Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM

This paper discusses designing of weights for both mixed-sensitivity and signal-based H_∞ controller synthesis for active magnetic bearing (AMB) systems using genetic algorithm (GA) optimization. In mixed-sensitivity problem formulation, the weights represent desired upper bounds to closed loop transfer functions and in signal-based problem formulation, the weights represent desired system response under sinusoidal exogenous inputs. In order to cast weight design process as an optimization problem, appropriate cost functions are chosen to guarantee that desired performance objectives are satisfied with a stable controller. First, the validity of the method is demonstrated in simulation by comparing performances achieved using weights designed through the optimization to the weights selected as performance objectives. Then, the weight design via GA for H_∞ controller synthesis is tested experimentally on a small AMB test rig in a disturbance rejection scheme. The designed H_∞ controllers are implemented on the AMB system and tested up to the maximum design speed of 6000 rpm, where the rotor safely passed the first critical speed. Achieved performances are compared to a benchmark PID controller. Results demonstrate validity of using GA for weights design and show the superiority of H_∞ controllers over PID controller for disturbance rejection in AMB systems.

This article introduces a new type of active damper—elastic support/dry friction damper (ESDFD) for vibration control of rotor systems and its performances. The basic operation principle of ESDFD in rotor system was introduced. In particular, a two-dimensional friction model-ball/plate model was proposed, by which a dynamic model of rotor systems with ESDFD was established and verified. The damping performance of the ESDFD has been studied numerically. The simulation results show that the damping performance of ESDFD is closely related to the characteristics of the rotor’s mode. For obtaining the damper’s best performance, the damper should be located at the elastic support in which the vibration energy is concentrated. And the damper not only provides external damping to the rotor system, but also increases extra stiffness into the rotor system. The stiffness of the stationary disk and the tangential contact stiffness of the contact interface are connected in series between the moving disk and the mounting base of the stationary disk. The larger of this combined stiffness, the better of the damper’s damping performance. The application of ESDFD to the vibration suppression of a rotor system is investigated experimentally. A switch control scheme for the damper is introduced; the effectiveness and control characteristics with control scheme for attenuating the vibration of rotor systems are experimentally investigated.

In smart rotor technology the active magnetic bearing plays a vital role in controlling vibration for safe and efficient running of high speed machineries, and for its condition monitoring or system identification. Researchers mostly investigated the dynamics of cracked rotors independent of the internal damping. Nevertheless, the internal damping is also influenced by the presence of crack in a rotating system because of rubbing of crack fronts during its opening and closing throughout the shaft whirling. The present work deals with the identification of rotor dynamic parameters in the cracked Jeffcott rotor considering both external and internal damping through a model based technique. The active control of vibration that is caused due to the transverse crack, unbalance and internal damping can be done by using the magnetic bearing. Numerical rotor responses and AMB currents are investigated using the full spectrum tool, which can reveal directional nature of the vibration signature in frequency domain. The response and current harmonics due to the excitation force of crack function, which is found from full spectrum analysis, are input to the proposed identification algorithm. It estimates the additive crack stiffness, unbalance in rotor, external damping, internal damping and AMB parameters such as the force-displacement and force-current coefficients. For different noise levels in responses and currents the proposed identification algorithm is tested for validating its robustness against measurement noise.

Although hydrodynamic bearings have minimum contact between solid parts, under particular circumstances they might be susceptible to abrasion and wear. In order to mitigate the problem, it is proposed to apply active control methods to reduce the vibration level at critical situations: fluid induced instability and the first bending mode. However, damage in the bearing surface have direct influence over the oil-film pressure and, consequently, in the bearings equivalent coefficients. Although, initially, small variations may lead to minor performance loss, when it becomes more significant close-loop stability may be affected. Therefore, in this paper it is conducted a preliminary study on the effect of journal bearing wear depth effects in active controlled rotors. A structured uncertain model is proposed to include the possible fault coefficients in the model allowing to perform robust stability analysis. Based on the uncertain formulation a robust control solution is designed guaranteeing rotor stability for a certain damage range.

Typical rotor/active magnetic bearing (AMB) system layouts involving large, external stator AMBs may be difficult or inconvenient to apply to some rotor systems. Where space in the machine working envelope is at a premium, the space required by traditional AMBs may preclude them from inclusion in the design.To open up the possibility of using AMBs in next generation compact, high speed machines, a system topology whereby the magnetic bearing stators are positioned inside of hollow-shaft rotors is suggested. This leaves the entire rotor surface available for other machine elements. In such designs, it is probably that both the rotor and the secondary shaft may exhibit flexible behaviour, which adds complexities to the design of the AMB controller compared to the requirements in typical AMB systems. Satisfactory performance can only be achieved if the dynamic characteristics of both rotor and AMB support structure are considered. This paper investigates solutions to this control issue, particularly through the use of model based techniques.A unique experimental facility based on this system topology is presented. The rotor is sufficiently unbalanced so as to be unable to pass its first critical speed without experiencing excessive vibration. It is demonstrated how an appropriately designed AMB controller can reduce the vibration to a level which allows the rotor to reach up to three times its first critical speed. This also includes the rotor speed (i.e. excitation frequency) exceeding the natural frequency of the AMB support structure.

Rotating machines present some common inherent operational problems, such as the critical amplitude of motion that the machine may experience when passing through one or more of its natural frequencies. High vibration levels can be harmful to the machine and its attenuation is important to maintain the system working healthily. In this context, the paper proposes a proportional-integral-derivative (PID) controller acting with two pairs of electromagnetic actuators to reduce the vibration amplitude of a flexible rotor, supported by hydrodynamic journal bearings, crossing its first resonance. The oil film behavior of the hydrodynamic bearings is modeled both through linear equivalent stiffness and damping coefficients and by the complete solution of the Reynolds equation applied to short bearings. Next, the relay feedback test (a frequency response method) is applied to estimate the ultimate gain and ultimate period of the respective PID controllers. Finally, five different tuning methods are proposed to adjust the PID: the Ziegler-Nichols traditional method, three Ziegler-Nichols modifications to obtain less aggressive controllers, and a fifth method, the Tyreus-Luyben method, whose objective is to improve the robustness of the controller.

The installation of micro hydroelectric power plants has recently been growing in Brazil, where small hydraulic generators are combined with hydraulic turbines. Some technical solutions require different runaway factors, from 1.2 up to 3.0 times the synchronous speed of the generator, so that the mechanical design of them must be reinforced or changed to support this critical dynamic condition, affecting costs and reducing competitiveness. An effective technique to control vibration is the use of simple devices called ‘dynamic vibration neutralizers’. These devices can contain viscoelastic material to introduce high mechanical impedance onto the system to reduce its vibration levels. There is a special kind of neutralizer, called ‘angular viscoelastic dynamic neutralizer’ (angular VDN), which acts indirectly in slope degree of freedom controlling flexural vibration. They have the predicted ability to control more than one single mode once the device is assembled where the maximum slope happens. The aim of the current work is to present a methodology to design angular VDNs and validate it by using a simplified experimental rotor exploring two different geometries. The results show that, if well-tuned, this kind of control is effective not only for the frequency band of interest, but also over higher modes.

A rotor spinning within an active magnetic bearing (AMB) system will normally be levitated and hence operate without rotor-stator contact. External disturbances and inherent unbalance may be compensated with appropriate control to keep rotor deviations within the clearance gap. However, AMBs have limited dynamic load capacity due to magnetic material field saturation. Hence overload conditions may result in rotor-stator contact. A touchdown bearing (TDB) and rotor landing sleeve are usually included to protect the expensive rotor, magnetic bearing and sensor components from damage. Once rotor-TDB contact has been made, rotor dynamic conditions may ensue resulting in persistent rotor bouncing or rubbing limit cycle responses. Prolonged exposure to these severe dynamics will cause TDB degradation and require regular replacement. If possible, a clear aim should be to restore contact-free levitation through available control capability in an efficient manner. This paper is used to guide the control options that are available to restore contact-free levitation. The use of AMB control is appropriate if the required control forces are within saturation limits. It is also possible to actuate TDBs and destabilize persistent rotor dynamic contact conditions. For example, piezo-based actuation offers larger control forces than those from magnetic bearing systems. Hybrid control action involving both types of actuation system has the greatest potential for completely robust restoration of contact-free levitation.

Monitoring the behavior of rotating blades is a critical procedure to ensure safety and proper performance of turbomachinery. For a long time strain gages have been the only solution to measure blade vibrations in a rotating scenario, but with the advances in software and hardware over the last decades, the research on blade tip timing (BTT) data analysis, a non-intrusive technique has gained momentum. A major drawback comes with this approach: undersampling. Several methodologies can be found in the literature do deal with this undersampled signal and this work presents a parametric study of the most recent type of approach that has gained momentum in the BTT research: compressed sensing (CS). The results show what are the best conditions to apply CS on BTT data, in terms of probe placement, amount of sensors and number of rotations.

An analytical method is presented to investigate nonlinear transverse and in-plane vibrations of a thin rotating disk by using a theory of geometrically nonlinear thin plate. The nonlinear wave solutions of the rotating disk are obtained by Galerkin analysis. The disk is assumed to be isotropic and rotating at the constant speed. The influence of amplitude ratios and rotating speed on natural frequency is studied. Natural frequency and static waves for different nodal-diameter numbers are also calculated. This analytical method not only takes into account the vibration perpendicular to the middle surface of the disk but also the vibration in the middle surface of the disk. In addition, this analytical method provides a more accurate way to solve the severe vibration problems in rotating disks of turbine engine rotors.

Bladed wheel model with tie-boss couplings for numerical and experimental investigation of stiffening and friction damping between tie-bosses is introduced. The modal behavior of FE numerical models of the wheel for two contact limit states, i.e. open and bonded contacts, was ascertained. The experimental modal analysis of the wheel both for open and pre-stressed contacts were performed, too. For detail stiffening and damping effect investigation the physical model of three-blade-bundle was elaborated. The experiments were performed for different excitation forces, excitation frequencies and contact pre-stresses. The dynamics of the bundle with respect to different contact states was evaluated from vibration attenuation after short resonant excitation. It was observed that if the macroslips arise in contacts that eigen-frequencies of the bundle are very close to the eigen-frequencies of open contact model bundle and high damping effect is achieved. If the microslips arise in contacts the eigen-frequencies are close to eigen-frequencies of the bond contact model and low damping is achieved. Hence the stiffening effect is high only in the case of microslips. The slip transition is conditioned by the level of adhesion that must be exceeded by excitation force. The FE model of the wheel and blade triple model with dynamic frictional contacts in the tie-boss couplings were developed and calculated results are compared with experiment.

The flow through the rotor of a propeller is complex and cannot be solved by pure analytical methods. Varieties of numerical methods were used to handle this problem including the momentum theory, blade element theory, lifting line theory, panel methods and CFD analysis. The objective of this study is to look into the possible use of alternative airfoils (Joukowski and Göttingen) for use in small propellers calculated by a simple validated home-built FORTRAN code based on the momentum theory and blade element theory. This code was then used to investigate the effects of the airfoil section, chord and pitch angle distributions along the blade. The linear pitch distribution in blades of propeller reduced the coefficients of thrust and power and indicated higher blade loading at the intermediate region and lower loading at the tip region in comparison with the Göttingen 796 propeller with the reference pitch distribution. With reference to the two investigated airfoils sections, Göttingen 796 and generalized Joukowski, it was found that the thrust and the power coefficients and the efficiency of the generalized Joukowski propeller are greater than the respective coefficients of Göttingen 796 propeller for advanced ratio J = 0.85 and higher. The predicted results indicated that the use of the elliptical chord distribution instead of tapered blade reduces the blade loading at the tip region and increases it at the intermediate region of the blade, but also reduces the coefficient of thrust, torque and power in comparison with the blade having the reference chord distribution.

Flexible blades coupled to rotating systems are commonly used in industrial machines, such as compressors, exhausters, and turbines. These components are usually exposed to different operating conditions, including high speed, large centrifugal forces, high temperatures, and pressure. Considering the inevitable manufacturing flaws, cracks can emerge and grow particularly in blades of these systems. Thus, investigations on the dynamic behavior of cracked blades become mandatory to prevent failures. In this work, the development, solution, and instability analysis of a system composed of four flexible blades coupled to a flexible shaft are presented. The flexible blades are modeled as Euler-Bernoulli beams with tip masses attached at their ends. Their deformations are obtained by considering second order nonlinear terms to ensure that the centrifugal stiffness is correctly represented, thus characterizing a second order linearized model. The equations of motion are obtained by applying the so-called Newton-Euler-Jourdain method. The crack presence brings an additional flexibility to the blades, which is introduced in the model by using a torsional spring. The resulting blade stiffness is obtained through the beam elastic equation. The Newmark time integration method is associated with the Newton-Raphson iteration procedure to integrate the equations of motion. The system was evaluated for different situations, regarding the depth of the crack in the blades, as well as the operating condition of the rotor-blade system. Finally, the instability map and the vibration responses of the system is determined. The obtained results indicate the instability condition of the rotor-blade system for a certain combination of rotating speed, angular position of the blades, and crack depth.

In rotating machinery, such as axial-flow compressor, gas turbine and aero-engine, the small clearance between the rotational blade and casing can increase the system efficiency, but may also lead to the rubbing between the blade and casing. The severe rubbing can bring about damages of the blade or casing. In this paper, two mathematical models of blade: a uniform-thickness-shell (UTS) model and a uniform-thickness-twisted-shell (UTTS) model, are established to compare the effects of the blade twist angle on the rubbing-induced vibration responses. The natural characteristics obtained from the two models are compared. Dynamic behaviors obtained from two models considering the combined effects of centrifugal force and aerodynamic force are also compared. Moreover, considering the effects of the misalignment angle and radial misalignment, the transient responses caused by rubbing using the two models are discussed. The results exhibit that the resonance in the radial direction cannot be observed when the blade twist angle is ignored (using UTS model). However, this resonance can be observed using the UTTS model, i.e., taking the influences of twist angle into account.

A new method for blade modal analysis is introduced in this paper by using continuous optical fiber sensors and optical backscatter reflectometer technology. The main advantage is that the sensor is few invasive and does not affect substantially system parameters. Moreover, the optical fiber sensor can be embedded in composite blades, for instance directly woven in carbon fiber fabric. This allows the sensor to be always installed and ready to use for continuous condition monitoring of the blade. Differently from classical sensors, which can be placed independently from the others, in this case, all the measurement points are placed on the same wire (the fiber itself), characterized by a finite length. Furthermore, due to the physical characteristics of the fiber, some constraints on how the fiber is placed, such as maximum fiber curvature, must be considered. Moreover, strain measurements are collected and precise positioning is required to reconstruct correctly the displacement modal shapes from the strains.In the literature, many optimal placement methods for sensors are proposed, but they are all referred to independent sensors. An optimal method for optical sensor placing on the blade for modal analysis is first introduced in the paper. Then, numerical and experimental tests performed on some blades are shown.

In the present work, a rotor train system is connected by a flexible coupling and integrated with an auxiliary active magnetic bearing. Due to angular misalignment that exists between the shafts, coupling stiffness varies with shaft rotation. A mathematical function that is time-dependent and which can yield integer harmonics has been chosen to numerically model coupling additive stiffness. The equations of motion have been obtained from Lagrange’s equation. The amplitude and phase of peaks of rotor vibration and AMB current signatures have been obtained in time and frequency domains using least-squares regression technique and full spectrum technique, respectively. They are eventually utilized to identify the intact and additive stiffness of coupling, viscous damping, unbalance magnitude and phase, and the AMB displacement and current stiffness. A SIMULINKTM has been built to generate time domain responses of discs and AMB current. From the EOM of rotors regression equations have been formed in frequency domain to create an inverse problem. The identification algorithm has been found to be robust against noise levels up to 5%.

Instability issues and excessive vibration amplitudes are common problems encountered in large rotating machinery applications. In order to predict problems and overcome them, reliable rotor models are required. In the previous decades there has been a great improvement on finite element modeling, which was extensively used in rotordynamics problems. However, there is a great difficulty when bearings have to be considered, and the unbalance present in the machine must be known for good response prediction. This paper proposes a method of bearing and unbalance parameter estimation from measured responses at the bearings and considering a Finite Element model of the shaft. The proposed algorithm utilizes the adaptive filtering technique known as the RLS filter employing the QR decomposition. Simulations were conducted and good results were achieved for both stationary and speed-dependent bearing parameters.

Tie rod built-up rotor structures are widely used in power machinery for different types of gas turbine engines. Typical tie rod rotor structure consists from several disks and intermediate parts that are tightened together by central tie rod shaft. This type of construction allows assembling together compressor or turbine disks made from high strength materials whose welding is impossible or hard. Another benefit over solid cast rotor of the same size is lighter weight and possibility to replace damaged parts/disks during repair or retrofit. However modeling of this type of rotors is more complicated, time consuming and different from modeling of solid cast rotors or rotors with shrink fit disks/parts, since multiple interfaces between the built-up rotor components can reduce the shaft stiffness significantly. Fine meshed solid models are known to get a very accurate and close value with natural frequencies of real structures, however significant amount of time usually is required to get solution for them and further application of these models for rotordynamic simulations is not convenient. Thus beam models are still widely used, but cautions must be taken when preparing them, since obtained beam rotor model might be much more rigid than the real structure. Current paper is focused on rotordynamic modeling of typical built-up gas turbine rotor with central tie rod shaft. Paper describes a method how to correct beam model in order to achieve a better matching with fine meshed solid model. Described method was further used for rotor modeling of real 2 MW gas turbine rotor. Obtained simulation results were compared with experimental results from modal testing and good agreement was achieved.

The current work uses two types of excitation on a rotating shaft to identify its modal frequencies. The first one is a non-contact excitation where an oscillating magnet is placed near the shaft, eddy currents generated by the oscillating magnetic field excites vibrations in the shaft. In the second type of excitation, a miniature electrodynamical exciter powered by a decoder amplifier board is placed on the shaft to excite vibrations with predefined frequencies in a signal (mp3 format) stored on the USB flash drive connected to the board. The shaft is rotated at different speeds and vibration accelerations are measured using a small data logger placed on the shaft while excited using these two excitation systems. These two types of asynchronous excitation on the shaft excites both forward and backward whirl vibration modes of the rotor system. The modal frequencies are identified at the peak amplitudes in the waterfall plots of the measured vibration accelerations to a chirp excitation of the shaft. A Campbell diagram is plotted with the identified modal frequencies of the shaft in the rotating frame of reference.

Rotating structures exhibit speed dependent natural frequencies and mode shapes that play an important role in the overall dynamics. Accurate experimental identification of these phenomena is of great importance for validating uncertainties in numerical models and for detecting potentially dangerous asynchronous frequencies, often obscured by the imbalance synchronous vibrations. As the speed dependent natural frequencies cannot be assessed experimentally without actually rotating the structure at the vicinity of these speeds, the task of exciting and measuring asynchronous frequencies during rotation without risking the integrity of the machine, becomes a great challenge.The present paper proposes an automatic and efficient method to excite a rotating structure at a selected modeshape, while controlling the vibration amplitude, such that a non-destructive test takes place.Automatic excitation of marginally stable vibration occurs upon introducing a phase shifting filter and a nonlinear feedback element. A digital signal processor carries out the latter, therefore the system behavior and the vibration levels are fully controllable.Theoretical analysis, based on the describing function method and modal filtering, is carried out and verified by numerical simulations. Finally, some experimental results are described and analyzed. The experimental system exhibits different modes of vibration that are excited selectively, at any desired speed of rotation and at any desired magnitude. This approach effectively reconstructs the Campbell diagram with only basic knowledge of the system’s modal behavior. It is also shown that one can switch, in situ while rotating the system, between modes of vibration in the presence of large imbalance forces.

An experimental facility for testing full-scale bladed disks in vacuum conditions and under centrifugal load is described in this paper. The special feature of the PHARE#1 test rig is its multichannel excitation system which allows to excite woven composite fan blades with any spatial and phase distribution as well as synchronous or non-synchronous vibration forcing with respect to rotation speed. The configuration of the excitation system allows each blade to be excited independently and therefore nodal diameter excitations can be performed with traveling (forward, backward or mixed) or standing waves. First rotations of the PHARE#1 test rig produced results at different rotation speeds, for several modes, nodal diameters and excitation levels. Typical results analysis and findings are presented in this paper.

In this work, it was proposed to use Kriging surrogate models for rotordynamics prediction in rotor-bearing systems. The motivation is to significantly reduce computation effort when evaluating the design space. First, fundamentals of rotordynamics are reviewed and the rotor-bearing system is modeled using the Finite Element (FE) method. Modal analysis is used to determine whirl frequencies and critical speeds while system dynamic behavior is evaluated in terms of the unbalance response. Subsequently, approximations of the input/output relationships created by the FE simulations are obtained by applying the Kriging interpolating method. The derived models work as fast-running surrogates for the full model. Comparison of the results from Kriging surrogates obtained using different training samples shows that the proposed methodology provides a computationally efficient and low-dimension mathematical relationship that can accurately predict rotor-bearing system outputs with considerably low training effort.

Rotating drilling for oil or geothermic applications uses a very slenderness structure hanging from to a derrick and made of a drill-string inside the drill well and linked to the bottom hole assembly (BHA). Vibrations provided by the nonlinear dynamics is due to the distributed unbalance masses, to well-assembly interactions, pulsating mud flow, bit-bouncing, stick-slip phenomena, etc. Understanding and controlling the vibration level of the rotating assembly in the well becomes an important key to avoid the fatigue failures and improve the reliability of the drilling operations. The paper focuses on the finite element modelling of the drilling assembly non-linear dynamics. The drill string-well bore contacts are modeled by a set of elastic stops. First, the static position of drilling assembly in the 3D-geometry well is calculated. Therefore, contact points and pre-stresses are predicted. The effect of the speed of rotation on the eigenvalues is then studied by plotting the Campbell diagram.

The paper investigates experimentally and numerically the nonlinear dynamics of a rotor supported by Active Magnetic Bearings (AMBs) and subjected to more or less severe motions from its support. In case of strong base excitations, the rotor can contact its touchdown bearings (TDBs) which are emergency bearings. The objective is to analyze the effect of the combination of mass unbalance forces, base motion excitations and contact nonlinearities on a rotor-AMB system response. The Finite Element method was used to model the on-board rotor. External force vectors and matrices with parametric coefficients related to the base motions appear in the equations of motion. The contact was modelled with a bilinear normal contact law and the tangential sliding friction effects are considered. Experiments were carried out on a lab-scale test rig that was mounted on a 6-axis shaker. At this stage, only harmonic base motions were considered. The numerical model was able to describe accurately the observed phenomena. AMBs were able to maintain the system under control, and the system remains stable even during the contact phase.

The seal force and oil-film force are two of the main factors which would cause the instability of rotor system, so it is important to further study the nonlinear dynamic characteristics of the multi-disk rotor-bearing-seal system. In order to establish the multi-disk rotor-bearing-brush seal system model of a gas turbine, the seal force model of brush seal and the nonlinear oil-film force model based on short bearing theory were adopted considering the lateral deflection of the disks. The equation of motion was solved by time simulation using the fourth order Runge-Kutta method. The influences of key parameters including rotor speed and eccentricity phase-difference on the vibration response and dynamic behavior of multi-disk rotor-bearing-brush seal system were discussed. The result showed that the system became more stable when the eccentricity phase-difference decreased.

The present work tackles the dead band clearance problem of rotors guided by ball or roller bearings. There are situations when the rotor can be only temporary in contact with the casing. The closed-loose nature of the rotor-stator contact leads to a non-linear rotordynamic response. A test rig dedicated to the experimental analysis of this problem was presented in a previous paper [8]. The test rig is based on a vertical rotor guided by ball bearings and lifted by an aerostatic thrust bearing. The ball bearings are mounted with three different radial clearances: “small”, “medium” and “large”. The results for the low and mild radial clearances showed a linear behavior of the rotor characterized by synchronous responses with forward or backward whirls. A non-linear signature of the rotor was obtained for the large radial clearance with sub-synchronous bifurcations and internal resonances. The present paper presents the numerical analysis of the same rotor and is intended to reproduce the experimental results. The rotor was modeled with Timoshenko beam elements. Full non-linear calculations were performed by simulating a constant acceleration of the rotor from zero to 400 Hz in 50 s. Calculations showed that the value of the dead-band clearance is a capital parameter for triggering non-linear responses of the rotor.

This paper presents both experimental and numerical study on the dropdown of a generator rotor in a two-stage radial gas turbine utilizing AMB system. The simulation unifies the FE-model of the flexible rotor and the dynamic model of backup bearings. The system under investigation includes a flexible rotor, an axial and two radial AMBs and two backup bearings, double row angular contact ball bearings. The recorded behavior of the studied rotor in the sudden failure of the electromagnetic field is demonstrated. Furthermore, the fine-tuned rotor-system model is used for studying the contact force and the contact stress in the backup bearing. The comparison between the measured results and the simulated results confirms that the used simulation tool can be applied for the design consideration of rotor-backup bearing system and enables to investigate the effect of various design parameters on the dynamic behavior of rotor in the dropdown.

One of the most important malfunction that can cause severe damage in rotating machines is the contact between fixed and rotating parts. The most common sources for rubbing is mass unbalance and instabilities due to fluid-rotor interaction. In this way, this paper presents a continuous rotor model for rubbing applications considering transverse shear, rotatory inertia, and gyroscopic moments. The contribution of it is to present a model to be applied in cases where these effects are not negligible. It is shown that for low slenderness ratio the model is equivalent to the commonly used Euler-Bernoulli continuous model. The normal and friction contact forces between the rotor and the stator are modeled using the Hertz contact theory, which is a nonlinear contact model, and the Coulomb friction model, respectively. In addition, the response of the rotor under impact was studied in the frequency domain using Wavelet Techniques for detection and characterization of rubbing phenomenon.

This paper discusses a modified model reduction technique for the nonlinear rubbing analysis of a rotor disk with its stator. The rotor system consisting of a rigid disk, shaft and bearings is modeled using finite elements, incorporating the effects of rotary inertia and gyroscopic moments of both shaft and disk. The stator is modeled as an added stiffness to the rotor system without considering the stator dynamics and dry friction effect at the contact. The nonlinearities are localized at the rub location which permits the use of model reduction techniques, making the finite element model more compact. Component Mode Synthesis with a Craig-Bampton type sub-structuring is an efficient technique for model reduction. But, this method has some limitations due to the presence of nonlinearities in the system. In this paper, a modified Component Mode Synthesis method with dynamic sub-structuring is developed for the reduction of complete finite element model into a smaller model containing nonlinear degrees of freedom (DOF) only. This method has an advantage over existing methods is that it can be used for systems with non-symmetric element matrices. The reduced model is solved using Harmonic Balance Method (HBM) coupled with a hypersphere based continuation algorithm.

The analysed rotordynamic system is modeled as a non-linear variable mass system and represents a part of a production line where an axially moving material is coiled on a rotating drum. The suitable and accurate simulation of the vibrations in a coiling process is important to predict the vibrations during standard operation and for special non-steady operation conditions. Variable parameters are present and bending vibrations of the rotor with the coiling drum and the transversal oscillations of the elastic strip are coupled. The longitudinal and transversal motion of the axially moving strip and the bending deflection of the coiling drum are considered by Rayleigh-Ritz approximations which involve the application of the extended equation of Lagrange for open systems. Simulations are performed for a non-linear rotordynamic system for different operation conditions. The results computed with a semi-analytic time-integrations algorithm are shown.

Linear rotor-dynamic analyses such as Campbell diagrams of damped eigenvalues and unbalance response analyses are well established for the practical design layout of rotors. They are also required according to many standards such as API. Nonlinear analyses are widely avoided because of their complexity, even if they would be necessary for relevant practical answers. Sometimes questionable substitute linear analyses are carried out in such cases. In this paper four cases requiring nonlinear analyses are described: A vertical pump with water lubricated bearings, a turbocharger with semi-floating oil lubricated bearings, an electric motor with rolling element bearings running through a resonance and a Pelton turbine on tilting pad bearings losing two buckets. The vertical pump is linearly unstable, because of the unloaded bearings. The nonlinear analyses are necessary to receive the limit cycles of the unstable system. In case of the turbocharger the outer oil film of the semi-floating ring bearing is highly nonlinear and cannot be correctly described linearly. In case of the motor running through a resonance the dynamic bearing loads are very high, because the rolling element bearings are not able to provide much damping. The behavior then becomes nonlinear. Moreover, the bearing clearance can lead to nonlinear behavior, if the bearings are not preloaded. The blade loss for the Pelton turbine leads to nonlinear behavior due to the high dynamic bearing load.

In this paper, the functionality of a swashplate mechanism coupled with a series of one-way overrunning clutches is studied. The novel mechanism is constructed by coupling a swashplate and one-way overrunning clutch with other mechanical components to allow producing a continuously varying gear ratio. To access the capability of the proposed mechanism, a multibody dynamic simulation of the said mechanism was carried out as follows. First, the kinematics of the components making the mechanism is studied, then followed by the dynamics of the entire system. Preliminary predictions dictate that the proposed mechanism has the potential to produce continuously variable output motion including the zero-output using a constant input. However, the results indicate that the swashplate mechanism should be studied further to allow obtaining a smooth output. Initial results indicate that the proposed mechanism has the potential of converting a constant rotational motion to a continuously variable rotational speed.

The drilling process consists basically of a drive motor at the top end (surface) that provides torque to rotate a cut tool (drill-bit) at the bottom end. To connect these extremities there is a torque transmitting slender element so-called drill-string. Due to the slenderness, the borehole wall/drill-string, and, mainly, the drill-bit/rock interactions, the system undergoes axial, lateral and torsional vibrations. Among these modes, torsional vibration is present in most drilling processes and may reach an undesired severe phenomenon: stick-slip. In this work, we perform experiments on a torsional test rig, which executes dry friction-induced vibrations. The test bench consists in a DC-motor, a low-stiffness shaft and two discs. The motor provides rotation to the whole set-up: one disc ($$R_1$$) is placed on the opposite extremity of the motor, and the second one is intermediately placed ($$R_2$$). Resistive torques may be applied in both discs and the behaviour of the system is analysed. It is possible to observe torsional vibrations and the stick- slip when a friction torque is applied on $$R_1$$ and during this phenomenon, another friction torque is applied on $$R_2$$. The presence of the second frictional torque as strategy of mitigation has a major influence on the dynamics as it may change from a stable limit cycle to a stable equilibrium and then preventing stick-slip phenomenon.

Vibrations in turning machining are one of the most common sources of problems. Bad quality finishing, decrease of the tool life, dimensional errors, and noise are some of the issues generated by these vibrations. To understand the role of each component, this work presents a model of a metal lathe including its drivetrain, and simulates it during the internal turning operation. The drivetrain is composed by an electric motor connected to the spindle through a pulley and belt transmission. The spindle was modeled as a rotor supported by rolling bearings, while the chuck with jaws and the workpiece were considered to be rigidly attached to the spindle. The interface between the workpiece and the tool was modeled considering their relative displacement and the machining condition, thus generating a set of cutting and drag forces that varies during the operation. The tool holder was modeled by three-node finite volume beam elements that are attached to the turret. The turret was connected to the machine frame through a total joint (configured as prismatic). This model was implemented in the dynamic simulation software MBDyn and a module was developed in C++ to mimic the interaction between workpiece and tool. Different configurations of the machine were tested, such as the diameter of the tool holder and the rotation speed of the spindle, and their influence on the drivetrain is reported.

In conventional automotive gearboxes, all gears are engaged, but not all of them are involved in transmitting power to the wheels. These unloaded gear pairs are, nevertheless, subjected to light forces due to slight torque and speed variations and also to the interaction between the tooth surfaces and the lubricant. Under certain circumstances, these conditions can lead to repeated impacts among teeth flanks and counter flanks. As a consequence, undesirable vibrations and noises are produced, which are commonly denominated as rattle phenomena, that result in premature fails and damage of other elements coupled to the transmission, as well as in a lack of passengers comfort. Within this framework, in this study, a survey of the available formulations, which simulate the forces behavior in lubricant environment under rattle conditions, has been performed. In a previous work, the authors assessed different formulations for this purpose, observing significant differences among them and also concluding that two effects should be considered in order to properly model rattle conditions. One is linked with the pressure variation due to the fluid entrance in the tooth conjunction, whilst the other is related to the lubricant squeeze when teeth profiles are approaching. Having this in mind, in this paper, the dynamic behavior of gear transmissions under low-torque conditions were assessed with different hydrodynamic formulations, which consider both squeeze and fluid entrance effects. With this purpose, these nonlinear forces derived from each formulation were obtained and compared for a sample transmission, simulating several working conditions of torque, speed and lubricant viscosity. The results are shown by means of the dynamic transmission error as well as the forces present in the conjunction.

This paper aims at constructing a novel hysteretic (non-reversible) bit-rock interaction model for the torsional dynamics of a drillstring. Non-reversible means that the torque on bit is not represented only in terms of the bit speed, but also of the bit acceleration, producing a hysteretic behavior. Here, the drillstring is considered as a continuous system which is discretized by means of the finite element method, where a reduced-order model is applied using the normal modes of the associated conservative system. The nonlinear torsional vibrations of the drillstring system are analyzed comparing the proposed bit-rock interaction model to a commonly used reversible model (without hysteresis). The parameters of the proposed hysteretic bit-rock interaction and of the commonly used reversible model are fitted to field data. Results show the system including a bit-rock interaction model with hysteresis effects reproduces a good approach of stick-slip cycle, and the simulated drillstring dynamics using the bit-rock interaction presents a similar behavior comparing to the field data.

In current Internal Combustion Engines (ICE), efforts have been conducted in order to reduce emissions levels and improve fuel efficiency. Some alternatives consistent with this strategy are: engine downsizing and reduction of the idling speed. However, adopting such strategies incur in a trade-off between ICE efficiency and increased torsional vibration levels that could damage Front-End Accessory Drive (FEAD) systems and components. The alternator pulley is another potential source of increased torsional vibration due to being coupled to the largest inertia of the FEAD assembly. Therefore, alternator pulley technologies have evolved aiming to provide vibration attenuation capability. The objectives of this work are to demonstrate the development of an alternator pulley to reduce the torsional vibration in the FEAD, and the development of a virtual model to evaluate the FEAD performance. Development of alternator pulleys to reduce torsional vibration generated by the crankshaft fluctuation can avoid premature failure and durability issues with other components of the system. Usually, these pulleys employ two distinct types of springs: a clutch spring and a torsion spring. Through analytical and numerical models previously developed for each spring, the set of springs of the decoupling pulley under development could be properly designed. Finally, functional prototypes are evaluated in static torque tests, dynamic evaluation in test benches and in-vehicle test. Simulations based on finite element method has demonstrated excellent correlation on vibration attenuation levels of the FEAD, based on a comparison with experimental results.

A planetary gearbox of a horizontal axis wind turbine drive train is modelled as a vibratory system and vibration response is investigated for detecting a typical gear tooth flaw. A detailed dynamic model involving two translational and one rotational degree of freedom for each component of the planetary stage is formulated. The gearbox stage considered in the study is a low speed planetary gear stage (three identical planets with spur teeth, sun and fixed ring gear) as the typical arrangement commonly used in wind turbine industry. The effect of gravity is incorporated in the mathematical formulation as the mass of the drivetrain components is considerable in such application. The vibration response of the elements is influenced by the gear mesh stiffness variations. The presence of a tooth crack shifts the localized mean value of gear mesh stiffness to a lower value. The localized change in turn influences the vibration response of all the components. In order to extract fault-induced vibration features, a difference signal is generated from the synchronous time domain vibration signals for the healthy and cracked tooth. The time domain and frequency domain data of the proposed difference signal are studied. They reveal useful information for the purpose of detection of gear tooth crack. The spectral characteristics can be used for condition monitoring and early detection of gear tooth crack for a wind turbine gearbox.

Theoretical investigations on rotor-stator rub phenomenon are available on wide range of problems. However the experimental studies are limited in numbers. Further, the measurement studies on torsional vibration during rub are hardly any. The present work reports and discusses measurement of rotor’s torsional vibrations during its contact with the stator and examines the possible rub diagnostic features. A simple rotor bearing system is made to interact with a stator pin mounted on a stiffer stator frame. The rotor assembly, with two discs and two support bearings, intends to model a turbopump where the central disc simulates the impeller and the overhanging disc is meant to represent turbine. A flexible coupling between the driver and the driven unit is provided to reduce the effects of any misalignment remaining in the system and to isolate the rotor from the motor. The measurement of torsional vibration is carried out using a torsional laser vibrometer. The measured signals during rub and no rub conditions are compared in time as well as in frequency domain to bring out the torsional vibrations features related to rub. Excitation of various torsional modes of the rotor system is experienced due to the frictional torque caused by the occurrence of rub. The presence of rotor’s torsional mode frequencies, rotational harmonics and the bending natural frequency in the spectrum of torsional velocity signals are indicative of rub.