Bond Graph Simulation of Bicycle Model

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Bond Graph Simulation of Bicycle Model
E579 Mechatronic Modeling and Simulation

• Instructor Dr. Shuvra Das
• By Vishnu Vijayakumar

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Contents

• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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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

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Low-Speed Cornering
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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

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• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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Bicycle Model
Bicycle model 1
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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
• Caf Cornering Stiffness of front tires 464
  lb/deg
• Car 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

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Equations
Equations for steering angles and slip angles 2
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• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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Bond Graph Representation
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• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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Steer Angle with Velocity
Understeer
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Change of Steer angle with time
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Steer Angle Vs Lateral Acceleration
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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

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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

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• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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Future Work

• Enhance the model
• Load Transfer (Longitudinal)

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• Introduction
• Bicycle Model
• Bond-graph Modeling
• Results and Discussion
• Future Work
• References

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References

1. Karnopp, Margolis, Rosenberg, System Dynamics,
   Third Edition, 2000
2. Thomas Gillespie, Fundamentals of Vehicle
   Dynamics, 1992
3. J.Y.Wong, Theory of Ground Vehicles, 1993
4. Divesh Mittal, Characterization of Vehicle
   Parameters affecting dynamic roll-over
   propensity, SAE2006-01-1951

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Questions?