Nucleation and growth of rolling contact failure of 440C bearing steel

A 'two-body' elasto-plastic finite element model of 2-dimensional rolling and rolling-plus-sliding was developed to treat the effect of surface irregularities. The model consists of a smooth cylinder in contact with a semi-infinite half-space that is either smooth or fitted with one of 0.4 microns deep or 7 microns deep groove, or a 0.4 microns high ridge-like asperity. The model incorporates elastic-linear-kinematic hardening-plastic (ELKP) and non-linear-kinematic hardening-plastic (NLKP) material constitutive relations appropriate for hardened bearing steel and the 440C grade. The calculated contact pressure distribution is Hertzian for smooth body contact, and it displays intense, stationary, pressure spikes superposed on the Hertzian pressure for contact with the grooved and ridged surface. The results obtained for the 0.4 microns deep groove compare well with those reported by Elsharkawy and Hamrock for an EHD lubricated contact. The effect of translating the counterface on the half space as opposed to indenting the half space with the counter face with no translation is studied. The stress and strain values near the surface are found to be similar for the two cases, whereas they are significantly different in the subsurface. It is seen that when tiny shoulders are introduced at the edge of the groove in the finite element model, the incremental plasticity and residual stresses are significantly higher in the vicinity of the right shoulder (rolling direction is from left to right) than at the left shoulder. This may explain the experimental observation that the spall nucleation occurs at the exit end of the artificially planted indents. Pure rolling calculations are compared with rolling + sliding calculations. For a coefficient of friction, mu = 0.1, the effect of friction is found to be small. Efforts were made to identify the material constitutive relations which best describe the deformation characteristics of the bearing steels in the initial few cycles. Elastic-linear-kinematic hardening-plastic (ELKP) material constitutive relations produce less net plastic deformation in the initial stages for a given stress, than seen in experiments. A new set of constitutive relations: non-linear-kinematic hardening-plastic (NLKP) was used. This material model produces more plasticity than the ELKP model and shows promise for treating the net distortions in the early stages. Techniques for performing experimental measurements that can be compared with the finite element calculations were devised. The measurements are being performed on 9mm-diameter, 440C steel cylindrical rolling elements in contact with 12.5 mm-diameter, 52100 steel balls in a 3-ball-rod fatigue test machine operating at 3600 RPM. Artificial, 7 microns deep, indents were inserted on the running track of the cylindrical rolling elements and profilometer measurements of these indents made, before and after the rolling. These preliminary measurements show that the indents are substantially deformed plastically in the process of rolling. The deformations of the groove calculated with the finite element model are comparable to those measured experimentally

On q-Gaussians and Exchangeability

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.Comment: 14 page

Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

CP violating asymmetry in H±→W±h1H^\pm\to W^\pm h_1 decays

The CP violating asymmetry from the decay rates $H^\pm\to W^\pm h_1$ of charged Higgs bosons into the lightest neutral Higgs boson and a $W^\pm$ boson is calculated and discussed in the complex MSSM. The contributions from all complex phases are considered, especially from the top-squark trilinear coupling, which induces a large contribution to the CP asymmetry.Comment: 19 pages, 10 figures, version published in JHE

Mechanisms of rolling contact spalling

The results of a study aimed at analyzing the mechanical material interactions responsible for rolling contact spalling of the 440 C steel, high pressure oxygen turbopump bearings are presented. A coupled temperature displacement finite element analysis of the effects of friction heating under the contact is presented. The contact is modelled as a stationary, heat generating, 2 dimensional indent in an elastic perfectly plastic half-space with heat fluxes up to 8.6 x 10000 KW/m sq comparable to those generated in the bearing. Local temperatures in excess of 1000 C are treated. The calculations reveal high levels of residual tension after the contact is unloaded and cools. Efforts to promote Mode 2/Mode 3 fatigue crack growth under cyclic torsion in hardened 440 C steel are described. Spalls produced on 440 C steel by a 3 ball/rod rolling contact testing machine were studied with scanning microscopy. The shapes of the cyclic, stress strain hysteresis loops displayed by hardened 440 C steel in cyclic torsion at room temperature are defined for the plastic strain amplitudes encountered in rolling/sliding contact. Results of these analyses are discussed in detail