Me 457 some concepts in vehicle dynamics steve rohde ph d steve@quantumsignal com
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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. [email protected]

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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


The chevrolet ssr

The Chevrolet SSR

SSR Movie


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


Somewhat simplified model

Somewhat Simplified Model


The real thing

The Real Thing!


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!


Forces acting on a two axle vehicle

Forces Acting on a Two Axle Vehicle


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


Forces acting on a tractor semitrailer

Forces Acting on a Tractor-Semitrailer


Examples of math model use in gm

Examples of Math Model Use in GM


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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