1. Bond Graph Simulation of Bicycle Model
E579 – Mechatronic Modeling and Simulation
Bond Graph Simulation of Bicycle Model
Instructor: Dr. Shuvra Das
By: Vishnu Vijayakumar

2. E579 - Term Project - Bicycle Model
Contents
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

3. E579 - Term Project - Bicycle Model
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

4. E579 - Term Project - Bicycle Model
Low-Speed Cornering
E579 - Term Project - Bicycle Model

5. E579 - Term Project - Bicycle Model
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

6. E579 - Term Project - Bicycle Model
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

7. E579 - Term Project - Bicycle Model

8. E579 - Term Project - Bicycle Model
Parameters
L = Wheel Base = 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

9. E579 - Term Project - Bicycle Model
Equations
Equations for steering angles and slip angles [2]
E579 - Term Project - Bicycle Model

10. E579 - Term Project - Bicycle Model
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

11. Bond Graph Representation
E579 - Term Project - Bicycle Model

12. E579 - Term Project - Bicycle Model
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

13. Steer Angle with Velocity
Understeer
E579 - Term Project - Bicycle Model

14. Change of Steer angle with time
E579 - Term Project - Bicycle Model

15. Steer Angle Vs Lateral Acceleration
E579 - Term Project - Bicycle Model

16. E579 - Term Project - Bicycle Model
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

17. E579 - Term Project - Bicycle Model

18. E579 - Term Project - Bicycle Model
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

19. E579 - Term Project - Bicycle Model
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

20. E579 - Term Project - Bicycle Model
Future Work
Enhance the model
Load Transfer (Longitudinal)
E579 - Term Project - Bicycle Model

21. E579 - Term Project - Bicycle Model
Introduction
Bicycle Model
Bond-graph Modeling
Results and Discussion
Future Work
References
E579 - Term Project - Bicycle Model

22. E579 - Term Project - Bicycle Model
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”, SAE
E579 - Term Project - Bicycle Model

23. Questions?