George Y. Baaklini

Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks

The coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigenfrequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks.Copyright

NDE using sensor based approach to propulsion health monitoring of a turbine engine disk

Rotor health monitoring and on-line damage detection have been increasingly gaining interest to manufacturers of aircraft engines, primarily to increase safety of operation and lower the high maintenance costs. But health monitoring in the presence of scatter in the loading conditions, crack size, disk geometry, and material property is rather challenging. However, detection factors that cause fractures and hidden internal cracks can be implemented via noninvasive types of health monitoring and or nondestructive evaluation techniques. These evaluations go further to inspect materials discontinuities and other anomalies that have grown to become critical defects that can lead to failure. To address the bulk of these concerning issues and understand the technical aspects leading to these outcomes, a combined analytical and experimental study is being thought. Results produced from the experiments such as blade tip displacement and other data collected from tests conducted at the NASA Glenn Research Centers Rotordynamics Laboratory, a high precision spin rig, are evaluated, discussed and compared with data predicted from finite element analysis simulating the engine rotor disk spinning at various rotational speeds. Further computations using the progressive failure analysis (PFA) approach with GENOA code [6] to additionally assess the structural response, damage initiation, propagation, and failure criterion are also performed. This study presents an inclusive evaluation of an on-line health monitoring of a rotating disk and an examination for the capability of the in-house spin system in support of ongoing research under the NASA Integrated Vehicle Health Management (IVHM) program.

Quantifying residual stresses by means of thermoelastic stress analysis

This study focused on the application of the Thermoelastic Stress Analysis (TSA) technique as a tool for assessing the residual stress state of structures. TSA is based on the fact that materials experience small temperature changes when compressed or expanded. When a structure is cyclically loaded, a surface temperature profile results which correlates to the surface stresses. The cyclic surface temperature is measured with an infrared camera. Traditionally, the amplitude of a TSA signal was theoretically defined to be linearly dependent on the cyclic stress amplitude. Recent studies have established that the temperature response is also dependent on the cyclic mean stress (i.e., the static stress state of the structure). In a previous study by the authors, it was shown that mean stresses significantly influenced the TSA results for titanium and nickel based alloys. This study continued the effort of accurate direct measurements of the mean stress effect by implementing newly developed temperature correction curves. In addition, a more in-depth analysis was conducted which involved analyzing the second harmonic of the temperature response. By obtaining the amplitudes of the first and second harmonics, the stress amplitude and the mean stress at a given point on a structure subjected to a cyclic load can be simultaneously obtained. The experimental results showed good agreement with the theoretical predictions for both the first and second harmonics of the temperature response. As a result, confidence was achieved concerning the ability to simultaneously obtain values for the static stress state as well as the cyclic stress amplitude of structures subjected to cyclic loads using the TSA technique. With continued research, it is now feasible to establish a protocol that would enable the monitoring of residual stresses in structures utilizing the TSA technique.

Challenges in Integrating Nondestructive Evaluation and Finite Element Methods for Realistic Structural Analysis

Capabilities and expertise related to the development of links between nondestructive evaluation (NDE) and finite element analysis (FEA) at Glenn Research Center (GRC) are demonstrated. Current tools to analyze data produced by computed tomography (CT) scans are exercised to help assess the damage state in high temperature structural composite materials. A utility translator was written to convert velocity (an image processing software) STL data file to a suitable CAD-FEA type file. Finite element analyses are carried out with MARC, a commercial nonlinear finite element code, and the analytical results are discussed. Modeling was established by building MSC/Patran (a pre and post processing finite element package) generated model and comparing it to a model generated by Velocity2 in conjunction with MSC/Patran Graphics. Modeling issues and results are discussed in this paper. The entire process that outlines the tie between the data extracted via NDE and the finite element modeling and analysis is fully described.

Thermoelastic Stress Analysis: The Mean Stress Effect in Metallic Alloys

The primary objective of this study involved the utilization of the thermoelastic stress analysis (TSA) method to demonstrate the mean stress dependence of the thermoelastic constant. Titanium and nickel base alloys, commonly employed in aerospace gas turbines, were the materials of interest. The repeatability of the results was studied through a statistical analysis of the data. Although the mean stress dependence was well established, the ability to confidently quantify it was diminished by the experimental variations. If calibration of the thermoelastic response to mean stress can be successfully implemented, it is feasible to use the relationship to determine a structure residual stress state.

NDE Methodologies for Composite Flywheels Certification

Manufacturing readiness of composite rotors and certification of flywheels depend in part on the maturity of nondestructive evaluation (NDE) technology for process optimization and quality assurance, respectively. Capabilities and limitations of x-ray-computed tomography and radiography, as well as advanced ultrasonics were established on NDE ring and rotor standards with EDM notches and drilled holes. Also, intentionally seeded delamination, tow break, and insert of bagging material were introduced in hydroburst-rings to study the NDE detection capabilities of such anomalies and their effect on the damage tolerance and safe life margins of subscale rings and rotors. Examples of possible occurring flaws or anomalies in composite rings as detected by NDE and validated by destructive metallography are shown. The general NDE approach to ensure quality of composite rotors and to help in the certification of flywheels is briefly outlined.

Application of Nonlinear Dynamics Tools for Diagnosis of Cracked Rotor Vibration Signatures

The nonlinear model of the cracked Jeffcott rotor is investigated, with the particular focus on study of rotors vibrational response using tools of nonlinear dynamics. The considered model accounts for nonlinear behavior of the crack and coupling between lateral and torsional modes of vibrations. Load torque is applied to the rotor which is laterally loaded with a constant radial force (gravity force) and unbalance excitation. The co-existence of frequencies of lateral modes in the frequency spectra of torsional mode are characteristics of the coupling response of lateral and torsional vibrations. When only the lateral excitations are applied, vibration amplitude bifurcation plot with the shaft speed as a control parameter, demonstrates some speed ranges for which vibrations of the rotor dramatically increase. Furthermore, the torsional response amplitude at the same speed ranges also increases and chaotic behavior can be observed due to the lateral excitations. These phenomena cannot be observed for pure lateral vibration response with the torsionally rigid rotor assumption.

Analysis of Transient Response of Cracked Flexible Rotor

The transient vibration response of a cracked flexible rotor passing through its critical speed is analyzed for crack detection and monitoring. The effects of different factors such as various crack depths, acceleration, damping, torque, unbalance eccentricity, and rotor weight on the rotor vibrational response are studied. The breathing types of cracks are analyzed using simple hinge model in a case of shallow cracks, and the cosine function is employed in the case of deep cracks. The developed strategy enables the analysis of cracked rotor vibrational response with and without weight dominance, taking into account also the nonsynchronous rotor whirl. In addition, the local cross-flexibility for deep cracks is taken into account. Lastly, the effect of the crack depth on “stalling” of the rotor due to the limited driving torque is investigated.

Coupled Lateral and Torsional Vibrations of a Cracked Rotor

Rotor crack problems present a significant safety and loss hazard in nearly every application of modern turbomachinery, particularly in the power generation industry. However, early crack detection is not easily achieved during the operation of machinery. The difficulty is based on the fact that a crack produces an undetectable change in the overall structural response. This paper analyzes the coupling of torsional and lateral vibrations for an unbalanced cracked rotor. The rotor equations of motion for a system with cracked shaft, obtained using Lagrangian dynamics, show coupling and nonlinear interaction between the torsional and lateral vibrations. To investigate the effect of a transverse surface crack on the dynamic rotor response the breathing crack model was employed. By applying an external torsional excitation together with the excitation due to unbalance, signature responses were observed in the rotor vibration spectrum at sum and difference frequencies. These signature responses were due to the nonlinear effect of the crack. The observed phenomena, analytically defined here, offers a new methodology concerning crack detection and prognosis in rotors.Copyright

Nondestructive evaluation of ceramic matrix composites coupled with finite element analyses

Ceramic matrix composites (CMC) are engineered materials filled with manufacturing anomalies, such as voids, delamination, or fiber cracking. In this paper a non- destructive evaluation (NDE) of a CMC tensile specimen is coupled with a finite element analysis to locate the failure location prior to the actual testing. The tensile CMC specimen is scanned with computed tomography (CT) along various planes. The majority of the observed anomalies are porosities in the matrix. The CT images are then used to reconstruct a 3-D volume of the specimens gage section using velocity2 (an image processing software). Subsequently, a three dimensional finite element analysis (FEA) is carried out to include the scanned porosities. The stress variations along the scanned CT planes are determined, comparison of the FEA results with those extracted via NDS, and the test data are reported.