Probabilistic Lifetime Analysis for Turbine Blades Based on a Combined Direct Monte Carlo and Response Surface Approach

The paper addresses a probabilistic approach to lifetime prediction of cooled gas turbine blades. Variations of load and material parameters are taken into account by a combination of a direct Monte Carlo Simulation and a Response Surface Method. The proposed approach allows a reduction in the number of finite element analyses especially for problems with low failure probability. Therefore, the computational effort becomes acceptable even for full-scale 3D and 2D analysis models. Results of a probabilistic life assessment are shown for two cooled turbine blades. The probability of failure and the sensitivity of material and loading parameters are presented.

Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk

This paper deals with the characterization of the blade manufacturing geometric tolerances in order to get a given level of amplification in the forced response of a mistuned bladed-disk. It is devoted to an industrial application in order to validate the theory previously developed [1] and in order to show that this theory is suited to any industrial bladed-disks. It should be noted that the development of an adapted methodology for solving the inverse problem, in order to characterize the manufacturing tolerances, is an important challenge for industries in this area. Let us recall that this theory is based on the use of a nonparametric probabilistic model of random uncertainties in the blade [2]. The dispersion parameters controlling the nonparametric model are estimated as a function of the geometric tolerances. Such an identification is carried out in a computational context by using the numerical Monte Carlo simulation and by using the reduced model method presented in [3]. The industrial application is devoted to the mistuning analysis of a 22 blades wide chord fan stage. Centrifugal stiffening due to rotational effects is also included. The results obtained validate the efficiency and the reliability of the method on three dimensional bladed disks.

High Speed, High Temperature, Fault Tolerant Operation of a Combination Magnetic-Hydrostatic Bearing Rotor Support System for Turbomachinery

Closed loop operation of a single, high temperature magnetic radial bearing to 30,000 RPM (2.25 million DN) and 540°C (1,000°F) is discussed. Also, high temperature, fault tolerant operation for the three axis system is examined. A novel, hydrostatic backup bearing system was employed to attain high speed, high temperature, lubrication free support of the entire rotor system. The hydrostatic bearings were made of a high lubricity material and acted as journal-type backup bearings. New, high temperature displacement sensors were successfully employed to monitor shaft position throughout the entire temperature range and are described in this paper. Control of the system was accomplished through a stand alone, high speed computer controller and it was used to run both the fault-tolerant PID and active vibration control algorithms.

Uncertainty Evaluation for Structural Damage Parameters Prediction Methodology

Structural component life estimated from damage tracking parameters in real-time are a subject of recent studies. The proposed project consists of determining parametric equations for the structural damage variables, metal temperature and stress, as a function of design performance parameters, exercising these equations through material property algorithms generated as a function of material characterization, and evaluating the uncertainty of the damage accumulated from a simulated military mission. Thermal and structural finite element results obtained during the component design phase were used as the dependent response for the stress and metal temperature equations. The independent variables used in the statistical linear regression analysis were mission performance parameters. A time function was implemented to account for the response time characteristic of the component metal temperature during transient conditions. The material property algorithm combined critical metal temperatures and stresses with probabilistic material capability generated from stochastic material characterization. Validation of the methodology was accomplished by the statistical analysis performed between predicted results and expected values from the design analysis. Uncertainty analysis established the confidence bound about the predicted result.

Modelling a New Three-Pad Active Bearing

This paper describes investigations into a new type of active bearing to be implemented in the field of rotating machinery. Active bearings are based on the concept that journal oil flow can be modified during operation by active devices. Here, the concepts of the flexible pads and the oil-filled chambers that control their deflection are used. Three active pads are positioned around the journal with three oil-filled chambers positioned behind them. One of them, the load-bearing pad located at the bottom of the bearing, acts as a passive device and is equipped with a very thin film chamber, which acts as a source of damping. Such a damper was found in previous work to be effective in dissipating energy. Here, in a departure from previous work, two additional small pads with deep oil-filled chambers have been added in order to allow control theory to be implemented. They are located in the upper part of the active bearing. A non-linear system model is developed for the rotor-bearing system that includes the described active bearing. The flow inside the upper chambers that control motion of the active pads was neglected due to their large volume. It results in a uniform pressure distribution along the upper pads. The pressure distribution within the damper oil film (inside the lower chamber) and the journal oil film was modeled with the aid of the Reynolds equation. They were solved by means of the finite difference method and Gauss-Seidel technique. The same mesh used for solution of the Reynolds equation was used for the division of the flexible pads into the finite elements. The same approach was adopted for the modelling of the dynamic properties of the rotor. The mass and stiffness matrices for the pads and rotor were condensed down to 12 master generalized coordinates using Guyan condensation. The obtained system of matrix equations was converted to a system of first order equations and solved via the Runge-Kutta method. Some results of the numerical testing of the mathematical model developed are provided.

Steady State and Transient Modeling of a Micro-Turbine With Comparison to Operating Engine

Steady state and transient computer models of a micro turbine were produced. The engine under study was a micro-jet engine that when tested at 126,000 RPM provided 95 N thrust. The aero-thermal model uses generic performance maps for the compressor and turbine which were modified, based on operating data, to represent the components in the engine under study. The model also includes the inlet ducting connected to the engine. It simulates engine operation from idle to full power over the expected operating range of ambient temperature, pressure and humidity. A comparison of steady state model results to actual engine operating data is presented over the full range of speeds. The effect of ambient humidity on the engine operating point is examined for a micro-engine, in particular at temperatures above 30° Celsius. The techniques for introducing component faults are given and their effect on the engine operation is presented. The degraded components are the turbine and inlet flow passages. The methods for modeling the transient behavior of the engine are also presented. Results are presented for both acceleration and deceleration of the engine between steady state operating point. These results are also compared to the operating engine.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Discs With Friction Contact Interfaces

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed discs with friction contact interfaces has been developed. The method allows, for the first time, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disc with underplatform dampers and with shroud contacts.

Aerothermodynamics of Micro-Turbomachinery

Engineering foundation for micro-turbomachinery aerothermal design, as an enabling element of the MIT micro-gas turbine technology, is developed. Fundamental differences between conventional, large scale and micro turbomachinery operation are delineated and the implications on design are discussed. These differences are largely a consequence of low operating Reynolds number, hence a relatively higher skin friction and heat transfer rate. While the size of the micro-gas turbine engine is ∼ a few mm, several order of magnitude smaller than conventional gas turbine, the required compressor stage pressure ratio (∼3–4) and impeller tip Mach number (∼1 and greater) are comparable; however, the disparity in the size implies that the operating Reynolds number of the micro-turbomachiery components is correspondingly several order of magnitudes smaller. Thus the design and operating requirements for micro-turbomachinery are distinctly different from those of conventional turbomachinery used for propulsion and power generation. Important distinctions are summarized in the following. 1. The high surface-to-flow rate ratio has the consequence that the flow in micro-compressor flow path can no longer be taken as adiabatic; the performance penalty associated with heat addition to compressor flow path from turbine is a primary performance limiting factor. 2. Endwall torque on the flow can be significant compared to that from the impeller blade surfaces so that direct use of Euler Turbine Equation is no longer appropriate. 3. Losses in turbine nozzle guide vanes (NGVs) can be one order of magnitude higher than those in conventional sized nozzle guide vanes. 4. The high level of kinetic energy in the flow exiting the turbine rotor is a source of performance penalty, largely a consequence of geometrical constraints. It can be inferred from these distinctions that standard preliminary design procedures based on the Euler equation, the adiabatic assumption, the loss correlations for large Reynolds numbers, and the three-dimensional geometry, are inapplicable to micro-turbomachinery. The preliminary design procedure, therefore, must account for these important differences. Characterization of the effects of heat addition on compressor performance, modification of Euler turbine equation for casing torque, characterization of turbine NGV performance and turbine exhaust effects are presented.

Advancements in the Structural Stiffness and Damping of a Large Compliant Foil Journal Bearing: An Experimental Study

This paper presents the results of an experimental investigation into the dynamic structural stiffness and damping characteristics of a 21.6 cm (8.5inch) diameter compliant surface foil journal bearing. The goal of this development was to achieve high levels of damping without the use of oil, as is used in squeeze film dampers, while maintaining a nearly constant dynamic stiffness over a range of frequencies and amplitudes of motion. In the experimental work described herein, a full compliant foil bearing was designed, fabricated and tested. The test facility included a non-rotating journal located inside the bearing. The journal was connected to an electrodynamic shaker so that dynamic forces simulating expected operating conditions could be applied to the structurally compliant bump foil elements. Excitation test frequencies to a maximum of 400 Hz at amplitudes of motion between 25.4μm to 102μm were applied to the damper assembly. During testing, both compressive preload and unidirectional static loads of up to 1335N and 445N, respectively, were applied to the damper assembly. The experimental data from these tests were analyzed using both a single degree of freedom model and an energy method. These methods of data analysis are reviewed here and results are compared. Excellent agreement in results obtained from the two methods was achieved. Equivalent viscous damping coefficients as high as 1050 N.s/cm (600 lbf.s/in) were obtained at low frequencies. Dynamic stiffness was shown to be fairly constant with frequency.

Investigation of Blade and Disc Vibrations on the Upgraded Power Turbine for the THM 1304 Gas Turbine

As part of an ongoing uprating and upgrading program of the THM 1304 gas turbine directed towards increasing power output and efficiency as well as further improving the high level of availability, major design modifications were made on the power turbine (PT). New blades and vanes were designed for increased aerodynamic efficiency, improved high temperature capability, higher power output and higher nominal operating speed. This report presents the analytical and experimental investigations made on the vibration modes and frequencies of blades with pre-loaded interlocking tip shrouds. One focus is upon observed families of mode shapes at different nodal diameters. A comparison of finite-element results with test data shows how good predictions are in the case of coupled blade vibrations. The value of testing the vibration behavior of power turbine blades in the actual machine, over the complete speed range, becomes evident as an important addition to the numerical predictions and laboratory tests. Another focus is on the method of testing, including the telemetry system used and the problem of optimum placement of strain gages on the blades. The selected strain gage positions are crucial to the value and meaningfulness of the test results. The observed strain vibration amplitudes were compared with high-cycle-fatigue (HCF) data available for the blade material. It was shown that measured amplitudes were significantly below allowable levels over the complete range of operating power and speed. The analytical and experimental methods employed to determine blade mode shapes and frequencies for a blade system with pre-loaded tip shrouds are presented in detail.