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 Zaretsky, E. V. 1992. “STLE Life Factors for Rolling Bearings,”, STLE SP–34 Park Ridge, IL: STLE.  [Google Scholar]) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising the system and (2 Weibull, W. 1939. “A Statistical Theory of the Strength of Materials,”. In Ingenioersvestenskapsakademiens. Handl. 151 [Google Scholar]) 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.     

Rolling Bearing Service Life Based on Probable Cause for Removal—A Tutorial

In 1947 and 1952 G. Lundberg and A. Palmgren developed what is now referred to as the Lundberg-Palmgren model for rolling bearing life prediction based on classical rolling-element fatigue. Today, bearing fatigue probably accounts for less than 5% of bearings removed from service for cause. A bearing service life prediction methodology and tutorial indexed to eight probable causes for bearing removal, including fatigue, are presented that incorporate strict series reliability; Weibull statistical analysis; available published field data from the Naval Air Rework Facility; and ～224,000 rolling-element bearings removed for rework from commercial aircraft engines. Bearing service life L_serv can be benchmarked and calculated to the bearing L₁₀ fatigue life as follows: L_serv = X^1/m L₁₀, where X is the number of bearings removed from service because of fatigue divided by the total of all bearings removed from service regardless of cause and m is the Weibull modulus of the bearings removed from service. The most conservative bearing L₁₀ service life calculation is obtained assuming an exponential distribution where m = 1.1. Of the ～224,000 commercial engine bearings removed from service for rework, 1,977 or 0.88% were rejected because of fatigue. From the Naval Air Rework Facility bearing data, eliminating rolling–element fatigue as a cause for removal, the L₁₀ service life of these bearings would increase by approximately 3%.     

Effect of Rolling Bearing Refurbishment and Restoration on Bearing Life and Reliability

For nearly four decades it has been a practice in commercial and military aircraft application that rolling-element bearings removed at maintenance or overhaul be reworked and returned to service. The work presented extends previously reported bearing life analysis to consider the depth (Z₄₅) to maximum shear stress (τ₄₅) on stressed volume removal and the effect of replacing the rolling elements with a new set. A simple algebraic relationship was established to determine the L₁₀ life of bearing races subject to bearing rework. Depending on the extent of rework and based on theoretical analysis, representative life factors for bearings subject to rework ranged from 0.87 to 0.99% of the lives of new bearings. Based on bearing endurance data, 92% of the bearing sets that would be subject to rework would result in L₁₀ lives equaling and/or exceeding that predicted for new bearings, with the remaining 8% having the potential to achieve the analytically predicted life of new bearings when one of the rings is replaced at rework. The potential savings from bearing rework varies from 53 to 82% that of new bearings depending on the cost, size, and complexity of the bearing.     

Bearing Fatigue Life Tests of Two Advanced Base Oils for Space Applications Under Vacuum and Atmospheric Environments

Four series of rolling-element bearing fatigue tests were conducted with 51104 size thrust ball bearings with three balls made from SUJ2 (AISI 52100) steel lubricated with two advanced synthetic base oils used for space applications. The test lubricants were perfluoropolyether (PFPE) and multiply alkyated cyclopentane (MAC). Each oil was tested with bearings under vacuum and atmospheric environments. The bearings were tested at a maximum Hertzian stress of 4 GPa on the inner and outer races. The outer race was rotated at a speed of 250 rpm. A pool lubrication system was used. Fresh lubricant was used for each test bearing. Testing in vacuum conditions was at 5 × 10^?2 Pa. The test oils were analyzed to determine whether changes occurred as a result of operating in air and in a vacuum. In a vacuum environment, the PFPE 815Z oil exhibited a longer fatigue life than the MAC 2001A oil. However, in an air environment, the MAC 2001A oil had a longer L₁₀ fatigue life than the PFPE 815Z oil. The fatigue life tests of PFPE 815Z oil in vacuum resulted in a longer L₁₀ life than when tested in an air environment. In an air environment, hydrogen fluoride was generated in the bearing tests with the PFPE 815Z oils. Under vacuum conditions, hydrogen fluoride was not generated with the PFPE 815Z oil, resulting in longer bearing fatigue lives. The fatigue life tests of MAC 2001A oil in a vacuum resulted in shorter L₁₀ fatigue life than in an air environment. The shorter life was attributed to the lower elastohydrodynamic oil film formation with the MAC 2001A oil because of a higher operating temperature and decomposition of the oil in vacuum.     

A finite element model for rolling contact fatigue of refurbished bearings

Bearing refurbishing has become a popular method of extending the life of rolling element bearings. In the refurbishing process the raceways of the bearing may be ground to remove any surface damage prior to repolishing and reassembly with larger sized rolling elements. In the current study a continuum damage mechanics finite element model was developed to quantify the damage in original and refurbished bearings. After calculating the damage accumulation for a set number of contact cycles with the original bearing geometry, refurbishing is simulated by removing a layer of the original surface. The refurbished microstructural model is then subjected to additional computational contact cycles until a fatigue crack reaches the surface, signifying failure. This model preserves the fatigue damage accumulated prior to refurbishing and evaluates its influence on the refurbished bearing fatigue life. All refurbished bearing surfaces showed a significant amount of life after refurbishing with L₁₀ lives from the point of refurbishment, varying from 20% to 94% of the original L₁₀ life. The results indicate that the remaining life of the refurbished bearing population is inversely related to the time before refurbishing and is proportional to the depth of the regrinding. Results obtained from this investigation are in good agreement when compared to the Lundberg-Palmgren bearing life equation modified for analyzing the life of a refurbished bearing.     

Multi-Objective Optimization of Grooved Gas Journal Bearings for Robustness in Manufacturing Tolerances

Abstract

A tolerancing method highlighting trade-offs against key design variables of mechanical systems is proposed and applied to herringbone-grooved gas journal bearings. Gas bearings typically suffer from a subsynchronous instability, demanding a very tight tolerance on the bearing clearance and groove depth. Classical optimization techniques look for the most stable design, which does not necessarily lead to most robust design against manufacturing deviations. The proposed method uses a normalized multidimensional lookup table of stability score (critical mass), covering a large design space of gas bearings. It then dimensionalizes the table for a specific rotor–bearing system, highlighting regions of the hyperspace where the system is stable. The hyperspace is sliced into 2D maps and a Monte Carlo method creates windows within the stable domain along the two most critical design variables regarding manufacturing: the bearing clearance and the groove depth. Width and length of the windows represent the manufacturing tolerance allowed for the two parameters to remain stable. A Pareto front of optimum windows in the entire hyperspace is then compiled. It displays the trade-off between the tolerance against deviation in clearance and groove depth, allowing the designer to select a nominal geometry tailored to the available manufacturing methods. A test rotor is analyzed with this method and the effects of pressure, speed, viscosity, radius, mass, and centrifugal growth on manufacturing tolerances are investigated, highlighting that the radius and viscosity have the greatest impact on the robustness.     

Reevaluation of Rolling Element Bearing Load-Life Equation Based on Fatigue Endurance Data

The load-life exponents used in the modified life rating equation for rolling element bearings were determined by statistical analysis of the experimental data generated in the 1940s, following Lundberg and Palmgren's seminal work. Based on fracture mechanics arguments, the fatigue life is known to be inversely proportional to the square root of the size of the nonmetallic inclusions. However, modern high-performance vacuum induction melt–vacuum arc remelt (VIMVAR) bearing steels are clean and nonmetallic inclusions are no longer the weak link. Fatigue life predictions (L₁₀ life) for modern bearings using the modified load-life relations greatly underpredict observed life. Hence, there is a need to update parameters of these equations using more recent life data. Based on the endurance data reported in Harris and McCool (1), validation analysis of the modified life rating equation was performed to reevaluate the values of load-life exponent for both ball and cylindrical roller bearings. The results from this study indicate that the load-life exponent for ball bearings should be 4.1, instead of 3, and for roller bearings it should be 5.5, instead of 3.33. Bearing L₁₀ life calculated using the corrected load-life exponents values shows better agreement with observed life. Details of the sampling technique used for reducing epistemic uncertainty in experimental data and the process of statistical reevaluation using Bayesian updating are discussed in detail. The accuracy of reevaluated results is presented using logarithmic plots of the ratio of predicted to actual fatigue lives for all data samples.     

氮化硅陶瓷滚子轴承的加速寿命试验和断油润滑试验

本文介绍了一次组合陶瓷轴承的加速寿命试验和断油润滑试验,试验轴承是用于某航空发动机主轴前支承的短圆柱滚子轴承,滚动体由氮化硅陶瓷材料制成,套圈和保持架仍采用原钢轴承的套和保持架,试验设备为航空轴承专用试验台,试验表明,试验陶瓷轴承在高速条件下工作寿命和短期油润滑能力均好于同型号钢轴承。     

Evaluating Weibull Endurance Data by the Method of Maximum Likelihood

The method of maximum likelihood has been found to offer many advantages over existing methods for analyzing Weibull distributed rolling bearing fatigue data.

The purpose of this paper is to provide the rolling bearing engineer with what he needs to use the method of maximum likelihood for, 1) Unbiased estimation of Weibull L₁₀ life and shape parameter. 2) Setting confidence limits and testing hypotheses about Weibull L₁₀ life and shape parameter. 3) Unbiased estimation of the ratio of two population L₁₀'s and shape parameters. 4) Testing the significance of differences between two estimates of L₁₀ life or shape parameter.     

Materials in Rolling Element Bearings for Normal and Elevated (450°F) Temperature

The effect of vacuum melting has been under investigation by the author's company for several years. Fatigue testing has been conducted on races and balls in full-sized bearings, so that the results can be interpreted directly into bearing performance.

Studies have been made of both induction and consumable electrode vacuum melted steel. Material inspection has shown a more consistently high level of cleanliness in consumable electrode vacuum steel than that melted by induction.

Improvement in life of bearings made of vacuum melted steels does not appear to be commensurate with the improvement in cleanliness. This is regarded as confirming evidence to a long-held view that cleanliness is not the only factor involved in the fatigue property of steel. Fatigue studies have been made of both 52100 and high temperature steels. Bearing ratings range from 17% less than the AFBMA basic load rating to 23% greater than this rating for vacuum melted 52100 steel. In a test of vacuum melted tool steel (M–1), the bearing load rating was 22% greater than the basic load rating for 52100 steel.

There is no indication that vacuum melting has served to reduce the number of early failures more proportionately. Where there has been a change in life, the curve of bearing lives has been displaced, but retains the same general shape.     

Evaluation of Ion-Sputtered Molybdenum Disulfide Bearings for Spacecraft Gimbals

High-density, sputtered molybdenum disulfide films (MoS₂) were investigated as lubricants for the next generation of spacecraft gimbal bearings where low torque signatures and long life are required. Low friction in a vacuum environment, virtually no out-gassing, insensitivity to low temperature, and radiation resistance of these lubricant films are valued in such applications. One hundred and twenty five thousand hours of accumulated bearing lest time were obtained on 24 pairs of flight-quality bearings ion-sputtered with three types of advanced MoS₂ films. Life tests were conducted in a vacuum over a simulated duty cycle for a space pay bad gimbal. Optimum retainer and ball material composition were investigated. Comparisons were made with test bearings lubricated with liquid space lubricants.

Self-lubricating PTFE retainers were required for long life, i.e., > 40 million gimbal cycles. Bearings with polyimide retainers, silicon nitride ceramic balls, or steel balls sputtered with MoS₂ film suffered early torque failure, irrespective of the type of race-sputtered MoS₂ film. Failure generally resulted from excess film or retainer debris deposited in the ball track which tended to jam the bearing. Both grease lubricated and the better MoS₂ film lubricated bearings produced long lives, although the torque with liquid lubricants was lower and less irregular.     

Stability analysis of orthogonally displaced bearings

Journal bearings operating at high speeds often exhibit vibrational instability. Circular bearings are known to be prone to vibrations and, in general, a non-circular bearing geometry enhances shaft stability. Among the several possible configurations of non-circular bearings, elliptical, offset, three-lobe and tilted three-lobe bearings have attracted attention. The present analysis is a theoretical prediction of stability for a hybrid two-lobe bearing obtained by displacing the lobe centres of an elliptical bearing. It has been found that an orthogonally displaced bearing is more stable than the hitherto known bearings and at the same time it is easier to manufacture. Numerical results have been presented for nine combinations of horizontal and vertical displacements of lobes and three $\text{L}\text{D}$ ratios so that a suitable profile and $\text{L}\text{D}$ ratio can be selected by a designer in a specific application.     

Prognostics Models for Railroad Tapered Roller Bearings with Spall Defects on Inner or Outer Rings

Abstract

Rolling contact fatigue (RCF) is one of the major causes of failure in railroad bearings used in freight service. Subsurface inclusions resulting from impurities in the steel used to fabricate the bearings initiate subsurface fatigue cracks, which propagate upwards and cause spalling of the rolling surfaces. These spalls start small and propagate as continued operation induces additional crack formation and spalling. Studies have shown that the bearing temperature is not a good indicator of spall initiation. In many instances, the temperature of the bearing increases markedly only when the spall has spread across major portions of the raceway. In contrast, vibration signatures can be used to accurately detect spall initiation within a bearing and can track spall deterioration. No monitoring technique can indicate the growth rate of a spall or determine residual useful life. Hence, the main objective of this study is to develop reliable prognostic models for spall growth within railroad bearings that are based on actual service life testing rather than theoretical simulations. The data used to devise the models presented here were acquired from laboratory and field testing that started in 2010. Growth models are provided for spalls initiating on the bearing inner (cone) and outer (cup) rings. Coupling these prognostic models with a previously developed vibration-based bearing condition monitoring algorithm will provide the rail industry with an efficient tool that can be used to plan proactive maintenance schedules that will mitigate unnecessary and costly train stoppages and delays and will prevent catastrophic derailments.     

Research and Development of Materials for Use As Lubricants in a Liquid Hydrogen Environment

A program was conducted to evaluate materials that could be used as lubricants in rolling-contact bearings operating in a liquid hydrogen environment at DN values up to 4 million mm-rpm. A unique ball and plate test apparatus was used to test twenty candidate lubricant materials selected for screening in the initial phase of the program. The ball-plate tester eliminated the use of test bearings in the initial material screening phase where the important factor was to evaluate the lubricants and bearing materials without the confounding effect of other bearing parameters. No tests were conducted in a nuclear radiation field; however, consideration was given to such an environment in the selection of the candidate materials.

The lubricant investigation described herein resulted in the selection of four materials, bronze-filled fluorocarbon, bronze-filled polyimide, Ag-WSe₂-polyimide and Ag-MoS₂, for further evaluation in actual bearing tests. These materials show promise of providing a significant increase in bearing life when operating in a liquid hydrogen environment.     

空间相机扫描机构固体润滑轴承组件的寿命试验

开展了固体润滑轴承组件的真空加速寿命试验,以验证固体润滑轴承组件的设计是否满足在轨寿命要求。研究了MoS2基薄膜固体润滑轴承组件在小角度摆动情况下的寿命。试验采用4对轴承模拟在轨±6°连续往复摆动,通过检测轴承组件工作时的摩擦力矩、电机电流和轴承温升判断轴承运行状态。结果显示,寿命试验运行正常,累计摩擦次数为6.2×10~7次。寿命试验后对轴承进行了尺寸精度和旋转精度复测,然后对轴承组件进行了解剖分析。复测结果显示,轴承尺寸精度和旋转精度与试验前一致,轴承润滑状态良好。试验结果验证了固体润滑轴承组件寿命满足在轨任务要求,为其它空间相机小角度摆动的扫描机构固体润滑轴承组件的长寿命设计提供了依据。     

高速列车轴承可靠性试验时间的确定及可靠性寿命评估

受产品成本和试验时间的限制,高速列车轴承可靠性试验一般采用小样本、定时截尾试验方案。在此情况下,如何确定出可靠性试验时间和对轴承的可靠性寿命进行分析是值得深入研究的问题。从轴承疲劳寿命服从的分布入手,推导出高速列车轴承样本数和试验时间的数学模型,采用Bayes多层估计法对无失效试验数据进行了处理,建立起高速列车轴承的可靠性寿命评估模型,并以国产高速列车轴承为例给出仿真计算结果。     

In Situ Growth of Graphene on Carbon Fabrics with Enhanced Mechanical and Thermal Properties for Tribological Applications of Carbon Fabric–Phenolic Composites

ABSTRACT

Though the premature failures of wind turbine gearboxes are often attributed to bearing fatigue from overloading, there is compelling evidence that wear from underloading is a significant contributor. Here we attempt to gain insight into the relative contributions of over- and underloading by assessing planet bearing reaction forces from the Gearbox Reliability Collaborative (GRC) standard gearbox within a typical utility-scale wind turbine under realistic conditions. The results demonstrate that non-torque load sharing by the planetary stage increases and decreases planet bearing reaction forces at different locations within each rotor cycle regardless of wind speed. Planet bearing reaction forces exceeded the fatigue limit at wind speeds above 12 m/s and fell below the minimum load rating at wind speeds below 7 m/s. Based on analyses of published wind spectra from 10 U.S. sites, the expected fatigue life of the planet bearings ranged from 42 to 529 years even after accounting for non-torque load sharing. At the same 10 sites, planet bearings were underloaded (below 2% of the dynamic load rating) once per rotor cycle 40–70% of the time. Underloaded bearings are susceptible to surface damage when suddenly exposed to common transient events, such as yaw, wind gusts, braking, and grid faults. The resulting surface damage can initiate premature failure via wear (e.g., micropitting) or by reducing bearing fatigue life. The results suggest that carrier bearing clearance, non-torque load sharing, and planet bearing underloading are significant contributors to the premature failures of wind turbine planet bearings.     

Laboratory Experience with Long-Term Bearing Lubrication

This paper presents the results of laboratory testing of several types of size-204 ball bearings. Three of these bearings had lubricant compact ball separators; three other types of conventional bearings were operated without applied lubrication in the form of oils, greases, or dry powders. Bearing performance was judged from friction and wear life results.

Bearings with lubricant compact separators have operated for periods as long as 38,000 hours without failure in a vacuum environment of less than 3 × 10^?6 torr. The test conditions included 1,790-r pm rotational speeds, no applied heat, and a nominal axial load of seven pounds. Based on rate of weight loss, predictions were made on the expected wear lives of the bearings.

Conventional bearings, using three different ball separator designs, were subjected to the same test conditions (in vacuum) as the lubricant compact separator bearings, as well as to similar conditions in an air environment. Average wear lives are reported for the three types of bearings operating in air and for two of these operating in vacuum. The third type of bearing continues to operate in vacuum and a life prediction is made based upon the wear rate of another specimen.     

A novel reliability evaluation method on censored data

The effect of censored data on the average life of products was analyzed, and the relationships between the censored data and the reliability evaluation results were also given. A series of regression analysis function relationship was built to simplify the method of reliability evaluation on censored data. At a first step, a numerical simulation method was designed to create the random right censored data. Then the Bayesian and Markov chain Monte Carlo (MCMC) method was adopted to evaluate the reliability. Then we got the calculation deviation of Bayesian method under different sample sizes, different censored rates and different means of censored data. The relationships between the censored rates, the means of censored distribution and the reliability evaluation result were analyzed. Finally, we proposed the complete novel method through regression analysis. The corroboration of these relationships and the application to real life data demonstrate the advantages of the proposed methods.     

Optimizing the Design of Cluster Mill Rolling Bearings

The design of back-up roll bearings in cluster-type rolling mills has, historically, been dictated by past engineering trial and error experience. Thus, to cause the bearings to act, as nearly as practicable, similarly to conventionally supported bearings, the outer ring section is usually made very heavy precluding large ring deflections.

There exists controversy among bearing manufacturers as to whether a bearing having many rollers of small diameter or one having a smaller number of larger rollers is best in this application. The study herein presented examines bearing life under each condition while fully accounting for the effect of outer ring deflection on fatigue life.

The investigation further demonstrates that an optimum design with regard to outer ring section thickness in relation to diametral size and number of rollers per row does exist with respect to bearing fatigue life. Whether such design is compatible with possible outer ring destruction due to heavy roll loads can only be proved by on-site testing.