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Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations (identification of lifting rotor system parameters from transient response data), Phase 7-B

System identification methods have been applied to rotorcraft to estimate stability derivatives from transient flight control response data. While these applications assumed a linear constant coefficient representation of the rotorcraft, the computer experiments used transient responses in flap-bending and torsion of a rotor blade at high advance ratio which is a rapidly time varying periodic system. It was found that a simple system identification method applying a linear sequential estimator also called least square estimator or equation of motion estimator, is suitable for this periodic system and can be used directly if only the acceleration data are noise polluted. In the case of noise being present also in the state variable data the direct application of the estimator gave poor results.

Hohenemser, K. H.

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations (further experiments with progressing/regressing rotor flapping modes), Phase 7-C

The experiments with progressing/regressing forced rotor flapping modes have been extended in several directions and the data processing method has been considerably refined. The 16 inch hingeless 2-bladed rotor model was equipped with a new set of high precision blades which removed previously encountered tracking difficulties at high advance ratio, so that tests up to .8 rotor advance ratio could be conducted. In addition to data with 1.20 blade natural flapping frequency data at 1.10 flapping frequency were obtained. Outside the wind tunnel, tests with a ground plate located at different distances below the rotor were conducted while recording the dynamic downflow at a station .2R below the rotor plane with a hot wire anemometer.

Hohenemser, K. H.

Response of nonlinear panels to random loads

Lightweight aircraft structures exposed to a high intensity noise environment can fatigue prematurely if adequate consideration is not given to the problem. Design methods and design criteria for sonic fatigue prevention were developed based on analytical and experimental techniques. Most of the analytical work was based upon small deflection or linear structural theory which did not agree with the experimental results. A large deflection geometrical nonlinearity was incorporated into the analysis methods for determining the structural response to high intensity noise. The Karman-Herrmann large deflection equations with a single mode Galerkin approximation, and the method of equivalent linearization were used to predict mean square amplitude, mean square stresses, and nonlinear frequency at various acoustic loadings for rectangular panels. Both simply supported and clamped support conditions with immovable or movable inplane edges are considered. Comparisons with experimental results are presented.

Mei, C.

The Effect of a Non-Gaussian Random Loading on High-Cycle Fatigue of a Thermally Post-Buckled Structure

High-cycle fatigue of an elastic-plastic beam structure under the combined action of thermal and high-intensity non-Gaussian acoustic loadings is considered. Such loadings can be highly damaging when snap-through motion occurs between thermally post-buckled equilibria. The simulated non-Gaussian loadings investigated have a range of skewness and kurtosis typical of turbulent boundary layer pressure fluctuations in the vicinity of forward facing steps. Further, the duration and steadiness of high excursion peaks is comparable to that found in such turbulent boundary layer data. Response and fatigue life estimates are found to be insensitive to the loading distribution, with the minor exception of cases involving plastic deformation. In contrast, the fatigue life estimate was found to be highly affected by a different type of non-Gaussian loading having bursts of high excursion peaks.

Rizzi, Stephen A.

Probabilistic finite elements for fracture mechanics

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Besterfield, Glen

Improved estimation of random vibration loads in launch vehicles

Random vibration induced load is an important component of the total design load environment for payload and launch vehicle components and their support structures. The current approach to random vibration load estimation is based, particularly at the preliminary design stage, on the use of Miles' equation which assumes a single degree-of-freedom (DOF) system and white noise excitation. This paper examines the implications of the use of multi-DOF system models and response calculation based on numerical integration using the actual excitation spectra for random vibration load estimation. The analytical study presented considers a two-DOF system and brings out the effects of modal mass, damping and frequency ratios on the random vibration load factor. The results indicate that load estimates based on the Miles' equation can be significantly different from the more accurate estimates based on multi-DOF models.

Mehta, R.

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael

Calculation of Dynamic Loads Due to Random Vibration Environments in Rocket Engine Systems

An important part of rocket engine design is the calculation of random dynamic loads resulting from internal engine "self-induced" sources. These loads are random in nature and can greatly influence the weight of many engine components. Several methodologies for calculating random loads are discussed and then compared to test results using a dynamic testbed consisting of a 60K thrust engine. The engine was tested in a free-free condition with known random force inputs from shakers attached to three locations near the main noise sources on the engine. Accelerations and strains were measured at several critical locations on the engines and then compared to the analytical results using two different random response methodologies.

Christensen, Eric R.

Testing for Random Limit Load Versus Static Limit Load

This document is an effort to report the basic test findings in an ongoing quest for understanding how random load factors should be applied to structural components in order to verify the strength of space flight hardware. A Spacelab experiment known as the Atmospheric Emission Photometric Imager (AEPI) was subjected to both an expected flight random environment and the associated Miles' equation equivalent static load. During each of these tests, the fiberglass pedestal was instrumented with 16 triaxial strain gauges around its base. Component strains and invariant stresses were compared. As seen previously in other hardware tests, the stress distribution from the random environment was an order of magnitude below the comparable static stresses. With a proposed data acquisition system, a strain database will be developed that will quantify an empirical relationship between dynamic and static limit stresses. This event will allow a more accurate estimate of launch environment effects on new technology structural components.

Lee, H. M.

Equivalent constant-amplitude concept for crack growth under spectrum loading

To simplify crack-growth calculations, an equivalent constant-amplitude concept is developed based on the crack-closure phenomenon and on results of pilot tests that showed that the crack-opening load remained essentially constant while cracks grew under repeating random-load sequences containing several thousand load peaks. An equation of crack growth equivalence resulting from derivations based on the crack closure crack growth law is obtained and used to determine a relationship between an equivalent number of cycles of constant-amplitude loading and the distribution of the random loads, the exponent in the crack growth law, and the ratio of the crack-opening load to the maximum load. The validity of the concept is tested experimentally on six different random-load sequences. Good agreement is found between experimental results and theoretical predictions.

Elber, W.

Life considerations of the shuttle orbiter densified-tile thermal protection system

The Shuttle orbiter themal protection system (TPS) incorporates ceramic reusable surface insulation tiles bonded to the orbiter substructure through a strain isolation pad. Densification of the bonding surface of the tiles increases the static strength of the tiles. The densification proces does not, however, necessarily lead to an equivalent increase in fatigue strength. Investigation of the expected lifetime of densified tile TPS under both sinusoidal loading and random loading simulating flight conditions indicates that the strain isolation pads are the weakest components of the TPS under fatigue loading. The felt pads loosen under repetitive loading and, in highly loaded regions, could possibly cause excessive step heights between tiles causing burning of the protective insulation between tiles. A method of improving the operational lifetime of the TPS by using a strain isolation pad with increased stiffness is presented as is the consequence of the effect of increased stiffness on the tile inplane strains and transverse stresses.

Cooper, P. A.

Probabilistic structural analysis methods for critical SSME propulsion components

The development of a three-dimensional inelastic analysis methodology for the Space Shuttle main engine (SSME) structural components is described. The methodology is composed of: (1) composite load spectra, (2) probabilistic structural analysis methods, (3) the probabilistic finite element theory, and (4) probabilistic structural analysis. The progress in the development of generic probabilistic models for various individual loads which consist of a steady state load, a periodic load, a random load, and a spike, is discussed. The capabilities of the Numerical Evaluation of Stochastic Structures Under Stress finite element code designed for probabilistic structural analysis of the SSME are examined. Variation principles for formulation probabilistic finite elements and a structural analysis for evaluating the geometric and material properties tolerances on the structural response of turbopump blades are being designed.

Chamis, C. C.

Crack growth under spectrum loading: A crack closure model

A concept based on the crack-closure phenomenon was developed to replace random load spectra with constant amplitude loading in both analysis and tests. The maximum load and the crack opening load in the constant amplitude loading are chosen to be equal to those for the spectrum, so that both crack growth mode and the crack length at failure are equivalent to those under random load spectra. The number of cycles of constant- amplitude loading is chosen so that the amount of crack growth is equal to that due to a given sequence or block of the random spectrum loading. The concept was tested experimentally after predicting the equivalent number of constant-amplitude cycles for six different random load sequences. The agreement between predictions and test results was good.

Elber, W.

A review of crack propagation under unsteady loading

The theories and research current available on crack propagation under unsteady loadings, especially those of acoustic origin, are reviewed. Since the original theories on fatigue failure did not account for random loading conditions, modified theories which provide statistical methods for evaluating the random loading have emerged. The impact of acoustic fatigue in the aerospace industry, basic principles such as fatigue crack initiation and propagation and load interactions, and testing procedures are discussed. Attention is also given to metal and metal alloy structures, fiber-reinforced composites and nonmetallic structures, short crack growth, and the effects of temperature, moisture, and corrosion on structures. Suggestions for future research in this field are presented, namely, studies on the effect of 'snap-through' response and associated crack growth patterns, studies in microcrack and 'small crack'; propagation under unsteady loading conditions, and the development of an accurate analytical model to predict acceleration and retardation effects in fatigue crack growth under random loading conditions.

Bryan, H. H.

Aging Theories for Establishing Safe Life Spans of Airborne Critical Structural Components

New aging theories have been developed to establish the safe life span of airborne critical structural components such as B-52B aircraft pylon hooks for carrying air-launch drop-test vehicles. The new aging theories use the equivalent-constant-amplitude loading spectrum to represent the actual random loading spectrum with the same damaging effect. The crack growth due to random loading cycling of the first flight is calculated using the half-cycle theory, and then extrapolated to all the crack growths of the subsequent flights. The predictions of the new aging theories (finite difference aging theory and closed-form aging theory) are compared with the classical flight-test life theory and the previously developed Ko first- and Ko second-order aging theories. The new aging theories predict the number of safe flights as considerably lower than that predicted by the classical aging theory, and slightly lower than those predicted by the Ko first- and Ko second-order aging theories due to the inclusion of all the higher order terms.

Ko, William L.

Flight simulation testing equipment for composite material systems

A test program is discussed which aims at establishing the time-temperature-stress characteristics of several classes of high-temperature composite materials in order to determine their suitability for applications in supersonic cruise aircraft. Five advanced composite materials (a boron epoxy, a boron polyimide, a graphite epoxy, a graphite polyimide, and diffusion-bonded boron aluminum) are being evaluated using a flight-test simulator capable of long-term automatic testing based on random loading and realistic flight temperature profiles. The design, construction, and checkout of this simulator are described along with the digital load programmer, load magnitude controllers, the hydraulic pumping system, the heating and cooling systems, the control console, and the data recording system. Typical results for short-term tests performed at constant temperatures and accelerated load rates are presented in terms of a random-load spectrum and a wearout model.

Haskins, J. F.

Li-ion Battery Aging with Hybrid Physics-Informed Neural Networks and Fleet-wide Data

In this work, we propose a hybrid model for Li-ion battery discharge and aging prediction that leverages fleet-wide data to predict future capacity drops.The model is built upon an hybrid approach merging physics-based and empirical equations, as well as neural network models in a recurrent neural network cell. The hybrid physics-informed neural network can predict voltage discharge cycles given the loading profile, and estimate the used capacity of the battery under random-loading conditions by tracking aging parameters connected to the residual capacity of the battery. By merging information on the battery aging parameters with existing fleet-wide aging data, the model can predict the future residual capacity of the battery that is being monitored, and therefore enable predictions of voltage discharge curves far ahead in the battery life cycle. We validated the approach using the NASA Prognostics Data Repository Battery data-set, which contains experimental data on Li-ion batteries discharged at random loading conditions in a controlled environment. The approach also allows the identification of discrepancies between the battery aging trend and the trend observed at the fleet level, so that batteries behaving differently from the rest of the fleet can be subject to closer monitoring and further testing to refine predictions.

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