8/18/2019 4.0 Tire (4H)

1/33

CHAPTER 4:-TIRE

 JA 606VEHICLEDYNAMICS

CLO2: DESCRIBE AND CALCULATE THE BRAKING FORCES ACTING ON A

VEHICLE

8/18/2019 4.0 Tire (4H)

2/33

MENU

INTRODUCTION TO TIRE

CONTACT GEOMETRY

FORCES & TORQUES BY PRESSURE DISTRIBUTION

TIRE

8/18/2019 4.0 Tire (4H)

3/33

INTRODUCTION TO TIRE

TIRE

TIREDEVELOPMENT

TIRECOMPOSITION

TIRE FORCES &TORQUES

MEASURINGTYRE FORCES &

TORQUES

8/18/2019 4.0 Tire (4H)

4/33

TIRE DEVELOPMENT

INTRODUCTION TO TIRE

Milestones in tire developent

1839 Charles G!"ear# $%la'()a*('

18+, R-er* .(ll(a/ Th/0s'# (rs* 0'e%/a*( *(re2se$eral *h(' ('la*e! *%-es ('s(!e a lea*her $er

1888 4h' 5"! D%'l0# 0a*e'* r -("le 20'e%/a*( *(res

1893 The D%'l0 P'e%/a*( a'! T"re C6 G/-7 7a'a% Ger/a'"

189,

A'!re a'! E!%ar! M(hel('# 0'e%/a*( *(res r Pe%e*

Par(s:5r!ea%;:Par(s 2 /(les#,> *(re !ela*('s

== /0le*e (''er *%-e ha'es

1899 C'*('e'*al# ?l':l($e!@ *(res 2a00r;6 ,>> (l/e*er

19>+ Car-' a!!e!# -la *(res

19>8 Fra' Se(-erl('# r$e! *(res B(*h (/0r$e! ra! *ra*('

19== D%'l0# s*eel r! *hrea! (' *he *(re -ea!

19+= S"'*he*( r%--er -e/es e;*re/el" (/0r*a'* !%r(' ..II

19+3 C'*('e'*al# 0a*e'* r *%-eless *(res

19+ Ra!(al *(re19,= 7(h %al(*" '"l' *(re

8/18/2019 4.0 Tire (4H)

5/33

TIRE DEVELOPMENT

INTRODUCTION TO TIRE

19,= %'*(l 'B#:

R%':la* *(res

E'a-les *he $eh(le * '*('%e * -e

!r($e' a* re!%e! s0ee! 8>/h

A'! r l(/(*e! !(s*a'es 8>/

8/18/2019 4.0 Tire (4H)

6/33

TIRE DEVELOPMENT 

8/18/2019 4.0 Tire (4H)

7/33

TIRE COMPOSITION

INTRODUCTION TO TIRE

A /!er' *(re (s a /(;*%re s*eel a-r( a'! r%--er6

The /a(' /0'e'*s *(re B(*h a' $erall /ass 86, are l(s*e! -elB#

!"#$%# R!# ContiE'oCont('t

Re('re/e'*s# s*eel ra"' '"l' 1

R%--er# 'a*%rals"'*he*( 38C/0%'!s# ar-' s(l(a hal66 3>

S*e'er# (l res(' 1>

V%la'()a*('# s%l%r )(' ;(!e66 +

M(sella'e%s =

8/18/2019 4.0 Tire (4H)

8/33

TIRE FORCES & TORQUES

INTRODUCTION TO TIRE

Nr/al a'! r(*(' res are *ra's/(* Bhe' *here (s '*a* -e*Bee' *(rea'! ra! s%rae6

Nr/alre

Fr(*('re

The '*a* res a' -e %ll" !esr(-e! -" a res%l*(' re $e*r & a*r%e $e*r6

8/18/2019 4.0 Tire (4H)

9/33

TIRE FORCES & TORQUES

INTRODUCTION TO TIRE

The $e*rs are !esr(-e! (' a *ra:(;e! reere'e ra/e

.heelr*a*(' a;(s

8/18/2019 4.0 Tire (4H)

10/33

MEASURING TIRE FORCES &TORQUES

INTRODUCTION TO TIRE

O' ra! I'!r

: Us(' a s0e(al *es* *ra(ler6: Perr/e! %'!er real

0era*(' '!(*('s6

: Perr/e! ' !r%/s ' a la* -e!

: Ge* /re!(sa!$a'*aes

8/18/2019 4.0 Tire (4H)

11/33

CONTACT GEOMETRY

TIRE

5ASICAPPROAC7

LOCAL TRACHPLANE

TIRE DEFLECTION

LENGT7 OFCONTACT

PATC7

STATICCONTACT

PATC7

CONTACT POINTVELOCITY

DYNAMICROLLING RADIUS

8/18/2019 4.0 Tire (4H)

12/33

5ASIC APPROAC7

CONTACT GEOMETRY 

G($e' a %rre'* 0s(*(' a Bheel B(*h *he (;e! ;> "> a'! )> s"s*e/ -" Bheele'*er M a'! %'(* $e*r e"R (' *he (%re -elB#

The '*a* area r a' r!('ar" 0asse'er ar *(re a* 'r/al la! B(ll -ea00r;(/a*el" *he s()e 1, ; => /6

8/18/2019 4.0 Tire (4H)

13/33

LOCAL TRACH PLANE

CONTACT GEOMETRY 

The l('es (;e! -" *he 0('*s Q1 a'! Q 2 r  Q3 a'! Q 4 res0e*($el" !e('e *he('l('a*(' *he lal *ra 0la'e (' l'(*%!('al a'! la*eral !(re*('6

Lal *ra 'r/al 2e'#

|| 4312

4312

QQQQ

QQQQn

r r r r e

×

×=

8/18/2019 4.0 Tire (4H)

14/33

TIRE DEFLECTION

CONTACT GEOMETRY 

The area *he !ele*(' )'e has a re*a'%lar sha0e Bhe' ha/-er a'leγ = 0;  zb A   ∆=0

T(re !ele*(' S r r  z   −=∆ 0

8/18/2019 4.0 Tire (4H)

15/33

TIRE DEFLECTION

CONTACT GEOMETRY 

The /a'(*%!e *he *(re la' ra!((

γ  γ     tan

2

tan

2

br r and 

br r  S SRS SL   −=+=

.he' ha/-er a'le γ ≠ 0 a'! *he *(re (' %ll '*a* * *hera! *h(s '!(*(' a00l(e!

00   r r and r r  SRSL   ≤≤

Area !ele*(' )'e  *ra0e)(!al sha0e

br r br r r r  A S SLSR   )()]()[(2

1000   −=−+−=γ  

A* %ll '*a* *he *(re ha/-er a'le γ has ' ee* ' $er*(al *(re re -%**he B(!*h '*a* area B(ll ('rease B(*h *he a/-er a'le6

γ  cos

bwC   =

E%al()(' *he rss se*('A>JA    then Δ = ( 0 − )

8/18/2019 4.0 Tire (4H)

16/33

TIRE DEFLECTION

CONTACT GEOMETRY 

.he' ha/-er a'le γ ≠ 0 a'! *he *(re (' 0ar*(al '*a* **he ra! *h(s '!(*(' a00l(e!

00   r r and r r  SRSL  

Area !ele*(' )'e  *r(a'%lar sha0e

γ  γ   tan

)(

2

1  2

0   SRr r 

 A

  −=

A* 0ar*(al '*a* *he B(!*h '*a* area (s ($e' -"

γ  

γ  

γ  γ     sin

)tan2

(

costan

00

br r 

r r w

S SR

C 

+−

=−

=

E%al()(' *he rss se*('A>JA    thenγ  

γ  

tan

tan2

2

1

2

0

b

br r 

 z

s

  

   +−

=∆

8/18/2019 4.0 Tire (4H)

17/33

QUESTION 1

Reer * *he (%re 1 ('! *he !ele*e! )'e area *he *(re r*he llB(' ases #

16 A* %ll '*a* J > =6 A* %ll '*a* J =>K 36 A* 0ar*(al '*a* J 3>K ( rSR J1=> //

figure 1

8/18/2019 4.0 Tire (4H)

18/33

 ANSWER 1

1. At full contact , = 0 ; A0 = ∆z .b

=(40mm)(150mm)=6000 mm2

2. At full contact , = 20˚

 A = ½[(r0−r!) " (r0−r#)$ b = (r0 − r) b A  =(140mm%100mm)(150mm)= 6000 mm2

&. At 'artal contact , = &0˚ f r! =120 mm

 A  =12[ (140%120)2tan &0˚$

= &46.41 mm2

8/18/2019 4.0 Tire (4H)

19/33

)O* TO DETERMINE O+ERA,,

RIM-TIRE DIAMETER.

8/18/2019 4.0 Tire (4H)

20/33

)O* TO DETERMINE O+ERA,,

RIM-TIRE DIAMETER.

8/18/2019 4.0 Tire (4H)

21/33

mmh

mmh

 Height Section

S 

S 

3.101

10045225

=

×=

The speifi!"i#$ #f "ire is gi%e$ !s f#&'( 22)*4) +1,

mmd 

 Diameter Wheel

W    8.4314.25"17   =×=

)O* TO DETERMINE O+ERA,,

RIM-TIRE DIAMETER.

8/18/2019 4.0 Tire (4H)

22/33

"98.24@63.0@44.63@4.6348.431)3.101(2

2

)(

0

0

mcmmm Dmmmm

d h D

tirerim Diameter Overall

W S 

=

+=

+=

+

I$ #r-er "# fi$- #u" "he u$-ef#r.e- "ire r!-ius/ r 0

mmmr 

 Dr 

 Radius Initial

37.0@2.371

2

4.634

2

:

0

00

=∴

==

How o !" # $

8/18/2019 4.0 Tire (4H)

23/33

QUESTION 2

I *here (s a ha/-er a'le ' *(re !ele*(' (* B%l! -e l(e a*ra0e)(!al sha0e ' *he !ele*(' )'e *he *(re6 De*er/('e *hearea a !ele*(' a'! *he B(!*h '*a* area r *h(s s(*%a*('6The s()e *(re (s ==,+,R1< a'! ($e' *he $al%es r  SLJ =9,//r SRJ=8// a'! J8

 A$s'er(

 A 113103. 2 5 113.. 2

 22,2..5022,.

8/18/2019 4.0 Tire (4H)

24/33

STATIC CONTACT POINT

CONTACT GEOMETRY 

LATERAL DEVIATION 7Q OF CONTACT POINT AT FULL CONTACT#:

 A

 A y A y yQ

∆∆ΠΠ  +

−=

M('%s s(' r 2

ha/-er a'le

G($e' *he area *he Bhle rss se*(' area#

C w z A   ∆=

5ea%se *he e'*er re*a'%lar (s la*e!' *he e'*er l('e e/e*r( '*a* 0('*

"□ = 0

Therere

C 

C C 

Qw z

wbw

 A A y y

∆

×

−=−=   ∆∆)tan(

2

1

6

1 γ  

γ  

γ  

cos

tan

12

2

 z

b yQ

∆

−=

8/18/2019 4.0 Tire (4H)

25/33

STATIC CONTACT POINT

CONTACT GEOMETRY 

LATERAL DEVIATION 7Q OF CONTACT POINT AT PARTIAL CONTACT#:

)cos23

1(γ  

bw y C Q   −±=

O'l" r a *r(a'%lar 0ress%re !(s*r(-%*(' B(ll -e ass%/e!#

± ~ for +ve and –ve

camber angles

8/18/2019 4.0 Tire (4H)

26/33

8/18/2019 4.0 Tire (4H)

27/33

CONTACT POINT VELOCITY

CONTACT GEOMETRY 

Is %se! * al%la*e *he *(re res a'! *r%es Bh(h e'era*e! -" r(*('6

: The /0'e'* *he '*a* 0('* $el(*" (' l'(*%!('al !(re*(' (s

)( 0,*

0,00,00,   MQ R M 

T 

 x x   r vev   ×+=   ω 

: The /0'e'* *he '*a* 0('* $el(*" (' la*eral !(re*(' (s

)( 0,*

0,00,00,   MQ R M 

T 

 y y   r vev   ×+=   ω 

8/18/2019 4.0 Tire (4H)

28/33

DYNAMIC ROLLING RADIUS

CONTACT GEOMETRY 

.(*h a' a'%lar r*a*(' 2 ∆φ r 0 (s !e('e as %'la!e! a'! r  s r 0  ∆ r as la!e! r s*a*( *(re ra!(%s6

S r r and  xr    =∆=∆   ϕ ϕ    cossin 00

The /*(' (s /0are! B(*h *he rll(' r((! Bheel B(*h ra!(%s r D

ϕ ϕ    ∆==∆  Dr  xr   sin0

8/18/2019 4.0 Tire (4H)

29/33

DYNAMIC ROLLING RADIUS

CONTACT GEOMETRY 

.(*h se$eral '!(*('s a00l" a'! a00r;(/a*(' r s('e: a'! s('e:%'*('s*he e%a*(' B(ll -e

S  D   r r r 3

1

3

20 +=

Las*l" *he a$erae $el(*" a* Bh(h *he *rea! 0ar*(les are *ra's0r*e! *hr%h*he '*a* 0a*h (s -*a('e!

Ω=  Dt    r v

ϕ ϕ 

∆

∆=   sin0r r  D

7e'e *he !"'a/( *(re ra!(%s (s ($e' -"

8/18/2019 4.0 Tire (4H)

30/33

FORCES & TORQUES 5Y PRESSUREDISTRI5UTION

TIRE

TIPPING TORQUE

.7EEL LOAD

ROLLINGRESISTANCE

FORCES % TORQUE BY PRESSURE

8/18/2019 4.0 Tire (4H)

31/33

.7EEL LOAD

FORCES % TORQUE BY PRESSURE

DISTRIBUTION

 D

 z

S 

 z z   F F F    +=

The $er*(al *(re re 89 a' -e !e*er/('e! as a %'*(' 'r/al *(re!ele*(' ∆z a'! *he !ele*(' $el(*" ∆ż.

S*a*( 0ar*#   221   )(   za zaF 

S 

 z   ∆+∆=

 zd F   R D

 z  &∆=

.here

 N 

 z

 N  N  N  N 

F 

ccaand cca

42

22

22

2

2

2

1

−=−=

D"'a/( 0ar*# .here

dampingtireradiald  R  =

The 89 (s se0ara*e! ('* = 0ar*s s*a*( a'! !"'a/(#:

8/18/2019 4.0 Tire (4H)

32/33

FORCES % TORQUE BY PRESSURE

8/18/2019 4.0 Tire (4H)

33/33

ROLLING RESISTANCE

FORCES % TORQUE BY PRESSURE

DISTRIBUTION

I* har!l" ('l%e'es *he ha'!l(' 0r0er*(es a $eh(le a'! 0la"s a /ar 0ar* ('%el 's%/0*('6

Rll(' res(s*a'e e((e'* B(ll -e ('rease B(*h *he *ra$ell(' $el(*" a$eh(le6

)(

0

v f  f r 

 x f   R R

 R R   =⇒=

U'!er 'r/al 0era*(' '!(*('s *he R6R e((e'* r a *"0(al 0asse'er ar*(res as llB#

02.001.020020