Pnevmatike in diferencial Tyresanddifferentialgearweb.fs.uni-lj.si/kserv/images/upload/2_Pedagoska...Diferencial z usmerjanjem navora / Torquevectoringdifferential 23 • Funkcionalni

Prof. dr. Jernej Klemenc

Pnevmatike in diferencial

Tyres and differential gear

Konstrukcija radialne pnevmatike /

Composition of a radial-ply tire

Tekalna plast / Contact surface

Bočnica / support wall

Noga / Tyre foot

Pas / Belt

Karkasa / Carcass plies

Žično jedro /Core steel wire

Platišče /Wheel rim

Tesnilna plast / Sealing layer

2

Označevanje pnevmatik /

Tyre labeling

• 6,40-13/6 PR:

– Diagonalna pnevmatika

– Širina pnevmatike: 6,40”

– Premer platišča: 13”

– Višina pnevmatike: 0,95 (superbalon za D) * 6,40”

– Indeks nosilnosti: PR6

– Simbol hitrosti: -(najvišja hitrost = 150 km/h)

• 6,40-13/6 PR:

– Bias-ply tyre

– Tyre width: 6,40”

– Wheel-rim diameter: 13”

– Tyre-wall height: 0,95

(superballoon for D) *

6,40”

– Loading index: PR6

– Velocity index: no index

(maximum velocity =

150 km/h)

3


Tyre labeling

• 265/50 R 14 101 V:

– Radialna (R) pnevmatika

– Širina pnevmatike: 265 mm

– Premer platišča: 14”

– Višina pnevmatike: 0,50 * 265 mm

– Indeks nosilnosti: 101

– Simbol hitrosti: V (najvišja hitrost = 240 km/h)

• 265/50 R 14 101 V:

– Radial-ply tyre (R)

– Tyre width: 265 mm

– Wheel-rim diameter :

14”

– Tyre-wall height : 0,50 *

265 mm

– Loading index: 101

– Velocity index: V

(maximum velocity =

240 km/h)

4


Tyre labeling

• Datum proizvodnje / Production date: DOT xxyy

– xx => teden / week;

– yy => leto / year.

• Indeks nosilnosti pnevmatike / Tyre load index:

5


Tyre labeling

• Simboli hitrosti za pnevmatike:

– 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 => nad 210 km/h

– ZR=> nad 240 km/h

• Tyre 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

6

Pnevmatika kot torno gonilo – pospeševanje /

Tyre 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

Pnevmatika kot torno gonilo – zaviranje /

Tyre 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

Sojemalni diagram za radialne in diagonalne pnevmatike /

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

9

H

10 t

Radialna pnevmatika (nova) /Radial-ply tyre (new)

Diagonalna pnevmatika (nova) /Bias-ply tyre (new)

Radialna pnevmatika (stara) /Radial-ply tyre (old)

Sojemalni diagram za pospeševanje in zaviranje /

Traction diagram for accelerating and braking

10

Mikro-kontakt pnevmatike in vozne površine med

pospeševanjem / Micro-contact between tyre and driving

surface during acceleration

11

Mikro-kontakt pnevmatike in vozne površine med

zaviranjem / Micro-contact between tyre and driving surface

during braking

12

Pogon 4x4 / 4x4 wheel drive

• Sredinski razdelilnik pogona brez diferenciala na trdi podlagi:

• Teoretične obodne hitrosti:

• Dejanske obodne hitrosti:

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 ≠= 13


• Sredinski razdelilnik pogona brez diferenciala na trdi podlagi:

• Central power splitter without


surface:

14


• Sredinski razdelilnik pogona z diferencialom na trdi podlagi:

221

222111

mot

stst

MMM

RrvRrv

==

∝⋅=>∝⋅= ωω

15

• Central power splitter with a


surface:


• Sredinski razdelilnik pogona z diferencialom – trda podlaga zadaj, mehka podlaga spredaj, vožnja naravnost:

16

• Central power splitter with a

differential gear – hard

surface under the rear axle,

soft surface under the front

axle, straight driving:


-M1

+M1

-M2

+M2

M2

v1,0=v2,0

M1

v1=v2

Mmot

17

• Sredinski razdelilnik pogona brez diferenciala – trda podlaga zadaj, mehka podlaga spredaj, vožnja naravnost:

• Central power splitter

without differential gear –

hard surface under the rear

axle, soft surface under the

front axle, straight driving:

TORSEN diferencial /

TORSEN differential gear

18

Mehanski samozaporni diferencial z lamelami /

Mechanical self-locking differential gear with lamellas

19

Avtomatski samozaporni diferencial z lamelami /

Automatic self-locking differential gear - ASD

20

Kotno gonilo /

Angle bevel

gear

Krmilni tlak (desni) / Control pressure

(right)

Krmilni tlak (levi) / Control pressure

(left) Pritrjeno na ohišje kotnega gonila /

Attached to a housing

of a bevel gear

Diferencial z usmerjanjem navora /

Torque vectoring differential

21



Granzow 2013, str. 5. 22

• Učinek na vožnjo v ovinek: • Operation during cornering:



23

• Funkcionalni sestav diferenciala ZF Vector

drive:

• Functional assembly of a ZF

Vector drive differential

gear:

FaFa Fa Fa

Klasični diferencial s kotnim gonilom /

Conventional differential

gear with the angle

bevel gear

Leva enota za vektorsko usmerjanje navora /Left unit for torque-

vectoring

Desna enota za vektorsko usmerjanje navora /Right unit for torque-

vectoring

Večlamelna zavora / Multi-disc brake

Večlamelna zavora / Multi-disc brake




• Prikaz sestava: • System assembly:



25

• Princip delovanja brez vektorskega usmerjanja navora:

• Principle of operation

without torque-vectoring

function:

Fa=0 Fa=0MKG

M1=MKG /2 M2=MKG /2

Fk,1 Fk,2=Fk,1

Granzow 2013, str. 9.



• Princip delovanja z vektorskim usmerjanjem navora:


Fa=0 Fa>0MKG =2000 Nm

M1=480 Nm 420 Nm

Fk,1

Fk,2 >Fk,1

900 Nm

1100 Nm

980 Nm

120 Nm

Σ=1400 Nm

26

• Principle of operation by

applying the torque-

vectoring function:




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

27

• Princip delovanja z vektorskim usmerjanjem navora:

• Principle of operation by

applying the torque-

vectoring function:




• Prerez sestava: • Assembly cross-section:




• Aktivacija več-lamelne zavore planetne gredi:

• Activation of a multi-disc

brake of a planetary shaft:




• Aktivacija več-lamelne zavore planetne gredi:

• Activation of a multi-disc

brake of a planetary shaft:




• Diferencial z vektorskim usmerjanjem navora je mehatronski sistem:

• The torque-vectoring

differential is a mechatronic

system:

Bočna elastičnost pnevmatike /

Cornering stifness of a tyre

32

=0

Z

S

YPZ

S

x

dZ/dx( =0)

Dotikalna površina pnevmatike /

Contact surface

>0

S

x

dZ/dx( >0)

Y

x x

e

Koeficient sojemanja za prečno silo in kot poševnega

nakotaljevanja /

Lateral traction coefficient and side-slip angle

33

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

Kot zasuka krmilnih koles pri vožnji v ovinek /

Steering angle during cornering

34

λ …krmilni kot / steering angle

)(Rf=λ

Vpliv poševnega nakotaljevanja pri vožnji v ovinek /

Influence of side-slip rolling during cornering

35

Vpliv poševnega nakotaljevanja pri vožnji v ovinek /

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

36

Podkrmarjeno vozilo / Under-steered

vehicle: cs1>cs2

Če se poveča hitrost vožnje v ovinek, je treba

povečati krmilni kot λ.

37

v=20 km/h

v=60 km/h

v=100 km/h

=0 s

t.

=2 s

t.

If a vehicle‘s velocity is

increased during cornering,

the steering angle λ should

be increased.

Prekrmarjeno vozilo / Over-steered

vehicle: cs1<cs2

38

Če se poveča hitrost vožnje v ovinek, je treba zmanjšati krmilni kot λ.

If a vehicle‘s velocity is

increased during cornering,

the steering angle λ should

be reduced.

s

R

v=60 km/h

v=100 km/h

R=v2/( s*g)

R=l/[ s*(cs1-cs2)]

Zvišanje hitrosti vožnje pri R=konst. / Increase of velocity

for constant R.

Vpliv bočnega vetra /

Influence of a side wind

• Podkrmarjeno vozilo / Under-steered vehicle (cs1>cs2):

v

T Fv

v

T Fv

s1

s2

s1

s2

P

Fc

Centrifugalna sila stabilizira silo vetra.

39

The centrifugal force

stabilises the wind force.

Vpliv bočnega vetra /

Influence of a side wind

• Prekrmarjeno vozilo / Over-steered vehicle (cs1<cs2):

40

Centrifugalna sila destabilizira silo vetra.

The centrifugal force de-

stabilises the wind force.

Stabilizacija vozila pri vožnji v ovinek /

Vehicle stabilisation during cornering

• Podkrmarjeno vozilo / Under-steered vehicle:

• Prekrmarjeno vozilo / Over-steered vehicle:

41

v v

Fst

Fst

Dejansko stanje = želja /Actual cornering = wish

Stabilizacija / Stabilisation

Želja / Wish

Dejansko stanje /Actual cornering

Kritična hitrost prekrmarjenega vozila /

Critical velocity of over-steered vehicle

• Kritična hitrost prekrmarjenega vozila je tista hitrost, pri kateri je vozilo ob minimalni bočni motnji (npr. sunek vetra) sposobno voziti v ovinek brez zasuka krmilnih koles:

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

−

⋅=

42

• A critical velocity of the

under-steered vehicle is the

velocity at which the vehicle

can negotiate curves with a

zero steering angle, if subje-

cted to a lateral disturbance

(e.g. wind blow):

Postavitev vodilnih koles vozila /

Position of steered wheels

• Previs kolesa:

– Izniči zračnost v ležajih.

– Pozitivni previs zmanjšuje stranske vodilne sile pri vožnji v ovinek.

– Negativni previs izboljšuje stransko vodenje pri vožnji v ovinek.

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

43

• Camber angle:

– Nullifies bearing clearance.

– Positive camber angle

reduces lateral forces

during cornering.

– Negative camber angle

increased grip during heavy

cornering.



• Prečni nagib premnega sornika:

– Povzroči dviganje prednjega dela vozila pri zasuku vodilnih koles.

– Posledica je samodejno vzpostavljanje položaja koles za vožnjo naravnost, če voznik izpusti volan.

=5-10

44

• Lateral slope of a pivot line:

– It causes a raise of the

vehicle‘s front part during a

steering maneuvre.

– A consequence is self-

alignment of the steering

wheels if a driver releases

a steering wheel.



• Vzdolžni nagib premnegasornika (kot zaostajanja):

– Kot zaostajanja kolesa usmeri tako, da dosežemo večjo stabilnost zasukanih koles pri višjih hitrostih.

45

• Caster angle:

– Positive caster will make

the vehicle more stable at

high speeds, and will

increase tire lean when

cornering.



• Stekanje/raztekanje koles:

– Napenja pnevmatike in drogovje krmilnega mehanizma.

– Zmanjšuje opletanje koles.

46

• 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.

Seznam literature / 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 interfacehandbook. 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.

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Documents

Pnevmatike in diferencial Tyresanddifferentialgearweb.fs.uni-lj.si/kserv/images/upload/2_Pedagoska...Diferencial z usmerjanjem navora / Torquevectoringdifferential 23 • Funkcionalni