ABSTRACT. In rotating machinery, detrimental vibrations occur due to contact between the rotor and stator, causing the destruction of machinery products and serious accidents. Thus, high-precision simulations and understanding of the characteristics focusing on such dangerous vibrations are important for improving the safety of rotating machinery. To realize them, this study investigates the effects of the stator thickness on the nonlinear dynamics of a rotor-stator contact system through the numerical simulations considering the contact configurations between the rotor and stator. The analysis object is centered on the dual-disk rotor in contact with the stator at the middle part of the shaft and modeled via the finite element method. Contact between the rotor and stator is expressed using the external force and moment derived from the Kelvin-Voigt model. Bifurcation diagrams reveal that the bands where the detrimental vibrations such as the partial contact motion caused by internal resonance occur shift toward higher rotational speeds as the stator thickness increases because of the enhanced stiffening effect. This trend significantly depends on the eccentric phase difference between two disks. This is because the effects of the contact configurations are influenced by the switching of the vibration modes due to the change of the eccentric phase difference between two disks. The findings of this study can offer beneficial guidelines determining the appropriate thickness and arrangement of the stator in a rotor-stator contact system, improving the safety and optimized design of rotating machinery.

ABSTRACT. In flight states, aero-engine rotor-support system bears complex additional in-ertial loads, which can easily lead to vibrations exceeding limits, rotor-stator rub-impact, and even instability. Experimental studies were conducted on an engine rotor-support system with squeeze film dampers (SFD) under gyroscop-ic motions. A gyroscopic test bench combining base rotations with rotor dy-namics was built up, and then a rotor-damper-support system was established. Dynamic responses and damping performance of the rotor-damper-support sys-tem under pitching, yawing and coupled motions were investigated. The sig-nals of disk displacement, squirrel-cage strain, and support velocity changing with gyroscopic motions were measured in real-time. By introducing Vold-Kalman filter and order tracking (VKF_OT), data processing was performed on non-stationary signals. The results indicated that when the foundation under-goes pitch motions, even if the rotor is at rest, the squirrel-cage undergoes pe-riodic deformation owing to the gravity. And the signals of vibration dis-placements and strains were superimposed with low-frequency components during pitching motions. Moreover, the inertial forces caused by pitching (yawing) motions cause displacements and strains to shift along the horizontal (vertical) direction. As the angular velocity or rotating speed increases, the off-sets become greater. Overall, it provides experimental platform, testing meth-od and data support for structural design and vibration control of rotor-support systems to improve reliability and safety of engines in flight states.

ABSTRACT. Gyroscopic effect plays a key role in the dynamic response of rotating sys-tems, as it affects the terms proportional to speed within their equations of motion. In case of damped system, this contribution interacts with non-rotating and rotating damping, respectively, thus influencing the overall dy-namic stability of the rotor system. The apparent stiffness change associated to gyroscopy is often analyzed by simplified analytical models, but in solid FEM elements currently proposed by some commercial software tools, this effect is either poorly considered or ineffectively modelled. Current evolution of rotating machinery towards very fast supercritical rotors or precision ma-chinery for manufacturing makes that effect a critical issue for design. This contribution aims at introducing the above-mentioned phenomenon, by re-calling first the current state-of-the-arts, in terms of modelling approaches proposed in the literature, and by finite elements exploited within some commercial codes. A refined FEM formulation is then introduced, to include the deformations of rotor elements induced by gyroscopic effect, and evaluate their real impact upon the whirling motions of flexible rotors. A validation is finally proposed, being based on a benchmarking between software tools and on a direct comparison with the dynamic response of a test rig expressively set-up to that purpose. As far as test case shows, in whirling modes differ-ences are detected between in-plane and out-of-plane cases, a good agreement is found between numerical and physical evidences, influence looks depend-ent on rotor layout, scale and operation.

ABSTRACT. The reliability and safety of rotating machinery strongly depend on the condition of sliding bearings, where hydrodynamic instabilities such as oil whirl or oil whip can lead to severe failures. Traditional diagnostic indicators, including RMS, kur-tosis, and spectral analysis, often fail to capture subtle early-stage anomalies. This work introduces a novel diagnostic metric based on the angle between signal vec-tors, derived from vibration displacements measured along orthogonal axes. The proposed approach quantifies the degree of similarity between signals and pro-vides a geometric interpretation of the system’s dynamic behavior. Experimental studies were conducted on a dedicated test rig equipped with displacement sen-sors, enabling controlled transitions between stable, transitional, and unstable bearing states. The calculated vector angles demonstrated clear differentiation be-tween operating regimes: small angles corresponded to stable, ordered motion, while transitional and unstable states yielded significantly larger values, reflecting the growth of hydrodynamic disturbances. The method integrates information from multiple measurement channels into a single, easily interpretable indicator. With low computational requirements, it enables real-time monitoring and early detection of instability, offering a practical solution for predictive maintenance. The results confirm that vector angle analysis provides a sensitive and robust tool for diagnosing hydrodynamic disturbances in sliding bearings, complementing and extending traditional diagnostic techniques.

ABSTRACT. Remaining useful lifetime (RUL) estimation of lip seals is challenging in maritime environments due to the large dimensions and the operating environment of a maritime thruster. The RUL is estimated to schedule proper maintenance actions while optimizing the operational lifetime. Conventionally, the operating time of the seal is used to estimate the condition of the seal. This, however, is often not a reliable estimate, leading to losses related to time-based maintenance instead of the benefits offered by condition-based maintenance. Thus, accurately estimating the current wear of marine thruster lip seals is crucial. The present work proposes a novel method for real-time wear measurement of lip seals via capacitive displacement sensing. The garter spring of the seal is used as a sensing electrode of a capacitive displacement sensor and the rotating shaft liner as the ground. As the seal wears, the gap between the garter spring and the ground reduces, increasing the capacitance between the garter spring and the shaft liner. By measuring the capacitance, it is possible to provide a potential real-time estimate of the total seal wear. The present work retrofitted a marine lip seal with a capacitance-to-voltage measurement device and investigated the correlation between the output voltage of the measurement device and the wear of the seal.

ABSTRACT. Fault diagnosis is a pivotal aspect of condition monitoring in rotating machinery. Although fault diagnosis methods that use deep-learning approaches have achieved significant success, they require massive, labelled datasets from operating machines, which are often impractical and expensive for industrial applications. To overcome this challenge, simulation-driven fault diagnosis provides a scalable alternative by generating simulated data for training diagnostic models. This study presents a simulation-driven diagnostic framework for a physical test rig, where fault characteristics are learned via a multibody dynamics (MBD) model capable of incorporating more complex fault conditions in rotating machinery. The MBD model is first validated against experimental measurements from the physical test rig, demonstrating its capability to accurately replicate realistic fault signatures. The simulated dataset generated by the MBD model is then used to train a diagnostic model, which is further adapted to the physical test rig through transfer-learning methods. By capturing the realistic operating defect responses, this study demonstrates the potential of simulation-driven fault diagnosis and provides a promising foundation for future industrial integration.

ABSTRACT. Early fault detection in rotating machinery is critical for ensuring operational safety and minimizing maintenance costs. Datadriven methods, particularly deep learning models, have shown strong potential for automating diagnostic tasks with high accuracy. This work proposes a convolutional neural network (CNN)-based methodology for fault diagnosis that leverages vibration signals transformed into twodimensional frequency-domain representations, referred to as vibration images. The study evaluates the approach using two distinct rotating machinery test rigs to examine the model’s generalization capability. The main contribution lies in assessing CNN under cross-domain conditions– a critical scenario for industrial deployment–training the model exclusively on one machine and testing it on a different machine: an essential scenario for real industrial deployment, where domain shift often degrades accuracy. Furthermore, a progressive analysis is carried out by incrementally incorporating portions of the target machine’s data into the training set. This procedure enables a quantitative assessment of how transfer learning influences diagnostic accuracy and robustness. The model’s performance is systematically evaluated through classification accuracy, loss functions, confusion matrices, and computational feasibility. The results demonstrate the robustness of the vibration-image approach and provide quantitative insights into the minimum amount of target-domain data required to achieve effective cross-domain adaptation in machine-learning-based diagnostics. Findings reveal that incorporating as little as 1-4% of target-machine samples significantly improves accuracy, enabling practical transfer learning strategies for industrial deployment.

ABSTRACT. Reliable fault prediction in rotating machinery is crucial for maintaining operational efficiency, reducing maintenance costs, and minimizing downtime. Building on recent advances in deep-learning-based diagnostics, this study investigates the benefits of employing multi-channel neural network architectures that integrate convolutional neural networks (CNN) and multilayer perceptrons (MLP) in different configurations. The proposed approach leverages both accelerometer and microphone signals, comparing their performance against single-channel models, with particular emphasis on classification accuracy. Additionally, training time is examined to evaluate computational efficiency and the potential for lighter models in practical applications. Given the strong performance of CNNs with two-dimensional inputs, the vibration image technique was employed as a preprocessing strategy to improve feature representation. Across both time and frequency domains, the inclusion of a second channel (i.e., an additional input signal) consistently improved classification accuracy relative to single-channel models, with the CNN–CNN architecture achieving the best overall performance throughout the tests conducted in this study.

ABSTRACT. This work presents modeling strategies for a rotor and its support structure. The rotor is modeled via finite elements (FE) and reduced by the Craig–Bampton method, retaining boundary DoFs at the bearing locations. The foundation is experimentally characterized and coupled to the rotor using different coupling techniques. The adopted approach is dynamic substructuring with virtual points at each bearing location, enabling coupling without prior knowledge of bearing coefficients while allowing tilting motions to be considered and improving agreement with experimental results. A comparative analysis is conducted to evaluate the accuracy and practical aspects of all approaches, highlighting the differences between the virtual point coupling and traditional methods based on impedance or modal representations of the foundation.

ABSTRACT. This work investigates the numerical stability of time integration schemes applied to rotor dynamic analyses. Time integration schemes are essential for analysis of dynamic problems, especially when analytical solutions are unavailable or impractical, but its accuracy strongly depends on the properties of the chosen method and the selected time step. Typical analyses of time integration schemes are based on the equations of motion of structural dynamics and wave propagation problems, described by symmetric inertia, damping and stiffness matrices. In rotating systems, the gyroscopic effect is described with the aid of a skew-symmetric matrix - the gyroscopic matrix - which is not diagonalizable by the eigenvectors matrix. Even if the rotating system is conservative, the mathematical description of the internal forces contains a term proportional to the velocity, altering the numerical behavior of standard integration algorithms. Key metrics include the spectral radius and its associate stability limit. To quantify these effects, a simple rotor model with non central disc is adopted, since its analytical solution enables error assessment, while also providing a foundation for extending the methodology to more complex rotor models lacking closed-form solutions. Several widely used time integration schemes are evaluated, including the 4th-order Runge–Kutta, Central Difference, Houbolt, Newmark, Wilson-Theta, and Bathe methods. Numerical performance is assessed by the spectral radius of amplification matrices and is illustrated numerically for the model problem under varying time step sizes. The findings provide practical guidelines for selecting suitable time integration schemes in transient rotor dynamics simulations, ensuring accurate predictions.

ABSTRACT. Fluid-film bearings are a fundamental component in rotating machinery and are extensively used in applications ranging from small-scale industrial equipment to large turbomachinery. However, these bearings are well known for exhibiting self-excited vibration phenomena, most notably oil-whirl and oil-whip instabilities. These dynamic effects can significantly compromise machine performance and reliability, making their study of both theoretical and practical importance. For an ideally balanced rotor, the onset of oil-whirl can be described as a Hopf bifurcation, where a stable equilibrium gives rise to periodic limit cycle oscillations as a system parameter, the shaft rotational speed, is varied. On the other hand, when rotor imbalance is introduced, these pure limit cycles no longer remain strictly periodic; instead, they evolve into quasi-periodic solutions, adding complexity to the system’s dynamic response. These quasi-periodic solutions can be obtained with traditional time-domain numerical integration methods; however, they are generally computationally intensive for large rotor-foundation systems and may obscure the underlying bifurcation structure of the system. To address this limitation, the present work employs the center manifold reduction (CMR) technique, enhanced through the parameterization method for invariant manifolds. This approach makes it possible to obtain quasi-periodic solutions associated with fluid-film instabilities, allowing for the precise prediction of rotor orbits without the need for extensive time-domain simulations. Therefore, the contribution of this work lies in providing an efficient tool to evaluate the dynamic response of rotor-foundation systems subjected to oil-whirl\whip instabilities.

ABSTRACT. The performance of hydrodynamic bearings is a key factor in the efficiency and reliability of rotating machines such as turbomachinery and engines. The pressure distribution in the lubricant, which determines bearing load capacity, is governed by the Reynolds equation. Its conventional solution through Finite Difference Methods (FDM) is widely applied, but often computationally expensive due to its iterative nature. This study investigates the Galerkin method as an alternative approach to solve the Reynolds equation, focusing on composite thrust bearings and cylindrical journal bearings. The main objective of this work is to assess the method efficiency, accuracy, and potential for providing semi-analytical solutions that enhance both precision and computational performance. The methodology involved reformulating the Reynolds equation in cylindrical and polar coordinates, applying Galerkin’s weighted residual framework, and implementing the resulting systems in MATLAB®. Different sets of basis functions (trigonometric, polynomial, and hybrid) were tested to evaluate their influence on accuracy. The results demonstrate that while purely trigonometric bases are not always optimal, hybrid combinations reduce relative errors. Moreover, the Galerkin method achieved reliable results with only four or five trial functions, indicating substantial computational savings compared to dense FDM grids. These findings highlight the Galerkin method as a promising tool for hydrodynamic bearing analysis, capable of delivering fast and accurate predictions while reducing overall numerical and computing costs.

ABSTRACT. Squeeze film dampers (SFDs) are widely used in high-speed rotor systems to suppress vibrations by providing additional damping and improving system stability. Their performance is significantly affected by geometric and design features, such as the presence of a central supply groove and feed holes. These features influence the pressure distribution in the fluid film, which in turn affects the hydrodynamic forces. Although experimental studies have provided valuable insights into SFD behavior, numerical modeling remains essential for capturing the nonlinear oil film forces involved. The Reynolds equation, which governs the pressure field in the lubricant film, can be discretized using various numerical approaches, including the finite difference and finite element methods. In this work, the finite element method is employed to discretize the Reynolds equation and evaluate the pressure field within the damper. Two sets of boundary conditions are investigated: Case-1, representing an SFD without a central supply groove, and Case-2, representing an SFD with a central supply groove. The developed model provides a basis for evaluating how film thickness and groove geometry affect the force coefficients of SFDs for rotor–bearing system analyses. In addition, the dynamic response of the rotor for Case-1 is examined using a simple rotor model to study how changes in static eccentricity influence the orbit size and shape.

ABSTRACT. Hydrodynamic bearings play a critical role in supporting rotors in high-speed rotating machinery, where accurate cavitation modeling is essential for predicting dynamic behavior. Cavitation occurs in the divergent region of the lubricant film, where local pressure drops below ambient levels, causing dissolved gases to be released. This phenomenon alters the pressure distribution within the bearing and significantly impacts its load-carrying capacity and affects rotor stability. This work investigates the influence of mass-conserving cavitation models on the dynamics of a flexible rotor-bearing system, in which shaft flexibility is explicitly considered to capture fluid-induced instability phenomena. Cavitation is modeled using both a classical non-mass-conserving model and the Ausas mass-conserving formulation, which improves numerical stability and consistency in pressure and film fraction distributions. Linear and nonlinear dynamic responses are compared to assess how mass conservation affects system behavior under varying operating conditions. The influence of mass conserving cavitation can be analyzed through orbit motion, lubricant film fraction and overall rotor vibration in both time and frequency domains. The proposed model provides a more comprehensive representation of real rotating systems, considering unbalance, rotor flexibility, and fluid-structure interaction effects. Results highlight the importance of adopting mass-conserving cavitation models for reliable stability predictions, providing deeper insight into how cavitation modeling strategies influence the performance of flexible rotor–bearing systems.

ABSTRACT. We present the design and experimental characterisation of the first actively controlled gas foil bearing (AGFB) with multi-axis geometry adjustment dur-ing operation. As established numerical models do not yet exist, we developed a dedicated laboratory rig that fully isolates the bearing from environmental vibrations and structural feedthrough. The bearing (34 mm journal) employs three independently driven pads to vary the effective diameter/clearance across 15 discrete settings, thereby altering the gas-film geometry and foil pre-load. The bearing is excited both harmonically (using an electrodynamic shak-er) and impulsively (using a modal hammer). Responses are captured using non-contact laser displacement sensors and a triaxial accelerometer; the result-ing input–output data are used to identify the direct stiffness and damping co-efficients of the compliant foil system using a linearised bearing model. The measurements reveal repeatable trends across the diameter sweep: de-creasing radial clearance increases the direct stiffness, while the effective damping exhibits a maximum at intermediate clearances. These results provide the first comprehensive coefficient maps for this class of AGFB and enable the calibration of simplified gas-film models tailored to active geometry control.

ABSTRACT. Rotordynamic aspects of a recent encounter with very challenging axial vibrations are examined. When a clear excitation source was not readily apparent, nonlinearities within the compressor's fluid film thrust bearing were suspected given that the observed vibrations were more than half the bearing's clearance. Simplified and high fidelity nonlinear transient simulations confirmed that the vibrations were due to subharmonic resonance with the primary excitation coming from the compressor's pocket pass pulsations. After initiation, the subharmonic could be quenched with a relatively small reduction in pocket pass excitation magnitude. Thrust bearing starvation and support stiffness were also found to be highly influential on the behavior.

ABSTRACT. Loose bolts in rotor systems may cause high vibration magnitudes and coupling faults like rub impacts or fatigue cracks. Thus, to ensure the safety of rotor systems, this paper proposes a new diagnostic method using the inner product of feature vectors. Firstly, considering equivalent nonlinear forces caused by loose bolts, the nonlinear rotor dynamic model is built with the finite element method. Then, applying output responses and structural parameters of the sub-rotor dynamic model, a new diagnostic index based on the inner product of feature vectors from healthy and damaged rotor systems is defined. Lastly, numerical studies are performed, and results illustrate that the proposed index and related method can successfully detect and localize single/multiple loose bolts in rotor systems. Meanwhile, results of effects of different rotating speeds show that the diagnostic speed should be close to the rotor critical speed to obtain larger diagnostic index values.

ABSTRACT. Eddy current displacement sensors are frequently used in the condition monitoring of rotating machinery. One of the primary applications is vibration measurement directly from rotating shafts. These sensors operate by inducing eddy cur-rents in the target material The strength of the induced eddy currents vary based on the sensor-to-target distance and therefore changes in displacement can be measured. However, the intensity of the eddy currents is also influenced by variations in the material properties of the target. The sensor can detect the changes in material properties as a change in displacement, introducing errors into the displacement measurements. These errors are commonly referred to as electrical runout. The goal of this paper is to briefly review the recent advancements in research related to causes and mitigation of electrical runout. Furthermore, the future perspectives and existing research gaps are discussed.

ABSTRACT. Hydrodynamic journal bearings are mechanical elements susceptible to degradation, mainly in rotating machines operating under several start-stop cycles or high vibration levels. The bearing wear occurrence may significantly influence the rotor’s dynamic response and vibrational characteristics, potentially leading to performance losses or even operational failures. Although numerous studies have investigated the identification of wear in hydrodynamic bearings, they assume the wear depth in the bearing width as constant. In this context, the present study aims to identify bearing profiles, in which the wear depth varies in the bearing axial coordinate. To this end, two numerical models of hydrodynamic bearings affected by axial wear are developed. The first model assumes that the shaft does not experience tilting due to axial wear, such that the shaft center is described exclusively by its translational coordinates in the horizontal and vertical directions. Conversely, the second model incorporates shaft tilting, whereby the shaft position is defined not only by translational coordinates but also by angular components around the horizontal and vertical axes. Based on these formulations, a neural network is trained to identify wear profiles along the axial direction of the bearing, enabling the evaluation of which model demonstrates superior accuracy in the identification of axial wear. The results show the influence of the shaft tilting and the capacity of the neural network on the identification of wear faults with depth varying in the bearing axial direction, contributing to the development of more efficient methods for monitoring of hydrodynamic bearings.

ABSTRACT. Rolling element bearings (REB) are crucial components of many rotating machines, such as spindles, aircraft engines, and turbines. Many researchers start testing their detection and diagnostic tools by relying on common benchmark datasets like the CWRU (Case Western Reserve University) Bearing Data Center or the Paderborn Bearing Dataset. Besides the well-known bearing datasets mentioned, we carried out our research on localized damage on roller bearings. In the available works, researchers most often measure vibrations on the bearing housing, which is fully justified because in practice these are often the only available positions. In addition to the mentioned measurements, for later correlation with the results of the simulation models, it is planned to carry out measurements of the vibration displacement on the shaft sleeve in the immediate vicinity of the roller bearing with localized fault. If the shaft is rigid, the elastic shaft's dynamics can be ignored, and the measured vibrations on the shaft sleeve near the bearing are equal to the inner ring's vibrations. The measurements will be performed at a rotational speed of 1500 rpm and a sampling frequency of 20 kS/s. The measurement results will be presented in the form of a fast kurtogram and envelope spectrogram, while preprocessing will be done with Variational Mode Decomposition.

ABSTRACT. Active Magnetic Bearings (AMBs) are widely employed in industrial applications, ranging from turbo-molecular pumps and compressors to high speed turbines for power generation. In such systems, the rotor is levitated and supported by magnetic forces produced by actuators integrated into the bearings. This enables fully contactless operation, eliminating friction and material wear, and thereby enhancing the suitability of AMBs for rotating machinery applications. However, the magnetic forces responsible for shaft levitation are inherently unstable, requiring the implementation of a control system to guarantee both operational performance and safety. In recent years, research efforts have primarily focused on the design and implementation of controllers aimed at improving system stability and robustness. Within this context, the present work proposes the use of surrogate models for the control of a rotating machine supported by two AMBs. The proposed controller is evaluated for different rotational speeds, with design strategies addressing the variation of vibration amplitudes. Experimental validation is carried out under multiple operating conditions, including steady-state, transient responses, and run-up scenarios subject to large amplitude disturbances. The results demonstrate that the proposed methodology effectively ensures shaft stability across a range of operating speeds and unbalance conditions.

ABSTRACT. The use of air foil bearings enables simple oil free support for rotating machinery. This offers substantial benefits in sectors where oil particle contamination is detrimental, such as air circulation, pharmaceuticals, and the food industry. However, the widespread application of air foil bearings in larger machinery is limited by their low load bearing capacity at low rotational speeds, leading to significant wear during start up and shut down, and by their inherently low damping, which can cause excessive vibrations and system failure. Extensive research has sought to address these limitations through novel bearing designs, hybridisation, regularisation and active control, using both numerical simulations and experimental approaches. Promising results have been obtained by augmenting journal bearings with radial high pressure air injection, creating hybrid regulated bearings. Further numerical studies indicate that introducing control into the air injection system can yield favourable system dynamics. This paper demonstrates the significant benefits of implementing active control for radial air injection in an air foil journal bearing, supported by both numerical and experimental results. An experimental validated high-fidelity multi-physics numerical model is used to predict system dynamics, from which a reduced order linear model is obtained to design a simple LQG control scheme. The presented results include unbalance response and frequency response functions, showing a marked increase in damping and substantial improvements in system dynamics.

ABSTRACT. For some applications involving induction motors, foundation vibrations are an important issue. There are many different kinds of excitation in induction motors, e.g. mechanical excitations like unbalance and misa-lignment, but also electromagnetic excitations like e.g. magnetic forces in the air gap. This paper here focus on a specific kind of excitation caused by pulsating air gap torques in converter-driven induction motors. The paper presents a theoretical analysis of a converter driven induction motor based on a simplified 3D-Model, where current-controlled electrodynamic actuators are positioned between motor feet and an elastic steel frame foundation and where the vertical motor feet vibrations are lead back to separate controllers, representing an active vibration control system (AVCS). Based on this model, the mathematical coherences are presented as well as a numerical example of a converter driven induction motor, where the foundation vibrations due to dynamic air gap torques are analyzed. The paper demonstrates that this kind of vibration can also be significantly reduced by the AVCS compared to an induction motor mounted directly on a steel frame foundation.

ABSTRACT. Understanding the mechanical behavior of an electrical machine and its load is becoming increasingly important. In this paper, a method is proposed to identify the mechanical system connected to a motor operated by a variable frequency drive (VFD). The method has been implemented using a new open software platform available for commercial VFDs.

To identify a system with either torsional or horizontal vibration modes, the VFD excites the system with a train of torque pulses with a desired frequency content and then records a motor speed or vibration sensor signal. We utilized the specific characteristic of the pulse train spectrum in conjunction with the maximum likelihood method. In subsequent signal processing, both non-parametric identification (transfer function) and parametric identification are performed.

Experimental verification on a two-mass system consisting of two motors connected by a belt has shown to result in accurate and repeatable estimation of inertias, spring- and damping constants, as well as resonance and anti-resonance frequencies. Impact of load changes on damping is shown, as well as other parameter variations during the operation of the system.

ABSTRACT. Gas foil bearings (GFBs) are aerodynamic bearings that use ambient gas as a lubricant. Their oil-free operation and high-speed capabilities make them an attractive choice for small turbomachinery such as fuel cell compressors. Despite their wear-free characteristics at normal operating speeds, rotor–bearing contact is inevitable during start–stop cycles. These contacts can cause gradual bearing/rotor wear, affecting the load-carrying capacity of the GFB and, in extreme cases, leading to failure. Therefore, proper lubrication condition monitoring helps prevent such consequences by identifying GFB malfunctions at an early stage.

Acoustic emission (AE) measurement offers a suitable basis for such condition monitoring in GFBs. To achieve this, statistical features of the AE signals can be calculated and fed to a classifier that determines the lubrication regime. Training such a classifier requires accurate knowledge of the lift-off speed for state labeling. However, the conventional lift-off reference, friction torque (FT), lacks the accuracy required to determine the lift-off speed. To address this issue, electrical contact resistance (ECR) measurement has been used in this study. Since ECR is directly influenced by the amount of asperity contact, it enables a more accurate identification of the transition from mixed to aerodynamic lubrication, i.e. the lift-off speed, compared to FT measurement. A GFB, accommodating an AE sensor directly on its top foil, is used for monitoring the lubrication regime. The results give new insight into the tribological behavior of GFBs and demonstrate the promising potential of real-time lift-off state monitoring based on AE measurement.

ABSTRACT. Gas Polymer Bearings (GPBs) as well as Gas Foil Bearings (GFBs) are highly innovative machine elements for supporting high-speed rotors in oil-free turbomachinery applications. By using air as the lubricating medium, the need for oil as a lubricant and auxiliary components is eliminated. In order to investigate the functionality of the bearings, the reaction torque is commonly measured to determine the transition from mixed lubrication to fluid film lubrication. The point of transition is defined by the lift-off speed, where the lowest frictional force is expected. However, this information is often hard to assess. With minimum points not well defined, the data can be challenging to interpret, as the vibrations can interfere with the lift-off behavior. In this context, the paper focuses on the dynamical analysis of a lift-off test rig and discusses potential dynamical problems, which could lead to deviations in the measurement results. To address these problems, different test rig setup configurations are considered, and the acquired experimental results are compared across theoretical modal analyses of the rig's main structure, along with the influence of each configuration on the lift-off identification. With this study, the present work aims to provide a better understanding of the influence of test rig dynamics on the lift-off speed identification from experimental results.

ABSTRACT. Elastohydrodynamic (EHD) lubrication plays a crucial role in the performance of rolling bearings, improving bearing life by establishing an oil film layer between contact surfaces. However, incorporating the bearing behavior into the rotor simulation is impractical due to the high computational cost of solving the Reynolds equation. In this context, this work proposes a two-step database model for rolling elements bearing parameters and reaction forces. The first database incorporates nondimensional outcomes of the EHD lubrication simulation based and referenced by Moes parameters and the ellipticity of the contact. The bodies mutual approach and a proposed parameter for the damping raceway are a result of numerically solving the EHD system of equations for a range of Moes parameters, which enables a broad data in-formation to be stored. The second step database is based on the first one, dimensionalised by the bearing geometry and operational conditions, creating a grid map that relates load, displacement, and film thickness. This enables efficient evaluation of EHD behavior without the cost of fullscale simulations.

ABSTRACT. In modern energy systems, numerous micro-power devices are used in place of large energy sources. In this context, energy microturbines, capable of utilising locally available renewable and non-renewable fuels, are becoming more widely used. This article discusses one of the stages in the development of a new gas microturbine with an external combustion chamber, designed to operate at a nominal power of 30 kW at a speed of 96,000 rpm. The advantage of the technology under development is that it uses hot air to drive the microturbine, rather than exhaust gases directly from the combustion chamber. This positively affects the durability of the microturbine, as it is not exposed to the contaminants produced during combustion. During preliminary tests of the prototype microturbine, it was found that one of the key factors significantly affecting the proper functioning of the bearing system is the axial force acting on the rotating system. This force is generated by the flow of gas through the compressor and turbine blade systems. Preliminary laboratory tests have shown that the axial force generated during rotor run-up can vary not only in amplitude but also in direction. Therefore, this aspect required further research, the results of which are discussed in this article. Based on the results obtained, general design recommendations were developed, which should be considered when designing fluid-flow machinery operating under similar conditions.

ABSTRACT. A tuned mass damper is a well-known concept that can be used to reduce undesired oscillation of structures in resonance. In structures with changing dynamic properties an adaptation of the tuning is needed. In this study a broadband mass damper is presented as a solution for controlling bearing vi-brations in an electric motor. The results are based on field measurements in laboratory and powerplant. First the motor was studied in laboratory in order to find out the natural frequency of the motor itself. Then the motor was studied at the application site located in a powerplant. After resonance situa-tion was identified, the broadband mass damper was installed to reduce the bearing vibration levels. The damper proved to work excellently in power-plant, and vibration levels were decreased approximately 60 - 80 %. The stud-ied broadband mass damper can be used in industrial and transport applica-tions where resonance vibration occurs.

ABSTRACT. Bearings are fundamental components in rotating machinery, playing a key role in ensuring smooth and efficient operation. In recent years, the demand for higher performance, lower operational costs, and reduced environmental impact has driven existing technologies close to their limits. This challenge has created a growing interest in advanced solutions, particularly those integrating mechatronic principles with tribology. Among the most notable developments in this area are active bearings, which offer the ability to enhance a machine’s dynamic response, efficiency, and overall reliability. To achieve these improvements, different controllable parameters can be targeted, the change in geometric configurations being very promising when speaking about hydrodynamic bearings. More specifically, changing the geometry of fluid-film bearings will directly impact the fluid-film thickness. Then, the bearing’s main dynamic characteristics – stiffness, damping, power loss, and load-carrying capability – can be controlled. Therefore, implementing such control requires strategies for actively altering the bearing’s internal geometry, particularly its surface profile. However, before selecting actuators and designing control algorithms, it is crucial to define the optimal geometric configuration that achieves the desired performance objectives. In this context, the present study aims to determine the best internal shapes for two-lobe and three-lobe bearings in order to minimise power loss and reduce the overall system vibration. The optimisation process will involve adjusting geometric variables—such as lobe offset and preload—as well as introducing modifications to the oil film profile through additional terms, for example, using Fourier series expansions

ABSTRACT. This study investigates the rotor dynamics of three distinct rotor designs for a 27 kW electric machine operating at 100,000 rpm. The configurations include two axially laminated anisotropic synchronous reluctance rotors and one permanent magnet rotor, each featuring unique structural characteristics. The objective is to assess how variations in rotor topology influence dynamic behavior and overall rotor performance. The research encompasses both design and manufacturing aspects, with particular emphasis on the structural challenges posed by high-speed operation. Finite element analysis (FEA) is employed to simulate the mechanical and modal proper-ties of each rotor, providing insights into their dynamic responses and structural integrity. Additionally, the study examines how rotor topology affects the manufacturing process across the three designs. Comparative analysis reveals differences in modal and structural behavior among the rotor geometries, which are critical for ensuring stability and reliability in high-speed electric machines. The findings contribute to rotor design optimization and support the development of efficient, robust electric motors.

ABSTRACT. Shredder machines are widely employed in the recycling industry for the treatment of end-of-life vehicles and other metallic waste. Despite their industrial relevance, their design remains largely empirical, due to the inherent complexity of their operation. The rotor is typically composed of disks with many pivoting hammers. It is subjected to dynamic and impulsive loads, being highly dependent on several factors: type, size, and configuration of the incoming scrap, shredder’s speed, and the wear state of the hammers, which significantly affects the system dynamic response during service. That variability introduces several significant uncertainties, preventing the establishment of a systematic design and scaling methodology for machines dedicated to different scrap streams. This work describes the development of a dynamic model of a hammer-type shredder, aiming at balancing the need for high-fidelity of models with computational efficiency, and enabling its use in the design optimization studies and sensitivity analyses. The model incorporates rotor dynamics, hammer kinematics, and variable loading conditions, while remaining lightweight enough for Design of Experiments (DOE) and repeated simulations. Moreover, this model aims at playing the role of digital twin, to support condition monitoring and predictive maintenance, once validated. This approach to design looks key to increase the reliability and sustainability of shredder technology in metal recycling.

ABSTRACT. Every rotating machine presents some degree of misalignment, which can be compensated for by a flexible coupling within acceptable limits. Although misalignment is a prominent cause of failures in machinery, the vibration impact of a misaligned flexible coupling on a mechanical system is not fully understood, as these couplings have different compositions and may behave linearly or nonlinearly. The lack of an accurate general model for all flexible couplings under misalignment, combined with the sometimes-conflicting results in the literature about which harmonics are excited in misalignment, leaves a gap for analytical and experimental studies on each of these couplings. For these reasons, this paper partially fills the gap on excited harmonics caused by misalignment and proposes a simplified finite element model of the shafts and coupling, which is compared to an experimental investigation of the vibration characteristics of a two-stage gearbox rig. The rig has both planetary and parallel shaft gearboxes and Sure-Flex couplings, which are nonlinear and commonly employed in pumps. The maximum allowable parallel misalignment was applied to the coupling, and the vibration displacement response was measured at shaft speeds of 1 and 10 Hz. Order tracking was applied to the vibration signal to analyze the waveform and spectrum, and then compared to the aligned condition to evaluate the vibration impact arising from misalignment. Results show the 1x shaft component is the strongest, followed by 2x and then 3x harmonics. The 2x component grows significantly with parallel misalignment and rotational speed increase.

ABSTRACT. In the development of rotating machinery, rotordynamic analysis is essential for predicting dynamic behaviour. It is known that narrow gaps between shrouds and hubs, e.g. annular seals or bearings, generate hydrodynamic forces and moments that act on the rotor, influencing its dynamic response. While the force characteristics of such components and their impact on rotor behaviour have been extensively investigated, the corresponding moment characteristics have received considerably less attention. In this study, the rotordynamic behaviour of a multi-stage pump is analysed using both one-dimensional (1D) and three-dimensional (3D) finite element methods (FEM) to evaluate the effect of modelling depth on predicted rotor dynamics. The hydro-dynamic effects of narrow gaps are represented by rotordynamic coefficients derived from a model based on the integro–differential approach, in which the inter-action between radial and axial gaps is treated explicitly. The resulting rotordynamic behaviour under different modelling degrees is illustrated by means of Campbell and stability diagrams. The findings highlight the importance of including rotordynamic moment characteristics in the analysis and demonstrate good consistency between the 1D and 3D finite element approaches.

ABSTRACT. Squeeze film dampers (SFDs) reduce shaft vibrations and enhance stability in rotating machinery. However, operation at a high squeeze velocity, vs = amplitude of rotor motion (r) x whirl frequency (w), draws air into the film to make a bubbly mixture that changes the SFD reaction force. During dynamic load tests with a SFD of diameter D=127 mm, length L=0.36 D, and radial clearance c=0.18 mm, an air-in-oil mixture with known gas volume fraction (GVF) is supplied to the damper. Single frequency and impact loads exerted on the elastically supported damper produce its dynamic stiffness (K), damping (C) and added mass (M) coefficients. The largest vs = 9.4 mm/s from r ~ 0.08c and w ranging from 20 Hz to 100 Hz. Operating with ISO VG 10 oil (GVF=0), K reduces with w, hence showing a significant M. When supplied with a bubbly mixture, K hardens with frequency (M < 0). C from single frequency loads decreases monotonically as the GVF increases toward 1, whereas C from impact loads first increases with GVF to ~ 0.4 and then drops continuously as the GVF→ 1. The measurements demonstrate journal kinematics affect the forced response of a SFD undergoing persistent air ingestion.

ABSTRACT. This paper presents experimental results on the rotor-stator rubbing-impact behavior of the labyrinth seal system. The objective of the work is to reveal the response characteristics and rotor-stator coupled resonance excitation conditions of thin-walled structures. A test rig consisting of a thin-walled drum rotor with a seal fin and a matching thin-walled drum stator was developed. Rubbing tests under various scenarios were performed when rotor operated near the coupled resonance speed. Time-domain vibration responses were recorded and both amplitude characteristics and spectral features were analyzed. The results indicate that no experimental evidence is found to support the occurrence of rotor–stator coupled resonance under partial rubbing conditions induced by rotor unbalance. Under these conditions, the vibration response spectrum contains contributions from multiple nodal-diameter mode vibrations. In contrast, partial rubbing induced by forced resonance of the stator can reliably initiates the coupled resonance. During resonance, the vibration amplitude increases significantly, and the response spectrum is dominated by the nodal diameter mode associated with the coupled resonance speed.

ABSTRACT. The dynamic simulations of high-speed turbomachinery that utilize gas foil bearings necessitate solving fluid-structure coupled nonlinear Reynolds' equation at every time step, which is computationally intensive for high-speed applications. A novel solution framework is proposed here with an objective to predict gas film pressure at each time step with lower computational effort. The pressure variation along the bearing length is defined as a basis function satisfying ambient boundary conditions at the bearing ends. The Galerkin method employs the same function as a test function to eliminate the axial coordinate, effectively reducing the dimensionality of the Reynolds equation to circumferential coordinate only. The reduced-order model is subsequently solved utilizing the pseudo spectral method (PSM) to assess pressure and gas film reaction forces. A rigid rotor supported on gas bearings was analyzed for its dynamic behavior using a two-dimensional and reduced-order model for the Reynolds equation. A visible reduction in computational effort has been observed when using the proposed model without losing accuracy. So this reduced model with the pseudo spectral framework can be used for further dynamic simulations and stability analysis.

ABSTRACT. Centrifugal pumps are generally equipped with axial force balancing mechanisms, such as thrust collars or balance pistons, to compensate for the inherently induced axial forces by the pressure increase over the impellers. Within these pistons, the system utilises immanent pressure differences to induce a counteracting axial force on the rotor. As with annular seals within centrifugal pumps, balance pistons are manufactured with surface profiles, such as saw-tooth patterns or labyrinth seal grooves. Consequently, the liquid film within the annuli exerts hydrodynamic forces and moments on the rotor, thereby rendering the balance pistons a potential source of rotordynamic instability. The present study investigates the influence of axial balancing devices on the rotordynamic characteristics of modern centrifugal pumps. In order to achieve this objective, computational fluid dynamic simulations of double pistons consisting of three narrow gaps (two radial and one axial) are conducted using Open-FOAM. The static characteristics of the machine element are investigated, including leakage, induced static axial and radial forces, and restoring moments of the pistons. The investigations are conducted over a typical parameter range that is representative of common pumps in modern power plants. In order to obtain the stiffness characteristics of the pistons, additional full 3D simulations are performed. The results are then compared with those obtained from a calculation method based on the integral-differential approach. The model calculates the different annular gaps, i.e. the radial and axial gap of the double piston, separately from each other. In addition to comparing the predictions to the CFD results, the possibility of superimposing the different calculations by the model for each gap to calculate arbitrary piston designs is investigated.

ABSTRACT. This work investigates the influence of asymmetric radial clearances in the tilting-pad journal bearing of a real hydroelectric generating unit from the Foz do Chapecó power plant in the Uruguai River, Brazil. Field measurements obtained from proximity probes revealed vibration amplitudes significantly higher than those expected for the nominal clearance, thus indicating the existence of geometric deviations. A subsequent inspection confirmed substantial differences among the twelve pads of the radial tilting-pad bearing. To represent the unit numerically, a comprehensive multiphysics model was developed, integrating the rotor, hydrodynamic bearings, generator, and turbine. To reduce computational cost while enabling each pad to be modeled with its measured clearance, Kriging surrogate models were employed to estimate the hydrodynamic forces of the individual pads. Numerical results show that including the measured asymmetric clearances is essential for reproducing the actual dynamic behavior of the unit, with simulated vibration amplitudes differing by less than 7% from the field data.

ABSTRACT. Rotor vibration displacement plays a pivotal role in ensuring the operational reliability of aero-engines, while the bearing reaction force (BRF) not only significantly influences system vibration behavior but also acts as a primary source of excitation for stator components. In view of the phase uncertainty inherent in multi-unbalance scenarios, this study introduces an interval-based analytical approach to evaluate rotor vibration displacement and BRF under varying phase combinations. Beginning with a rigid rotor theoretical model, the effects of phase variations on system response are examined. To extend the analysis to real-world conditions, a numerical model of low-pressure (LP) rotor assemblies is developed, with unbalance magnitudes and locations de-rived from modal strain energy distributions. To address the challenge of phase uncertainty, an extreme phase conditions enveloping (EPCE) strategy is proposed, allowing efficient estimation of response intervals by encom-passing a limited set of representative phase cases. Results from two numeri-cal examples confirm that the proposed method provides accurate upper-bound predictions for both rotor vibration displacement and BRF intervals. Nevertheless, discrepancies in lower-bound predictions are observed near certain anti-resonance frequencies of the low-pressure rotor, primarily due to the influence of higher-order modal effects. The quantified upper bounds can offer valuable inputs for evaluating rotor-stator clearances and analyzing vibration characteristics of associated stator structures in aero-engines.

ABSTRACT. Residual shaft bow in rotor systems supported by active magnetic bearings (AMBs) generates synchronous disturbances, resulting in enlarged rotor orbits and reduced control effectiveness. This study proposes a channel specific Linear Quadratic Gaussian (LQG) tuning strategy to suppress bow-induced vibrations in a megawatt class electrical machine driveline consisting of a quill-shaft coupling. The shaft bow is first identified by analyzing displacement sensor responses with the rotor supported on AMBs at low speed, utilizing the 1X harmonic component from frequency-domain analysis. The extracted bow parameters are then used to adjust the Linear Quadratic Gaussian (LQG) controller gains for individual AMB channels while preserving overall closed-loop stability. A finite element model of the rotor–AMB system is utilized to validate the baseline controller and the modified controller for bow compensation. Experimental validation on test platform demonstrates that the proposed channel-specific tuning approach effectively suppresses the residual vibrations, significantly enhances disturbance rejection, and improves overall rotor dynamic performance.

ABSTRACT. As a key enabler for rotating machinery operating at very high speeds with higher efficiency, active magnetic bearings (AMBs) bring many advantages, including lubricant-, and friction-free operation. As AMBs are open-loop unstable, they require feedback control, and good results for multiple-input multiple-output AMB-rotor-systems are typically achieved with state-space methods, requiring state estimators. Further, AMBs' performance in rotor systems is impacted by effects such as unbalances and changing loading, which can be interpreted as unknown parameters that one may want to estimate. Today, in rotor-AMB systems, commonly, variants of the Kalman filter are employed. By design, they approximate the system dynamics, e.g., in the form of linearization, and are often tuned for a specific operation speed. Parameter estimation introduces further nonlinearities in the problem, and parameters are rarely subject to purely aleatoric uncertainty or following a Gaussian distribution. Often, bounds for physical parameters are known from engineering insight, but cannot be directly used in variants of the Kalman filter. In contrast, moving horizon estimation (MHE), an estimation method formulating and solving online the underlying estimation problem as a nonlinear optimization problem over a moving window of past measurements, can overcome these deficiencies. It can naturally deal with nonlinear dynamics and with bounded parameters to estimate, where the latter is useful also for diagnostic purposes. Due to its numerical and theoretical complexity, it is presently not as popular as Kalman filtering in engineering applications. This contribution investigates whether MHE can realize foundational theoretical advantages in a prototypical test scenario for AMB-rotor systems.

ABSTRACT. Accurate estimation of machine parameters is essential for reliable control and thermal monitoring of wound-rotor synchronous machines (WRSMs), particularly under transient operating conditions. This paper pre-sents a resistance estimation framework based on the Unscented Kalman Filter (UKF) for simultaneous tracking of stator and rotor winding resistances. Unlike approaches that assume constant parameters or operate only under steady-state conditions, the proposed method is validated during dynamic scenarios involv-ing speed variations, torque step commands, and concurrent resistance changes. To benchmark performance, the UKF is compared with the Extended Kalman Filter (EKF). Simulation results show that both filters successfully track re-sistance variations; however, the UKF consistently provides faster convergence and higher estimation accuracy, especially in the presence of strong nonlineari-ties and measurement noise. Current and torque responses are also analyzed to provide insight into the coupled electromechanical dynamics during resistance variations. The results confirm that UKF offers significant advantages over EKF and conventional observers for online parameter estimation in WRSMs, making it a promising tool for temperature monitoring and fault detection applications.

ABSTRACT. In this paper, a torque reconstruction method for elec- tric motor driven powertrains is presented. Accurate knowledge of shaft torque in electric powertrains is essential for performance op- timization, torsional vibration diagnostics, and optimal control. Di- rect measurement of shaft torque typically requires sensors at various points in the system, increasing costs in manufacturing and mainte- nance. Reducing the number of required sensors would be a valuable improvement, which makes various torque estimation methods an attractive alternative to physical sensors. This paper presents an es- timation framework that leverages data on motor torque and shaft rotation velocity combined with a convex optimization algorithm to provide torque information for the entire powertrain. The method applies piecewise trend filtering to suppress measurement noise and reconstruct the powertrain’s unknown inputs and states. A simulation study is performed on a powertrain to create an initial analysis of the optimization performance. These results indicate a potential method of shaft torque estimation as a robust and cost-effective solution for powertrain monitoring, control, and fault detection in shaftline sys- tems.

ABSTRACT. One of the requirements for the operation of high-speed rotating machines is mini-mizing energy losses and wear in the support elements. This can be achieved by the application of superconducting bearings, which utilize magnetic levitation for their operation. They consist of a rotating part formed by a permanent magnet attached to the shaft journal and of a block of superconducting material connected to the stationary part. The performed research was focused on investigating the effect of superconducting bearings on dynamical properties and behavior of rotors by means of computational and experimental modelling. In the computational models, the shaft was represented by a beam-like body discretized into finite elements and the superconducting bear-ings were implemented by force couplings. The interaction between the permanent magnet and the superconductor was expressed by the frozen mirror image method. A small laboratory device was designed and manufactured for experimental modelling. The superconducting material was cooled by liquid nitrogen. Lateral vibration of the rotor was measured by laser sensors. The performed research led to better understanding of the effect of several design strategies based on spectral tuning and application of contactless electrodynamic dampers on suppression of the rotor vibration, energy dissipation, stability of the rotor oscillation, critical speed, and force transmission between the rotor and its sta-tionary part.

ABSTRACT. The problem of identifying "rotor modes" in a rotor-dynamic model of a rotor supported in magnetic bearings and potentially incorporating substructure, seal, and other component models is addressed. Implicit in this approach is the assumption that the intent of identifying "rotor modes" in industry standards such as API 617, Annex D, is that these modes will potentially be destabilized by unmodelled effects such as damping in the rotating frame due to assembly fits or highly uncertain effects such as seal damping. Consequently, the standard's stability requirements for these modes are more stringent than for other system modes. By associating rotor damping and/or seal property uncertainty with the free-free model, it is possible to readily discriminate modes of the full system that are strongly sensitive to these uncertain effects and these modes are then identified as "rotor modes" in this sense. The approach uses a sensitivity function analysis: determining frequencies at which the sensitivity is high (stability margin on the uncertain parameters is low) and identifying system model modes with natural frequencies near these peaks. An example industrial HVAC rotor supported by magnetic bearings is analyzed using this method to illustrate the approach.

ABSTRACT. Climate goals are catalyzing the need for more efficient and sustainable turbomachines. Magnetic bearings use magnetic forces to provide a contactless solution to support rotors. Such force can be produced by permanent magnets (passive magnetic bearings – PMB) or by electromagnets controlled by a feed-back system (active magnetic bearings – AMB). Since AMBs do not need lubricants, greases (including the additional machinery necessary), and with reduced friction between the moving parts, the maintenance in AMB systems is considerably less frequent, making these bearings a candidate for working in harsh environments, including at high temperatures. In this context, this work investigates a multiphysics methodology for predicting the thermal effects on the dynamics of rotors levitated by magnetic bearings. Multiphysical models are derived, coupling the rotordynamics, the electromagnetism, the control, and the heat transfer domains, leading to a set of nonlinear differential equations which is simultaneously solved using numerical methods. The thermal effects predicted by the multiphysical model are validated using two dedicated test rigs with rotors levitated by AMBs and PMBs. One test rig allows isolation of temperature effects on bearings, rotor, and sensors, while the other is a laboratory flywheel prototype inside a vacuum chamber. The influence of the temperature increase on i) PMBs demagnetization, ii) AMBs coil resistance, iii) the bearing load capacity, and iv) rotor vibration stability is accurately quantified. With the multiphysical approach, the thermal-induced instabilities are predicted both in frequency and time, making the multiphysical model useful to aid in scheduling controller gains during the design phase.

ABSTRACT. Active magnetic bearings (AMBs)–rotor systems are widely used in high precision machinery and energy equipment due to their contactless support for rotor systems. When a rotor supported by AMBs is connected to a motor via a coupling, misalignment caused by manufacturing defects, assembly inaccuracies, or prolonged wear can introduce asymmetric excitation forces that drive rotor vibrations beyond acceptable limits. However, existing PID controller tuning methods, which mostly rely on empirical, frequency domain, or numerical optimization approaches, still have limitations in suppressing disturbances caused by coupling misalignment and ensuring system stability and safety margins. To address these issues, this paper proposes a controller parameter tuning method based on both the misalignment safety threshold and system stability constraints. Specifically, the tuning of controller parameters is driven by two constraints: the first is the misalignment safety threshold constraint, determined as the allowable misalignment safety area based on the nonlinear electromechanical model of the AMBs–rotor system with coupling misalignment; the second is the system stability constraint, evaluated through root locus analysis. This method maximizes the system’s tolerance to coupling misalignment while maintaining stability margins and introduces a novel criterion for tuning controller parameters in AMBs–rotor systems.