1. ME 457 Some Concepts in Vehicle Dynamics Steve Rohde, Ph.D. steve@quantumsignal.com Spring 2003

2. ME457 Mechatronic Modeling The Chevrolet SSR SSR Movie

3. ME457 Mechatronic Modeling Major Automotive Vehicle Subsystems Powertrain Accessories Brakes Steering Suspension Body

4. ME457 Mechatronic Modeling Automotive Vehicle Subsystem Interactions Powertrain Powertrain Body Body Brakes Accessories Suspension Steering Steering Heat, Noise, Vibration, Engine Vibration Torque Engine Speed Coolant Temp. Accessory Torque Load Battery Voltage Coolant Flow & Heat Loss Torque Delivered to Driven Wheels Driven Wheel Rotational Speeds Heat, Noise, Driver Visibility, Airflow Hydraulic/Pneumatic Pressure Hydraulic Flow, Electrical Voltage Vacuum Electrical Voltage Vacuum Load Electrical Current Heating & Cooling Loads Hydraulic/Pneumatic Flow Hydraulic Pressure, Electrical Current Braking Torque Wheel Rotational Speed Steering Angle Steering Forces Suspension Geometry Suspension Forces Vibration Noise Body Attitude & Position Aerodynamic drag

5. ME457 Mechatronic Modeling Coordinate System Yaw Pitch Roll c.g. y x z

6. ME457 Mechatronic Modeling Somewhat Simplified Model

7. ME457 Mechatronic Modeling The Real Thing!

8. ME457 Mechatronic Modeling “Top Level” Longitudinal Forces M F R D Ma = F – D - R a

9. ME457 Mechatronic Modeling M F R D Ma = F – D - R F = Tractive Force D = Aerodynamic Drag = ½ρAC D V 2 R = Rolling Resistance = Mg(r 0 +r 1 V) Longitudinal Forces

10. ME457 Mechatronic Modeling Forces on an Incline M F R D Ma = F – D – R – Mgsin(θ) M θsθs

11. ME457 Mechatronic Modeling Some Interesting Facts F > 0  Positive Tractive Effort (traction) F – D – R > 0  Accelerating F – D – R < 0  Decelerating │F│ > μN  Wheels Spin a max ~ g Ma = F – D – R

12. ME457 Mechatronic Modeling Instantaneous power: Integrating between 0 and T: Suppose engine is at P max and no losses: Consider WOT (max acceleration) Mav = Fv – Dv – Rv ½ Mv 2 = ∫Fvdt – ∫Dvdt – ∫Rvdt ½ Mv 2 ~ ∫Fvdt ½ Mv 2 ~ T*P max

13. ME457 Mechatronic Modeling Powertrain “Matching” Power Speed Engine Power Road Load ~ v 3

14. ME457 Mechatronic Modeling How about the energy you use driving a vehicle? E = ∫ FV Χ(F)dt Where X(F) = 1 iff F>0, =0 otherwise D B = ∫ FV Χ(-F)dt

15. ME457 Mechatronic Modeling Some simple approximate results E/(MS) = (7.741 r 0 + 111.2 r 1 ) + 113.4 AC D /M + 0.1518 D B /(MS) = 0.1518 - (2.064 r 0 + 22.83 r 1 ) – 18.05 AC D /M Tractive & Braking Energy are Linear with Mass!

16. ME457 Mechatronic Modeling Forces Acting on a Two Axle Vehicle

17. ME457 Mechatronic Modeling Equations of Motion Assume that θ s =0, forces at wheels are combined and aero & towing forces are neglected as are vertical and pitch accelerations. Then: 0 = W f + W r – W 0 = W f l 1 - W r l 2 + (F f + F r )h ma = F f + F r

18. ME457 Mechatronic Modeling Loads on Axles W f = W {l 2 /(l 1 +l 2 ) – h/(l 1 +l 2 )a/g} W r = W {l 1 /(l 1 +l 2 ) + h/(l 1 +l 2 )a/g}

19. ME457 Mechatronic Modeling Maximum Acceleration For a rear drive vehicle: a rmax = g l 1 /(l 1 +l 2 )/{1/µ – h/(l 1 +l 2 )} For a front drive vehicle: a fmax = g l 2 /(l 1 +l 2 )/{1/µ + h/(l 1 +l 2 )} Where µ = Coefficient of friction

20. ME457 Mechatronic Modeling Forces Acting on a Tractor-Semitrailer

21. ME457 Mechatronic Modeling Examples of Math Model Use in GM

22. ME457 Mechatronic Modeling Beetle Lane Change* * Courtesy of MSC.Software

23. ME457 Mechatronic Modeling Truck Rear Suspension* * Courtesy of MSC.Software

24. ME457 Mechatronic Modeling Durability Simulation* * Courtesy of MSC.Software

25. ME457 Mechatronic Modeling Large Vehicle Simulation* * Courtesy of MSC.Software

26. ME457 Mechatronic Modeling Tractor-Trailer Simulation* * Courtesy of MSC.Software

27. ME457 Mechatronic Modeling Motorcycle Drop Simulation* * Courtesy of MSC.Software