Shangwu Xiong

Steady-State Hydrodynamic Lubrication Modeled With the Payvar-Salant Mass Conservation Model

Steady-state smooth surface hydrodynamic lubrications of a pocketed pad bearing, an angularly grooved thrust bearing, and a plain journal bearing are simulated with the mass-conservation model proposed by Payvar and Salant. Three different finite difference schemes, i.e., the harmonic mean scheme, arithmetic mean scheme, and middle point scheme, of the interfacial diffusion coefficients for the Poiseuille terms are investigated by using a uniform and nonuniform set of meshes. The research suggests that for the problems with continuous film thickness and pressure distributions, the results obtained with these numerical schemes generally well agree with those found in the literatures. However, if the film thickness is discontinuous while the pressure is continuous, there may be an obvious deviation. Compared with both the analytical solution and other two schemes, the harmonic mean scheme may overestimate or underestimate the pressure. In order to overcome this problem artificial nodes should be inserted along the wall of the bearings where discontinuous film thickness appears. Moreover, the computation efficiency of the three solvers, i.e., the direct solver, the line-by-line the tridiagonal matrix algorithm (TDMA) solver, and the global successive over-relaxation (SOR) solver, are investigated. The results indicate that the direct solver has the best computational efficiency for a small-scale lubrication problem (around 40 thousand nodes). TDMA solver is more robust and requires the least storage, but the SOR solver may work faster than TDMA solver for thrust bearing lubrication problems. Numerical simulations of a group of grooved thrust bearings were conducted for the cases of different outer and inner radii, groove depth and width, velocity, viscosity, and reference film thickness. A curve fitting formula has been obtained from the numerical results to express the correlation of load, maximum pressure, and friction of an angularly grooved thrust bearing in lubrication.

An Efficient Elastic Displacement Analysis Procedure for Simulating Transient Conformal-Contact Elastohydrodynamic Lubrication Systems

A compliance operator is often utilized to evaluate the elastic displacement of surfaces in the simulation of transient and steady-state elastohydrodynamic lubrication of conformal-contact systems. The values of the compliance operator represent the elastic responses of all nodes when only one node is under a unit load. The accuracy of compliance operator values, computational cost, and storage size are important issues. Our study of steady-state conformal-contact elastohydrodynamic lubrication analyses suggests a method of selective-fine-mesh with selective-storage, as well as a special technique of the combined selective-fine-mesh with selective-storage mapping. These two techniques enable an efficient elasticity procedure for the simulation of steady-state and transient conformal-contact elastohydrodynamic lubrication systems by means of the finite element method.

Approaching Mixed Elastohydrodynamic Lubrication of Smooth Journal-Bearing Systems with Low Rotating Speed

When a conformal interface is under low velocity and heavy load conditions, solid contact (or dry contact) may occur even in a system with smooth surfaces. This paper presents two approaches for solving steady-state and transient mixed elastohydrodynamic lubrication problems of journal bearings with smooth surfaces under low rotating speed. The first approach uses the reduced Reynolds equation with a combined finite element–backward finite difference scheme and the second applies a zero film thickness equation to describe the mechanical behavior of mating surfaces at solid contact points. The major advantages of these two approaches are (1) no division of the solution domain into a lubricated area and a solid contact area is necessary and (2) the solid contact pressure, lubricant pressure, and eccentricity ratio can be solved simultaneously. Numerical examples are presented for the application of these approaches. For the steady-state cases under low velocity studied in this work, pressure distributions approach those found in a dry contact state. This comparison confirms that the contact treatments are proper. Moreover, a transient case under sinusoidal loading was analyzed with these two approaches, and the results showed good agreement. This comparison further supports the use of these approaches. Presented at the STLE Annual Meeting in Las Vegas, Nevada May 15-19, 2005 Review led by Alan Lebeck

Numerical simulation of three‐dimensional steady‐state rolling by the reproducing kernel particle method

This paper presents a numerical approach for analysing three‐dimensional steady‐state rolling by means of the reproducing kernel particle method (RKPM). The approach is based on the flow formulation for slightly compressible materials and a detailed description of RKPM and its numerical implementation is presented with the objective of providing the necessary background. Special emphasis is placed on the construction of shape functions and their derivatives, enforcement of the essential boundary conditions and treatment of frictional effects along the contact interface between the workpiece and the roll. The effectiveness of the proposed approach is discussed by comparing the theoretical predictions with the finite element calculations and experimental data found in the literature.

A Finite-Element Local-Enrichment (FE-LE) model for texturing journal-bearing surfaces

The effect of roughness is an important consideration in the lubrication analysis and surface geometric design of heavy-duty machine elements. Deterministic simulation techniques have been developed for the investigation of point-contact mixed-lubrication problems. Such approaches should also be extended to obtain deterministic mixed lubrication solutions for journal-bearing conformal-contact systems. However, journal-bearing mixed lubrication involves a much larger area of surface interaction as compared to that in point contact problems. It is difficult to use similar micro/nano scale meshes directly to journal bearings under the current computation capability. It is a great challenge to develop a new deterministic numerical model for the mixed lubrication of journal bearing systems with the consideration of the effect of surface geometry design. This paper presents a macro-micro scale finite-element local-enrichment model for the deterministic analysis of conformal-contact mixed lubrication, in which a coarse mesh is used to determine the elastic deformation of a journal bearing surface, whilst locally refined meshes are used for the analysis of the roughness effect. The results from investigating the performance of bearing surfaces with sinusoidal and dimple textures suggest that the minimum film thickness may be improved through an appropriate surface texture configuration.Copyright

Simulation of Bulk Metal Forming by Means of Finite Integral Mesh Free Methods

Abstract This paper draws from the fundamentals of the finite integral mesh free representation methods and of the rigid-plastic formulation for slightly compressible materials to the main aspects of computer implementation and modelling of bulk-metal forming processes. Fundamental research and development is based on the reproducing kernel particle method (RKPM) and the corrected smoothed particle hydrodynamics (CSPH) method. Special emphasis is placed on a wide range of theoretical and numerical subjects such as discretization procedures, numerical integration of the system matrices derived from the weak form, relief of volumetric locking, geometrical update of the deforming workpiece, and treatment of the frictional contact interface between the workpiece and tooling.

An efficient elastic deformation analysis procedure for simulating conformal-contact elastohydrodynamic lubrication systems

A compliance operator is often utilized to evaluate the elastic deformation during simulation of elastohydrodynamic lubrication of conformal-contact systems. The values of the compliance operator represent the elastic deformations of all nodes when only one node is under a unit external load. The accuracy of compliance operator values, computational cost, and storage size are important issues. It is found that values only in a small region surrounding the loading node should be used and those in other regions can be discarded. Moreover, the mesh refinement in thickness direction is found to be more important than that along the longitudinal and width directions. A simple formula is suggested as the relationship between the values of a compliance operator and refinement steps. These two approaches enable an efficient elasticity procedure for the simulation of conformal-contact Elastohydrodynamic lubrication systems.Copyright

An Efficient Elastic Deformation Analysis Procedure for Simulating Conformal-Contact Transient Elastohydrodynamic Lubrication Systems

A compliance operator, Eji , is often utilized to evaluate elastic deformation in the simulation of transient and steady state elastohydrodynamic lubrication of conformal-contact systems. The values of the compliance operator represent the elastic responses of all nodes when only one node is under a unit load. The accuracy of compliance operator values, computational cost, and storage size are important issues. Based on our previous study on steady-state conformal-contact elastohydrodynamic lubrication systems, an advanced method of selective-fine-mesh with selective storage is suggested, and a special technique of combined selective-fine-mesh with selective storage mapping is proposed. These two techniques enable an efficient elasticity procedure for the simulation of transient conformal-contact elastohydrodynamic lubrication systems.Copyright

Deterministic Simulation of Surfaces in Conformal-Contact Lubrication

Topography development is an important component of surface engineering. Surfaces with controlled micro geometry may help enhance the lubrication. The development and application of textured surfaces in bearing design requires deterministic analyses of the micro feature effect on lubrication. However, limited numerical tools are available on deterministic mixed lubrication solutions for conformal-contact systems with real engineering surfaces due to the difficulty that conformal geometry involves a much larger area of surface interaction as compared to point contact geometry. Generally, a huge amount of storage and computer time can be involved if a micro-scale fine mesh capable for asperity description is used for an overall conformal lubrication analysis. Although an absolute solution is difficult, the authors intend to try conditional solutions without losing generality. Reported in this presentation is a new deterministic model for the mixed lubrication of surfaces in conformal contact. Numerical schemes to accelerate computations are developed and tested, the model application to journal bearing lubrication is explored, and sample calculations are conducted.

Numerical simulation of slab edging process by the Reproducing Kernel Particle Method considering friction effect

A mesh-free approach is used for analysing the effect of the friction factor on three-dimensional steady state slab edging, which is based on the Reproducing Kernel Particle Method (RKPM, Liu et al., 1995) and the material flow formulation for slightly compressible materials (Osakada et al., 1982). In order to cope with the singularity at the corner of the roll entry, a simple technique with a very thin array of cells at the inlet region adjacent to the plastic deformation zone (Xiong et al., 2003) is used. The results show that the dog-bone shape becomes smaller with the increment of friction factor. The roll separating force and total rolling torque increase with the friction factor.