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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

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

E579 - Term Project - Bicycle Model

- 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

- Slow-speed (parking lot maneuvers)

E579 - Term Project - Bicycle Model

E579 - Term Project - Bicycle Model

- 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

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

E579 - Term Project - Bicycle Model

Bicycle model [1]

E579 - Term Project - Bicycle Model

- 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 for steering angles and slip angles [2]

E579 - Term Project - Bicycle Model

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

E579 - Term Project - Bicycle Model

E579 - Term Project - Bicycle Model

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

E579 - Term Project - Bicycle Model

Understeer

E579 - Term Project - Bicycle Model

E579 - Term Project - Bicycle Model

E579 - Term Project - Bicycle Model

- 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

E579 - Term Project - Bicycle Model

- 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

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

E579 - Term Project - Bicycle Model

- Enhance the model
- Load Transfer (Longitudinal)

E579 - Term Project - Bicycle Model

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

E579 - Term Project - Bicycle Model

- 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?