Results for “Weibull Distribution” — Page 6

NASA NTRS1978

Reproducibility of structural strength and stiffness for graphite-epoxy aircraft spoilers

Structural strength reproducibility of graphite epoxy composite spoilers for the Boeing 737 aircraft was evaluated by statically loading fifteen spoilers to failure at conditions simulating aerodynamic loads. Spoiler strength and stiffness data were statistically modeled using a two parameter Weibull distribution function. Shape parameter values calculated for the composite spoiler strength and stiffness were within the range of corresponding shape parameter values calculated for material property data of composite laminates. This agreement showed that reproducibility of full scale component structural properties was within the reproducibility range of data from material property tests.

Howell, W. E.↗

NASA NTRS1982

Reliability model for planetary gear

A reliability model is presented for planetary gear trains in which the ring gear is fixed, the Sun gear is the input, and the planet arm is the output. The input and output shafts are coaxial and the input and output torques are assumed to be coaxial with these shafts. Thrust and side loading are neglected. This type of gear train is commonly used in main rotor transmissions for helicopters and in other applications which require high reductions in speed. The reliability model is based on the Weibull distribution of the individual reliabilities of the transmission components. The transmission's basic dynamic capacity is defined as the input torque which may be applied for one million input rotations of the Sun gear. Load and life are related by a power law. The load life exponent and basic dynamic capacity are developed as functions of the component capacities.

Savage, M.↗

NASA NTRS1985

Life and reliability modeling of bevel gear reductions

A reliability model is presented for bevel gear reductions with either a single input pinion or dual input pinions of equal size. The dual pinions may or may not have the same power applied for the analysis. The gears may be straddle mounted or supported in a bearing quill. The reliability model is based on the Weibull distribution. The reduction's basic dynamic capacity is defined as the output torque which may be applied for one million output rotations of the bevel gear with a 90 percent probability of reduction survival.

Savage, M.↗

NASA NTRS1986

Grain boundary oxidation and an analysis of the effects of pre-oxidation on subsequent fatigue life

The effects of preoxidation on subsequent fatigue life were studied. Surface oxidation and grain boundary oxidation of a nickel-base superalloy (TAZ-8A) were studied at 600 to 1000 C for 10 to 1000 hours in air. Surface oxides were identified and the kinetics of surface oxidation was discussed. Grain boundary oxide penetration and morphology were studied. Pancake type grain boundary oxide penetrates deeper and its size is larger, therefore, it is more detrimental to fatigue life than cone-type grain boundary oxide. Oxide penetration depth, a (sub m), is related to oxidation temperature, T, and exposure time, t, by an empirical relation of the Arrhenius type. Effects of T and t on statistical variation of a (sub m) were analyzed according to the Weibull distribution function. Once the oxide is cracked, it serves as a fatigue crack nucleus. Statistical variation of the remaining fatigue life, after the formation of an oxide crack of a critical length, is related directly to the statistical variation of grain boundary oxide penetration depth.

Oshida, Y.↗

NASA NTRS1986

System life and reliability modeling for helicopter transmissions

A computer program which simulates life and reliability of helicopter transmissions is presented. The helicopter transmissions may be composed of spiral bevel gear units and planetary gear units - alone, in series or in parallel. The spiral bevel gear units may have either single or dual input pinions, which are identical. The planetary gear units may be stepped or unstepped and the number of planet gears carried by the planet arm may be varied. The reliability analysis used in the program is based on the Weibull distribution lives of the transmission components. The computer calculates the system lives and dynamic capacities of the transmission components and the transmission. The system life is defined as the life of the component or transmission at an output torque at which the probability of survival is 90 percent. The dynamic capacity of a component or transmission is defined as the output torque which can be applied for one million output shaft cycles for a probability of survival of 90 percent. A complete summary of the life and dynamic capacity results is produced by the program.

Savage, M.↗

NASA NTRS1985

Compatible atmospheres for a space suit, Space Station, and Shuttle based on physiological principles

Fundamental physiological principles have been invoked to design compatible environments for a space suit, Space Station and the spacecraft used to transport the astronauts from earth. These principles include the long-term memory of tissues for a bubble-provoking decompression, the intermittent nature of blood flow in the tight connective tissue(s) responsible for the bends whose incidence in aviators has been shown to be related to bubble volume by the Weibull distribution. In the overall design an astronaut breathing a mixture of 30 percent O2 in N2 for 4-5 h in a spacecraft at 11.9 psia can transfer to a Space Station filled with the same mix at 8.7 psia and, after a further 4-5 h, go EVA at any time without any oxygen prebreathing at any stage. The probable incidence of decompression sickness has been estimated as less than 0.5 percent using the present suit operating at 4.3 psia but the risk could be reduced to zero if the suit pressure were increased to 6.5 psia.

Hills, B. A.↗

NASA NTRS1985

Life and reliability modeling of bevel gear reductions

A reliability model is presented for bevel gear reductions with either a single input pinion or dual input pinions of equal size. The dual pinions may or may not have the same power applied for the analysis. The gears may be straddle mounted or supported in a bearing quill. The reliability model is based on the Weibull distribution. The reduction's basic dynamic capacity is defined as the output torque which may be applied for one million output rotations of the bevel gear with a 90 percent probability of reduction survival.

Savage, M.↗

NASA NTRS1988

Grain boundary oxidation and an analysis of the effects of oxidation on fatigue crack nucleation life

The effects of preoxidation on subsequent fatigue life were studied. Surface oxidation and grain boundary oxidation of a nickel-base superalloy (TAZ-8A) were studied at 600 to 1000 C for 10 to 1000 hours in air. Surface oxides were identified and the kinetics of surface oxidation was discussed. Grain boundary oxide penetration and morphology were studied. Pancake type grain boundary oxide penetrates deeper and its size is larger, therefore, it is more detrimental to fatigue life than cone-type grain boundary oxide. Oxide penetration depth, a (sub m), is related to oxidation temperature, T, and exposure time, t, by an empirical relation of the Arrhenius type. Effects of T and t on statistical variation of a (sub m) were analyzed according to the Weibull distribution function. Once the oxide is cracked, it serves as a fatigue crack nucleus. Statistical variation of the remaining fatigue life, after the formation of an oxide crack of a critical length, is related directly to the statistical variation of grain boundary oxide penetration depth.

Oshida, Y.↗

NASA NTRS1990

A case study of the Thunderstorm Research International Project storm of July 11, 1978. I - Analysis of the data base

The data obtained at the time of the Thunderstorm Research International Project storm at the Kennedy Space Center on July 11, 1978 are analyzed in a model-independent manner. The data base included data from three Doppler radars, a lightning detection and ranging system and a network of 25 electric field mills, and rain gages. Electric field measurements were used to analyze the charge moments transferred by lightning flashes, and the data were fitted to Weibull distributions; these were used to estimate statistical parameters of the lightning for both intracloud and cloud-to-ground flashes and to estimate the fraction of the flashes which were below the observation threshold. The displacement and the conduction current densities were calculated from electric field measurements between flashes. These values were used to derive the magnitudes and the locations of dipole and monopole generators by least squares fitting the measured Maxwell current densities to the displacement-dominated equations.

Nisbet, John S.↗

NASA NTRS1991

Structural reliability analysis of laminated CMC components

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications, design methods and protocols are a necessity. The time independent failure response of these materials is focussed on and a reliability analysis is presented associated with the initiation of matrix cracking. A public domain computer algorithm is highlighted that was coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Duffy, Stephen F.↗

NASA NTRS1991

ETARA PC version 3.3 user's guide: Reliability, availability, maintainability simulation model

A user's manual describing an interactive, menu-driven, personal computer based Monte Carlo reliability, availability, and maintainability simulation program called event time availability reliability (ETARA) is discussed. Given a reliability block diagram representation of a system, ETARA simulates the behavior of the system over a specified period of time using Monte Carlo methods to generate block failure and repair intervals as a function of exponential and/or Weibull distributions. Availability parameters such as equivalent availability, state availability (percentage of time as a particular output state capability), continuous state duration and number of state occurrences can be calculated. Initial spares allotment and spares replenishment on a resupply cycle can be simulated. The number of block failures are tabulated both individually and by block type, as well as total downtime, repair time, and time waiting for spares. Also, maintenance man-hours per year and system reliability, with or without repair, at or above a particular output capability can be calculated over a cumulative period of time or at specific points in time.

Hoffman, David J.↗

NASA NTRS1991

Solar F10.7 radiation - A short term model for Space Station applications

A new method is described for statistically modeling the F10.7 component of solar radiation for 91-day intervals. The resulting model represents this component of the solar flux as a quasi-exponentially correlated, Weibull distributed random variable, and thereby demonstrates excellent agreement with observed F10.7 data. Values of the F10.7 flux are widely used in models of the earth's upper atmosphere because of its high correlation with density fluctuations due to solar heating effects. Because of the direct relation between atmospheric density and drag, a realistic model of the short term fluctuation of the F10.7 flux is important for the design and operation of Space Station Freedom. The method of modeling this flux described in this report should therefore be useful for a variety of Space Station applications.

Vedder, John D.↗

NASA NTRS1991

A curved beam test specimen for determining the interlaminar tensile strength of a laminated composite

A curved beam type of test specimen is evaluated for use in determining the through-the-thickness strength of laminated composites. Two variations of a curved beam specimen configuration (semicircular and elliptical) were tested to failure using static and fatigue loads. The static failure load for the semicircular specimens was found to be highly sensitive to flaw content, with the specimens falling into two distinct groups. This result supports the use of proof testing for structural validation. Static design allowables are derived based on the Weibull distribution. Fatigue data indicates no measured increase in specimen compliance prior to final fracture. All static and fatigue failures at room temperature dry conditions occurred catastrophically. The elliptical specimens demonstrated unusually high failure strengths indicating the presence of phenomena requiring further study. Results are also included for specimens exposed to a wet environment showing a matrix strength degradation due to moisture content. Further testing is underway to evaluate a fatigue methodology for matrix dominated failures based on residual static strength (wearout).

Hiel, Clement C.↗

NASA NTRS1990

A curved beam test specimen for determining the interlaminar tensile strength of a laminated composite

A curved beam type of test specimen is evaluated for use in determining the through-the-thickness strength of laminated composites. Two variations of a curved beam specimen configuration (semi-circular and elliptical) were tested to failure using static and fatigue loads. The static failure load for the semi-circular specimens was found to be highly sensitive to flaw content, with the specimens falling into two distinct groups. This result supports the use of proof testing for structural validation. Static design allowables are derived based on the Weibull distribution. Fatigue data indicates no measured increase in specimen compliance prior to final fracture. All static and fatigue failures at room temperature dry conditions occurred catastrophically. The elliptical specimens demonstrated unusually high failure strengths indicating the presence of phenomena requiring further study. Results are also included for specimens exposed to a wet environment showing a matrix strength degradation due to moisture content. Further testing is under way to evaluate a fatigue methodology for matrix dominated failures based on residual static strength (wearout).

Hiel, Clement C.↗

NASA NTRS1991

Structural reliability analysis of laminated CMC components

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications, design methods and protocols are a necessity. The time independent failure response of these materials is focussed on and a reliability analysis is presented associated with the initiation of matrix cracking. A public domain computer algorithm is highlighted that was coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Duffy, Stephen F.↗

NASA NTRS1992

An application of synthetic seismicity in earthquake statistics - The Middle America Trench

The way in which seismicity calculations which are based on the concept of fault segmentation incorporate the physics of faulting through static dislocation theory can improve earthquake recurrence statistics and hone the probabilities of hazard is shown. For the Middle America Trench, the spread parameters of the best-fitting lognormal or Weibull distributions (about 0.75) are much larger than the 0.21 intrinsic spread proposed in the Nishenko Buland (1987) hypothesis. Stress interaction between fault segments disrupts time or slip predictability and causes earthquake recurrence to be far more aperiodic than has been suggested.

Ward, Steven N.↗

NASA NTRS1994

Spur, helical, and spiral bevel transmission life modeling

A computer program, TLIFE, which estimates the life, dynamic capacity, and reliability of aircraft transmissions, is presented. The program enables comparisons of transmission service life at the design stage for optimization. A variety of transmissions may be analyzed including: spur, helical, and spiral bevel reductions as well as series combinations of these reductions. The basic spur and helical reductions include: single mesh, compound, and parallel path plus revert star and planetary gear trains. A variety of straddle and overhung bearing configurations on the gear shafts are possible as is the use of a ring gear for the output. The spiral bevel reductions include single and dual input drives with arbitrary shaft angles. The program is written in FORTRAN 77 and has been executed both in the personal computer DOS environment and on UNIX workstations. The analysis may be performed in either the SI metric or the English inch system of units. The reliability and life analysis is based on the two-parameter Weibull distribution lives of the component gears and bearings. The program output file describes the overall transmission and each constituent transmission, its components, and their locations, capacities, and loads. Primary output is the dynamic capacity and 90-percent reliability and mean lives of the unit transmissions and the overall system which can be used to estimate service overhaul frequency requirements. Two examples are presented to illustrate the information available for single element and series transmissions.

Savage, Michael↗

NASA NTRS1994

Shoemaker-Levy 9 and the tidal disruption of comets

The break-up of Periodic Comet Shoemaker-Levy 9 into multiple pieces following its grazing encounter with Jupiter in July 1992 can be used to study tidally-induced fracture in comets. This spectacular event allows us not only to set limits on the size, strength and density of Shoemaker-Levy 9 itself, but provides invaluable guidance to numerical modeling of such encounters. In an extensive treatment of tidal breakup which assumed self-gravitating, homogeneous, perfectly elastic bodies, Dobrovolskis derived simple analytical expressions for the tidally-induced surface and central stresses. Both can be cast in such a way that Poisson's ratio is the only material dependent constant entering these expressions. Whether both surface and central failure must be initiated as a criterion for breakup, or either one of them is sufficient, remains a subject of disagreement. To resolve this debate, we model the details of cometary breakup using a three-dimensional Smooth Particle Hydrodynamics (SPH) code modified to simulate fracture in small solid objects. At lower stresses associated with brittle failure, we use a rate-dependent strength based on the nucleation of incipient flaws whose number density is given by a Weibull distribution.

Benz, W.↗