bma4723 vehicle dynamics chap 1

8/6/2019 BMA4723 Vehicle Dynamics Chap 1

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Chapter 1 : Fundamental of Vehicle

Dynamics

By

Mr. Gan Leong Ming

Semester 2007/2008-I


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In the period of early 1900s

There had been sporadic attempts to make thevehicle ride decently, but little had been done. The

rear passengers still functional as ballast, stuck out

behind the rear wheels. Steering was frequently

unstable and the front axle with front brakes madeshimmy almost inevitable. The engineers had made

all the parts function excellently, but when put

together the whole was seldom satisfactory.

Pick from Reminiscenes of Maurice Olley


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Vehicle Dynamics

Broadest sense encompassesall form of conveyance ships,airplanes, trains, rubber-tiredvehicles

Principles are diverse andextensive


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Vehicle Dynamics

Performance of the vehicle

- The motions accomplished in accelerating,

braking, cornering and ride

- A response to forces imposed

- Study of how and why the forces are

produced

- Handling and directional changingperformance


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Vehicle Dynamics

Two level of understanding:

- Empirical : derives from trial and error by

which one learns which factors influence

vehicle performance often lead to failure- Analytical : describe the mechanics of

interest based on the known laws of

physics so that the analytical model can beestablished predictive capability


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Introductory Terminology

General dimensions/Referencedimensions

Wheel Base

Wheel Track Sprung/Unsprung weight

Curb/Lumped weight

Center ofgravity height Weight distribution

Axis System


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Wheel Track

Front trackThe linear dimension between the rotational planes ofthefront wheels

on a vehicle.

Rear trackThe linear dimension between the rotational planes ofthe rear wheels

on a vehicle.

Production vehicles may useeitherequal, or dissimilar dimensionsforfront and rear track. Rear track may begreater than, equal to, or lessthanfront track.

Wheel track, with cgheight, affects weight transfer duringcornering and influences the roll-over potential.

Wheel track must be appropriate to end up with a reasonableweight transfer at the limits ofcornering.


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Wheel Base

The linear dimension between thefrontand rear wheels oneachside.Production vehicles, for obviousreasons, use square vehicles (sameL& R dimension)

The linear dimension between thefront andrear axle centerlines.

Wheel base affects weight transfer duringacceleration and braking.


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Curb/LumpedWeight

Curb/Lumped weightThe weight of the vehicle, fueled and prepared with all

liquids and equipment w/o passengers.

The vehicle as weighed.

Always consider in design the limits of vehicle weight and

analyze at curb wt. and fully laden.

For acceleration, braking, and most tuning analysis


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Sprung/Unsprung Weight

Sprung weightThe vehicle masses that are supported by the vehiclesprings. Sprung weight moves indirectly with the roadsurface. Body, passengers, parts of drive train, and

parts of suspension.

Unsprung weightThe vehicle masses that are directly driven by tire inputforces. Unsprung weight moves directly with the roadsurface. Wheels, tires, brakes, some suspension etc.

For ride analysis


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Center of gravity

Center ofGravity

The theoretical point in the X, Y, Z planes where all

the mass could be located and the weight

distribution ofthe vehicle would remain

unchanged.

Cgheight affects weight transfer during braking,

acceleration and cornering. 1st approximation

!

L

h

g

awWt

cg

long

!

t

h

g

awWt

cg

lat


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Weight Distribution

The distribution ofweight the vehicle weight in the X-Y plane.

Weight front, % Wf Weight rear, % WrWeight left, % Wl Weight right, % Wrt

Tractiveforces during acceleration are a function of% weight on the drive wheels during acceleration(including weight transfer)

Tractive forces required at each axleset during

braking are affected by static weight and weighttransfer.

Brake design choices may be in part affected bybrake requirements ofeach axle.


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SAE Vehicle Axis System


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Euler Angles

Relate the vehicle fixed coordination system to the earthfixed coordination system.

Determined by a sequence of three angular rotations.

Yaw [around z axis]

Pitch [around y axis]

Roll [around x axis]

momentumangularish

torqueappliednetisg

hdt

dg

LawEulers

!


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Forces : Newtons Second Law

Translational systems

Rotational systems

directionxin theonacceleratiisabodytheofmassisM

directionxin theforceisF

MaF

x

x

xx !

momentumlinearisP

Pdt

dv

dt

dMFx !!

axisabout xonacceleratiis

axisabout xinertiaofmomentisI

axisxabout thetorqueisT

IT

x

xx

x

xxxx

y!


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Dynamics Axle Loads

ah

AD

5

L

b

c

W

rW

hd

hh

hxR

hzR

h

xaW/g

W

5sinW

5cosW

Center of gravity,

CG

Drag force

Towing

force

Traction ForceRolling Resistance

xrF

xfFxf

xr

Hitch point

Road

gradient

Arbitrary forces acting on a vehicle

B


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Motion Analysis

By the SAE convention, a clockwise torque about Ais positive,

0coscW-sinhWdRhRhag

WhDLW hhzhhxxaAf !55

So,

/L)sinhWh-hag

WdR-hRcosc(WW axhhzhhx 55!

/L)sinhWhhag

W)L(dR-hRcosb(WW axhhzhhxr 55!

and


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Motion Analysis : Static Loads on Level ground

For road gradient = 0

L

bWW

L

cWW

rs

s

!

!


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Motion Analysis : Low Speed Acceleration

For road gradient = 0

No Drag force

No trailer hitch forces

L

hgaWW

L

hga

L

bWW

L

h

g

aWW

L

h

g

a

L

cWW

xrs

xr

xfs

xf

!

!

!

!


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Motion Analysis : Loads on Grades

Grade defined as the rise over the run

Grade = Tan (grade angle)

5!5!

5!

5!

LhWW

Lh

LbWW

L

hWW

L

h

L

cWW

rsr

s


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Motion Analysis

The curb weight of a Continental 4 doorSedan without passengers or cargo are 1049

kg on the front axle and 599.6 kg on the rear.

The wheel base, L is 2768.6 mm. Determinethe location of the cg to the front wheel and

rear wheel.


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Motion Analysis

A Taurus GL sedan with 3.0L engine acceleratesfrom a standing start up a 6 percent grade at an

acceleration of 1,83ft/s2. Find the load distribution

on the axles at this condition.

Relevant Data :

Curb weight (front) = 884 kg

Curb weight (rear ) = 497.6 kg

Wheel base, L = 2692.4 mmPassenger weight = 90 kg

Passenger weight distribution:

Front 49% Rear 51%

CG height, h = 508 mm

bma4723 vehicle dynamics chap 1

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