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.

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 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.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

Study of Frictional Impact Using a Nonsmooth Equations Solver

1999 ◽  
Vol 67 (2) ◽  
pp. 267-273 ◽  
Author(s):  
L. Johansson ◽  
A. Klarbring
Keyword(s):  
Numerical Algorithm ◽  
Newton's Method ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Direct Approach ◽  
Nonsmooth Equations ◽  
Usual Sense ◽  
Coulomb's Law

In this paper a mathematical formulation and a numerical algorithm for the analysis of impact of rigid bodies against rigid obstacles are developed. The paper concentrates on three-dimensional motion using a direct approach where the impenetrability condition and Coulomb’s law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton’s method. An experiment has also been performed and compared with predictions of the algorithm, with favorable results. [S0021-8936(00)01402-1]

Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. J. Richard ◽  
R. Anderson ◽  
G. C. Andrews
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
New Approach ◽  
System Description ◽  
Nonlinear Equations Of Motion ◽  
Systematic Formulation ◽  
Multi Body ◽  
Entire Procedure

This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

scholarly journals UNIVERSAL SOFTWARE SYSTEM “STADYO” FOR THE NUMERICAL SOLUTION OF LINEAR AND NONLINEAR PROBLEMS OF THE FIELD THEORY, STATICS, STABILITY AND DYNAMICS OF SPATIAL COMBINED SYSTEMS: GENERAL PARAMETERS AND SUPERELEMENTAL FEATURES

2018 ◽  
Vol 14 (3) ◽  
pp. 26-41 ◽  
Author(s):  
Alexander M. Belostotsky ◽  
Alexey L. Potapenko ◽  
Pavel A. Akimov
Keyword(s):  
Field Theory ◽  
Numerical Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Orthotropic Materials ◽  
Software System ◽  
Natural Oscillations ◽  
Dynamic Synthesis ◽  
Linear And Nonlinear

The distinctive paper presents the general papers of the science-based universal software system “STADYO” intended for the numerical solution of stationary and nonstationary problems of field theory, analy-sis of static, temperature and dynamic stress-strain state (SSS), stability and strength of arbitrary combined me-chanical systems (massive-shell-lamellar-membrane-rod with “rigid” bodies, fluid cavities and internal bonds, isotropic and orthotropic materials) into a flat axis, axisymmetric and three-dimensional linear and nonlinear formulations. The composition of the “STADYO” software system is briefly described; in terms of its theoretical foundations, the main provisions and matrix relationships of the superelement method (which is known to be one of the most effective ways to increase the universality and increase the computational efficiency of finite element algorithms) are presented, as well as methods for dynamic synthesis of substructures and submodelling. The su-perelement algorithm is also extended to solving a system of linear equations at each step of the implicit scheme of direct integration of the equations of motion, and at each iteration in the calculation of natural oscillations; however, an alternative and more efficient approach consists in constructing special superelement algorithms based on the direct condensation of the equations of motion and ideologically close to the method of dynamic synthesis of substructures. The submodelling options, in particular, are important for the refined analysis of the three-dimensional SSS of heavily loaded component parts of the objects under consideration. In general, the presentation of the global design model of the system as a set of substructures is also very convenient for its de-scription and creates the prerequisite for the creation (application) of effective pre- and postprocessor software. The paper also provides information on verification and experience in the use of the “STADYO” software sys-tem, as well as prospects for development. 

scholarly journals Dynamics of constrained many body problems in constant curvature two-dimensional manifolds

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170425 ◽  
Author(s):  
Andrzej J. Maciejewski ◽  
Maria Przybylska
Keyword(s):  
Constant Curvature ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Rigid Bodies ◽  
The Body ◽  
Two Dimensional ◽  
Many Body ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In this paper, we investigate systems of several point masses moving in constant curvature two-dimensional manifolds and subjected to certain holonomic constraints. We show that in certain cases these systems can be considered as rigid bodies in Euclidean and pseudo-Euclidean three-dimensional spaces with points which can move along a curve fixed in the body. We derive the equations of motion which are Hamiltonian with respect to a certain degenerated Poisson bracket. Moreover, we have found several integrable cases of described models. For one of them, we give the necessary and sufficient conditions for the integrability. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

Proposed Solution Methodology for the Dynamically Coupled Nonlinear Geared Rotor Mechanics Equations

1985 ◽  
Vol 107 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. D. Mitchell ◽  
J. W. David
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Three Dimensional ◽  
Dynamic Coupling ◽  
State Response ◽  
Shaft System ◽  
Coupling Terms ◽  
Solution Methodology

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

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