operative conditions. The model incorporates field-dependent material properties, magnetic saturation, and geometric asymmetries. The case study is the current FESS demonstrator under realisation at th Politecnico di Torino in its operating conditions. Several Halbach array configurations, including segmented and continuous ring topologies, are implemented and compared in terms of their magnetic field uniformity, and resulting rotor nonlinear dynamics. Through parametric studies, optimal segmentation patterns and Halbach configurations are identified to minimize cross-coupled stiffness and enhance passive stability while maintaining high energy density. The segmentation of the radial support magnets is shown to influence static suspension properties and the nonlinear dynamic behaviour of the rotor mainly in subcritical regime.