Coupled Multibody Dynamics and Discrete Element Modeling of Vehicle Mobility on Cohesive Granular Terrains

Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

Multibody dynamics and the discrete element method (DEM) are integrated into one solver for predicting the dynamic response of ground vehicles which run on wheels and/or tracks on cohesive soft soils (such as mud and snow). Multibody dynamics techniques are used to model the various vehicle components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints. An asperity-based friction model is used to model joint and contact friction. A soft cohesive soil material model (that includes normal and tangential inter-particle force models) is presented that can account for soil compressibility, plasticity, fracture, friction, viscosity, cohesive strength and flow. 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 the particles and polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. Numerical simulations of a typical vehicle going over a slopped soft soil terrain are presented to demonstrate the integrated solver. The solver can be used in vehicle design optimization.

Author(s):  
Akshay Sane ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

Multibody dynamics and the discrete element method are integrated into one solver for modeling the excavation and moving operation of cohesive soft soil (such as mud and snow) by bulldozers. A soft cohesive soil material model (that includes normal and tangential inter-particle force models) is presented that can account for soil flow, compressibility, plasticity, fracture, friction, viscosity, gain in cohesive strength due to compression, and loss in cohesive strength due to tension. Multibody dynamics techniques are used to model the various bulldozer components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints. 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 the particles and polygonal contact surfaces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. A numerical simulation of a bulldozer performing a shallow digging operation in a cohesive mud-type soil is presented to demonstrate the integrated solver. The solver can be used to improve the design of the various bulldozer components such as the blade geometry, tire design, and track design.


Author(s):  
Shahriar G. Ahmadi ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

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.


Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

Multibody dynamics and the discrete element method (DEM) are integrated into one solver for predicting the mobility characteristics (including the no-go condition, maximum speed, and required engine torque/power) of ground vehicles on rough off-road soft soil (such as mud and snow) terrains. High fidelity multibody dynamics models are used for the various vehicle systems including: suspension system, wheels, steering system, axle, differential, and engine. A penalty technique is used to impose joint and normal contact constraints. An asperity-based friction model is used to model joint and contact friction. A DEM model of the soil with a cohesive soft soil material model is used. The material model can account for the soil compressibility, plasticity, fracture, friction, viscosity, gain in cohesive strength due to compression, and loss in cohesive strength due to tension. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model can be used to predict the mobility of ground vehicles as a function of soil type, terrain long slope, and terrain side slope. Typical simulations of a Humvee-type vehicle are provided to demonstrate the model.


Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

Multibody dynamics and smoothed particle hydrodynamics (SPH) are integrated into one solver for predicting the dynamic response of tanker trucks. Multibody dynamics techniques are used to model the various vehicle components and connect those components using various types of joints and contact surfaces. A penalty technique is used to impose joint and normal contact constraints (between the tires and ground, and between the tank and the fluid particles). An asperity-based friction model is used to model joint and contact friction. The liquid in the tanks is modeled using an SPH particle-based approach. A contact search algorithm that uses a moving Cartesian Eulerian grid that is fixed to the tank 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 and the fluid particles. The governing equations of motion for the solid bodies and the fluid particles are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The integrated solver is used to predict the dynamic response of a typical tanker truck performing a braking test with an empty, half-full and full tank. The solver can be used in vehicle design optimization to simulate and evaluate various vehicle designs.


Author(s):  
Tamer M. Wasfy ◽  
Shahriar G. Ahmadi ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

An explicit time integration multibody dynamics code is used to create a three-dimensional model of sand. Sand is modeled using discrete cubical particles with appropriate normal contact force and tangential friction force models. The model is used to predict the sand angle of repose and flow rate during discharge from a conical hopper. A penalty technique is used to impose normal contact constraints (including particle-particle, particle-hopper and particle-ground contact). An asperity-based friction model is used to model friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. The governing equations of motion are solved along with contact constraint equations using a time-accurate explicit solution procedure. Parameter studies are performed in order to study the effects of the particle size and the orifice’s diameter of the hopper on the angle of repose and sand flow rate. The results of the simulations are validated using previously published experimental results.


Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters

Multibody dynamics and smoothed particle hydrodynamics (SPH) are integrated into one solver for predicting the water fording dynamic response of ground vehicles. Multibody dynamics models are used for the various vehicle systems including: suspension system, wheels, steering system, axles, differential, and engine. A penalty technique is used to impose joint and normal contact constraints (between the tires and ground, and between the tires/vehicle body and the fluid particles). An asperity-based friction model is used to model joint and contact friction. Water is modeled using an SPH particle-based approach along with a large eddy-viscosity turbulence model. A contact search algorithm that uses a Cartesian Eulerian grid around the water pool 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 (representing the tires and vehicle body) and the fluid particles. The governing equations of motion for the solid bodies and the fluid particles are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The integrated solver is used to predict the dynamic response of a Humvee-type vehicle moving through a shallow water pool.


Author(s):  
Adam D. Foltz ◽  
Tamer M. Wasfy ◽  
Erik Ostergaard ◽  
Ilya Piraner

High-powered Diesel engines typically use a timing gear train to couple/synchronize the camshaft rotation with the crankshaft and also to drive the accessories such as the fuel and oil pumps. In this paper a high-fidelity multibody dynamics model of a 6-cylinder inline Diesel engine and its timing gear train is presented. The multibody system representing the system is modeled using rigid bodies, torsional springs, revolute joints, prismatic joints, and rotational/linear actuators. A penalty model is used to impose joint and normal contact constraints. The normal contact penalty stiffness and damping techniques are used to model gear tooth stiffness and damping. The contact model detects contact between discrete points on the surface of a gear tooth (master contact surface) and a polygonal surface representation of the mating gear tooth (slave contact surface). A recursive bounding box/bounding sphere contact search algorithm is used to allow fast contact detection. Time-varying forces are applied to the cylinders to model the cylinder pressure variations due to combustion events as a function of the crank angle. 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 its predictions of the torsional vibrations of a Diesel engine’s crankshaft and moving parts to experimental measurements. Emphasis is given on the practicality of the modeling methods to industry.


Author(s):  
Tamer M. Wasfy ◽  
James O’Kins

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.


Author(s):  
Tamer M. Wasfy

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.


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