Post on 03-Apr-2020
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