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

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

2. The Chevrolet SSR SSR Movie

3. Major Automotive Vehicle Subsystems • Powertrain • Accessories • Brakes • Steering • Suspension • Body

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

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

6. Somewhat Simplified Model

7. The Real Thing!

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

9. Longitudinal Forces Ma = F – D - R D M F R F = Tractive Force D = Aerodynamic Drag = ½ρACDV2 R = Rolling Resistance = Mg(r0+r1V)

10. Forces on an Incline D F M M θs R Ma = F – D – R – Mgsin(θ)

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

12. Consider WOT (max acceleration) • Instantaneous power: • Integrating between 0 and T: • Suppose engine is at Pmax and no losses: Mav = Fv – Dv – Rv ½Mv2 = ∫Fvdt – ∫Dvdt – ∫Rvdt ½Mv2 ~ ∫Fvdt ½Mv2 ~ T*Pmax

13. Powertrain “Matching” Road Load ~ v3 Power Engine Power Speed

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

15. Some simple approximate results • E/(MS) = (7.741 r0 + 111.2 r1) + 113.4 ACD/M + 0.1518 • DB/(MS) = 0.1518 - (2.064 r0 + 22.83 r1) – 18.05 ACD/M Tractive & Braking Energy are Linear with Mass!

16. Forces Acting on a Two Axle Vehicle

17. Equations of Motion Assume that θs=0, forces at wheels are combined and aero & towing forces are neglected as are vertical and pitch accelerations. Then: 0 = Wf + Wr – W 0 = Wf l1 - Wrl2 + (Ff + Fr)h ma = Ff + Fr

18. Loads on Axles Wf= W {l2/(l1+l2) – h/(l1+l2)a/g} Wr= W {l1/(l1+l2) + h/(l1+l2)a/g}

19. Maximum Acceleration For a rear drive vehicle: armax= g l1/(l1+l2)/{1/µ – h/(l1+l2)} For a front drive vehicle: afmax = g l2/(l1+l2)/{1/µ + h/(l1+l2)} Where µ = Coefficient of friction

20. Forces Acting on a Tractor-Semitrailer

21. Examples of Math Model Use in GM

22. Beetle Lane Change* * Courtesy of MSC.Software

23. Truck Rear Suspension* * Courtesy of MSC.Software

24. Durability Simulation* * Courtesy of MSC.Software

25. Large Vehicle Simulation* * Courtesy of MSC.Software

26. Tractor-Trailer Simulation* * Courtesy of MSC.Software

27. Motorcycle Drop Simulation* * Courtesy of MSC.Software