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Über dieses Buch

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

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

The proceedings are divided into four volumes. This first volume covers the following main topics: Active Components and Vibration Control; Balancing; Bearings: Fluid Film Bearings, Magnetic Bearings, Rolling Bearings and Seals; and Blades, Bladed Systems and Impellers.



Numerical Identification of Nonlinear Hydrodynamic Forces

Bearings are key elements for a detailed dynamical analysis of rotating machines. In this way, a rotating component sustained by flexible supports and transmitting power creates typical problems that are found in several machines, being that small or large turbines, turbo generators, motors, compressors or pumps. Therefore, representative mathematical models, such as the use of bearings nonlinear forces modeling, have been developed in order to simulate specific systems working conditions. The numerical solution of the equation of motion, when considering nonlinear complete solution of finite hydrodynamic bearings, is highly expensive in terms of computational processing time. A solution to overcome this problem without losing the nonlinear characteristics of the component is use a high order Taylor series expansion to characterize the hydrodynamic forces obtained by the Reynolds equation. This procedure accelerates the nominal behavior predictions, facilitating fault models insertion and making feasible actions in control systems design. So, this papers aims to analyze the use of nonlinear coefficients, generated by the high order Taylor series expansion, to simulate the rotor dynamics under strong nonlinear bearing behavior. The results obtained were compared with Reynolds and linear simulations, and demonstrated that the nonlinear coefficients can be successful to represent bearing behavior even in extreme situations.

Diogo Stuani Alves, Katia Lucchesi Cavalca

Thermo-Hydrodynamic Model Influence on First Order Coefficients in Turbocharger Thrust Bearings

High rotation turbochargers, to automotive applications, are continually subjected to axial forces due to gas flows in the turbine and the compressor. These axial forces are supported by lubricated thrust bearings, and their effect is introduced in the dynamic system through its equivalent stiffness and damping coefficients. These coefficients are estimated utilizing a thermo-hydrodynamic model of the bearing, which is composed by the Generalized Reynolds Equation and Energy Equation, to estimate pressure and temperature distribution in the oil film. This work analyzes the influence of geometric and operational parameters of the fixed-geometry thrust bearings in pressure and temperature distributions along the fluid film, solving the governing equations by Finite Volume Method. Along with the pressure distribution, the supported axial load is evaluated and, after that, the equivalent coefficients are estimated. In this work, the Energy equation is solved utilizing 3D model and 2D model (neglecting the radial heat exchange), to check the difference in these results in a computationally less expensive model, and other simplifications, disregarding the conduction heat exchange in the circumferential direction and the convection heat exchange in the axial direction. The load capacity and the equivalent coefficients are compared with a purely hydrodynamic model, disregarding the viscosity variation through the oil film. In lower rotational speeds, the heat generated by fluid shear is small, so a HD model can be utilized considering a constant mean temperature of the oil film. This last approach can reduce the cost to solve the pressure distribution that govern the oil flow in the bearing clearance.

Thales Freitas Peixoto, Gregory Bregion Daniel, Katia Lucchesi Cavalca

Study of Stiffness Reduced Order Model Applied to Line and Elliptical Contact Under EHD Lubrication

Nonconforming contact study is fundamental to model the behavior of mechanical equipment such as bearings and gears. In order to predict lifetime of rolling element bearings, film thickness and pressure distribution can describe the lubrication condition, allowing the analysis of the contact response to load, rotation speed, oil parameters and geometry. The EHD elliptical contact can be approximate to an equivalent line contact when taken the central line at the major ellipsis axis, since the maximum Hertzian pressure, lubrication oil, rotation speed and radius of curvature are identical. A comparison between the stiffness reduced order model of elliptical contact and an equivalent line contact, based on an explicit load-distribution relation, is accomplished. Moes load and lubrication dimensionless parameters describe the contacts along with the elliptical contact ellipticity. The influence of speed and ellipticity were verified on the oil film and pressure in a range of load conditions, as well as EHD stiffness reduced order model parameters. The ellipticity range evaluates the similarity between both kinds of contact and verifies its equivalence.The present work analyses the contact reduced order model and its main parameter influence, the EHD stiffness. As the contact properties, film thickness and pressure distribution, directly affect the lifetime estimation of rolling element bearings, the study can bring useful insights during project stage. Moreover, an improved EHD nominal model can promisingly be applied in fault identification in rotating systems and other mechanisms.

Letícia Bizarre, Natália Akemi Hoshikawa Tsuha, Katia Lucchesi Cavalca

Stiffness and Damping Reduced Model in EHD Line Contacts

The increasing of operation speed and demand for precision in machinery make lubrication conditions a crucial aspect in order to maximize lifetime of rotor dynamic components. The elastohydrodynamic (EHD) regime more frequently occurs in nonconforming lubricated contacts with local elastic deformation due to high pressure in small contact area. The objective of this work is to analyze the EHD force reduced model applied to line contact based on restitutive and dissipative terms. In restitutive force term, an EHD stiffness approach is evaluated considering an explicit force-displacement relation with two independent parameters - stiffness and a constant surface separation force. Steady-state EHD contact numerical results allow estimating the restitutive parameters. The dissipative force term is composed by linear viscous damping. The damping is characterized by numerical simulation using the principle of energy conservation in transient elastohydrodynamic lubricated system. The influence of load and speed variations in damping fluctuations are investigated.The EHD reduced force model characterizes the lubricated contact in just three parameters (oil film stiffness, EHD constant surface separation force and viscous damping), simplifying the lubrication problem in comparison of solving EHD system of equations at each work condition and time step. This model can be applied to any nonconforming EHD line contact as cams, gears, needle element rolling bearings and cylindrical roller bearings in dynamic analysis and project stage development. Furthermore, an accurate contact model increases machine reliability, being promising to be used in model-based fault identification.

Natália Akemi Hoshikawa Tsuha, Fábio Nonato, Katia Lucchesi Cavalca

Dynamical Characteristic Analysis of Elastic Ring Squeeze Film Damper in Rotor System

By placing an elastic ring inside the oil chamber, elastic ring squeeze film damper (ERSFD) has better performance than classic squeeze film damper (SFD) in suppressing nonlinear characteristic and good application potential in aircraft engines and gas turbines. However, it is not easy to combine the deformation analysis on the elastic ring with the oil film analysis based on Reynolds equations and dynamic analysis of the ERSFD-supported rotor accurately. In this paper, based on the Kirchhoff assumption, the finite element method (FEM) is employed to investigate the deformation of elastic ring. First, the oil film pressure and force are analyzed by solving the Reynolds equations. Then the deformation of elastic ring, oil film force and rotor motion are determined simultaneously to analyze the oil film coefficients of ERSFD and the response of rotor system. Using the proposed procedure of calculation, dynamic characteristic of the ERSFD is investigated and we found that the ERSFD is better than the SFD in preventing bi-stable vibration of rotor by lightening the nonlinearity level of the oil film. Then influences of the ERSFD parameters, number of elastic ring boss, ring thickness and oil film thickness respectively, on the oil film characteristics are discussed. The study reveals that three effects of elastic ring make better dynamical performance of ERSFD than SFD.

Zhifei Han, Qian Ding, Wei Zhang

Unbalance Vibration Compensation Control Using Deep Network for Rotor System with Active Magnetic Bearings

Unbalance vibration directly affects the operational precision, stability and life of rotary machinery. Profiting from the active control speciality of active magnetic bearing (AMB), unbalance vibration of rotor system with AMBs can be compensated and controlled automatically. This paper considers unbalance vibration minimum for rotor system with AMBs. Deep learning theory is utilized to design a compensation controller, which is added to the PID feedback control. The structure of the compensation controller is established by a deep neural network with 2 hidden layers, and its operation algorithms are designed. Model of a 4-DOF rigid rotor with AMBs is established for controller parameter setting and simulation. The unbalance vibration control of different controllers at fixed rotational speed is simulated, and the control effects of the proposed controller are demonstrated via unbalance vibration analysis and control current analysis. This research provides a new adaptive control approach for AMB control of unbalance minimum compensation, and it can also be applied in other multi-dimension vibration control.

Xuan Yao, Zhaobo Chen, Yinghou Jiao

Unbalance Identification in a Rotor Supported by Active Magnetic Bearing

This paper presents a formulation for unbalance fault detection in flexible rotors supported by active magnetic bearings, AMB. The model-based procedure makes use of the correlation equations, through the matrix formulation of Ljapunov for stationary linear systems along with artificial neural networks. This procedure only uses measured state variables. Through the correlation of the output variables, a group of relations involving the physical parameters of the system together with the matrices of correlations of the measured variables is generated. Unbalance changes are detected through the monitoring of variation of physical parameters related to unbalance and comparison of theoretical and estimated correlation functions. Artificial neural networks are used to map correlations involving states that are not measured. The proposed method is applied in a flexible rotor model composed of four rigid disks, a pair of active four pole magnetic bearings with feedback control. The unbalance change is applied in individual planes and in several planes simultaneously.

Gilberto Machado da Silva, Robson Pederiva

Numerical Study on the Influence of Gas Foil Thrust Bearings on the Vibrational Behavior

Gas Foil Bearings (GFBs) have a promising future in high-speed turbomachinery such as air cycle machines and turbochargers. To achieve complete oil-free operation of the rotor support structure Gas Foil Thrust Bearings (GFTBs) can be used in combination with Gas Foil Journal Bearings (GFJBs). The present study numerically investigates the influence of GFTBs on the rotordynamic behaviour. In a first step the perturbation method is used to calculate linearized stiffness and damping coefficients. The perturbation approach used in this study is widely used in GFJBs resulting in uncoupled first-order equations to calculate the stiffness and damping parameters. Previously published approaches for GFTBs were relying either on coupled first order equations or were independent of excitation frequency. The calculated bearing parameters are validated against numerically calculated data published in the available literature. Linear stability analysis for a rigid rotor supported by GFTBs is performed and later extended for a rotor supported by both GFTBs and GFJBs.

Tomasz Pronobis, Alexander Ramin, Robert Liebich

Magnetic Bearings for Non-static Flywheel Energy Storage Systems (FESS)

Proper dimensioning of magnetic bearings for non-static gimballed FESS is currently hindered by the lack of models that can predict the maximum forces in the bearings. If FESS is to compete with conventional electro-chemical batteries in terms of energy density, the magnetic bearings must be dimensioned optimally for weight and size. Magnetically suspended FESS has been experimentally investigated; however, the methods for theoretically predicting magnetic bearing loads are still limited. This paper presents how to determine such magnetic bearing loads in a gimballed FESS subject to a moving foundation. The predicted forces are compared with measurements from an experimental test bench with good agreement. Furthermore, the maximum forces in a gimballed FESS are compared with maximum forces in a non-gimballed FESS. It was found that the gyroscopic forces in the non-gimballed case quickly become critical making the gimbal mount essential for reducing magnetic bearing loads.

Nikolaj Dagnaes-Hansen, Ilmar F. Santos

Application of the Controllable Magnetorheological Squeeze Film Dampers for Minimizing Energy Losses and Driving Moment of Rotating Machines

The energy losses generated in rolling element bearings rise with increasing magnitude of the force transmitted between the rotor and the stationary part. A frequently used technological solution, which makes it possible to minimize the transmitted force, consists in adding damping devices to the rotor supports. To achieve their optimum performance in a wide range of operating speeds, their damping effect must be adaptable to the current angular velocity. This is offered by magnetorheological squeeze film dampers. Their main parts are two concentric rings separated by a layer of magnetorheological oil. Its squeezing produces the damping force. As magnetorheological fluids are sensitive to magnetic induction, the change of magnetic flux passing through the lubricating film changes the damping force. The goal of the carried out investigations was to study the influence of controllable damping in rotor supports on energy losses and driving moment of the motor in different velocity ranges. The investigations were performed by computational simulations. The rotor was rigid, supported by magnetorheological squeeze film dampers, and excited by its unbalance. The results show that appropriate adaptation of the magnitude of the damping force to the current operating speed arrives at minimizing the energy losses generated in the rotor supports. The performed analysis shows a new possibility of magnetorheological squeeze film dampers, which leads to improvement of performance of rotating machines and points out at a new field of their prospective application.

Jaroslav Zapoměl, Petr Ferfecki, Jan Kozánek

Power Loss and Temperature Growth in the Backup Bearing of AMB-Supported High-Speed Electric Motor During a Dropdown

This paper presents a simulation model for the dropdown of a high-speed electric motor utilizing the active magnetic bearings (AMB). In the circumstance that there is not a sufficient electromagnetic field or the system experiences excessive load, the rotor drops instantly on the backup bearings. The dropdown is accompanied by a considerable friction between the surfaces of the rotor and backup bearings. This study evaluates the heat generation and thermal behavior of backup bearing that are essential for the design of AMB systems. The model enables to calculate the power loss resulted from the friction between the rotor and backup bearing. The simulation includes the FE-model of the rotor and the backup bearing model. The one-dimensional thermal network has been applied to the thermal model of the bearing. The study concentrates on evaluating the friction heat generated and thermal growth of the deep groove ball bearing type in the non-drive end of the motor.

Neda Neisi, Eerik Sikanen, Janne E. Heikkinen, Teemu Sillanpää, Jussi Sopanen

Simulation of a Test Rig and Identification of Annular Gas Seals Coefficients

This paper shows some preliminary results of an ongoing test rig for coefficients identification of annular gas seals. The test rig is being built in the Laboratory of Vibrations and Acoustics (LAVI) at the Federal University of Rio de Janeiro. The main objective of the rig is to determine both the damping and stifness created by annular gas seals (honeycomb, labyrinth, hole-pattern, etc.) to a flexible rotor. The paper is divided in three parts. First, the characteristics and components of the rig are shown. Then, a rotordynamic model is proposed based on the finite elementh method, in which the rotor is divided into smaller elements and the seals are represented as punctual stiffness and damping. Some simulated results of this model is shown and analyzed. Finally, preliminary experimental results are shown and discussed.

David Maldonado, Diego Godoy, Vinicius Côrtes, Fernando Pinto, Thiago Ritto

The Classical Linearization Technique’s Validity for Compliant Bearings

The Gas Foil Bearing (GFB) is a promising and environmentally friendly technology allowing support of high-speed rotating machinery with low power loss and without oil or electronics. Unfortunately, GFBs provide limited damping, making an accurate prediction of the Onset Speed of Instability (OSI) critical. This has traditionally been assessed using linearised coefficients derived from the perturbed Reynolds Equation with compliance included implicitly. Recent work has, however, revealed significant discrepancies between OSIs predicted using these techniques and those observed from nonlinear analysis. In the present work, the perturbation method’s underlying assumption on the pressure field is investigated by including the hitherto neglected pressure–compliance dependency directly. This leads to an extended perturbation akin to that commonly applied to tilting pad bearings and is shown to predict OSIs with much better agreement to time integration results. The extended perturbation method is cumbersome, but serves to highlight the error introduced when applying the classical perturbation method—as developed for rigid bearings by J. W. Lund—to GFBs.

Sebastian von Osmanski, Jon S. Larsen, Ilmar F. Santos

Rotordynamic Force Coefficients of Gas Seals — An Experimental Approach with Active Magnetic Rotor Excitation

Gas seals are important components in turbomachines to guarantee high internal efficiency by restricting undesired leakage flows. Moreover, it is important to identify their rotordynamic force coefficients for the use in rotordynamic analyses of turbomachinery. Experimental methods to determine the full set of rotordynamic coefficients require a relative motion between rotor and stator, e.g. using Active Magnetic Bearing (AMB) technology. A unique approach is used in the present test rig, where a single AMB is used as an exciter on a flexible rotor supported by two fluid film bearings. Following an AMB upgrade, a new measurement principle was introduced based on the mechanical impedance method. The present paper describes the upgrade measures on the test rig, the measurement procedure and the parameter identification method along with a calculation scheme for the combined measurement uncertainty. First measurements on a fully partitioned pocket damper seal are performed to validate the new hardware and parameter identification procedure.

Clemens Griebel

Analysis of the Rotor Supported by Gas Foil Bearings Considering the Assembly Preload and Hardening Effect

This article discusses a new method for modelling elastic deformations of a foil bearing’s structure, taking into account key phenomena influencing its characteristics. Special attention was paid to the assembly preload, which has an impact on the stiffness of the supporting system and thus also on the static and dynamic properties of the rotor. There has been proposed the method which allows for the inclusion of a selected preload into the bearing model. A new FEM model of the foil bearing’s structure has been described. This model was coupled with an in-house developed flow model of the bearing and the entire rotating system. Computations were made for several assembly preload values, taking into account changes in the bearing structure stiffness as the load increases. The changes in stiffness associated with the load changes were due to the nonlinear geometry of the foils, and also due to the contact phenomena, including friction between components. The applied calculation algorithm allowed to take into account all these phenomena. The results obtained using the developed model confirm the very high influence of the foil bearing’s pre-clamp and the progressive stiffness on the properties of the rotating system. Numerical models of this type can pave the way for a further development of foil bearings and for their wider use in modern high-speed fluid-flow machines.

Grzegorz Żywica, Jan Kiciński, Małgorzata Bogulicz

Selection of the Bearing System for a 1 kW ORC Microturbine

The article describes an analysis of various bearing systems for the rotor of an ORC turbine with an electric power of 1 kW. The nominal rotational speed of the newly designed single-stage axial-flow turbine is 100,000 rpm. The turbine is supplied with a low-boiling medium’s vapor and this medium is not compatible with all typical materials used for constructing power turbines. Additionally, the turbine must be an oil-free machine. In one of the design variants, the turbine rotor disk is to be made of plastic and the temperature of the working medium directed to the vanes will be approx. 150°C (at a pressure of 10 bar). Three different bearing systems were considered: 1. bearings lubricated with a low-boiling medium’s liquid; 2. gas bearings lubricated with a low-boiling medium’s vapor; 3. rolling bearings. After initial analysis, it was found that hydrodynamic bearings lubricated with a low-boiling medium did not work properly in this case and it was decided to conduct a detailed analysis of the second and third type of bearings. The two bearing systems are associated with changes in the geometry of the rotor, which in turn strongly affect the dynamic performance of the entire rotating system. The dynamic analysis of the rotor is the subject of the conducted research and constitutes part of the bearing selection process. This article presents the process of selecting and optimizing the bearing system for the rotor of a 1 kW turbine.

Łukasz Breńkacz, Grzegorz Żywica, Małgorzata Bogulicz

Experimental and Theoretical Comparison Between the Ball and Pinned Bearing Working as Backup Bearing for Magnetically Levitated Rotors

The papers focuses on the modelling and experimental validation the vibro-impact dynamic behaviour of rotors interacting with two types of backup bearings, i.e. one pinned backup bearing with polymeric pins (original contribution to the problem) and another common ball bearing (conventional). The impact forces are modelled using Hunt and Crossley approach. The parameters of the constitutive equation responsible for describing the contact forces are a priori identified in auxiliary tests. The vibro-impact model is built by coupling the nonlinear contact forces with the rotor-bearing system dynamics and the theoretical results are obtained by integrating the coupled equations in time. A fully-instrumented test bench is designed, built and used to validate the experimental results. The effectiveness of the pinned bearing is evaluated in terms of orbits and maximum vibration.

Cesar Augusto Fonseca, Hans Ingo Weber, Ilmar Ferreira Santos

Stochastic Analysis of Asymmetric Tilting-Pad Journal Bearings

Tilting-pad journal bearings (TPJBs) are symmetric from design. However, the machining and assembling tolerances of a TPJB can result in asymmetries of the pad position that strongly affect the final dynamic characteristics of the system. In this work, a numerical study is devised to analyze the stiffness and damping coefficients of an asymmetric TPJB with load-on-pad (LOP), evaluated by a thermo-hydrodynamic (THD) model for a wide range of Sommerfeld numbers. The uncertainty in the TPJB geometry is included in the model by varying the nominal bearing gap (assembled clearance) according to a distribution ruled by the Monte Carlo Method. The results show that, in most of the cases, the asymmetry represents a detrimental effect on the bearing characteristics. However, there are some cases where the asymmetry of the TPJB is beneficial, resulting in higher stiffness and damping than expected from designing a symmetric bearing.

Heitor Antonio Pereira da Silva, Rodrigo Nicoletti

Experimental Structural Analysis of Gas Foil Bearings

Gas foil Bearing (GFB) are oil-free, high-speed and light bearings, which work according to the principle of fluid film lubrication. Thanks to their elastic structure, GFBs are able to compensate for minor pressure changes in the lubrication films. This paper presents the experimental structural analysis of first-generation gas foil bearings. The aim of the experimental investigation is to determine the behaviour of GFBs at static and dynamic loads. The tests are carried out with rotor speeds close to 0 rpm. In the course of the static investigation, the GFB was mounted on shafts with different diameters and loaded with a force of −150 N to 150 N. Results from the static measurement show that not only the shaft diameter plays a role in determining the bearing clearance but also the number of activated bumps. It also shows that with a small bearing clearance ($$ {\le }10\,{\upmu }\mathrm{m} $$), the GFB has an almost linear static stiffness. In the dynamic study, the GFB was mounted on a non rotating shaft and was excited by the shaker with a mono-frequency load. The goal of the dynamic investigation was to determine the dynamic stiffness behaviour and damping behaviour of GFBs at different amplitudes (2 $$\upmu $$m, 6 $$\upmu $$m and 10 $$\upmu $$m) and over the frequency range of 30 Hz to 1000 Hz. In addition, this study aimed to find out whether the formation of subharmonic vibrations observed in the rotordynamic investigation can be attributed to the GFB structure. These subharmonic vibrations, as previous studies show, occur at speeds starting at about 20 000 rpm (333 Hz). For this reason, the dynamic measurement was performed up to 1000 Hz. The results show that the damping decreases with increasing frequency up to 490 Hz before rising again. This behaviour is amplitude independent. The stiffness of the bearings increases with increasing frequency. To verify the formation of subharmonic vibrations through the structure of GFBs, a Fourier transformation of the measurement signal was performed. However, no subharmonic vibration can be detected.

Cédric Kayo, Robert Liebich

Influence of Manufacturing Errors on the Unbalance Response of Aerodynamic Foil Bearings

The present work tackles the impact of manufacturing errors on the unbalance response of a Jeffcott rotor supported on aerodynamic foil bearings. The peculiarity of the model is the use of the Abaqus software for describing the dynamic response of the foil structure, for calculating the thin film pressures and for integrating the equations of motion of the rotor-bearing model. The numerical results show that the foil bearing without manufacturing errors and with a radial clearance of 31.8 µm is unstable for the tested operating conditions (30 krpm rotation speed, 10 N static load and G1 unbalance class). However, taking into account manufacturing errors may lead to a different result. Bump height manufacturing errors were added to the model. Five cases with random manufacturing errors but all with 10 µm standard deviation of the bump height were analyzed. In four cases, the unbalance response was a limit cycle dominated by the 0.5 Ω subsynchronous frequency. This result may explain the discrepancies between theoretical and experimental results reported up to now in the literature.

Aurelian Fatu, Mihai Arghir

Parametric Sensitivity Analysis of Tilting Pad Bearings to Investigate the Dynamic Behavior of Rotating Machines

This paper presents a parametric sensitivity analysis based on Design of Experiments (DoE) applied to tilting pad bearings. The main objective is to explore a set of design parameters and its influence on the dynamic response of a rotor system. In this way, the computational analysis was based on the integration of the commercial design software HEEDS® and a numerical code that was implemented in MATLAB® to simulate the rotordynamics phenomena. The rotor system was modelled as Timoshenko beam and the computational model was implemented using Finite Element Method (FEM). The Finite Volume Method (FVM) was applied to the tilting pad bearings in order to determine the synchronously reduced equivalent stiffness and damping coefficients. The results indicate that the fluid film bearing has a strong effect on dynamic behavior of the rotating system and that a correct choice for its main geometric parameters can result in a safer operation condition by increasing the values of the second critical speed components. Since small variations in the design parameters can significantly change the rotating machine behavior is necessary to rigidly control their values during both processes of manufacturing and assembly.

L. R. Ito, D. J. Ramos, Z. de C. Silveira, G. B. Daniel

Analysis of Analytical Hydrodynamic Bearing Models on a Reciprocating Compressor

Reciprocating compressors are one of the most common machines, as they are usually found in household refrigerators and air conditioners. The reciprocating compressor is a rotor-crankshaft-piston machine supported by lubricated bearings. They are sealed to retain and store the refrigerating gas, therefore, the maintenance of the compressor is difficult and expensive. Thus reciprocating compressors should be designed to last the life span of the appliance. Most models of reciprocating compressors considers rigid bearings, which completely neglects the influence of the hydrodynamic bearings on the dynamic behavior of the compressor. This work shows the modeling and analysis of a reciprocating compressor with flexible bearings. The rotor which is part of the motor is supported by a pair of hydrodynamic bearings that are modeled using three different analytical models: Capone, Vance and Butenschön. Analytical models of bearing are much faster than numerical ones, such as the ones that use the finite difference (FDM) or finite element method (FEM). The three models have different approaches to solve the Reynolds equation and, therefore, distinct results were found using each one of them. The model was developed in the OpenModelica software using the elements of the Mechanics.Multibody library. The Butenschön model was implemented in C and Fortran 95 and integrated to OpenModelica as an external library.

Eduardo Paiva Okabe, Jaime Hideo Izuka, Reinhard Resch

Radial Active Magnetic Bearing Design Optimization

This paper presents a design optimization approach to minimize the volume of a radial Active Magnetic Bearing (AMB) by comparing Genetic Algorithm (GA) and Pattern Search (PS) methods. The flexible rotor dynamic analysis is performed to determine AMBs dynamic load under different unbalance cases. Preliminary design parameters are generated and results are compared with optimization results, showing around 35% reduction in volume. The PS method resulted a bigger diameter but shorter bearing length compared with GA. Nevertheless, GA generated a thicker AMB with reduced external diameter. All designs (PD, PS and GA) satisfied design constraints as determined by rotor bearing dynamics while keeping the same bearing load capacity, also validating the PD methodology as a prototyping alternative to optimization strategies.

Javier Betancor, M. Necip Sahinkaya, Yahya H. Zweiri

Measurements of Rotordynamic Force Coefficients of Metallic Type Brush Seals

The present paper presents experimental measurements of rotordynamic force coefficients for a multistage arrangement of four identical brush seals. The bristles are metallic, with a lay angle of $$50^{\circ }$$ from radial centerline and have an initial radial interference with the shaft of 0.12 mm. According to a radial feeding groove, two pairs of two seals are tested face to face. The supply pressures are 0.54, 0.82, 1.1, 1.75 and 2.4 MPa, with a discharge pressure of 0.4 MPa. The working fluid is water. The rotor is centered and the operating spinning speeds are 50, 3000 and 6000 rpm. For given working conditions (supply pressure and rotor speed), a set of dynamic excitations (two directions and 8 frequencies), imposed to the rotor, provide complex impedances that are used for identifying rotordynamic force coefficients. Results are discussed in order to highlight the respective impact of rotor speed and supply pressure on brush seals performances.

Pascal Jolly, Olivier Bonneau, Mihai Arghir, Florent Cochain, Jérôme Dehouve

Kriging Surrogate Model Dedicated to a Tilting-Pad Journal Bearing

In this contribution, a kriging surrogate model was used to represent a tilting-pad hydrodynamic bearing of a Francis hydropower unit. The rotating machine is composed by a vertical shaft and three hydrodynamic bearings, namely (i) a combined tilting-pad radial/thrust bearing, which is located close to the generator; (ii) an intermediate radial tilting-pad bearing; (iii) and a cylindrical bearing located close to the Francis turbine. During the solution of the equations of motion, it was verified that the bearings are critical regarding the associated computational cost. Thus, the bearings were represented in the hydropower unit model by using surrogate models. The kriging model dedicated to the intermediate radial bearing is presented in this paper, in which the equilibrium position of the shaft and the inlet oil temperature were used as input values. The bearing supporting forces, maximum oil film pressure, and maximum oil film temperature were considered as output values. A thermohydrodynamic model of the bearing was used to determine the output variables from the input ones. Consequently, the kriging surrogate model was determined. The obtained results demonstrate the effectiveness of the proposed approach.

Arinan De P. Dourado, Jefferson S. Barbosa, Leonardo Sicchieri, Aldemir A. Cavalini, Valder Steffen

Effect of Lubricant Supply Pressure on SFD Performance: Ends Sealed with O-rings and Piston Rings

A well-designed SFD must deliver enough damping to aid in decreasing rotor amplitudes of motion. Piston rings (PRs) and O-rings (ORs) are commonly used as end seals in dampers for commercial and military gas turbine engines, respectively. The paper details dynamic load tests conducted on a short length SFD (L/D = 0.2) sealed with either (a) PRs or (b) ORs and the experimentally estimated damping and inertia force coefficients. Lubricant (ISO VG2) flows thru one feedhole at the land middle plane with supply pressure increasing from 0.7 bar(g) to 6.2 bar(g). In the PR-SFD, oil leaves the film land through the rings’ abutted ends making a slit. The OR-SFD effectively seals any leakage; hence, lubricant flows out through a discharge hole at a location halfway of the film (upper) land length. Multiple sets of single frequency (10 Hz–100 Hz) dynamic loads produced circular centered orbits with amplitude (r) equal to 30% of the radial clearance. For both PR-SFD and OR-SFD, the viscous damping coefficient diminishes quickly as the lubricant supply pressure drops below 3 bar(g). The added mass coefficient, on the other hand, remains nearly constant for the PR-SFD and slightly increases for the OR-SFD. The OR-SFD delivers ~10% more viscous damping than the PR-SFD albeit it demands of a larger flow rate. Analysis of the recorded film dynamic pressures shows their peak-peak magnitude increases with whirl frequency. However, operation at the lowest oil supply pressure, 0.7 bar(g), generates film peak pressures not increasing as the excitation frequency rises, thus evidencing the presence of air ingestion and entrapment, as vividly shown by recorded film dynamic pressure waves, in particular for the PR-SFD.

Luis San Andrés, Bonjin Koo

SEMAJIB: A Versatile High Performance Smart Bearing

The experimental development of the Smart Electro-Magnetic Actuator Journal Integrated Bearing (SEMAJIB) is presented in this paper. The SEMAJIB is a smart high performance integrated bearing that combines a fluid film bearing (FFB) with an electro-magnetic actuator (EMA) in one integrated device. In all cases, the fluid film bearing shall carry the load, whereas the electro-magnetic actuator can be used as a pure controller or both as a controller and a load carrying element. In the latter case the electro-magnetic actuator can be considered as an active magnetic bearing (AMB). This paper summarizes the development of the SEMAJIB as a compact integrated bearing. It is shown that the SEMAJIB can easily transgress the multiple critical speeds of the 2-inch laboratory rotor, as well as suppress not only the first mode oil whip, but also the second mode oil whip, and additionally can control the rotor unbalance. The use of PD, H∞ and Fuzzy Logic control to control the SEMAJIB is presented and compared. It is shown that the SEMAJIB is a high performance bearing that is versatile and can replace tilting-pad bearings in high performance rotating machinery.

Aly El-Shafei

Measurement Corrections for Active Magnetic Bearing Control

Rotor shaft position measurement is an important part of the algorithm performance in the active magnetic bearing control. The shaft centerline is estimated based on the measurement of the shaft surface distance to the sensor position. When the shaft surface has a large curvature, the measurement needs to be corrected in order to eliminate geometric correlations between measurements in the two axes. Such correlations have an impact on the control algorithm performance. The objective of this work is to propose a geometric model to estimate a more accurate position of the shaft centerline, considering also possible deviations of the sensor alignment. Corrections were applied to a control algorithm in an experimental active magnetic bearing workbench, showing an improvement of the control performance based on average distance to operation center criterion.

L. C. A. Almeida, J. M. A. Barbosa, F. C. G. Santos, P. M. G. del Foyo

Calculating Rotordynamic Coefficients of Liquid Annular Seals by CFD for Vibration Analysis and Validation at the Test Rig

This article presents a simulation methodology for calculating rotordynamic coefficients of liquid annular seals using the open source software OpenFOAM. Therefore, stationary fluid solutions for several boundary conditions are generated to represent the rotational shaft speed, the eccentricity and the whirling motion. Analyzing the acting forces in a whirling coordinate frame leads to a simple curve fit to determine the rotordynamic seal coefficients. The CFD approach is validated with an analytical solution and the coefficients of characteristic states are compared to literature results. Finally, the methodology is applied to our test rig’s geometry to calculate its dynamic behavior. The comparison between the simulated and measured behavior shows good agreement.

Christian Wagner, Stephan Sinzig, Thomas Thümmel, Daniel Rixen

Coupled Simulation of Rotor Systems Supported by Journal Bearings

Oil whirl and whip phenomena are fundamental to rotor systems supported by journal bearings. Published studies opt for a reduced formulation of the Reynolds equation of lubrication in order to aid the computations. In the current study, the complete Reynolds equation is solved using Pseudo Spectral Methods (PSM) and results compared with reduced solutions. The possibility of certain trends being missed in reduced model simulations is also brought out using a simple example. Rotor shaft and journal bearing systems are numerically modelled and coupled simulations have been carried out for test rotors inspired from literature. A semi analytical derivative estimation method is demonstrated to be superior to conventional finite difference methods in terms of processor load. This will be a useful addition for iterative solvers applied on rotors with more complicated geometry. Time transient analysis is carried out for two test rotors in order to bring out the oil whirl and whip phenomena, where the second one, with an added nonlinear node, shows a whirl along a branch which went undetected in the published reference. In the light of the above trends, the importance of full model numerical simulation is further emphasized.

Nidish Narayanaa Balaji, I. R. Praveen Krishna

Effect of Texture Region on the Static and Dynamic Characteristic of Partially Textured Journal Bearings

The effect of the texturing region on the static and dynamic characteristics of partially textured bearings, of which the texturing area is limited on the bearing surface in the circumferential direction, were investigate theoretically. The load carrying capacity and stiffness and damping coefficients of some partially textured journal bearings with the different textured region were calculated by using a numerical model considering the effects of both fluid inertia and energy loss at the edges of the dimples. The results showed that when the surface texturing was formed in the unloaded region of the journal bearing surface, the load carrying capacity maintains as much as the smooth bearing for a wide range of Sommerfeld number. The linear stability threshold speeds of a symmetrical rigid rotor supported in two identical textured bearings was also calculated with the dynamic coefficients of the oil film. The results obtained showed that when the texture region starts from 270° from the top of the bearing in the rotating direction, the stability threshold speeds are higher than those of the fully textured bearing at relatively high Sommerfeld number. From these results, it was concluded that an appropriate partial texturing formed on the bearing surface can improve both the load carrying capacity and the stability characteristics simultaneously.

Hiroo Taura

Optimized Tribo-Design of Lubricants for Power Loss Reduction in Journal Bearings Used in Process Industry

The aim of the paper is to optimize the tribological characteristics of lubricating oils that are used in the process industry during machining. In several cases, the machines employed are organized in several “stands” forming “lines” and are equipped by several spindles supported by journal bearings, fed by the same oil. Typically, the spindles supported by the bearings rotate at increasing speeds from the feeding of the blank material to the outlet of the machined one. The power loss on the single spindle is different from the others, not only for the different rotational speed, but also because the oil with which the single bearing is fed has different temperature and, thus, different viscosity. At present, standard mineral oils for typical use are employed. Owing to the large power loss in these kinds of plants, an attractive idea for power saving is, therefore, to formulate a lubricating oil which, globally, along the entire line, has the best rheological characteristics depending on the actual rotational speed of all spindles. In this paper, the modelling of the line is presented, by using a TEHD (thermo-elasto-hydro-dynamic) model for the calculation of the power dissipated in each journal bearing and the lubricating oil characteristics are defined by means of a multivariate optimization on the parameters of viscosity, temperature and thickness of the oil film. Finally, the optimized dynamic viscosity curve is obtained and can be used for the formulation of an oil, not necessary of mineral origin, with suitable additives.

Steven Chatterton, Paolo Pennacchi, Andrea Vania

Numerical Modeling of Spiral Vibrations Caused by the Presence of Brush Seals

Clearance is of paramount importance for turbomachinery manufacturers to meet today’s aggressive power output, efficiency, and operational life goals. To minimize leakages, there are various seal types used, and new sealing concepts are in development. Because of their inherent flexibility and compliance, brush seals are capable of significantly reducing the leakage, and allow sufficient geometrical margins to accommodate design and operational variations of turbomachines. Brush seals can be assembled at very tight or zero radial clearance or even with interference on the rotor to minimize the leakage. This means that the risk of contact between the rotor and the seal bristles exists, especially in case of zero clearance or interference. If the contact occurs, a hot-spot develops on the rotor and this may cause the vibration to diverge, resulting in a synchronous instability, the so-called Newkirk effect. The objective of this paper is the development of a numerical model to analyze the dynamic behavior of real turbomachines subject to thermally-induced vibration caused by light-rub of the rotor against brush seals. The model developed in the paper is based on the work of Bachschmid et al. [1]: the dynamics is analyzed in the frequency domain using the standard rotordynamic model, whereas the heat transfer analysis, to calculate the temperature distribution and the associated thermal bow, is studied in the time domain. The contact analysis has been deeply revised, aiming at estimating suitable normal and tangential force and the friction heating generated by the contact.

Paolo Pennacchi, Filippo Cangioli, Andrea Vania, Steven Chatterton

Development and Validation of a Bulk-Flow Model for Staggered Labyrinth Seals

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists in reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements.Eventually, the experimental data are compared to numerical results obtained with the new bulk-flow model (BFM) introduced in this paper.

Filippo Cangioli, Giuseppe Vannini, Paolo Pennacchi, Lorenzo Ciuchicchi, Leonardo Nettis, Steven Chatterton, Andrea Vania

Effects of Severe Operating Conditions (High Loads/Low Rotational Speeds) on Sleeve Journal Bearings

Journal bearings are often employed in rotating machines and several papers deal with their modelling and design. On the contrary, experimental tests are seldom presented, in particular when the bearings are used in severe operating conditions, i.e. with very high values of specific pressure and very low rotational speeds. This paper presents an experimental investigation about the influence of the applied static load on the behavior of a cylindrical journal bearing with two axial grooves. The profiles of the pressure and the oil-film thickness during the shaft rotation have been measured by one pressure probe and one proximity probe installed in the rotating shaft. Measurements of the shaft center position, dynamic coefficients, hydrodynamic pressure, temperature distributions on the bearing, oil-film thickness, and bearing profile deformation under several operating conditions are presented and discussed.

Paolo Pennacchi, Steven Chatterton, Andrea Vania

Investigation of Cooled Pads for Tilting-Pad Bearings

Several rotating machines are nowadays equipped with both thrust and journal tilting-pad bearings. The maximum temperature in the pads is critical for applications running at high speeds and loads, where significant temperatures can originate, due to shear stresses in the oil-film or by the surroundings. In these cases, the minimum oil-film thickness and the pad thermal crowning must be considered. Leading edge groove bearings can partially solve the problem by controlling the oil inlet temperature in the shoes. Other attempts to reduce the bearing temperature can be found in several industrial bearings and are mainly focused on the nozzles of the oil inlet. Another approach for the reduction of the heat generated in the lubricant fluid, is based on the use of suitable cooling circuits inside the pads, where the pads are cooled by an external cooling fluid. This method can be applied both to the pads of tilting-pad thrust bearings (axial load) and tilting-pad journal bearings (radial load). The cooling circuit among consecutive pads of the bearing can be also optimized considering for the temperature distribution in the bearing. Furthermore, the same oil used for the lubrication process can be used as cooling fluid. Because rotating machines are already equipped with an external cooling system for the lubricant fluid, negligible modifications in the machine layout can be required for the installation of this kind of pads, if the same lubricating oil is used as cooling fluid. Conversely, a more suitable and efficient cooling fluid can be adopted. The manufacturing issues of the cooling channels inside the pad, can be solved with the additive manufacturing technology. In the paper, the results of numerical simulations for a cooled pad bearing will be described. Several paths and cross sections of the cooling circuit will be investigated by means of computational fluid dynamics (CFD) simulation allowing the maximum temperature reduction to be obtained.

Steven Chatterton, Paolo Pennacchi, Andrea Vania

Vibration Control of a Gas Turbine-Generator Rotor in a Combined Cycle System by Means of Active Magnetic Bearings

It is well known that many lateral vibration problems occur in rotating machinery systems, for which nowadays in most cases passive measures are used to mitigate these vibrations. With the requirements for more powerful, efficient and secure rotating machinery with high availability the demand for more efficient vibration reduction measures increases. Active magnetic bearings (AMB) can be used as a possible solution, since it generates magnetic fields and forces to control the rotor vibrations, without rotor-bearing contact. AMBs are often used in special applications, for example in high-speed/high-performance turbomachinery like turbo-compressors for the oil and gas industry or in machine tool applications. The main problems of implementing active vibration control by means of AMBs are the energy transfer towards the rotating system, best suited concepts to control the lateral vibrations and the design of reliable backup bearings for special applications. One of the most common causes of high vibration amplitudes is the unbalance of a rotor, which leads to 1xN vibrations. In this work it will be shown, how these unbalance vibrations can be best controlled by an AMB. This paper consists of a purely numerical analysis for a combined cycle turbine, in which two separated cases are studied: 1. the complete analysis of the operational setup, where the turbine is supported with radial oil-film bearings (RFBs) only, and 2. The oil-film bearing in the gas turbine side, where the vibration amplitudes are higher due to the unbalance generated by the fluid flow, is replaced by one AMB.

Rafael Pilotto, Rainer Nordmann
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