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.

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.

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.

Asperity Spring Friction Model With Application to Belt-Drives

2003 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Belt Drive ◽  
Finite Element Code ◽  
Time Step ◽  
Stick Slip ◽  
Normal Contact ◽  
Belt Drives ◽  
Coulomb Friction Model

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.

Analysis, Design, and Modeling of a Rotary Vane Engine (RVE)

2004 ◽  
Vol 126 (4) ◽  
pp. 711-720 ◽  
Author(s):  
B. V. Librovich ◽  
A. F. Nowakowski
Keyword(s):  
Coulomb Friction ◽  
Simple Structure ◽  
Dynamical Behavior ◽  
Friction Model ◽  
Reciprocating Engine ◽  
Torque Transmission ◽  
Analysis Design ◽  
Work Units ◽  
Coulomb Friction Model ◽  
Moving Parts

This paper introduces a mathematical model to analyze the dynamic behavior of a novel rotary vane engine (RVE). The RVE can be considered to have a number of advantages when compared to a majority of other reciprocating engine types. The advantages are found in the simple structure and the small number of moving parts. In this paper the geometrical structure and dynamical behavior of engines with a different number of work units is considered in detail. This has been examined through a study of torque transmission with a particular reference to how this is affected by the noncircular geometry of gear pitch curves. Using the Coulomb friction model, consideration has been given to the mechanical power loss due to friction in different parts of the engine, which must be taken into account. The study also proposes a possible method for balancing of asymmetric cogwheels. The analysis concludes that by using an appropriate design and arrangement of cogwheels and all moving parts, vibration can be attenuated due to impulsive gas torque.

Control for Robots With Braking Actuators in a Uniform Force Field

2015 ◽  
Author(s):  
Erlend Framstad ◽  
Mark D. Bedillion
Keyword(s):  
Force Field ◽  
Control Strategy ◽  
Coulomb Friction ◽  
Energy Equation ◽  
High Accuracy ◽  
Friction Model ◽  
Second Law ◽  
Inclined Plane ◽  
Position And Orientation ◽  
Coulomb Friction Model

This paper concerns the control strategy of a robot with controllable brakes placed in a uniform force field. Without loss of generality this force field is assumed to be gravity, and the robot to be an object resting on an inclined plane. The controller’s objective is then to use the brakes to lead the robot into a desired position and orientation. The system’s dynamics were derived from Newton’s second law with a Coulomb friction model. The controller was derived from geometric properties and the energy equation. The controller was then tested using Matlab and Simulink on the dynamics that were derived. The results of the simulation shows high accuracy even with some disturbances, and uncalibrated parameters.

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.

High-Fidelity Modeling of a Backhoe Digging Operation Using an Explicit Multibody Dynamics Code With Integrated Discrete Particle Modeling Capability

2013 ◽  
Author(s):  
Shahriar G. Ahmadi ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Multibody Dynamics ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Friction ◽  
Contact Detection ◽  
High Fidelity ◽  
Normal Contact ◽  
Contact Search

A high-fidelity multibody dynamics model for simulating a backhoe digging operation is presented. The backhoe components including: frame, manipulator, track, wheels and sprockets are modeled as rigid bodies. The soil is modeled using cubic shaped particles for simulating sand with appropriate inter-particle normal and frictional forces. A penalty technique is used to impose both joint and normal contact constraints (including track-wheels, track-terrain, bucket-particles and particles-particles contact). An asperity-based friction model is used to model joint and contact friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model can help improve the performance of construction equipment by predicting the actuator and joint forces and the vehicle stability during digging for various vehicle design alternatives.

scholarly journals Recent Developments and Trends in the Friction Testing for Conventional Sheet Metal Forming and Incremental Sheet Forming

Metals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 47 ◽  
Author(s):  
Tomasz Trzepiecinski ◽  
Hirpa G. Lemu
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Coulomb Friction ◽  
Sheet Forming ◽  
Friction Model ◽  
Friction Resistance ◽  
Friction Testing ◽  
Coulomb Friction Model

Friction is the main phenomenon that has a huge influence on the flow behavior of deformed material in sheet metal forming operations. Sheet metal forming methods are one of the most popular processes of obtaining finished products, especially in aerospace, automobile, and defense industries. Methods of sheet forming are carried out at different temperatures. So, it requires tribological tests that suitably represent the contact phenomena related to the temperature. The knowledge of the friction properties of the sheet is required for the proper design of the conditions of manufacturing processes and tools. This paper summarizes the methods used to describe friction conditions in conventional sheet metal forming and incremental sheet forming that have been developed over a period of time. The following databases have been searched: WebofKowledge, Scopus, Baztool, Bielefield Academic Search Engine, DOAJ Directory of Open Access Journals, eLibrary.ru, FreeFullPdf, GoogleScholar, INGENTA, Polish Scientific Journals Database, ScienceDirect, Springer, WorldCat, WorldWideScience. The English language is selected as the main source of review. However, in a limited scope, databases in Polish and Russian languages are also used. Many methods of friction testing for tribological studies are selected and presented. Some of the methods are observed to have a huge potential in characterizing frictional resistance. The application of these methods and main results have also been provided. Parameters affecting the frictional phenomena and the role of friction have also been explained. The main disadvantages and limitations of the methods of modeling the friction phenomena in specific areas of material to be formed have been discussed. The main findings are as follows—The tribological tests can be classified into direct and indirect measurement tests of the coefficient of friction (COF). In indirect methods of determination, the COF is determined based on measuring other physical quantities. The disadvantage of this type of methods is that they allow the determination of the average COF values, but they do not allow measuring and determining the real friction resistance. In metal forming operations, there exist high local pressures that intensify the effects of adhesion and plowing in the friction resistance. In such conditions, due to the plastic deformation of the material tested, the usage of the formula for the determination of the COF based on the Coulomb friction model is limited. The applicability of the Coulomb friction model to determine the COF is also very limited in the description of contact phenomena in hot SMF due to the high shear of adhesion in total contact resistance.

scholarly journals Laminar momentum jets in a stratified fluid

1971 ◽  
Vol 45 (3) ◽  
pp. 561-574 ◽  
Author(s):  
E. J. List
Keyword(s):  
Fourier Transforms ◽  
Equations Of Motion ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Stratified Fluid ◽  
Integral Representations ◽  
Return Flow ◽  
Horizontal Flows ◽  
Creeping Flows ◽  
Finite Distance

Solutions are presented for creeping flows induced by two-and three-dimensional horizontal and vertical momentum jets in a linearly stratified unbounded diffusive viscous fluid. These linear problems are solved by replacing the momentum jet by a body force singularity represented by delta functions and solving the partial differential equations of motion by use of multi-dimensional Fourier transforms. The integral representations for the physical variables are evaluated by a combination of residue theory and numerical integration.The solutions for vertical jets show the jet to be trapped within a layer of finite thickness and systems of rotors to be induced. The horizontal two-dimensional jet solution shows return flows above and below the jet and a pair of rotors. The three-dimensional horizontal jet has no return flow at finite distance and the diffusive contribution is found to be almost negligible in most situations, the primary character of the horizontal flows being given by the non-diffusive solution. Stokes's paradox is found to be non-existent in a density-stratified fluid.

Sign in / Sign up

Export Citation Format

Share Document