Control system design for flexible rotors supported by actively lubricated bearings

This article presents a methodology for calculating the gains of an output feedback controller for active vibration control of flexible rotors. The methodology is based on modal reduction. The proportional and derivative gains are obtained by adjusting the first two damping factors of the system and keeping the lengths of the two eigenvalues constant in the real-imaginary plane. The methodology is applied to an industrial gas compressor supported by active tilting-pad journal bearings. The unbalance response functions and mode shapes of the flexible rotor with and without active control are presented, showing significative improvement in damping reserve with the control. The importance of sensor location is emphasized, on the basis of the energy necessary to operate the active system over the entire frequency range studied. The best results are obtained by a decentralized controller, observing displacement and velocity of the shaft at the bearing positions.

The impact of geometric non-linearities on the fatigue analysis of trailing edge bond lines in wind turbine rotor blades

The accurate prediction of stress histories for the fatigue analysis is of utmost importance for the design process of wind turbine rotor blades. As detailed, transient, and geometrically non-linear three-dimensional finite element analyses are computationally weigh too expensive, it is commonly regarded sufficient to calculate the stresses with a geometrically linear analysis and superimpose different stress states in order to obtain the complete stress histories. In order to quantify the error from geometrically linear simulations for the calculation of stress histories and to verify the practical applicability of the superposition principal in fatigue analyses, this paper studies the influence of geometric non-linearity in the example of a trailing edge bond line, as this subcomponent suffers from high strains in span-wise direction. The blade under consideration is that of the IWES IWT-7.5-164 reference wind turbine. From turbine simulations the highest edgewise loading scenario from the fatigue load cases is used as the reference. A 3D finite element model of the blade is created and the bond line fatigue assessment is performed according to the GL certification guidelines in its 2010 edition, and in comparison to the latest DNV GL standard from end of 2015. The results show a significant difference between the geometrically linear and non-linear stress analyses when the bending moments are approximated via a corresponding external loading, especially in case of the 2010 GL certification guidelines. This finding emphasizes the demand to reconsider the application of the superposition principal in fatigue analyses of modern flexible rotor blades, where geometrical nonlinearities become significant. In addition, a new load application methodology is introduced that reduces the geometrically non-linear behaviour of the blade in the finite element analysis.

Dynamic Simulations of Rotors during Drop on Retainer Bearings

The active magnetic bearings have recently been intensively developed because of noncontact support having several advantages compared to conventional bearings. Due to improved materials, strategies of control, and electrical components, the performance and reliability of the active magnetic bearings are improving. However, additional bearings, retainer bearings, still have a vital role in the applications of the active magnetic bearings. The most crucial moment when the retainer bearings are needed is when the rotor drops from the active magnetic bearings on the retainer bearings due to component or power failure. Without appropriate knowledge of the retainer bearings, there is a chance that an active magnetic bearing supported rotor system will be fatal in a drop-down situation. This study introduces a detailed simulation model of a rotor system in order to describe a rotor drop-down situation on the retainer bearings. The introduced simulation model couples a finite element model with component mode synthesis and detailed bearing models. In this study, electrical components and electromechanical forces are not in the focus. The research looks at the theoretical background of the finite element method with component mode synthesis that can be used in the dynamic analysis of flexible rotors. The retainer bearings are described by using two ball bearing models, which include damping and stiffness properties, oil film, inertia of rolling elements and friction between races and rolling elements. Thefirst bearing model assumes that the cage of the bearing is ideal and that the cage holds the balls in their predefined positions precisely. The second bearing model is an extension of the first model and describes the behavior of the cageless bearing. In the bearing model, each ball is described by using two degrees of freedom. The models introduced in this study are verified with a corresponding actual structure. By using verified bearing models, the effects of the parameters of the rotor system onits dynamics during emergency stops are examined. As shown in this study, the misalignment of the retainer bearings has a significant influence on the behavior of the rotor system in a drop-down situation. In this study, a stability map of the rotor system as a function of rotational speed of the rotor and the misalignment of the retainer bearings is presented. In addition, the effects of parameters of the simulation procedure and the rotor system on the dynamics of system are studied.

Design and implementation of FPGA-based LQ control of active magnetic bearings

The need for high performance, high precision, and energy saving in rotating machinery demands an alternative solution to traditional bearings. Because of the contactless operation principle, the rotating machines employing active magnetic bearings (AMBs) provide many advantages over the traditional ones. The advantages such as contamination-free operation, low maintenance costs, high rotational speeds, low parasitic losses, programmable stiffness and damping, and vibration insulation come at expense of high cost, and complex technical solution. All these properties make the use of AMBs appropriate primarily for specific and highly demanding applications. High performance and high precision control requires model-based control methods and accurate models of the flexible rotor. In turn, complex models lead to high-order controllers and feature considerable computational burden. Fortunately, in the last few years the advancements in signal processing devices provide new perspective on the real-time control of AMBs. The design and the real-time digital implementation of the high-order LQ controllers, which focus on fast execution times, are the subjects of this work. In particular, the control design and implementation in the field programmable gate array (FPGA) circuits are investigated. The optimal design is guided by the physical constraints of the system for selecting the optimal weighting matrices. The plant model is complemented by augmenting appropriate disturbance models. The compensation of the force-field nonlinearities is proposed for decreasing the uncertainty of the actuator. A disturbance-observer-based unbalance compensation for canceling the magnetic force vibrations or vibrations in the measured positions is presented. The theoretical studies are verified by the practical experiments utilizing a custom-built laboratory test rig. The test rig uses a prototyping control platform developed in the scope of this work. To sum up, the work makes a step in the direction of an embedded single-chip FPGA-based controller of AMBs.

Multibody models for examination of touchdown bearing systems

Increased rotational speed brings many advantages to an electric motor. One of the benefits is that when the desired power is generated at increased rotational speed, the torque demanded from the rotor decreases linearly, and as a consequence, a motor of smaller size can be used. Using a rotor with high rotational speed in a system with mechanical bearings can, however, create undesirable vibrations, and therefore active magnetic bearings (AMBs) are often considered a good option for the main bearings, as the rotor then has no mechanical contact with other parts of the system but levitates on the magnetic forces. On the other hand, such systems can experience overloading or a sudden shutdown of the electrical system, whereupon the magnetic field becomes extinct, and as a result of rotor delevitation, mechanical contact occurs. To manage such nonstandard operations, AMB-systems require mechanical touchdown bearings with an oversized bore diameter. The need for touchdown bearings seems to be one of the barriers preventing greater adoption of AMB technology, because in the event of an uncontrolled touchdown, failure may occur, for example, in the bearing’s cage or balls, or in the rotor. This dissertation consists of two parts: First, touchdown bearing misalignment in the contact event is studied. It is found that misalignment increases the likelihood of a potentially damaging whirling motion of the rotor. A model for analysis of the stresses occurring in the rotor is proposed. In the studies of misalignment and stresses, a flexible rotor using a finite element approach is applied. Simplified models of cageless and caged bearings are used for the description of touchdown bearings. The results indicate that an increase in misalignment can have a direct influence on the bending and shear stresses occurring in the rotor during the contact event. Thus, it was concluded that analysis of stresses arising in the contact event is essential to guarantee appropriate system dimensioning for possible contact events with misaligned touchdown bearings. One of the conclusions drawn from the first part of the study is that knowledge of the forces affecting the balls and cage of the touchdown bearings can enable a more reliable estimation of the service life of the bearing. Therefore, the second part of the dissertation investigates the forces occurring in the cage and balls of touchdown bearings and introduces two detailed models of touchdown bearings in which all bearing parts are modelled as independent bodies. Two multibody-based two-dimensional models of touchdown bearings are introduced for dynamic analysis of the contact event. All parts of the bearings are modelled with geometrical surfaces, and the bodies interact with each other through elastic contact forces. To assist in identification of the forces affecting the balls and cage in the contact event, the first model describes a touchdown bearing without a cage, and the second model describes a touchdown bearing with a cage. The introduced models are compared with the simplified models used in the first part of the dissertation through parametric study. Damages to the rotor, cage and balls are some of the main reasons for failures of AMB-systems. The stresses in the rotor in the contact event are defined in this work. Furthermore, the forces affecting key bodies of the bearings, cage and balls can be studied using the models of touchdown bearings introduced in this dissertation. Knowledge obtained from the introduced models is valuable since it can enable an optimum structure for a rotor and touchdown bearings to be designed.

Mancais magnéticos ativos para atenuação de vibrações em eixos rotativos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

Accuracy of modelling and identification of malfunctions in rotor systems: experimental results

The accuracy of modelling of rotor systems composed of rotors, oil film bearings and a flexible foundation, is evaluated and discussed in this paper. The model validation of different models has been done by comparing experimental results with numerical results by means. The experimental data have been obtained with a fully instrumented four oil film bearing, two shafts test rig. The fault models are then used in the frame of a model based malfunction identification procedure, based on a least square fitting approach applied in the frequency domain. The capability of distinguishing different malfunctions has been investigated, even if they can create similar effects (such as unbalance, rotor bow, coupling misalignment and others) from shaft vibrations measured in correspondence of the bearings.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Split converter-fed SRM drive for flexible charging in EV/HEV applications

Electric vehicles (EVs) and hybrid EVs are the way forward for green transportation and for establishing low-carbon economy. This paper presents a split converter-fed four-phase switched reluctance motor (SRM) drive to realize flexible integrated charging functions (dc and ac sources). The machine is featured with a central-tapped winding node, eight stator slots, and six rotor poles (8/6). In the driving mode, the developed topology has the same characteristics as the traditional asymmetric bridge topology but better fault tolerance. The proposed system supports battery energy balance and on-board dc and ac charging. When connecting with an ac power grid, the proposed topology has a merit of the multilevel converter; the charging current control can be achieved by the improved hysteresis control. The energy flow between the two batteries is balanced by the hysteresis control based on their state-of-charge conditions. Simulation results in MATLAB/Simulink and experiments on a 150-W prototype SRM validate the effectiveness of the proposed technologies, which may provide a solution to EV charging issues associated with significant infrastructure requirements.

Intégration de pales en céramique dans un rotor de microturbine axiale en configuration renversée

Le marché de l'énergie distribuée est actuellement en pleine expansion et favorise l'intégration d'une multitude de sources d'énergie, et les machines à combustion interne ne sont pas exclues. Les moteurs à piston sont actuellement les principaux acteurs du marché, en raison de leur rendement élevé et de leur faible coût en capital. Cependant, la réglementation de plus en plus sévère sur les émissions ainsi que les coûts liés à la maintenance et les temps d'arrêt sont prohibitifs pour ce type de machines, en particulier dans le segment de basse puissance et de production d’énergie et de chaleur combinées (CHP). C'est là que les microturbines opérant sous le cycle récupéré – de petites turbines à gaz qui produisent moins de 1 MW de puissance – ont un avantage concurrentiel, grâce à moins de pièces en mouvement, une combustion plus propre et une température élevée d'échappement. Les petites turbomachines récupérées doivent atteindre des températures d'entrée de turbine (TIT) très élevées, requises pour atteindre 40% de rendement thermique. Les céramiques non refroidies offrent une solution très attrayante, avec plusieurs essais mais des résultats peu concluants dans la littérature. Ce travail présente une nouvelle architecture qui prend en charge des pales en céramique monolithique dans un environnement d’opération à chaud. La turbine renversée en céramique (ICT) est constituée d'un moyeu métallique flexible qui fournit une base souple pour les pales individuelles en céramique qui sont supportées par l'extérieur par un anneau en composite carbone-polymère. Les forces centrifuges chargent les pales en compression au lieu d’en tension, exploitant ainsi la résistance en compression typiquement élevée des céramiques techniques. Le document présente la validation expérimentale entreprise pour vérifier l'intégrité structurelle d’un prototype de configuration ICT à petite échelle, dans des conditions de fonctionnement à froid et à chaud, ainsi que les étapes qui y ont mené. Les résultats expérimentaux montrent que l'ICT supporte des pales en alumine dans les tests à froid et le nitrure de silicium pour des températures d'entrée du rotor jusqu'à 1000 K, avec des vitesses de pointe de pale atteignant 271 m/s. L’incursion d’objet domestique, l'événement le plus désastreux à se produire dans les turbines en céramique dans la littérature, n'a pas causé de dommages aux pales dans cette configuration. Ces résultats indiquent que l'architecture ICT est robuste et viable, et que le développement peut être poursuivi pour augmenter la TIT et la vitesse de pointe de la turbine, afin d’éventuellement parvenir à une microturbine récupérée en céramique de 1600 K de TIT.

Combined Retrograde Flexible Ureteroscopic Lithotripsy with Holmium YAG Laser for Renal Calculi Associated with Ipsilateral Ureteral Stones

Purpose: The purpose of this study was to evaluate the effectiveness of combined ureteroscopic holmium YAG lithotripsy for renal calculi associated with ipsilateral ureteral stones. Materials and Methods: Between August 2002 and March 2007, retrograde flexible ureteroscopic stone treatment was attempted in 351 cases. Indication for treatment was concurrent symptomatic ureteral stones in 63 patients (group I). Additional operative time and perioperative complication rates were compared to a group of 39 patients submitted to ureteroscopic treatment for ureteral calculi exclusively (group II). Results: Mean ureteral stone size was 8.0 +/- 2.6 mm and 8.1 +/- 3.4 mm for groups I and II, respectively. Mean operative time for group I was 67.9 +/- 29.5 minutes and for group 2 was 49.3 +/- 13.2 minutes (p < 0.001). Flexible ureteroscopic therapy for renal calculi increased 18 minutes in the mean operative time. The overall complication rate was 3.1% and 2.5% for groups I and II, respectively (p = 0.87). Mean renal stone size was 10.7 +/- 6.4 mm, overall stone free rate in group I was 81%. However, considering only patients with renal stones smaller than 15 mm, the stone free rate was 88%. Successful treatment occurred in 81% of patients presenting lower pole stones, but only 76% of patients with multiple renal stones became stone free. As expected, stone free rate showed a significant negative correlation with renal stone size (p = 0.03; r = -0.36). Logistic regression model indicated an independent association of renal stones smaller than 15 mm and stone free rate (OR = 13.5; p = 0.01). Conclusion: Combined ureteroscopic treatment for ureteral and ipsilateral renal calculi is a safe and attractive option for patients presenting for symptomatic ureteral stone and ipsilateral renal calculi smaller than 15 mm.

Automatic tuning method for the design of supplementary damping controllers for flexible alternating current transmission system devices

The design of supplementary damping controllers to mitigate the effects of electromechanical oscillations in power systems is a highly complex and time-consuming process, which requires a significant amount of knowledge from the part of the designer. In this study, the authors propose an automatic technique that takes the burden of tuning the controller parameters away from the power engineer and places it on the computer. Unlike other approaches that do the same based on robust control theories or evolutionary computing techniques, our proposed procedure uses an optimisation algorithm that works over a formulation of the classical tuning problem in terms of bilinear matrix inequalities. Using this formulation, it is possible to apply linear matrix inequality solvers to find a solution to the tuning problem via an iterative process, with the advantage that these solvers are widely available and have well-known convergence properties. The proposed algorithm is applied to tune the parameters of supplementary controllers for thyristor controlled series capacitors placed in the New England/New York benchmark test system, aiming at the improvement of the damping factor of inter-area modes, under several different operating conditions. The results of the linear analysis are validated by non-linear simulation and demonstrate the effectiveness of the proposed procedure.

Integrating structural and input design of a 2-DOF high-speed parallel manipulator: A flexible model-based approach

This paper discusses the integrated design of parallel manipulators, which exhibit varying dynamics. This characteristic affects the machine stability and performance. The design methodology consists of four main steps: (i) the system modeling using flexible multibody technique, (ii) the synthesis of reduced-order models suitable for control design, (iii) the systematic flexible model-based input signal design, and (iv) the evaluation of some possible machine designs. The novelty in this methodology is to take structural flexibilities into consideration during the input signal design; therefore, enhancing the standard design process which mainly considers rigid bodies dynamics. The potential of the proposed strategy is exploited for the design evaluation of a two degree-of-freedom high-speed parallel manipulator. The results are experimentally validated. (C) 2010 Elsevier Ltd. All rights reserved.

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process. The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert`s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index. In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology. (C) 2009 Elsevier Inc. All rights reserved.