EXPERIMENTAL STUDIES OF TIRE SHEAR FORCE MECHANICS

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EXPERIMENTAL STUDIES
OF
T I RE
SHEAR FORCE
MECHANICS
--
A
SUMMARY
REPORT
P.
S. Fa n c h e r,
J r.
H.
Dugof f
K.
6.
Lud,ema
L,
S e g e l
Highway
Sa f e t y Resear ch I ns
ti
t u t e
The Un i v e r s i t y of Mi chi gan
Huron Parkway and
Baxt er
Road
Ann Ar bor,
Michigan
48105
JULY
30,
1970
Summary
Fi na l
Report
Pr epar ed f o r
Ti r e
Syst ems Se c t i o n
Of f i ce
of Vehi cl e
Syst.ems
Resear ch
Nat i onal
Bureau
o f
St andar ds
Washi ngt on,
D.C.
20234
Th i s r e p o r t was p r e p a r e d i n f u l f i l l me n t o f t h e Na t i o n a l
Bur e a u o f S t a n d a r d s Co n t r a c t
CSrI'-928-5
( f u n d e d
b y
t h e
Na t i o n a l Hi ghway S a f e t y Bur e a u t h r o u g h t h e NBS, Co n t r a c t
FH-
1 1 - 6 0 9 0 ).
The o p i n i o n s, f i n d i n g s, a nd c o n c l u s i o n s
e x p r e s s e d i n t h i s p u b l i c a t i o n a r e t h o s e o f t h e a u t h o r s
a nd n o t n e c e s s a r i l y t h o s e o f t h e Na t i o n a l Bur e a u o f
S t a n d a r d s n o r t h e Na t i o n a l Hi ghway S a f e t y Bu r e a u.
Thi s summary r e por t
i s
a d i g e s t of f i ndi ngs from an
exper i ment al i nve s t i ga t i on of t he mechanics of t i r e s he a r f or c e
gener at i on under gener al condi t i ons of s t e e r i n g and br aki ng.
The i nve s t i ga t i on was conduct ed
by
t he Highway Sa f e t y Research
I n s t i t u t e
{HSRI)
of The Uni ver s i t y of Michigan under t he spon-
s or s hi p of t he Of f i ce of Vehi cl e Systems Research of t he Nat i onal
Bureau of St andar ds.
INTRODUCTION
---
I n oper at i on, t he t i r e i s r equi r ed t o c a r r y a v e r t i c a l l oad,
absor b bumps and shocks wi t hout f a i l u r e, be dur abl e, and pr ovi de
l a t e r a l and l ongi t udi na l t r a c t i o n f or c e s. I n s e ve r e ve hi c l e
maneuvers r e l a t e d t o acci dent avoi dance, t he l a t e r a l and l ongi t u-
di na l t i r e f or ces a r e ext remel y i mpor t ant. These f or ces a r e
det ermi ned by an exceedi ngl y complex s e t of event s which t ake
pl a c e i n t he c ont a c t pat ch between t i r e and r oad. To d a t e, t he r e
i s no complete o r t o t a l l y s a t i s f a c t o r y model of t i r e s he a r f or c e
gener at i on. Recent l y,
h ~we v e r,
t hr e e s i mpl i f i e d t h e o r e t i c a l
anal yses of t he mechanics of t i r e t r a c t i o n under s t e e r i n g and
br aki ng condi t i ons have been performed
[
1,2,3].
The de r i va t i ve
mat hemat i cal models, which agr ee q u a l i t a t i v e l y wi t h each ot he r and
wi t h exper i ment al d a t a, expr ess t he l ongi t udi na l and l a t e r a l
f or ces
on
a gi ven s ur f a c e a t f i x e d v e r t i c a l l oad as f unct i ons of
l ongi t udi na l and l a t e r a l s l i p ( s l i p a ngl e ).
During a s ever e maneuver, t he l ongi t udi na l s l i p, s l i p angl e,
and v e r t i c a l l oad of a v e h i c l e's t i r e s var y wi del y and hence cause
g r e a t v a r i a t i o n i n t he l ongi t udi na l and l a t e r a l t i r e
f or c e s.
How
t he s e f or ces devel op det ermi nes whet her t he ve hi c l e t ur ns and s t ops
under c ont r ol, s p i n s, or s ki ds s t r a i g h t ahead. The t i r e s hear f or c e
r e pr e s e nt a t i on devel oped by HSRI has been i ncor por at ed
i n
a compre-
hensi ve ve hi c l e s i mul at i on
and
employed t o q u a n t i t a t i v e l y anal yze
t he i nf l ue nc e of t i r e t r a c t i o n c h a r a c t e r i s t i c s on ve hi c l e behavi or
[ I ].
Thi s s i mul at i on has a l s o been used t o e va l ua t e t he i nf l ue nc e
of a nt i - l oc k braki ng c ont r ol syst ems on ve hi c l e d i r e c t i o n a l
s t a b i l i t y
[ 4 ]
and t o st udy t he
limits
of ve hi c l e response t o
s t e e r i n g and br aki ng i nput s
[ 5 ]
.
Cl ear l y, t he degree of v a l i d i t y
of t he devel oped t i r e model has obvious and i mpor t ant i mpl i cat i ons
r e l a t i v e t o t he accuracy of t hese s i mul at i on r e s u l t s.
Under
NBS
Cont ract No.
CST- 928- 5, HSRI
has gat her ed and
anal yzed a comprehensive body of s t r uc t ur e d dat a on t he devel op-
ment of t i r e s hear f or ces over a wide range of oper at i ng condi t i ons.
The da t a were obt ai ned usi ng two
complementary
pi eces of t e s t
equipment: a l a bor a t or y- i ns
t a l l e d
f l a t b e t t e s t e r (FBT)
permi
t ki ng
pr e c i s e c ont r ol of t e s t condi t i ons a t
low
speed, and a
vehi cl e-
towed mobile t i r e t e s t e r
(MTT)
pr ovi di ng a c a pa bi l i t y f o r over-
t he- r ead measurements a t
r e a l i s
t i c highway speeds
.
Complete
de s c r i pt i ons of t hes e two t i r e t e s t e r s appear i n Ref.
6,
A
de-
t a i l e d
accourit
of t he conduct and f i ndi ngs of t he exper i ment al
program
w i l l
appear i n a subsequent publ i c a t i on.
The purpose of t h i s r e por t
i s
t o pr ovi de a conci se
suinmary
of t he exper i ment al f i ndi ngs and t o make s p e c i f i c recommendations
--
f or
f ut ur e r es ear ch di r e c t e d towards t he development of
a
s c i e n-
t i f i c ba s i s f o r t he c ha r a c t e r i z a t i on and s p e c i f i c a t i o n of t i r e
t r a c t i o n performance.
SUMMARY
OF
EXPERIMENTAL
-
RESULTS
A.
Combined Sl i p and Sl i p Angle Data from t he Mobile Ti r e Tes t er
The
mobile t i r e t e s t e r pr ovi des t he unique c a pa bi l i t y of
on-
t he- r oad measurements of t i r e s hear f or ces under combined
:;l i p
and
s l i p angl e oper at i on a t highway speeds. The da t a pr es ent ed her e
was obt ai ned by l oweri ng a t i r e ont o
tile
r oad
a t a f i xe d
s l i p
angl e
and var yi ng t he t e s t wheel speed from f r e e r o l l i n g t o lockup by
an e l e c t r o- hydr a ul i c c ont r ol syst em. Each of t he curves pr es ent ed
i n Fi gur es 1-10 i s t he average of f i v e r e p l i c a t i o n s. They have
been
s e l e c t e d from a much
l a r g e r
s e t of curves
t o
i l.l ust r al;e
t he
t ype of r e s u l t s obt ai ned.
Dry Concr et e Dat a. Fi gur e
1
shows t he r e s u l t s obt ai ned
f o r a b e l t e d b i a s t i r e wi t h a f or war d
MTT
s peed of
30
mph,
wi t h
t he t i r e s e t a t
0°,
l o,
Z O,
4",
8",
and 16" s l i p a ngl e s.
The
g r e a t i nf l ue nc e of s l i p angl e on l ongi t udi na l f o r c e, t h a t
:is,
br aki ng f or c e i n t he wheel pl a ne,
i s
appar ent. As t he s l i p angl e
i s
i nc r e a s e d, t he peak of t he l ongi t udi na l f or c e ver s us s l i p cur ve
occhr s
a t hi ghe r val ues of s l i p.
At
hi gh s l i p angl es t he peak
l ongi t udi na l f or c e i s obt ai ned a t l ockup. The l a r ge r educt i on i n
l a t e r a l f or c e caused by i nc r e a s i ng l ongi t udi na l s l i p can
be
s een
i n Fi gur e
I.
Fi gur es
2
and
3
show s i mi l a r
r e s u 1.t ~
f o r a r a d i a l t i r e and
a c r os s b i a s t i r e. For bot h of t he s e t i r e s, as wi t h t h e b e l t e d
bi a s t i r e, t he l a t e r a l f or c e f a l l s o f f wi t h i nc r e a s i ng s l i p and
t he peak of t he l ongi t udi na l f or c e ver s us s l i p cur ve becomes l e s s
pronounced as
s
l i p angl e i nc r e a s e s.
Si nce t he d a t a i n Fi gur es
l
t hr ough 3 were c o l l e c t e d on
d i f f e r e n t days wi t h var yi ng t emper at ur e and humi di t y and
on
d i f -
f e r e n t s e c t i o n s of roadway,
t hey
do n o t c o n s t i t u t e an a ppr opr i a t e
b a s i s f o r q u a n t i t a t i v e compari sons of t i r e q u a l i t i e s. Fur t he r,
t he t h r e e t e s t e d t i r e s d i f f e r i n t r e a d compounds and
t r e a d
p a t -
t e r n s, as we l l as i n c a r c a s s c ons t r uc t i on. The da t a a r e i nt ended
onl y t o i l l u s t r a t e q u a l i t a t i v e v a r i a b i l i t y i n t i r e s he a r f or c e
per f or mance. I n Fi gur e
4,
t he
0"
and
16"
s l i p angl e da t a f o r
aPP
t h r e e t i r e s have been p l o t t e d on t he same gr aph t o emphasi ze t h e
wi de r ange of r e s u l t s p o s s i b l e.
For t he r a d i a l t i r e and t he b e l t e d bi a s t i r e, t he form of
t he t i r e f or c e cur ves does not change wi t h v e l o c i t y. For t he
c r os s b i a s t i r e, a l ower peak and a hi gher s l i d i n g l ongi t udi na l
f or c e were obt ai ned a t
50
mph t han were obt ai ned a t
30
mph.
Thi s
r e s u l t i s i l l u s t r a t e d i n Fi gur e
5.
Wet Sur f ace Condi t i ons. The mobi l e t i r e t e s t e r c a r r i e s
-
a
s uppl y of wat er and has a pump and nozzl e syst em f o r we t t i ng
t he
r oad ahead
of
t h e t e s t t i r e. The nozzl e openi ng i s changed
BELTED BIAS TIRE
30
YPH
1000 LBS.
DRY
CONCRETE
0
10
20
30
40
50
60
70
00
90100
WHEEL SLIP%
Fi gur e
1
CROSS BIAS TIRE
30 MPH
1000
LBS.
DRY CONCRETE
O O
BELTED RADIAL
TIRE
30
MPH
1.000
LBS.
DRY
CONCRETE
WHEEL SLIP
%
Fi gur e
2
RANGE OF RESULTS
30
MPH
1000
LEE
DRY CONCRETE
-
~I-T-.v]
B E L T E D BIAS
0
WHEEL SLIP
%
Fi gur e
3
WHEEL
SLIP
$
Fi gur e
4
CROSS
BIAS
TIRE
0'
1000
LBS.
DRY
Fi gur e
5
crrhI,"
h
k
x i
crr
WHEEL
SLIP
%
wi t h t e s t ve hi c l e speed t o l a y wat er t o a dept h of about
0,,0ZM.
Data f o r each of t he t hr e e t ypes of t i r e s oper at i ng on wet t ed
concr et e a r e shown i n Fi gur es
6,
7,
and
8.
As
expect ed, t he peak l ongi t udi na l f or c e on t he wet road
i s
lower t han on t he dry r oad, though t he l os s
i s
onl y 10 t o
1 5 %.
The f a l l o f f of l ongi t udi na l f or ce beyond t he peak
i s
much
nor e
pronounced on t he wet concr et e s ur f a c e t han on t he dry concr et e.
The l a t e r a l f or c e a t zer o s l i p r eaches a maximum a t a s l i p angl e
of
16'
o r l e s s on t he wet s ur f a c e.
I n
ge ne r a l, t he same t ype
of performance
was
obt ai ned on t he wet concr et e as on dry con-
c r e t e, wi t h t he except i on t h a t t he l ongi t udi na l f or c e
f a l l s
of f
more r a pi dl y wi t h s l i p.
Fi gur e
9,
l i k e Fi gur e 4,
i s
i ncl uded t o show t he wide range
of r e s u l t s obt ai ned
f o r
t he t hr e e d i f f e r e n t t i r e s.
BELTED BIAS TI RE
30
MPH
1 0 0 0
LBS.
WET CONCRETE
9- 18- 69
T=63OF
'.O o
BELTED RADIAL TI RE
3 0 MPH
1 0 0 0
LBS.
WET CONCRETE
WHEEL SLI P
$
Figure
6
CROSS BIAS TI RE
30
MPH
1 0 0 0
LBS.
WET CONCRETE
1.0117-
WHEEL SLI P
$
Fi gur e
7
RANGE
OF
RESULTS
3 0
MPH
1 0 0 0
LEIS.
.
B E L T E D BIAS TI RE
CROSS BIAS TI RE
WHEEL SLI P
%
Fi g u r e
8
WHEEL SLI P
%
Figure
9
Typi cal da t a i l l u s t r a t i n g t he i nf l uence of ve l oc i t y on
wet s ur f a c e s a r e pr es ent ed i n
Figlire
10. Si mi l a r r e s u l t s
were obt ai ned f o r a l l t hr e e t ypes of t i r e s.
CROSS
BIAS
TIRE
8 O
1-000
LBS.
WET
CONCRE'I'E
Figure
10
WHEEL
SLEP
%
B.
e e r i m e n t a l
Resul t s
-
f o r Locked Wheels
I n
Pa r t
A,
exper i ment al da t a a r e pr e s e nt e d f o r l ongi t udi na l
s l i p,
s,
r angi ng from
0
t o
1.0
( 0
t o 100% wheel s l i p ). Locked
wheel oper at i on of t he t i r e corresponds
t o
s
=
1.0. For t he
l ocked wheel condi t i on ( a t any s l i p angl e
a ),
t he s l i d i n g vel oc-
i t y a t ever y poi nt
i n
t he cont act pat ch between t i r e and road
i s t he same and t he d i r e c t i o n of s l i d i n g corresponds t o t he s l i p
angl e of t he t i r e. I f t he f r i c t i o n a l c h a r a c t e r i s t i c s of t he
t i r e - r o a d i n t e r f a c e a r e i s o t r o p i c, t hen t he t i r e s he a r f or c e
w i l l
oppose t he d i r e c t i o n of s l i d i n g as shown i n Fi gur e
I l a.
I n t h i s cas e,
F
/F
=
t an
a.
Y
x
Direction of
I
Wheel Center
Direction of
1
Wheel Center
Velocity
Direction
of
Total
Shear
Force
a.
Isotropic,
p=p
=p
X Y
Direction of
Total
Shear
Force
Velocity
I
Wheel
Plane
I
Orientation
b.
Px
f.
Py
Figure
11.Directional
Characteristics
of
Tire/Road
Friction
I f
t he r e s ul t a nt shear
f or ce
does not oppose t he di r e c t i on of
s l i d i n g, t hen, as shown i n
Fi gure
l l b,
F
/F
does not equal t a n a.
Y X
Thus
the
quant i t y
F
/F
t an a equal s 1.0
i f
t he t o t a l shear f or ce
Y X
opposes t he di r e c t i on of s l i d i n g and does not equal 1.0
ot herwi se.
Table
I
i s
a
t abul at i on
of
F
/F
t an
a
val ues computed from dat a
Y X
f o r
locked wheels towed a t s l i p angl es
of
8'
and
16'.
These r e s u l t s i ndi c a t e t ha t t he di r e c t i on of
t i r e
s hear
f or ce
i s
not c ol l i ne a r wi t h t he di r e c t i on of s l i d i n g
on
a wet s ur f ace.
This may be due t o t he t r e a d pa t t e r n and t he di f f er ence between
l ongi t udi nal
and l a t e r a l wiping a c t i on on
t he
wet
road.
Cl ear l y,
t he
di f f er ence
i n t he di r e c t i on
of
shear
f or ce between wet and
dry
roads
i s
very
l a r ge.
On t he wet r oad,
F
i s
much
l a r ge r
t han
Y
AVERAGE VALUES,
V
=
20,
30,
40,
50
MPH:
F,
=
1000
LB,
TRAFFIC
PAINT*
CROSS
BI AS
BELTED
BI AS
RADI AL
Fx
t a n a, i ndi c a t i ng t h a t t he r a t i o of l a t e r a l f or c e t o
l l ongi t udi nal
f or c e
i s
g r e a t e r on
a
wet r oad t han on a dr y r oad.
PAMF+ZETERS
F OR
CHAIIACTERIZING
TI RE
TRACTION
PEKFORJIANCE
--
--------
-
One goal of our t h e o r e t i c a l and exper i ment al
i nves t i,gat i ons
of t i r e mechanics i s t o c ha r a c t e r i z e t he s he a r f or c e performance
*The
HSRI
t e s t f a c i l i t y a t Willow Run Ai r por t has a s p e c i a l l y
pr epar ed s t r i p of a s pha l t which has been pa i nt e d wi t h t r a f f i c
p a i n t. When wet, t h i s s ur f a c e has low f r i c t i o n and wat er does n o t
dr a i n t hr ough
i t
e a s i l y. Although t h i s
t.ype
of s ur f a c e i s a r t i -
f i c i a l,
i t
pr ovi des a r e l a t i v e l y low c o e f f i c i e n t of f r i c t i o n which
i s easy t o mai nt ai n.
of a t i r e i n terms of a few c a r e f ul l y s e l e c t e d paramet ers t h a t
can be conveni ent l y measured. By means of t hes e par amet er s,
and formul ae ( char act er i zi ng f unct i ons ) r e l a t i n g them t o s hear
f or c e out put, we a r e at t empt i ng t o obt ai n a
mat!lsmatical
cles-
c r i p t i o n o r pr e di c t i on of performance t h a t
i s
v a l i d over
t:he
f u l l range of oper at i ng va r i a bl e s.
I n Ref.
1,
t he t i r e i s c ha r a c t e r i z e d i n terms of two
e l a s t i c par amet er s,
Cs
and
Ca
and a "f r i c t i o n expr es s i on."
?
For exper i ment al work, t he l ongi t udi na l e l a s t i c par amet er,
Cs,
i s def i ned as t he abs ol ut e val ue of t he s l ope of t he curve of
l ongi t udi na l f or ce ver sus l ongi t udi na l s l i p, s, eval uat ed a t
s
=
0,
f o r t he s l i p angl e, a, equal zer o. Si mi l a r l y, t he l a t -
e r a l
e l a s
t i c par amet er,
Ca'
i s def i ned as t he abs ol ut e
val ue
of t he r a t e of change
of l a t e r a l f or ce wi t h r e s pe c t t o
s l i p
angl e eval uat ed a t a
=
0
f o r
s
=
0.
For smal l val ues of
l ongi t udi na l s l i p
and
s l i p angl e ( l a t e r a l s l i p ), t he pr e di c t e d
t i r e f or c e s a r e i ndependent of t he f r i c t i o n expr essi on which
i s
used t o compute t he maximum s hear f or c e i n t e n s i t y between t he
t i r e and t he r oad. This expr essi on account s bot h f o r t he de-
cr eas e i n br aki ng f or c e beyond t he maximum of t he
l ongi t udi na l
f or c e ver sus s l i p cur ve, and f o r a decr ease i n cor ner i ng f or c e
a t l a r ge l a t e r a l s l i p. In our pr evi ous st udy
[ I ],
a formul a
expr essi ng f r i c t i o n c oe f f i c i e nt as a l i n e a r f unct i on of
s l i d i n g
ve l oc i t y was used t o obt ai n t i r e s hear f or c e s i n q u a l i t a t i v e
agreement wi t h exper i ment al r e s u l t s a t l a r ge val ues of
l ongi t u-
di na l and l a t e r a l s l i p.
Examination of t he ext ens i ve da t a c ol l e c t e d dur i ng t he
pr e s e nt st udy l eads t o t he f ol l owi ng concl usi ons r e l a t i v e t o
t i r e c ha r a c t e r i z i ng paramet ers and f unct i ons:
(1) The cor ner i ng s t i f f n e s s,
Ca,
and t he br aki ng
( l ongi t udi na l ) s t i f f n e s s,
C
s
,
a r e
good
paramet ers
f o r r epr es ent i ng t i r e s he a r f or ce i n t he low
sl - i p
angl e and
l ongi t udi na l
s l i p r ange,
r e s pe c t i ve l y.
( 2 )
A
paramet er ( or par amet er s) c ha r a c t e r i z i ng t he
l ongi t udi na l d i s t r i b u t i o n of normal pr es s ur e i n
t he cont act pat ch ( di f f e r e nt f o r d i f f e r e n t t ypes
of car cas s c ons t r uc t i ons ),
i s
needed t o des cr i be
c ha r a c t e r i s t i c di f f e r e nc e s i n s he a r f or c e pe r -
formance observed i n t he
3"
t o
8'
s l i p angl e range.
( 3)
A
l a r ge i nc r e a s e i n t he
v e r t i c a l
l oad c a r r i e d
Iby
t he t i r e r e s u l t s i n a s i g n i f i c a n t r educt i on i n t he
i n t e r f a c i a l f r i c t i o n c o e f f i c i e n t. Thi s phenomenon
shoul d be s t udi e d i n more d e t a i l. None of t h e
t hr e e s i mpl i f i e d t i r e models s i t e d pr evi ous l y
t r e a t s t he i nf l uences of v e r t i c a l l oad adequat el y.
( 4 ) The
rnaximum
s hear f or c e p o t e n t i a l a t t he t i r e - r o a d
i n t e r f a c e
( f r i c t i o n c o e f f i c i e n t ) ge ne r a l l y va r i e s
as a compl i cat ed f unct i on of s l i d i n g ve l oc i t y and
v e r t i c a l l oad.
A
l i n e a r f unc t i on of s l i d i n g
vel oc-
i t y
i s
adequat e f o r r epr es ent i ng t he s he a r
forlzes
produced under c e r t a i n i n t e r f a c e condi t i ons.
( 5)
The l ongi t udi na l and l a t e r a l t i r e f or c e s produced
a t hi gh val ues of s l i p on wet s ur f a c e s s ugges t t he
pr eval ence of e f f e c t i v e l ongi t udi na l and l a t e r a l
c o e f f i c i e n t s
of
f r i c t i o n which a r e unequal i n
mag-
n i
t ude
.
A.
Work Towards
-
Es t a bl i s hi ng a Concise Se t of Paramet ers and
Char act er i zi ng Funct i ons Descr i bi ng Ti r e Shear Force Per -
---- -
formance Should
be
Contrnued
--
The t h r e e models devel oped i n Refs.
1- 3
r e pr e s e nt a good
s t a r t towards def i ni ng us e f ul par amet er s and
c ha r a c t e r i z i ~z g
f unc t i ons. Based on t he r es ear ch r epor t ed he r e, t he t e s t
program out l i ne d i n Fi gur e
1 2
i s
proposed as a means of
qua nt i -
f yi ng t i r e s he a r f or c e performance, e va l ua t i ng s p e c i f i c t i r e
par amet er s, and r e f i n i n g e x i s t i n g c ha r a c t e r i z i ng
function:^.
Designation
of Test Machine
Type
Used
-7
1.
Determine
I
FBT
2.
Determine FBT
Cs
F
";.=soand
Fz
1
FBT
- - - - - -
ElTT
-
5.
Combined
I
FB1
F and
F
x
Y
-----
Ver t i cal
Loads
t
Required
Conditions and Form of Resul t s
1.
Safet y Walk
2.
Low s l i p angl es, F
<.3F
maximum a t t ha F
Y
Y
used
3. 400 l bs
(
FZ
(
2,000
l bs
I
I
4. Pl ot s of
F
vs.
u
a t vari ous
F
val ues
Y
1.
Safet y walk
2.
Low s l i p val ves such t h a t
r
<
.3
F max.,
e.g.,
s e t
Fx
t o
FZ/5,
FZ/lO,
0,
-FZ/lO,
-F
/5,
and read s l i p
3.
400
1bs
(
/F = I
5
2,000
l b s
4. Pl ot s of F
vs,
s
a t vari ous F val ues
1.
Concrete s l a b
2.
Carpet Pl ot F f o r
a
=
2O
t o
20°
and
Y
F
=
400
I bs
t o 2,000
l bs
1.
Wet and dry concret e sur f aces
2.
F f o r
a
=
2O,
4O,
6O,
El0,
l o o,
and
l b O
a t
v
t he speeds and l oads shown i n Chart
A
1.
Concrete s l a b
2. Carpet Pl ot
F
f o r
s
=
0 t o max. possi bl e,
Fz
=
400 t o 2,000 l b s
1.
Wet and dry concret e sur f aces
2. F f o r
0
( s
(
1.0 a t t he speeds and l oads
shown i n Chart
A
--
-
1.
Concrete s l ab
2.
F vs. F a t
a
=
Z O,
4O,
eO,
B O,
l o 0,
12O,
Y
160,
20°
f o r
FZ
=
400 t o 2,000 l bs
1.
Wet and dry concret e sur f aces
2. F
a n d F
vs. s
f o r a =
Z O,
4O,
e O,
e O,
x
Y
l o 0,
and
16O
a t t he speeds and l oads shown
i n Chart
A
Parameters or
Charact eri zi ng
Funcr
i ons Involved
and
2. C vs.
r
and
1. A
parameter
charac-
t er'i zi ng
t he pr essur e
di s t r i but i on
2.
y
VS.
Fz
Y
3.
)J
vs.
Vs,
wet and dry
Y
1,
i?
parameter charac-
termizing
t he pr essur e
di s t r i but i on
2.
p
vs.
Fz
3.
px
vs
Vs,
wet and dry
1.
Fr i ct i on r u l e appi i ed
t o combined f or ce
generat i on
2.
Check on a l l t he ot her
papameters
Note: FBT
=
Fl a t
Bed Test er
MTT
=
Mobile Ti r e Test er
ux
=
Longi t udi nal Fr i ct i on Coef f i ci ent
)J
=
Lat er al Fr i ct i on Coef f i ci ent
Y
0 Opt i onal
CHART
A
FIGURE 12.
A
PROF'OSED
TEST PROGRAM
The proposed t e s t program
i s
di vi ded i n t o f i v e t e s t s e r i e s.
The f i r s t two t e s t s e r i e s a r e i nt ended t o e va l ua t e t h e low
s he a r f or c e (normal dr i vi ng) performance of t h e t i r e. The next
two cover l a t e r a l and l ongi t udi na l f or c e s e pa r a t e l y, but i nvol ve
al most a l l of t he condi t i ons t o which a t i r e
i s
l i k e l y t o be
s ubj e c t e d dur i ng s ever e ve hi c l e maneuvers on a l e v e l s ur f a c e.
Fi n a l l y, combined l ongi t udi na l and l a t e r a l f or c e c h a r a c t e r i s t i c s
a r e consi der ed i n t he f i f t h cat egor y.
The machine used, t he t e s t s ur f a c e, t he range of t e s t con-
d i t i o n s, and t he form of t he out put da t a a r e l i s t e d f o r each
t ype of t e s t. The f i n a l column i n Fi gur e
1 2
i ndi c a t e s t he
paramet er or c ha r a c t e r i z i ng f unc t i on which would be eval uat ed
from each p a r t i c u l a r t e s t.
B.
At t empt s
-...
.-
Should Be Made t o Develop, Procedures f o r Gradi ng
--------
Ti r e Tr act i on Performance i n Terms of a Se l e c t e d Subset of
---.----
--.--
t he Paramet ers
*
and Char act er i zi ng Funct i ons Mentioned i n
P
Recommendation
A
----.-
Si nce t i r e t r a c t i o n
i s
dependent upon many v a r i a b l e s, no
one
si mpl e
paramet er o r measure would be adequat e t o e qui t a bl y
r a t e di f f e r e nc e s i n t i r e s. Those par amet er s and c ha r a c t e r i z i ng
f unct i ons most i mpor t ant i n a c c i de nt avoi dance maneuvers such
as a s t o p, a swerve, and a combined s t o p and swerve, shoul d be
s e l e c t e d f o r r a t i n g t i r e t r a c t i o n,
Al so, s i nc e t he t i r e must oper at e under a wide
ran;e
of
condi t i ons and of i nput commands, one t i r e can be s upe r i or i n
some q u a l i t i e s and r e l a t i v e l y i n f e r i o r i n ot he r s. Thus, agai n,
more t han one measure
i s
needed
t o
adequat el y r a t e t he d i f f e r e n t
t ypes of t i r e s hear f or c e performance.
A
proven working s e t of t i r e par amet er s and c ha r a c t e r i z i ng
f unct i ons i s not a va i l a bl e
now,
I n t he l a s t column of Fi gur e
1 2,
a pos s i bl e s e t of paramet ers and c ha r a c t e r i z i ng f unct i ons
i s
i ndi c a t e d. They a r e:
Ca,
Cs,
a par amet er f o r c ha r a c t e r i z i ng t he
pr e s s ur e d i s t r i b u t i o n;
p~
and
\
as f unct i ons of
Vs
and
FZ;
and a f r i c t i o n r u l e which a ppl i e s t o combined l ongi t udi na l
and l a t e r a l f or c e condi t i ons.
Means f o r deduci ng t he pr e s s ur e d i s t r i b u t i o n par amet er
and
p
and
px
from t he exper i ment al r e s u l t s have not been
Y
devel oped y e t. Use of t he proposed approach
i s
hi ghl y de-
pendent upon devi si ng si mpl e t e s t s t o eval uat e t he necessar y
t i r e par amet er s and c ha r a c t e r i zi ng f unc t i ons.
C.
-
Ef f o r t s Should Be Made Toward t he Development of a Det ai l ed
Model t o Aid i n t he Underst andi ng of How Shear Force
-
i s
Generat ed
by
t he Ti r e
--
-
I n a pr evi ous publ i c a t i on
[ 7 ],
Frank and Hof f er ber t h
di s cus s ed b a s i c phi l os ophi cal and concept ual cons i der at i ons of
t he mat hemat i cal modeling of t i r e t r a c t i o n mechanics. I n par -
t i c u l a r, t hey di s t i ngui s he d between two b a s i c approaches
:
(1)
a d e t a i l e d f or mul at i on proceedi ng from a mi cr oscopi c exami nat i on
of ma t e r i a l pr ope r t i e s and mechani cs, and
( 2 )
a s i mpl i f i e d
approach employing "phys i cal - equi val ent" models on a
macro!jcopic
s c a l e
( e.g.,
t he s t r e t c h e d s t r i n g concept ). They poi nt e d out
t he l i mi t a t i o n s of t he s i mpl f i e d approach, but concl uded
t h a t
t he comput at i onal d i f f i c u l t i e s a s s oc i a t e d wi t h any s u f f i c i e n t l y
comprehensive d e t a i l e d model pr obabl y r ul e d out t he f e a s i b i l i t y
of t h a t approach gi ven t he anal og and d i g i t a l computer t ech-
nol ogy of t h e day
( 1967).
I n t he s h o r t t i me s i nc e, t he hybr i d
computer has been devel oped i n t o a uni quel y powerful t o o l f o r
s ol vi ng p a r t i a l d i f f e r e n t i a l equat i ons. The i t e r a t i v e and
s t or a ge c a p a b i l i t i e s of t h e hybr i d computer al l ow t i me s har i ng
of anal og equipment which i n t ur n makes t he s o l u t i o n of
d e t a i l e d
f i n i t e el ement models of cont i nuous syst ems p r a c t i c a l. I t now
appear s appr opr i at e t o at t empt t o e x p l o i t t he new hybr i d t ech-
nology t o implement a d e t a i l e d f i n i t e el ement t i r e model. Such
a model ( i f s uc c e s s f ul l y devel oped) would pr ovi de r e a l i n s i g h t
i n t o t he mechanisms o f s hear f or c e gener at i on and would s e r ve as
a us e f ul r e f e r e nc e f o r e va l ua t i ng s i mp l i f i e d
r epr esent at i or i s
such
a s t he WSRI model pr es ent ed i n Ref. 1.
14
ACKNOWLEDGMENT
The f i r s t use of t he mobi l e t i r e t e s t e r was
p a r t i a l l y
suppor t ed by t he Ford Motor Company. Thanks a r e due t o
Messrs. Warren Van
Wi ckl i n
and Al l en Wright of Ford f o r t h e i r
cooper at i on.
REFERENCES
1. H.
Dugoff,
P.
Fancher, and
L.
Segel,
"Ti r e
Performance
Char act er i s t i c s Af f ect i ng Vehi cl e Response t o
St e e r i ng and Braki ng Cont r ol I nput s
,"
Fi na l Report,
Nat i onal Bureau of St andar ds Cont r act CST-
460,
August 1969.
2.
H.
Sakai, "Theor et i cal Study of t he Ef f e c t of Tr a c t i ve
and Braki ng Forces on Corneri ng Cha r a c t e r i s t i c s
of Ti r e s," Paper No.
4,
JSAE Saf et y Tour i n
U.S.IZ.,
Oct.
-
Nov.
1969.
3.
D.
Li vi ngst on and
J.
Brown, "Physi cs of t h e Sl i ppi ng
Wheel
11.
Sl i p Under
Both
Tr act i ve and La t e r a l
For ces," pr es ent ed t o t he Di vi si on of Rubber
Chemi st ry, American Chemical Soci et y, Buf f al o,
N.Y.
,
Oct.
14- 17,
1969.
4.
B.
Y i m,
G.
Ol sson, P. Fi e l di ng, and
G.
Balmer,
"Highway
Vehi cl e S t a b i l i t y i n Braki ng Manuevers," SAE Paper
No. 700515, May 1970.
5.
H.
Dugoff,
R.
D.
Er vi n, and
L.
Segel,
"Vehi cl e Handling
Te s t Procedures
,"
Fi n a l Repor t, Nat i onal Highway
Sa f e t y Bureau Cont r act
FH-11-
7297, t o be publ i shed.
6.
11.
Dugoff
and
B.
J.
Brown,
"Measurement
of Ti r e Shear
For ces," SAE Paper No. 700092, Januar y 1970.
7.
F.
Frank and
W,
Hof f er ber t h,
"Mechanics
of
t he
Pneumatic
Ti r e," Rubber Chemistry and Technology, Vol. 40
?
No.
I,
February
1967.