Bond graph simulation of bicycle model
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E579 – Mechatronic Modeling and Simulation. Bond Graph Simulation of Bicycle Model. Instructor: Dr. Shuvra Das By: Vishnu Vijayakumar. Contents. Introduction Bicycle Model Bond-graph Modeling Results and Discussion Future Work References. Introduction. Types of Cornering

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Bond Graph Simulation of Bicycle Model

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Bond graph simulation of bicycle model

E579 – Mechatronic Modeling and Simulation

Bond Graph Simulation of Bicycle Model

Instructor: Dr. Shuvra Das

By: Vishnu Vijayakumar


Contents

Contents

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


Introduction

Introduction

  • Types of Cornering

    • Slow-speed (parking lot maneuvers)

      • No Lateral Forces

      • Therefore center of turn must lie on the projection of the rear axle

    • High-speed

E579 - Term Project - Bicycle Model


Low speed cornering

Low-Speed Cornering

E579 - Term Project - Bicycle Model


High speed cornering

High- Speed Cornering

  • Turning equations differ because lateral acceleration will be present

  • Tires must develop lateral forces

  • Slip Angles will be present at each wheel

  • For purpose of analysis it is convenient to represent the vehicle by a bicycle model

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


Bicycle model

Bicycle Model

Bicycle model [1]

E579 - Term Project - Bicycle Model


Parameters

Parameters

  • L = Wheel Base = 100.6 in = 8.38ft

  • R = Radius of turn = 200 ft

  • V = Forward Speed

  • g = Gravitational Acceleration = 32.2ft/s2

  • Wf = Load on front axle = 1901 lb

  • Wr = Load on rear axle = 1552 lb

  • Cαf = Cornering Stiffness of front tires = 464 lb/deg

  • Cαr = Cornering Stiffness of rear tires = 390 lb/deg

  • Tire Friction coefficient = 0.7 (Assumed)

  • Yaw Mass moment of Inertia = 600 lb-ft2 [4]

    Example Problem [2]

E579 - Term Project - Bicycle Model


Equations

Equations

Equations for steering angles and slip angles [2]

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


Bond graph representation

Bond Graph Representation

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


Steer angle with velocity

Steer Angle with Velocity

Understeer

E579 - Term Project - Bicycle Model


Change of steer angle with time

Change of Steer angle with time

E579 - Term Project - Bicycle Model


Steer angle vs lateral acceleration

Steer Angle Vs Lateral Acceleration

E579 - Term Project - Bicycle Model


Validation

Validation

  • Measurement of Understeer Gradient Using Constant Radius Method

    • Understeer can be measured by operating the vehicle around a constant radius turn and observing steering angle and lateral acceleration

    • Vehicle speed is increased in steps that will produce lateral accelerations at reasonable increments

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

E579 - Term Project - Bicycle Model


Validation1

Validation

  • At 60 mph velocity the lateral acceleration gain was calculated using the formula

  • Lateral Acceleration was calculated using the formula

  • From graph Lateral Acceleration gain = 0.407g/deg

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


Future work

Future Work

  • Enhance the model

  • Load Transfer (Longitudinal)

E579 - Term Project - Bicycle Model


Bond graph simulation of bicycle model

  • Introduction

  • Bicycle Model

  • Bond-graph Modeling

  • Results and Discussion

  • Future Work

  • References

E579 - Term Project - Bicycle Model


References

References

  • Karnopp, Margolis, Rosenberg, “System Dynamics”, Third Edition, 2000

  • Thomas Gillespie, “Fundamentals of Vehicle Dynamics”, 1992

  • J.Y.Wong, “Theory of Ground Vehicles”, 1993

  • Divesh Mittal, “Characterization of Vehicle Parameters affecting dynamic roll-over propensity”, SAE2006-01-1951

E579 - Term Project - Bicycle Model


Questions

Questions?


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