Kuo-Chiang Cha

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

Comparisons of contact pressures of crowned rollers

Abstract The present work determines the contact pressure and stress concentration between the crowned roller and the raceway by using three-dimensional finite element analysis. A number of crowned profiles with various dimensions were examined. Fine meshes and node-to-Hermit-surface contact elements were used along the contact surface in order to obtain accurate analysis results. A table was generated to show the stress concentration near the roller edge for various crowned profiles and dimensions. This table indicates that the exponential profile is the optimal crowned profile to eliminate stress concentration.

A Deformation Formula for Circular Crowned Roller Compressed Between Two Flat Plates

The main purpose of this paper is to develop a deformation equation for the circular crowned roller compressed between two plates. First, the roller is divided into three parts, two crowned parts and one cylindrical part. The superposition method is then introduced to obtain the roller stiffness. The stiffness contribution of the crowned parts is calculated by the classical Hertzian contact solution and the stiffness contribution of the noncrowned part is obtained by the Hoeprichs formula. Comparisons with various finite element results indicate that the deformation equation derived in this paper can be a good deformation formula for the circular crowned roller.

Evaluating stress intensity factors of a surface crack in lubricated rolling contacts

The three-dimensional finite element method and the least-squares method were used to find the stress intensity factors (SIFs) of a surface crack in a lubricated roller. A steel roller on a rigid plane was modeled, in which a semi-elliptical surface crack is inclined at an angle ψ to the vertical axis. A distance c is set between the crack base and the roller edge. The results indicate that the mode-I SIF reaches the maximum value when the angle θ is equal to 0° (on the roller surface), and the mode-II SIF reaches the absolute maximum value when the angle θ is near or equal to 90° (inside the roller), where θ is the angle of the semi-ellipse from 0° to 180°. The influence of mode-III SIFs in this model is minor since they are much smaller than the mode-I and mode-II SIFs. The SIFs increase greatly when the crack location approaches the uncrowned edge. At this time, a crowned profile can be used to significantly reduce the SIFs near the roller edge.

A Study of Parallel Efficiency of Modified Direct Algorithm Applied to Thermohydrodynamic Lubrication

This study examines the parallel computing as a means to minimize the execution time in the optimization applied to thermohydrodynamic (THD) lubrication. The objective of the optimization is to maximize the load capacity of a slider bearing with two design variables. A global optimization method, DIviding RECTangle (DIRECT) algorithm, is used. The first approach was to apply the parallel computing within the THD model in a shared-memory processing (SMP) environment to examine the parallel efficiency of fine-grain computation. Next, a distributed parallel computing in the search level was conducted by use of the standard DIRECT algorithm. Then, the algorithm is modified to provide a version suitable for effective parallel computing. In the latter coarse-grain computation the speedups obtained by the DIRECT algorithms are compared with some previous studies using other parallel optimization methods. In the fine-grain computation of the SMP machine, the communication and overhead time costs prohibit high speedup in the cases of four or more simultaneous threads. It is found that the standard DIRECT algorithm is an efficient sequential but less parallel-computing-friendly method. When the modified algorithm is used in the slider bearing optimization, a parallel efficiency of 96.3% is obtained in the 16-computing-node cluster. This study presents the modified DIRECT algorithm, an efficient parallel search method, for general engineering optimization problems.

Workstation Computing of Discretized Reynolds Equations

In this study, the solution methods suitable for use in a workstation to solve the discretized incompressible and compressible fluid Reynolds equations are examined. The workstation used for computing consists of dual six-core central processing units (CPUs) and a 256-core graphics processing unit (GPU) dedicated for computing. To compare the computational performance, the Reynolds equations are solved by a parallel iterative method using multithreaded and GPU computing. Multithreaded computing is conducted by OpenMP directives and GPU computing is executed using either NVIDIAs compute unified device architecture (CUDA) programming or the accelerator programming model (APM). The lubrication models used are an inclined surface slider with or without a central recess and an air journal bearing. In GPU computing, both the CUDA and APM are subjected to communication latency to achieve efficient fine-grained computations. The results show that the performance of the less expensive GPU computing is close to that of multithreaded computing in which the grid sizes are large in the analyses. The performance of the OpenMP-like APM programming is compatible with CUDA computing in the slider cases but is significantly worse for air bearings. This study illustrates the workstation computing for lubrication analyses in which the computing devices can be multi-core CPUs or many-core GPUs.

Applications of Unconstrained Minimization Methods to the Dynamic Analysis of Air-Lubricated Bearings

This study deals with the procedure to estimate the stiffness and damping of air-lubricated bearings under dynamic conditions. Unconstrained minimization methods were used in the nonlinear least squares (NLS) analysis to obtain the dynamic parameters of simulated noisy data with small signal-to-noise ratios (SNR). In the analysis the contaminating noise, either uniform or normally distributed noise, was scaled to give a known SNR and added to a simulated noise-free data. Even with poor initial-guess in the NLS as demonstrated in this study, both simplex and Powells methods reach minimal variance with far fewer searching steps than those of the lattice and Hookes methods. In the example of experimental study, the effect of an arbitrary data truncation point on the parameter estimation can be minimized in the fitting process by adding additional parameter-phase angle. The result shows good agreement between experimentally determined stiffness and theoretical prediction. This study provides a general procedure for dynamic analysis of air-lubricated bearings from noisy experimental measurements. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Seattle, Washington, October 1–4, 2000

Dynamics and Cutting Stability of Dynamically Loaded Worktable Subjected to Elastic Supports

This paper investigated the dynamic characteristics and the cutting stability of a dynamically loaded worktable on elastic supports in a surface grinder. The operation of worktables is usually dynamically loaded in various positions, which results in a complex system of governing equations. In this study, the assumptions of elastic and rigid body modes of a free-free beam were specified in analyzing the worktable. By combining the Lagrange energy method with the technique of assumed mode expansion, the system of equations was developed. The absolute value of the maximum negative real part of the overall dynamic compliance (MNRPODC) and the limiting chip width were used as the performance indicators to evaluate the structural characteristics of the worktable during simulated machining. The 3D stability lobe diagram was then computed. The cutting stability was verified by comparing the results obtained in time-domain analysis with the lobe diagram. The procedure presented in this study to improve the dynamics performance of a surface grinder can also be implemented in a similar fashion for many other machine tool applications.