Nenzi Wang

Engineering Optimum Design of Fluid-Film Lubricated Bearings

This study presents an engineering approach for optimizing performance of fluid-film lubricated bearings. Unconstrained nonlinear programming methods, lattice search and simplex method, were used as the optimization schemes to improve the merit of studied bearings with two or more design variables. The analysis of elliptical bearings shows high eccentricity ratio and two large pressure zones for high-speed stability can be obtained by maximizing film pressures in the upper and lower lobes. In this study, lattice method exhibits slightly more efficient search compared with that of simplex method in several two-variable optimum designs. The automatic mesh generation technique used in the pocket-shaped bearing analysis makes the numerical optimization as a flexible design tool. The effect of side flow restrictions on the load-carrying capacity of an optimized pocket-shaped slider bearing is clearly verified. The analysis of the aerostatic bearing explains an example of multi-objective minimization. A similar procedure can be easily adopted to analyze bearings with other profiles, or to maximize user-defined performance using more complicated models. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

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. Newtons 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 per...

A parametric study of an open-source distributed computing environment for tribological studies

A parametric study of a single system image cluster is presented for parallel computing applications in the tribology field. The trend to use a cluster to solve computationally intensive tasks is emerging for high performance/cost ratio, scalability, and freely available open source. At the present time such a system is very easy to construct and to maintain for cluster computing. An air-bearing model with four design variables was used for simulating light to moderate and variable computational loads. The factors considered in this parametric study are network connecting speed, master node capability, and computing task size. The subjects of the task allocation method and task load balancing are also discussed to elaborate the characteristics of the cluster. Although computational problems in the tribology field are diversified in every aspect, the parametric survey can assist in the construction of a cluster as well as the selection of suitable parallel algorithms for computationally intensive simulations.

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 Taguchis 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.

Comparison of Iterative Methods for the Solution of Compressible-Fluid Reynolds Equation

This study presents an efficacy comparison of iterative solution methods for solving the compressible-fluid Reynolds equation in modeling air- or gas-lubricated bearings. A direct fixed-point iterative (DFI) method and Newtons method are employed to transform the Reynolds equation in a form that can be solved iteratively. The iterative solution methods examined are the Gauss-Seidel method, the successive over-relaxation (SOR) method, the preconditioned conjugate gradient (PCG) method, and the multigrid method. The overall solution time is affected by both the transformation method and the iterative method applied. In this study, Newtons method shows its effectiveness over the straightforward DFI method when the same iterative method is used. It is demonstrated that the use of an optimal relaxation factor is of vital importance for the efficiency of the SOR method. The multigrid method is an order faster than the PCG and optimal SOR methods. Also, the multigrid and PCG methods involve an extended coding work and are less flexible in dealing with gridwork and boundary conditions. Consequently, a compromise has to be made in terms of ease of use as well as programming effort for the solution of the compressible-fluid Reynolds equation.

A Hybrid Search Algorithm for Porous Air Bearings Optimization

The study deals with the development of a hybrid search algorithm for efficient optimization of porous air bearings. Both the compressible Reynolds equation and Darcys law are linearized and solved iteratively by a successive-over-relaxation method for modeling parallel-surface porous bearings. Three factors affecting the computational efficiency of the numerical model are highlighted and discussed. The hybrid optimization is performed by adopting genetic algorithm (GA) for initial search and accelerated by simplex method (SM) for refined solution. A simple and useful variable transformation is presented and used to convert the unconstrained SM to a constrained method. In this study, the hybrid search algorithm for a multi-variable design exhibits better efficiency compared with the search efficiency by using the SM. The proposed hybrid method also eliminates the need of several trials with random initial guesses to ensure high probability of global optimization. This study presents a new approach for optimizing the performance of porous air bearings and other tribological components. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

Exploration on a Fast EHL Computing Technology for Analyzing Journal Bearings with Engineered Surface Textures

Solving elastohydrodynamic lubrication (EHL) problems is a complex and time-consuming process due to the interactive solutions of the Reynolds equation and contact elasticity. Analyzing journal bearing EHL problems is even more difficult due to the scale difference in the structural and surface features, which may span four orders of magnitude. This article presents a fast EHL computing technology utilizing a parallel numerical iterative method (the red–black successive overrelaxation method) and multithreaded computing scheme conducted by OpenMP directives. The fast computational approaches allow the construction of high-density EHL meshes for effective descriptions of important texture features of journal bearing surfaces.

Effects of Shaft Axial Motion and Misalignment on the Lubrication Performance of Journal Bearings Via a Fast Mixed EHL Computing Technology

A mixed elastohydrodrynamic (EHL) model for journal bearings considering an axial flow due to shaft axial motion and misalignment is developed for lubrication performance evaluation. A new, faster mixed EHL computing technology utilizing the odd–even successive overrelaxation (OESOR) parallel numerical iterative method is proposed based on the red–black successive overrelaxation (RBSOR) method to minimize the execution time prolonged by the complexity caused by the axial flow and misalignments. The multithreaded computing scheme conducted by the OpenMP directive using different meshes and threads suggests that the OESOR method exhibits better efficiency. A series of transient analyses was conducted to solve the mixed EHL model with the parallel OESOR method. The results show that the axial flow and misalignments significantly affect the average pressure, hydrodynamic and asperity contact pressure, elastic deformation, and other characteristics of the journal bearings.

Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Iterative solution methods are usually used for solving a variety of Reynolds equations in lubrication analysis due to their simplicity and effectiveness. The objective of this study is to present a robust stopping criterion for iterative methods, by which the iterative process of the methods can be terminated for high execution efficiency without sacrificing the solution accuracy. In this study, the compressible and incompressible fluid Reynolds equations are solved by popular relaxation methods. A very efficient preconditioned conjugate gradient method is also applied in a case for verification. The proposed stopping criterion for iterative methods is based on a coarse-grid truncation error analysis. Three different gridwork groups are required for estimating the truncation errors, which involves only a small amount of additional execution time. In the numerical models examined, the amount of truncation error in a model is insensitive to the gridwork used. It is also found that in a calculation the best prediction of truncation error for terminating the iteration is obtained by using the average fluid film pressure. It is shown that for all the cases tested the proposed stopping criterion can meet the objective stated. The stopping criterion can also be applied when the efficiency of iterative methods is to be compared in solving Reynolds equations.

Parallel Optimum Design of Foil Bearing Using Particle Swarm Optimization Method

Numerical optimization of tribological elements usually demands extended computations. The particle swarm optimization (PSO) method is known for its simple implementation and high efficiency in solving multifactor optimization problems. In this study, several parallel computing schemes using PSO for air foil bearing design are compared. The parallel programming models applied are multicore computing by OpenMP and many-core graphics processing unit (GPU) computing using Compute Unified Device Architecture (CUDA) and OpenACC. The best case was obtained when the OpenMP coding was applied at the algorithm level of optimization. The performance of CUDA was found to be compatible with OpenMP when parallel computing was used to solve the bearing model. Due to excess data communications computing using OpenACC was significantly slower than the other approaches. The parallel computing scheme recommended in this study is independent of PSO, which is applicable to tribological studies requiring global optimization analysis.