Bond Graph Simulation of Bicycle Model Instructor: Dr. Shuvra Das By: Vishnu Vijayakumar E579 –...
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Transcript of Bond Graph Simulation of Bicycle Model Instructor: Dr. Shuvra Das By: Vishnu Vijayakumar E579 –...
Bond Graph Simulation of Bicycle Model
Instructor: Dr. Shuvra Das
By: Vishnu Vijayakumar
E579 – Mechatronic Modeling and Simulation
E579 - Term Project - Bicycle Model 2
Contents
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
E579 - Term Project - Bicycle Model 3
Introduction
Types of CorneringSlow-speed (parking lot maneuvers)
No Lateral ForcesTherefore center of turn must lie on the
projection of the rear axleHigh-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 wheelFor purpose of analysis it is convenient
to represent the vehicle by a bicycle model
E579 - Term Project - Bicycle Model 6
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
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
RgC
VW
RgC
VW
R
L
r
rr
f
ff
rf
..
.
..
.
3.57
2
2
Equations for steering angles and slip angles [2]
E579 - Term Project - Bicycle Model 10
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
E579 - Term Project - Bicycle Model 11
Bond Graph Representation
RFront_tire_friction
RRear_Tire_friction
1OneJunction1
1OneJunction2
0ZeroJunction1
0ZeroJunction2
MTFb_cos_delta
MTFsine_delta
MTFinverse_cos_delta
TFc
MGYMGY1
IMass_x
IMoment_of_Inertia
IMass_y
1OneJunction3
1OneJunction4
1OneJunction5
Submodel2
Submodel3
Submodel4
mass
SignalGenerator3
MSfMSf1
d/dt
Differentiate1
SignalGenerator2
delta_calc
E579 - Term Project - Bicycle Model 12
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
E579 - Term Project - Bicycle Model 13
0 5 10 15 20 25 30 35Velocity
2
2.5
3
3.5
4Steer angle
Understeer
Steer Angle with Velocity
E579 - Term Project - Bicycle Model 14
Change of Steer angle with time
Steer Angle Vs Time
0 5 10 15 20time {s}
2.2
2.4
2.6
2.8
3
3.2Steer Angle
E579 - Term Project - Bicycle Model 15
Steer Angle Vs Lateral Acceleration
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Lateral Acceleration
2.2
2.4
2.6
2.8
3
3.2Delta
E579 - Term Project - Bicycle Model 16
Validation
Measurement of Understeer Gradient Using Constant Radius MethodUndersteer 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
deg/475.0
3.571
3.572
2
g
LgKVLg
Vay
gRg
Vay 2.1
2.32200
8822
R
Vay
2
E579 - Term Project - Bicycle Model 19
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
E579 - Term Project - Bicycle Model 20
Future Work
Enhance the model Load Transfer (Longitudinal)
E579 - Term Project - Bicycle Model 21
IntroductionBicycle ModelBond-graph ModelingResults and DiscussionFuture WorkReferences
E579 - Term Project - Bicycle Model 22
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
Questions?