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The two Weibull parameters based upon the method of maximum likelihood are determined. The test data used were failures observed at inspection intervals. The application was the reliability analysis of the SSME oxidizer turbine blades.
The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.
A generalized life and reliability model is presented for parallel shaft geared prop-fan and turboprop aircraft transmissions. The transmission life and reliability model is a combination of the individual reliability models for all the bearings and gears in the main load paths. The bearing and gear reliability models are based on classical fatigue theory and the two parameter Weibull failure distribution. A computer program was developed to calculate the transmission life and reliability. The program is modular. In its present form, the program can analyze five different transmission arrangements. However, the program can be modified easily to include additional transmission arrangements. An example is included which compares the life of a compound two-stage transmission with the life of a split-torque, parallel compound two-stage transmission, as calculated by the computer program.
A generalized life and reliability model is presented for parallel shaft geared prop-fan and turboprop aircraft transmissions. The transmission life and reliability model is a combination of the individual reliability models for all the bearings and gears in the main load paths. The bearing and gear reliability models are based on classical fatigue theory and the two parameter Weibull failure distribution. A computer program was developed to calculate the transmission life and reliability. The program is modular. In its present form, the program can analyze five different transmission arrangements. However, the program can be modified easily to include additional transmission arrangements. An example is included which compares the life of a compound two-stage transmission with the life of a split-torque, parallel compound two-stage transmission as calculated by the comaputer program.
The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.
Timely transmission overhauls increase in-flight service reliability greater than the calculated design reliabilities of the individual aircraft transmission components. Although necessary for aircraft safety, transmission overhauls contribute significantly to aircraft expense. Predictions of a transmission's maintenance needs at the design stage should enable the development of more cost effective and reliable transmissions in the future. The frequency is estimated of overhaul along with the number of transmissions or components needed to support the overhaul schedule. Two methods based on the two parameter Weibull statistical distribution for component life are used to estimate the time between transmission overhauls. These methods predict transmission lives for maintenance schedules which repair the transmission with a complete system replacement or repair only failed components of the transmission. An example illustrates the methods.
This paper describes two methods, the maximum distortion energy (MDE) and the principle of independent action (PIA), developed for the analysis of the reliability of a single continuous composite lamina. It is shown that, for the typical laminated plate structure, the individual lamina reliabilities can be combined in order to produce the upper and the lower bounds of reliability for the laminate, similar in nature to the bounds on properties produced from variational elastic methods. These limits were derived for both the interactive and the model failure considerations. Analytical expressions were also derived for the sensitivity of the reliability limits with respect to changes in the Weibull parameters and in loading conditions.
The Weibull weak-link theory allows for the computation of distribution functions for both the fracture location and the applied far-field stress. Several authors have suggested using the fracture location information from tests to infer Weibull parameters, and others have used the predictive capabilities of the theory to calculate average fracture locations for brittle bodies. By a simple set of example calculations, it is shown that the fracture location distribution function is distinctly more sensitive to perturbations in the stress state than the fracture stress distribution function is. In general, the average fracture location is more subject to stress perturbations than the average fracture stress. The results indicate that care must be exercised in applying fracture location theory.
The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.
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.
The fast fracture strength distribution of uniaxially ground, alpha silicon carbide was investigated as a function of grinding angle relative to the principal stress direction in flexure. Both as-ground and ground/annealed surfaces were investigated. The resulting flexural strength distributions were used to verify reliability models and predict the strength distribution of larger plate specimens tested in biaxial flexure. Complete fractography was done on the specimens. Failures occurred from agglomerates, machining cracks, or hybrid flaws that consisted of a machining crack located at a processing agglomerate. Annealing eliminated failures due to machining damage. Reliability analyses were performed using two and three parameter Weibull and Batdorf methodologies. The Weibull size effect was demonstrated for machining flaws. Mixed mode reliability models reasonably predicted the strength distributions of uniaxial flexure and biaxial plate specimens.
This report describes the use of computer program 'SEEK' which works in conjunction with two user-written subroutines and an input data file to perform an optimization procedure on a user's problem. The optimization method uses a modified feasible directions gradient technique. SEEK is written in ANSI standard Fortran 77, has an object size of about 46K bytes, and can be used on a personal computer running DOS. This report describes the use of the program and discusses the optimizing method. The program use is illustrated with four example problems: a bushing design, a helical coil spring design, a gear mesh design, and a two-parameter Weibull life-reliability curve fit.
CARES/LIFE predicts probability of failure of monolithic ceramic component as function of service time. Assesses risk that component fractures prematurely as result of subcritical crack growth (SCG). Effect of proof testing of components prior to service also considered. Coupled to such commercially available finite-element programs as ANSYS, ABAQUS, MARC, MSC/NASTRAN, and COSMOS/M. Also retains all capabilities of previous CARES code, which includes estimation of fast-fracture component reliability and Weibull parameters from inert strength (without SCG contributing to failure) specimen data. Estimates parameters that characterize SCG from specimen data as well. Written in ANSI FORTRAN 77 to be machine-independent. Program runs on any computer in which sufficient addressable memory (at least 8MB) and FORTRAN 77 compiler available. For IBM-compatible personal computer with minimum 640K memory, limited program available (CARES/PC, COSMIC number LEW-15248).
Tensile strengths of as-received HPZ fiber and those surface coated with BN, BN/SiC, and BN/Si3N4 have been determined at room temperature using a two-parameter Weibull distribution. Nominally approx. 0.4 micron BN and 0.2 micron SiC or Si3N4 coatings were deposited on the fibers by chemical vapor deposition using a continuous reactor. The average tensile strength of uncoated HPZ fiber was 2.0 +/- 0.56 GPa (290 +/- 81 ksi) with a Weibull modulus of 4.1. For the BN coated fibers, the average strength and the Weibull modulus increased to 2.39 +/- 0.44 GPa (346 +/- 64 ksi) and 6.5, respectively. The HPZ/BN/SiC fibers showed an average strength of 2.0 +/- 0.32 GPa (290 +/- 47 ksi) and Weibull modulus of 7.3. Average strength of the fibers having a dual BN/Si3N4 surface coating degraded to 1.15 +/- 0.26 GPa (166 +/- 38 ksi) with a Weibull modulus of 5.3. The chemical composition and thickness of the fiber coatings were determined using scanning Auger analysis. Microstructural analysis of the fibers and the coatings was carried out by scanning electron microscopy and transmission electron microscopy. A microporous silica-rich layer approx. 200 nm thick is present on the as-received HPZ fiber surface. The BN coatings on the fibers are amorphous to partly turbostratic and contaminated with carbon and oxygen. Silicon carbide coating was crystalline whereas the silicon nitride coating was amorphous. The silicon carbide and silicon nitride coatings are non-stoichiometric, non-uniform, and granular. Within a fiber tow, the fibers on the outside had thicker and more granular coatings than those on the inside.
Planetary gear transmissions are compact, high-power speed reductions which use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane transmission, the planet gear has no size at a ratio of two. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary with a fixed size, gear ratio, input speed power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.
The general goal of this project is to establish design protocols that enable the engineer to analyze and predict certain types of behavior in ceramic composites. Sections of the final report addresses the following: Description of the Problem that Motivated the Technology Development, Description of the New Technology that was Developed, Unique and Novel Features of the Technology and Results/Benefits of Application (year by year accomplishments), and Utilization of New Technology in Non-Aerospace Applications. Activities for this reporting period included the development of a design analysis as part of a cooperative agreement with general Electric Aircraft Engines. The effort focused on modifying the Toughened Ceramics Analysis and Reliability Evaluation of Structures (TCARES) algorithm for use in the design of engine components fabricated from NiAl. Other activities related to the development of an ASTM standard practice for estimating Weibull parameters. The standard focuses on the evaluation and reporting of uniaxial strength data, and the estimation of probability distribution parameters for ceramics which fail in a brittle fashion.
Planetary gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increase, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed reduction ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.
Planetary-gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed-reduction ratio, input speed, power and materials. The planetary-gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.