lec4-1Cornering

7/29/2019 lec4-1Cornering

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Vehicle Responses to Cornering

From a control point of view, cornering is the.

Note: In vehicle dynamics terminology, cornering or turningof the vehicle is referred to as yaw or yawing of thevehicle.

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The Wheel while CorneringThe Sli An le is measured from theCenter line of the Tire (in the traveling

direction) to the Direction of the

Cornering Force.

2


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Cornering Very SlowCofG

- no slip angles at the tires

- Instantaneous direction of

. .

Travel

Vehicle

path

C/L R

www.racing-car-technology.com.au 3

travel is at right angles to turn

radius, R.

- is the attitude angleCar is pointing out from the

turn.

Instantaneous Turn

Centre

Cornering Neutral SteerVehicle

C/L

- Dir. of Travel and R stay.

- The lateral force forces slip

Inst. Dir.

Travel

Vehicle

path

R


angles, , front and rear.- The vehicle rotates in thedirection of the turn.

- The car is nowpo inting in to

the corner.

Instantaneous Turn

Centre

The neutral vehicle

maintains the

intended path


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3

Cornering OversteerVehicle

C/L

Inst. Dir.

Travel

Intended

Vehicle Path

R

- Slip angles increase at the rear,

faster than the front


Instantaneous Turn

Centre

- The car rotates further in the

direction of the turn, increasingthe attitude angle, .- The turn radius, R is shorten.

vers eer

Vehicle Path

Note: The rear tyres

are not sliding

Cornering Understeer

Vehicle

Understeer

Vehic le Path

Inst. Dir.

Travel

R

- Slip angles increase at the

front, faster than the rear


Intended

Vehicle

pathInstantaneous Turn

Centre

- the car rotates out of the turn,

reducing the attitude angle.

- Turn radius, R is lengthened

Note: The front tyres

are not sliding


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4

Lateral Forces and US or OSMoments around the CG

b a

- Balanced (neutral)

- Net rotational force around the CG

(cause US or OS).Atti tude Angle

Front

FR

CG

FF


For neutral steer, FF x a = FR x b, i.e. the rotational forces are balanced.

For oversteer, FF x a > FR x b, i.e. decreasing relative rear grip, increasing attitude angle.

For understeer, FF x a < FR x b, i.e. decreasing relative front grip, decreasing attitude angle.

Slip Angle vs Lateral LoadMaximum grip is at

6 deg slip angle.

For a given Fz of 1800lbs.Goodyear Eagle 215-60-15

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Cornering Stiffness , C , isthe initial slope of t he curve.

RCVD, Milliken and Milliken, p25


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Lateral Force Vs Slip Angle (as Fz varied)Max grip, shown for

each vertical load.

Fy = Fz

9

Notice the change of the Max-Lateral Force vs. The Vertical Load !!!

Lateral Force vs. Vertical LoadStatics Weight Dist . 400 kg

Lat. Force: 560*2 = 1120 kg

(1.4g Cornering Capacity)

At 80% Lateral Load Transfer:

Outboard : 720 kg

Inboard: 80 kg

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a . orce g

Lat. Force (IB) 120 kg

Total Lat. Force 1056 kg

(1.32g Cornering Capacity )


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Control Front vs. Rear BalanceBalance Limits Grip: axle-pair of tires that reach the top of

the curve first (the tires are saturated), limit the other pair.

Lateralforce

Rear Tires

Front TiresLateralforce

Rear Tires

Front Tires Lateralforce

Rear Tires

Front Tires

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Slip angleSlip angle Slip angle

Neutral Steer OverSteer (OS)UnderSteer (US)

The sketches show t he car neutral in the linear range for all three examples. This is true for

small slip angles. In reality, most cars will start to buil d US or OS well inside the linear range.

Oversteer and Understeer Control/Optimization Maximising grip at all four tires

, , , ,

Because of the transient nature of handling, maximiseoverall grip with attention to spring frequency - springs,ARBs and shocks controlling ride, roll pitch rate are alsoimportant.

Balancing the car for oversteer/understeer must alsonot be overlooked. Ideally we look to stick the looseend so as to increase overall grip.



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Tuning for Grip and BalanceA set of tires and a competent driver are

.

Factors determine the performance:

y Tires traction (Choices!!)

y Dynamic loading of the tires (Design!!)

Desi n Variables:

y Track width & CG Height (Difficult to change)y Roll Center Height (Difficult to adjust, but crucial)

y Roll Stiffness (Springs, ARB, Dampers)

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Track Width, CG, and RC

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For Left Turn:

- Tire forces acting at the ground level

- Accelerate through the Center of Turn (Centripetal)

- Resisting inertial force is created (Centrifugal)

- Overturning moment causes the weight transfer


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15

Equivalent Forces System at the RC:

- FR and FL are created by the cornering forces at the right and left tires

- FI and MI represent the roll moment

- Distance of RC-CG affects the magnitude of MI- The higher RC, the lesser MI (vice versa)

- BUT....Overall weight transfer characteristic is not altered!


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Equivalent Forces System at the RC:

- FT is the summation of FR and FL- FH and FV represent axial components of FT- FH accelerates the vehicle toward the turn

- FV represent a Jacking Force lifting the vehicle during the turn!

- The higher the CG, the larger the FV


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9


Most Designer: Low RC just above the ground

Commonly used: 2 inches for Front

3 6 inches for Rear (??)

Suspension Designer spends a lot of time

keeping RC unchanged in any condition

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Simple Roll Stiffness (Lateral Weight Transfer)

,

transfer is a function of

- the cornering force

- vehicle mass

- CG height

- the track measurement The roll stiffness or weight transfer concept issometimes called roll moment distribution in

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e ex oo s.

But by changing thepropor tion of roll stiffness, front vs. rear, this total weight

transfer can be manipulated between the front and the rear of the car.

The lateral grip at each end of the car is then varied, thus influencing attitude

angle change, as per the previous slides.


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Total Weight Transfer CalculationThe Total Weight Transfer is calculated as follows:

Lateral Force = Vehicle Mass*Lateral Acceleration

Lateral Weight Transfer = Lateral Force*CG Height/Track

The lateral force is reacted by

the tires.

The faster car, for a given

lateral force po tential, will

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(CG) and a wider track.

Total Weight Transfer CalculationThe Total Weight Transfer is calculated as follows:

Lateral Force = Vehicle Mass*Lateral Acceleration

Lateral Weight Transfer = Lateral Force*CG Height/Track

The lateral force is reacted bythe tires.

Forces for the suspended

mass and non suspended

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force at the CG.


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Total Weight Transfer CalculationTotal Weight Transfer is the sum of three very important components:

Non Suspended Weight Transfer :

,

uprights, brakes etc. We take the axle height as a close approximation to thecenter of mass, or centre of gravity, (CG), for the non suspended mass.

And two components of Suspended Weight Transfer :

Geometric Weight Transfer :

Due to the component of lateral force, applied directly at the Roll CentreRC . Geometric WT is reacted directl throu h the sus ension linka es and

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does not induce body roll.

Elastic Weight Transfer :

Due to the component of lateral force, applied at the Suspended Mass CG, and

does induce body roll. This force is reacted in the springs, anti-roll bars andshocks, and is the only one of the three components of total weight transfer that

does induce body roll.

Total Weight Transfer Calculation

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Roll Resistance

Weight transfer exist in any case

The amount of roll depending on the

spring and/or ARB stiffness

The stiffer the spring, the lesser degree

of roll

Now what ha en when ou have

y Equally stiff front and rear springs?y Stiffer front spring than the rear?

y Stiffer rear spring than the front?

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Roll Resistance

Equally stiff springs:

y e c e en er ng e corner

y Weight transfer starts

y Body rolls due to moment by some degree

depending on the moment magnitude

yAssuming that the RC front and rear are the

,

and rear are the same.

y What happen if we change the spring

stiffness? (Modification?)

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Roll Resistance

Stiffer front spring:

y , , o y ro s

y Stiffer front spring creates force oppose to the

roll force fast ! (not the rate but the motion...and reducesthe degree of roll

y The reduction of the degree of roll decreases the

wei ht transfer at the rear end roll lesser amountlesser force opposes to the roll force, lesser weight transfer)

y Increasing of the weight transfer reduces grip!

y Less grip at the front, Good grip at the rear

y Understeer

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Roll Resistance

Stiffer rear spring:

y , , o y ro s

y Stiffer rear stop the rear end roll faster

(againnot the rate, but the motion) with a highmagnitude of weight transfer

y Increasing of the weight transfer reduces grip!

,

y Oversteer

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Roll Resistance

Come back to the Equally stiff springs:

y a appen we c ange e spr ng

stiffness? (Modification?)

yAdjusting the spring stiffness for both front

and rear would not adjust the grip balance

. Useless (in other words)

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Roll Resistance

What about the Damper?

y e oc y sens ve ev ce

y Its effects can be felt during transient period e.g.

cornering entry or exist

(while adjusting the roll resistance by the spring

and ARB has more effects on mid-corner)

yAdjusting the damper is normally done at the

advance level of modifications. (Dynamic Roll

Stiffness Adjustment)

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Roll Resistance

29Time Sequence of Cornering Forces and Roll

Tuning for Grip and Balance Static Roll Resistance: The most basic set-up

y norma y cu

y Spring and ARB

To satisfy the Ride Height and Roll Resistance Req.

Dynamic Roll Adjustment:

y RC (normally difficult)

y Dampers

To satisfy transient performance during cornering

entry (roll) and exist (deroll)

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Static Roll Stiffness Spring Rate and Wheel Rate

Kw= R2Ks

R = a/b

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Heavy Car : Stiff Spring (for a good ride height)

or Soft Spring w ith a larger motion ratio + Damping Adjustment

Static Roll Stiffness Spring Rate and Wheel Rate

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Kw= R2Ks

R = r3/r1Bellcrank

Suspension


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Static Roll Stiffness Starting Point of the Spring and ARB

y ee a e a c e g

0.7:1 for normal road

1 1.3 for Small Size Open Wheeler & Stock Race

1.6 - 2.4 for Open Wheeler

y 1.6 : Formula 2000, 1.9 : Formula Atlantic, 2.3 : CART

,

selectedy For Road: Front 10% - 15% Softer for Flat Ride

y For Race: Front 5% - 20% Stiffer for Control

yARB is to add 10% - 20% to the roll stiffness33

Dynamic Roll Stiffness Corner-Entry

y vers eer

Increase bump on front/ decrease rebound at rear

More bump front -> more weight transfer -> less grip

Corner-Exit

y Oversteer

Decrease rebound on front/ decrease bump at rear

Less rebound front -> more weight transfer -> less grip

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Example for Tuning Front:

Track = 60 in500 500

Front

RC = 2 in

Spring = 500 lb/in

USpW = 100 lb

Tire R = 26 in

Rear:Track = 60 in

RC = 4 in

Spring = 400 lb/in

USpW = 200 lb

500

lb

500

lb

Tire R = 26 in

Overall:Wheel Base = 100 in

CG = 16 in

Total Weight = 2000 lb

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Curve Weight

Goal: Balanced Car with One

Degree Roll at 1.2 G


Track = 60 in181 819

Front

RC = 2 in

Spring = 500 lb/in

USpW = 100 lb

Tire R = 26 in Rear:

Track = 60 in

RC = 4 in

Spring = 400 lb/in

USpW = 200 lb

179

lb

821

lb

.

50.2%

0.98 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering


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Track = 60 in174 826

Front

RC = 2 in

Spring = 400 lb/in (500)

USpW = 100 lb

Tire R = 26 in

Rear:Track = 60 in

RC = 4 in


USpW = 200 lb

186

lb

814

lb

.

49.1%

1.26 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Changing Spring to Add ARB


Track = 60 in161 839

Front

RC = 2 in


USpW = 100 lb


Track = 60 in

RC = 4 in


USpW = 200 lb

199

lb

801

lb

.

47.0%

1.76 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Changing Spring to Add ARB


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Track = 60 in102 898

Front

RC = 2 in

Spring = 200 lb/in (500) + ARB of 100 lb/in

USpW = 100 lb

Tire R = 26 in

Rear:Track = 60 in

RC = 4 in


USpW = 200 lb

258

lb

742

lb

.

37.8%

1.60 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Adding F-ARB of 100lb/in


Track = 60 in192 808

Front

RC = 2 in


USpW = 100 lb


Track = 60 in

RC = 4 in


USpW = 200 lb

168

lb

832

lb

.

37.8%

1.18 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Adding R-ARB of 100lb/in


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Track = 60 in146 854

Front

RC = 2 in


USpW = 100 lb

Tire R = 26 in

Rear:Track = 60 in

RC = 4 in


USpW = 200 lb

214

lb

786

lb

.

44.7%

0.93 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Adding F-ARB of another

100lb/in


Track = 60 in145 855

Front

RC = 2 in


USpW = 100 lb


Track = 60 in

RC = 10 in (4)


USpW = 200 lb

215

lb

785

lb

.

44.6%

0.93 Degree Roll

Tire R = 26 in


CG = 16 in


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1.2 G Cornering

Raising R-RC to 10 in


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Total Weight Transfer CalculationPerformance Set-Up

The indication of the oversteer/understeer balance of the car.

If the front "Distrib of Total Weight Transfer is the same as the static front weightpercentage, the car is neutral. The front "Distrib of Total Weight Transfer that is

lower than neutral moves the car in the direction of oversteer.

For both road car and race car set ups, we use an approximation of 3% - 5%

higher than static front weight percentage - ie in the direction of understeer.

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What do the racers do? Wedging (Diagonal Weight Transfer Adj)

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