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ME 457 Some Concepts in Vehicle Dynamics Steve Rohde, Ph.D. [email protected] Spring 2003. The Chevrolet SSR. SSR Movie. Major Automotive Vehicle Subsystems. Powertrain Accessories Brakes Steering Suspension Body. Automotive Vehicle Subsystem Interactions.

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Me 457 some concepts in vehicle dynamics steve rohde ph d steve@quantumsignal com

ME 457Some Concepts in Vehicle DynamicsSteve Rohde, Ph.D. [email protected]

Spring 2003



Major automotive vehicle subsystems
Major Automotive Vehicle Subsystems

  • Powertrain

  • Accessories

  • Brakes

  • Steering

  • Suspension

  • Body


Automotive vehicle subsystem interactions
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


Coordinate system
Coordinate System

y

Pitch

c.g.

x

Roll

Yaw

z




Top level longitudinal forces
“Top Level” Longitudinal Forces

D

M

a

F

R

Ma = F – D - R


Longitudinal forces
Longitudinal Forces

Ma = F – D - R

D

M

F

R

F = Tractive Force

D = Aerodynamic Drag = ½ρACDV2

R = Rolling Resistance = Mg(r0+r1V)


Forces on an incline
Forces on an Incline

D

F

M

M

θs

R

Ma = F – D – R – Mgsin(θ)


Some interesting facts
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


Consider wot max acceleration
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


Powertrain matching
Powertrain “Matching”

Road Load ~ v3

Power

Engine Power

Speed


How about the energy you use driving a vehicle
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


Some simple approximate results
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!



Equations of motion
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


Loads on axles
Loads on Axles

Wf= W {l2/(l1+l2) – h/(l1+l2)a/g}

Wr= W {l1/(l1+l2) + h/(l1+l2)a/g}


Maximum acceleration
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




Beetle lane change
Beetle Lane Change*

* Courtesy of MSC.Software


Truck rear suspension
Truck Rear Suspension*

* Courtesy of MSC.Software


Durability simulation
Durability Simulation*

* Courtesy of MSC.Software


Large vehicle simulation
Large Vehicle Simulation*

* Courtesy of MSC.Software


Tractor trailer simulation
Tractor-Trailer Simulation*

* Courtesy of MSC.Software


Motorcycle drop simulation
Motorcycle Drop Simulation*

* Courtesy of MSC.Software


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