Abdallah A. Elsharkawy

Effects of axial preloading of angular contact ball bearings on the dynamics of a grinding machine spindle system

Abstract A mathematical model based on a five degrees of freedom dynamic system is utilized to study the effects of axial preloading of angular contact ball bearings on the vibration behavior of a grinding machine spindle. The grinding forces (as a function of grinding wheel wear rate percentage for five different workpiece materials) were used to simulate external loading on the grinding machine spindle. The results show that the initial axial preload applied on the bearings plays a significant role to reduce the vibration levels of the grinding machine spindle system and consequently results in better accuracy for the finished surfaces. The vibration levels of grinding machine spindle system increases as wheel wear rate percentage increases and/or the hardness of the workpiece material increase. This analysis can be used to calculate the optimum initial axial preload in order to obtain high accuracy for surface finish.

An inverse solution for finite journal bearings lubricated with couple stress fluids

This paper presents an inverse solution for finite journal bearings lubricated with couple stress fluids to estimate the eccentricity ratio and the couple stress parameter for a given experimentally measured pressure distribution. The least-squares optimization technique is used to solve the inverse problem. An efficient numerical scheme is developed to solve the direct lubrication problem, which consists of the modified Reynolds equation, the film thickness equation, and the boundary conditions for the pressure field. The flexibility of the bearing liner is considered in the film thickness equation by a simple elastic model. The proposed inverse algorithm was tested using numerically simulated pressure distribution. The results showed that as the percentage of random error added to the numerically calculated pressure data points increases, the number of iterations required for convergence increases slightly, and the accuracy of the predictions decreases especially in the case of elastic liner.

Effect of grinding forces on the vibration of grinding machine spindle system

In this paper the effects of dynamic changes in the grinding force components due to changes in the grinding wheel wear flat area and the workpiece material on the vibration behavior of the grinding spindle are studied. The steady-state dynamics and vibration behavior of the grinding machine spindle is simulated by a five degree of freedom model. The results indicate that when grinding different materials using a grinding wheel with fixed wear flat area, different vibration behavior is noticed. As the grinding wheel flat area increases, the level of vibration increases for all the degrees of freedom, which indicates that there is an upper limit for the level of wear on the grinding wheel that can be tolerated, and after that level dressing operation must be conducted on the grinding wheel.

An inverse solution for low-velocity impact in composite plates

Abstract An inverse model for estimating the mass and velocity of the impactor in low-velocity impact of composite plates is presented. In the model, a least-squares optimization technique is used to optimally reconstruct the force–time history by comparing direct model simulations of the impact response with experimental measurements. Guidelines for better initial guesses and faster direct models that are based on an impact characterization procedure are provided to the inverse algorithm. Three sets of experimental data covering a wide range of impact response are used to validate the model with excellent results.

Stretch-bending analysis of U-section beams

A complete analysis for stretch-bending of U-section beams is introduced. The variations of the applied bending moment with the applied axial load for fully elastic, elastic-plastic and fully plastic conditions are derived. The ultimate goal of such simulation technique is to develop a simple and fast technique to determine stresses, strains, springback and residual stresses as functions of parameters such as material characteristics, forming loads and the required geometry of U-section beams. The model proposed in the present study can be considered as a major step for computer simulation of stretch-bending at the design stage which will provide useful data and criteria for equipment selection and tooling design. The significance of various material parameters from productibility, ease of fabrication and tool design viewpoints can also be evaluated by the model. Furthermore, the failure modes of the stretch-bending process are also introduced and the region for safe operations are defined in a very useful and practical set of curves.

Effect of friction on subsurface stresses in sliding line contact of multilayered elastic solids

A numerical integral scheme based on Fourier transformation approach is employed to investigate the effect of friction on subsurface stresses arising from the two-dimensional sliding contact of two multilayered elastic solids. The analysis incorporates bonded and unbonded interface boundary conditions between the coating layers. Two line contact problems are presented. The first one is the contact problem between a rigid cylinder and a two-layer half space and the second one is the indentation of a multilayered elastic half-space by a flat rigid punch. The effects of the surface coating on the contact pressure distribution and subsurface stress field are presented and discussed.

Visco-elastohydrodynamic lubrication of line contacts

A numerical solution for the visco-elastohydrodynamic lubrication problem of line contacts is introduced. The surface displacements of the bounding solids are calculated from the linear viscoelastic half-space theory. A standard linear model is used to characterize the viscoelastic behavior of the bounding solids. The mathematical formulation of visco-elastohydrodynamic lubrication is based mainly on solving the Reynolds equation coupled with the viscoelasticity equations. The proposed mathematical model is solved numerically by using an iterative Newton-Raphson scheme. The effects of viscoelastic behavior of the bounding solids on the pressure profiles and film shapes are presented and discussed.

Effects of misalignment on the performance of finite journal bearings lubricated with couple stress fluids

A mathematical model for the hydrodynamic lubrication of misaligned journal bearings with couple stress lubricants is presented. A modified form for Reynolds equation in which the effects of couple stresses arising from the lubricant blended with various additives is used. The journal misalignment is allowed to vary in magnitudes as well as in direction with respect to the bearing boundaries. The flexibility of the bearing liner was incorporated into the analysis by using the thin liner model. A numerical solution for the mathematical model using a finite difference scheme is introduced. The predicted performance characteristics are compared with available theoretical and experimental results. The effects of the degree and angle of misalignment, the length-to-diameter ratio, and the couple stress parameter on static performance such as pressure distribution, load-carrying capacity, friction coefficient, and side leakage flow and misalignment moment are presented and discussed.

A Numerical Solution for Dry Contact Between Two Viscoelastic Rollers

A systematic numerical scheme is developed to solve the steady-state rolling contact problem between two viscoelastic cylinders. The contact problem is formulated as an integral equation in which the contact pressure and the contact area are to be determined. The analysis is restricted lo the normal contact problem. A standard linear model is used to characterize the viscoelastic behavior of the bounding solids. The effects of the viscoelastic behavior of the material of the contacting cylinders on the contact pressure distribution, contact area, and subsurface stress field are studied and discussed. Presented as a Society of Tribologlsts and Lubrication Engineers paper at the STLE/ASME Tribology Conference in Kissimmee, Florida, October 8–11, 1995

Direct and Inverse Solutions for Elastohydrodynamic Lubrication of Finite Porous Journal Bearings

In this paper a numerical solution for the elastohydrodynamic lubrication of a finite porous journal bearing is presented. The Brinkman-extended Darcy model was applied within the porous layer to incorporate the viscous shear stresses into the analysis. A s. elastic model is used to describe the elastic deformation of the liner. An inverse model is introduced to estimate the permeability parameter and/or the eccentricity ratio from experimentally obtained pressure data. As experimental measurements were not conducted, these data were simulated numerically. It consists of a direct solution for the pressure, for given parameters (permeability parameter and/or the eccentricity ratio), to which a normally distributed random error is added. The least-squares optimization technique is used to solve the proposed inverse problem. A unique solution was obtained for one-parameter estimation. The two-parameter estimation case, however, leads to multiple solutions lying on a constant load line.