Finite Element Modeling of the Dynamic Response of Tracked Vehicles

2009 ◽  
Author(s):  
Tamer M. Wasfy ◽  
James O’Kins
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Friction ◽  
Flexible Bodies ◽  
Tracked Vehicles ◽  
Joint Contact

A time-accurate finite element model for predicting the dynamic response of tracked vehicles is presented. The model supports flexible continuous belt-type tracks and segmented-tracks consisting of rigid and/or flexible links connected using revolute joints. The flexible multibody system representing the tracked vehicle is modeled using rigid bodies, flexible bodies, joints and actuators. Flexible bodies are modeled using total-Lagrangian brick, membrane, beam, truss and linear/rotational spring elements. The penalty method is used to impose the joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A recursive bounding box contact search algorithm is used to allow fast contact detection between finite elements and other elements as well as general triangular/quadrilateral 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 design of tracked vehicles including increasing the vehicle’s stability and durability.

High-Fidelity Modeling of Flexible Timing Belts Using an Explicit Finite Element Code

2011 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Search Algorithm ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Friction ◽  
High Fidelity ◽  
Explicit Finite Element ◽  
Contact Points ◽  
Joint Contact

A time-accurate high-fidelity finite element model for timing belt-drives is presented. The belt is modeled using flexible spatial lumped parameters beam elements. Each finite element belt node can be considered as a rigid body whose contact geometry is used to model the contact surfaces of the belt teeth. The sprockets and pulleys are modeled as rigid bodies. A penalty model is used to impose the joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A recursive bounding box contact search algorithm is used to allow fast contact detection between contact points on the belt surface (master contact surface) and a polygonal surface representation of the sprockets/pulleys. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model is partially validated by comparing to a previously published steady-state study where the belt tooth loads over the driven sprocket were experimentally measured. The model can help improve the design of timing belts including increasing the range of operating speeds, reduce the vibrations and noise and increase the drive durability.

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.

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.

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

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.

Influence of Flexible Bodies in Military Tracked Vehicle Dynamics

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
S. Jothi ◽  
V. Balamurugan ◽  
K.M. Mohan
Keyword(s):  
Dynamic Simulation ◽  
Rigid Bodies ◽  
The Finite Element Method ◽  
Tracked Vehicle ◽  
Finite Element Method Result ◽  
Flexible Bodies ◽  
Tracked Vehicles ◽  
Dynamic Studies ◽  
The Military ◽  
Test Result

Tracked vehicles are meant to be used in the harsh cross country environment. In particular, the military tracked vehicles are highly exposed to severe terrains and critical handling conditions. Yet while carrying out the dynamic studies, the tracked vehicles, in general, are modeled as rigid bodies. Hence in this article, an attempt has been made to understand closely the dynamics of a tracked vehicle with the inclusion of some parts of the tracked vehicle viz., hull side plates and road wheel arms, as flexible bodies in the dynamic analysis using the finite element method. Result of the flexible dynamic simulation is also compared with the tracked vehicle analysis with the same parts modeled as rigid bodies. In this investigation, dimensions of the standard staggered trapezoidal blocks terrain meant for testing the tracked vehicles is used to carry out the dynamic studies on the tracked vehicle. The dynamic simulation result of the flexible tracked vehicle model is also compared with the experimental test result of the actual tracked vehicle conducted in the actual trapezoidal blocks terrain.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

Real-Time Explicit Flexible Multibody Dynamics Solver With Application to Virtual-Reality Based E-Learning

2011 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Virtual Reality ◽  
Finite Elements ◽  
Rigid Body ◽  
Real Time ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Rigid Bodies ◽  
Flexible Bodies ◽  
Joint Contact ◽  
E Learning

A flexible multibody dynamics explicit time-integration parallel solver suitable for real-time virtual-reality applications is presented. The hierarchical “scene-graph” representation of the model used for display and user-interaction with the model is also used in the solver. The multibody system includes rigid bodies, flexible bodies, joints, frictional contact constraints, actuators and prescribed motion constraints. The rigid bodies rotational equations of motion are written in a body-fixed frame with the total rigid body rotation matrix updated each time step using incremental rotations. Flexible bodies are modeled using total-Lagrangian spring, truss, beam and hexahedral finite elements. The motion of the elements is referred to a global inertial Cartesian reference frame. A penalty technique is used to impose joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A bounding box binary tree contact search algorithm is used to allow fast contact detection between finite elements and other elements as well as general triangular/quadrilateral rigid-body surfaces. The real-time solver is used to model virtual-reality based experiments (including mass-spring systems, pendulums, pulley-rope-mass systems, billiards, air-hockey and a solar system) for a freshman university physics e-learning course.

Random Base Excitation of Timoshenko Beam Traversed by Moving Load

2011 ◽  
Author(s):  
Fahim Javid ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Base Excitation ◽  
Lateral Direction ◽  
Beam Dynamic

The study of dynamic response of Timoshenko beam traversed by moving load subjected to random base excitation is carried out. By applying the theory of dynamic response of Timoshenko beam as well as finite element theory, beam finite element governing equations of motion are developed and they are solved using Galerkin method. To validate the model, some results of the model are compared with those available in literatures and very close agreement is achieved. The beam is subjected to travelling load and random base excitation in lateral direction simultaneously. Three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, are considered and beam dynamic behavior; such as deflection, velocity, and bending moment of beam midpoint, with all so-called boundary conditions are studied. To get better understanding of base excitation effects on the beam dynamic performance, all the results are presented with and without base excitation, in which considerably difference is observed. Moreover, the effect of base excitation on beam with different span-length is monitored.

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