Romuald Rzadkowski

Structural Properties of Foil Bearings: A Closed-Form Solution Validated with Finite Element Analysis

Fluid film thickness in a compliant foil bearing is greatly influenced by the deflection of the bearing structure. Therefore, in order to properly model performance of a foil bearing, it is mandatory that the deflection of the compliant bearing structure due to the generated hydrodynamic pressure is determined accurately. This article proposes an easy-to-use two-dimensional model, which takes into account detailed geometry of the bump foil-top foil assembly and the interaction between bumps and which can predict the bearing deflection and stresses due to an arbitrary pressure load. The proposed model is first validated using a finite element analysis and the results available in the literature and then used to conduct a parametric study investigating the influence of bump foil geometry, the coefficient of friction between the bearing components, and the type of loading on the structural properties of the bearing. The most important parameters are also identified. The proposed analytical model is completely algebraic and can be easily implemented using any programming language, a spreadsheet, or even a calculator. The resulting solution can also be coupled with the appropriate hydrodynamic model to predict static performance of compliant foil bearings.

Unsteady Load of Partial Admission Control Stage Rotor of a Large Power Steam Turbine

Partial admission flow in the control stage of a 200MW steam turbine is investigated with the help of a RANS solver with k-ω SST turbulence model in the code Fluent. A 2D model of flow at the mid-span section of the full annulus is assumed. The results exhibit interesting details of the process of expansion in the control stage. Unsteady forces acting on the single rotor blades of the control stage are calculated, and are subject to Fourier analysis. Single blade forces are summed up to obtain the unsteady load at the rotor (forces acting at the rotor disc are neglected due to the assumed 2D model). The calculations take into account pressure pulsations at the entry to the nozzle boxes and rotor blade mistuning / geometrical imperfections.Copyright

3D Unsteady Forces of the Transonic Flow Through a Turbine Stage With Vibrating Blades

Numerical calculations of the 3D transonic flow of an ideal gas through turbomachinery blade rows moving relatively one to another with taking into account the blades oscillations is presented. The approach is based on the solution of the coupled aerodynamicstructure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem, as the blades oscillations and loads, acting on the blades, are a part of solution. An ideal gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite-volume difference scheme of GodunovKolgan and moving hybrid H-H grid. The structure analysis uses the modal approach and 3D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations with the modal coefficients depending on time. The algorithm proposed allows to calculate turbine stages with an arbitrary pitch ratio of stator and rotor blades, taking into account the blade oscillations by action of unsteady loads caused both outer flow nonuniformity and blades motion. There has been performed the calculation for the stage of the turbine with rotor blades of 0.765 m. The numerical results for unsteady aerodynamic forces due to stator-rotor interaction are compared with results obtained with taking into account the blades oscillations. NOMENCLATURE IBPA interblade phase angle [deg.],

Analysis of Middle Bearing Failure in Rotor Jet Engine Using Tip-Timing and Tip-Clearance Technique

The reported problem is the failure of the middle bearing in an aircraft rotor engine. Tip-timing and tip-clearance and variance analyses are carried out on a compressor rotor blade in the seventh stage above the middle bearing. The experimental analyses concern both an aircraft engine with a middle bearing in good working order and an engine with a damaged middle bearing. A numerical analysis of the seventh stage blade free vibration are conducted to explain the experimental results. This appears to be an effective method of predicting middle bearing failure. The blade vibration variance increases when there is bearing failure.© 2014 ASME

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1 — Free Vibration Analysis

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.© 2012 ASME

Multistage Coupling of Mistuned Aircraft Engine Bladed Discs in a Forced Vibration Analysis

Considered here is the effect of multistage coupling on the dynamics of an aircraft engine rotor with eight mistuned bladed discs on a drum-disc shaft. Each disc had a different number of rotor blades. Free and forced vibrations were examined using finite element models of single rotating blades, bladed discs, and an entire rotor. Calculations of the global rotating mode shapes of flexible mistuned bladed discs-shaft assemblies took into account the excitation of the turbine bladed disc with 0EO, 1EO and 2EO forces. The thus obtained maximal stress values of all of the rotor blades were carefully examined and compared with a tuned system to discover resonance conditions and coupling effects. Mistuning changes the stress distribution in individual rotor blades and the level of maximum stress increases or decreases as compared to bladed discs which are analyzed without the shaft.Copyright

Forced Vibration of Eight Mistuned Bladed Disks on a Solid Shaft—Excitation of the First Compressor Bladed Disc

Considered here is the effect of multistage coupling on the dynamics of an aircraft engine rotor with eight mistuned bladed discs on a drum-disc shaft. Each disc had a different number of rotor blades. Free and forced vibrations were examined using finite element models of single rotating blades, bladed discs, and an entire rotor. Calculations of the global rotating mode shapes of flexible mistuned bladed discs-shaft assemblies took into account the excitation of the first compressor bladed disc with 0EO, 1EO and 2EO forces. The obtained maximal stress values of all of the rotor blades were carefully examined and compared with a tuned system to discover resonance conditions and coupling effects. Mistuning changes the stress distribution in individual rotor blades and the level of maximum stress increases or decreases as compared to bladed discs which are analyzed without the shaft.

A higher-order linear theory for isotropic plates. II: Numerical realization

Abstract The paper presents a numerical technique for a higher-order linear theory for isotropic plates [see Blocki (1992), Int. J. Solids Structures29(7), 825–836], whereby the natural frequencies of free vibration of a circular “moderately” thick disc of varying thickness profile may be determined when the disc is subjected to the centrifugal loading. The in-plane stress level, arising from rotational eflects, is determined by means of a spline interpolation technique. The results of the analysis are compared with the other numerical solutions for thin and moderately thick circular plates.

Numerical Analysis of the Three-Dimensional Nonstationary Flow of Ideal Gas in the Last Stage of Turbine Machine Taking into Consideration the Nonaxisymmetric Exhaust Pipe Branch

A problem related to the forecast of the aeroelastic behavior and aeroelastic instability of blades (in particular self-oscillations, flutter, and resonance vibrations) becomes of great importance for the development of high-loaded compressor and vent rows and the last turbine stages whose long and flexible blades can be exposed to such phenomena. The solution of this problem requires the development of new models for the nonstationary three-dimensional flow, the use of contemporary numeric methods and the comparison of theoretical and experimental data. This scientific paper gives the data of numerical simulation of the 3-D flow of ideal gas passing through the last stage of turbine machine taking into account the flow nonuniformity caused by guide blades and nonuniform pressure distribution in the exhaust pipe branch and also nonstationary effects caused by blade vibrations. The numerical method is based on the solution of combined aeroelastic problem for the 3-D flow of ideal gas passing through the turbine stage and the nonaxisymmetric exhaust pipe branch including the annular diffuser. To solve the combined problem a partially integral method was used that includes integral equations of gas dynamics (Euler equations) and vibrating blade dynamics (modular approach) at each time step with the information exchange. The given method of the solution of combined aeroelastic problem allows us to predict the amplitude-frequency spectrum of blade vibrations in the three-dimensional flow of ideal gas including forced self-excited vibrations and self-vibrations to increase efficiency and reliability of the blade units of turbine machines.

Steam turbine stress control using NARX neural network

Abstract Considered here is concept of steam turbine stress control, which is based on Nonlinear AutoRegressive neural networks with eXogenous inputs. Using NARX neural networks,whichwere trained based on experimentally validated FE model allows to control stresses in protected thickwalled steam turbine element with FE model quality. Additionally NARX neural network, which were trained base on FE model, includes: nonlinearity of steam expansion in turbine steam path during transients, nonlinearity of heat exchange inside the turbine during transients and nonlinearity of material properties during transients. In this article NARX neural networks stress controls is shown as an example of HP rotor of 18K390 turbine. HP part thermodynamic model as well as heat exchange model in vicinity of HP rotor,whichwere used in FE model of the HP rotor and the HP rotor FE model itself were validated based on experimental data for real turbine transient events. In such a way it is ensured that NARX neural network behave as real HP rotor during steam turbine transient events.