Charles Cross

The Evaluation of the Damping Characteristics of a Hard Coating on Titanium

Engine failures due to fatigue have cost the Air Force an estimated d400 million dollars per year over the past two decades. Damping treatments capable of reducing the internal stresses of fan and turbine blades to levels where fatigue is less likely to occur have the potential for reducing cost while enhancing reliability. This research evaluates the damping characteristics of magnesium aluminate spinel, MgO+Al2O3, (mag spinel) on titanium plates from an experimental point of view. The material and aspect ratio were chosen to approximate the low aspect ratio blades found in military gas turbine fans. In the past, work has generally been performed on cantilever supported beams, and thus the two-dimensional features of damping were lost. In this study plates were tested with a cantilevered boundary condition, using electrodynamic shaker excitation. The effective test area of each specimen was 4.5 in × 4.5 in. The nominal plate thickness was 0.125 in. Mag spinel was applied to both sides of the plate, at a thickness of 0.01 in, and damping tests were run at room temperature. The effect of the coating was evaluated at the 2nd bending mode (mode 3) and the chord wise bending mode (mode 4). A scanning laser vibrometer revealed the frequency and shape of each mode for the plates. Sine sweeps were used to characterize the damping of the coated and uncoated specimens for the modes tested. The coating increased damping nonlinearly for both modes tested in which the general outcome was similar to that found in beams.

Development of an Improved High Cycle Fatigue Criterion

An integrated computational-experimental approach for prediction of total fatigue life applied to a uniaxial stress state is developed. The approach consists of the following elements: (1) development of a vibration based fatigue testing procedure to achieve low cost bending fatigue experiments and (2) development of a life prediction and estimation implementation scheme for calculating effective fatigue cycles. A series of fully reversed bending fatigue tests were carried out using a vibration-based testing procedure to investigate the effects of bending stress on fatigue limit. The results indicate that the fatigue limit for 6061-T6 aluminum is approximately 20% higher than the respective limit in fully reversed tension-compression (axial). To validate the experimental observations and further evaluate the possibility of prediction of fatigue life, an improved high cycle fatigue criterion has been developed, which allows one to systematically determine the fatigue life based on the amount of energy loss per fatigue cycle. A comparison between the prediction and the experimental results was conducted and shows that the criterion is capable of providing accurate fatigue life prediction.

Goodman Diagram Via Vibration-Based Fatigue Testing

A new vibration-based fatigue testing methodology for assessing high-cycle turbine engine material fatigue strength at various stress ratios is presented. The idea is to accumulate fatigue energy on a base-excited plate specimen at high frequency resonant modes and to complete a fatigue test in a much more efficient way at very low cost. The methodology consists of (1) a geometrical design procedure, incorporating a finite-element model to characterize the shape of the specimen for ensuring the required stress state/ pattern; (2) a vibration feedback empirical procedure for achieving the high-cycle fatigue experiments with variable-amplitude loading; and finally (3) a pre-strain procedure for achieving various uniaxial stress ratios. The performance of the methodology is demonstrated with experimental results for mild steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to a fully reversed bending, uniaxial stress state.

Multi-Axial Fatigue-Life Prediction via a Strain-Energy Method

A strain-energy-based method has been developed to predict the fatigue life of a structure subjected to either shear or biaxial bending loads at various stress ratios. The framework for this method is an advancement of previously conducted research that validates a uniaxial energy-based fatigue-life-prediction approach. The understanding behind the approach states that the total strain energy dissipated during a monotonic fracture and a cyclic process is the same material property, where the experimental strain-energy density of each can be determined by measuring the area underneath the monotonic true stress-strain curve and the area within a hysteresis loop, respectively. The developed framework consists of two elements: a life-prediction method that calculates shear fatigue-life cycles and a multi-axial life-prediction method capable of calculating biaxial fatigue-life cycles. A comparison was made between the two framework elements and experimental results from three different aluminum alloys. The comparison shows encouraging agreement, thus providing credence in the prediction capabilities of the proposed energy-based framework.

A New Multiaxial Fatigue Testing Method for Variable-Amplitude Loading and Stress Ratio

A new vibration-based multiaxial fatigue testing methodology for assessing high-cycle turbine engine material fatigue strength at various stress ratios is presented. The idea is to accumulate fatigue energy on a base-excited plate specimen at high-frequency resonant modes and to complete a fatigue test in a much more efficient way at very low cost. The methodology consists of (1) a topological design procedure, incorporating a finite element model, to characterize the shape of the specimens for ensuring the required stress state/ pattern, (2) a vibration feedback empirical procedure for achieving the high-cycle fatigue experiments with variable-amplitude loading, and finally (3) a yielding procedure for achieving various uniaxial stress ratios. The performance of the methodology is demonstrated by the experimental results from mild steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to fully reversed bending for both uniaxial and biaxial stress states.

Hysteresis-loop representation for strain energy calculation and fatigue assessment

Improvements have been made to the cyclic strain energy density expression used in a fatigue life prediction method. The theory behind the prediction method is based on the understanding that the same amount of strain energy is dissipated during a monotonic fracture and a cyclic fatigue process. From this understanding, the failure cycle for a fatigue process can be determined by dividing monotonic strain energy by the average strain energy per cycle. Though this technique has been shown to be acceptable, it needs to be improved to account from the experimentally observed increase in the strain energy per cycle as the loading cycles approach fatigue. In order to improve the fatigue life prediction technique, experimental strain energy density per cycle is observed during the fatigue process of Aluminium 6061-T6 (Al 6061-T6) specimens. The results show exponential change in the strain energy density through the first 20 per cent and the last 30 per cent of the total failure cycles. The results lead to a new representation of strain energy density per cycle, which leads to an improved fatigue life prediction method. A comparison is made between the improved prediction method and experimental fatigue results. The comparison result validates the precision of the new hysteresis-loop representation.

On Antiresonance in the Forced Response of Mistuned Bladed Disks

Mistuning in bladed disks usually increases the maximum local forced response leading to shortened component life in turbine engines. This paper investigates mistuning using a transfer function approach where the frequency response functions (FRFs) are described by natural frequencies and antiresonant frequencies. Using this approach, antiresonant frequencies are shown to be a critical factor in determining the maximum local response. Two insights are gained by formulating antiresonant frequencies as the eigenvalues of reduced system matrices: 1) Mistuning a particular blade has no affect on that blades antiresonant frequencies. 2) Engine orders N and N/2, where N is the number of blades on the disk, tend to produce the highest maximum local response. Numerical examples are given using a lightly damped spring mass oscillator model of a bladed disk. Pole-zero loci of mistuned bladed disks show that increased maximum response is often due to the damping of antiresonant frequencies. An important conclusion is that antiresonant frequencies can be arranged such that a mistuned bladed disk has a lower maximum response than a tuned bladed disk.

Probabilistic Mistuning Assessment Using Nominal and Geometry Based Mistuning Methods

Two deterministic mistuning models utilizing component mode synthesis methods are used in a Monte Carlo simulation to generate mistuned response distributions for a geometrically perturbed Integrally Bladed Rotor. The first method, a frequency-perturbation approach with a nominal mode approximation used widely in academia and industry, assumes airfoil geometric perturbations alter only the corresponding modal stiffnesses while its mode shapes remain unaffected. The mistuned response is then predicted by a summation of the nominal modes. The second method, a geometric method utilizing non-nominal modes, makes no simplifying assumptions of the dynamic response due to airfoil geometric perturbations, but requires recalculation of each airfoil eigen-problem. A comparison of the statistical moments of the mistuned response distributions and prediction error is given for three different frequency ranges and engine order excitations. Further, the response distributions are used for a variety of design and testing scenarios to highlight impacts of the frequency-based approach inaccuracy. Results indicate the frequency-based method typically provides conservative response levels.Copyright

An Energy-Based Method for Uni-Axial Fatigue Life Calculation

An energy based fatigue life prediction framework has been developed for calculation of remaining fatigue life of in-service gas turbine materials. The purpose of the life prediction framework is to account for the material aging effect on fatigue strength of gas turbine engines structural components which are usually designed for infinite life. Previous studies [1–7] indicate the total strain energy dissipated during a monotonic fracture process and a cyclic process is a material property that can be determined by measuring the area underneath the monotonic true stress-strain curve and the sum of the area within each hysteresis loop in the cyclic process, respectively. The energy-based fatigue life prediction framework consists of the following entities: (1) development of a testing procedure to achieve plastic energy dissipation per life cycle and (2) incorporation of an energy-based fatigue life calculation scheme to determine the remaining fatigue life of in-service gas turbine materials. The accuracy of the remaining fatigue life prediction method was verified by comparison between model approximation and experimental results of Aluminum 6061-T6 (Al 6061-T6). The comparison shows promising agreement, thus validating the capability of the framework to produce accurate fatigue life prediction.Copyright

Component-Mode Reduced-Order Models for Geometric Mistuning of Integrally Bladed Rotors

Two methods that explicitly model airfoil geometry surface deviations for mistuning prediction in integrally bladed rotors are developed by performing a modal analysis on different degrees of freedom of a parent reduced-order model. The parent reduced-order model is formulated with Craig–Bampton component-mode synthesis in cyclic symmetry coordinates for an integrally bladed rotor with a tuned disk and airfoil geometric deviations. The first method performs an eigenanalysis on the constraint-mode degrees of freedom that provides a truncated set of interface modes, whereas the second method includes the disk fixed-interface normal mode in the eigenanalysis to yield a truncated set of ancillary modes. Both methods can use tuned or mistuned modes, where the tuned modes have the computational benefit of being computed in cyclic symmetry coordinates. Furthermore, the tuned modes only need to be calculated once, which offers significant computational savings for subsequent mistuning studies. Each geometric mist...