M. Sarangi

Microstructure and Mechanical Performance of Friction Stir Spot-Welded Aluminum-5754 Sheets

Friction stir spot welding (FSSW) is a recent trend of joining light-weight sheet metals while fabricating automotive and aerospace body components. For the successful application of this solid-state welding process, it is imperative to have a thorough understanding of the weld microstructure, mechanical performance, and failure mechanism. In the present study, FSSW of aluminum-5754 sheet metal was tried using tools with circular and tapered pin considering different tool rotational speeds, plunge depths, and dwell times. The effects of tool design and process parameters on temperature distribution near the sheet-tool interface, weld microstructure, weld strength, and failure modes were studied. It was found that the peak temperature was higher while welding with a tool having circular pin compared to tapered pin, leading to a bigger dynamic recrystallized stir zone (SZ) with a hook tip bending towards the upper sheet and away from the keyhole. Hence, higher lap shear separation load was observed in the welds made from circular pin compared to those made from tapered pin. Due to influence of size and hardness of SZ on crack propagation, three different failure modes of weld nugget were observed through optical cross-sectional micrograph and SEM fractographs.

Elastohydrodynamically lubricated ball bearings with couple-stress fluids, Part I Steady-state analysis

Conventional elastohydrodynamic lubrication (EHL) analysis of point contacts is extended to include couple-stress effects in lubricants blended with polymer additives. A transient pressure differential equation, generally referred to as a modified Reynolds equation, is derived from the Stokes microcontinuum theory and solved using the finite difference method with a successive over-relaxation scheme. The solution is obtained under isothermal conditions, assuming a suitable exponential relation of pressure-viscosity variation. A nondimensional couple-stress parameter, which can be considered the molecular length of the additives in the lubricant, is used in the analysis. From the results obtained, the influence of the couple-stress parameter on the EHL point contacts is apparent and cannot be neglected. Lubricants with couple stresses provide an increase in the load-carrying capacity and reduction in friction coefficient as compared to Newtonian lubricants. Empirical formulas for the calculation of central and minimum film thicknesses of lubricated point contacts with couple-stress fluids are derived with the nonlinear least-squares curve-fitting technique using different numerically evaluated data. This may help to avoid the time-consuming numerical calculations.

Stiffness and damping characteristics of lubricated ball bearings considering the surface roughness effect. Part 1: Theoretical formulation:

Abstract The stiffness and damping characteristics of isothermal, elastohydrodynamically lubricated point contact problems are evaluated numerically considering the surface roughness effect and variation in viscosity with pressure. A set of equations under steady-state and dynamic conditions is derived from the classical Reynolds equation using the linear perturbation method. The elasticity equation and steady-state Reynolds equation are solved simultaneously using the finite difference method with the successive over-relaxation scheme, whereas the dynamic pressures are found after solving the set of perturbed equations using the previously obtained steady-state pressures. The load capacity is obtained from the steady-state pressure distribution. The stiffness and damping coefficients of the contact are determined using the dynamic pressures. Then the overall stiffness and damping matrices of the ball bearing are obtained from the load distribution, coordinate transformation, and compatibility relations.

Stiffness and damping characteristics of lubricated ball bearings considering the surface roughness effect. Part 2: Numerical results and application

Abstract A numerical solution for the stiffness and damping characteristics of an isothermal, elastohydrodynamically lubricated point contact is presented considering the surface roughness effect and variation in viscosity with pressure. An attempt has been made to derive empirical formulae for the calculation of stiffness and damping coefficients of lubricated point contacts with a non-linear least-squares curve-fitting technique using different numerically evaluated data, thereby avoiding time-consuming numerical calculations. From this the overall stiffness and damping matrices of the ball bearing are obtained with a proper load distribution. A comparative study on the dynamics of a rotor-bearing system is carried out for a dry contact ball bearing, a lubricated contact ball bearing and a plain journal bearing.

Elastohydrodynamically lubricated ball bearings with couple-stress fluids, Part II Dynamic analysis and application

Stiffness and damping coefficients of isothermal elastohydrodynamically lubricated point-contact problems are evaluated numerically with couple-stress fluids. A set of equations under steady-state and dynamic conditions is derived from the modified Reynolds equation using a linearized perturbation method. This paper is the second part of the present study; the modified Reynolds equation derived from the Stokes micro-continuum theory is used in the previous article. Dynamic pressures are found after solving the set of perturbed equations using the previously obtained steady-state pressure from the modified Reynolds equation. The stiffness and damping coefficients of the film are determined using the dynamic pressures. Then the overall stiffness and damping matrices of the ball bearing are obtained from load distribution, coordinate transformation, and compatibility relations. The bearing coefficients are introduced into a rotor system to simulate the response. It has been observed that the influence of couple-stress fluids on the dynamics of a rotor supported on lubricated ball bearings is marginal; hence, Newtonian theory can be used instead for simplicity. However, with increasing content of polymer additives in lubricant, for an accurate analysis the effect of couple stresses in a fluid should not be neglected.

On the Dynamics of Lubricated Cylindrical Roller Bearings, Part I: Evaluation of Stiffness and Damping Characteristics

The stiffness and damping coefficients of a single roller-to-race contact of lubricated cylindrical roller bearings are numerically evaluated using a linearized perturbation method for both elastohydrodynamic lubrication (EHL) finite and infinite contact theories. A steady-state pressure equation is solved by a multilevel method and the elastic deformation is evaluated with the multilevel multi-integration method. Dynamic pressures are obtained by solving a set of perturbed pressure equations and are used to calculate the stiffness and damping coefficients. The influence of various nondimensional parameters (load parameter, speed parameter, material parameter, edge radius, and geometrical parameter) on the stiffness and damping are studied. The results show that a finite line contact gives higher values of stiffness and damping coefficients compared to an infinite contact, particularly at higher load and lower speed values. Based on the numerically evaluated data, curve-fitted relations for the stiffness and damping coefficients of a single roller-to-race contact are developed that can be used in the dynamic analysis of rotor–bearing systems.

Effects of texture shape and fluid–solid interfacial slip on the hydrodynamic lubrication performance of parallel sliding contacts

The aim of this paper is to study the effect of texture shape and fluid–solid interfacial slip on the hydrodynamic lubrication performance of parallel sliding contact. The modified Reynolds equation is solved using finite difference method with a Gauss–Seidel relaxation scheme. The two-component slip length model has been used in order to calculate the slip velocity terms. Results indicate that the consideration of fluid slip around the surface texture enhances the hydrodynamic performance of textured parallel sliding contact as compared to the conventional textured surface. It is concluded that the surface texture should be designed with lower texture height ratio and aspect ratio in order to achieve better hydrodynamic lubrication performance. Furthermore, it is observed that the lower critical threshold shear stress and the higher slip length coefficient improve the performance of parallel sliding contact.

On the Dynamics of Lubricated Cylindrical Roller Bearings, Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.