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NASA NTRS2005

Method for Estimating Thread Strength Reduction of Damaged Parent Holes with Inserts

During normal assembly and disassembly of bolted-joint components, thread damage and/or deformation may occur. If threads are overloaded, thread damage/deformation can also be anticipated. Typical inspection techniques (e.g. using GO-NO GO gages) may not provide adequate visibility of the extent of thread damage. More detailed inspection techniques have provided actual pitch-diameter profiles of damaged-hardware holes. A method to predict the reduction in thread shear-out capacity of damaged threaded holes has been developed. This method was based on testing and analytical modeling. Test samples were machined to simulate damaged holes in the hardware of interest. Test samples containing pristine parent-holes were also manufactured from the same bar-stock material to provide baseline results for comparison purposes. After the particular parent-hole thread profile was machined into each sample a helical insert was installed into the threaded hole. These samples were tested in a specially designed fixture to determine the maximum load required to shear out the parent threads. It was determined from the pristine-hole samples that, for the specific material tested, each individual thread could resist an average load of 3980 pounds. The shear-out loads of the holes having modified pitch diameters were compared to the ultimate loads of the specimens with pristine holes. An equivalent number of missing helical coil threads was then determined based on the ratio of shear-out loads for each thread configuration. These data were compared with the results from a finite element model (FEM). The model gave insights into the ability of the thread loads to redistribute for both pristine and simulated damage configurations. In this case, it was determined that the overall potential reduction in thread load-carrying capability in the hardware of interest was equal to having up to three fewer threads in the hole that bolt threads could engage. One- half of this potential reduction was due to local pitch-diameter variations and the other half was due to overall pitch-diameter enlargement beyond Class 2 fit. This result was important in that the thread shear capacity for this particular hardware design was the limiting structural capability. The details of the method development, including the supporting testing, data reduction and analytical model results comparison will be discussed hereafter.

Johnson, David L.↗
NASA NTRS2005

Fluids and Combustion Facility: Combustion Integrated Rack Modal Model Correlation

The Fluids and Combustion Facility (FCF) is a modular, multi-user, two-rack facility dedicated to combustion and fluids science in the US Laboratory Destiny on the International Space Station. FCF is a permanent facility that is capable of accommodating up to ten combustion and fluid science investigations per year. FCF research in combustion and fluid science supports NASA's Exploration of Space Initiative for on-orbit fire suppression, fire safety, and space system fluids management. The Combustion Integrated Rack (CIR) is one of two racks in the FCF. The CIR major structural elements include the International Standard Payload Rack (ISPR), Experiment Assembly (optics bench and combustion chamber), Air Thermal Control Unit (ATCU), Rack Door, and Lower Structure Assembly (Input/Output Processor and Electrical Power Control Unit). The load path through the rack structure is outlined. The CIR modal survey was conducted to validate the load path predicted by the CIR finite element model (FEM). The modal survey is done by experimentally measuring the CIR frequencies and mode shapes. The CIR model was test correlated by updating the model to represent the test mode shapes. The correlated CIR model delivery is required by NASA JSC at Launch-10.5 months. The test correlated CIR flight FEM is analytically integrated into the Shuttle for a coupled loads analysis of the launch configuration. The analysis frequency range of interest is 0-50 Hz. A coupled loads analysis is the analytical integration of the Shuttle with its cargo element, the Mini Payload Logistics Module (MPLM), in the Shuttle cargo bay. For each Shuttle launch configuration, a verification coupled loads analysis is performed to determine the loads in the cargo bay as part of the structural certification process.

McNelis, Mark E.↗
NASA NTRS2003

Methods Developed by the Tools for Engine Diagnostics Task to Monitor and Predict Rotor Damage in Real Time

Tools for Engine Diagnostics is a major task in the Propulsion System Health Management area of the Single Aircraft Accident Prevention project under NASA s Aviation Safety Program. The major goal of the Aviation Safety Program is to reduce fatal aircraft accidents by 80 percent within 10 years and by 90 percent within 25 years. The goal of the Propulsion System Health Management area is to eliminate propulsion system malfunctions as a primary or contributing factor to the cause of aircraft accidents. The purpose of Tools for Engine Diagnostics, a 2-yr-old task, is to establish and improve tools for engine diagnostics and prognostics that measure the deformation and damage of rotating engine components at the ground level and that perform intermittent or continuous monitoring on the engine wing. In this work, nondestructive-evaluation- (NDE-) based technology is combined with model-dependent disk spin experimental simulation systems, like finite element modeling (FEM) and modal norms, to monitor and predict rotor damage in real time. Fracture mechanics time-dependent fatigue crack growth and damage-mechanics-based life estimation are being developed, and their potential use investigated. In addition, wireless eddy current and advanced acoustics are being developed for on-wing and just-in-time NDE engine inspection to provide deeper access and higher sensitivity to extend on-wing capabilities and improve inspection readiness. In the long run, these methods could establish a base for prognostic sensing while an engine is running, without any overt actions, like inspections. This damage-detection strategy includes experimentally acquired vibration-, eddy-current- and capacitance-based displacement measurements and analytically computed FEM-, modal norms-, and conventional rotordynamics-based models of well-defined damages and critical mass imbalances in rotating disks and rotors.

Baaklini, George Y.↗
NASA NTRS2004

Finite Element Modeling Used to Study Stress Distribution on the Foot

A method to study the stress distribution inside the forefoot during walking was developed at the Cleveland Clinic Foundation by a researcher from the NASA Glenn Research Center. In this method, a semiautomated process was outlined to create a three-dimensional, patient-specific, finite element model (FEM) of the forefoot using magnetic resonance images (MRI). The images were processed in Matlab using the k-nearest neighbor (k-NN) classification algorithm and Sobel edge detection to separate the different tissue types: bone, skin, fat, and muscle. This information was used to create curves and surfaces that were exported to an FEM preprocessor known as Truegrid. In Truegrid, eight-noded or brick elements were created by using surface mapping. The FEM was processed and postprocessed in Abaqus. Material properties of the models were obtained from past experiments such as fat pad confined compression, skin axial and biaxial tests, muscle in vivo compressive tests, and reference literature (bone properties). Nonlinear (hyperelastic) material models were used for the skin (epidermis and dermis), fat, and muscles; and a linear elastic model was used for the bones. Muscle activation during walking yielded uncertainties in the muscle material model since contracted muscles are stiffer than relaxed muscles. These uncertainties were resolved by performing a sensitivity analysis of the muscle material properties. The original properties were multiplied by arbitrary factors of 2, 3, 0.5, and 0.33. The strain and stress distributions, as well as the locations of peak values, were similar in all cases. The peak contact pressure P obtained for each case varied with respect to the applied factor f as follows:

Morales, Nelson↗
NASA NTRS2005

20 Meter Solar Sail Analysis and Correlation

This paper describes finite element analyses and correlation studies to predict deformations and vibration modes/frequencies of a 20-meter solar sail system developed by ATK Space Systems. Under the programmatic leadership of NASA Marshall Space Flight Center's In-Space Propulsion activity, the 20-meter solar sail program objectives were to verify the design, to assess structural responses of the sail system, to implement lessons learned from a previous 10-meter quadrant system analysis and test program, and to mature solar sail technology to a technology readiness level (TRL) of 5. For this 20 meter sail system, static and ground vibration tests were conducted in NASA Glenn Research Center's 100 meter diameter vacuum chamber at Plum Brook station. Prior to testing, a preliminary analysis was performed to evaluate test conditions and to determine sensor and actuator locations. After testing was completed, an analysis of each test configuration was performed. Post-test model refinements included updated properties to account for the mass of sensors, wiring, and other components used for testing. This paper describes the development of finite element models (FEM) for sail membranes and masts in each of four quadrants at both the component and system levels, as well as an optimization procedure for the static test/analyses correlation.

Taleghani, B. K.↗
NASA NTRS2007

Theoretical Noise Analysis on a Position-sensitive Metallic Magnetic Calorimeter

We report on the theoretical noise analysis for a position-sensitive Metallic Magnetic Calorimeter (MMC), consisting of MMC read-out at both ends of a large X-ray absorber. Such devices are under consideration as alternatives to other cryogenic technologies for future X-ray astronomy missions. We use a finite-element model (FEM) to numerically calculate the signal and noise response at the detector outputs and investigate the correlations between the noise measured at each MMC coupled by the absorber. We then calculate, using the optimal filter concept, the theoretical energy and position resolution across the detector and discuss the trade-offs involved in optimizing the detector design for energy resolution, position resolution and count rate. The results show, theoretically, the position-sensitive MMC concept offers impressive spectral and spatial resolving capabilities compared to pixel arrays and similar position-sensitive cryogenic technologies using Transition Edge Sensor (TES) read-out.

Smith, Stephen J.↗
NASA NTRS2007

Quiet Spike Build-Up Ground Vibration Testing Approach

NASA's Dryden Flight Research Center uses a modified F-15B (836) aircraft as a testbed for a variety of flight research:experiments mounted underneath the aircraft fuselage. The F-15B was selected to fly Gulfstream Aerospace Corporation's (GAC)QuietSpike(TM)(QS) project; however, this experiment is very unique and unlike any of the previous testbed experiments flown on the F-15B. It involves the addition of a relatively long quiet spike boom attached to the radar bulkhead of the aircraft. This QS experiment is a stepping stone to airframe structural morphing technologies designed to mitigate sonic born strength of business jets over land. The QS boom is a concept in Which an aircraft's front-end would be extended prior to supersonic acceleration. This morphing would effectively lengthen the aircraft, reducing peak sonic boom amplitude, but is also expected to partition the otherwise strong bow shock into a series of reduced-strength, non-coalescing shocklets. Prior to flying the Quietspike(TM) experiment on the F-15B aircraft several ground vibration tests (GVT) were required in order to understand the QS modal characteristics and coupling effects with the F-15B. However, due to the project's late hardware delivery of the QS and the intense schedule, a "traditional" GVT of the mated F-1513 Quietspike(tm) ready-for-flight configuration would not have left sufficient time available for the finite element model update and flutter analyses before flight testing. Therefore, a "nontraditional" ground vibration testing approach was taken. The objective of the QuietSpike (TM) build-up ground testing approach was to ultimately obtain confidence in the F-15B Quietspike(TM) finite element model (FEM) to be used for the flutter analysis. In order to obtain the F15B QS FEM with reliable foundation stiffness between the QS and the F-15B radar bulkhead as well as QS modal characteristics, several different GVT configurations were performed. EAch of the four GVT's performed had a specific objective. The overall intent was to provide adequate data which would replicate a "traditional" F-15B QS GVT with actual ready-for-flight hardware. NASA Dryden was tasked with the conduct of the 1st, 2nd and 4th GVT and the 3rd GVT was GAC's responsibility. In order for this build-up GVT approach to be feasible, it was absolutely critical that each GVT configuration matched as closely as possible the connection interface configuration between the and aircraft bulkhead.

Spivey, Natalie D.↗
NASA NTRS2009

Thermal Residual Stress in Environmental Barrier Coated Silicon Nitride - Modeled

When exposed to combustion environments containing moisture both un-reinforced and fiber reinforced silicon based ceramic materials tend to undergo surface recession. To avoid surface recession environmental barrier coating systems are required. However, due to differences in the elastic and thermal properties of the substrate and the environmental barrier coating, thermal residual stresses can be generated in the coated substrate. Depending on their magnitude and nature thermal residual stresses can have significant influence on the strength and fracture behavior of coated substrates. To determine the maximum residual stresses developed during deposition of the coatings, a finite element model (FEM) was developed. Using this model, the thermal residual stresses were predicted in silicon nitride substrates coated with three environmental coating systems namely barium strontium aluminum silicate (BSAS), rare earth mono silicate (REMS) and earth mono di-silicate (REDS). A parametric study was also conducted to determine the influence of coating layer thickness and material parameters on thermal residual stress. Results indicate that z-direction stresses in all three systems are small and negligible, but maximum in-plane stresses can be significant depending on the composition of the constituent layer and the distance from the substrate. The BSAS and REDS systems show much lower thermal residual stresses than REMS system. Parametric analysis indicates that in each system, the thermal residual stresses can be decreased with decreasing the modulus and thickness of the coating.

Ali, Abdul-Aziz↗
NASA NTRS2005

Force Limited Vibration Testing

This slide presentation reviews the concept and applications of Force Limited Vibration Testing. The goal of vibration testing of aerospace hardware is to identify problems that would result in flight failures. The commonly used aerospace vibration tests uses artificially high shaker forces and responses at the resonance frequencies of the test item. It has become common to limit the acceleration responses in the test to those predicted for the flight. This requires an analysis of the acceleration response, and requires placing accelerometers on the test item. With the advent of piezoelectric gages it has become possible to improve vibration testing. The basic equations have are reviewed. Force limits are analogous and complementary to the acceleration specifications used in conventional vibration testing. Just as the acceleration specification is the frequency spectrum envelope of the in-flight acceleration at the interface between the test item and flight mounting structure, the force limit is the envelope of the in-flight force at the interface . In force limited vibration tests, both the acceleration and force specifications are needed, and the force specification is generally based on and proportional to the acceleration specification. Therefore, force limiting does not compensate for errors in the development of the acceleration specification, e.g., too much conservatism or the lack thereof. These errors will carry over into the force specification. Since in-flight vibratory force data are scarce, force limits are often derived from coupled system analyses and impedance information obtained from measurements or finite element models (FEM). Fortunately, data on the interface forces between systems and components are now available from system acoustic and vibration tests of development test models and from a few flight experiments. Semi-empirical methods of predicting force limits are currently being developed on the basis of the limited flight and system test data. A simple two degree of freedom system is shown and the governing equations for basic force limiting results for this system are reviewed. The design and results of the shuttle vibration forces (SVF) experiments are reviewed. The Advanced Composition Explorer (ACE) also was used to validate force limiting. Test instrumentation and supporting equipment are reviewed including piezo-electric force transducers, signal processing and conditioning systems, test fixtures, and vibration controller systems. Several examples of force limited vibration testing are presented with some results.

random vibration testing↗
NASA NTRS2010

Ares I-X Flight Test Vehicle Modal Test

The first test flight of NASA's Ares I crew launch vehicle, called Ares I-X, was launched on October 28, 2009. Ares I-X used a 4-segment reusable solid rocket booster from the Space Shuttle heritage with mass simulators for the 5th segment, upper stage, crew module and launch abort system. Flight test data will provide important information on ascent loads, vehicle control, separation, and first stage reentry dynamics. As part of hardware verification, a series of modal tests were designed to verify the dynamic finite element model (FEM) used in loads assessments and flight control evaluations. Based on flight control system studies, the critical modes were the first three free-free bending mode pairs. Since a test of the free-free vehicle was not practical within project constraints, modal tests for several configurations during vehicle stacking were defined to calibrate the FEM. Test configurations included two partial stacks and the full Ares I-X flight test vehicle on the Mobile Launcher Platform. This report describes the test requirements, constraints, pre-test analysis, test execution and results for the Ares I-X flight test vehicle modal test on the Mobile Launcher Platform. Initial comparisons between pre-test predictions and test data are also presented.

Buehrle, Ralph D.↗
NASA NTRS2010

Ares I-X Launch Vehicle Modal Test Overview

The first test flight of NASA's Ares I crew launch vehicle, called Ares I-X, is scheduled for launch in 2009. Ares IX will use a 4-segment reusable solid rocket booster from the Space Shuttle heritage with mass simulators for the 5th segment, upper stage, crew module and launch abort system. Flight test data will provide important information on ascent loads, vehicle control, separation, and first stage reentry dynamics. As part of hardware verification, a series of modal tests were designed to verify the dynamic finite element model (FEM) used in loads assessments and flight control evaluations. Based on flight control system studies, the critical modes were the first three free-free bending mode pairs. Since a test of the free-free vehicle is not practical within project constraints, modal tests for several configurations in the nominal integration flow were defined to calibrate the FEM. A traceability study by Aerospace Corporation was used to identify the critical modes for the tested configurations. Test configurations included two partial stacks and the full Ares I-X launch vehicle on the Mobile Launcher Platform. This paper provides an overview for companion papers in the Ares I-X Modal Test Session. The requirements flow down, pre-test analysis, constraints and overall test planning are described.

Buehrle, Ralph D.↗
NASA NTRS2010

Predicting the Dynamic Crushing Response of a Composite Honeycomb Energy Absorber Using Solid-Element-Based Models in LS-DYNA

This paper describes an analytical study that was performed as part of the development of an externally deployable energy absorber (DEA) concept. The concept consists of a composite honeycomb structure that can be stowed until needed to provide energy attenuation during a crash event, much like an external airbag system. One goal of the DEA development project was to generate a robust and reliable Finite Element Model (FEM) of the DEA that could be used to accurately predict its crush response under dynamic loading. The results of dynamic crush tests of 50-, 104-, and 68-cell DEA components are presented, and compared with simulation results from a solid-element FEM. Simulations of the FEM were performed in LS-DYNA(Registered TradeMark) to compare the capabilities of three different material models: MAT 63 (crushable foam), MAT 26 (honeycomb), and MAT 126 (modified honeycomb). These material models are evaluated to determine if they can be used to accurately predict both the uniform crushing and final compaction phases of the DEA for normal and off-axis loading conditions

Jackson, Karen E.↗
NASA NTRS2010

Improving Bone-Health Monitoring in Astronauts: Recommended Use of Quantitative Computed Tomography [QCT] for Clinical and Operational Decisions by NASA

DXA measurement of areal bone mineral density [aBMD,g/cm2] is required by NASA for assessing skeletal integrity in astronauts. Due to the abundance of population-based data that correlate hip and spine BMDs to fragility fractures, BMD is widely applied as a predictor of fractures in the general aging population. In contrast, QCT is primarily a research technology that measures three-dimensional , volumetric BMD (vBMD,mg/cm3) of bone and is therefore capable of differentiating between cortical and trabecular components. Additionally, when combined with Finite Element Modeling [FEM], a computational tool, QCT data can be used to estimate the whole bone strength of the hip [FE strength] for a specific load vector. A recent report demonstrated that aBMD failed to correlate with incurred changes in FE strength (for fall and stance loading) by astronauts over typical 180-day ISS (International Space Station) missions. While there are no current guidelines for using QCT data in clinical practice, QCT increases the understanding of how bone structure and mineral content are affected by spaceflight and recovery on Earth. In order to understand/promote/consider the use of QCT, NASA convened a panel of clinicians specializing in osteoporosis. After reviewing the available, albeit limited, medical and research information from long-duration astronauts (e.g., data from DXA, QCT, FEM, biochemistry analyses, medical records and in-flight exercise performance) the panelists were charged with recommending how current and future research data and analyses could inform clinical and operational decisions. The Panel recommended that clinical bone tests on astronauts should include QCT (hip and lumbar spine) for occupational risk surveillance and for the estimation of whole hip bone strength as derived by FEM. FE strength will provide an improved index that NASA could use to select astronauts of optimal bone health for extended duration missions, for repeat missions or for specific mission operations.

Sibonga, J. D.↗
NASA NTRS2010

Bone Health Monitoring in Astronauts: Recommended Use of Quantitative Computed Tomography [QCT] for Clinical and Operational Decisions

This slide presentation reviews the concerns that astronauts in long duration flights might have a greater risk of bone fracture as they age than the general population. A panel of experts was convened to review the information and recommend mechanisms to monitor the health of bones in astronauts. The use of Quantitative Computed Tomography (QCT) scans for risk surveillance to detect the clinical trigger and to inform countermeasure evaluation is reviewed. An added benefit of QCT is that it facilitates an individualized estimation of bone strength by Finite Element Modeling (FEM), that can inform approaches for bone rehabilitation. The use of FEM is reviewed as a process that arrives at a composite number to estimate bone strength, because it integrates multiple factors.

Sibonga, J. D.↗
NASA NTRS2011

Finite Element Model Characterization Of Nano-Composite Thermal And Environmental Barrier Coatings

Thermal and environmental barrier coatings have been applied for protecting Si based ceramic matrix composite components from high temperature environment in advanced gas turbine engines. It has been found that the delamination and lifetime of T/EBC systems generally depend on the initiation and propagation of surface cracks induced by the axial mechanical load in addition to severe thermal loads. In order to prevent T/EBC systems from surface cracking and subsequent delamination due to mechanical and thermal stresses, T/EBC systems reinforced with nano-composite architectures have showed promise to improve mechanical properties and provide a potential crack shielding mechanism such as crack bridging. In this study, a finite element model (FEM) was established to understand the potential beneficial effects of nano-composites systems such as SiC nanotube-reinforced oxide T/EBC systems.

Yamada, Yoshiki↗
NASA NTRS2011

Full-Scale Test and Analysis of a PRSEUS Fuselage Panel to Assess Damage-Containment Features

Stitched composite technology has the potential to substantially decrease structural weight through enhanced damage containment capabilities. The most recent generation of stitched composite technology, the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) concept, has been shown to successfully arrest damage at the sub-component level through tension testing of a three stringer panel with damage in the form of a two-bay notch. In a joint effort undertaken by the National Aeronautics and Space Administration (NASA), the Federal Aviation Administration (FAA), and the Boeing Company, further studies are being conducted to characterize the damage containment features of the PRSEUS concept. A full-scale residual strength test will be performed on a fuselage panel to determine if the load capacity will meet strength, deformation, and damage tolerance requirements. A curved panel was designed, fabricated, and prepared for residual strength testing. A pre-test Finite Element Model (FEM) was developed using design allowables from previous test programs to predict test panel deformation characteristics and margins of safety. Three phases of testing with increasing damage severity include: (1) as manufactured; (2) barely visible impact damage (BVID) and visible impact damage (VID); and (3) discrete source damage (DSD) where the panel will be loaded to catastrophic failure. This paper presents the background information, test plan, and experimental procedure. This paper is the first of several future articles reporting the test preparations, results, and analysis conducted in the test program.

Bergan, Andrew↗
NASA NTRS2012

Compression After Impact on Honeycomb Core Sandwich Panels with Thin Facesheets, Part 2: Analysis

A two part research study has been completed on the topic of compression after impact (CAI) of thin facesheet honeycomb core sandwich panels. The research has focused on both experiments and analysis in an effort to establish and validate a new understanding of the damage tolerance of these materials. Part 2, the subject of the current paper, is focused on the analysis, which corresponds to the CAI testings described in Part 1. Of interest, are sandwich panels, with aerospace applications, which consist of very thin, woven S2-fiberglass (with MTM45-1 epoxy) facesheets adhered to a Nomex honeycomb core. Two sets of materials, which were identical with the exception of the density of the honeycomb core, were tested in Part 1. The results highlighted the need for analysis methods which taken into account multiple failure modes. A finite element model (FEM) is developed here, in Part 2. A commercial implementation of the Multicontinuum Failure Theory (MCT) for progressive failure analysis (PFA) in composite laminates, Helius:MCT, is included in this model. The inclusion of PFA in the present model provided a new, unique ability to account for multiple failure modes. In addition, significant impact damage detail is included in the model. A sensitivity study, used to assess the effect of each damage parameter on overall analysis results, is included in an appendix. Analysis results are compared to the experimental results for each of the 32 CAI sandwich panel specimens tested to failure. The failure of each specimen is predicted using the high-fidelity, physicsbased analysis model developed here, and the results highlight key improvements in the understanding of honeycomb core sandwich panel CAI failure. Finally, a parametric study highlights the strength benefits compared to mass penalty for various core densities.

Mcquigg, Thomas D.↗
NASA NTRS2012

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

Basinger, Scott A.↗