A Compact Model for Spherical Rough Contacts

The contact of rough spheres is of high interest in many tribological, thermal, and electrical fundamental analyses. Implementing the existing models is complex and requires iterative numerical solutions. In this paper a new model is presented and a general pressure distribution is proposed that encompasses the entire range of spherical rough contacts including the Hertzian limit. It is shown that the non-dimensional maximum contact pressure is the key parameter that controls the solution. Compact expressions are proposed for calculating the pressure distribution, radius of the contact area, elastic bulk deformation, and the compliance as functions of the governing non-dimensional parameters. The present model shows the same trends as those of the Greenwood and Tripp model. Correlations proposed for the contact radius and the compliance are compared with experimental data collected by others and good agreement is observed.

Enhancing Tribological Conditions in Tube Hydroforming by Using Textured Tubes

The effects of textured tubes on the tribological performance in Tube Hydroforming (THF) are discussed. Textured surfaces, namely sand blasted, knurled, and as rolled surfaces were tested under various interface pressure and sliding velocity conditions. Sand blasted textured tubes were found to have the best tribological performance. It was also found that the interface pressure has a great influence on the attainment of Micro-Plasto HydroDynamic Lubrication (MPHDL) and Micro-Plasto HydroStatic Lubrication (MPHSL) conditions at the tool-workpiece interface. Preliminary finite element simulations on the deformation behavior of tube surface shows that surface textures can be optimized to enhance tribological performance.

Simulation of Frictional Sliding Under Impact Shear Loading

Results from recent and ongoing investigations of frictional sliding under dynamic loading conditions are discussed. The configuration analyzed consists of two identical elastic plates with an interface characterized by a rate- and state-dependent frictional law. The calculations are carried out within a framework where two constitutive relations are used: a volumetric constitutive relation between stress and strain and a surface constitutive relation that characterizes the frictional behavior of the interface. The simulations discussed predict a variety of sliding modes including a crack-like mode and several pulse-like modes as well as circumstances where the sliding tip speed can exceed the longitudinal wave speed.

Height-Dependent Asperity Radii of Curvatures in a Contact and Friction Model

The effect of a height-dependent asperity radius of curvature is accounted for in a recently developed scale-dependent model of contact and friction. The contact and friction model includes the effects of adhesion, using the Maugis model, and of scale-dependent friction, using the Hurtado and Kim single asperity friction model. This multi-asperity model has been modified to include the effect of non-contacting asperities. The results indicate the types of conditions under which the effects of a height-dependent asperity radius of curvature affects friction.

Transient Solution of the Inhomogeneous Thermoelastic Contact Problem Using Fast Speed Expansion

Numerical integration has been widely used in commercial FEA software to solve transient problems. However, for the large-scale inhomogeneous thermoelastic contact problem (ITEC), this method is found to be extremely computation-intensive. This paper introduces a new approach to solve the ITEC transient problem with much lower computational complexity. The method is based on the transient modal analysis (TMA) method in conjunction with the fast speed expansion (FSE) method. The TMA method is used to obtain the inhomogeneous transient solution by expressing the solution in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. If the sliding speed is constant, the eigenfunctions can be found by one run of the commercial software program ‘HotSpotter’. However, if the speed varies, the eigenfunctions change and numerous runs of HotSpotter are needed, making the method computationally inefficient. However, the FSE method employs an efficient algorithm to interpolate and expand the eigenfunctions and eigenvalues over a range of speeds. This reduces the number of eigenvalue solutions required and results in a significant reduction in computation time. The method is illustrated with application to an axisymmetric transmission clutch problem.

A Non-Phenomenological Account of Friction/Vibration Interaction in Rotary Systems

The mathematical formulation relates the tribological events at micron-scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a visco-elastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the micro- and macro-scale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to reduce with decrease in the normal load and/or increase in structural damping of the system.

Experimental Identification of Elastic, Damping and Adhesion Forces in Collision of Spherical Sliders With Stationary Magnetic Disks

This paper deals with the experimental identification of elastic, damping and adhesion forces in the dynamic collision of a spherical slider with a stationary magnetic disk. We used rough Al2O3TiC and smooth glass spherical sliders with a radius of 1 mm, and magnetic disks with four different lubricant film thicknesses of 0, 1, 2, and 3 nm. We found that the Al2O3TiC slider shows ordinary approach and rebound processes, whereas the glass slider showed a velocity drop at the end of the rebound process when the lubricant thickness was 1, 2 and 3 nm. We identified the elastic force factors in the approaching and rebound processes, based on the Herztian contact theory, and the damping force factors based on a damping force model that is proportional to slider velocity and penetration depth (contact area). From the drop in velocity when the slider and disk separated, we found that the dynamic adhesion force is almost equal to the static pull-off force, except for with a 3nm lubricant thickness. The dynamic adhesion force with 3 nm lubricant thickness is significantly higher probably because of squeeze damping effect.

Surface Temperature in Oscillating Sliding Interfaces

A model is developed to predict the behavior of two sliding bodies undergoing oscillatory motion. A set of four dimensionless groups is introduced to characterize the transient dimensionless surface temperature rise. They are: the Peclet number Pe, the Biot number Bi, the amplitude of oscillation A, and the Hertzian semi-contact width α. Also considered in the analysis is the effect of the ratio β = A/α of the amplitude to the semi-contact width. The results of a series of simulations, covering a range of these independent parameters, are presented and examples are provided to illuminated the utility of the model.

Fast Speed Expansion Technique for the Transient Analysis of Automotive Clutches

The transient modal analysis method (TMA) has been used to solve the inhomogeneous (loaded) transient thermoelastic contact problem (ITTEC). In the TMA method, the solution of the inhomogeneous transient problem is expressed in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. However, for the large-scale ITTEC problem, this method is found to be extremely time-consuming, because of the computation-intensive of the eigen-solutions. This paper describes a new approach to solve the large-scale ITTEC problem with a dramatic reduction in computational complexity. The method is referred to as fast speed expansion method (FSE). With the FSE method, full eigen-solutions are performed only at a limited number of sparsely located speeds. For speeds between these speeds, eigenvectors are solved by linear interpolation, while the eigenvalues are computed from Taylor series. The method is illustrated with application to an automotive clutches.

Theoretical Investigation in Thermoelastohydrodynamic Lubrication With Non-Newtonian Lubricants Under Heavy Load Change

The time-dependent thermal compressible elastohydrodynamic (EHD) lubrication of sliding line contact has been developed to investigate the effect of a sudden load change. The time-dependent modified Reynolds equation with non-Newtonian fluids has been formulated using power law’s model. In this study, the non-Newtonian dilatant fluids for liquids-solid lubricants have been purposed experimentally using the common solid particles namely, Molybdenum disulfide (MoS2) and Polytetrafluoroethylene (PTFE). The simultaneous systems of modified Reynolds and elasticity and energy equations with initial conditions were solved numerically using multigrid multilevel technique. The performance characteristics of the thermoelastohydrodynamic under line contact were presented with varying time for the pressure distribution, temperature distribution and oil film thickness. The transient response of the line contact between two surfaces was simulated under a heavy step load function. The coefficients of friction were also presented in this work at steady state condition with varying particle concentration. This simulation showed a significant effect of liquid-solid on thermoelastohydrodynamic (TEHD) lubrication under heavy load conditions.