ME 457 Some Concepts in Vehicle Dynamics Steve Rohde, Ph.D. [e-mail]

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ME 457Some Concepts in Vehicle
DynamicsSteve Rohde, Ph.D. steve_at_quantumsignal.
com

• Spring 2003

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The Chevrolet SSR
SSR Movie
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Major Automotive Vehicle Subsystems

• Powertrain
• Accessories
• Brakes
• Steering
• Suspension
• Body

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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
Body
Brakes
Accessories
Suspension
Steering
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
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Coordinate System
y
Pitch
c.g.
x
Roll
Yaw
z
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Somewhat Simplified Model
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The Real Thing!
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Top Level Longitudinal Forces
D
M
a
F
R
Ma F D - R
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Longitudinal Forces
Ma F D - R
D
M
F
R
F Tractive Force D Aerodynamic Drag
½?ACDV2 R Rolling Resistance Mg(r0r1V)
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Forces on an Incline
D
F
M
M
?s
R
Ma F D R Mgsin(?)
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Some Interesting Facts
Ma F D R

• F gt 0 ? Positive Tractive Effort (traction)
• F D R gt 0 ? Accelerating
• F D R lt 0 ? Decelerating
• F gt µN ? Wheels Spin
• amax g

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Consider WOT (max acceleration)

• Instantaneous power
• Integrating between 0 and T
• Suppose engine is at Pmax and no losses

Mav Fv Dv Rv
½ Mv2 ?Fvdt ?Dvdt ?Rvdt
½ Mv2 ?Fvdt
½ Mv2 TPmax
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Powertrain Matching
Road Load v3
Power
Engine Power
Speed
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How about the energy you use driving a vehicle?

• E ?FV ?(F)dt
• Where X(F) 1 iff Fgt0, 0 otherwise
• DB ?FV ?(-F)dt

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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!
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Forces Acting on a Two Axle Vehicle
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Equations of Motion
Assume that ?s0, 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
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Loads on Axles
Wf W l2/(l1l2) h/(l1l2)a/g Wr W
l1/(l1l2) h/(l1l2)a/g
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Maximum Acceleration
For a rear drive vehicle armax g
l1/(l1l2)/1/µ h/(l1l2) For a front drive
vehicle afmax g l2/(l1l2)/1/µ h/(l1l2)
Where µ Coefficient of friction
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Forces Acting on a Tractor-Semitrailer
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Examples of Math Model Use in GM
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Beetle Lane Change
Courtesy of MSC.Software
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Truck Rear Suspension
Courtesy of MSC.Software
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Durability Simulation
Courtesy of MSC.Software
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Large Vehicle Simulation
Courtesy of MSC.Software
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Tractor-Trailer Simulation
Courtesy of MSC.Software
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Motorcycle Drop Simulation
Courtesy of MSC.Software