scholarly journals A Review of Elastic–Plastic Contact Mechanics

2017 ◽  
Vol 69 (6) ◽  
Author(s):  
Hamid Ghaednia ◽  
Xianzhang Wang ◽  
Swarna Saha ◽  
Yang Xu ◽  
Aman Sharma ◽  
...  
Keyword(s):  
State Of The Art ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Single Asperity ◽  
Current State ◽  
Metallic Contacts ◽  
Contact Models ◽  
Rough Surface Contact ◽  
Elastic And Plastic Deformation ◽  
Very High

In typical metallic contacts, stresses are very high and result in yielding of the material. Therefore, the study of contacts which include simultaneous elastic and plastic deformation is of critical importance. This work reviews the current state-of-the-art in the modeling of single asperity elastic–plastic contact and, in some instances, makes comparisons to original findings of the authors. Several different geometries are considered, including cylindrical, spherical, sinusoidal or wavy, and axisymmetric sinusoidal. As evidenced by the reviewed literature, it is clear that the average pressure during heavily loaded elastic–plastic contact is not governed by the conventional hardness to yield strength ratio of approximately three, but rather varies according to the boundary conditions and deformed geometry. For spherical contact, the differences between flattening and indentation contacts are also reviewed. In addition, this paper summarizes work on tangentially loaded contacts up to the initiation of sliding. As discussed briefly, the single asperity contact models can be incorporated into existing rough surface contact model frameworks. Depending on the size of a contact, the material properties can also effectively change, and this topic is introduced as well. In the concluding discussion, an argument is made for the value of studying hardening and other failure mechanisms, such as fracture as well as the influence of adhesion on elastic–plastic contact.

Stick-Slip Compensation of Micro-Positioning Using Elastic-Plastic Static Friction Model

2008 ◽  
Vol 47-50 ◽  
pp. 246-249
Author(s):  
Min Gyu Jang ◽  
Chul Hee Lee ◽  
Seung Bok Choi
Keyword(s):  
Static Friction ◽  
Friction Model ◽  
Smart Structure ◽  
Asperity Contact ◽  
Stick Slip ◽  
Elastic Plastic ◽  
Highly Nonlinear ◽  
Bridge Type ◽  
Structural Parts ◽  
Rough Surface Contact

In this paper, a stick-slip compensation for the micro-positioning is presented using the statistical rough surface contact model. As for the micro-positioning structure, PZT (lead(Pb) zirconia(Zr) Titanate(Ti)) actuator is used to drive the load for precise positioning with its high resolution incorporating with the PID (Proportional Integral Derivative) control algorithm. Since the stick-slip characteristics for the micro structures are highly nonlinear and complicated, it is necessary to incorporate more detailed stick-slip model for the applications involving the high precision motion control. Thus, the elastic-plastic static friction model is used for the stick-slip compensation considering the elastic-plastic asperity contact in the rough surfaces statistically. Mathematical model of the system for the positioning apparatus was derived from the dynamic behaviors of structural parts. Since the conventional piezoelectric actuator generates the short stroke, a bridge-type flexural hinge mechanism is introduced to amplify the linear motion range. Using the proposed smart structure, simulations under the representative positioning motion were conducted to demonstrate the micro-positioning under the stick-slip friction.

Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
A. Megalingam ◽  
M. M. Mayuram
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rough Surface ◽  
Contact Area ◽  
Model Analysis ◽  
Contact Model ◽  
Contact Load ◽  
Asperity Contact ◽  
Single Asperity ◽  
Contact Models

The study of the contact stresses generated when two surfaces are in contact plays a significant role in understanding the tribology of contact pairs. Most of the present contact models are based on the statistical treatment of the single asperity contact model. For a clear understanding about the elastic-plastic behavior of two rough surfaces in contact, comparative study involving the deterministic contact model, simplified multi-asperity contact model, and modified statistical model are undertaken. In deterministic contact model analysis, a three dimensional deformable rough surface pressed against a rigid flat surface is carried out using the finite element method in steps. A simplified multi-asperity contact model is developed using actual summit radii deduced from the rough surface, applying single asperity contact model results. The resultant contact parameters like contact load, contact area, and contact pressure are compared. The asperity interaction noticed in the deterministic contact model analysis leads to wide disparity in the results. Observing the elastic-plastic transition of the summits and the sharing of contact load and contact area among the summits, modifications are employed in single asperity statistical contact model approaches in the form of a correction factor arising from asperity interaction to reduce the variations. Consequently, the modified statistical contact model and simplified multi-asperity contact model based on actual summit radius results show improved agreement with the deterministic contact model results.

Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact

1996 ◽  
Vol 49 (5) ◽  
pp. 275-298 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Friction And Wear ◽  
Rough Surfaces ◽  
Asperity Contact ◽  
Elastic Solids ◽  
Elastic Plastic ◽  
Single Asperity ◽  
Real Area Of Contact ◽  
Single Asperity Contact ◽  
Indentation Problem ◽  
Real Area

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict the real area of contact which affects friction and wear of an interface. The contact of two macroscopically flat bodies with microroughness is reduced to the contact at multiple asperities of arbitrary shapes. Most of deformation at the asperity contact can be either elastic or elastic-plastic. In this paper, a comprehensive review of modeling of a single asperity contact or an indentation problem is presented. Contact analyses for a spherical asperity/indenter on homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The analyses reviewed in this paper fall into two groups: (a) analytical solutions, primarily for elastic solids and (b) finite element solutions, primarily for elastic-plastic problems and layered solids. Implications of these analyses in friction and wear are discussed.

Design Potentials of External Gear Machines With Asymmetric Tooth Profile

2013 ◽  
Author(s):  
Ram Sudarsan Devendran ◽  
Andrea Vacca
Keyword(s):  
Design Principle ◽  
State Of The Art ◽  
Design Method ◽  
Optimization Procedure ◽  
Tooth Profile ◽  
Design Parameters ◽  
Simulation Tool ◽  
Performance Potentials ◽  
Current State ◽  
Very High

This paper describes the design, optimization and the performance potentials of external gear machines with asymmetric tooth profiles. Conventionally, the design of these machines is entirely based on symmetric involute profile. A design method has been developed to derive the tooth profiles based on a modified rack-cutter profile which is assumed to be used for manufacturing the gears with asymmetric involute surfaces and trochoidal fillet profiles. The study is based on the simulation tool HYGESim (HYdraulic GEar machines Simulator) which is being developed and has been validated by the authors’ research group to accurately analyze the performance of the machine. For the purpose of this research, HYGESim was adapted to simulate the particular case of non-symmetric gear profiles. A specific optimization procedure based on genetic algorithm was implemented to find the maximum performance of the new design, in terms of volumetric efficiency, fluid borne noise, internal pressure peaks and localized cavitation acting on the design parameters that characterize the tooth profile. The results of the optimization process are compared to the current state of the art for external gear machines. This comparison show very high potentials for this new design principle, particularly concerning the reduction of the fluid borne noise.

Study on the Normal Contact Stiffness of Rough Surface in Mixed Lubrication

2018 ◽  
Author(s):  
Huifang Xiao ◽  
Yunyun Sun ◽  
Xiaojun Zhou ◽  
Zaigang Chen
Keyword(s):  
Rough Surface ◽  
Contact Stiffness ◽  
Equivalent Model ◽  
Lubricant Layer ◽  
Asperity Contact ◽  
Normal Contact ◽  
Liquid Lubricant ◽  
Single Asperity ◽  
Rough Surface Contact ◽  
Film Stiffness

In this paper, a general contact stiffness model is proposed to study the mixed lubricated contact between a rough surface and a rigid flat plate, which is the equivalent model for the contact between two rough surfaces and is the general case for engineering contact interfaces. The total interfacial contact stiffness is composed of the dry rough surface contact stiffness and the liquid lubricant contact stiffness. The GW model is used for surface topography description and the contact stiffness of a single asperity is derived from the Hertz contact theory. The whole dry rough contact stiffness is obtained by multiple the single asperity contact stiffness with the number of contact asperities, which is derived based on the statistical model. The liquid film stiffness is derived based on a spring model. The stiffness contributions from the asperity contact part and lubricant layer part are separated and analyzed.

Sensitivity of Rogue Wave Prediction to the Oceanic Stratification

2015 ◽  
Author(s):  
Qiuchen Guo ◽  
M.-Reza Alam
Keyword(s):  
State Of The Art ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Offshore Structures ◽  
High Accuracy ◽  
Current State ◽  
Spatial Domains ◽  
The Waves ◽  
Very High ◽  
Accurate Wave

Oceanic rogue waves are short-lived very large amplitude waves (a giant crest typically followed or preceded by a deep trough) that appear and disappear suddenly in the ocean causing damage to ships and offshore structures. Assuming that the state of the ocean at the present time is perfectly known, then the upcoming rogue waves can be predicted via numerically solving the equations that govern the evolution of the waves. State of the art radar technology can now provide accurate wave height measurements over large spatial domains and when combined with advanced wave-field reconstruction techniques together render deterministic details of the current state of the ocean (i.e. surface elevation and velocity field) at any given moment of time with a very high accuracy. The ocean density is, however, stratified (mainly due to the salinity and temperature differences). This density stratification, with today’s technology, is very difficult to measure accurately. As a result, in most predictive schemes these density variations are neglected. While the overall effect of the stratification on the average state of the ocean may not be significant, here we show that these density variations can strongly affect the prediction of oceanic rogue wave. Specifically, we consider a broadband oceanic spectrum in a two-layer density stratified fluid and study, via extensive statistical analysis, the effects of the strength of the stratification (difference between densities) and the depth of the thermocline on the prediction of upcoming rogue waves.

The Contact Mechanics for Indentation of Single Asperity and Rough Surfaces

2022 ◽  
pp. 1-32
Author(s):  
Zhaoning Sun ◽  
Xiaohai Li
Keyword(s):  
Rough Surfaces ◽  
Real Contact Area ◽  
Rigid Sphere ◽  
Asperity Contact ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Single Asperity ◽  
Plastic Yield ◽  
Plastic Deformation Region ◽  
Contact Parameters

Abstract A Finite Element Analysis of a rigid sphere contact with a deformable elastic-plastic plat called indentation model is studied. The numerical results are applied on the rough surfaces contact of the GW model. A series of the relationships of the rough surfaces contact parameters are obtained. The contact parameters of the indentation model and the flattening model are compared in detail and the reasons for their differences are analyzed. In the case of single asperity contact, for ω/ωc > 1, the Indentation model reaches the initial plastic yield while the flattening model is ω/ωc = 1. In ω/ωc = 10, the plastic yield reaches the contact surface for the first time, and the corresponding point of ψ = 0.5 the flattening model is relatively earlier in . The contact parameters of rough surface in different plasticity indexes are compared again. On the point of ω/ωc = 6, the contact parameters of the flattening model and the indentation model coincide perfectly. For 0.5 < ψ < 4, the difference between the parameters curves become larger and larger. To the point of ψ = 4, when the distance difference reaches the maximum, it begins to decrease until the two curves are close to coincide again. The dimensionless elastic-plastic contact hardness is introduced. The relation between real contact area and the contact pressure of the indentation model can be acquired quickly. The results show that the geometric shape of deformable contact parts has an important effect on the contact parameters, especially for the extension of plastic deformation region within a specific range of plasticity index.

A FEM Based Multiple Asperity Deterministic Contact Model

2009 ◽  
Author(s):  
A. Megalingam ◽  
M. M. Mayuram
Keyword(s):  
Friction And Wear ◽  
Statistical Approach ◽  
Present Model ◽  
Contact Model ◽  
Real Contact Area ◽  
Clear Understanding ◽  
Asperity Contact ◽  
Single Asperity ◽  
Contact Models ◽  
Single Asperity Contact

Knowledge of contact stresses generated when two surfaces are in contact play a significant role in understanding most mechanisms of friction and wear. Most of present contact models are based on the Greenwood-Williamson (GW) single asperity contact model and a statistical approach is adopted to calculate the real contact area for the entire surface based on the assumption that all the summits have uniform radius of curvatures and their heights vary randomly. But in real cases, the asperity radii vary. For a clear understanding about those aspects, a multiple asperity contact model, based on 3-D rough surface generated is analyzed using a commercial FEM package. Salient aspects of the present model are presented here and results are compared with a single asperity contact model.

scholarly journals Efficient Side-Channel Protections of ARX Ciphers

2018 ◽  
pp. 627-653 ◽  
Author(s):  
Bernhard Jungk ◽  
Richard Petri ◽  
Marc Stöttinger
Keyword(s):  
High Performance ◽  
State Of The Art ◽  
Side Channel ◽  
First Order ◽  
Current State ◽  
Assembly Instructions ◽  
Improved Performance ◽  
Good Trade ◽  
Published Result ◽  
Very High

The current state of the art of Boolean masking for the modular addition operation in software has a very high performance overhead. Firstly, the instruction count is very high compared to a normal addition operation. Secondly, until recently, the entropy consumed by such protections was also quite high. Our paper significantly improves both aspects, by applying the Threshold Implementation (TI) methodology with two shares and by reusing internal values as randomness source in such a way that the uniformity is always preserved. Our approach performs considerably faster compared to the previously known masked addition and subtraction algorithms by Coron et al. and Biryukov et al. improving the state of the art by 36%, if we only consider the number of ARM assembly instructions. Furthermore, similar to the masked adder from Biryukov et al. we reduce the amount of randomness and only require one bit additional entroy per addition, which is a good trade-off for the improved performance. We applied our improved masked adder to ChaCha20, for which we provide two new first-order protected implementations and achieve a 36% improvement over the best published result for ChaCha20 using an ARM Cortex-M4 microprocessor.

scholarly journals Evaluating Elastic-Plastic Wavy and Spherical Asperity-Based Statistical and Multi-Scale Rough Surface Contact Models with Deterministic Results

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3864
Author(s):  
Nolan Ryan Chu ◽  
Robert L. Jackson ◽  
Xianzhang Wang ◽  
Arup Gangopadhyay ◽  
Hamed Ghaednia
Keyword(s):  
Contact Problem ◽  
Rough Surface ◽  
Computing Time ◽  
Multiscale Model ◽  
Deterministic Models ◽  
Elastic Plastic ◽  
Multi Scale ◽  
Surface Contact ◽  
Contact Models ◽  
Rough Surface Contact

The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.

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