Design Methods of Friction Damping at Blade-Disk Joints

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

Effect of Scaling of Blade Row Sectors on the Prediction of Aerodynamic Forcing in a Highly-Loaded Transonic Compressor Stage

An investigation of the sensitivity of a geometrical scaling technique on the blade forcing prediction and mode excitability has been performed. A stage of a transonic compressor is employed as test object. A scaling ratio is defined which indicates the amount of scaling from the original geometry. Different scaling ratios are selected and 3D Navier Stokes unsteady calculations completed for each scaled configuration. A full annulus calculation (non-scaled) is performed serving as reference. The quantity of interest is the generalized force, which gives a direct indication of the mode excitability. In order to capture both up- and downstream excitation effects the mode excitability has been assessed on both rotor and stator blades. The results show that first harmonic excitation can be predicted well for both up- and downstream excitation using moderate amount of scaling. On the other hand, the predictions of second harmonic quantities do show a higher sensitivity to scaling for the investigated test case.

Blade Forcing Function and Aerodynamic Work Measurements in a High Speed Centrifugal Compressor With Inlet Distortion

Centrifugal compressors operating at varying rotational speeds, such as in helicopters or turbochargers, can experience forced response failure modes. The response of the compressors can be triggered by aerodynamic flow non-uniformities, such as with diffuser-impeller interaction or with inlet distortions. The work presented here addresses experimental investigations of forced response in centrifugal compressors with inlet distortions. This research is part of an ongoing effort to develop related experimental techniques and to provide data for validation of computational tools. In this work measurements of blade surface pressure and aerodynamic work distribution were addressed. A series of pressure sensors were designed and installed on rotating impeller blades and simultaneous measurements with blade-mounted strain gauges were performed under engine representative conditions. To the best knowledge of the authors, this is the first publication which presents comprehensive experimental unsteady pressure measurements during forced response for highspeed radial compressors. Experimental data were obtained for both resonance and off-resonance conditions with uniquely tailored inlet distortion. This paper covers aspects relating to the design of fast response pressure sensors and their installation on thin impeller blades. Additionally, sensor properties are outlined with a focus on calibration and measurement uncertainty estimations. The second part of this paper presents unsteady pressure results taken for a number of inlet distortion cases. It will be shown that the intended excitation order due to inlet flow distortion is of comparable magnitude to the second and third harmonics which are consistently observed in all measurements. Finally, an experimental method will be outlined that enables the measurement aerodynamic work on the blade surface during resonant crossing. This approach quantifies the energy exchange between the blade and the flow in terms of cyclic work along the blade surface. The phase angle between the unsteady pressure and the blade movement will be shown to determine the direction of energy transfer between the blade and the fluid.

An Empirical Method for Dynamic Stress Prediction in Turbomachinery

The effectiveness of fatigue and life prediction methods depends heavily on accurate knowledge of the static and dynamic stresses acting on a structure. Although stress fields may be calculated from the finite element shape functions if a finite element model is constructed and analyzed, in many cases the cost of constructing and analyzing a finite element model is prohibitive. Modeling errors can severely affect the accuracy of stress simulations. This paper presents an empirical method for predicting a transient dynamic stress response of a structure based on measured load and strain data that can be collected during vibration tests. The method applies the proper orthogonal decomposition to a measured data set to filter noise and reduce the size of the identification problem and then employs a matrix deconvolution technique to decouple and identify the reduced coordinate impulse response functions for the structure. The method is applied to simulation data from an axial compressor blade model and produces accurate stress predictions compared to finite element results.

The Use of Strain Energy and Fracture Correlation to Determine Life Expectancy for Notched Components

An energy-based method for predicting fatigue life of half-circle notched specimens, based on the nominal applied stress amplitude, has been developed. This developed method is based on the understanding that the total strain energy dissipated during a monotonic fracture and a cyclic process is the same material property, where the density of each can be determined by measuring the area underneath the monotonic true stress-strain curve and measuring the sum of the area within each Hysteresis loop in the cyclic process, respectively. Using this understanding, the criterion for determining fatigue life prediction of half-circle notched components is constructed by incorporating the stress gradient effect through the notch root cross-section. Though fatigue at a notch root is a local phenomenon, evaluation of the stress gradient through the notch root cross-section is essential for incorporating this method into finite element analysis minimum potential energy process. The validation of this method was carried out by comparison with both notched and unnnotched experimental fatigue life of Aluminum 6061-T6 (Al 6061-T6) specimens under tension/compression loading at the theoretical notch fatigue stress concentration factor of 1.75. The comparison initially showed a slight deviation between prediction and experimental results. This led to the analysis of strain energy density per cycle up to failure, and an improved Hysteresis representation for the energy-based prediction analysis. With the newly developed Hysteresis representation, the energy-based prediction comparison shows encouraging agreement with unnotched experimental results and a theoretical notch stress concentration value.

Experimental and Analytical Studies on Flexure Pivot Tilting Pad Gas Bearings With Dampers Applied to Radially Compliant Pads

Hydrodynamic flexure pivot tilting pad gas bearings (FPTPGBs) can enable successful operation of oil-free microturbomachinery, and FPTPGBs with radially compliant pads (FPTPGB-Cs) permit rotor centrifugal and/or thermal growth to exceed original bearing clearances and achieve higher speeds. This work presents the experimental and analytical study of such bearings and the application of dampers behind the pad radial compliance structure. A time domain orbit simulation method was implemented as the primary analysis tool to predict rotor-bearing response to imbalance, the presence and location of critical speeds, etc., and compare with test results. Experiments demonstrate the stable hydrodynamic operation of FPTPGBs with a ∼28.6 mm, 0.8 kg rotor above 120 krpm for the first time. The rotor-bearing system was intentionally destabilized in tests by increasing bearing clearances, and viscoelastic dampers added behind the FPTPGB pads delayed the onset of subsynchronous vibrations (from 43 krpm without damper to above 50 krpm with damper). Midrange subsynchronous vibrations of the destabilized system initiated at ∼20 krpm were suppressed by ∼25 krpm due to the stabilizing effect of rotor centrifugal growth. The viscoelastic dampers had a negligible effect on suppressing these midrange subsynchronous vibrations in experiments, but this was not demonstrated in simulations, presumed to be due to much lower stiffness contribution of the damper at lower frequencies.

Study on Probabilistic Model of GH4133B for Fatigue-Creep Failure

GH4133B is a nickel-base superalloy which was developed for use in the manufacture of aero-engine turbine disks and other high-temperature components. Since these components are operated at high temperature and under cyclic loading, damage resulting from fatigue-creep interaction is the main factor. The situation is often simulated in laboratories at high temperature low-cycle fatigue. The interactive effect between different loading levels should be considered. The fatigue-creep experiments for alloy GH4133B at 600 Celsius degree have been carried out at continuous cyclic creep (CF) loading to investigate the interaction of creep damage and fatigue damage. Fracture surfaces are examined under the scanning electron microscope (SEM). Then a nonlinear fatigue-creep failure criterion function proposed by Hongyin Mao is employed to fit the experimental data. The probabilistic model of GH4133B under CF loading is established based on the deterministic failure function. Firstly, the random variables influencing the fatigue-creep life and values of the distribution parameters are investigated. Then fatigue-creep damage interaction is discussed and a linear damage accumulation rule is considered, according to which the limit state function used to express the probability of failure is proposed. Lastly, reliability analysis under fatigue-creep failure is proceeded by applying analytical and simulation methods. Furthermore, the random variable with low sensitivity index through the sensitivity analysis can be treated as deterministic parameter during the reliability analysis and reliability design in order to improve the computing efficiency.

Turbocharger Dynamic Analysis Using First Order System Step Response

This work presents the dynamic modeling of an automotive turbocharger in a hot gas test stand. The objective is to develop a methodology to determine the main turbocharger dynamic properties as moment of inertia, response time, static gain constant, frequency gain amplitude and phase shift. The turbocharger used is the Master Power APL-240 set. The moment of inertia is obtained through the deceleration curve from an instantaneous fuel cut-off in the combustion chamber. The response time and static gain constant, as well the frequency gain amplitude and phase shift curves in function of a signal frequency, are obtained through a step variation. The turbocharger is modeled as a first order system. It is also presented a turbocharger sine excitation by the combustion chamber, generating a rotational speed sine signal output that simulates an engine intermittent acceleration. The rotational speed signal frequency gain and phase shift are compared to the values obtained in the step curves. The rotational speed frequency gain amplitude and phase shift modeled through the step test presents deviation of 16% and 13%, respectively, from the values from sine test.

The Whole-Engine Model for Clearance Evaluation

The evaluation of the blading clearance at the design stage is important for heavy duty gas turbine efficiency. The minimum clearance value at base load is limited by the pinch point clearance during startup and/or shutdown. Therefore, transient analysis is necessary for different operating conditions. 3D transient analysis of a whole engine is labor-intensive; however 2D axisymmetric analysis does not allow consideration of different 3D effects (e.g. twisting, bending, ovality, rotor alignment). In order to overcome these cost and time limitations, the combination of 2D, axisymmetric, whole-engine model results and the scaled deflections caused by different 3D effects is used for the axial and radial clearance engineering assessment during engine operation. The basic rotor and stator closures are taken from the transient analysis using a 2D finite element (FE) model composed of axisymmetric solid and plane stress elements. To take into account 3D effects of airfoil twisting and bending, the 3D FE displacements of the blade are included in the clearance evaluation process. The relative displacements of airfoil tip and reference point at the blade or vane hub are taken from 3D steady-state FE analyses. Then the steady-state displacements of the airfoils are scaled for transient conditions using the proposed technique. Different 3D rotor / stator effects (cold-build clearances and their tolerances, rotor position with respect to stator after assembly, casing bending, deformations of compressor and turbine vane carrier inducing of casing ovalization, exhaust gas housing movements, movements of the rotor in bearings and CVC and TVC support, etc.) are also included as a contributor to the clearances. The results of the calculations are analyzed and compared with good agreements to the clearances measured in engine testing under real operation conditions. The proposed methodology allows assessing the operating clearances between the stator and rotor during the design phase. Optimization of the running clearance is one key measure to upgrade and improve the engine performance during operating experience.

The Method of Accounting for Loading Cycle Asymmetry in Cyclic Durability Analysis

The proposed method has been demonstrated on the universal slopes equation (Manson 1965) and the modified universal slopes equation (Muralidharan & Manson 1998). New equations take into account independence of the transient strain range from the cycle average stress, define more precisely the impact of the cycle average stress upon the durability, take into account the impact of cycle average strain plastic constituent upon the durability. The resulted equations have been validated with finite element analyses of non-notched samples and full-scale parts, for which the results of cyclic tests in the conditions of asymmetric loading are available. The analyses have been performed employing an elastic-plastic approach using cyclic strain curves taken from original durability equations. The use of new equations ensured a good match between design and experimental durability values. Also, the new equations were used to plot Smith, Hay and Wo¨hler diagrams for low, mean and high durability. The resulted analytical diagrams represent a high quality illustration of the experimental diagrams found in the publications. The presented approach to the accounting for cycle average stress and strain will also apply when using experimental cyclic durability curves specific for the material.