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Über dieses Buch

IFToMM conferences have a history of success due to the various advances achieved in the field of rotor dynamics over the past three decades. These meetings have since become a leading global event, bringing together specialists from industry and academia to promote the exchange of knowledge, ideas, and information on the latest developments in the dynamics of rotating machinery.

The scope of the conference is broad, including e.g. active components and vibration control, balancing, bearings, condition monitoring, dynamic analysis and stability, wind turbines and generators, electromechanical interactions in rotor dynamics and turbochargers.

The proceedings are divided into four volumes. This fourth volume covers the following main topics: aero-engines; turbochargers; eolian (wind) generators; automotive rotating systems; and hydro power plants.

Inhaltsverzeichnis

Frontmatter

Aero-Engines

Frontmatter

Quantitative Analysis Method of Whole Aero-Engine Structural Design Based on Structural Efficiency

In the design of advanced Aero-Engines, it is necessary to carry out an effective quantitative analysis of the internal relations between structural features and mechanical characteristics. According to the structural features, function and performance of aero gas turbine engine, the conception and connotation of Structural Efficiency are proposed. By evaluating the Structural Efficiency, the benefits of the structural system can be quantitatively analyzed, to evaluate the contribution of the structure adopted in the Aero-Engine design process to the performance improvement of the whole engine. In this paper, the structural efficiency coefficient of one typical high bypass ratio turbofan engine is calculated by establishing appropriate evaluation parameters, and consequently the direction of structural optimization is pointed out.

Gang Peng, Chao Li, Huaqiang Zheng, Yanhong Ma, Jie Hong

Dynamic Model and Theoretical Investigation for the Fan-Blade Out Event in the Flexible Rotor System of Aero-Engine

The fan-blade out (FBO) from a turbofan rotor is a real possibility during the complex operation cycling of an aero-engine. This paper aims to understand the dynamic behavior of the aero-engine rotor system with the FBO event by theoretical approaches and numerical simulations. The physical process of the FBO and its effects on the rotor system are analyzed first, from which the main mechanical characteristics on different time scales are acquired. Then a timeliness dynamical model considering the whole process of FBO event is put forward based on the structural and mechanical characteristics of rotor. Moreover, some simulations for the flexible rotor in aero-engine with FBO are carried out and vibration characteristics are achieved.The dynamic response of FBO rotor is driven by a combination of typical mechanical processes. The results reveal that the sudden unbalance will increase the transient response and excite modal vibration of the rotor system. The asymmetry of inertia and the deceleration will introduce the parametric excitations into the rotor system. The blade-casing rubbing can increase the resonance speed of the rotor and cause the abundant frequency components, while the vibration amplitude and reaction force of the transient response are decreased. For the practical rotor system in aero-engine, this research can provide some theoretical guidance for the safety design.

Yanhong Ma, Yongfeng Wang, Jie Hong

Vibration Suppression of Additional Unbalance Caused by the Non-continuous Characteristics of a Typical Aero-Engine Rotor

The advanced aero engines have various features such as light weight, high efficiency and high power, so its rotor system is comparably weak, while the rotor often has to endure heavier weight loads. With loads of assembling and operating, the relative position between jointing interfaces will variate due to the relative slide of the interfaces and the changes of contact status. Dislocation of jointing interfaces can induce a deviation of the center of mass (CM) of the rotor system from its rotating axis, which implies an additional unbalance and may cause an engine vibration problem. In this article, a mechanism model is established to study the random influence of joints over the unbalance of rotor system. Then researchers use a typical aero-engine rotor as an example to investigate this topic. This study indicates that the additional unbalance of rotor system can be ascribed to the relative dislocation between jointing interfaces. The additional unbalance also shows a strong uncertainty due to the randomness of interfaces’ dislocation. Methods to control the technological parameters of joints should be utilized during the designing span of a rotor system in order to significantly depress the unbalance of rotor system and prevent engine from vibration effectively.

Chen Xueqi, Ma Yanhong, Hong Jie

Automotive Rotating Systems

Frontmatter

Vibration Analysis of an Electric Wheel Hub Motor at Stationary Operating Points

In the context of environmentally friendliness and challenging pollution limits the electrification of passenger cars becomes more and more important. In this contribution an innovative electrical drive for automobiles is presented and its vibration behavior is analyzed experimentally. In special, the vibrations of an electric wheel hub motor are studied in detail. For this purpose, a laser scanning vibrometer is used. To be able to measure the vibrations at the running engine a derotator is needed additionally to the laser scanning vibrometer. The electric wheel hub motor is investigated on a test bench at different stationary operating points which differ in the rotational speed as well as in the torque that is applied by an electric brake. Analyzing the vibroacoustic behavior of this special electric machine is of utmost importance as its sound radiation is directed straight to the passers-by of the car. The sound radiation of conventional cars drives is normally shielded and attenuated by the vehicle body and for this reason less critical. Moreover, the application of damping materials is more difficult if the engine is placed within a wheel. In the paper at hand different prototype stages of the electric wheel hub motor are presented. The working principle of this special engine is also explained. For the numerical simulations a holistic simulation workflow has been developed which takes into account the electromagnetic field as the most important vibration excitation as well as the structural vibrations coupled with an air volume around the engine to calculate the sound pressure. First, the electromagnetic forces are calculated which are then applied to excite the structural vibrations of the engine. Finally, the calculated surface velocity is used to excite the surrounding air volume under free field conditions to determine the radiated sound pressure level. In all three steps of the holistic methodology, the finite element method (FEM) is used for the numerical simulations. Beside identifying weak points of the engine prototype as well as obtaining a general understanding of such an electrical machine, the experimental data are used to validate a numerical model of the electric wheel hub motor. With the help of both the validated model and the gained experimental experiences the design of the wheel hub motor is improved. However, this contribution focusses on the experimental analysis of the structural vibrations of the running wheel hub motor.

Fabian Duvigneau, Sebastian Koch, Christian Daniel, Elmar Woschke, Ulrich Gabbert

Application of Pattern Recognition for the Mitigation of Systematic Errors in an Optical Incremental Encoder

The accuracy and reliability in the measurement of the instantaneous angular speed (IAS) by incremental encoders are fundamental for speed and torque control systems. An error in the acquisition of this variable may cause instabilities or even render the system unfeasible. Many works deal with this problem, which in some cases is caused by the imperfections in the disk manufacturing or also shaft misalignments. Due to the systematic character of these type of error, in this work an error pattern in the encoder signal of a vehicle dynamometer was identified by means of a calibration process and detected along the experiment by minimizing the total variation of the corrected angular speed curve. By making use of this procedure, not only the measurement became more accurate, but also the direction of rotation and angular position of the rotary system could be detected with only one channel of the encoder sensor being acquired. After the application of this method, the measurement error was reduced by 84.22%, even in transient conditions, without the application of further filtering methods, which may unwantedly lead to phase shifting in the IAS signal.

Elvis Bertoti, Rodrigo Y. Yamashita, Jony J. Eckert, Fabio M. Santiciolli, Franco G. Dedini, Ludmila C. A. Silva

Dynamic Behavior of Very-High Speed Rotors at Non-stationary Conditions

Speed reducers with input shafts spinning at very high speeds (up to 42 000 rpm) are generally associated to electric motors, which are more and more used especially in the automotive field, in order to bring the rotational speed to the most efficient window. Accurate modeling of those rotating machinary behavior is crucial to improve product reliability and to prolong machinery life. Many studies are conducted with an imposed angular speed, which is in most of the cases considered as constant or, in best cases, which follows a given variation law. In this paper, the study is performed with no assumption on the rotational speed. A variable driving torque is induced to the input shaft and the instantaneous angular speed (IAS) is deduced from the dynamic problem coupled to an angular approach. As a result, the IAS takes into account not only the induced torque perturbations but also the periodic geometry of the whole structure (e.g.: bearings and gears). The aim of this work is to extend the existing model based on the Finite Element Method by introducing an enhancement of the gyroscopic effect matrices without any assumption on the spinning speed. This model will lead to the introduction of coupling between the flexural and torsional degrees of freedom as well as to a non-linearity in the modeling of the studied system. The aim is to improve the accuracy of simulations for the rotor dynamics in non-stationary conditions especially when getting through critical speeds.

Emna Sghaier, Adeline Bourdon, Didier Remond, Jean-Luc Dion, Nicolas Peyret

Balancing

Frontmatter

Residual Modal Unbalance Evaluation Method by Mode Shape Weighted Optimization

In order to allow for good vibration performance of turbo machinery, high speed balancing of individual turbo-generator components in the balance facility is performed. High speed balance quality of a rotor with flexible behavior can be expressed in terms of residual vibration or residual modal unbalance. The traditionally used residual vibration method has the disadvantage that the balance quality significantly depends on bearing and support types, measuring system and other factors. Residual modal unbalances have very little sensitivity to these factors and can hence be used for direct comparison of the results from different balancing facilities. It also permits setting universal limits for a rotor frame-size that apply to all balancing facilities.The paper presents the Mode Shape Weighted Optimization Method for evaluating residual modal unbalances. This method allows considering all vibration amplitudes for all bearings and all resonance and service speeds at the same time. The method relies on the knowledge of mode shapes and takes advantage of their low dependency on support system properties. It allows evaluation of modal unbalances for modes below and above service speed. The optimization algorithm calculates the residual unbalance vector (compensation unbalance) in one step. Finally, the residual modal unbalance values are obtained by weighting the compensation unbalance vector with the corresponding mode shape.The Mode Shape Weighted Optimization Method allows for higher quality control of turbo-generator components and ensures comparability between different balancing facilities. Numerical and experimental investigations are presented to prove the suitability of the method.

Max L’vov, Bernd Lacombe, Ulrich Ehehalt

Simulation of the Ball Kinetic in Ball-Type Automatic Balancing Devices by Solving the Axisymmetric Navier-Stokes Equations in Annular Cavities

Automatic balancing devices are useful in order to balance rotating systems, which show variable unbalance configurations during operation, e.g. centrifuges, without the need for active components like controllers or actuators. The design of a ball-balancer consists of an annulus symmetric to the axis of rotation. It is filled with a viscous fluid and counterbalancing balls, which can move freely and oppose the rotor unbalance in the plane of the annulus when operated at supercritical speed. In order to determine the time for the balancing effect to be reached once the critical speed of the rotor is surpassed, sufficient modelling depth is needed to describe the movement of the balls during rotor run-up. Derived from transient simulations the influence of the balancer design parameters on the balancing process can be evaluated. A non-linear model of a ball-type automatic balancer is presented with which frictional forces based on Hertzian contact pressure and drag forces induced by the surrounding fluid are considered. Latter are obtained by solving the axisymmetric Navier-Stokes equations in the annular cavity by the method of finite differences. As a consequence, only one friction coefficient has to be quantified empirically. The model is included in multi-body simulations of tabletop centrifuges and the resulting angular movement of the balls is held against experimental data gained from video material of a balancer specimen with a transparent lid. Furthermore, the rotor deflection is compared with the simulation results.

Lars Spannan, Christian Daniel, Elmar Woschke

Balancing of Turbomolecular Pumps: Modal Balancing Approach and Experimental Results

Customer requests in terms of noise and vibration are becoming very challenging in most high-speed rotor applications. In turbomolecular pumps the main source of noise is the vibration due to rotor unbalance that is transmitted to the pump’s body through the bearings. Additionally, turbomolecular pumps may present several critical speeds that amplify the unbalance response and the generated acoustic noise. Therefore, a very accurate balancing process is required for the entire speed range of the pump.The goal of the present paper is to present and test a method for the identification of balancing mass sets for high speed rotors that allows to selectively balance one critical speed at a time while having minimum impact on the remainder of the unbalance response in the speed range of interest. The proposed method is used to obtain sets of balancing masses calculated to minimize the amplitude of critical speeds and the acoustic noise generated by the pump. Finally, the calculated mass sets are used to balance a group of turbomolecular pump prototypes. The results of the new balancing process are compared to the standard balancing process in terms of performance and process time showing relevant improvement in both parameters.

Carmelo Quartarone, Julian Beqari, Joaquim Girardello Detoni, Flavio Cometti, Enrico Emelli

Modal Balancing Using Parametric Combination Resonance

In traditional modal balancing, a representative response of each mode to be balanced must be present in the measurement data. This is usually achieved by measuring the rotor response close to each critical speed corresponding to the modes of interest. The main disadvantage of this procedure is the time consumed during run-up/run-down cycles: at least one for each test mass configuration for determining the influence coefficients. Besides, several critical speeds are passed, which may cause high levels of vibration or even several run-ups if the resulting unbalance is critical. This paper proposes a balancing method for which the system needs to rotate up to the first critical speed only. It is known that parametric combination resonance has the ability to transfer kinetic energy between the mode shapes of a flexible structure (modal interaction). Therefore, controllable bearings such as active magnetic bearings are used to introduce a parametric excitation at different parametric combination resonances, inducing a modal energy transfer from the first critical speed to higher modes. This energy transfer has a similar effect to that obtained if the rotor is operated near higher critical speeds. This allows for estimating influence coefficients and corresponding correction masses using a procedure similar to the traditional modal balancing. The proposed method avoids the need for spinning the rotor above its first critical speed; thus, saving time and allowing for high-speed rotor balancing at low speed. The theory of the proposed balancing method using parametric excitation is presented along with simulations to illustrate its potential.

Ricardo Ugliara Mendes, Fadi Dohnal

Effect of Magnet Mass Distribution on Balancing Quality of the High-Speed Permanent Magnet Turbo Generator

The main objective of this paper is to study the importance of rotor assembly procedure on balancing behavior of a high-speed rotor. The rotor consists of series of magnets in the electric motor section is considered as a case study. This study employs 3D beam elements based on the Timoshenko beam theory to model the model the dynamic behavior of the rotor. One of the solutions for accurate balancing is the minimization of unbalance force due to the assembly of parts with the prior balancing of those parts. In this case, although magnets had a unique design, by reason of manufacturing tolerances they have a different mass that can vary around 1.5$$\%$$ from their nominal mass, that can be considered as the subject of the importance of magnet arrangement. Based on the mass histogram of the real magnets, several sets of magnet masses are randomly generated. In the scope of the study, two critical speeds are covered by the speed range of analysis. The result emphasizes the need for making the arrangement prior assembly. The model is partially validated by experimental results.

Hamed Ghasemi, Behnam Ghalamchi, Toni Hartikainen, Jussi Sopanen

Numerical Analysis of Influence Coefficients for On-Site Balancing of Flexible Rotors

Balancing of flexible rotors by means of Influence Coefficients is a well-known method in the theory of rotor dynamics. For a successful application of the method Influence Coefficients are needed. They are defined as the vibration response at one measurement point due to a single unbalance in one of the balancing planes. Influence Coefficients are usually determined by measurements in test runs with defined test weights. However, Influence Coefficients can also be determined by means of a numerical analysis. This needs of course a very good model for the rotor train, including all important rotor dynamic effects. In this project a trial is made to determine Influence Coefficients by means of modelling and numerical simulation.

Rainer Nordmann, Eric Knopf, Bastien Abrate

Electromechanical Interactions in Rotordynamics

Frontmatter

The Influence of the Vibration Suppression on the Rotor Crack Detection Performance

The feasibility of controlling the vibrations of rotating machines while performing online crack detection is addressed in this paper. For this purpose, two controllers are compared, namely $$ LQR $$ and $$ H_{\infty } $$, which represent optimal and robust control strategies, respectively. A non-dimensional Jeffcott rotor model is employed to simulate the dynamic behavior of a rotating machine. In addition, a crack is introduced in the shaft using the so-called Mayes’ model. An active magnetic bearing (AMB) is placed as an actuator at the disc location along the rotor. For each control technique, different strategies are implemented to evaluate their effectiveness on both attenuating the vibration level and detecting the fatigue crack. Conclusions are drawn regarding the effectiveness of the control strategy for each phenomenon.

L. S. Leão, A. Sahinkaya, A. A. Cavalini, V. Steffen, J. T. Sawicki

A Co-energy Based Approach to Model the Rotordynamics of Electrical Machines

New technological fields of application, as for example electric vehicles and closely related lightweight design increase the sensitivity of electrical machines towards torsional and lateral rotor oscillations. The modelling of such electro-mechanical processes is a challenging multiphysical task. In this context, a vast majority of scientific publications use direct approaches to model the problem. These methods derive the equations of motion from Newton’s and Kirchhoff’s laws. In contrast to that, this work proposes a fully coupled indirect approach to the problem using Lagrange-Maxwell equations and the involved magnetic co-energy functional. Such an indirect approach provides for distinct advantages concerning energetical consistency, electro-mechanical coupling and computational effectiveness. Modelling implications like the dependency of the magnetic force on the mechanical motion are outlined and the applicability is shown for a transient simulation of a cage induction machine.

Felix Boy, Hartmut Hetzler

Influence of Various Control Strategies on Transient Torsional Vibrations of Rotor-Machines Driven by Asynchronous Motors

In the paper, a dynamic electromechanical interaction between the selected kind of rotating machines and their driving electric motors is investigated. These are the high-speed beater mills and crushers as well as blowers, pumps and compressors, all driven by the asynchronous motors through elastic couplings with linear and non-linear characteristics. In particular, there is considered an influence of negative electromagnetic damping generated by the motor on a possibility of excitation of resonant torsional vibrations. Moreover, for the asynchronous motor in transient and steady-state operating conditions, there are tested several control strategies which are based on the closed-loop vector and scalar principles. The theoretical calculations have been performed by means of the advanced structural mechanical models. Conclusions drawn from the computational results can be very useful during a design phase of these devices as well as helpful for their users during a regular maintenance.

Tomasz Szolc, Robert Konowrocki, Dominik Pisarski, Andrzej Pochanke

Vibration Effect by Unbalanced Magnetic Pull in a Centrifugal Pump with Integrated Permanent Magnet Synchronous Motor

Unbalanced magnetic pull (UMP) effect in a permanent magnet synchronous machine (PMSM) is investigated. The force model is established analytically based on previously studied model by modulating the fundamental magnetomotive force (MMF) wave by air gap permeance and the corresponding force components are evaluated via Maxwell stress tensor method. For considering real rotor dynamic condition, mixed (i.e. static and dynamic) and axial-varying eccentricity are modeled. The rotor bearing system including this UMP model is established by two methods. In the first method, UMP is included as a linear negative spring in the rotor model, while in the second method, the UMP is added as an external force. Rotor dynamics of a centrifugal pump driven by integrated PMSM is modeled using beam elements and different modeling approaches for UMP are applied. From the results, vibration effect of UMP is investigated and difference between two methods is interpreted. For verifying the analysis results, experimental work is conducted for the pump test rig, where the eccentricity condition are produced and the frequency spectra result are obtained. Through these analysis and experimental work, negative stiffness effect and additional vibration excitation by UMP are observed and interpreted.

Heesoo Kim, Atte Posa, Janne Nerg, Janne Heikkinen, Jussi Sopanen

Characteristic Parameters Estimation of Uncertainties Present in an Active Magnetic Bearing Integrated Flexible Rotor System Using Dynamic Reduction Technique

In this article, an identification algorithm is developed to estimate the characteristic parameters of uncertainties present in rotating machines. A dynamic system consists of two flexible shafts each having a rigid disc and an active magnetic bearing (AMB) at its mid–span, mounted on flexible bearings at ends and connected together with a flexible coupling is considered for numerical simulation. Finite element method (FEM) is used to obtain dynamic equations of motion (EOMs) for coupled flexible rotor system integrated with AMBs. An identification algorithm based on least squares technique is developed to estimate the characteristic parameters of uncertainties/faults (i.e., bearing, coupling and residual unbalance) present in the rotor system. FEM is more accurate and realistic approach to model real rotor test rigs but degrees of freedom (DOFs) of the system increases as the number of nodes increases. Accessibility of these DOFs and accurate displacement measurements are the most challenging problems in the real rotor test rigs. To overcome this difficulty, a dynamic reduction technique is applied in the developed identification algorithm to eliminate some linear and all angular DOFs (that are practically immeasurable and to avoid difficulties of number of sensors). A Proportional Integral Derivative (PID) controller is used to obtain the controlling current for AMBs to stabilize the rotor system. The EOMs derived is solved by fourth order Runge–Kutta method to generate the displacement and current responses. The time domain responses are converted into frequency domain using Fast Fourier Transform (FFT). Full spectrum analysis is performed to estimate the desired characteristic parameters. The effectiveness of the algorithm is checked for measurement error and found to be excellent.

Sampath Kumar Kuppa, Mohit Lal

Progress in Calibrating Active Magnetic Bearings with Numerical and Experimental Approaches

This paper shows numerical approaches to simulate the static solution for magnetic bearings. The virtual work method is used to compute the force from the vector potential field. The partial differential equation for static magnetic fields is derived from theory and solved with an FEM approach. This is done using two different software programs, MATLAB and the open-source software femm. Also, a test rig is presented to validate the calculated forces. The results provide good conformity although deeper research needs to be done on material characterization. At the end, an outlook is given for use of calibrated magnetic bearings and also where further research is necessary.

Johannes Maierhofer, Christian Wagner, Thomas Thümmel, Daniel Rixen

Fluid Structure Interactions in Rotordynamics

Frontmatter

Nonlinear Dynamics of a Rotary Drill-String Immersed in a 3D Geometry Well

Oil or geothermic rotary drilling is composed with a very slenderness drill-string which is subjected in particular to the tool-bit excitations. Therefore a great number of vibratory phenomena concerned with the axial, lateral and torsional behavior are exhibited: whirling, bit bouncing, stick slip to cite just a few. In order to predict the rotordynamics of such a structure, the model proposed is based on Timoshenko beam elements immersed in a 3D geometry well. A constant rotation speed in imposed at the top of drill-string. A fluid-structure interaction model that takes into account the drilling mud is used. The effect of drilling mud in drill-string vibration is studied by varying the well trajectories.

Q.-T. Tran, K.-L. Nguyen, Lionel Manin, M.-A. Andrianoely, Sebastien Baguet, Stephane Menand, Regis Dufour

Modeling the Rotor Vibrations of a Hydropower Unit During a Runaway Regime

The lateral vibrations of the shaft of a 72-MW propeller turbine are modeled and compared to experimental data for a runaway regime. The lateral forces acting on the runner and the generator are calculated and thereafter applied as input to the rotordynamic model. The CFD (Computational Fluid Dynamics) model considers the full geometry. Fortran routines are used to implement the movement of the guide vanes using a moving-mesh technique and to vary the runner speed according to the torque balance. The electromagnetic forces are modeled before disconnection from the grid.Attention is devoted to the modeling of the two guide bearings. A linear model using dynamic coefficients and a nonlinear model solving the full Reynolds equation are incorporated into the transient analysis of the rotor. The rotordynamic model can capture the lateral vibrations of the shaft despite some discrepancies. The response of the nonlinear bearing model has better agreement with experimental measurements than that of the linear model. The presence of cavitation in the CFD model slightly improves the results.

Samuel Cupillard

Constructing Accurate Phenomenological Surrogate for Fluid Structure Interaction Models

The accurate prediction of structural instability caused by vortex shedding behind bodies or by nonlinear unsteady aerodynamic is fundamental to avoid the degradation of structural performance or even failure of the system. Numerous approaches can represent analytical models to modeling both the structure and fluid. The CFD (Computational Fluid Dynamics) approaches consists of solving the Navier-Stokes equations directly, mostly limited by heavily computational costs that, many times, are tough to satisfy in the practical engineering. To increase the expectations of solving practical problems, the use of phenomenological surrogate models, are an alternative approach for the underlying physics, where phenomenological equations emulate the fluid dynamic forces acting on the structure, have become an essential tool to simplify the analysis and can be a very useful tool in broad industrial applications. However, constructing accurate surrogate models introduce additional challenges that will be addressed in this work. Most of these models present a series of empirical parameters that need to be calibrated from experimental data. To build an accurate phenomenological model we need putting this parameter variability in the general context of Uncertainty Quantification (UQ). We present a phenomenological model for fluid-structure interaction to be calibrated. In the first stage of this processes, we do global sensitivity analysis for the empirical parameters of the model, where uncertainty source is introduced earlier using the Sparse Grid Stochastic Collocation method. After this, a backward parameter estimation analysis is done using a Bayesian technique to calibrate these empirical parameters, through exploring posterior density functions. Synthetic data were generated as reference simulating experimental data to show the calibration technique used. This kind of analysis can help to understand the effects of varying empirical parameters in the response variables. The influence of these parameters and other coefficients that affect the dynamical response is analyzed and also discussed.

Gabriel M. Guerra, Rodolfo Freitas, Fernando A. Rochinha

Hydro Power Plant

Frontmatter

Input Force Identification in a Francis Hydro Turbine Unit Model

This work aims to present a force identification process applied to a Francis hydropower generating unit. The evaluation of the forces that are exciting a rotating machinery under operation condition can be used to monitor the health of the structure, thus reducing the risks of malfunctions. Here, a model-based methodology for force identification of mechanical systems is presented, aiming at both detecting and monitoring the appearance and development of abnormal forces. A force identification methodology based on orthogonal functions was developed considering that the modal base of the healthy rotating system is known, which permits to perform the modal force identification by using a reduced number of measures. The methodology conveyed is based on the integration property of orthogonal functions, which transforms the matrix differential equation that governs the dynamic behavior of the system into an algebraic equation. In a previous work, the methodology was applied to a laboratory test rig, where the identification procedure was validated both numerically and experimentally for a cracked rotor. Herein, the methodology is applied to a Francis hydropower unit, intending to demonstrate its applicability for industrial and complex systems. The vertical machine is supported by three radial bearings and one thrust bearing and its forces were evaluated for different scenarios. The obtained results demonstrated that the proposed modal force identification methodology can be potentially used to evaluate the forces actuating on the hydraulic turbine.

Tobias S. Morais, Aldemir Ap. Cavalini, Gilberto P. Melo, Valder Steffen

Parametric and Self-Excitation in Rotordynamics

Frontmatter

Balancing High-Speed Rotors at Low Rotation Speeds Using Parametric Excitation

Presented is a novel method allowing to perform mass balancing of flexible vibration modes, while rotating at low speeds. Through special external excitation, the projection of imbalance forces on vibration modes corresponding to high rotation speed can be found. The main merit of this method is that it uses measurements taken at low speeds, which anticipate the imbalance effects at considerably higher speeds. Standard mass balancing procedures of flexible bending modes, require the rotor to be rotated up to its operating speed. High speed rotors such as small jet engines and turbochargers cannot be rotated to such high speeds at laboratory conditions, and therefore are usually balanced using commercial balancing machines that are limited to low speeds. At low speeds it is impossible to detect the projection of imbalance forces on high frequency modes and thus low-speed balancing can worsen vibrations once the system is operational.The present paper outlines a method whereby parametric excitation is employed to selectively amplify the imbalance response, and find the projection of the imbalance on any desired mode of vibration while rotating at low speeds. This means that the effect of imbalance at any critical speed, can be found without the need to actually rotate the device at these speeds.In order to perform the proposed procedure, the system to be balanced is driven by actuators with signals containing several frequencies. These signals create an excitation pattern that creates large sensitivity to the forces caused by imbalance at low-speeds.

Shachar Tresser, Amit Dolev, Izhak Bucher

Rotordynamics of Micro, Nano and Cryogenic Machines

Frontmatter

Experimental Investigations on Vibration Characteristics for Bearing-Rotor System of Micro Gas Turbine

The dynamic characteristics of the rotor-bearing system for micro-gas turbine are the key factors that affect the safe and stable operation of the micro-gas turbine. This paper carried out the experimental investigations on the vibration characteristics during the speed-up process of rotating shaft, based on rotor structure of micro gas turbine generator supported by aerostatic bearings. Rotor vibration characteristics during conical whirling critical speed area, mixed control area, surge area, self-holding speed area, and bending critical speed area were analyzed. Simultaneously effects of bearing supply pressure and radial clearance on the shaft vibration characteristics were studied by experiments. The results showed that the ignition fuel flow has stepped increase when the ignition fuel valve was opened, which caused easily the rotor and bearing rubbing. And the reasonable bearing radial clearance and gas supply pressure can effectively restrain the occurring of the low frequency whirling and gas film oscillation, and improve the bearing-rotor system stability.

Dongjiang Han, Long Hao, Jinfu Yang

Dynamic Analysis of Rotating Motor Protein (ATP Synthase) Using FEM

The ATP synthase is a vital protein structured enzyme for energy production in our cells which synthesize the molecule adenosine tri-phosphate (ATP). ATP synthase is located at the inner membranes of mitochondria. The protein consists of two coupled rotary molecular motors, called F0 and F1, the former one being membrane embedded and the latter one being solvent exposed. Molecular motor can produce constant 40 pN·nm torque, over broad range of speed 10 to 400 rps, works in high efficiency. Structure of a rotating motor protein is very interesting and much different than classical engineering motors. Motor protein has one rotor sharing by two motors. Therefore, it rotates in two reciprocal purposes. Most of the research on ATP synthase is based on experimental observations. There are some computer simulation studies on the motor proteins to determine their mode shapes. Upon this, rotor dynamics analysis can help to estimate the correct mode shapes during the rotation and, to determine the critical rotational speeds. In this study, the dynamics of rotating motor protein will be investigated by using finite element modeling based on beam theory. Campbell diagram and resonance profiles has been obtained.

Ismail Tirtom, Xu Luo, Eiji Hatayama

Turbochargers

Frontmatter

Application of Regularised Cavitation Algorithm for Transient Analysis of Rotors Supported in Floating Ring Bearings

In order to analyse the dynamical behaviour of fast-rotating, lightly loaded rotors with floating ring bearings, which mainly occur in turbochargers, a suitable simulation method is required. For that purpose, an online solution of the Reynolds differential equation within a transient rotor dynamic simulation is applied. In addition to the hydraulic coupling of inner and outer lubrication film in the floating ring bearing, a mass-preserving cavitation model is introduced. Therefore, the algorithm of Elrod is adopted by use of a regularisation scheme in the differential equation in order to eliminate the originally occurring numerical problems under transient loads. The developed program is validated based on data available in the literature, as well as on the basis of test rig measurements for a passenger car turbocharger. Finally, the achievable result quality is examined in relation to the computational cost under successive reduction of the hydrodynamic modeling depth.

Steffen Nitzschke, Elmar Woschke, Christian Daniel

Influence of Temperature and Injection Pressure of Lubrication in the Vibration of an Automotive Turbocharger

The strategy of supercharging using turbochargers coupled to internal combustion engines (ICE) is becoming ever more used in the transportation industry. The power density increase, fuel consumption reduction and downsizing are some of its main advantages. To ensure the system operation durability, some factors must be considered in order to avoid deterioration and early turbocharger failure, mainly in the thrust bearing. Therefore, this work aims to correlate injection temperatures and lubricating oil pressures of an automotive turbocharger with the amplitude of component vibration, presenting experimental results of axial synchronous response obtained through tests performed in a standard turbochargers test bench. In these experiments, the turbocharger is submitted to a run-up speed profile. It is possible to perform a quantitative analysis with the obtained data, that correlates the aforementioned parameters and shows the impact that each change has with the vibrational response amplitudes.

Oscar R. Sandoval, Luiz H. Machado, Bryan Caetano, Isadora F. Lara, Ramon Molina

Uncertainties, Reliability and Life Predictions of Rotating Machinery

Frontmatter

Stochastic Collocation Approach to Bayesian Inference Applied to Rotating System Parameter Identification

The analyzed problem is the identification of fault parameters taking into account the stochastic characteristic of the system. The objective is to estimate the unbalance parameters, as the unbalance moment, phase angle and axial position of the unbalance force applied to the rotor. Therefore, experimental tests with the rotor to obtain the unbalance response is performed. This work aims the comparison between Bayesian inference with Markov Chain Monte Carlo method (MCMC), using Delayed Rejection Adaptive Metropolis algorithm (DRAM), and Stochastic Collocation through Generalized polynomial chaos expansion. This method has computational cost smaller than the MCMC methods, and it could be used as an alternative method for stochastic simulation. The Bayesian inference with MCMC and DRAM is based on previous works. However, the application of the MCMC have a high computational cost. Therefore, the Stochastic collocation is introduced into the likelihood function of the Bayes theorem for a faster convergence rate. The low computational cost of the collocation is evaluated and the results of both methods are compared to determine the convergence and precision of the collocation method.

Gabriel Yuji Garoli, Natalia Cezaro Tyminski, Helio Fiori de Castro

Application of Stochastic Collocation on Eigenfrequencies Analysis of a Rotor-Bearing System

Rotating machines have a remarkable importance on industry and understanding their behavior may be crucial for the production. Rotors supported by journal bearings are subjected to fluid-induced instability and the occurrence of this phenomenon is influenced by parameters that may vary randomly, so the problem of the identification of the stability threshold is stochastic. This paper applies the Stochastic Collocation method to solve this problem for a given rotor system. The validation of the method is made by the comparison of the results to the results of Monte Carlo simulations for the same problem. The Monte Carlo method requires a great number of simulations for a proper convergence of the results, while the Stochastic Collocation method requires fewer simulations. This difference implies on a considerable processing time difference for the two methods, several hours for the Monte Carlo against some minutes for the Stochastic Collocation. The results of the methods differ on some features: the probability density function generated by the Stochastic Collocation doesn’t fit the normalized histogram generated by the Monte Carlo and the variance of the stability threshold present a considerable difference on the methods. However, the lower and upper limits of the stability threshold on both methods is nearly the same, as well as the mean value for the stability threshold.

Laís Bittencourt Visnadi, Gabriel Yuji Garoli, Hélio Fiori de Castro

Stochastic Modeling of Rotordynamics for Electrical Fuel Pump Application

Electrical fuel pumps play a key role in the automotive area, having the function to delivery fuel at proper pressure and flow rate to the injectors of internal combustion engines. In-tank centrifugal type of fuel pump, located submerged in the fuel tank, is currently the most widely used in the market. There is an increasing demand to control and minimize vibration levels experienced by fuel pump under operation that must comply with the requirements. Evaluation of the 8th harmonic order is critically important once its represents the vibration caused by the sliding contact among spring loaded carbon brushes and segments of commutator of electrical machine. In the present paper, a stochastic model in rotordynamics is developed considering uncertainties in the parameters that influence the dynamic responses of fuel pump system. The uncertainty analysis is conducted by applying Monte Carlo simulation method combined with the Latin Hypercube sampling. The obtained results show that the presented stochastic model is able to ascertain design parameters of fuel pumps reasonably.

Andre Morais Ferreira, Helio Fiori de Castro

Effect of Uncertainty in External Forcing on a Fluid Lubricated Bearing

Developments in industrial applications motivate improvements in fluid lubricated bearing technology, enabling smaller face clearances and increased rotation rates. Associated film lubrication technology aims to improve efficiency and reliability. A bearing model is developed to evaluate the effect of external, potentially destabilising, random forcing applied to a pair of highly rotating axisymmetric bearing faces, separated by a thin fluid film. Two cases of random external force are examined. A first study considers an imposed random force disturbance constrained to a fixed period, where the average minimum face clearance together with the probability it reaches a specified gap tolerance. More general uncertainties are associated with more complex external forcing and takes the form of a white or coloured noise. In this case the average time for the face clearance to reach a prescribed tolerance is examined.Results can inform bearing design, providing an indication of the effect of disturbances on the average lifetime and identify constraints on operating conditions for safe and reliable behaviour.

N. Y. Bailey, S. Hibberd, H. Power, M. V. Tretyakov

Dynamic Analysis of Rotating Systems Considering Uncertainties in the Bearings’ Parameters

Industrial applications, like steam turbines and pumps, require an adequate rotor and bearing modeling to predict its dynamic behavior. The use of robust models allows simulating the dynamic condition in order to prevent critical operation and possible faults. In general, the dynamic analyses of rotating systems are performed with deterministic models, however, they do not take into account uncertainties that could affect the system response. Thus, uncertainties analysis related to the components that compose the rotating machines are important to better estimate the response and guarantee the adequate operational conditions of the rotor system. This paper aims to analyze the dynamic behavior of rotors considering journal bearing parametric uncertainties. The shaft is modeled with the Timoshenko beam and a computational model is constructed by means of the Finite Element Method (FEM), where the rotor is supported by short fluid film bearings (Orcvik model). Uncertainties in the bearings’ parameters are taken into account. The probability theory is used for the uncertainty modeling, and Monte Carlo simulations are applied to approximate the statistics of the response. The analyses performed in this paper evaluate mainly the influence of uncertainties in the first natural frequency and the vibration orbit of the shaft inside the bearing. It has been observed that the response of the system, for instance, the first natural frequency and the rotor’s orbit, might change due to uncertain bearing coefficients, and the radial clearance is the most influent parameter in the simulations delevoped.

Douglas J. Ramos, Adamo R. Ferraz, Gregory B. Daniel, Thiago G. Ritto

Modal Strain Energy Approach Applied in an Uncertainty Propagation Analysis Dedicated to Rotating Machines

The vibration responses of rotating machines can be affected by the inherent uncertainties of their parameters. Therefore, the study of uncertainty quantification in rotating machines is relevant aiming at both increasing the performance of the machine and preventing failures. Among the various stochastic approaches used to model the uncertainties affecting the system, the stochastic finite element method received attention in the last few years. Uncertain parameters are commonly discretized by using Karhunen-Loève expansion together with Latin Hypercube and Polynomial Chaos. In the present contribution, the uncertain information is treated by using the Latin Hypercube approach. In this context, uncertainty analysis based on stochastic methods is an expensive task when applied to rotating machines of industrial interest. Thus, reduced models become an interesting alternative. The Modal Strain Energy (MSE) approach is commonly used due to the representativeness of the obtained reduced model and computational time savings. In this context, this paper is dedicated to the analysis of the uncertainties that affect the dynamic behavior of a horizontal rotating machine, composed by a flexible shaft containing two rigid discs and supported by two ball bearings. The finite element model of the considered rotor system was reduced by using the MSE approach. The obtained results demonstrated the efficiency of the methodology conveyed.

Daniel F. Gonçalves, Tatiane N. da Costa, Romes A. Borges, Aldemir Ap. Cavalini, Valder Steffen

Wind Turbines and Generators

Frontmatter

Aerodynamic Performance and Annual Energy Production of Small Horizontal Axis Windmill Using Different Airfoils

Wind energy is considered as a clean energy source of dominated technology and well accepted by the populations. The literature shows more than 80 countries having wind installations and there is the expectation to have expanded investments to about U$ 3.6 trillion until 2040. High capacity wind generators are well developed and usually installed offshore where the wind velocity is relatively high and constant over most of the year. On the other hand, small windmills are usually installed for individual and community use in urban and isolated areas. These machines are usually supposed to generate energy at relatively low wind speeds, have simple construction and relatively low maintenance cost. This paper seeks to determine the aerodynamic performance and annual energy production for small horizontal axis windmill of 10 kW nominal power using airfoil of families NACA, Gottingen and Selig. The formulation of the aerodynamic model is based on the combined momentum and blade element theory. A numerical code is developed and validated against available numerical results showing good agreement. From the numerical predictions, it was found that for nominal speed of 10 m/s Gottingen airfoil produced the highest amount of energy. Further numerical investigation was realized to determine details of the rotor blades such as chord and twist angle distributions along the blade, variation of the axial and tangential induction factors and distributions of thrust and torque along the blade length. The results indicated that the Gottingen airfoil GO482 produced the highest values of coefficient of power and the biggest annual energy production in comparison with the investigated NACA and Selig airfoils. Because of this good performance it can be recommended for small windmills applications.

W. M. Okita, K. A. R. Ismail, L. F. M. Moura

Dynamic Response of a Lightweight Stator Structure for a Large Diameter Direct-Drive Wind Turbine Generator

A lightweight wheel structure developed for rotor and stator use in large diameter direct-drive wind turbine generator is presented. The wheel structure uses layered sheet-steel elements to form the spokes and rim. This novel wheel structure is assumed to be more flexible than the existing conventional machine designs. Concerns with the dynamic response of the structure form the key motivation of the study presented here. As such, a computationally efficient methodology to predict the dynamic response has been presented. The dynamic model is employed to simulate the transient effects at startup and effects of cogging excitation on the direct-driven wind turbine.

Charles Nutakor, Scott Semken, Janne Heikkinen, Jussi Sopanen, Aki Mikkola

Simulation and Analysis of the Influence of the Support Structure on a Wind Turbine Gear Set

This work presents the numerical modeling, simulation and analysis of a wind turbine gearset supported by a flexible structure model. Gearboxes based on epicyclic gear trains applied to wind turbines have some advantages, i.e., compactness, robustness and low maintenance requirements. The gearbox is one of its main components because it is responsible for transforming the low angular speed of the rotor into the higher operation speed of the induction generator. Failures in this component cause loss of efficiency and directly impact the energy generated. The gearbox is attached to the nacelle, which is supported by the wind turbine tower. Wind gusts and shear can cause vibration that affects the tower and the nacelle and, therefore, all the components attached to them. To model these phenomena, a detailed model of a 600 kW turbine was built using the MBDyn software. The bearing, gear and the induction generator models were implemented as user-defined modules and were further integrated into the complete model of the wind turbine. Results showed that the gearbox components were affected by the dynamic behavior of the support structure and, therefore, its influence should be accounted for in the design of wind turbines.

Eduardo Paiva Okabe, Pierangelo Masarati

Aerodynamic Evaluation of Gottingen and Joukowski Airfoils for Use in Rotors of Small Wind Turbines

Climatic changes and global warming resulting from production and utilization of fossil fuels and other human activities accelerated research to replace effectively fossil fuels. Wind energy appears at the top of the list of the viable candidates to reduce dependence on fossil fuels. The technology for large and medium wind turbines is well dominated and usually installed to supply electricity for distribution grids. Small wind turbines are usually installed in remote and isolated areas. This work investigates alternative airfoils, Gottingen and Joukowski, for application in small wind turbines capable to operate efficiently at small wind velocities. The investigation includes aerodynamic analysis of the effects of varying airfoil, the chord distribution and number of blades on the torque and power coefficients. A home-built numerical code based on the Blade Element Momentum (BEM) theory validated against available experimental and numerical results is used. The numerical code and the Xfoil software were used to adjust the aerodynamic data of the airfoils. The elliptic chord distribution and the linearly tapered blades are found to be viable and efficient. The increase of the number of blades increases the torque at low velocities but not enough to achieve the maximum power. Friction losses and limitations imposed by the rotational speed due to high solidity ratios reduce the gains in efficiency of rotors with more than four blades. The airfoils J9.513 and GO447 are found more efficient than the reference airfoil S832 at small velocities but show inferior performance at speed ratios more than 7.

Thiago Canale, Kamal A. R. Ismail, Fatima A. M. Lino

Development of a Wind Turbine Blade with Dedicated Profiles by Schmitz’s Optimum Dimensioning Systematization

The wind energy always has been a source used by man, since antiquity with Dutch mills and sailing craft, but only nowadays, it has become attention center of studies, once glimpsed the economic viability of the application for big scale generation of electric energy, the abundance of appropriate regions in Brazilian territory and their sustainable character, indispensable today. Given this new energy scenario, there is a need to develop new technologies and components that optimize and reduce their cost. Seeing the nationalization of this technology as a way to reduce costs, the objective of this work is the development of a new wind turbine blade, with total power rating of 2.6 MW, power rating control by variation of pitch angle, operational wind velocity of 11.0 m/s, rotor rotation of 2.2 rad/s and 48.7 m length using dedicated wind turbine aerodynamic profiles by the systematization of the methodology in use. Through the blade element theory (BET) with computation of losses developed by Schmitz [1], we came to the automation of the development of this component with the aid of computational tools such as electronic tables and the CAD environment. In this way, the present work not only resulted in a new wind turbine blade geometry, but also in a systematization of the dimensioning methodology, which allows the development of infinite geometries, by simply changing the key criteria that describes the meteorological conditions and the parameters of generation, giving rise to a wide industrial application.

A. R. de Oliveira, A. B. da Rocha, E. da T. Marcelino, R. I. Lopes, J. V. de M. Rodrigues, R. N. C. Duarte
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