Brian Vlcek

Determination of Rolling-Element Fatigue Life From Computer Generated Bearing Tests

Two types of rolling-element bearings representing radial loaded and thrust loaded bearings were used for this study. Three hundred and forty (340) virtual bearing sets totaling 31400 bearings were randomly assembled and tested by Monte Carlo (random) number generation. The Monte Carlo results were compared with endurance data from 51 bearing sets comprising 5321 bearings. A simple algebraic relation was established for the upper and lower L10 life limits as function of the number of bearings failed for any bearing geometry. There is a fifty percent (50%) probability that the resultant bearing life ill be less than the calculated. The maximum and minimum variation between the bearing results life and the calculated life correlate with the 90-percent confidence limits for a Weibull slope of 1. 5. The calculated lives for bearings using a load-life exponent p of 4 for ball bearings and 5 for roller bearings correlated with the Monte Carlo generated bearings lives and the bearing data. STLE life factors for bearing steel and processing provide a reasonable accounting for differences between bearing life data and calculated life. Variations in Weibull slope from the Monte Carlo testing and bearing data correlated. There was excellent agreement between percent of individual components failed from Monte Carlo simulation and that predicted. Presented at the 58th Annual Meeting in New York City April 28–May 1, 2003

Monte Carlo Simulation of Sudden Death Bearing Testing

Monte Carlo simulations combined with sudden death testing were used to compare resultant bearing lives to the calculated bearing life and the cumulative test time and calendar time relative to sequential and censored sequential testing. A total of 30,960 virtual 50-mm bore deep-groove ball bearings were evaluated in 33 different sudden death test configurations comprising 36, 72, and 144 bearings each. Variations in both life and Weibull slope were a function of the number of bearings failed independent of the test method used and not the total number of bearings tested. Variations in L 10 life as a function of number of bearings failed were similar to variations in life obtained from sequentially failed real bearings and from Monte Carlo (virtual) testing of entire populations. Reductions up to 40% in bearing test time and calendar time can be achieved by testing to failure or the L 50 life and terminating all testing when the last of the predetermined bearing failures has occurred. Sudden death testing is not a more efficient method to reduce bearing test time or calendar time when compared to censored sequential testing.

Rolling-Element Fatigue Testing and Data Analysis—A Tutorial

In order to rank bearing materials, lubricants and other design variables using rolling-element bench-type fatigue testing of bearing components and full-scale rolling-element bearing tests, the investigator needs to be cognizant of the variables that affect rolling-element fatigue life and be able to maintain and control them within an acceptable experimental tolerance. Once these variables are controlled, the number of tests and the test conditions must be specified to assure reasonable statistical certainty of the final results. There is a reasonable correlation between the results from elemental test rigs with those results obtained with full-scale bearings. Using the statistical methods of Weibull and Johnson, the minimum number of tests required can be determined. This article brings together and discusses the technical aspects of rolling-element fatigue testing and data analysis and makes recommendations to assure quality and reliable testing of rolling-element specimens and full-scale rolling-element bearings.

Investigation of Low Temperature Combustion Regimes of Biodiesel With N-Butanol Injected in the Intake Manifold of a Compression Ignition Engine

In this study, the in-cylinder soot and NOx trade off was investigated in a compression engine by implementing premixed charge compression ignition (PCCI) coupled with low temperature combustion (LTC) for selected regimes of 1–3 bars IMEP. In order to achieve that, an omnivorous (multifuel) single cylinder diesel engine was developed by injecting n-butanol in the intake port while being fueled with biodiesel by direct injection in the combustion chamber. By applying this methodology, the in-cylinder pressure decreased by 25% and peak pressure was delayed in the power stroke by about 8 CAD for the cycles in which the n-butanol was injected in the intake manifold at the engine speed of 800 rpm and low engine loads, corresponding to 1–3 bars IMEP. Compared with the baseline taken with ultra-low sulfur diesel no. 2 (USLD#2), the heat release presented a more complex shape. t 1–2 bars IMEP, the premixed charge stage of the combustion totally disappeared and a prolonged diffusion stage was found instead. At 3 bars IMEP, an early low temperature heat release was present that started 6 deg (1.25 ms) earlier than the diesel reference heat release with a peak at 350 CAD corresponding to 1200 K. Heat losses from radiation of burned gas in the combustion chamber decreased by 10–50% while the soot emissions showed a significant decrease of about 98%, concomitantly with a 98% NOx reduction at 1 IMEP, and 77% at 3 IMEP, by controlling the combustion phases. Gaseous emissions were measured using an AVL SESAM FTIR and showed that there were high increases in CO, HC and NMHC emissions as a result of PCCI/LTC strategy; nevertheless, the technology is still under development. The results of this work indicate that n-butanol an be a very promising fuel alternative including for LTC regimes.

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.

Effect of Silicon Nitride Balls and Rollers on Rolling Bearing Life

Three decades have passed since the introduction of silicon nitride rollers and balls into conventional rolling-element bearings. For a given applied load, the contact (Hertz) stress in a hybrid bearing will be higher than that of an all-steel rolling element bearing. The silicon nitride rolling-element life as well as the lives of the steel races were used to determine the resultant bearing life of both hybrid and all-steel bearings. Life factors were determined and reported for hybrid bearings. Under nominal operating speeds, the resultant calculated lives of the deep-groove, angular-contact, and cylindrical roller hybrid bearings with races made of post-1960 bearing steel increased by factors of 3.7, 3.2, and 5.5, respectively, from those calculated using the Lundberg-Palmgren equations. An all-steel bearing under the same load will have a longer life than the equivalent hybrid bearing under the same conditions. Under these conditions, hybrid bearings are predicted to have a lower fatigue life than all-steel bearings by 58% for deep-groove bearings, 41% for angular contact bearings, and 28% for cylindrical roller bearings.

RCCI Operation With PFI of n-Butanol and DI of Biodiesel Compared With DI of Binary Mixtures of n-Butanol and Biodiesel

In this study the Reactive Controlled Combustion Ignition (RCCI) obtained by early port fuel injection (PFI) of n-butanol and direct injection (DI) of biodiesel were compared with in cylinder direct injected binary mixture of n-butanol and biodiesel with the same mass ratio of 3:1 in both fuelling strategies. The combustion and emissions characteristics were investigated at 5 bars IMEP at 1400 rpm. The ignition for DI of n-butanol-biodiesel binary blends showed a delay by approximately 7.5°CAD compared with the PFI case. For the binary mixture, n-butanol-biodiesel, the combustion pressure has decreased by 50% compared to the PFI of butanol. The maximum in cylinder gas temperature decreased by 100K for the n-butanol-biodiesel mixture versus ULSD#2 and has also experienced a 10° CAD delay. The premixed charge combustion has been split into two regions of high temperature heat release, an early one BTDC, and a second stage, ATDC for the PFI strategy. Increasing the load to 7.5 bars IMEP, heavy knock occurred for the PFI case. The soot emissions showed a 90% decrease with n-butanol injection PFI and by 98% reduction for DI of n-butanol binary mixture with the biodiesel, while the NOx emissions were reduced by 40% in both cases. The aldehyde emissions exhibited a significant 95% decrease for the n-butanol-biodiesel binary mixture compared with the n-butanol PFI. The mechanical efficiency at 80% and thermal efficiency and 38% were found similar, for both fuelling strategies.The results of this work suggest that the DI of n-butanol-biodiesel binary mixtures is more effective in reducing emissions than PFI of n-butanol combined with DI of biodiesel and also less likely to produce knock.Copyright

Cotton Seed FAME Combustion and Emissions Research in a DI Diesel Engine

This study investigates the combustion characteristics of cotton seed fatty acid methyl esters (FAME), with C100 (100% cotton seed biodiesel) and C20 (20% cotton seed biodiesel, 80% ultra-low sulfur diesel #2), in a direct injection diesel engine and compares the results with ultra-low sulfur diesel #2 (ULSD#2). The dynamic viscosity of C100 was found to meet the American Society for Testing and Materials (ASTM) standard. The lower heating value obtained for C100 was 37.7 MJ/kg, compared to 42.7 MJ/kg for ULSD#2. ULSD#2 and C100 displayed ignition delays of 9.6 crank angle degrees (CAD) and 7 CAD representing 1.14 ms and 0.83 ms respectively and a combustion time of 4ms (35 CAD) at 1400 rpm and 8 bar indicated mean effective pressure (IMEP) (100% load). The apparent heat release of the tested fuels at 8 bar IMEP showed both a premixed and diffusion phase and produced maximum values of 122 and 209 J/CAD for C100 and ULSD#2 respectively, with a decreasing trend occurring with increase in percentage of FAME. The 50% mass burnt (CA50) for 100% biodiesel was found to be 3 CAD advanced, compared with ULSD#2. The maximum total heat flux rates showed a value of 3.2 MW/m2 for ULSD#2 at 8 bar IMEP with a 6% increase observed for C100. Mechanical efficiency of ULSD#2 was 83% and presented a 5.35% decrease for C100, while the overall efficiency was 36% for ULSD#2 and 33% for C100 at 8 bar IMEP. The nitrogen oxides (NOx) for C100 presented an 11% decrease compared with ULSD#2. Unburned hydrocarbons value (UHC) for ULSD#2 was 2.8 g/kWh at 8 bar IMEP, and improved by 18% for C100. The carbon monoxide (CO) emissions for C100 decreased by 6% when compared to ULSD#2 at 3 bar IMEP but were relatively constant at 8 bar IMEP, presenting a value of 0.82 g/kWh for both fuels. The carbon dioxide (CO2) emissions for C100 increased by 1% compared with ULSD#2, at 3 bar IMEP. The soot value for ULSD#2 was 1.5 g/kWh and presented a 42% decrease for C100 at 8 bar IMEP. The results suggest a very good performance of cotton seed biodiesel, even at very high content of 100%, especially on the emissions side that showed decreasing values for regulated and non-regulated species.Copyright

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

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