Dynamic Modeling of Flat Belt Drives Using the Elastic-Perfectly-Plastic Friction Law

2009 ◽  
Author(s):  
Dooroo Kim ◽  
Michael Leamy ◽  
Aldo Ferri
Keyword(s):  
Equations Of Motion ◽  
Element Model ◽  
Friction Model ◽  
Local Perturbation ◽  
Belt Drive ◽  
Equilibrium Solutions ◽  
Friction Law ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Nonlinear Equations Of Motion

An analysis of a physically-motivated friction model called the Elastic/Perfectly-Plastic (EPP) friction model was performed on a steadily rotating flat belt drive. The EPP friction law is modeled as an elastic spring in series with an ideal Coulomb damper. The belt kinematics were developed and the nonlinear equations of motion and equilibrium solutions were derived using Hamilton’s Principle. Unlike the belt mechanics analyzed with Coulomb friction, the current study predicts the absence of adhesion zones. A stability analysis demonstrates that the non-linear equilibrium solution found is stable under local perturbation. A two-pulley belt drive with equal radii is analyzed and the dynamic response is studied. The results are compared to those computed using a dynamic finite element model. Excellent agreement between the two methods is documented.

Dynamic Modeling and Stability Analysis of Flat Belt Drives Using an Elastic/Perfectly Plastic Friction Law

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Dooroo Kim ◽  
Michael J. Leamy ◽  
Aldo A. Ferri
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Piecewise Linear ◽  
Equations Of Motion ◽  
Belt Drive ◽  
Equilibrium Solutions ◽  
Friction Law ◽  
Solution Approach ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

This paper presents an analysis of a nonlinear (piecewise linear) dynamical model governing steady operation of a flat belt drive using a physically motivated elastic/perfectly plastic (EPP) friction law. The EPP law models frictional contact as an elastic spring in series with an ideal Coulomb damper. As such, the friction magnitude depends on the stretch of the elastic belt and is integral to the solution approach. Application of the extended Hamilton’s principle, accounting for nonconservative work due to friction and mass transport at the boundaries, yields a set of piecewise linear equations of motion and accompanying boundary conditions. Equilibrium solutions to the gyroscopic boundary value problem are determined in closed form together with an expression for the minimum value of the EPP spring constant needed to transmit a given torque. Unlike equilibrium solutions obtained from a strict Coulomb law, these solutions omit adhesion zones. This finding may be important for interpreting belt drive test-stand results and the experimentally determined friction coefficients obtained from them. A local stability analysis demonstrates that the nonlinear equilibrium solutions found are stable to local perturbations. The steady dynamical operation of the drive is also studied using an in-house corotational finite element code. Comparisons of the finite-element solutions with those obtained analytically show excellent agreement.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 2: Analysis of Repeated Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 75-82 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Shear Strain ◽  
Element Model ◽  
Rolling Contact ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rolling Contacts ◽  
Elastic Perfectly Plastic ◽  
Multiple Translations ◽  
Contact Part

This paper presents finite element analyses of two-dimensional (plane strain), elastic-plastic, repeated, frictionless rolling contact. The analysis employs the elastic-perfectly plastic, cycle and strain-amplitude-independent material used in the Merwin and Johnson analysis but avoids several assumptions made by these workers. Repeated rolling contacts are simulated by multiple translations of a semielliptical Hertzian pressure distribution. Results at p0/k = 3.5, 4.35, and 5.0 are compared to the Merwin and Johnson prediction. Shakedown is observed at p0/k = 3.5, but the comparisons reveal significant differences in the amount and distribution of residual shear strain and forward flow at p0/k = 4.35 and p0/k = 5.0. The peak incremental, shear strain per cycle for steady state is five times the value calculated by Merwin and Johnson, and the plastic strain cycle is highly nonsymmetric.

Effect of Rubber Material Properties on Steady-State Flat Belt Response

2019 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy
Keyword(s):  
Steady State ◽  
Internal Combustion Engines ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Solution Procedure ◽  
Friction Model ◽  
Rigid Bodies ◽  
Rubber Matrix ◽  
Belt Drive

Abstract Belt-drives are used to transmit power between rotational machine elements in many mechanical systems such as industrial machines, home appliances, and internal combustion engines. The belt cross-section typically consists of axially stiff tension cords (made of steel or polyester strands) embedded in a rubber matrix. The rubber matrix provides the friction interface between the belt and the pulleys through which mechanical torque is transmitted. In this paper, the effect of the rubber’s Young’s modulus and Poisson’s ratio on the steady-state belt normal, tangential and axial stresses, average belt slip, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of a flat belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s cords are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using a time-accurate explicit solution procedure.

Applications of a New Element Model of Solid Bodies in Plasticity

2013 ◽  
Vol 690-693 ◽  
pp. 1800-1805
Author(s):  
Jiang Ke
Keyword(s):  
Composite Material ◽  
Element Model ◽  
Fiber Reinforced Composite ◽  
Perfectly Plastic ◽  
Reinforced Composite ◽  
Applied Forces ◽  
Elastic Perfectly Plastic ◽  
External Forces ◽  
Solid Bodies ◽  
Reinforced Composite Material

Based on the deformations under the equivalent external forces are the same, a new element model of elastic perfectly-plastic and orthotropic solid bodies is presented, and the elastic perfectly-plastic and isotropic materials is a special subclass. Furthermore, the method for determining the displacements, the stresses and the strains of a body under the action of applied forces has been given. A new method for predicting the engineering elastic constants of a fiber-reinforced composite material is also presented. It can be found that the precision by using the new element method is good, and the limit analysis has the highest precision in all methods.

An Elastic-Plastic Finite Element Model of Rolling Contact, Part 1: Analysis of Single Contacts

1985 ◽  
Vol 52 (1) ◽  
pp. 67-74 ◽  
Author(s):  
V. Bhargava ◽  
G. T. Hahn ◽  
C. A. Rubin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Rolling Contact ◽  
Stress And Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Contact Width ◽  
Elastic Perfectly Plastic

This paper describes a two-dimensional (plane strain) elastic-plastic finite element model of rolling contact that embodies the elastic-perfectly plastic, cycle and amplitude-independent material of the Merwin and Johnson theory, but is rigorous with respect to equilibrium and continuity requirements. The rolling contact is simulated by translating a semielliptical pressure distribution. Both Hertzian and modified Hertzian pressure distributions are used to estimate the effect of plasticity on contact width and the continuity of the indentor-indentation interface. The model is tested for its ability to reproduce various features of the elastic-plastic indentation problem and the stress and strain states of single rolling contacts. This paper compares the results derived from the finite element analysis of a single, frictionless rolling contact at p0/k = 5 with those obtained from the Merwin and Johnson analysis. The finite element calculations validate basic assumptions made by Merwin and Johnson and are consistent with the development of “forward” flow. However, the comparison also reveals significant differences in the distribution of residual stress and strain components after a single contact cycle.

Elasto-Plastic Finite Element Analysis of Repeated, Two-Dimensional Rolling-Sliding Contacts

1988 ◽  
Vol 110 (1) ◽  
pp. 44-49 ◽  
Author(s):  
G. Ham ◽  
C. A. Rubin ◽  
G. T. Hahn ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Tangential Force ◽  
Element Model ◽  
Sliding Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Pure Rolling ◽  
Tangential Surface ◽  
Elastic Perfectly Plastic

The stresses, strains, and deformations produced by repeated, two-dimensional rolling-sliding contact are analyzed using a modified finite element model developed by Bhargava et al. [1]. Rolling and sliding are simulated by translating an appropriate set of normal and tangential surface tractions across an elastic-perfectly plastic half space. The study examines a peak-pressure-to-shear strength ratio of po/k = 4.5 and normal to tangential force ratios of T/N = 0.20 and T/N = 0.17. The calculations describe the residual stresses, displacements and the continuing cyclic radial, shear and equivalent strains generated at various depths in the rim. The results are compared with previous calculations by Johnson and Jefferis [2] of rolling-sliding contact and with pure rolling. The present work predicts much higher deformations than previously calculated.

Response and Instability of Sloping Seabed Supporting Small Marine Structures: Wave-Structure-Soil Interaction Analysis

2021 ◽  
pp. 1-20
Author(s):  
Amin Rafiei ◽  
M.S. Rahman ◽  
M.A. Gabr
Keyword(s):  
Interaction Analysis ◽  
Plastic Material ◽  
Wave Structure ◽  
Element Model ◽  
Induced Response ◽  
Perfectly Plastic ◽  
Marine Hydrokinetic ◽  
Elastic Perfectly Plastic ◽  
The Stability ◽  
Wave Induced

Abstract Wave-induced liquefaction in seabed may adversely impact the stability and bearing capacity of the foundation elements of coastal structures. The interaction of wave, seabed, and structure has been studied mostly for only mildly sloping seabed (<5°) using a decoupled approach. However, some of the marine hydrokinetic devices (MHKs) may be built on or anchored to the seabed with significant steepness. The wave-induced response and instantaneous liquefaction within sloping seabed supporting a small structure (representing a small MHK device) are evaluated herein by developing an almost fully coupled finite element model. The effects of coupling approach on the stress response and liquefaction of the seabed soils are investigated. Subsequently, post-liquefaction deformation of seabed soils around the structure is assessed. The poroelasticity equations governing the seabed response coupled with those for other domains are solved simultaneously. For post-liquefaction analysis, the soil is modeled as elastic perfectly plastic material. The development of instantaneously liquefied zones near the foundation is studied in terms of seabed steepness and wave parameters. The changes in the effective stress paths due to the development of liquefied zones are evaluated in view of the soil's critical state. The results indicate that the decoupled solution yields significantly larger stresses and liquefaction zones around the structure. The seabed response and the liquefaction zones become smaller for steeper slopes. The presence of liquefied zones brings the stress state closer to the failure envelope, reduces the confining stresses, and induces larger plastic strains around the foundation element.

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