Bond Graph Simulation of Bicycle Model

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

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

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

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

7. Bicycle Model Bicycle model [1] E579 - Term Project - Bicycle Model

8. 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

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

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

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

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

22. 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

23. Questions?