Reliability-based design optimization of slider air bearings

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO’s results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.     

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.     

The Application of Nearly Embarrassingly Parallel Computation in the Optimization of Fluid-Film Lubrication©

The combination of powerful, yet inexpensive PCs and readily available open sources for parallel computation marks a new era of easy access to massive computation for the tribology community. The study demonstrates the applicability of embarrassingly parallel computation in the optimization of air-lubricated porous bearings with four design variables. To achieve high speedup without increasing the coding complexity, the master computer implements the lattice method to allocate the near-the-same computational load in the master-slave cluster. The effect of master capability on the cluster performance is also presented. The results are compared with that of an unparallelized simplex method and indicate a significant reduction in execution time due to parallelism. In a simulated analysis, a high speedup can also be obtained in dealing with a problem with many design variables. This study provides the framework for optimization of applications with complex tribological models to be solved with minimum execution time.     

The Performance of a Hybrid Ceramic Ball Bearing Under High Speed Conditions with the Under-Race Lubrication Method

Large bore (150 mm) hybrid ceramic ball bearings and all-M50 steel bearings were tested with under-race lubrication to compare the heat generation and the temperature rise at speeds up to 2.25 million DN. Furthermore, oil shut-off tests were carried out with both bearings over 2.25 million DN.

The experimental results of the heat generation for both bearings were nearly the same at an axial load of 19.6 kN. at 34.3 kN, the heat generation of the hybrid bearing was lower than that of the M50 steel bearing at low speed. The heat generation of both bearings gradually approached each other with increasing speed and became nearly equal at a speed of 15,000 rpm. The survivability of the hybrid bearing in the oil shut-off test was superior to that of the M50 bearing. These experimental results were explained by the calculation results using a computer analysis software which simulates the kinematics and the performance of ball bearings.     

Optimum design of externally pressurized air bearing using Cluster OpenMP

This study presents a performance evaluation of a new portable parallel programming paradigm, the Cluster OpenMP (CLOMP) for distributed computing, in conducting an optimum design of air bearings. The multi-objective optimization was carried out by using a genetic algorithm (GA) incorporating Pareto optimality criterion. Since the GA is natural parallel evolution algorithm, the computation of the search was carried out in parallel by using the CLOMP. In this study, the performance of a CLOMP cluster of four dual-core computers for the air bearing optimization was compared with a shared-memory processing (SMP) computer equipped with two quad-core processors. To examine the parallel efficiency of the CLOMP in the GA optimization, several multithread applications of various task sizes were tested. It is shown that the air bearing optimization can be effectively dealt with by the CLOMP (parallel efficiency of 96.2-98.8%) as well as the SMP computing (93.1-99.4%) in the studied cases. The CLOMP retains the characteristics of directive-based OpenMP, such as incremental programming and serial-coding compatibility. The verified high parallel efficiency of the CLOMP cluster demonstrates its potential applications of the scalable computing in many tribological optimizations.     

A Simulated Air Bearing Analysis by Design of Experiments and Its Applications in Optimization

This study presents an air-bearing design procedure by using Taguchi's Design of Experiments (TDE) to simulate the analysis of systems without adequate models. Instead of taking data from experiments, the performance of air bearings is obtained by an empirical verified numerical model. This arrangement eliminates the errors inevitably introduced in tests. When comparing with full factorial analysis, the number of tests is significantly reduced by using TDE in the demonstrated study. The optimum set of the variables predicted by TDE is numerically verified in the cases investigated. The analysis of orthogonal arrays consisting of three levels shows better performance prediction than the two levels analysis. The straightforward and easy to use procedure can be applied conjunction with numerical optimization technique to give an excellent start-point to minimize search time in a multi-variable design as illustrated in this report.     

An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearings

This study deals with the development of a computational procedure for solving the isothermal compressible Reynolds equation as the governing equation of air-bearing analysis. Newton's method is used to linearize Reynolds equation and an iterative successive relaxation process is adopted to solve for the air film pressure. The optimal value of relaxation factor for the cases studied is suggested in this report for numerical stability and computational efficiency. The model is verified numerically by examining the conservation of mass flow of the lubricant. The dimensional analysis of the governing equation permits the model to be readily applied to any given film geometry.

The computer model developed can evaluate the air film pressure distribution, load capacity, frictional force, and mass flow of an air bearing. The proposed computational scheme efficiently analyzes the performance of air-lubricated journal bearings at large eccentricity ratios. A similar procedure can be employed to investigate the performance of highspeed noncircular air bearing or gas-lubrication film under slip-flow conditions. This study gives an analytical basis for the design of orifice-compensated externally pressurized air-lubricated bearing.     

Experimental study of porous foil bearings for web-handling

In this paper, new type of hybrid porous foil bearings for web-handling is presented, in which the traveling web is supported by the externally pressurized porous foil bearings with the hybrid effects of hydrodynamic pressure, due to web movements, and hydrostatic pressure, due to pressurized, added flow through the hollow porous shaft. The relations between web spacing height (air film thickness) and web traveling velocity are measured under various supply pressures. Moreover, the relations between web spacing height and web tension are examined. From these measured relations, the hybrid effects of porous foil bearing on the web spacing height characteristics are clarified experimentally, and it is concluded that the hybrid porous foil bearings presented here have an advantage of controlling the web spacing height to keep suitable web-handling conditions.     

Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems.     

气体静压小孔节流与多孔质节流性能的比较

本文给出了传统的小孔节流和多孔质节流轴承的理论分析，分析了外部供压气体轴承的进气形式对轴承性能的影响，对于不同类型的小孔节流和多孔质节流的轴承，本文给出了实验结果，并对轴承的性能参数即承载能力，刚度等进行了比较，作者分析了小孔节流和多孔节流止推轴承的承载能力和刚度，结果表明多孔质止推轴承同小孔节流轴承相比，具有高的承载能力。     

Air Injection as a Thermal Management Technique for Radial Foil Air Bearings

A thermal management technique for radial foil air bearings was experimentally evaluated. The technique is based on injecting air directly into the internal circulating fluid-film to reduce bulk temperatures and axial thermal gradients. The tests were performed on a single top foil, Generation III, radial foil bearing instrumented with three thermocouples to monitor internal temperatures. A through hole in the bearing shell coincident with the gap between the top foil's fixed and free ends provided entry for the injection air. The tests were conducted at room temperature with the bearing operating at speeds from 20 to 40 krpm while supporting 222 N. Two different mass flow rates of injection air were evaluated for this method, 0.017 and 0.051 kg/min. Test results suggest that the air injection approach is a viable thermal management technique capable of controlling bulk temperatures and axial thermal gradients in radial foil air bearings.     

间歇过程PSO SQP混合优化算法研究*

针对SQP算法在求解具有复杂约束的间歇过程优化时容易陷入局部极值点的问题,本文提出一种PSO-SQP混合优化算法。该算法首先采用外点罚函数法将间歇过程有约束的优化问题转换为无约束的优化问题,利用PSO强大的全局搜索能力对其进行求解,并把搜索结果作为SQP搜索初始点,以此弥补SQP全局搜索弱的缺点,再利用SQP良好的局部收敛性和较强的非线性收敛速度对原优化问题进行精细搜索,弥补了PSO局部搜索弱的缺点,通过不断的迭代最终获得优化问题的全局最优解。该算法充分利用了SQP和PSO的优缺点,增强了其对复杂约束优化问题的求解能力。将本文提出的算法用于连续搅拌化学反应系统温度控制中,仿真结果表明产物浓度能够充分逼近期望值,且反应器的温度轨迹收敛,从而验证了该算法的有效性和实用价值。     

On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal

Foil gas bearings have been applied successfully to a wide range of high-speed rotating machinery such as air cycle machines (ACMs) and auxiliary power units (APUs). The performance of these bearings are based on the high pressure gas in a very thin layer between the journal and the bearing governed by the Reynolds equations. Generation of heat in these bearings especially at high journal rotating speed and high loads or at high ambient temperature directly affect their performance. Thermal and fluid flow analysis of an advanced compliant foil journal bearing/seal are presented. The side flow (known as leakage) and the approximate temperatures are the results of this analysis. The result of preliminary analysis shows that the major portion of the heat is carried through conduction and using the modified Couette flow approximation for the present working fluid, air, helped in analysis of the temperature magnitude, which can be related to the gas viscosity behavior and thin gas film thicknesses.     

A Divide-and-Conquer Parallel Computing Scheme for the Optimization Analysis of Tribological Systems

The trend of using commercial products and open source packages to construct a scalable computer cluster for distributed computing to minimize the execution time of numerical optimization has long been expected. However, in the tribology field progress has been slow due to the complexity of parallel coding and the lack of easy-to-implement parallel algorithms. This study presents an optimization analysis of constrained problems by using a divide-and-conquer scheme suitable for parallel computation. A porous air bearing model of moderate computational load is used to illustrate the optimization procedure. In the optimization process, the design space is subdivided and each of the subdivisions is dealt with by Taguchi's Design of Experiments to achieve the local optimum. The global optimum is then determined when all the local optima are obtained. Two task-assignment strategies in the cluster computing are implemented and discussed. Reasonable speedup and parallel efficiency were obtained for the highly uneven task-load calculations. The approach does not require the knowledge of parallel programming techniques associated with message passing libraries. The presented scheme has high portability, low cost of evaluation process, and algorithm-machine scalability, which should be an easy-to-implement and efficient tool for many tribological studies.     

Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery

The performance and durability of advanced, high temperature foil air bearings are evaluated under a wide range (10 to 50 kPa) of loads at temperatures from 25° to 650 °C. The bearings are made from uncoated nickel based superalloy foils. The foil surface experiences sliding contact with the shaft during initial start/stop operation. To reduce friction and wear, the solid lubricant coating, PS304, is applied to the shaft by plasma spraying. PS304 is a NiCr based Cr₂O₃ coating with silver and barium fluoride/calcium fluoride solid lubricant additions.

The results show that the bearings provide lives well in excess of 30,000 cycles under all of the conditions tested. Several bearings exhibited lives in excess of 100,000 cycles. Wear is a linear function of the bearing load. The excellent performance measured in this study suggests that these bearings and the PS304 coating are well suited for advanced high temperature, oil-free turbomachinery applications.     

Performance analysis of Pareto optimal bearings subject to surface error variations

A Pareto optimization study was carried out on a flat pad aerostatic bearing design. Some of the Pareto optimal configurations were then subjected to surface profiling errors including tilt, concavity, convexity and waviness and key performance parameters such as load capacity, stiffness and flow rate determined. From these studies it was concluded that multi-orifice aerostatic flat pad bearings are highly sensitive to surface profile variations and these surface profile variations are inherent limitations of the current manufacturing techniques. A technique to account for the sensitivity to manufacturing tolerance within air bearing optimization studies is also proposed.     

多孔质气体静压径向轴承倾斜状态特性研究

为研究倾斜状态对多孔质气体静压轴承性能的影响,基于一维流动模型应用有限元方法对多孔质气体静压轴承进行数值分析,研究渗透率、初始偏心距、倾斜角度等重要因素对多孔质径向轴承承载能力和弯矩的影响。结果显示:轴承初始偏心距对轴承承载能力影响很大;在相同初始偏心距时,倾斜状态下的径向轴承承载能力随着轴承倾角的增大而增大;在相同倾斜角度时,径向轴承承载能力分别随着轴承初始偏心距和轴承渗透率的增大而增大,并且初始偏心距越大,渗透率对承载能力的影响越大。     

Oil Exchange between Ball Bearings and Porous Polyimide Ball Bearing Retainers

The kinetics of the absorption of lubricating oils and moisture from air into porous polyimide, as well as the exchange of oil between porous polyimide retainers and oil baths or operating bearings, have been measured. Oil absorption into porous polyimide is much faster than into cotton-phenotic. Water is absorbed by oil-impregnated polyimide, but little or no oil is lost during the process. Oil is absorbed by air-equilibrated polyimide at a slower rate than by dry polyimide. Porous polyimide is much easier to impregnate with oil than cotton-phenolic, and is also much more tolerant, of storage in air once impregnated. Oil within a porous polyimide ball bearing retainer exchanges slowly with oil in a bath in which the retainer is placed. The exchange is due to diffusion of the oils, and the diffusion coefficient is determined to be 3 × 10^?9 cm²/s for the oils used in these experiments. Oil is exchanged quickly between polyimide retainers and well-lubricated operating bearings. The exchange is faster than a diffusion process, and is probably driven by bearing action. In these experiments, the authors could detect no net gain or loss of oil from the retainer or the bearing parts. Only about one-half of the oil originally supplied to the parts is available to the retainer; the rest remains elsewhere in the bearing.     

Current Status of Hybrid Bearing Damage Detection

Advances in material development and processing have led to the introduction of ceramic hybrid bearings for many applications. The introduction of silicon nitride hybrid bearings into the high-pressure oxidizer turbopump on the space shuttle main engine led NASA to solve a highly persistent and troublesome bearing problem. Hybrid bearings consist of ceramic balls and steel races. The majority of hybrid bearings utilize Si₃N₄ balls. The aerospace industry is currently studying the use of hybrid bearings and, naturally, the failure modes of these bearings become an issue in light of the limited data available.

In today's turbine engines and helicopter transmissions, the health of the bearings is detected by the properties of the debris found in the lubrication line when damage begins to occur. Current oil debris sensor technology relies on the magnetic properties of the debris to detect damage. Because the ceramic rolling elements of hybrid bearings have no metallic properties, a new sensing system must be developed to indicate the system health if ceramic components are to be safely implemented in aerospace applications. The ceramic oil debris sensor must be capable of detecting ceramic and metallic component damage with sufficient reliability and forewarning to prevent a catastrophic failure.

The objective of this research is to provide a background summary on what is currently known about hybrid bearing failure modes and to report preliminary results on the detection of silicon nitride debris in oil using a commercial particle counter.     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.