A Shakedown Limit under Hertz Contact Pressure

2011 ◽  
Vol 291-294 ◽  
pp. 1506-1510
Author(s):  
Jim S. Shiau
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Mathematical Programming ◽  
Contact Mechanics ◽  
Contact Pressure ◽  
Hertz Contact ◽  
Moving Surface ◽  
Load Limit ◽  
Shakedown Limit ◽  
Surface Loads

In his "Contact Mechanics" book, Professor K. L. Johnson described an analytical lower bound shakedown approach to predict the shakedown load limit under repeated Hertz moving surface loads. Based on Bleich-Melan shakedown theorem, this problem will be revisited in this paper using finite element techniques and mathematical programming.

Hertz Contact Problem between Wheel and Rail

2013 ◽  
Vol 837 ◽  
pp. 733-738 ◽  
Author(s):  
Tiberiu Axinte
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Contact Problem ◽  
Contact Pressure ◽  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Contact ◽  
Hertz Contact ◽  
Shakedown Limit ◽  
Plastic Shakedown

Rail-wheel contact problems have been analyzed by the use of the three-dimensional finite element models. Based on these models, the paper presents a study regarding the applicability of the Hertz contact to rail-wheel contact problems. Beside a standard rail, the study also considers a crane rail and a switching component. The bodies of the contact problem are the standard rail UIC60 and the standard wheel UICORE. The maximum contact pressure which the material can support in the elastic range in steady state conditions is known as the shakedown limit. With an operating contact pressure below the shakedown limit the rail would be expected to remain elastic a long period of its lifecycle. However, examination of rail cross-sections shows severe plastic deformation in a sub-surface layer of a few tens of microns thickness; the contact patch size is in tens of millimeters. Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted in order to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. The Hertz theory is restricted to frictionless surfaces and perfectly elastic solids, but it is the best method for determining deformations and stress from pitch of contact. Form change due to wear and plastic deformation of a rail can reduce the service life of a track. The purpose of this investigation was to study the development of these damage mechanisms on new and three years old rails in a commuter track over a period of two years.

THE EFFECT OF ASPHERICITY OF ACETABULAR BEARING SURFACE ON CONTACT MECHANICS OF UHMWPE TOTAL HIP IMPLANTS BY FINITE ELEMENT ANALYSIS

2017 ◽  
Vol 17 (01) ◽  
pp. 1750011 ◽  
Author(s):  
XUAN ZHANG ◽  
LING WANG ◽  
XIFENG PENG ◽  
DICHEN LI ◽  
JIANKANG HE ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Contact Mechanics ◽  
Contact Pressure ◽  
Surface Profile ◽  
Surface Measurement ◽  
Element Analysis ◽  
Actual Surface ◽  
Total Hip ◽  
Measuring Machine

Asphericity and out-of-roundness are generally used to evaluate the manufacturing quality of ultra-high molecular weight polyethylene (UHMWPE) cup inner surfaces, which can potentially affect initial clinical wear and contribute to osteolysis of total hip arthroplasty. This study measured the location and magnitude of asphericity and the out-of-roundness value for four UHMWPE cups in a single set, and then investigated the effects of the asphericity on the contact mechanics of UHMWPE cups. A co-ordinate measuring machine (CMM) was used for the surface measurement and finite element analysis (FEA) was adopted for contact mechanics study. The results demonstrated that the asphericity varied between cups with the maximum value as 0.088[Formula: see text][Formula: see text][Formula: see text]0.004[Formula: see text]mm. Although such a value met the ISO specification, large difference of volume appeared for the asphericity above 0.060[Formula: see text]mm. Actual surface profile accounting for the asphericity was found to affect the value of contact pressure and contact area by around 12%. The inferior asphericity resulted in a nonsmoothly distributed contact pressure, which had a negative effect on the contact mechanics of UHMWPE cups and the edge loading was predicted to occur for the sample with a large asphericity. In conclusion, the asphericity of UHMWPE cup could affect the contact mechanics of the articular bearings and may subsequently contribute to initial wear during bedding-in phase.

THEORETICAL AND FINITE ELEMENT ANALYSIS TO DETERMINE CONTACT PRESSURE, VONMISSES STRESSES AND WEAR IN CAM AND FOLLOWER FOR VARIOUS CAM ROTATIONAL ANGLES IN IC ENGINE

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Jayakumar K ◽  
Aldrin Raj J ◽  
Somesh Subramanian S
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Contact Pressure ◽  
Compressive Force ◽  
Surface Wear ◽  
Hertz Contact ◽  
Element Analysis ◽  
Ic Engine ◽  
Rotational Angle ◽  
Base Circle

The contact between the cam and follower that exists in the valve strain system of IC engine influences wear. The dynamic analysis of cam and follower system in carried to find the normal compressive force for various cam rotational angles. Based on this compressive force on the cam, the hertz contact stresses and surface wear are calculated theoretically. Finite element analysis was carried out in the three critical portions of the cam such as cam nose region, cam tangent region and cam base circle region to compare the results. The results showed that cam rotational angle directly affects the contact pressure. The max contact pressure occurs in the nose end of the cam. The results showed that principle stress and wear also increases with cam rotational angle

scholarly journals A closed-form formulation for the conformal articulation of metal-on-polyethylene hip prostheses: Contact mechanics and sliding distance

2018 ◽  
Vol 232 (12) ◽  
pp. 1196-1208 ◽  
Author(s):  
Ehsan Askari ◽  
Michael S Andersen
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Contact Mechanics ◽  
Contact Pressure ◽  
Contact Point ◽  
Contact Stresses ◽  
Computational Time ◽  
Physiological Loading ◽  
Sliding Distance ◽  
Inertia Forces

Using Hertz contact law results in inaccurate outcomes when applied to the soft conformal hip implants. The finite element method also involves huge computational time and power. In addition, the sliding distance computed using the Euler rotation method does not incorporate tribology of bearing surfaces, contact mechanics and inertia forces. This study, therefore, aimed to develop a nonlinear dynamic model based on the multibody dynamic methodology to predict contact pressure and sliding distance of metal-on-polyethylene hip prosthesis, simultaneously, under normal walking condition. A closed-form formulation of the contact stresses distributed over the articulating surfaces was derived based upon the elastic foundation model, which reduced computational time and cost significantly. Three-dimensional physiological loading and motions, inertia forces due to hip motion and energy loss during contact were incorporated to obtain contact properties and sliding distance. Comparing the outcomes with that available in the literature and a finite element analysis allowed for the validation of our approach. Contours of contact stresses and accumulated sliding distances at different instants of the walking gait cycle were investigated and discussed. It was shown that the contact point at each instant was located within the zone with the corresponding highest accumulated sliding distance. In addition, the maximum contact pressure and area took place at the stance phase with a single support. The stress distribution onto the cup surface also conformed to the contact point trajectory and the physiological loading.

scholarly journals Direct Validation of Human Knee-Joint Contact Mechanics Derived From Subject-Specific Finite-Element Models of the Tibiofemoral and Patellofemoral Joints

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Wei Gu ◽  
Marcus G. Pandy
Keyword(s):  
Finite Element ◽  
Knee Joint ◽  
Contact Mechanics ◽  
Contact Pressure ◽  
Weight Bearing ◽  
Human Knee ◽  
Human Knee Joint ◽  
Joint Contact ◽  
Joint Contact Pressure

Abstract The primary aim of this study was to validate predictions of human knee-joint contact mechanics (specifically, contact pressure, contact area, and contact force) derived from finite-element models of the tibiofemoral and patellofemoral joints against corresponding measurements obtained in vitro during simulated weight-bearing activity. A secondary aim was to perform sensitivity analyses of the model calculations to identify those parameters that most significantly affect model predictions of joint contact pressure, area, and force. Joint pressures in the medial and lateral compartments of the tibiofemoral and patellofemoral joints were measured in vitro during two simulated weight-bearing activities: stair descent and squatting. Model-predicted joint contact pressure distribution maps were consistent with those obtained from experiment. Normalized root-mean-square errors between the measured and calculated contact variables were on the order of 15%. Pearson correlations between the time histories of model-predicted and measured contact variables were generally above 0.8. Mean errors in the calculated center-of-pressure locations were 3.1 mm for the tibiofemoral joint and 2.1 mm for the patellofemoral joint. Model predictions of joint contact mechanics were most sensitive to changes in the material properties and geometry of the meniscus and cartilage, particularly estimates of peak contact pressure. The validated finite element modeling framework offers a useful tool for noninvasive determination of knee-joint contact mechanics during dynamic activity under physiological loading conditions.

Contact mechanics analysis of measured wheel-rail profiles using the finite element method

2001 ◽  
Vol 215 (2) ◽  
pp. 65-72 ◽  
Author(s):  
T Telliskivi ◽  
U Olofsson
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Half Space ◽  
Contact Pressure ◽  
Material Model ◽  
Fe Method ◽  
Significant Difference ◽  
Mechanics Analysis ◽  
First Contact ◽  
Maximum Contact

A tool has been developed for contact mechanics analysis of the wheel-rail contact. Using measurements of wheel and rail profiles as input, the tool is based on the finite element (FE) code ANSYS. Traditionally, two methods have been used to investigate the rail-wheel contact, namely Hertz's analytical method and Kalker's software program Contact. Both are based on the half-space assumption as well as on a linear-elastic material model. The half-space assumption puts geometrical limitations on the contact. This means that the significant dimensions of the contact area must be small compared with the relative radii of the curvature of each body. Especially in the gauge corner of the rail profile, the half-space assumption is questionable since the contact radius here can be as small as 10 mm. By using the FE method (FEM) the user is not limited by these two assumptions. The profile measurement system Miniprof was used to measure the wheel and rail profiles that were used as input when generating the FE mesh. As a test case, a sharp curve (303 m radius) in a unidirectional commuter train track used by X1 and X10 trains was chosen. The results of two contact cases were compared with the results of the Hertz analytical method and the program Contact. In the first contact case the wheel was in contact with the rail gauge corner. In the second case the wheel was in contact with the rail head. In both contact cases Hertz and Contact presented very similar results for the maximum contact pressure. For the first contact case, a significant difference was found between the FE method and the Hertz method and the program Contact in all of output data. The Hertz and Contact methods both presented a maximum contact pressure that was three times larger (around 3 GPa) than the FE solution. Here, the difference was probably due to the combination of both the half-space assumption and the elastic-plastic material model. For the second contact case, there was no significant difference between the maximum contact pressure results of the three different contact mechanics methods employed.

Finite Element Simulation of Tire-Rim Interface

1989 ◽  
Vol 17 (4) ◽  
pp. 305-325 ◽  
Author(s):  
N. T. Tseng ◽  
R. G. Pelle ◽  
J. P. Chang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Finite Element Simulation ◽  
Contact Pressure ◽  
Element Model ◽  
Experimental Measurements ◽  
Inflation Pressure ◽  
Interference Fit ◽  
Element Simulation ◽  
Rubber Composite

Abstract A finite element model was developed to simulate the tire-rim interface. Elastomers were modeled by nonlinear incompressible elements, whereas plies were simulated by cord-rubber composite elements. Gap elements were used to simulate the opening between tire and rim at zero inflation pressure. This opening closed when the inflation pressure was increased gradually. The predicted distribution of contact pressure at the tire-rim interface agreed very well with the available experimental measurements. Several variations of the tire-rim interference fit were analyzed.

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

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