Michael Savage

Computer modeling of rack-generated spur gears

Abstract A general method is presented for describing external involute spur gears produced from the basic rack form. The resulting description is a computer graphic drawing of the cut tooth as an individual tooth, several teeth in a segment or a complete gear. It is established that the surface normal vector at the cutting point must pass through the instant center. Equations describing the tooth root, fillet, involute and top land are derived based on this fact. The points of demarcation between these tooth sections are also found. The tooth description is based on the tooth addendum and dedendum, the number of teeth on the gear, the rack pressure angle, the diametral pitch and the rack tip radius. The effect of tool shift on the cut tooth is included. The importance of the rack from addendum on involute interference is also presented.

Fatigue Life Analysis of a Turboprop Reduction Gearbox

Abstract : A fatigue life analysis of the Allison T56/501 turboprop reduction gearbox was developed. The life and reliability of the gearbox was based on the lives and reliabilities of the main power train bearings and gears. The bearing and gear lives were determined using the Lundberg-Palmgren theory and a mission profile. The five planet bearing set had the shortest calculated life among the various gearbox components, which agreed with field experience where the planet bearing had the greatest incidences of failure. The analytical predictions of relative lives among the various bearings were in reasonable agreement with field experience. The predicted gearbox life was in excellent agreement with field data when the material life adjustment factors alone were used. The gearbox had a lower predicted life in comparison with field data when no life adjustment factors were used or when lubrication life adjustment factors were used either alone or in combination with the material factors. Keywords: Turboprop engines, Fatigue life, and Life adjustment factors.

Determination of Turboprop Reduction Gearbox System Fatigue Life and Reliability

Two computational models to determine the fatigue life and reliability of a commercial turboprop gearbox are compared with each other and with field data. These models are (1) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising the system and (2) two-parameter Weibull distribution function for bearings and gears comprising the system using strict-series system reliability to combine the calculated individual component lives in the gearbox. The Monte Carlo simulation included the virtual testing of 744,450 gearboxes. Two sets of field data were obtained from 64 gearboxes that were first-run to removal for cause, were refurbished and placed back in service, and then were second-run until removal for cause. A series of equations were empirically developed from the Monte Carlo simulation to determine the statistical variation in predicted life and Weibull slope as a function of the number of gearboxes failed. The resultant L 10 life from the field data was 5,627 h. From strict-series system reliability, the predicted L 10 life was 774 h. From the Monte Carlo simulation, the median value for the L 10 gearbox lives equaled 757 h. Half of the gearbox L 10 lives will be less than this value and the other half more. The resultant L 10 life of the second-run (refurbished) gearboxes was 1,334 h. The apparent load-life exponent p for the roller bearings is 5.2. Were the bearing lives to be recalculated with a load-life exponent p equal to 5.2, the predicted L 10 life of the gearbox would be equal to the actual life obtained in the field. The component failure distribution of the gearbox from the Monte Carlo simulation was nearly identical to that using the strict-series system reliability analysis, proving the compatibility of these methods.

Computerized Life and Reliability Modelling for Turboprop Transmissions.

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.

Maximum life spur gear design

Optimization procedures allow one to design a spur gear reduction for maximum life and other end-use criteria. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial guess values. The optimization algorithm is described and the models for gear life and performance are presented. The algorithm is compact and has been programmed for execution on a desktop computer. In the program, the designer is given the opportunity to change the mathematical optimum to a more practical design for comparative evaluation. Two examples are presented to illustrate the method and its application.

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 reductions 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.

Spur, Helical, and Spiral Bevel Transmission Life Modeling.

Abstract : 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 reverted 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.

Comparative Fatigue Lives of Rubber and PVC Wiper Cylindrical Coatings

Three coating materials for rotating, cylindrical, coated wiping rollers were fatigue tested in two Intaglio printing presses. The coatings were a hard, cross-linked, plasticized polyvinyl chloride (PVC) thermoset (P-series); a plasticized PVC (A-series); and a hard nitrile rubber (R-series). Both two- and three-parameter Weibull analyses and a cost-benefit analysis were performed. The mean value of life for the R-series coating is 24 and 9 times longer than that of the P- and A-series coatings, respectively. At a very high probability of survival, the R-series coating is approximately 2 and 6 times the lives of the P- and A-series, respectively, before the first failure occurs. The cost and replacement rate for the R-series coating is significantly less than those for the P- and A- series coatings. When all coatings are run to failure, using the mean (life) time between removal (MTBR) for each coating to calculate the number of replacements and costs provides qualitatively similar results to those using a Weibull analysis. For these coatings, at a given operating temperature, the higher that temperature above the glass transition temperature, the longer the fatigue life. Presented at the 57th Annual Meeting in Houston, Texas May 19–23, 2002

Space Shuttle Rudder Speed Brake Actuator-A Case Study Probabilistic Fatigue Life and Reliability Analysis

The U.S. Space Shuttle fleet was originally intended to have a life of 100 flights for each vehicle, lasting over a 10-year period, with minimal scheduled maintenance or inspection. The first space shuttle flight was that of the Space Shuttle Columbia (OV-102), launched April 12, 1981. The disaster that destroyed Columbia occurred on its 28th flight, February 1, 2003, nearly 22 years after its first launch. In order to minimize risk of losing another Space Shuttle, a probabilistic life and reliability analysis was conducted for the Space Shuttle rudder/speed brake actuators to determine the number of flights the actuators could sustain. A life and reliability assessment of the actuator gears was performed in two stages: a contact stress fatigue model and a gear tooth bending fatigue model. For the contact stress analysis, the Lundberg-Palmgren bearing life theory was expanded to include gear-surface pitting for the actuator as a system. The mission spectrum of the Space Shuttle rudder/speed brake actuator was combined into equivalent effective hinge moment loads including an actuator input preload for the contact stress fatigue and tooth bending fatigue models. Gear system reliabilities are reported for both models and their combination. Reliability of the actuator bearings was analyzed separately, based on data provided by the actuator manufacturer. As a result of the analysis, the reliability of one half of a single actuator was calculated to be 98.6% for 12 flights. Accordingly, each actuator was subsequently limited to 12 flights before removal from service in the Space Shuttle.

Determination of Turboprop Reduction Gearbox System Fatigue-Life and Reliability From Computer Generated Tests

Two computational models for the fatigue life and reliability of a turboprop gearbox are compared with each other and with field data. The two models are (1) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising a gearbox and (2) life analysis of the bearings and gears in the gearbox using the two-parameter Weibull distribution and the Lundberg-Palmgren life theory. These results were compared with field life results from 75 gearbox failures. Field data for the gearbox resulted in an L10 life of 2100 hrs. and a Weibull slope of 1.3. The Lundberg-Palmgren method resulted in a calculated L10 life of 1735 hours and a Weibull slope of 1.17. For the life estimation produced by the Monte Carlo method, the median L10 life approached 1775 hours and the Weibull slope approached a value of 1.21. There is reasonably good engineering correlation between the life results obtained from the field data and those predicted from the Lundberg-Palmgren analysis and the Monte Carlo simulation.Copyright