Instytut Podstawowych Problemów Techniki

Streszczenie:

We created a Physics-Informed Neural Network (PINN) to model the propagation of fatigue cracks. The analyzed object is a high-pressure Nozzle of an industrial gas turbine. The models are based on a Recurrent Neural Network with an embedded Feedforward Neural Network to estimate the stress intensity factor. The thermal stresses are calculated based on engine operational data, leveraging a Finite Element Analysis. However, the time series are available just for 54% of the start-stop cycles, and only 13 crack measures were recorded. Three separate models were trained based on ten, two, and one observation, respectively. The importance of the empirical data was regulated during the training to avoid solutions inconsistent with the underlying physics. The models generalize well and predict accurately also outside the training domain. Additionally, we propose a novel method of scaling models based on PINNs and transferring knowledge between domains. It enables predicting in the target domain, even if damage measures are unavailable. The obtained results confirm the effectiveness of this approach.

Słowa kluczowe:

Physics-informed neural networks , Predictive maintenance , Fatigue cracks , Regression analysis , Small data , Turbomachinery

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Many industrial rotating machines driven by asynchronous motors are often affected by detrimental torsional vibrations. In this paper a method of attenuation of torsional vibrations in such objects is proposed. Here, an asynchronous motor under a proper control can simultaneously operate as a source of drive and actuator. Namely, by means of the proper control of motor operation it is possible to suppress torsional vibrations in the object under study. Using this approach, transient and steady- state torsional vibrations of the rotating machine drive system can be effectively attenuated as well as its precise operational motions can be assured. The theoretical investigations are carried out by means of a structural mechanical model of the drive system and an advanced circuit model of the asynchronous motor controlled using two methods: the direct torque control – space vector modulation (DTC-SVM) and the rotational velocity controlled torque (RVCT) based on the momentary rotational velocity of the driven machine working tool. From the obtained results it follows that by means of the RVCT technique steady-state torsional vibrations induced harmonically and transient torsional vibrations excited by switching various types of control on and off can be suppressed as effectively as using the advanced vector method DTC-SVM.

Słowa kluczowe:

rotating machine,drive system,control methods,asynchronous motor,torsional vibrations

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The principal features essential for the success of an orthopaedic implant are its shape, dimensional accuracy, and adequate mechanical properties. Unlike other manufactured products, chemical stability and toxicity are of increased importance due to the need for biocompatibility over an implants life which could span several years. Thus, the combination of mechanical and biological properties determines the clinical usefulness of biomaterials in orthopaedic and musculoskeletal trauma surgery. Materials commonly used for these applications include stainless steel, cobalt-chromium and titanium alloys, ceramics, polyethylene, and poly(methyl methacrylate) (PMMA) bone cement. This study reviews the properties of commonly used materials and the advantages and disadvantages of each, with special emphasis on the sensitivity, toxicity, irritancy, and possible mutagenic and teratogenic capabilities. In addition, the production and final finishing processes of implants are discussed. Finally, potential directions for future implant development are discussed, with an emphasis on developing advanced personalised implants, according to a patient’s stature and physical requirements.

Słowa kluczowe:

orthopaedic surgical procedures, biomaterials, implants, biocompatible materials, alloys, ceramic, polyethylene

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New technologies are being developed to elaborate cutting-edge electrical jet engines to replace classical constructions. These new concepts consider the possibility of using electrical machines both as starters and generators, as well as suspension systems for the turbine shafts of aircraft engines. The paper will present mathematical analysis regarding active magnetic bearing (AMB) implementation for rotor–shaft support. This technology allows the elimination of friction forces between cooperating kinematic pairs (stator and rotor), reduces the adverse effects of classic bearings, and increases operating speed range and an operational susceptibility. The mathematical and numerical analysis of active magnetic suspension systems are presented. Next, a comparison of the theoretical studies using Comsol Multiphysics software and its experimental verification are described. A discussion regarding the mathematical analysis and experimental effects is also provided. The conclusion summarizes the theoretical and experimental features of heteropolar radial active magnetic bearings in new electric aircraft engines.

Słowa kluczowe:

active magnetic bearings,electric jet engine,current stiffness coefficient,displacement stiffness coefficient

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The number of overweight and obese patients in developed countries is gradually increasing. It was reported that 1287 (64%) out of 2007 adults operated on in 2017 had a body mass index (BMI) greater than 25 kg/m2, and 26.4% even greater than 30, while the BMI of the most obese patient was as high as 57.6 kg/m2. Such distressing statistics raised an issue related to the inadequate durability of implants used for the fixation of bone fractures. Implants for the lower-extremity fractures may not be durable enough to fit the requirements of overweight and obese patients. This case report presents the history of a 23-year-old obese male with a BMI of 38.7, who bent the angularly stabile titanium plate stabilizing his broken lateral ankle and torn distal tibiofibular syndesmosis. Biomechanical analysis showed that the maximal static bending moment registered during one-leg standing was equal to 1.55 Nm. This value was circa one-third of the maximally admissible bending moment for this particular plate (5.34 Nm) that could be transmitted without its plastic deformation. Since dynamic forces exceed static ones several (3–12) times during typical activities, such as walking, climbing the stairs, running, and jumping, unpredictable forces may occur and increase the risk of loosening, bending, and even breaking implants. None of these situations should have occurred for the typical patient’s body mass of 75 kg, or even for the analyzed mass of the young patient (120 kg) who tried to avoid excessive loading during his daily routine. Subsequent implant bending and destabilization of the fracture shows that for the significantly high and still growing number of obese patients, a very strict physical regime should be recommended to prevent overabundant dynamic loads. On the other hand, the geometry of implants dedicated to these patients should be reconsidered.

Słowa kluczowe:

ankle injuries surgery, bone plate, obesity, postoperative complications, implant failure

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The aim of the article is to develop a method for the analysis of tram dynamics related to safety during operation. To achieve this, a mathematical model of the vehicle represented by a multibody simulation MBS system is used. Models of tram with a classic and innovative drive, based on a system of independently rotating wheels on crank axles are analyzed. A new configuration of an innovative drive control of the considered vehicle with the use of braking of independent wheels is proposed. A new geometry of test track is presented. During numerical investigation the values of 'Y' leading forces of tram wheels with the considered innovative drive proved to be lower than in the corresponding vehicle with standard wheelsets. It has been demonstrated that the active control systems are of key importance and should be applied in such innovative tram drives.

Słowa kluczowe:

maintenance of safety, reliability of trams, derailment of tramcar, numerical tests, drive with independently rotating wheel

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In this paper several statistical learning algorithms are used to predict the maximal length of fatigue cracks based on a sample composed of 31 observations. The small-data regime is still a problem for many professionals, especially in the areas where failures occur rarely. The analyzed object is a high-pressure Nozzle of a heavy-duty gas turbine. Operating parameters of the engines are used for the regression analysis. The following algorithms are used in this work: multiple linear and polynomial regression, random forest, kernel-based methods, AdaBoost and extreme gradient boosting and artificial neural networks. A substantial part of the paper provides advice on the effective selection of features. The paper explains how to process the dataset in order to reduce uncertainty; thus, simplifying the analysis of the results. The proposed loss and cost functions are custom and promote solutions accurately predicting the longest cracks. The obtained results confirm that some of the algorithms can accurately predict maximal lengths of the fatigue cracks, even if the sample is small.

Słowa kluczowe:

empirical models, fatigue cracks, predictive maintenance, regression analysis, small data, statistical learning, turbomachinery

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The rotating machines with overhung rotors form a wide class of devices used in many types of industry. For this kind of rotor machines in the paper there is investigated an influence of dynamic and static unbalance of a?rotor, parallel and angular misalignments of shafts as well as inner anisotropy of rigid couplings on system dynamic responses. The considerations are performed by means of a hybrid structural model of the machine rotor-shaft system, which consists of continuous beam finite elements and discrete oscillators. Numerical calculations are carried out for parameters characterizing a heavy blower applied in the mining industry. The main goal of the research is to assess a?sensitivity of the above-mentioned imperfections on excitation severity of rotor-shaft lateral vibrations and on motion stability of the machine in question.

Słowa kluczowe:

overhung rotor-shaft, lateral vibrations, stability and sensitivity analysis, system imperfections

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This paper deals with research on the magnetic bearing control systems for a high-speed rotating machine. Theoretical and experimental characteristics of the control systems with the model algorithmic control (MAC) algorithm and the proportional-derivative (PD) algorithm are presented. The MAC algorithm is the non-parametric predictive control method that uses an impulse response model. A laboratory model of the rotor-bearing unit under study consists of two active radial magnetic bearings and one active axial (thrust) magnetic bearing. The control system of the rotor position in air gaps consists of the fast prototyping control unit with a signal processor, the input and output modules, power amplifiers, contactless eddy current sensors and the host PC with dedicated software. Rotor displacement and control current signals were registered during investigations using a data acquisition (DAQ) system. In addition, measurements were performed for various rotor speeds, control algorithms and disturbance signals generated by the control system. Finally, the obtained time histories were presented, analyzed and discussed in this paper.

Słowa kluczowe:

magnetic bearing; predictive algorithm; high speed rotating machine

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The purpose of this study is to create a concept for what would be a structurally simple and perationally robust support for the automotive turbocharger rotor in electrodynamic passive magnetic bearings. Because this kind of magnetic suspension-in its fundamental version-is dynamically unstable, to avoid the disadvantages contained therein, what is being proposed is the addition of external damping through the employment of the newly designed combined self-stabilizing electrodynamic passive magnetic bearing. The electromagnetic stiffness and damping characteristics of combined electrodynamic passive magnetic bearings have been determined for various shaft rotational speeds by means of the advanced 3D finite element method. In this study, a dynamic interaction between the turbocharger rotor shaft and the passive magnetic suspension is proposed as a support for both the fundamental electrodynamic passive magnetic bearings and the suggested combined self-stabilizing passive magnetic bearings. Here, the main attention is focused on the asymptotic stability of both the rotor shaft suspension variants. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh-Hurwitz stability criterion.

Słowa kluczowe:

rotor dynamics, combined electrodynamic passive magnetic bearings, turbocharger flexible rotor shaft, stability analysis, stabilizing damping magnitude

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Streszczenie:

Electro-dynamic passive magnetic bearings are now viewed as a feasible option when looking for support for high-speed rotors. Nevertheless, because of the skew-symmetrical visco-elastic properties of such bearings, they are prone to operational instability. In order to avoid this, the paper proposes the addition of external damping into the newly designed vibrating laboratory rotor-shaft system. This may be achieved by means of using simple passive dampers that would be found among the components of the electro-dynamic bearing housings along with magnetic dampers, which satisfy the operational principles of active magnetic bearings. Theoretical investigations are going to be conducted by means of a structural computer model of the rotor-shaft under construction, which will take into consideration its actual dimensions and material properties. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh-Hurwitz stability criterion.

Słowa kluczowe:

rotor-dynamics, electrodynamic passive magnetic bearings, flexible rotor-shaft, active magnetic damper, stability analysis

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In this paper, a semi-active damping approach is used for reduction of vibrations in a laboratory drivetrain system. The considered drivetrain system is powered by an electric, asynchronous motor at the one side and loaded with a harmonically varying torque on the other side. Here, an influence of electromechanical interaction, i.e., an electromechanical coupling, between the electric motor and the mechanical system has been taken into consideration. The harmonic load signal induces torsional vibrations in the system, which in the steady-state phase of motion become periodic. The aim of the work is to determine the optimal control function for a semi-active damping element, leading to vibration reduction and considering only the steady-state phase of system motion. The optimal control is derived by using a semi-analytical approach based on the optimal control theory aided with supplementary numerical computations. The proposed methodology is fully general, and it can be directly applied to any type of a periodically oscillating system.

Słowa kluczowe:

electric motor, electromechanical coupling, optimal control, periodic torsional vibrations, semi-active damping

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This paper aims to investigate, both experimentally and theoretically, the electromechanical dynamic interaction between a driving stepping motor and a driven laboratory belt-transporter system. A test-rig imitates the operation of a robotic device in the form of a working tool-carrier under translational motion. The object under consideration is equipped with measurement systems, which enable the registration of electrical and mechanical quantities. Analytical considerations are performed by means of a circuit model of the electric motor and a discrete, non-linear model of the mechanical system. Various scenarios of the working tool-carrier motion and positioning by the belt-transporter are measured and simulated; in all cases the electric current control of the driving motor has been applied. The main goal of this study is to investigate the influence of the stepping motor control parameters along with various mechanical friction models on the precise positioning of a laboratory robotic device.

Słowa kluczowe:

Belt transporter system, Precise positioning, Stepping motor, Current control, Experimental verification

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This paper presents a dynamic analysis of torsional vibrations of the railway drive system. A dynamic electromechanical drive model has been created and then integrated with the railway wheelset-rail system to simulate self-excited torsional vibrations of the considered system. Results of this analysis are used in order to investigate the drive system’s sensitivity to torsional oscillations. Here, the dynamic electromechanical interaction between the electric driving motor and the rotating wheelset is considered. This investigation has proved that the torsional stiffness and damping of drivetrain system strongly affect amplitudes of the self-excited vibrations. A self-excited vibrations affecting on an energy consumption of the electric motor of the considered system are studied.

Słowa kluczowe:

torsional vibrations, electromechanical coupling, wheel-rail adhesion, wheelset drivetrain dynamic

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In the paper there is proposed an algorithm of an efficient semi-active control of steady-state periodic lateral vibrations of the overhung rotor-shaft system. This algorithm has been developed using fundamentals of the Optimal Control Theory. In the considered system the control is realized by means of the linear dampers withthe magneto-rheological fluid built in the bearing housing. The computational example demonstrates possibilities of the applied approach resulting in an additional reduction of out-of-resonance and near resonance harmonic oscillation amplitudes in comparison withan analogous passive control.

Słowa kluczowe:

overhung rotor-shaft, lateral vibrations, semi-active control, Optimal Control Theory

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Streszczenie:

Periodical vibrations are common phenomenon affecting a wide range of mechanical systems. Most frequently it affects machines designed to work in a steady-state conditions like: turbine, pump, rail vehicle, etc. In those kinds of machines it is always possible to decompose the system motion to basic average-speed constant component and oscillatory component. Usually the second term is treated as undesirable and various techniques are applied in order to minimize it as far as it is possible. These techniques refers to both the hardware selection – meaning the type of damping system (active, semi-active, passive) and the control method selection – meaning the damping system control method. Concerning the control methods, there are many algorithms available in literature devoted to transient systems. One of typical application is to use them in systems experiencing sudden, external force excitation. After destabilization of the system, caused by excitation, the role of the control algorithm is to restore the system stable position and additionally to reach the extreme of some additional criterion. Typical criterions are minimization of the time, of restoring the stable position, minimizing the consumed control energy, etc. On the other hand, considering the steady-state systems, especially based on semi-active damping elements, there are not so many control methods available.This paper focuses on developing the proper methodology for deriving the optimal control strategy of semi-active damping element, to be used in periodically vibrating mechanical system. The control strategy is developed on the basis of the Optimal Control Theory. Numerical computations are involved in order to solve the optimal control problem for the considered test system. Problem solution reveals the periodical nature of optimal control function.

Słowa kluczowe:

Optimal Control Theory, Periodical Vibrations, Vibration Reduction

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In the paper dynamic electromechanical coupling between the structural model of the rotating machine drive system and the circuit model of the asynchronous motor has been investigated. By means of the computer model of the rotating machine drive system the results of experimental testing have been confirmed. From the obtained results of computations and measurements it follows that the coupling between the considered rotating system and the installed rotary dampers with the magneto-rheological fluid (MRF) results in effective energy dissipation leading to significant reduction of undesired torsional vibrations.

Słowa kluczowe:

Electromechanical Coupling, Machine Drive Systems, Rotary MRF Actuator, Torsional Vibrations, Wavelet Transform (WT)

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The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for an accurate representation of the probability density functions with an exponential behavior, which appears to be characteristic for the investigated rotor-shaft responses. Performing multiple numerical tests for a range of sample sizes it was found that the sparse polynomial chaos method provides the best balance between the accuracy and computational effectiveness in estimating the unknown probability distribution of the maximal vibration amplitude.

Słowa kluczowe:

stochastic moment estimation, sparse polynomial chaos expansion, maximum entropy principle, rotor, uncertainties, hybrid mechanical model, random unbalance distribution

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In the paper dynamic electromechanical interaction between the rotating machine drive system and the electric driving motor is considered. The investigations are performed by means of the circuit model of the asynchronous motor as well as using an advanced structural hybrid model of the drive system. Using the analytical solutions applied for the electrical and the mechanical systems the electromagnetic stiffness and coefficient of damping, both generated by the electric motor rotationally interacting with the mechanical system of the given dynamic properties, were determined. By means of experimentally validated computational responses obtained for torsional harmonic excitation induced by the driven machine working tool, a modification of dynamic properties of the mechanical system by the electromagnetic flux between the stator and the rotor has been studied.

Słowa kluczowe:

Machine drive system, Asynchronous motor, Electromechanical coupling

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In the paper there is presented a discrete - continuous model of the Split Hopkinson Pressure Bar (SHPB) for numerical simulations of a dynamic behaviour of material specimens under high strain - rates. For this purpose several material theories describing visco-elasto-plastic properties of the tested specimens can be applied. Using this model impact-type dynamic responses are sought by means of the longitudinal elastic wave analytical solution of the d’Alembert type. The proposed model enables us theoretical strength investigations for various elasto-plastic materials under great deformation velocities as well as structural parameter de termination of the real SHPB designed to play a role of the laboratory test-rig.

Słowa kluczowe:

Hopkinson bar, elastic wave propagation, d’Alembert solution, numerical simulation

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The analysis of damped rotating systems using actuators with magnetorheological fluid is the subject of interest. The main purpose of this research is minimization of vibration amplitudes in order to increase fatigue durability of the most responsible machine elements. Here, control damping torques are generated by magnetorheological fluid of adjustable viscosity.
The theoretical investigations are based on a hybrid and finite element structural model (FEM) of the mechanical structure as well as on sensitivity analysis of the response with respect to the actuators damping characteristics. The analysis performed in the paper combines experimental verification using the laboratory test rig with theoretical computations.

Słowa kluczowe:

rotating systems, torsional vibrations, actuators with a magnetorheological fluid, rotary actuators

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The aim of this paper is to present a method of the semi-active control of torsional vibrations in a working machine drive system by means of rotary actuators with a magneto-rheological fluid. The simple open-loop control strategy is proposed for a mechanical system vibrating in steady-state operating conditions. This semi-active control approach is based on the principle of optimum viscous damping and frictional properties realized by the magneto-rheological fluid, where its respective parameters are determined by the applied control electric currents. The analysis is performed theoretically by means of structural electro-mechanical models of the considered drive system as well as experimentally using a laboratory test rig in the form of a rotor-shaft system co-operating with two asynchronous motors generating properly programmed driving and retarding electro-magnetic torques

Słowa kluczowe:

semi-active control, torsional vibrations, magneto-rheological rotary dampers

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Streszczenie:

From all kinds of vibrations, torsional ones are very important as naturally associated with fundamental rotational drive system motion. The aim of this paper is to present semi-active control of torsional vibrations of the working machine drive systems, which is performed using a rotary damper with the magnetorheological fluid. The main purpose of this research is vibration amplitudes minimization in order to increase fatigue durability of the most responsible machine elements. The special control strategies are proposed for steady-state torsional vibrations suppression. The semi-active control method is based on a principle of determinational optimum current damping coefficient values, which is realized by the magneto-rheological fluid application. The analysis performed in the paper combines experimental verification using the laboratory test rig with theoretical computations. This experiment was designed in the form of the laboratory drive system co-operating with two asynchronous motors generating properly programmed driving and retarding electromagnetic torques.

Słowa kluczowe:

semi-active control, torsional vibrations, rotary dampers, magnetorheological fluid, electromechanical drive system

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Streszczenie:

The commonly observed nowadays tendency to weight minimization of rotor-shafts of the rotating machinery leads to a decrease of shaft bending rigidity making a risk of dangerous stress concentrations and rubbing effects more probable. Thus, a determination of the optimal balance between reducing the rotor-shaft weight and assuring its admissible bending flexibility is a major goal of this study. The random nature of residual unbalances of the rotor-shaft as well as randomness of journal-bearing stiffness have been taken into account in the framework of robust design optimization. Such a formulation of the optimization problem leads to the optimal design that combines an acceptable structural weight with the robustness with respect to uncertainties of residual unbalances – the main source of bending vibrations causing the rubbing effects. The applied robust optimization technique is based on using Latin hypercubes in scatter analysis of the vibration response. The so-called optimal Latin hypercubes are used as experimental plans for building kriging approximations of the objective and constraint functions. The proposed method has been applied for the optimization of the typical single-span rotor-shaft of the 8-stage centrifugal compressor.

Słowa kluczowe:

Rotor-shaft system, Robust design optimization, Lateral vibrations, Rubbing effects, Random unbalance distribution

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In the paper, an analysis of transient and steady-state electro-mechanical vibrations of a precise drive system driven by a stepping motor is performed. These theoretical investigations are based on a hybrid structural model of the mechanical system as well as on the classical circuit model of the stepping motor. The main purpose of these studies is to indicate essential differences between the torsional dynamic responses obtained for the considered object regarded respectively as electromechanically coupled and uncoupled. From the computational results, it follows that these differences are qualitatively and quantitatively essential from the viewpoint of possibly precise and reliable operation of the drive systems. Here, torsional vibrations of the drive system significantly influence the electro-mechanical coupling effects, which emphasizes the ir importance in dynamic analyses

Słowa kluczowe:

electro-mechanical vibrations, drive system, stepping motor,hybrid model

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Streszczenie:

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration responses is the inherently random nature of residual unbalances as well as stiffness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based on Taylor series expansion in most of the analysed cases fail to approximate the rotor-shaft response statistics.

Słowa kluczowe:

Scatter analysis, rotor-shaft vibrations

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Streszczenie:

In this paper there is proposed a semi-active control technique based on the linear actuators with the magneto-rheological fluid (MRF) connecting the drive system planetary gear housing with the immovable rigid support. Here, control damping torques are generated by means of the magneto-rheological fluid of adjustable viscosity. Such actuators can effectively suppress amplitudes of severe transient and steady-state rotational fluctuations of the gear housing position and in this way they are able to minimize dangerous oscillations of dynamic torques transmitted by successive shaft segments in the entire drive system. The general purpose of the considerations is to control torsional vibrations of the real power-station coal-pulverizer geared drive system driven by means of the asynchronous motor. The investigations have been carried out using the experimental test rig based on the real object, where the measurement results were compared with analogous theoretical ones obtained by the use of computer simulations.

Słowa kluczowe:

torsional vibrations, magneto-rheological dampers, semi-active control

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Streszczenie:

In the paper semi-active control of torsional vibrations of the rotating machine drive system driven by an electric motor is performed by means of rotary actuators with the magneto-rheological fluid. The main purpose of these studies is a minimisation of vibration amplitudes in order to increase the fatigue durability of the most responsible elements, assure possibly precise motion of the driven machine working tool as well as to reduce a generated noise level. For suppression of steady-state torsional vibrations excited by dynamic external torques generated by the motor and by the driven object there are proposed control strategies based on a principle of optimum current damping coefficient values realized by the magneto-rheological fluid. The theoretical control concepts are experimentally verified using the laboratory test rig in the form of drive system co-operating with two asynchronous motors generating properly programmed driving and retarding electromagnetic torques.

Słowa kluczowe:

semi-active control, torsional vibrations, rotary actuators, magneto-rheological fluid

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Streszczenie:

W pracy przedstawiono model matematyczny do badania dynamicznego oddziaływania między częściami elektromechanicznymi w systemie napędowym z hybrydowym silnikiem skokowym. W przypadku takiego systemu musi być zapewniony precyzyjny ruch obrotowy, dlatego już w procesie projektowania trzeba przewidzieć i uwzględnić efekt sprzężenia elektromechanicznego, a można to uczynić jedynie z wykorzystaniem dostatecznie dokładnych modeli matematycznych układu mechanicznego i silnika napędowego. Z przeprowadzonych obliczeń symulacyjnych wynika, że wpływ oddziaływania elektromechanicznego na właściwości systemu napędowego z silnikiem skokowym może być znaczne.

Słowa kluczowe:

układ napędowy, silnik skokowy, oddziaływanie elektromechaniczne, modele matematyczne

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In the paper there is performed an analysis of transient and steady-state electro-mechanical vibration s of the laboratory micro-drive system driven by the stepping motor. The main purpose of these studies is to indicate significant differences between the dynamic responses obtained for the considered object regarded respectively as electro-mechanically coupled and uncoupled. These theoretical investigations are based on a hybrid structural model of the mechanical system as well as on the classical circuit model of the stepping motor. From the computational results it follows that these differences are qualitatively and quantitatively essential from the viewpoint of possibly precise and reliable operation of the micro-drive systems.

Słowa kluczowe:

Transient coupled elektromechanical, vibration analysis, micro-drive system

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In the paper a stochastic method for fault detection and identification in the shafts of rotating machines is proposed. This approach is based on the Monte Carlo simulations of rotor-shaft lateral–torsional–longitudinal vibrations mutually coupled by transverse cracks of various possible and randomly selected depths and locations on the shaft. For this purpose the structural hybrid model of a real faulty object is applied. This model is characterized by a high practical reliability and great computational efficiency, so important for many hundred thousand single numerical simulations necessary for a creation of the databases applied for inverse problem solution finally leading to crack identification. These databases are created with an arbitrary assumed probability densities of crack parameters which ensures appropriate spread of the dynamic responses of the considered faulty mechanical system. A sufficiently large database determined for the investigated object enable us to estimate almost immediately, i.e. within less than 1 s, the crack depth and axial position with identification errors not exceeding 9% and 5%, respectively. Thus, the proposed method seems to be a very convenient diagnostic tool for engineering applications in the industry.

Słowa kluczowe:

Rotor-shaft system, Dynamic diagnostics, Crack identification, Monte Carlo simulation, Coupled vibration analysis

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Streszczenie:

In the paper several stochastic methods for detection and identification of cracks in the shafts of rotating machines are proposed. All these methods are based on the Monte Carlo simulations of the rotor-shaft lateral-torsional-longitudinal vibrations mutually coupled by transverse cracks of randomly selected depths and locations on the shaft. For this purpose there is applied a structural hybrid model of a real cracked rotor-shaft. This model is characterized by a high practical reliability and great computational effi-ciency, so important for hundreds of thousands numerical simulations necessary to build databases used in solving the inverse problem, i.e. crack parameter identifications. In order to ensure a good identification accuracy, for creating the Monte Carlo samples of data points there are proposed special probability density functions for locations and depths of the crack. Such an approach helps in enhancing databases corresponding to the most probable faults of the rotor-shaft system of the considered rotor machine. In the presentedstudy six different database sizes are considered to compare identification efficiency and accuracy of considered methods. A sufficiently large database enables us to estimate almost immediately (usually in less than one second) the crack parameters with precision that is in most of the cases acceptable in practice. Then, as a next stage, one of the proposed fast improvement algorithms can be applied to refine identification results in a reasonable time. The proposed methods seem to provide very convenient diagnostic tools for industrial applications.

Słowa kluczowe:

Crack rotor dynamics, Nonlinear and parametric vibrations, Hybrid modeling, Monte Carlo simulation, Crack identification methods

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In this paper the numerical method for prediction of fatigue life of structure is presented. The fmite element model-ling and damage parameter calculation are based on the algorithm de-scribed originally by Chaboche (1987), Luccioni et al. (1996) and 011er et al. (2005). This al-gorithm is simplified, i.e. the Goodman relationships between the mean and stress amplitude are included. It is extended and applied for simulation of crack propagation in the rotor shaft. The mate-rial constitutive model includes plastic effects and damage. The S—N fatigue func-tions taken from experiment are modi-fied so as to be dependent on the real ratio between minimum and maximum stress in the critical zones. So the coupling between damage, plastic-ity and fatigue is taken into account.

Słowa kluczowe:

metal fatigue, damage mechanics

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Streszczenie:

In the paper active control of transient torsional vibrations induced by the electric motor during run-ups of the radial compressor drive system is performed by means of couplings with the magneto-rheological fluid. The main purpose of these studies is a minimisation of vibration amplitudes in order to increase the fatigue durability of the most responsible elements. The theoretical investigations are based on a hybrid structural model of the vibrating mechanical system and sensitivity analysis of the response with respect to the damping characteristics of the control couplings.

Słowa kluczowe:

active control, transient vibrations, drive system, electric motor

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IN THE PAPER the wave method of fault identification in rods, shafts and beams is proposed. This method is based on dynamical models consisting of structural macro-elements with continuously distributed inertial-visco-elastic properties, represented by individual segments of the investigated objects. The fault detection and identifi-cation reduces to simulations of diagnostic wave propagation and wave reflections in these models. These simulations are performed directly in time domain by means of analytical solutions of the partial differential equations of motion. In the computa-tional examples, reflected waves were sought in the cracked cantilever rod and beam. These results have been compared with the analogous findings obtained by other au-thors, using the spectral finite element method. The natural continuous character of the applied elastic macro-elements enables us to apply a straightforward simulation of wave effects, which makes the proposed approach a promising and effective tool for fault identification in various structure and mechanical systems.

Słowa kluczowe:

Continuous elastic macroelements, crack detection, spectral finite element method

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The objective of this research is to include mixed friction effects into existing models of hydrodynamic journal bearings described e.g. in [1]. The problem of partial hydrodynamic lubrication caused by roughness of sliding surfaces has been investigated for many years by numerous researchers. But majority of theoretical studies in this field were focused on very fundamental aspects taking into consideration general principles of bearing operation from the viewpoint of flow determination between sliding surfaces of various roughness description. The considerations in this paper are devoted to partial hydrodynamic lubrication effects in typical cylindrical transverse journal bearings applied for supporting of heavy rotor-shafts of the rotating machines. For this purpose there is used the average flow theory for an oil film interaction with rough journals and bushings. In order to carry out a qualitative analysis of the problem a simple mechanical model of the partially lubricated “super-bearing” is assumed. This model consists of the rigid mass rotating with constant speed and performing translational in-plane motion within the non-rotating rigid ring which is elastically suspended in this plane. The rigid mass represents the entire inertia of the rotating parts of the rotor machine and the rigid ring corresponds to the housing of such “super bearing”. Translational in-plane motion of the rigid mass is coupled with translational motion of the rigid ring by means of mass-less springs and dampers representing respectively visco-elastic properties of the oil film in the “super-bearing” with rough sliding surfaces. These visco-elastic properties of the oil film in such bearing are determined by numerical solving of the average Reynolds equation describing partial oil flow between the rough journal and bushing. Here, according to, the pressure flow factors and the shear flow factors standing in the average Reynolds equations are determined analytically using proper empirical formulae obtained by numerical simulations of the model flows between partially lubricated surfaces for various roughness geometry and average oil film thicknesses. Solving in this way the average Reynolds equation for the entire oil gap by means of the finite difference method enables us to determine resultant viscous friction retarding force as well as transverse hydrodynamic load of the bearing. For various roughness geometry the former enables us to determine the frictional power yielded by the bearing and the latter makes possible calculation of stiffness and damping coefficients of the mass-less springs representing visco-elastic properties of the oil film in the assumed model of the “super-bearing”. In the numerical examples numerous roughness amplitudes of the journal and the bushing surface as well as various directional orientations of roughness asperities, which follow from final machining of the journal and the bushing, are taken into consideration in order to investigate their influence on kineto-static and dynamic behaviour of the transverse oil-film bearing. In the next steps of research in this field, beyond the partial lubrication, also the metal-to-metal friction effects are going to be investigated, i.e. for so high loadings of the journal bearing, when the hydrodynamic lubrication theory for the oil film stops to be in force

Słowa kluczowe:

partial hydrodynamic lubrication, journal bearings, mixed friction effects

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High static and dynamic overloads caused by the aircraft landing gears moving on the airport runways are a source of uncontrolled cracking of the runway upper layers. In order to investigate this problem the proper analytical model of the runway under moving load is proposed. The finite distance of the runway upper layer is represented by the rectangular continuous Kirchhoff's plate resting on the visco-elastic foundation playing a role of dynamic interface with the runway supporting layer. The plate heterogeneity caused by the runway transverse notches has been taken into consideration in the form of fictitious external response-dependent elastic bending moments. The initial deflections of the runway upper layer due to thermal forces are induced in the model by the equivalent mechanical loads imposed to the plate. Excitation of the plate due to the aircraft landing-gear is represented by the set of moving non-inertial forces, mutual spacing and number of which correspond respectively to the structure and the total number of wheels of the real landing-gear of the assumed aircraft. Numerical simulation of dynamic interaction between the runway and the aircraft landing-gear has been performed by means of the modal approach for various running speeds of the heavy aircraft. The quantities of interests are the dynamic transverse deflections of the plate as well as the normal stress in the notch cross-sections.

Słowa kluczowe:

dynamic overloads, dynamic interaction, runway,aircraft landing gear, analytical approach

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The rotating machines with overhung rotors form a wide class of devices used in many types of industry. For this kind of rotor machines in the paper there is investigated an influence of dynamic and static unbalance of a rotor, parallel and angular misalignments of shafts as well as inner anisotropy of rigid couplings on system dynamic responses. The considerations are performed by means of a hybrid structural model of the machine rotor-shaft system, which consists of continuous beam finite elements and discrete oscillators. Numerical calculations are carried out for parameters characterizing a heavy blower applied in the mining industry. The main goal of the research is to assess a sensitivity of the above-mentioned imperfections on excitation severity of rotor-shaft lateral vibrations and on motion stability of the machine in question.

Słowa kluczowe:

motion stability, rotating machines, overhung rotors, industrial fan, numerical calculations, experimental test

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In the paper dynamic electromechanical interactions between the rail-way drive systems and their driving electric motors are investigated. These are drive systems of high-speed trains (HST) and locomotives driven by AC motors. In particular, there is considered an influence of negative electromagnetic damp-ing generated by the asynchronous motor on a possibility of excitation of reso-nant torsional vibrations. 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 ob-jects as well as helpful for their users during a regular maintenance.

Słowa kluczowe:

railway drive, electromechanical interactions, AC Motors, railway dynamic, numerical investigation

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The existing European standard EN 14363 covers all necessary tests for different railway vehicles, but it is inadequate for tram vehicles, especially in safety against a derailment examination. Its operational conditions are much different. Trams overcome horizontal curves with much smaller radii than railway vehicles. There is a large diversity in wheel-rail pairing, i.e. almost every public transport operator uses a different wheel profile. In the running gear design much more rubber-metal elements are used in order to ensure a low-floor interior and to keep the kinematic envelope. Apart from standard vehicle configuration, i.e., a carbody on two bogies, in modern tram designs numerous arrangements are applied: wagons with one outer bogie, wagons with one centered bogie, wagons without bogies (sedan) etc., where twisting shims cannot be used to achieve the required twist. The described issues imply that the methodology of safety against derailment described in EN 14363 standard cannot be applied without any modifications. This paper presents a new proposal for a simulation safety against derailment for a vehicle with an arbitrary configuration of wagons and running gears. The numerical analyses have been performed by means of the Simpack Rail software

Słowa kluczowe:

Safety against derailment, Tram vehicle Numerical, simulation Running dynamics, Simpack rail software

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Torsional vibrations of steam turbo-generator rotor-shaft-lines coupled with bending vibrations of exhaust blades still constitute an important operational problem for this type of rotor-machines. Therefore, this work proposes a relatively simple approach for efficient suppression and control of transient and steady-state turbo-generator shaft torsional vibrations excited by short circuits in a generator or power-lines, faulty synchronization, negative sequence currents and by sub-synchronous resonances in the turbo-generator-electric network system. This target has been achieved by means of semi-actively controlled rotary dampers with the magneto-rheological fluid. Regular operation of such devices installed in a given turbo-generator rotor-shaft line enables suppression of dangerous torsional oscillations.

Słowa kluczowe:

control of torsional vibrations, the turbo-generator, rotary magneto-rheological dampers, Bi-directional active torsional vibration damper

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In the paper, simulation results of safety against derailment for a tramway vehicles with an arbitrary configuration of wagons and bogies is presented. The existing European standard EN 14363 covers all necessary tests for different railway vehicles, but it is inadequate for tramway vehicles, especially in safety against a derailment examination. Its operational conditions are much different. The described observations suggest that the methodology of safety against derailment testing described in the EN 14363 standard cannot be used without any modifications in the case of testing of tramway vehicles. On the basis of the computational results, a significant influence of different configurations of urban tramway vehicles on the wheel-rail contact forces was discussed, in particular on the Y/Q derailment factor.

Słowa kluczowe:

tramway dynamics, safety against derailment, simpack, numerical study

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In the paper there is presented a reliable structural model of the rotating mechanical systems as well as mathematical models of the stepping, synchronous and asynchronous motors, by means of which electromechanical coupling effects can be thoroughly investigated. An importance and severity of these phenomena, not sufficiently explored till present, have been demonstrated by results obtained for transient and steady-state operational conditions in the computational examples concerning torsional vibrations of drive trains with various electric motors.

Słowa kluczowe:

structural model, electric motors, mechanical systems, electromechanical coupling

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The purpose of this paper is to create a concept of the structurally simple and operationally robust support of high-speed rotors in the electrodynamic passive magnetic bearings (EDPMB). Since this kind of a magnetic suspension in its fundamental version is dynamically unstable, in order to avoid such an essential disadvantage there is proposed the addition of external damping by the use of the newly designed combined, self-stabilizing electrodynamic passive magnetic bearing. The electromagnetic stiffness- and damping characteristics of the combined EDPMB have been determined for various shaft rotational speeds by means of the advanced 3D finite element method. The dynamic investigations are performed for a single-span, high-speed flexible rotor-shaft. In the computational part a dynamic interaction between the rotor-shaft and the passive magnetic suspension is carried out for a support in the fundamental EDPMBs and in the proposed combined, self-stabilizing passive magnetic bearings. Here, the main attention is focused on asymptotic stability of the both rotor-shaft suspension variants. In addition, for the considered rotor-shaft-bearing system amplitude-frequency characteristics of forced steady-state bending vibrations have been determined. By means of this investigation there is demonstrated a resonance suppression ability using the external damping generated by the proposed combined EDPMBs.

Słowa kluczowe:

magnetic bearing, electrodynamic passive magnetic bearings, EDPMB, rotor-shaft suspension, high-speed rotors

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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.

Słowa kluczowe:

Rotor-machine, Asynchronous motor, Electromechanical interaction, Torsional vibrations, Control strategies

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In the paper a dynamic behaviour of the selected typical group of rotating machines applied in the mining industry is investigated. These are the beater mills and crushers as well as blowers and compressors, all driven by the asynchronous motors. In particular, there is considered an influence of various types of machine working tool loadings on the system lateral steady-state dynamic responses as well as a mutual torsional electromechanical interaction between the driving motor and the driven machine in transient operational conditions. The theoretical calculations have been performed by means of the advanced structural mechanical models. The conclusions drawn from computational results can be very useful during design phase of these devices as well as helpful for their users during regular maintenance.

Słowa kluczowe:

mining industry, electromechanic coupling, design and maintenance of mill, torsional vibrations

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In the paper dynamic investigations on the automotive turbocharger rotor-shaft supported on the electro-dynamic passive magnetic bearings (EDPMB) and on the traditional floating-ring journal bearings have been carried out using a computer model. The results of computations obtained for the two mutually compared kinds of suspension are demonstrated in the form of Campbell diagrams and amplitude-frequency characteristics. Here, the main attention is focused on resonant-free operation ability assured by the support on the EDPMBs. Moreover, conditions of stability for the support on the journal bearings and on the EDPMBs have been investigated by means of the eigenvalue analysis. There is studied an influence of skew-symmetrical dynamic properties of the both kinds of rotor-shaft suspensions caused by the bearing stiffness negative cross-coupling terms as well as by the gyroscopic effects which are particularly severe at turbocharger high rotational speeds.

Słowa kluczowe:

turbocharger rotor, electrodynamic passive magnetic bearings, rotor dynamics, stability analysis

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The electrodynamic passive magnetic bearings became now a very promising kind of support for high-speed rotors. Nevertheless, because of skew-symmetrical visco-elastic properties of such bearings, they are sensitive to operational instability. In order to avoid this disadvantage, in the paper there are proposed stabilization concepts reducing to an introduction of a sufficient magnitude of additional external damping into the vibrating rotor-shaft system. This purpose is going to be realized by means of simple and effective passive dampers built in the electrodynamic bearing housings as well as using heteropolar magnetic dampers which realize operational principles of the active magnetic bearing. The theoretical investigations are going to be carried out by means of a structural computer model of the rotor-shaft system, taking into consideration its full geometry and material properties.

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In the paper there will be presented fundamental advantages and problems connected with an application possibility of the highly-energetic, impact-type technique of the copper ore comminution in a comparison with the analogous methods used till present by the ore pro-cessing plants belonging to the company KGI-IM — Polska Miedt S.A. In this aspect the main technical and exploitation requirements expected from the high-speed beater mills for impact-type copper ore comminution in a dry mode shall be considered. In particular, there will be discussed dynamic phenomena associated with an operation of such devices as well as modern computational methods enabling us an expectation of their positive and negative consequences for an operational effectiveness, durability and robustness of the most respon-sible working elements. The mechanical vibrations can be regarded here as one of the most detrimental phenomenon caused by the highly dynamic interaction between the beater-wheel and the comminuted ore. First of all, these are bending and torsional vibrations of the beater.

Słowa kluczowe:

copper ore highly-energetic comminution, beater mill, dynamic analysis

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Modelowanie i symulacje numeryczne są obecnie nieodłączną częścią projektowania i optymalizacji różnorodnych procesów technologicznych. Zastosowanie metod numerycznych w projektowaniu procesów mechanicznego urabiania i przeróbki rud metali jest w dalszym ciągu stosunkowo niewielkie. Procesy odspajania kawałków skały od calizny i ich rozdrobnienia z zastosowaniem różnego rodzaju maszyn, wiążą się silnie nieciągłymi zjawiskami zniszczenia materiału i są bardzo trudne do modelowania za pomocą standardowych metod numerycznych, takich jak metoda elementów skończonych, opartych na ciągłym sformułowaniu zagadnienia mechaniki ciała stałego. Duże możliwości w zastosowaniu do tych procesów ma intensywnie rozwijana w ostatnich latach metoda elementów dyskretnych, w której materiał jest reprezentowany przez liczny zbiór ziaren, oddziałujących między sobą poprzez siły kontaktu. Model ten w sposób naturalny uwzględnia materiał rozdrobniony. Uwzględnienie wiązań kohezyjnych między ziarnami oraz możliwości ich zrywania umożliwia modelowanie inicjacji i propagacji pęknięć w materiale. W niniejszej pracy zostaną przedstawione możliwości wykorzystania metody elementów dyskretnych do symulacji urabiania skał za pomocą noży stożkowych i dysków oraz do symulacji zachowania się materiału w młynie. Sprzężenie metody elementów dyskretnych z modelem przepływu płynu umożliwi modelowanie zawiesiny pyłowej rozdrabnianego materiału.

Słowa kluczowe:

modelowanie dyskretne, mechaniczne urabianie, rudy metali

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In the paper there is investigated experimentally and theoretically electromechanical dynamic interaction between the driving stepping motor and the driven laboratory belt-transporter system imitating an operation of the robotic device in the form of working tool-carrier under translational motion. The considered object is properly equipped with measurement systems enabling us a registration of studied electrical and mechanical quantities. The analytical considerations are performed by means of the circuit model of the electric motor and of the discrete, non-linear model of the mechanical system. In the investigated examples various scenarios of the working tool-carrier motion and positioning by the belt-transporter are measured and simulated, where in the all cases the electric current control of the driving motor has been applied.

Słowa kluczowe:

Belt transporter system, Precise positioning, Stepping motor, Current control, Experimental verification

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In the paper there is studied dynamic electromechanical interaction between the geared drive system of a rotating machine and the driving induction (asynchronous) motor. The investigations are performed by the use of experimental measurements carried out on the real object as well as by means of a theoretical approach using a circuit model of the electric motor in the form of Park’s equations and the advanced drive system hybrid, i.e. discrete-continuous, mechanical model of an identical structure and parameters as the classical preliminarily applied one-dimensional finite element model. The experimental and theoretical considerations are focused on the steady-state operating conditions, where severe torsional vibrations are excited by variable components of the driven machine retarding torque as well as by the electromagnetic torque generated by the induction motor. The qualitative analysis is performed by means of the harmonic balance method applied for Park’s equations and using the modal approach for the experimentally identified mechanical model. In order to minimize torsional vibration amplitudes induced by the electromechanical interaction in the considered system, the semi-active control technique based on actuators with the magneto-rheological fluid has been tested.

Słowa kluczowe:

electromechanical dynamic coupling, electric motor, torsional vibrations, experimental investigation

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Torsional vibrations are in general rather troublesome to control from the viewpoint of proper control torque generation as well as because of difficulties of imposing the control torques on quickly rotating parts of the drive- or rotor-shaft systems. In this paper there is proposed an active control technique based on the linear actuators with the magneto-rheological fluid (MRF) connecting the drive system planetary gear housing with the immovable rigid support. Here, by means of the magneto-rheological fluid of adjustable viscosity control damping torques are generated. Such actuators can effectively suppress amplitudes of severe transient and steady-state rotational fluctuations of the gear housing position and in this way they are able to minimize dangerous oscillations of dynamic torques transmitted by successive shaft segments in the entire drive system. The general purpose of the considerations is to control torsional vibrations of the power-station coal-pulverizer drive system driven by means of the asynchronous motor and the single stage planetary gear. In the computational examples drive system transient torsional vibrations induced by the electromagnetic motor torques during start-ups as well as steady-state vibrations excited by the variable dynamic retarding torques generated by the coal pulverizer during nominal operation have been significantly attenuated.

Słowa kluczowe:

Torsional vibrations, rotational fluctuation, magneto-rheological fluid

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The commonly observed nowadays tendency to weight minimization of rotor-shafts of the rotating machinery leads to a decrease of shaft bending rigidity making a risk of dangerous stress concentrations and rubbing effects more probable. Thus, a determination of the optimal balance between reducing the rotor-shaft weight and assuring its admissible bending flexibility is a major goal of this study. The random nature of residual unbalances of the rotor-shaft as well as randomness of journal bearing stiffness have been taken into account in the framework of robust design optimization. Such a formulation of the optimization problem leads to the optimal design that combines an acceptable structural weight with the robustness with respect to uncertainties of residual unbalances, the main source of bending vibrations causing the rubbing effects. The applied robust optimization technique is based on using Latin hypercubes in scatter analysis of the vibration response. The so-called optimal Latin hypercubes are used as experimental plans for building kriging approximations of the objective and constraint functions. The proposed method has been applied for the optimization of the typical single-span rotor-shaft of the 8-stage centrifugal compressor.

Słowa kluczowe:

Rotor-shaft system, robust design optimization, lateral vibrations, rubbing effects, random unbalance distribution

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In the paper control of transient and steady-state torsional vibrations of the driven by the asynchronous motor laboratory drive system of the imitated coal pulverizer is performed by means of actuators with the magneto-rheological fluid. The main purpose of these studies is a minimisation of vibration amplitudes in order to increase the fatigue durability of the most responsible elements. The theoretical investigations are based on a hybrid and finite element structural model of the vibrating mechanical system as well as on sensitivity analysis of the response with respect to the actuator damping characteristics. For suppression of transient torsional vibrations excited by electro-magnetic torques generated by the motor and by the coal pulverizer tool there is proposed a control strategy based on actuators in the form of rotary control dampers.

Słowa kluczowe:

Semi-active control, torsional vibrations, electro-mechanical drive system, control dampers, magneto-rheological fluid

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In the presented paper by means of the continuous model a dynamic interaction between the airport runway and the aircraft landing-gear is considered in order to investigate the controlled cracking process of the initially notched runway plates. For this purpose normal stresses induced by the static and dynamic loads in the runway plate notched areas are going to be determined by means of the continuous mechanical model and analytical mathematical solution of the problem.

Słowa kluczowe:

dynamic load, analytical mathematical solution, airport runway

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Streszczenie:

Pojazdy tramwajowe charakteryzują się dużą różnorodnością w zakresie konfiguracji struktur nadwozi oraz układów biegowych. Ma to związek z ich eksploatacją w wysoko zurbanizowanych obszarach miejskich i koniecznością przystosowania do masowej obsługi podróżnych o różnych potrzebach przewozowych
(osoby o ograniczonej możliwości ruchowej, osoby na wózkach inwalidzkich, osoby z wózkami dziecięcymi). Nie bez znaczenia jest również istniejąca infrastruktura (minimalne wartości promieni łuków poziomych i pionowych, wysokości krawędzi przystankowej względem poziomu główki szyn). W stosunku do pojazdów kolejowych nie istnieją międzynarodowe regulacje dotyczące badań ruchowych, w tym w szczególności dla warunków bezpieczeństwa przed wykolejeniem. W związku z tym opracowano nową, uniwersalną metodykę badań symulacyjnych kryteriów bezpieczeństwa przed wykolejeniem pojazdów tramwajowych, bez względu na konfgurację nadwozi danego tramwaju, typu wózka czy szerokość toru. Zaprezentowano założenia nowej metodyki oraz przeprowadzono symulacje dla kilku popularnych na rynku konfguracji tramwajów. Porównano wyniki, otrzymane dla pojazdów z klasycznymi zestawami kołowymi oraz dla pojazdów wyposażonych w zestawy kołowe z niezależnie obracającymi się kołami.

Słowa kluczowe:

Pojazdy tramwajowe, układy biegowe, symulacje, zestawy kołowe z niezależnie obracającymi się kołami

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Majority of industrial machinery and several mechanisms are driven by asynchronous motors. Such electro-mechanical systems are often affected by detrimental torsional vibrations, suppression of which is commonly performed by more or less effective passive, semi active and active dampers. In this paper there is proposed an alternative method of attenuation of torsional vibrations in such objects. Here, an asynchronous motor under the proper vector control can simultaneously operate as a source of drive and actuator. Using this approach, transient and steady-state torsional vibrations of the driven mechanical system can be effectively suppressed as well as its precise operational motion can be assured. The theoretical investigations are carried out by means of an advanced structural mechanical model of the drive system and circuit model of the asynchronous motor controlled using two methods: the direct torque control (DTC-SVM) and the rotational velocity controlled torque method (RVCT) originally developed in this paper. In the computational examples performed for three representative drive systems torsional vibration control ability is analyzed for various dynamic properties of the mechanical part and several parameters of the asynchronous motor control. From the obtained results it follows that for majority of tested parameters, transient torsional vibrations excited by step-wisely disturbed loadings of the driven object are successfully attenuated using both abovementioned vector control strategies. However, a suppression effectiveness of resonant steady-state torsional vibrations by means of these methods depends on the specific case of an asynchronous motor with a given electromagnetic stiffness in the stable operational range of its static characteristics.

Słowa kluczowe:

active control, torsional vibrations, asynchronous motor, rotating systems, driving asynchronous motor, driving motor

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Streszczenie:

In recent years, magnetic bearing technology has been implemented in many practical applications. In
comparison with mechanical bearings, the magnetic ones have decreased stiffness coefficients and increased
damping coefficients of radial bearings reducing the critical rotor speeds, [1]. These features are given the
magnetic bearings a considerable potential to become a key element in rotating machines, like jet engines,
turbo-compressors, generators and many others, [2]. Active magnetic bearings allow precise control of a
rotor position and enable “online” monitoring, diagnosing, and identifying high-speed machines, [3].
The magnetic bearings are structurally unstable. Namely, an effective control system with a proper controller
ought to be designed to ensure defined control quality indicators. In general, control systems of magnetic
bearings are mostly restricted for using proportional-integral-derivative (PID) controllers. However, robust
and slide control methods are also used in similar systems, [4]. Some predictive control algorithms were
implemented in the analyzed AMB control loop [1].
The paper presents the research results of a parametric predictive control algorithm implemented in a highspeed
rotor machine’s magnetic bearing support system. The theoretical and experimental analyses of the
control system with the Extended Horizon Adaptive Control (EHAC) algorithm are presented using an
AutoRegressive with eXogenous input (ARX) model. A laboratory model of the magnetic suspension system
consists of two active radial magnetic bearings and one axial (thrust) active magnetic bearing. The levitated
rotor displacement in air-gaps and control current signals in control loops were measured for various rotor
speeds and several parameters of the control algorithm, and they were presented in the form of time histories.
Moreover, the power consumption of the magnetic bearing system with the predictive control algorithms was
analysed, and the influence of a tuning factor and control horizon on rotor dynamic properties were
determined. The theoretical studies were carried out using Matlab and Simulink software, whereas the
experimental studies were performed using an appropriately dedicated test rig.
References
[1] Kurnyta-Mazurek P., Szolc T., Henzel M., Falkowski K.: „Control system with nonparametric predictive algorithm
for the high-speed rotating machine with magnetic bearings”, Bulletin of the Polish Academy of Sciences: Technical
Science, 2021
[2] Brusa: “Semi-active and active magnetic stabilisation of supercritical rotor dynamics by contra-rotating damping”,
Mechatronics 24, 2014, pp. 500–510, //doi.org/10.1016/j.mechatronics.2014.06.001.
[3] R. Siva Srinivas, R. Tiwari, Ch. Kannababu: “Application of active magnetic bearings in flexible rotordynamic
systems – A state-of-the-art review”, Mechanical Systems and Signal Processing, 106, 2018, pp. 537-572
[4] A. Tonoli, A. Bonfitto, M. Silvagni, and L. D. Suarez, “Rotors on Active Magnetic Bearings: Modeling and Control
Techniques”, in Advances in Vibration Engineering and Structural Dynamics. London, United Kingdom:
IntechOpen, 2012 [Online]. Available: https://www.intechopen.com/chapters/41670 doi: 10.5772/51298

Słowa kluczowe:

active magnetic bearings, pramaetric predictive control, high-speed machines

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The notion of rotor dynamics should be defined as a branch of dynamics of mechanical systems including dynamic investigations of machines and devices, the main working elements of which are under rotational motion. One of the main subjects of the rotor dynamics is a quantitative and qualitative examination of steady-state and transient bending/lateral, torsional and axial vibrations of these elements and the influence of these vibrations on the environment and cooperating objects, e.g. electric motors and generators. Because of design and technological reasons, these fundamental rotating operational elements are usually in the form of stepped rotor-shafts with segmentally constant or approximately constant cross sections. Such relatively simple geometric shape and realistic frequency ranges of practically tested vibration processes allow the use of one-dimensional structural dynamic models of the beam type ensuring an appropriate efficiency and reliability of results of theoretical analyzes carried out for this type of mechanical systems. According to the above, a one-dimensional discrete-continuous structural modeling seems to be a particularly useful modeling method for studying dynamic processes in rotating machinery. It consists in a hybrid combination of flexurally, torsionally and longitudinally deformable continuous beam finite macro-elements representing individual cylindrical or quasi-cylindrical segments of the real rotor-shaft with discrete oscillators corresponding to its bearing supports, rotor disks, coupling flanges, flywheels, etc., in accordance with a structure of the real object. Mutual connections of the successive macro-elements creating the stepped shaft as well as their interactions with the discrete oscillators and other objects, e.g. electric machines or magnetic supports, are described by equations of boundary conditions. These equations contain geometrical conditions of conformity for translational, rotational and axial displacements of extreme cross sections of the adjacent continuous elastic macro-elements. The second group of boundary conditions are dynamic ones, which contain linear, nonlinear and parametric equations of equilibrium for external forces and torques, static and dynamic unbalance forces and moments, inertial, elastic and external damping forces, support reactions and gyroscopic moments. For the local partial differential equations of motion of these macro-elements there are applied analytical solutions in the form of series in orthogonal eigenfunctions leading to the description of motion in modal coordinates. Such approach allows, on the one hand, to effectively obtain simulation results in the time domain of linear and non-linear forced vibrations and quickly-varying shock processes. On the other hand, they make it possible to conduct qualitative tests of the considered rotor-shaft systems in the form of natural vibration analyzes, generation of amplitude-frequency characteristics and determination of dynamic stability limits. Moreover, a relatively clear mathematical description of the adopted discrete-continuous (hybrid) models of the rotor-shaft systems enables us a convenient coupling of motion equations of the mechanical objects under study with circuit voltage equations being mathematical models of electric motors and generators cooperating with these objects, or with equations describing an interaction of magnetic supports. Summing up, it should be stated that the degree of complexity of the mathematical description and numerical advancement necessary to obtain reliable solutions using this method of modeling of the above-mentioned objects can be classified as a kind of intermediate between the classical finite element modeling and traditional discrete modeling, now called “multi-body modeling". Owing to this, an application of the proposed structural discrete-continuous (hybrid) models for dynamic analyzes is associated with much smaller problems of physical parameters identification compared to a usually burdensome determination of such parameters of discrete models of respectively the same objects. As a result, this leads to an achievement of actual accuracy of calculations results comparable or identical to those obtained using analogous FEM models, while additionally there is obtained much greater numerical efficiency justified by the need to solve smaller numbers of mathematical relationships describing motion of discrete-continuous (hybrid) models.

Słowa kluczowe:

hybrid modelling, rotor-shaft systems, lateral-torsional vibrations, rotor dynamics

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Trams with independently rotating wheels (IRW) enable to increase a comfort of traveling by lowering the floor level along the entire length of the vehicle, in particular above the bogies. In these trams such solution imposes a different design of motor bogies. In this construction of the bogies, four independent motors mounted on the bogie frame are connected each by a gear-stage with a single running-wheel. By means of the appropriate control algorithm guiding driving torques in curved sections of the railway track can be generated. Trams must ensure a high level of safety of passengers, and one of its aspect is safety against derailment. This article presents an original simulation method to investigate a level of safety against derailment for such vehicles. Principles of this method are independent of the tram car configuration. Using this approach, structural analysis of trams was carried out, which tested drive control in the boogie equipped with independently rotating wheels. Here, numerous simulations of motion on curved tracks were performed by means of various wheel drive control algorithms.

Słowa kluczowe:

research safety, safety against derailment, derailment of trams, trams with independently rotating wheels, independently rotating wheels

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Torsional vibrations of steam turbo-generator rotor-shaft-lines coupled with bending vibrations of exhaust blades still constitute an important operational problem for this type of rotor-machines. Therefore, this work proposes a relatively simple approach for efficient suppression and control of transient and steady-state turbo-generator-shaft torsional vibrations excited by short circuits in a generator or power-lines, faulty synchronization, negative sequence currents and by sub-synchronous resonances in the turbo-generator-electric network system. This target has been achieved by means of semi-actively controlled rotary dampers with the magneto-rheological fluid. Regular operation of such devices installed in a given turbo-generator rotor-shaft-line enables suppression of dangerous torsional oscillations.

Słowa kluczowe:

control of torsional vibrations, turbo-generator, shaft-lines vibrations, rotary magneto-rheological dampers, new rotary dampers

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The aim of investigation is developed a reliable structural model of the traction vehicle with AC motors which drive it. Changes of parameters resulting from the movement of the vehicle in relation to the conditions of the wheel-rail co-operation might be the reason for system instability. For a reliability and security of drive system of railway vehicles driven by electric motors, the electromagnetic output traction force and torques should drive stably. Otherwise, the train drive-shaft vibrations caused by motor torque ripple will affect fatigue life of the responsible drive system components and an operation security of the driven railway vehicles. The methods developed by the authors and presented in this paper could be applied for creating some basis of vehicle drive system designs with more efficient movement-traction parameters and for increasing an efficiency of the traction vehicles characterized by high levels of power and travelling speeds.

Słowa kluczowe:

railway drive system, electromechanical coupling, AC motor, full sprung wheelset drive

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In In the paper, a new proposal of simulations safety against derailment for a tramway vehicles with an arbitrary configuration of wagons and running gears is presented. The existing European standard EN 14363 [1] covers all necessary tests for different railway vehicles, but it is inadequate for tramway vehicles, especially in safety against a derailment examination. Its operational conditions are much different. Tramways overcome horizontal curves with much smaller radii than railway vehicles. There is a large diversity in wheel-rail pairing, i.e. almost every public transport operator uses a different wheel profile. Apart from standard vehicle configuration, i.e., a carbody on two bogies, in modern tram designs varoius arrangements are applied. The described problems suggest that the methodology of safety testing before derailment described in the EN 14363 standard cannot be used without any modifications in the case of testing tramway vehicles.
Based on the obtained computational results, an essential influence of various municipal tramway vehicle designs and configurations on wheel-rail contact forces, in particular, on the derailment factor Y/Q, is discussed. The simulation results confirm the assumption that the track conditions for safety against derailment described in standard [1] addressed to the railway vehicles are not suitable for investigations of the light municipal trams. Moreover, one can remark that relatively low travelling speeds of trams do not guarantee a sufficient safety against derailment with specific vehicle configuration and extreme track geometry (small arc radius and zero cant). Such observations cause the need for further analysis of the discussed topic.

Słowa kluczowe:

tramway dynamics, safety against derailment, Simpack Rail, MBS

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The knowledge about torsional vibrations of drive transmission systems of railway vehicles is of a great importance in the dynamics of such mechanical systems. To ensure a reliability and unconditional security of high speed electric multiple unit (HSEMU) drive by AC motors, the electromagnetic output traction force and torques should drive stably. Otherwise, the shaft train vibration caused by motor torque ripple will affect a fatigue life of this device and the operation on the driven object. In the paper, a dynamic interaction between the torsionally vibrating HST drive sys-tem and the driving asynchronous motor was investigated. The results of wheelset torsional vibration analysis have shown that the first mode with torsional eigenfre-quency of the considered wheelset with electric motor is equal to109 Hz and the sec-ond torsional eigenfrequency is equal to 680 Hz. The basic torsional eigenvibration property is that the first wheel vibration direction is opposite to that of second wheel. The second torsional eigenvibration property is that the vibration directions of two wheels are coincident and the direction of electric motor connection elements is op-posite to the wheels. In the paper there was shown that static torque characteristics of the AC motor are correlated with its electromagnetic negative damping zones. This negative damping can be responsible for instability of the entire drive train. Concern-ing the transient and steady-state dynamic responses determined for the considered HST drive system, one can state that the studied phenomenon of electromechanical interactions should become an object of further investigations.

Słowa kluczowe:

Railway drive system,The direct-drive, Electromechanical coupling, AC motors

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Existing European standard EN 14363 covers all necessary tests for different railway vehicles, but it is inadequate for tram vehicles, especially in safety against a derailment examination. Its operational conditions are much different. Trams overcome horizontal curves with much smaller radii than railway vehicles. There is a large diversity in wheel-rail pairing, i.e. almost every public transport opera-tor uses a different wheel profile. In the running gear design much more rubber-metal elements are used in order to ensure a low-floor interior and to keep the kinematic envelope. Apart from standard vehicle configuration, i.e., a carbody on two bogies, in modern tram designs numerous arrangements are applied: wagons with one outer bogie, wagons with one centered bogie, wagons without bogies (sedan) etc., where twisting shims cannot be used to achieve the required twist. It should be also mentioned that in the low-floor trams there are frequently applied independently rotating wheels (IRW) which are individually driven. The dynamic behaviour of the trams equipped with the IRW wheelsets is significantly different from that of the vehicles with the classical wheelsets. The described issues imply that the methodology of safety against derailment described in EN 14363 stand-ard cannot be applied without any modifications. This paper presents a new pro-posal for a simulation safety against derailment for a vehicle with an arbitrary configuration of wagons and running gears. The numerical analyzes have been performed be means of the SIMPACK software.

Słowa kluczowe:

safety against derailment, tram vehicle, numerical simulation, run-ning dynamics, SIMPACK software

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In the paper a dynamic behaviour of the selected typical group of rotating machines applied in the mining industry is investigated. These are the beater mills and crushers as well as blowers and compressors, all driven by the asynchronous motors. In particular, there is considered an influence of various types of machine working tool loadings on the system lateral steady-state dynamic responses as well as a mutual torsional electromechanical interaction between the driving motor and the driven machine in transient operational conditions. The theoretical calculations have been performed by means of the advanced structural mechanical models. The conclusions drawn from computational results can be very useful during design phase of these devices as well as helpful for their users during regular maintenance.

Słowa kluczowe:

rotating mill machinery, electric motor interaction, electromechanical model, torsion vibration

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To ensure a reliability and unconditional security of drive system of machine and railway vehicles drive by electric motors, the electromagnetic output traction force and torques should drive stably, otherwise the shaft train vibration caused by motor torque ripple will affect the fatigue life of the device and the operation security of the driven object. For this reason an investigation of the dynamic response and stability of a electromechanical drive train system was done. The obtained results have demonstrated that the electromagnetic transient processes generated in the electric motor should be taken into account for the use of the assessing the stability of the system. The knowledge about stability of drive transmission systems of machines and railway vehicles is of a great importance in the field of dynamics and material fatigue of the mechanical systems.

Słowa kluczowe:

electric motor, torsional vibrations, electromechanical coupling, wheel-rail adhesion, wheelset drivetrain dynamic

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The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The most important sources of the observed response scatter are inherently random rotor-shaft residual unbalances as well as stiffness and damping properties of the journal bearings. A relevant representation of these parameters leads to multidimensional stochastic models. The compared stochastic moment estimation methods include sampling techniques, the dimension reduction method and the polynomial chaos expansion method. Two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbogenerator. It is shown that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. Methods employing polynomial chaos expansion perform well in the case of reduced stochastic models. On the other hand, low accuracy of the methods based on Taylor series expansion very often renders these techniques unsuitable for the robust design optimization of vibrating rotor shafts.

Słowa kluczowe:

ibrations, robustness, numerical analysis, stochastic phenomena

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In the paper the structural one-dimensional hybrid dynamical model of the entire vibrating rotor-shaft system and the three-dimensional fmite element model of its cracked shaft zone were applied for a fatigue life prediction of the machine faulty segment under coupled bending-torsional-axial vibrations. The steady-state dynamic response amplitudes, obtained by means of the one-dimensional model of the system, have been used for the three-dimensional model as an input data for determination of maximal stresses and stress intensity factors at the crack tip. These quantities together with the Wohler curves enable us an approximate determination of load limits responsible for a probable further crack propagation. By means of the proposed approach one can predict a damage probability of the faulty rotor-shaft system of arbitrary structure operating under various dynamic and quasi-static loads affecting a crack of various sizes and shaft locations. From the investigations performed for various crack axial locations on the shaft with respect to bearing supports of the single- and double-span rotor-shaft systems, it follows that a strength of the cracked zone is much more sensitive to normal stresses due to bending and axial oscillations than to tangential stresses caused by torsional vibrations.

Słowa kluczowe:

hybrid dynamical mode, vibrating rotor-shaft system, fatigue analysis

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