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Rotor dynamic force coefficients of gas seals strongly depend on the machine operational conditions. These force coefficients influence the overall dynamical response and modal properties of machines, consequently defining the machine vibration levels. Accurate estimations of the rotor dynamic coefficients are required for designing machines with low vibration amplifications and well-defined stability margins throughout the operational range. Experimental methods applied to test benches are used to validate such force coefficients and they normally rely on (i) the quality of the measurements and (ii) the assumption that the mathematical model is able to capture the whole system dynamics. If relevant dynamical contributions in a system are neglected by the mathematical model, the contribution will erroneously be concluded to originate from the seal being tested. The theoretical and experimental investigation in this paper focuses on quantifying and qualifying the effect of neglected system dynamics modelling on the estimation of seals force coefficients and stability margins. The in-situ identification of seal forces shows that the direct stiffness, cross-coupling stiffness, and direct damping coefficient estimations for a gas seal with high preswirl are statistically significantly affected by the baseline model. Nevertheless, the baseline model leads to small deviations of the seal force coefficient estimations. The prediction accuracy of stability margins is found to be more influenced by the baseline model describing the system dynamics than by the deviations between the seal force coefficient estimations.

This article deals with the design of a test bench and its dynamic testing. The test bench is composed of a rotor levitated by radial active magnetic bearings and axially by a permanent magnet bearing. The rotor housing is mounted in a passive gimbal and the foundation can translate and rotate to emulate a vehicle accelerating, manoeuvring, and subject to outer perturbations such as waves. The work is motivated by a lack of publically available experimental designs and experimental data for magnetically suspended flywheels on moving foundations. The article will describe the test rig design and subcomponents, present experimental results, and afterwards the test rig will be used to experimentally validate a mathematical model governing the dynamics of the system. It is found that the model successfully captures the dynamics of rotor and housing both in a gimballed and non-gimballed flywheel energy storage system when subject to accelerations of the foundation. The simulated maximum housing accelerations are found to deviate 2% from the experiments while the maximum rotor displacements are found to deviate 37%, but only for rotor displacements larger than 100 μm where the linear approximation to the magnetic forces is no longer accurate.

The vibro-impact response of a single-degree of freedom model with the coefficient of restitution is analyzed using pointwise mapping and a standard averaging combined with non-smooth transformations. Experimental data are taken from a cantilever beam with attached mass and unilateral constraint submitted to different gap configurations and levels of excitation. Numerical simulations are used to reproduce empirical observations to a certain extent and validate theoretical predictions. Investigations on the coefficient of restitution show its dependence on the forcing frequency and pre-contact velocity. The effect of gap variations due to sliding of the constraint during frequency sweep is analyzed experimentally.

This paper considers the problem of real-time estimation of ground vehicle mass, based on longitudinal dynamics. Compared to previous contributions, this work relies on basic data from the vehicle controller area network bus. This allows for application to a very broad range of vehicles, by not using vehicle specific parameters such as current gear indicator and engine torque. The current gear ratio is predicted based on the engine and vehicle speeds. The engine torque is modelled by the mass air flow rate of the engine. The road gradient is estimated with an inertial measurement unit, with fusion of gyroscope and accelerometer using a complementary filter. To handle prolonged dynamic conditions affecting the performance of the filter, compensation of external accelerations is made by use of the vehicle speed from the controller area network bus. The mass is estimated with a recursive least squares filter with forgetting factor. The model is validated experimentally with data obtained from test drives with two different petrol powered passenger cars, equipped with a manual transmission and dual clutch automatic transmission respectively. The test drives consist of various driving conditions with different vehicle loads. The resulting mass estimates are generally good for both vehicles with variations within ± 5% of the actual masses.

Flywheel energy storage systems (FESSs) with active and passive magnetic bearings are generating interest due to their increasing energy-storing potential caused by advances in motor, bearing and fibre-composite technology. Magnetically suspended FESS are used commercially on static foundations while vehicle applications pose challenges due to manoeuvring, impacts, and other outer perturbations and have thus only seen successful experimental application in a few research projects where the FESS has been mounted in a passive gimbal to avoid gyroscopic forces. Although experimentally implemented, a mathematical model is still missing that determines motions and forces when the FESS is suspended in magnetic bearings, gimbal-mounted, and subject to outer perturbations. This work thoroughly describes how to set up a mathematical model that couples the multi-body dynamics of a flywheel rotor, housing, and gimbal-mount with the magnetic forces of the bearings. The model is used to simulate the behaviour of a FESS with and without gimbal and subject to various perturbations. The results demonstrate how the gimbal mount effectively removes gyroscopic forces but introduces other potential challenges such as large rotor and housing displacements due to dynamical interactions between the rotor, active magnetic bearings, housing, and gimbal.

Rotors on magnetic bearings rely on external controls to guarantee stability and are designed in case of partial or total failures, when impacts happen and potentially lead to a breakdown. Therefore backup bearings are indispensable. In such rotor-stator interactions the main undesired phenomenon is the backward whirl. The current work investigates the experimental behavior of a horizontal rigid rotor interacting laterally with two types of backup bearings during run up testing. The experimental data is analyzed by orbit analysis, spectrum analyzers, and force magnitudes collected by sensors installed. It is shown experimentally the nonlinear behavior of the rotor-bearing system and the elimination of backward whirl. The advantages and drawbacks of each type of backup bearing are given.

The dynamics of air foil bearings (AFBs) are not yet fully captured by any model. The recent years have, however, seen promising results from nonlinear time domain models, and simultaneously coupled formulations are now available, avoiding the previous requirements for undesirably small time steps and temporal convergence studies. In the present work, an alternative foil structure model is substituted for the simple elastic foundation model to avoid its inherent limitations. The new foil model is based on a truss representation from the literature, but incorporates the foil mass and a dynamic friction model. As a consequence of the friction model's velocity dependency, the foil mass is included to obtain a set of differential equations that can be coupled to the rotor and fluid domains while allowing a simultaneous solution. Considerations leading to a practically applicable implementation are discussed and numerical results are compared with experimental data. The model predicts natural frequencies and mode shapes well, but it is not yet capturing the unbalance response when friction is considered. Possible causes for this discrepancy are discussed and it is suggested that sticking is a more prevalent state than previously assumed.

This is part I of a twofold paper series, of theoretical and experimental nature, presenting the design and implementation of model-based controllers meant for assisting the hybrid and developing the feedback-controlled lubrication regimes in active tilting-pad journal bearings (active TPJBs). In part I, the flexible rotor-active TPJB modelling is thoroughly covered by establishing the link between the mechanical and hydraulic systems for all regimes. The hybrid lubrication is herein covered in depth; from a control viewpoint, an integral controller to aid such a regime is designed using model-based standard tools. Results show slight improvement on the system dynamic performance by using the hybrid lubrication instead of the passive one. Further improvements are pursued with the active lubrication in part II.

This is part II of a twofold paper series dealing with the design and implementation of model-based controllers meant for assisting the hybrid and developing the feedback-controlled lubrication regimes in active tilting pad journal bearings (active TPJBs). In both papers theoretical and experimental analyses are presented with focus on the reduction of rotor lateral vibration. This part is devoted to synthesising model-based LQG optimal controllers (LQR regulator + Kalman Filter) for the feedback-controlled lubrication and is based upon the mathematical model of the rotor-bearing system derived in part I. Results show further suppression of resonant vibrations when using the feedback-controlled or active lubrication, overweighting the reduction already achieved with hybrid lubrication, thus improving the whole machine dynamic performance.

This work constitutes the first step in a research effort aimed at studying the feasibility of introducing an active lubrication concept in tilting pad journal bearings (TPJBs) that feature the leading edge groove (LEG) lubrication system. The modification of the oil flow into each pad supply groove by means of servovalves renders the bearing active. This article focus on obtaining and validating a numerical model capable of simulating the studied system, in terms of its steady state and dynamics characteristics. The developed model is then used to simulate a simple system, in order to portray the feasibility of affecting its static and dynamic properties by introducing this novel active bearing design.

The lack of damping of radial gas bearings leads to high vibration levels of a rotor supported by this type of bearing when crossing resonant areas. This is even more relevant for flexible rotors, as studied in this work. In order to reduce these high vibration levels, an active gas bearing is proposed. The control action of this active bearing is selected based on two different strategies: a simple proportional integral derivative controller and an optimal controller. Both controllers are designed based on a theoretical model previously presented. The dynamics of the flexible rotor are modelled aided by the finite element method and the rotor–fluid interaction in the gas bearing is included using the solution of a modified version of the Reynolds equation for compressible fluids, taking into account the piezoelectrically controlled jet action. Performance and accuracy of both model-based controllers are compared against experimental results, showing good agreement. Theoretical and experimental results show a significant increase in the damping ratio of the system, enabling the flexible rotor to run safely across the critical speeds and up to 12,000 rev/min, i.e. 50 percent over the second critical speed without any instability problems.

In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved in the frequency domain by the methods of Finite Difference and pseudo-arclength continuation. The theoretical findings are validated against experiments carried out using a dedicated test-rig and a special device for characterisation of the magnetic anisotropy. The characterisation of the magnetic anisotropy shows that it can be quantified as magnetic eccentricities having an amplitude and a phase, which result in linear and parametric excitation. The magnetic eccentricities are also determined using the steady-state response of the rotor–bearing system due to forcing from the magnetic anisotropies and several levels of mass imbalance. Discrepancies in the results from the two methods in terms of magnetic eccentricity magnitude are due to additional geometric eccentricities in the shaft. The steady-state system response shows clear nonlinear phenomena, e.g. bent resonance peaks, jump phenomena and nonlinear cross-coupling between the two orthogonal directions, especially during counter-phase motion between shaft and bearings. The clear nonlinear behaviour is facilitated by the lack of damping resulting in relatively large vibrations. The overall nonlinear dynamic behaviour is well captured by the theoretical model, thereby validating the modelling approach.

The dynamic characteristics of rotors supported by Gas Foil Bearings (GFBs) are commonly assessed using linear force coefficients, which are usually derived from an analytical perturbation in combination with an implicit compliance model. This remains common practice even though discrepancies have been reported between the Onset Speed of Instability (OSI) predicted using such linear coefficients and observations from non-linear time integration. For the first time, the present paper pinpoints the root cause of this discrepancy by demonstrating an extended perturbation, akin to that used for tilting pad journal bearings, to predict exactly the same OSIs as obtained from an eigenvalue analysis based on the Jacobian of the full non-linear system of equations. To demonstrate this, the OSIs predicted using (i) the classical perturbation, (ii) the extended perturbation, and (iii) the Jacobian eigenvalues are compared over a range of compliance levels covering essentially rigid bearings to modern heavily loaded industrial GFBs. Using carefully aligned implementations, the deficiency of the classical method is demonstrated to increase with the compliance level (up to 13% for the benchmark case), while the extended perturbation provides OSIs in agreement with the Jacobian eigenvalues for all compliance levels. Furthermore, the mode shapes attainable from the three approaches, encompassing only the rotor, the rotor and foil, and the rotor, foil and pressure respectively, are compared.

The magnetic bearing rotors are present nowadays in many industrial applications. However, a damage or a malfunctioning of the magnetic bearing can produce a dangerous high lateral vibration.Backup bearings hold them to protect the machine integrity. The present study investigates the effectiveness of a pinned bearing on a horizontal rotor compared with a conventional rolling bearing. Experimental tests have been conducted; a mathematical model to describe the motion is then developed and validated numerically. It is shown that both the simulation and the test rig are in good agreement with each other and that the pinned bearing is able to reduce the interval of impacting velocities. The experimental set up is able to gather data fast enough to observe the dynamics and the forces acting on the structure. The orbits and the magnitudes of the impact forces are the key elements to assess the validity of the pinned in contrast to the rolling one as a relevant type of backup bearing.

The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.

This paper presents an improved completely interconnected procedure for estimating the losses, cooling flows, fluid characteristics and temperature distribution in a gearless mill drive using real life data. The presented model is part of a larger project building a multi-physics model combining electromagnet, thermal and structural interactions. This multi-physics model will later on be used for simulating and parameter optimization of a gearless mill drive. What has been proposed is a multi-physics model where the core losses are determined through a series of static finite element magnetic calculations applied to the principle of separation of losses where the losses of each harmonic are summed up. These losses have then been used in the thermal part of the model as heat generation and is modeled by the finite difference and finite element method. The cooling flow, which properties are updated iteratively according to the heat flux transferred to the fluid, is modeled as a lumped model with two nodes interconnected by 11 channels and one pump. The flow model is based on Bernoulli’s energy equation and solved by Newton–Raphson method. All the results from the three physical areas have been verified and have shown to be in good agreement with the found values.

We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. As a proof of concept the three methods are successfully implemented and tested for a harmonically forced impact oscillator with a hardening spring nonlinearity, and controlled by electromagnetic actuators. We show that under certain conditions it is possible to quantify the instability in terms of finite-time Lyapunov exponents. As a special case we study an isolated branch in the bifurcation diagram brought into existence by a 1:3 subharmonic resonance. On this isola it is only possible to determine stability using one of the three methods, which is due to the fact that only this method guarantees that the equilibrium state can be restored after measuring stability.

Dynamic characteristics of polymer faced tilting pad journal bearings are presented. Investigations are conducted using a single pad, load on pad configuration over a range of shaft speeds and loads. Two polyether ether ketone (PEEK) faced pads, one polytetrafluoroethylene (PTFE) faced pad and two entirely PEEK pads are investigated to determine the effect of varying mean bearing pressure and pivot characteristics as well as different material properties of the polymer layer. Experimental results indicate increased damping and decreased stiffness and slightly increased oil film temperature for entirely PEEK pads compared to pads with a PEEK lining and steel backing. Similar effects were observed by using a softer (PTFE) pad liner with a steel backing.

This paper is part two of a two part series. The originality of part one was the proposal of a novelty approach for wind turbine supervisory control and data acquisition (SCADA) data mining for condition monitoring purposes. The novelty concerned the usage of adaptive neuro-fuzzy interference system (ANFIS) models in this context and the application of a proposed procedure to a wide range of different SCADA signals. The applicability of the set up ANFIS models for anomaly detection was proven by the achieved performance of the models. In combination with the fuzzy interference system (FIS) proposed the prediction errors provide information about the condition of the monitored components. Part two presents application examples illustrating the efficiency of the proposed method. The work is based on continuously measured wind turbine SCADA data from 18 modern type pitch regulated wind turbines of the 2 MW class covering a period of 35 months. Several real life faults and issues in this data are analyzed and evaluated by the condition monitoring system (CMS) and the results presented. It is shown that SCADA data contain crucial information for wind turbine operators worth extracting. Using full signal reconstruction (FSRC) adaptive neuro-fuzzy interference system (ANFIS) normal behavior models (NBM) in combination with fuzzy logic (FL) a setup is developed for data mining of this information. A high degree of automation can be achieved. It is shown that FL rules established with a fault at one turbine can be applied to diagnose similar faults at other turbines automatically via the CMS proposed. A further focus in this paper lies in the process of rule optimization and adoption, allowing the expert to implement the gained knowledge in fault analysis. The fault types diagnosed here are: (1) a hydraulic oil leakage; (2) cooling system filter obstructions; (3) converter fan malfunctions; (4) anemometer offsets and (5) turbine controller malfunctions. Moreover, the graphical user interface (GUI) developed to access, analyze and visualize the data and results is presented.

A stable rotor—supported laterally by passive magnetic bearings and longitudinally by magnetic forces and a clutch—loses suddenly its contact to the clutch and executes abruptly longitudinal movements away from its original equilibrium position as a result of small increases in angular velocity. Such an abrupt unstable behaviour and its reasons are thoroughly theoretically as well as experimentally investigated in this work. In this context, this paper gives theoretical as well as experimental contributions to the problem of two dimensional passive magnetic levitation and one dimensional pointwise contact stability dictated by mechanical–magnetic interaction. Load capacity and stiffness of passive multicylinder magnetic bearings (MCMB) are thoroughly investigated using two theoretical approaches followed by experimental validation. The contact dynamics between the clutch and the rotor supported by MCMB using several configurations of magnet distribution are described based on an accurate nonlinear model able to reliably reproduce the rotor-bearing dynamic behaviour. Such investigations lead to: (a) clear physical explanation about the reasons for the rotor's unstable behaviour, losing its contact to the clutch and (b) an accurate prediction of the threshold of stability based on the nonlinear rotor-bearing model, i.e. maximum angular velocity before the rotor misses its contact to the clutch as a function of rotor, bearing and clutch design parameters.

This paper deals with the theoretical study of a horizontal shaft, partially levitated by a passive magnetic bearing, impacting its stator. Rigid body dynamics are utilised in order to describe the governing nonlinear equations of motion of the shaft interacting with a passive magnetic bearing and stator. Expressions for the restoring magnetic forces are derived using Biot Savart law for uniformed magnetised bar magnets and the contact forces are derived by use of a compliant contact force model. The theoretical mathematical model is verified with experimental results, and shows good agreements. However, the simulated contact forces are higher in magnitude compared to the experimental results. The cause of this disagreement is addressed and shows that the formulation of the theoretical contact force model slightly overestimates the forces acting during a full annular backward whirl motion.

We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required by Newton's method we find two almost disjoint sets of suitable control parameters. Control-based continuation succeeds reliably in producing the full bifurcation diagram including both stable and unstable equilibrium states for an appropriately tuned controller.

This paper treats the experimental study on a shaft impacting its stator for different cases. The paper focuses mainly on the measured contact forces and the shaft motion in two different types of backup bearings. As such, the measured contact forces are thoroughly studied. These measured contact forces enable the hysteresis loops to be computed and analyzed. Consequently, the contact forces are plotted against the local deformation in order to assess the contact force loss during the impacts. The shaft motion during contact with the backup bearing is verified with a two-sided spectrum analyses. The analyses show that by use of a conventional annular guide, the shaft undergoes a direct transition from normal operation to a full annular backward whirling state for the case of external excitation. However, in a self-excited vibration case, where the speed is gradually increased and decreased through the first critical speed, the investigation revealed that different paths initiated the onset of backward whip and whirling motion. In order to improve the whirling and the full annular contact behavior, an unconventional pinned backup bearing is realized. The idea is to utilize pin connections that center the rotor during impacts and prevent the shaft from entering a full annular contact state. The experimental results show that the shaft escapes the pins and returns to a normal operational condition during an impact event.

During rotor–stator contact dry friction plays a significant role in terms of reversing the rotor precession. The frictional force causes an increase in the rotor's tangential velocity in the direction opposite to that of the angular velocity. This effect is crucial for defining ranges of dry whip and whirl motions in rotor–stator contact investigations. Dry friction coefficient is therefore estimated using two different experimental setups: (a) standard pin-on-disk tests and (b) rotor impact test rig fully instrumented. The findings in both setups indicate that the dry friction coefficient for brass-aluminum configuration significantly varies in a range of 0.16–0.83. The rotor enters a full annular contact mode shortly after two impacts with a contact duration of approximately 0.004 s at each location. It is experimentally demonstrated that the friction force is not present when the rotor enters a full annular backward motion.

This paper is aimed at presenting results regarding the static and thermal behavior of a tilting-pad journal bearing operating under controllable regime. The bearing is rendered controllable by injecting high pressure oil into the clearance using holes drilled across the bearing pads in the radial direction. The modification of the injection pressure enables to modify the bearing static and dynamic properties according to the operational needs. The results presented are obtained using a theoretical model, which considers all the effects that determine the bearing behavior (controllable elastothermohydrodynamic lubrication regime), as well as using a test rig designed and built to this effect. The comparison between experimental and theoretical results provides solid ground to determine the accuracy of the available model for the the prediction of the steady-state behavior of the tilting-pad bearing with controllable lubrication. Among the parameters considered for the study are: oil film temperature field, resulting forces over rotor and pads, and rotor equilibrium position. The results obtained show good agreement between theory and experiment, as long as the assumptions on which the model is based are respected. Also, it is shown that some improvements are possible when it comes to model the steady-state behavior of the controllable bearing with the injection system turned off.

This paper proposes a system for wind turbine condition monitoring using Adaptive Neuro-Fuzzy Interference Systems (ANFIS). For this purpose: (1) ANFIS normal behavior models for common Supervisory Control And Data Acquisition (SCADA) data are developed in order to detect abnormal behavior of the captured signals and indicate component malfunctions or faults using the prediction error. 33 different standard SCADA signals are used and described, for which 45 normal behavior models are developed. The performance of these models is evaluated in terms of the prediction error standard deviations to show the applicability of ANFIS models for monitoring wind turbine SCADA signals. The computational time needed for model training is compared to Neural Network (NN) models showing the strength of ANFIS in training speed. (2) For automation of fault diagnosis Fuzzy Interference Systems (FIS) are used to analyze the prediction errors for fault patterns. The outputs are both the condition of the component and a possible root cause for the anomaly. The output is generated by the aid of rules that capture the existing expert knowledge linking observed prediction error patterns to specific faults. The work is based on continuously measured wind turbine SCADA data from 18 turbines of the 2 MW class covering a period of 30 months. The system proposed in this paper shows a novelty approach with regard to the usage of ANFIS models in this context and the application of the proposed procedure to a wide range of SCADA signals. The applicability of the set up ANFIS models for anomaly detection is proved by the achieved performance of the models. In combination with the FIS the prediction errors can provide information about the condition of the monitored components. In this paper the condition monitoring system is described. Part two will entirely focus on application examples and further efficiency evaluation of the system.

The possible contact between rotor and stator is considered a serious malfunction that may lead to catastrophic failure. Rotor rub is seen as a secondary phenomenon caused by a primary source, i.e. sudden mass unbalance, instabilities generated by aerodynamic and hydrodynamic forces in seals and bearings among others. The contact event gives rise to normal and friction forces exerted on the rotor at impact events. The friction force plays a significant role by transferring some rotational energy of the rotor to lateral motion. A mathematical model has been developed to capture this for a conventional backup annular guide setup. It is reasonable to superpose an impact condition to the rub, where the rotor spin energy can be fully transformed into rotor lateral movements. Using a nonideal drive, i.e. an electric motor without any kind of velocity feedback control, it is even possible to stop the rotor spin under rubbing conditions. All the rotational energy will be transformed in a kind of “self-excited” rotor lateral vibration with repeated impacts against the housing. This paper studies the impact motion of a rotor impacting a conventional backup annular guide for the case of dry and lubricated inner surface of the guide. For the dry surface case, the experimental and numerical analysis shows that the rotational energy is fully transformed into lateral motion and the rotor spin is stopped. Based on this study this paper proposes a new unconventional backup bearing design in order to reduce the rub related severity in friction and center the rotor at impact events. The analysis shows that the rotor at impacts is forced to the center of the backup bearing and the lateral motion is mitigated. As a result of this, the rotor spin is kept constant.

When designing a permanent magnet motor, several geometry and material parameters are to be defined. This is not an easy task, as material properties and magnetic fields are highly non-linear and the design of a motor is therefore often an iterative process. From an engineering point of view, we usually want to maximize the efficiency of the motor and from an economic point of view we want to minimize the cost of the motor. As these two things seldom go hand in hand, the goal is to find the best efficiency per cost. The scope of this paper is therefore to investigate the applicability of evolution strategies, ES to effectively design and optimize parameters of permanent magnet motors. Single as well as multi-objective optimization procedures are carried out. A modified way of creating the strategy parameters for the ES algorithm is also proposed and has together with the standard ES algorithm undergone a comprehensive parameter study for the parameters @r and @l. The results of this parameter study show a significant improvement in stability and speed with the use of the modified ES version. To find the most effective selector for a multi-objective optimization, MOO, of the motor a performance examination of 4 different selectors from the group of programs called PISA has been made and compared for MOO of the efficiency and cost of the motor. This performance examination showed that the indicator based evolutionary algorithm, IBEA, and hypervolume estimation algorithm, HypE, selectors performed almost equally good on this MOO problem where the HypE selector only had a slightly better performance indicator.

Active bearings represent a mechatronic answer to the growing industrial need to high performance turbomachinery. The present contribution aims at demonstrate the feasibility of applying active lubrication to gas journal bearings. The principle of operation is to generate active forces by regulating radial injection of lubricant through the means of piezoelectric actuators mounted on the back of the bearing sleeves. A feedback law is used to couple the dynamic of a simplified rotor-bearing system with the pneumatic and dynamic characteristics of a piezoelectric actuated valve system. Selected examples show the considerable performance advantages of such new kind of bearing.

The stability properties of actively lubricated tilting-pad journal bearings are investigated theoretically. The bearing preload factor and control system gains are varied, and stable and unstable regions are identified. It is seen, that the control system influences bearing stability, and that the nature and magnitude of this influence depends on the rotor mass, preload factor and rotational speed. Furthermore, it is shown that assuming the bearing pads to be rigid can produce a substantial error. A rigid pad model will overpredict the stable range of the bearing, thus it may lead to failure if trusted.

The dynamic performance of tilting-pad journal bearings with controllable radial oil injection is theoretically investigated, exploring the synergetic effect between passive elastohydrodynamics and active radial lubricant injection. The flexible tilting-pads are modelled as linearly elastic using finite elements. To reduce computational work, a pseudo-modal reduction is applied. Curves of dynamic bearing coefficients as well as the corresponding phase-magnitude plots are presented. Strong synergy between elastohydrodynamics and active control is observed, in particular for bearings with injection orifices far from the pivot line.

A simplified torsional model with a reduced number of degrees-of-freedom is used in order to investigate the potential of the technique. A time-dependent gear mesh stiffness function is introduced and expanded in a Fourier series. The necessary number of Fourier terms is determined in order to ensure sufficient accuracy of the results. The method of time-variant modal analysis is applied, and the changes in the fundamental and the parametric resonance frequencies as a function of the rotational speed of the gears, are found. By obtaining the stationary and parametric parts of the time-dependent modes shapes, the importance of the time-varying component relative to the stationary component is investigated and quantified. The method used for calculation and subsequent sorting of the left and right eigenvectors based on a first order Taylor expansion is explained. The advantages and drawbacks of applying the methodology to wind turbine gearboxes are addressed and elucidated.

This work deals with the mathematical modelling of multibody systems interconnected via thin fluid films. The dynamics of the fluid films can be actively controlled by means of different types of actuators, allowing significant vibration reduction of the system components. In this framework, this paper gives a theoretical contribution to the combined fields of fluid–structure interaction and vibration control. The methodology is applied to a reciprocating linear compressor, where the dynamics of the mechanical components are described with help of multibody dynamics. The crank is linked to the rotor via a thin fluid film, where the hydrodynamic pressure is described by the Reynolds equation, which is modified to accommodate the controllable lubrication conditions. The fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the reciprocating linear compressor. The system of equations is numerically solved for the case when the system operates with conventional hydrodynamic lubrication and for several cases of the bearing operating under controlled hybrid lubrication conditions. The analysis of the results is carried out with focus on the behaviour of the journal orbits, maximum fluid film pressure and minimum fluid film thickness.

An active control system is developed to control blade as well as rotor vibrations in a coupled rotor–blade system where rotor lateral and blade flexible movements are coupled. In order to cope with the periodic time-varying dynamics of such systems, a periodic modal controller, based on time-variant modal analysis, is designed. The periodic time-varying equations of motion are transformed into a time-invariant modal form, which is used for designing the periodic controller. The modal decoupling of the equations of motion allows a system order reduction resulting in a simpler and more implementable controller addressing only specific vibration modes, which can cause problems. Moreover, the time-varying modal matrices, used for the modal decoupling, are also used for controllability and observability analyses in order to achieve optimal actuator and sensor placement in the system. The applicability of the controller design methodology is evaluated by a numerical example where a coupled periodic time-variant system built by a rigid rotor with four flexible blades is simulated. In the simulation model tip masses are added at the end of the blades with the aim of emphasizing the blade inertia effects and the time periodicity of the system. Rotor angular movements and the gyroscopic effect are neglected for simplicity, and the blades are modelled as flexible Bernoulli beams. Three different control schemes are designed using the described methodology. The results demonstrate that the designed controllers are capable to cope with the time periodicity of the system and suppress very efficiently only the vibration modes addressed.

This work makes a theoretical and experimental contribution to the problem of rotor–blades dynamic interaction. A validation procedure of mathematical models is carried out with the help of a simple test rig, built by a mass–spring system attached to four flexible rotating blades. With this test rig, it is possible to highlight some dynamic effects and experimentally simulate the structural behaviour of a windmill in two dimensions (2-D model). Only lateral displacement of the rotor in the horizontal direction is taken into account. Gyroscopic effect due to angular vibrations of the rotor is eliminated in the test rig by attaching the rigid rotor to a flexible foundation. The blades are modelled as Euler–Bernoulli beams. Using three different approaches to describe the beam deformation one achieves: (a) a linear model; (b) a linear beam model with second order terms; (c) a fully non-linear model. Tip masses at the end of the blades emphasize the coupling between the dynamic and elastic terms. The shape functions are chosen in order to reduce the mathematical model, so that only the first bending mode of the beam is taken into account. The resulting equations of motion have five degrees of freedom and illustrate linear, non-linear and time-dependent terms in a very transparent way. Although neither gyroscopic effect due to rotor angular vibrations nor higher blade mode shapes are considered in the analysis, the equations of motion of the rotor–blades system are still general enough for the purpose of the work: validation of different linear and non-linear models with time dependent (periodic) coefficients. Experiments are carried out in the time and frequency domains while the rotor operates with different constant angular velocities.

Tilting-pad journal bearings with multiple orifices hybrid lubrication are analysed by means of a thermohydrodynamic theory. Adiabatic boundary conditions are adopted, and a bidimensional model is used to represent the fluid flow behavior in the bearing gap. The influence of operational conditions on the temperature distribution, when different bore arrangements in the pads are used, is discussed and compared to the theoretical values coming from the conventional hydrodynamic case (without radial oil injection).