Asist. Prof. dr. Simon Oman

Tires and differential gear

Composition of a radial-ply tire

2

Tire labeling

• 6,40-13/6 PR:

– Bias-ply tire

– Tire width: 6,40”

– Wheel-rim diameter: 13”

– Tire-wall height: 0,95 (super

balloon for D) * 6,40”

– Loading index: PR6

– Velocity index: no index

(maximum velocity = 150

km/h)

3

• 265/50 R 14 101 V:

– Radial-ply tire (R)

– Tire width: 265 mm

– Wheel-rim diameter : 14”

– Tire-wall height : 0,50 * 265

mm

– Load index: 101

– Velocity index: V (maximum

velocity = 240 km/h)

Tire labeling

• Production date: DOT xxyy

– xx => week;

– yy => year.

• Tire load index:

4

Tire labeling

• Tire velocity index:

– P => 150 km/h

– Q => 160 km/h

– S => 180 km/h

– T => 190 km/h

– H => 210 km/h

– V => 240 km/h

– W => 270 km/h

– Y => 300 km/h

– VR => above 210 km/h

– ZR=> above 240 km/h

5

Difference between radial and bias tire

Tire as a friction wheel - acceleration

H

tr,g

tr,m

10 t

konstrZM

v

vv

Z

F

HstH

t

kh

⋅=⋅⋅=

−=

=

µµ

σ

µ

0

0

v

v0

M

rst

Ft

Z

7

Tire as a friction wheel - braking

H

tr,g

tr,m

-10 t

konstrZM

v

vv

Z

K

HstH

t

h

⋅=⋅⋅=

−=

=

µµ

σ

µ

0

8

Difference between rolling and sliding

Traction diagram for radial-ply tires and bias-ply tires

10

Traction diagram for accelerating and braking

11

Micro-contact between tire and driving surface during

acceleration

12

Micro-contact between tyre and driving surface during

braking

13

4x4 wheel drive

20,20,210,10,1 RrvRrv stst ∝⋅=>∝⋅= ωω

• Central power splitter without differential gear on a hard

surface:

• Theoretical tangential velocities:

• Actual tangential velocities:

2121 ; MMvv ≠=14

R1

R2

P

R1,R2 >> 0R1

R2

P

Power splitter

without central differential

gear

4x4 wheel drive

• Central power splitter without differential gear on a hard

surface:

15

-M1

+M1 -M2

+M2

v1,0 v2,0

v1,0; v2,0 … theoretical velocities

v1; v2 … actual velocities

|+M

2|=

|-M

1|

v1 = v2

Mmot=0Mmot>0

+M

mo

t-M

1

+M

2

4x4 wheel drive

221

222111

mot

stst

MMM

RrvRrv

==

∝⋅=>∝⋅= ωω

16

• Central power splitter with a differential gear on a hard

surface:Pmot

R1

R2

P

P2

Pmot/2

P1

Pmot/2

Power splitter

with a central differential

gear

4x4 wheel drive

17

• Central power splitter with a differential gear – hard surface

under the rear axle, soft surface under the front axle, straight

driving:

4x4 wheel drive

-M1

+M1

-M2

+M2

M2

v1,0=v2,0

M1

v1=v2

Mmot

18

• Central power splitter without differential gear – hard surface

under the rear axle, soft surface under the front axle, straight

driving:

TORSEN differential gear

19

Agle

bevel

gear

Diffe

ren

tia

l g

ea

r

Worm

wheel

Worm gear

Animation

Mechanical self-locking differential gear with lamellas

20

Automatic self-locking differential gear - ASD

21

Angle bevel

gear

Diffe

ren

tia

l g

ear

Control pressure

(right)

Control pressure

(left)

Attached to a housing

of a bevel gear

Torque vectoring differential

22

ICE

Gear-box

Torque-vectoring

differential gear

Mz > MnMn

Fk,n Fk,z

Agile cornering

Gear-box

Mz < MnMn

Fk,n Fk,z

Safety – vehicle

stabilisation

Gear-box

Bigger torque to

a wheel with a

better traction

Fk,2Fk,1

Improved traction

M2 > M1M1

ICE ICE

Torque-vectoring

differential gear

Torque-vectoring

differential gear

Steering torque on

traction wheels

Steering torque

on traction wheels

Torque vectoring differential

Granzow 2013, str. 5. 23

• Operation during cornering:

Torque vectoring differential

24

• Functional assembly of a ZF Vector drive differential gear:

FaFa Fa Fa

Conventional differential

gear with the angle

bevel gear

Left unit for torque-

vectoringRight unit for torque-

vectoring

Multi-disc brake Multi-disc brake

Torque vectoring differential

Granzow 2013, str. 8. 25

• System assembly:

Torque vectoring differential

Granzow 2013, str. 15. 26

• Assembly cross-section:

Torque vectoring differential

27

• Principle of operation without torque-vectoring function:

Fa=0 Fa=0

MKG

M1=MKG /2 M2=MKG /2

Fk,1 Fk,2=Fk,1

Granzow 2013, str. 9.

Torque vectoring differential

Granzow 2013, str. 10.

Fa=0 Fa>0

MKG =2000 Nm

M1=480 Nm 420 Nm

Fk,1

Fk,2 >Fk,1

900 Nm

1100 Nm

980 Nm

120 Nm

Σ=1400 Nm

28

• Principle of operation by applying the torque-vectoring

function:

Torque vectoring differential

Granzow 2013, str. 11.

Fa=0 Fa>0MKG =0 Nm

M1=510 Nm 590 Nm

Fk,1

Fk,2

1100 Nm

1100 Nm

980 Nm

120 Nm

Σ=390 Nm

29

• Principle of operation by applying the torque-vectoring

function:

Torque vectoring differential

Granzow 2013, str. 18. 30

• Activation of a multi-disc brake of a planetary shaft:

Torque vectoring differential

Granzow 2013, str. 19. 31

• Activation of a multi-disc brake of a planetary shaft:

Torque vectoring differential

Granzow 2013, str. 27. 32

• The torque-vectoring differential is a mechatronic system:

Cornering stifness of a tire

33

ω=0

Z

S

Y

PZ

S

x

dZ/dx(ω=0)

Contact surface

ω>0

S

x

dZ/dx(ω>0) dY

/dx(ω

>0),

theo

retical

(dZ

/dx)µ

tr(m

)

(dZ

/dx)µ

tr(g

)

dY

/dx(ω

>0),

rea

listic

Y

x x

e

Lateral traction coefficient and side-slip angle

34

eYM s ⋅=

αs …kot poševnega nakotaljevanja /

Side-slip angle

Z

Ss =µ

µs …bočni koeficient sojemanja /

lateral traction coefficient

s

sss tgc

µ

αβ ==

cs …bočna elastičnost pnevmatike /

cornering stifness of a tyre

S

dY/dx(ω>0), realistic

Y

x

e

αs

µs

αs

βs

side-slip angle

lateral traction coefficient

cornering stiffness of a tire

Steering angle during cornering

35

λ …krmilni kot / steering angle

)(Rf=λ

steering angle

Influence of side-slip rolling during cornering

36

Influence of side-slip rolling during cornering

R

v

g

G

R

vmF vc

22

⋅=⋅=

l

lFF

l

lFFRRRRR cccc

';"

0, 212121 ⋅⋅ ≈≈⇒≈≈⇒>>

R

v

gG

Fcs

21⋅==µ

sss

sss

sss

c

c

µα

µα

µµµ

⋅=

⋅=

≈≈

22

11

21

[ ])(

)(21

21

sss

sscc

lRRl

−⋅−=⇒⋅−−=

µλααλ

37

Under-steered vehicle: cs1>cs2

38

If a vehicle‘s velocity is

increased during cornering,

the steering angle λ should

be increased.

µs

R

R=v2/(µs*g)

R=l/[λ−µs*(cs1-cs2)]

Increase of velocity

for constant R.

Over-steered vehicle: cs1<cs2

39

If a vehicle‘s velocity is

increased during cornering,

the steering angle λ should

be reduced.

µs

R

R=v2/(µs*g)

R=l/[λ−µs*(cs1-cs2)]λ=

0 s

t.

Increase of velocity

for constant R.

Influence of a side wind

• Under-steered vehicle (cs1>cs2):

v

T Fv

v

T Fv

s1

s2

s1

s2

P

Fc

40

The centrifugal force

stabilizes the wind force.

Influence of a side wind

• Over-steered vehicle (cs1<cs2):

41

The centrifugal force de-

stabilizes the wind force.

Vehicle stabilization during cornering

• Under-steered vehicle:

• Over-steered vehicle:

42

Wish

v

Stabilisation

Actual cornering = wish

v

Fst

Fst

Actual cornering

v v

Fst

Fst

Actual cornering = wish

Stabilisation

WishActual cornering

Critical velocity of over-steered vehicle

12 ss cc >

0;0 >= Rλ

s

s

v

gR

R

v

g µµ

22 11⋅=⇒⋅=

)(

1

21

2

ssss

krit

cc

lv

gR

−⋅−=⋅=

µµ

12( ss

kritcc

glv

−

⋅=

43

• A critical velocity of the over-steered vehicle is the velocity at

which the vehicle can negotiate curves with a zero steering

angle, if subjected to a lateral disturbance (e.g. wind blow):

Position of steered wheels

>0 <0=+0,3/+1,5 =-0,5/-2

44

• Camber angle:

– Nullifies bearing clearance.

– Positive camber angle reduces lateral forces during cornering.

– Negative camber angle increased grip during heavy cornering.

Position of steered wheels

=5-10

45

• Lateral slope of a pivot line:

– It causes a raise of the vehicle‘s front part during a steering

maneuver.

– A consequence is self-alignment of the steering wheels if a

driver releases a steering wheel.

Position of steered wheels

46

• Caster angle:

– Positive caster will make

the vehicle more stable at

high speeds, and will

increase tire lean when

cornering.

Position of steered wheels

47

• Toe angle:

– The angle derived from pointing the tires inward or outward from

a top view.

– The steering mechanism is pre-stressed to nullify clearance.

– Reduces lateral wheel twisting.

List of references

• Granzow C.: ZF Vector Drive – better driving dynamics and

driving safety through Torque Vectoring. Praktischer Entwurf

mechatronischer Systeme, Karlsruhe 13.12.2013.

• Lewis R., Olofsson U. (editors): Wheel-rail interface

handbook. Boca Raton: Woodhead Publishing in Mechanical

Engineering, 2009.

• Wong J.Y.:Theory of Ground Vehicles, 3rd edition. New

York: John Willey & Sons, 2001.

• Simić D.: Motorna vozila. Beograd: Naučna knjiga, 1988.

• Janičijević N., Janković D., Todorović J.: Konstrukcija

motornih vozila. Beograd: Mašinski fakultet, 1979.

• Goljar M.: Motorna vozila, osnove konstruiranja. Ljubljana:

Fakulteta za strojništvo, 1977.

48