Identification of stiffness, damping and mass coefficients of rotor-bearing system using impulse response method

The article describes the method for determining the 24 coefficients of dynamic system composed of a rotor and two bearings based on impulse excitation between two bearings. The method of calculating the coefficients of bearings is an experimental method. This work aims to present the expansion of the algorithm known from the literature for calculating the coefficients of stiffness and damping coefficients, adding the calculation of bearing mass coefficients capability. The calculation diagram has been verified based on a numerical model of the rotor modeled in the Samcef Rotors software. Based on the proposed algorithm, we obtain four stiffness coefficients, 4 damping coefficients, and 4 mass coefficients for each bearing. The mass coefficients correspond to the part of weight of the shaft which is involved in vibration of the system. The total weight of the rotor is the sum of the mass coefficients. On their basis we can calculate the mass of the rotor. Stiffness and damping coefficients cannot be determined directly, so indirect methods need to be used to calculate them, which are described in the article. The mass of the rotor is a direct measurable parameter. The mass coefficients, calculated indirectly can be compared with the known mass of the rotor. Knowing the error of estimation of the mass coefficients we can estimate the uncertainty of bearing dynamic coefficients, which, in the initial phase, are unknowns. Expanding the calculation algorithms to calculate mass coefficients in a single operation increases the correctness of calculation of a set of coefficients which makes the results become more reliable. The article shows the actual state of the art about the experimental calculation of bearing dynamic coefficients. This paper presents a method for calculating the stiffness, damping and mass coefficients. It also includes the excitation and responses signals used to calculate these coefficients on the basis of the rotating system with two journal bearings. It is also shown how the calculated values of the mass, stiffness and damping coefficients are effected when identifying frequency range was changed

Vibration damping of the anti-vibration platform intended for use in combination with audio/music devices

The article presents research on the damping properties of an anti-vibration platform (designed and manufactured by Stacore), which is intended for use in combination with high class audio devices. The platform comprises two parts that are capable of passive vibration damping. The design of this platform is unique and has been developed by applying several technical solutions in a combination not found on any other anti-vibration platform on the audio market. These solutions are described in the article. The first part of the platform is pneumatically operated and the second part uses ball bearings. The casing also fulfils the most important function – vibration damping. It is made of amorphous slate (known for its good vibration-damping properties) and includes a metal plate covered with a special visco-elastic layer that fulfils the role of binding material. The first part of the platform realises the pneumatic damping. It comprises four elastomer pneumatic springs, each with its own air tank. The air tanks are designed to operate at a maximum pressure of 5 bar. The second vibration-damping part of the platform is located above the first part (pneumatic) and consists of ball bearings, used for the isolation of transverse vibration, being relatively difficult to deal with pneumatic springs. The upper part consists of three bearings, each of which comprises of a polished, deep hardened steel racings and a ball made of tungsten carbide. The scientific literature describes many solutions enabling vibration damping, including many anti-vibration platforms. However, the literature lacks the descriptions of analyses conducted on anti-vibration platforms for audio devices. This article is a novelty in the literature as it concerns the experimental research aimed at verifying the vibration-damping capacity of the anti-vibration platform that can be used with audio devices owned by people who appreciate high-quality music. The article describes in detail the whole measurement procedure applied to the vibration damping platform. For research purposes, the anti-vibration platform was suspended on flexible ropes. At first, an electromagnetic vibration exciter was attached to the base on which the platform rested, and then the displacements of the upper and lower part of the platform were measured using laser sensors. Based on these signals, the vibration damping capability (transmissibility) of the platform was determined in two mutually perpendicular directions. In addition to the graph that shows the vibration damping capability of the anti-vibration platform, the signals of the applied force and displacements measured during the research are also presented in this article

Vibration based diagnostics of the multi-stage microturbine operating in the medium-temperature ORC system

This article discusses a vibrodiagnostic system designed for the prototypical microturbine operating in an ORC-based power plant with an electrical capacity of around 100 kW. The first part of the article is devoted to the numerical analysis of the microturbine, which was conducted with taking into account the fact that the asynchronous electro-generator is connected to the microturbine shaft by a reduction gear. Based on the results of the analysis, the diagnostic system dedicated for the microturbine has also been developed. The second part of the article presents a vibrodiagnostic system in detail. The system with a dedicated measuring and monitoring software (developed using the LabVIEW programming environment) was described. The developed solution enables not only constant monitoring of the test object, but also protects the microturbine against propagation of damage and failure

Selection of the oil-free bearing system for a 30 kW ORC microturbine

The article discusses results of the analyses of various bearing systems for the rotor of an ORC (Organic Rankine Cycle) microturbine with an electric power of 30 kW. It is impossible to choose the appropriate bearing system taking into account only basic parameters of the bearings. When designing a new power turbine, it is important to conduct the dynamic and strength analysis of the entire rotor-bearings-supporting structure system. The nominal rotational speed of the newly designed single-stage axial-flow turbine is 40,000 rpm. The turbine will be powered using the vapour of a low-boiling working medium. The chosen working medium cannot be used in combination with all materials that are commonly used for turbine constructions. An additional requirement was that the turbogenerator must be oil-free. The temperature of the working medium directed to the rotor blades could exceed a value of 200 °C. Three bearing systems were considered: bearings lubricated with a low-boiling fluid (in the liquid form), gas bearings lubricated with the vapour of a low-boiling medium and rolling bearings. Since the rotors used in those three systems have different geometries, their dynamic properties vary as well. The rotor dynamics analyses were carried out using computer programs belonging to the MESWIR environment, which had been developed at the Institute of Fluid-Flow Machinery of the Polish Academy of Sciences (IMP PAN) in Gdańsk. The computational model, based on the finite element method, was used to prepare graphs on which are presented vibration amplitudes as functions of the rotational speed. The computational model, based on the finite element method, served to perform calculations on the basis of which graphs presenting vibration amplitudes as functions of the rotational speed were prepared. Moreover, vibration trajectories of individual nodes of the computational model were shown. Besides analyses of the bearings themselves, calculations were also carried out to assess the dynamic properties of the rotors supported by those bearings in a wide range of rotational speeds. As a result of the conducted analyses, the concept of an innovative turbogenerator was created. Its rotor can operate at a very high rotational speed, and the bearings do not require oil lubrication

Investigation of dynamic properties of the microturbine with a maximum rotational speed of 120 krpm – predictions and experimental tests

Advances in the development of analysis and design methods for fluid-flow machines have enabled both their multi-criteria optimisation and miniaturisation. To decrease the size of such a machine whilst, at the same time, maintaining its output power level, the rotor’s rotational speed needs to be increased. It is the reason for serious difficulties with respect to the rotor dynamics and the selection of a bearing system. This article discusses the simulation analysis and experimental research carried out on a prototypical microturbine, designed for use in a domestic ORC (organic Rankine cycle) cogeneration system. During the design process, the basic assumption was to develop a turbomachine, whose dimensions would have been as small as possible and whose output electric power would have been about 1 kilowatt. A supersonic impulse turbine, with a nominal rotational speed of 100,000 rpm, was used in order to obtain high flow efficiency. The maximum speed of the rotor was determined at a level of 120,000 rpm. The article presents the results of analyses made at the design stage and preliminary results of the experimental research. The numerical simulations covered the bearing system optimisation and the rotor dynamics analysis. Next, based on the outcomes of these analyses, a decision was made to use non-conventional gas bearings which are fed by the low-boiling medium’s vapour that comes from the ORC system. Within the framework of the experimental research, the dynamic behaviour of the turbogenerator was examined in terms of the rotational speed and produced energy. The performed measurements are proof of very good dynamic properties of the tested machine and after the research was over it was concluded that there were absolutely no signs of wear of the turbogenerator’s subassemblies

Investigation of dynamic properties of the microturbine with a maximum rotational speed of 120 krpm – predictions and experimental tests

Advances in the development of analysis and design methods for fluid-flow machines have enabled both their multi-criteria optimisation and miniaturisation. To decrease the size of such a machine whilst, at the same time, maintaining its output power level, the rotor’s rotational speed needs to be increased. It is the reason for serious difficulties with respect to the rotor dynamics and the selection of a bearing system. This article discusses the simulation analysis and experimental research carried out on a prototypical microturbine, designed for use in a domestic ORC (organic Rankine cycle) cogeneration system. During the design process, the basic assumption was to develop a turbomachine, whose dimensions would have been as small as possible and whose output electric power would have been about 1 kilowatt. A supersonic impulse turbine, with a nominal rotational speed of 100,000 rpm, was used in order to obtain high flow efficiency. The maximum speed of the rotor was determined at a level of 120,000 rpm. The article presents the results of analyses made at the design stage and preliminary results of the experimental research. The numerical simulations covered the bearing system optimisation and the rotor dynamics analysis. Next, based on the outcomes of these analyses, a decision was made to use non-conventional gas bearings which are fed by the low-boiling medium’s vapour that comes from the ORC system. Within the framework of the experimental research, the dynamic behaviour of the turbogenerator was examined in terms of the rotational speed and produced energy. The performed measurements are proof of very good dynamic properties of the tested machine and after the research was over it was concluded that there were absolutely no signs of wear of the turbogenerator’s subassemblies

The Experimental Identification of the Dynamic Coefficients of two Hydrodynamic Journal Bearings Operating at Constant Rotational Speed and Under Nonlinear Conditions

Hydrodynamic bearings are commonly used in ship propulsion systems. Typically, they are calculated using numerical or experimental methods. This paper presents an experimental study through which it has been possible to estimate 24 dynamic coefficients of two hydrodynamic slide bearings operating under nonlinear conditions. During the investigation, bearing mass coefficients are identified by means of a newly developed algorithm. An impact hammer was used to excite vibration of the shaft. The approximation by means of the least squares method was applied to determine bearing dynamic coefficients. Based on the performed research, the four (i.e. two main and two crosscoupled) coefficients of stiffness, damping and mass for each bearing were obtained. The mass coefficients add up to the complex shaft weight. These values are not required for modeling dynamics of the machine because the rotor mass is usually known, however, they may serve as a good indicator to validate the correctness of the stiffness and damping coefficients determined. Additionally, the experimental research procedure was described. The signals of displacements in the bearings and the excitation forces used for determination of the bearing dynamic coefficients were shown. The study discussed in this article is about a rotor supported by two hydrodynamic bearings operating in a nonlinear manner. On the basis of computations, the results of bearing dynamic coefficients were presented for a selected speed

Zastosowanie operatora energetycznego Teagera-Kaisera w diagnostyce łożyska hydrodynamicznego

The paper presents the use of the Teager-Kaiser energy operator (TKEO) to evaluate the state of rotor unbalance. The method was developed in 1990 by Kaiser and involves a simple calculation of signal energy. It has been used before in diagnostics, e.g. during the evaluation of instability of hydrodynamic bearings and as a diagnostic symptom of gearbox damage. This paper is the first to present the use of the Teager-Kaiser method to evaluate the rotor unbalance in hydrodynamic bearings.W artykule przedstawiono zastosowanie operatora energetycznego Teagera-Kaisera (TKEO) do oceny stanu niewyważenia wirnika. Metoda ta opracowana została w 1990 roku przez Kaisera i polega na prostym obliczeniu energii sygnału. Wykorzystywana była już wcześniej w diagnostyce np. przy ocenie niestabilności łożysk hydrodynamicznych oraz jako symptom diagnostyczny uszkodzenia przekładni. W artykule tym po raz pierwszy przedstawiono możliwość wykorzystania metody Teagera-Kaisera do oceny niewyważenia wirnika pracującego na łożyskach hydrodynamicznych

An experimental investigation conducted in order to determine bearing dynamic coefficients of two hydrodynamic bearings using impulse responses

The paper presents the experimental investigation carried out in order to identify bearing dynamic coefficients of two hydrodynamic bearings from impulse responses. In this method the stiffness, damping and mass coefficients of two hydrodynamic bearings were calculated in a single algorithm. For each rotational speed, were obtained 12 dynamic coefficients which enable to fully describe the dynamic state of the rotor. Exciting force signals, applied using an impact hammer were shown. Displacements of the shaft were measured by eddy current sensors. The measurements were carried out at various rotational speeds, including resonance speeds. The vibration amplitude in a resonance case increases significantly with time after the excitation was induced by an impact hammer. Excitations of the rotor with an impact hammer were recorded using a high-speed camera. These unique recordings and simultaneous analysis of the trajectory of the bearing journals depict the contact phenomena that occur during impulse excitation of the rotor

Ocena stanu dynamicznego turbiny wodnej o mocy 600 kW

The article discusses the results of experimental studies to assess the dynamic state of the turbine set with the Kaplan turbine. The dynamic assessment was made on the basis of appropriate standards, based on the measurement results of selected parameters of vibration, which have been measured for several states of the machine load. In addition, we attempted to identify the causes of the increased vibration levels based on the measured vibration spectrum and the temperature distribution on the machine casing. On the basis of analysis results, the tested fluidflow machine was qualified in the appropriate zone (defining the state of vibration) and identified the source of high levels of vibration.W artykule omówiono wyniki badań eksperymentalnych mających na celu ocenę stanu dynamicznego hydrozespołu z turbiną Kaplana. Oceny stanu dynamicznego dokonano w oparciu o odpowiednie normy, na podstawie wyników pomiarów wybranych wielkości charakterystycznych drgań, które zostały zmierzone dla kilku stanów obciążenia maszyny. Dodatkowo, podjęto próbę wskazania przyczyn podwyższonego poziomu drgań w oparciu o zmierzone widma drgań oraz rozkład temperatury na korpusie maszyny. Na podstawie przeprowadzonych analiz zakwalifikowano badaną maszynę przepływową do odpowiedniej strefy (określającej jej stan drganiowy) oraz wskazano źródło podwyższonego poziomu drgań