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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Gear Performance Improved by Coating

Gears, bearings, and other mechanical elements transmit loads through contacting surfaces. Even if properly designed, manufactured, installed, and maintained, gears and bearings will eventually fail because of the fatigue of the working surfaces. Economical means for extending the fatigue lives of gears and bearings are highly desired, and coatings offer the opportunity to engineer surfaces to extend the fatigue lives of mechanical components. A tungsten-containing diamondlike-carbon coating exhibiting high hardness, low friction, and good toughness was evaluated for application to spur gears. Fatigue testing was done at the NASA Glenn Research Center on both uncoated and coated spur gears. The results showed that the coating extended the surface fatigue lives of the gears by a factor of about 5 relative to the uncoated gears. For the experiments, a lot of spur test gears made from AISI 9310 gear steel were case-carburized and ground to aerospace specifications. The geometries of the 28-tooth, 8-pitch gears were verified as meeting American Gear Manufacturing Association (AGMA) quality class 12. One-half of the gears were randomly selected for coating. The method of coating was selected to achieve desired adherence, toughness, hardness, and low-friction characteristics. First the gears to be coated were prepared by blasting (vapor honing) with Al2O3 particles and cleaning. Then, the gears were provided with a thin adhesion layer of elemental chromium followed by magnetron sputtering of the outer coating consisting of carbon (70 at.%), hydrogen (15 at.%), tungsten (12 at.%), and nickel (3 at.%) (atomic percent at the surface). In total, the coating thickness was about 2.5 to 3 microns. As compared with the steel substrate, the coated surface was harder by a factor of about 2 and had a smaller elastic modulus. All gears were tested using a 5-centistoke synthetic oil, a 10,000-rpm rotation speed, and a hertzian contact stress of at least 1.7 GPa (250 ksi). Tests were run until either surface fatigue occurred or 300 million stress cycles were completed. Tests were run using either a pair of uncoated gears or a pair of coated gears (coated gears mated with uncoated gears were not evaluated). The fatigue test results, shown on Weibull coordinates in the graph, demonstrate that the coating provided substantially longer fatigue lives even though some of the coated gears endured larger stresses. The increase in fatigue life was a factor of about 5 and the statistical confidence for the improvement is high (greater than 99 percent). Examination of the tested gears revealed substantial reductions of total wear for coated gears in comparison to uncoated gears. The coated gear surface topography changed with running, with localized areas of the tooth surface becoming smoother with running. Theories explaining how coatings can extend gear fatigue lives are research topics for coating, tribology, and fatigue specialists. This work was done as a partnership between NASA, the U.S. Army Research Laboratory, United Technologies Research Corporation, and Sikorsky Aircraft.

Krantz, Timothy L.↗
NASA NTRS2011

Failure Modes in Capacitors When Tested Under a Time-Varying Stress

Power-on failure has been the prevalent failure mechanism for solid tantalum capacitors in decoupling applications. A surge step stress test (SSST) has been previously applied to identify the critical stress level of a capacitor batch to give some predictability to the power-on failure mechanism [1]. But SSST can also be viewed as an electrically destructive test under a time-varying stress (voltage). It consists of rapidly charging the capacitor with incremental voltage increases, through a low resistance in series, until the capacitor under test is electrically shorted. When the reliability of capacitors is evaluated, a highly accelerated life test (HALT) is usually adopted since it is a time-efficient method of determining the failure mechanism; however, a destructive test under a time-varying stress such as SSST is even more time efficient. It usually takes days or weeks to complete a HALT test, but it only takes minutes for a time-varying stress test to produce failures. The advantage of incorporating a specific time-varying stress profile into a statistical model is significant in providing an alternative life test method for quickly revealing the failure mechanism in capacitors. In this paper, a time-varying stress that mimics a typical SSST has been incorporated into the Weibull model to characterize the failure mechanism in different types of capacitors. The SSST circuit and transient conditions for correctly surge testing capacitors are discussed. Finally, the SSST was applied for testing Ta capacitors, polymer aluminum capacitors (PA capacitors), and multi-layer ceramic (MLC) capacitors with both precious metal electrodes (PME) and base metal electrodes (BME). The test results are found to be directly associated with the dielectric layer breakdown in Ta and PA capacitors and are independent of the capacitor values, the way the capacitors were built, and the capacitors manufacturers. The test results also show that MLC capacitors exhibit surge breakdown voltages much higher than the rated voltage and that the breakdown field is inversely proportional to the dielectric layer thickness. The SSST data can also be used to comparatively evaluate the voltage robustness of capacitors for decoupling applications.

Liu, David (Donhang)↗
NASA NTRS2022

Statistical Distribution of Gear Surface Fatigue Lives at High Reliability

The reliability of gears is important for a wide variety of applications, and the gearing community has a desire for better prediction of fatigue life at very high reliability. To improve predictions, a set of 950 NASA-conducted gear surface fatigue test results were gathered, pooled together using the general standardized Weibull variate, and then fit to a Weibull three-parameter distribution. An iterative fitting method was developed and then applied to the gear fatigue data to determine the values of the distribution parameters. Additional analyses were done using bearing and gear data that demonstrate a trend of increasing minimum life coefficient as correlated to the timeframe of the fatigue testing, and material cleanliness is proposed as a primary explanation for such correlation. It is noted that this observed trend supports published findings from analytical modeling and experimental studies that improvements to material cleanliness improves minimum fatigue life. Further use and study of the three-parameter Weibull distribution is recommended as a tool to quantify fatigue life most accurately in the high reliability regime.

gear↗
NASA NTRS1994

Statistical scaling relationships and size effects in the strength and creep rupture of fibrous composites

In this presentation we discuss a new theoretical model and supporting experimental results for the strength and lifetime in creep rupture of unidirectional, carbon fiber/epoxy matrix composites at ambient conditions. First we review the 'standard' Weibull/power-law methodology that has been standard practice. Then we discuss features of a recent model which build on the statistical aspects of fiber strength, micromechanical aspects of stress transfer around fiber breaks, and time-dependent creep of the matrix. The model is applied to 'microcomposites' consisting of seven fibers in a matrix for which strength and creep-rupture data are available. The model yields Weibull distributions in an envelope format for both strength and lifetime. The respective shape, scale and power-law parameters depend on such parameters as the Weibull shape parameter for fiber strength, the exponent for matrix creep, the effective load transfer length (which grows in time due to matrix creep) and the critical cluster size for failed fibers. The experimental results are consistent with the theory, though time-dependent debonding appears to be part of the failure process.

Phoenix, S. Leigh↗
NASA NTRS1985

Fatigue criterion to system design, life and reliability

A generalized methodology to structural life prediction, design, and reliability based upon a fatigue criterion is advanced. The life prediction methodology is based in part on work of Weibull and Lundberg and Palmgren. The approach incorporates the computed life of elemental stress volumes of a complex machine element to predict system life. The results of coupon fatigue testing can be incorporated into the analysis allowing for life prediction and component or structural renewal rates with reasonable statistical certainty.

Zaretsky, E. V.↗
NASA NTRS1986

Improved silicon nitride for advanced heat engines

Silicon nitride is a high temperature material currently under consideration for heat engine and other applications. The objective is to improve the net shape fabrication technology of Si3N4 by injection molding. This is to be accomplished by optimizing the process through a series of statistically designed matrix experiments. To provide input to the matrix experiments, a wide range of alternate materials and processing parameters was investigated throughout the whole program. The improvement in the processing is to be demonstrated by a 20 percent increase in strength and a 100 percent increase in the Weibull modulus over that of the baseline material. A full characterization of the baseline process was completed. Material properties were found to be highly dependent on each step of the process. Several important parameters identified thus far are the starting raw materials, sinter/hot isostatic pressing cycle, powder bed, mixing methods, and sintering aid levels.

Yeh, H. C.↗
NASA NTRS1985

Fatigue criterion to system design, life and reliability

A generalized methodology to structural life prediction, design, and reliability based upon a fatigue criterion is advanced. The life prediction methodology is based in part on work of W. Weibull and G. Lundberg and A. Palmgren. The approach incorporates the computed life of elemental stress volumes of a complex machine element to predict system life. The results of coupon fatigue testing can be incorporated into the analysis allowing for life prediction and component or structural renewal rates with reasonable statistical certainty.

Zaretsky, E. V.↗
NASA NTRS2009

Bayes Analysis and Reliability Implications of Stress-Rupture Testing a Kevlar/Epoxy COPV using Temperature and Pressure Acceleration

Composite Overwrapped Pressure Vessel (COPVs) that have survived a long service time under pressure generally must be recertified before service is extended. Sometimes lifetime testing is performed on an actual COPV in service in an effort to validate the reliability model that is the basis for certifying the continued flight worthiness of its sisters. Currently, testing of such a Kevlar49(registered TradeMark)/epoxy COPV is nearing completion. The present paper focuses on a Bayesian statistical approach to analyze the possible failure time results of this test and to assess the implications in choosing between possible model parameter values that in the past have had significant uncertainty. The key uncertain parameters in this case are the actual fiber stress ratio at operating pressure, and the Weibull shape parameter for lifetime; the former has been uncertain due to ambiguities in interpreting the original and a duplicate burst test. The latter has been uncertain due to major differences between COPVs in the data base and the actual COPVs in service. Any information obtained that clarifies and eliminates uncertainty in these parameters will have a major effect on the predicted reliability of the service COPVs going forward. The key result is that the longer the vessel survives, the more likely the more optimistic stress ratio is correct. At the time of writing, the resulting effect on predicted future reliability is dramatic, increasing it by about one nine , that is, reducing the probability of failure by an order of magnitude. However, testing one vessel does not change the uncertainty on the Weibull shape parameter for lifetime since testing several would be necessary.

Phoenix, S. Leigh↗
NASA NTRS2009

Bayes Analysis and Reliability Implications of Stress-Rupture Testing a Kevlar/Epoxy COPV Using Temperature and Pressure Acceleration

Composite Overwrapped Pressure Vessels (COPVs) that have survived a long service time under pressure generally must be recertified before service is extended. Flight certification is dependent on the reliability analysis to quantify the risk of stress rupture failure in existing flight vessels. Full certification of this reliability model would require a statistically significant number of lifetime tests to be performed and is impractical given the cost and limited flight hardware for certification testing purposes. One approach to confirm the reliability model is to perform a stress rupture test on a flight COPV. Currently, testing of such a Kevlar49 (Dupont)/epoxy COPV is nearing completion. The present paper focuses on a Bayesian statistical approach to analyze the possible failure time results of this test and to assess the implications in choosing between possible model parameter values that in the past have had significant uncertainty. The key uncertain parameters in this case are the actual fiber stress ratio at operating pressure, and the Weibull shape parameter for lifetime; the former has been uncertain due to ambiguities in interpreting the original and a duplicate burst test. The latter has been uncertain due to major differences between COPVs in the database and the actual COPVs in service. Any information obtained that clarifies and eliminates uncertainty in these parameters will have a major effect on the predicted reliability of the service COPVs going forward. The key result is that the longer the vessel survives, the more likely the more optimistic stress ratio model is correct. At the time of writing, the resulting effect on predicted future reliability is dramatic, increasing it by about one "nine," that is, reducing the predicted probability of failure by an order of magnitude. However, testing one vessel does not change the uncertainty on the Weibull shape parameter for lifetime since testing several vessels would be necessary.

Phoenix, S. Leigh↗
NASA NTRS1991

Improved silicon nitride for advanced heat engines

The results of a four year program to improve the strength and reliability of injection-molded silicon nitride are summarized. Statistically designed processing experiments were performed to identify and optimize critical processing parameters and compositions. Process improvements were monitored by strength testing at room and elevated temperatures, and microstructural characterization by optical, scanning electron microscopes, and scanning transmission electron microscope. Processing modifications resulted in a 20 percent strength and 72 percent Weibull slope improvement of the baseline material. Additional sintering aids screening and optimization experiments succeeded in developing a new composition (GN-10) capable of 581.2 MPa at 1399 C. A SiC whisker toughened composite using this material as a matrix achieved a room temperature toughness of 6.9 MPa m(exp .5) by the Chevron notched bar technique. Exploratory experiments were conducted on injection molding of turbocharger rotors.

Yeh, Harry C.↗
NASA NTRS1986

Management of SSME hardware life utilization

Statistical and probabilistic reliability methodologies were developed for the determination of hardware life limits for the Space Shuttle Main Engine (SSME). Both methodologies require that a mathematical reliability model of the engine (system) performance be developed as a function of the reliabilities of the components and parts. The system reliability model should be developed from the Failute Modes and Effects Analysis/Critical Items List. The statistical reliability methodology establishes hardware life limits directly from the failure distributions of the components and parts obtained from statistically-designed testing. The probabilistic reliability methodology establishes hardware life limits from a decision analysis methodology which incorporates the component/part reliabilities obtained from a probabilistic structural analysis, a calibrated maintenance program, inspection techniques, and fabrication procedures. Probilistic structural analysis is recommended as a tool to prioritize upgrading of the components and parts. The Weibull probability distribution is presently being investigated by NASA/MSFC to characterize the failure distribution of the SSME hardware from a limited data base of failures.

Pauschke, J. M.↗
NASA NTRS1983

Establishment of a center of excellence for applied mathematical and statistical research

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Woodward, W. A.↗
NASA NTRS1995

An overview of engineering concepts and current design algorithms for probabilistic structural analysis

The article begins by examining the fundamentals of traditional deterministic design philosophy. The initial section outlines the concepts of failure criteria and limit state functions two traditional notions that are embedded in deterministic design philosophy. This is followed by a discussion regarding safety factors (a possible limit state function) and the common utilization of statistical concepts in deterministic engineering design approaches. Next the fundamental aspects of a probabilistic failure analysis are explored and it is shown that deterministic design concepts mentioned in the initial portion of the article are embedded in probabilistic design methods. For components fabricated from ceramic materials (and other similarly brittle materials) the probabilistic design approach yields the widely used Weibull analysis after suitable assumptions are incorporated. The authors point out that Weibull analysis provides the rare instance where closed form solutions are available for a probabilistic failure analysis. Since numerical methods are usually required to evaluate component reliabilities, a section on Monte Carlo methods is included to introduce the concept. The article concludes with a presentation of the technical aspects that support the numerical method known as fast probability integration (FPI). This includes a discussion of the Hasofer-Lind and Rackwitz-Fiessler approximations.

Duffy, S. F.↗
NASA NTRS1986

Statistical analysis of failure data on controllers and SSME turbine blade failures

The expressions for the maximum likelihood functions are given when the failure data are censored at a given point or at multiple points, or when the data come in groups. Different models applicable to failure data are presented with their characteristics. A graphical method of distinguishing different models by using cumulative hazard fucnction is discussed. For the failure data on controllers the model is determined by cumulative hazard function and chi-square goodness of fit. Using the Weibull Model the maximum likelihood estimators of the shape parameter and the failure rate parameter are obtained. The confidence intervals, meantime between failures, and B1 are determined. Similarly, for the data on Space Shuttle Main Engine (SSME) blade failures the maximum likelihood estimators are obtained for the Weibull parameters. The variances, confidence intervals, meantime between failures, and reliability are determined. The analysis is performed under assumption of grouped data as well as randomly placed data.

Patil, S. A.↗
NASA NTRS1994

A new approach for determining fully empirical altimeter wind speed model functions

A statistical technique is developed for determining fully empirical model functions relating altimeter backscatter (sigma(sub 0)) measurements to near-surface neutral stability wind speed. By assuming that sigma(sub 0) varies monotonically and uniquely with wind speed, the method requires knowledge only of the separate, rather than joint distribution functions of sigma(sub 0) and wind speed. Analytic simplifications result from using a Weibull distribution to approximate the global ocean wind speed distribution; several different wind data sets are used to demonstrate the validity of the Weibull approximation. The technique has been applied to 1 year of Geosat data. Validation of the new and historical model functions using an independent buoy data set demonstrates that the present model function not only has small overall bias and root mean square (RMS) errors, but yields smaller systematic error trends with wind speed and pseudowave age than previously published models. The present analysis suggests that generally accuracte altimeter model functions can be derived without the use of colocated measurements, nor is additional significant wave height information measured by the altimeter necessary.

Freilich, M. H.↗
NASA NTRS1992

Design prediction for long term stress rupture service of composite pressure vessels

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Robinson, Ernest Y.↗
NASA NTRS1990

Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process

The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures.

Wheeler, J. T.↗
NASA NTRS1997

A Statistical Simulation Approach to Safe Life Fatigue Analysis of Redundant Metallic Components

This paper introduces a dual active load path fail-safe fatigue design concept analyzed by Monte Carlo simulation. The concept utilizes the inherent fatigue life differences between selected pairs of components for an active dual path system, enhanced by a stress level bias in one component. The design is applied to a baseline design; a safe life fatigue problem studied in an American Helicopter Society (AHS) round robin. The dual active path design is compared with a two-element standby fail-safe system and the baseline design for life at specified reliability levels and weight. The sensitivity of life estimates for both the baseline and fail-safe designs was examined by considering normal and Weibull distribution laws and coefficient of variation levels. Results showed that the biased dual path system lifetimes, for both the first element failure and residual life, were much greater than for standby systems. The sensitivity of the residual life-weight relationship was not excessive at reliability levels up to R = 0.9999 and the weight penalty was small. The sensitivity of life estimates increases dramatically at higher reliability levels.

Matthews, William T.↗