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

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

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

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

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

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

E579 - Term Project - Bicycle Model 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

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

Bond Graph Representation 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

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

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

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

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

E579 - Term Project - Bicycle Model

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

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 Future Work Enhance the model Load Transfer (Longitudinal) 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

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”, SAE2006-01-1951 E579 - Term Project - Bicycle Model

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