Prediction of the Normal and Tangential Friction Forces for Thick Flat Belts Using an Explicit Finite Element Code

2013 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Coulomb Friction ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Rubber Matrix ◽  
Necessary Condition ◽  
Friction Forces ◽  
Tangential Contact ◽  
Explicit Finite Element ◽  
One Dimensional

A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the normal and tangential contact forces between the belt and the pulleys. In previous papers those contact forces were predicted using one dimensional thin beam elements and approximate Coulomb friction models. However, typically flat belts have a small thickness and the reinforcements are typically near the top surface of the belt. In this paper the effect of the belt thickness on the normal and tangential contact forces and on the average slip between the belt and the pulleys is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. The belt reinforcements are modeled using one dimensional truss elements at the top surface of the belt. 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.

Effect of Flat Belt Thickness on Steady-State Belt Stresses and Slip

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Tamer M. Wasfy ◽  
Cagkan Yildiz ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Coulomb Friction ◽  
Equations Of Motion ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Friction Model ◽  
Rigid Bodies ◽  
Rubber Matrix ◽  
Necessary Condition ◽  
Belt Drive ◽  
Coulomb Friction Model

A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the belt stresses, pulley angular velocities, belt slip, and belt-drive energy efficiency. In previous papers, those quantities were predicted using thin shell, beam, or truss elements along with a Coulomb friction model. However, flat rubber belts have a finite thickness and the reinforcements are typically located near the top surface of the belt. In this paper, the effect of the belt thickness on the aforementioned response quantities is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. Belt reinforcements are modeled using one-dimensional truss elements at the top surface of the belt. 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.

Dynamic Modeling of Synchronous Belt-Drives Using an Explicit Finite Element Code

2005 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Fixed Number ◽  
Friction Model ◽  
Rigid Bodies ◽  
Finite Element Code ◽  
Tooth Contact ◽  
Friction Forces ◽  
Normal Contact ◽  
Explicit Finite Element

A time-accurate explicit time-integration finite element code is used to simulate the dynamic response of synchronous belts-drives. The belt is modeled using beam or truss elements. The sprockets are modeled as cylindrical rigid bodies. Normal contact between the belt and a sprocket is modeled using the penalty technique and friction is modeled using an asperity-based approximate Coulomb friction model. The belt teeth/grooves are assumed to be located at the belt nodes (every fixed number of belt nodes). The nodes in-between teeth are subjected to the normal contact and tangential friction forces. The belt and sprocket teeth are assumed to be trapezoidal. The equivalent belt-sprocket tooth stiffness and damping coefficients in the normal tooth contact direction are used to calculate a normal tooth contact force at the belt teeth nodes. The tooth contact model also includes the effect of the tooth engagement tolerance. For validation purposes, a two-sprocket drive is modeled and a comparison is made between tooth loads predicted by the finite element model and experimental data available in the literature. Reasonable agreement between the simulation and experimental results is found of the drive’s tooth loads. Also, the dynamic response of a hybrid sprocket – flat pulley belt-drive is studied.

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.

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.

scholarly journals Identification of the Dynamic Parameters of a Parallel Kinematics Mechanism with Prismatic Joints by Considering Varying Friction

2020 ◽  
Vol 10 (14) ◽  
pp. 4820
Author(s):  
Abdur Rosyid ◽  
Bashar El-Khasawneh
Keyword(s):  
Dynamic Model ◽  
Coulomb Friction ◽  
Optimization Technique ◽  
Dynamic Parameter ◽  
Friction Model ◽  
Parallel Kinematics ◽  
Friction Forces ◽  
Normal Forces ◽  
Novel Approach ◽  
Friction Parameters

This study proposed a novel approach for the offline dynamic parameter identification of parallel kinematics mechanisms in which the friction is significant and varying. Since the friction is significant, it should be incorporated to provide an accurate dynamic model. Furthermore, the varying normal forces as a result of the changing posture of the mechanism lead to varying friction forces, specifically varying static and Coulomb friction forces. By considering this variation, the static and Coulomb friction parameters are identified as coefficients instead of forces. A bound-constrained optimization technique using an iterative global search tool was employed in this work to minimize the residual errors while maintaining the physical feasibility of the solutions. Moreover, the friction was modeled by using the nonlinear Stribeck friction model since a linear friction model was not sufficient, whereas the variation of the friction followed the variation of the normal forces, which were evaluated through the Lagrange multipliers in the constrained dynamic model of the mechanism. The solutions obtained were verified by using some trajectories that were different from those used in the identification.

scholarly journals A Two-Dimensional Discrete Model for Dynamic Analysis of Belt Transmission with Dry Friction

2014 ◽  
Vol 61 (4) ◽  
pp. 571-593
Author(s):  
Krzysztof Kubas
Keyword(s):  
Dynamic Analysis ◽  
Dry Friction ◽  
Discrete Model ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Friction Forces ◽  
Calculation Results ◽  
Model Of Friction ◽  
Belt Transmission

Abstract The paper presents a model for dynamic analysis of belt transmission. A twodimensional discrete model was assumed of a belt consisting of rigid bodies joined by translational and torsion spring-damping elements. In the model, both a contact model and a dry friction model including creep were taken into consideration for belt-pulley interaction. A model with stiffness and damping between the contacting surfaces was used to describe the contact phenomenon, whereas a simplified model of friction was assumed. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Equations of motion of separate elements of the belt and pulleys were solved numerically by using adaptive stepsize integration methods. Calculation results are presented of the reaction forces acting on the belt as well as contact and friction forces between the belt body and pulley in the sample of the belt transmission. These were obtained under the influence of the assumed drive and resistance torques.

A Kinetic Friction Model for Viscoelastic Contact of Nominally Flat Rough Surfaces

2007 ◽  
Vol 129 (3) ◽  
pp. 684-688 ◽  
Author(s):  
K. Farhang ◽  
A. Lim
Keyword(s):  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Tangential Velocity ◽  
Surface Profile ◽  
Friction Model ◽  
Contact Forces ◽  
Profile Measurement ◽  
Tangential Contact ◽  
Force Velocity

Approximate closed-form equations are derived for normal and tangential contact forces of rough surfaces in dry friction. Using an extension of the Greenwood and Tripp (1970, Proc, Inst. Mech. Eng., 185, pp. 625–633) model, in which the derivations permit asperity shoulder-to-shoulder contact and viscoelastic asperity behavior, mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. A statistical approach is forwarded in which dependence of the asperity tangential contact force on relative tangential velocity of two asperities can be cast as corrective factors in the mathematical description of tangential force. In this regard two corrective coefficients are derived: force directionality corrective coefficient and force–velocity directionality corrective coefficient. The results show that for a moderate to high load ranges the contact force can be analytically described to within 20% accuracy of that from a numerical integration of the contact equations, well below the uncertainties due to surface profile measurement.

Identification of Friction Model Parameters Using the Inverse Harmonic Method

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Abdallah Hadji ◽  
Njuki Mureithi
Keyword(s):  
Contact Region ◽  
Signal Reconstruction ◽  
Superposition Principle ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Contact Forces ◽  
Fourier Series Expansion ◽  
Model Parameters ◽  
Stick Slip ◽  
Friction Forces

A hybrid friction model has been developed by Azizian and Mureithi (2013, “A Hybrid Friction Model for Dynamic Modeling of Stick–Slip Behavior,” ASME Paper No. PVP2013-97249) to simulate the general friction behavior between surfaces in contact. However, identification of the model parameters remains an unresolved problem. To identify the parameters of the friction model, the following quantities are required: contact forces (normal and tangential or friction forces), the slip velocity, and the displacement in the contact region. Simultaneous direct measurement of these quantities is difficult. In the present work, a beam clamped at one end and simply supported with the consideration of friction at the other is used as a mechanical amplifier of the friction effects at the microscopic level. Using this simplified approach, the contact forces, the sliding velocity, and the displacement can be indirectly obtained by measuring the beam vibration response. The inverse harmonic balance method is a new method based on nonlinear modal analysis which is developed in this work to calculate the contact forces. The method is based on the modal superposition principle and Fourier series expansion. Two formulations are possible: a harmonic form formulation and a subharmonic form formulation. The approach based on subharmonic forms coupled with spline fitting gave the best results for signal reconstruction. Signal reconstruction made it possible to accurately identify the parameters of the hybrid friction model with a multiple step approach.

Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion

2000 ◽  
Vol 123 (4) ◽  
pp. 661-669 ◽  
Author(s):  
Fitsum A. Tariku ◽  
Robert J. Rogers
Keyword(s):  
Mechanical Systems ◽  
Friction Model ◽  
Contact Forces ◽  
Force Balance ◽  
Two Dimensional ◽  
Lumped Mass ◽  
Stick Slip ◽  
Normal Contact ◽  
One Dimensional ◽  
Friction Models

In many mechanical systems, the tendency of sliding components to intermittently stick and slip leads to undesirable performance, vibration, and control behaviors. Computer simulations of mechanical systems with friction are difficult because of the strongly nonlinear behavior of the friction force near zero sliding velocity. In this paper, two improved friction models are proposed. One model is based on the force-balance method and the other model uses a spring-damper during sticking. The models are tested on hundreds of lumped mass-spring-damper systems with time-varying excitation and normal contact forces for both one-dimensional and two-dimensional stick-slip motions on a planar surface. Piece-wise continuous analytical solutions are compared with solutions using other published force-balance and spring-damper friction models. A method has been developed to set the size of the velocity window for Karnopp’s friction model. The extensive test results show that the new force-balance algorithm gives much lower sticking velocity errors compared to the original method and that the new spring-damper algorithm exhibits no spikes at the beginning of sticking. Weibull distributions of the sticking velocity errors enable maximum errors to be estimated a priori.

The Influence of Pulley Deformations on the Shifting Mechanism of Metal Belt CVT

2005 ◽  
Vol 127 (1) ◽  
pp. 103-113 ◽  
Author(s):  
G. Carbone ◽  
L. Mangialardi ◽  
G. Mantriota
Keyword(s):  
Coulomb Friction ◽  
Rate Of Change ◽  
Groove Width ◽  
Speed Ratio ◽  
Dimensional Model ◽  
Friction Forces ◽  
One Dimensional ◽  
Mode Behavior ◽  
Radial Thickness ◽  
Transversal Width

This paper is concerned with the shifting behavior of a metal belt CVT. The calculations are performed for the chain belt case by using a one-dimensional model of the belt: the radial thickness of the belt is neglected. The friction forces are modeled on the basis of the Coulomb friction hypothesis. The deformation of the belt, i.e., the variation of its transversal width, is shown to be negligible with respect to the variation of the local groove width caused by the elastic deformation of the pulleys and by the clearance in the bearings. The particular shape of the deformed pulley is described on the basis of Sattler model (1999) who showed that the variation of the groove angle and that one of the local groove width of the pulley can be easily described by simple trigonometric formulas. The paper shows that the characteristic behavior of the transmission during slow shifting maneuvers, referred to as “creep mode,” is caused by the bending of the pulleys, that is to say for rigid pulleys no “creep mode” can be observed. Moreover, the model shows that increasing the rate of change of speed ratio a transition from the “creep-mode” to the so called “slip-mode” behavior of the variator takes place, as experimentally observed.

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