Contact mechanics in fretting fatigue

This paper studies the contact mechanics in a line contact during fretting fatigue conditions. In literature one can find numerical and analytical solutions of normal and tangential stresses for a variety of loading cases. However, a unified solution valid for all loading cases during fretting fatigue conditions is not available. We present in this paper a strategy to combine existing contact mechanics theories into a unified calculation procedure. Therefore, the relevant contact mechanics theories for an idealized cylinder-on-flat contact are selected and bundled. Two clear flowcharts group the existing theories, which results in a unified strategy that can easily be implemented in a programming language. A Matlab script was programmed and calculates the normal and tangential stress distribution based on the applied forces, the geometry of the contact, the coefficient of friction and the material properties. The present theory can be used to automate the calculation of the stress distributions, or as validation of new numerical techniques. The script is modular and can be extended to calculate the lifetime of a component, by adding lifetime criteria

Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory

Neutron matter presents a unique system for chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present the first complete N3LO calculation of the neutron matter energy. This includes the subleading three-nucleon (3N) forces for the first time and all leading four-nucleon (4N) forces. We find relatively large contributions from N3LO 3N forces. Our results provide constraints for neutron-rich matter in astrophysics with controlled theoretical uncertainties.Comment: 5 pages, 4 figures; improved version, 3N ring and 2pi-contact contributions corrected, conclusions unchanged; v3: minor changes, published versio

Marginal stability in jammed packings: quasicontacts and weak contacts

Maximally random jammed (MRJ) sphere packing is a prototypical example of a system naturally poised at the margin between underconstraint and overconstraint. This marginal stability has traditionally been understood in terms of isostaticity, the equality of the number of mechanical contacts and the number of degrees of freedom. Quasicontacts, pairs of spheres on the verge of coming in contact, are irrelevant for static stability, but they come into play when considering dynamic stability, as does the distribution of contact forces. We show that the effects of marginal dynamic stability, as manifested in the distributions of quasicontacts and weak contacts, are consequential and nontrivial. We study these ideas first in the context of MRJ packing of d-dimensional spheres, where we show that the abundance of quasicontacts grows at a faster rate than that of contacts. We reexamine a calculation of Jin et al. (Phys. Rev. E 82, 051126, 2010), where quasicontacts were originally neglected, and we explore the effect of their inclusion in the calculation. This analysis yields an estimate of the asymptotic behavior of the packing density in high dimensions. We argue that this estimate should be reinterpreted as a lower bound. The latter part of the paper is devoted to Bravais lattice packings that possess the minimum number of contacts to maintain mechanical stability. We show that quasicontacts play an even more important role in these packings. We also show that jammed lattices are a useful setting for studying the Edwards ensemble, which weights each mechanically stable configuration equally and does not account for dynamics. This ansatz fails to predict the power-law distribution of near-zero contact forces, $P(f)\sim f^\theta$.Comment: final submitted versio

Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism

Modelling High Speed Machining with the SPH Method

The purpose of this work is to evaluate the use of the Smoothed Particle Hydrodynamics (SPH) method within the framework of high speed cutting modelling. First, a 2D SPH based model is carried out using the LS-DYNA® software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control allows a “natural” workpiece/chip separation. The developed SPH model proves its ability to account for continuous and shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Then, The SPH model is used in order to improve the general understanding of machining with worn tools. At last, a milling model allowing the calculation of the 3D cutting forces is presented. The interest of the suggested approach is to be freed from classically needed machining tests: Those are replaced by 2D numerical tests using the SPH model. The developed approach proved its ability to model the 3D cutting forces in ball end milling

Formulation to Predict Lower Limb Muscle Forces during Gait

The human body has more muscles than Degrees of Freedom (DoF), and that leads to indeterminacy in the muscle force calculation. This study proposes the formulation of an optimization problem to estimate the lower-limb muscle forces during a gait cycle of a patient wearing an instrumented knee prosthesis. The originality of that formulation consists of simulating muscle excitations in a physiological way while muscle parameters are calibrated. Two approaches have been considered. In Approach A, measured contact forces are applied to the model and all inverse dynamics loads are matched in order to get a physiological calibration of muscle parameters. In Approach B, only the inverse dynamics loads not affected by the knee contact loads are matched. With that approach, contact forces can be predicted and validated by comparison with the experimental ones. Approach B is a test of the optimization method and it can be used for cases where no knee contact forces are available

Spanning the Scales of Granular Materials: Microscopic Force Imaging

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. We describe here experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the unexpected mechanical response of the packing, and reveals a surprising microscopic particle deformation enhancement mechanism.Comment: Data and code available at http://www.phy.duke.edu/~nb108

A fast time-domain model for wheel/rail interaction demonstrated for the case of impact forces caused by wheel flats

The prediction of impact forces caused by wheel flats requires the application of time-domain models that are generally more computationally demanding than are frequency-domain models. In this paper, a fast time-domain model is presented to simulate the dynamic interaction between wheel and rail, taking into account the non-linear processes in the contact zone. Track and wheel are described as linear systems using impulse-response functions that can be precalculated. The contact zone is modelled by non-linear contact springs, allowing for loss of contact. This general model enables the calculation of the vertical contact forces generated by the small-scale roughness of rail and wheel, by parametric excitation on a discretely supported rail and by discrete irregularities of rail and wheel. Here, the model is applied to study the excitation caused by wheel flats by introducing a flat on a rotating wheel whose profile in the contact zone is updated in every time step. To demonstrate the functioning of the model, simulation results are compared to field measurements of impact forces and a brief parameter study is presented

Investigation of inner contact and friction conditions of a spherical roller bearing using multi-body simulation

At the Institute of Machine Elements, Gears, and Transmission (MEGT, University of Kaiserslautern) a spherical roller bearing has been modeled in an multi body system (MBS) environment. The use of the commercial MBS (multi-body system) software (MSC ADAMS) allows the development of user-written subroutines for contact recognition and the calculation of contact forces. Those subroutines can help understanding the principles of friction phenomena inside spherical roller bearings, while the measurement of those effects is difficult.Measurements on a friction torque test rig for roller bearings are used to validate the MBS models. Since the sum of all contact forces equals the friction of the bearing, this test stand provides a way for validation of the contact and friction calculations