Tire Stiffness and Damping Determined_NASA_Technical Paper 1671

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    NASA Technical

    Paper

    1671

    NASA

    TP

    1 6 7 1

    c. 1

    Robert

    K.

    Sleeper

    and

    Robert C. Dreher

    JULY 1980

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    TECH

    LIBRARY KAFB, NM

    NASA

    Technical

    Paper 1671

    Tire Stiffness and Damping Determined

    From Static and Free-Vibration Tests

    Robert

    K.

    Sleeper

    and

    Robert

    C.

    Dreher

    Langley ResearchCenter

    Hatnpton Virginia

    National Aeronautics

    and Space Administration

    Scientific and Technical

    Information Office

    1980

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    SUMM RY

    Stiffness anddampingof a nonro lling ti r e a re determined experimentally

    from both s t a t i c force-displacement re la tio ns and thefree-vibration behavior

    of a cable-suspended platenpressedagainst he t i r e periphery.Lateral and

    fore-and-aftspringconstants and damping fac to rs of a 4 9

    x

    1 7 s i z e a i r c r a f t

    t i re fo r dif fer en t t i r e pr es su res and v ert ical loads are measuredassuming

    a rate-independent dampingorm.

    I n

    addition, a technique

    i s

    applied or

    estim ating he magnitude of the t i r e masswhich participates i n the vibratory

    motion of the dynamic te st s.Re sults show th at both the l a t e r a l and fore-and-

    a f t spring constants generally ncrease

    w i t h

    t i r e pressure

    b u t

    only the lat ter

    increased significantly

    w i t h

    v e rt ic a l ir e loading. The fore-and-aftspring

    con stan ts were gre ate r than those

    i n

    the a te ra ldir ec tio n. The static -spr ing -

    constan t variation s were s im ilar o t h e

    dynamic

    varia t ions

    b u t

    exhibited lower

    magnitudes. Dampingwas small and in se nsi ti ve o ir e oad in g . Furthermore,

    s t a t i c damping accounted for a sig ni fi ca nt po rt io n of th at found dynamically.

    Ef fec tiv e tir e masseswere a ls o small.

    INTRODUCTION

    Ti re stif fn ess anddamping i n the la te r a l and fore-and-aft dire ctio ns are

    important properties

    i n

    dynamic analyses of a i r c r a f t wheel

    shimmy

    and antiskid

    braking systems. S ta ti c e s ts on nonrolling t i r e s havebeenused for a number

    of years to measure ti r e s t i f fn ess (e.g. e f.

    1 ) .

    Tests on a ro ll in g ir ea r e

    preferred b u t equipnent and f ac ili ty lim it at io ns make such te st s d if f ic u lt to

    implement.

    As

    a resu l t , i reproper t i e sa regenerally measured

    us ing

    a platen

    loaded vert ical ly

    w i t h

    a t i r e and supported on bearings (e.g. re fs . 2 and 3

    where the propertiesar e deduced rom the response of the pl at en oapplied

    fo rc es . Such a support system, however, ty p ic a ll y n je c ts indeterm inant motion

    e f f e c t s

    and

    limits

    t e s t s os ta t i cap pl ica t io ns . While uch st a t i c e st s remain

    a primary source

    of

    stiffness anddamping information, measurements ob tained

    from vi br at io n es ts appear to be more rep res en tat ive of the operati ng

    environment.

    The objective of

    t h i s

    report i s todiscuss the re su lts of

    an

    experimental

    ef fo rt to measure s tif fn es s anddamping prop ert ies of a nonro lling t i r e

    us ing

    a cable-suspended platenpressedagainst the t i r e periphery. Both s t a t i c and

    dynamic t e s t s were performed t o determine spr ing cons tan ts anddamping factors

    of a large aircraft i re displace d

    i n

    ei ther the la te ra l orfore-and-aftdirec-

    tion. Damping is t rea ted i n a rate-independent form.Three pl at en s were

    employed

    i n

    the dynamic t e s t s to provide

    an

    in di ca tio n of t i r e mass involvement

    i n

    thevibratory motion. The

    s t u d y

    was conducted on

    a

    4 9 x 1 7

    s i ze t i r e over

    a range of v e r t i c a l loads and i nfl at io n pre ss ur es extending to th e i r maximum

    ratedvalues.

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    SYMBOLS

    Values are

    g i v e n n b o t h

    S I

    and U.S. CustomaryUnits.

    C

    damping forceo e f f i c i e n t ,

    N-sec/m

    ( lb f - sec / in . )

    c.

    g. c e n t e r of g r a v i t y

    F

    complex appliedo r c e ,

    N

    ( l b f )

    Fmaxaximum appliedorcemagni tude , N ( l b f

    1

    FO i n i t i a lp p l i e do r c ea g n i t u d e ,

    N

    ( l b f )

    F V

    t i r e v e r t i c a l load, N ( l b f )

    Fx=0 appliedor ce when displac ement

    i s

    zero ,

    N

    ( l b f )

    f o s c i l l a t i o nr e q u e n c y ,

    Hz

    - = / z i -

    k

    kC

    k t

    Q.

    m

    mP

    m t

    N

    t

    X

    X 0

    XN

    t o t a l

    s p r i n gc o n s t a n t , N/m ( l b f / i n . )

    c a b l e n t e r a c t i o ns t i f f n e s s ,

    N/m

    ( l b f / i n . )

    t i r e s p r i n gc o n s t a n t ,

    N/m

    ( l b f / i n . )

    cable

    l e n g t h , m ( f t )

    v i b r a t i n g

    mass,

    kg (lbm)

    p l a t e n

    mass,

    kg l h )

    e f f e c t i v e tire mass, kg lbm)

    number ofc y c l e s

    time, sec

    complexdisplacement, m ( i n . )

    or ig ina ld i sp lacementampl i tude ,

    m

    ( i n .

    1

    displacement amplitude of Nthcycle, m ( i n . )

    5

    viscous damping fac tor

    T

    f requency period, sec

    w c i r c u l a ro r c i n grequency, sec-1

    2

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    APPROACH

    Tire

    sp r in g c o n s t a n t s anddamping f a c t o r s i n b o t h t h e

    l a t e r a l

    and ore-

    a n d - a f t d i r e c t i o n s were determined rom

    s t a t i c

    anddynamic tests using a cable-

    s u s p e n d e dp l a t e np r e s s e da g a i n s t h ep e r ip h e ry of t h e t i re . S t a t i cc h a r a c t e r -

    is t ics were derived rommeasurementsof platen d i s p l a c e m e n t r e s u l t i n g from

    s l o w l yapp l ie d o rc es . The s t a t i c s p r i n gc o n s t a n t was de te rmined rom hes lope

    of

    t h e a x i s of t h e h y s t e r e s i s loop des cr i bed by the o rce -d isp lacement re la t ion-

    ship , and

    a

    damping factor was der ived rom

    i t s

    width . Dynamic ch ar ac te r i s t ic s

    were obtained rom

    simple,

    s ing ledegreeof reedom ree-v ibra t ion tests of the

    t e s t p la t e n . Thus, fo r h e l a t t e r

    tests

    t h es p r i n gc o n s t a n t was derived rom

    t h ev i b r a t i o n a lf r e q u e n c ya n dp l a t e n mass sp ec i f ic a t io ns , and th e damping

    fac tor

    was de te rmined run hed isp lacementampl i tudedecay

    rate. Estimates

    o f th e

    e f f e c t i v e

    t i r e

    masses p a r t i c i p a t i n g i n t h e o s c i l l a t o r y m o t i o n s of thedynamic

    tests

    were determined romc ha ng es i n h e f r e q u e n c y r e s u l t i n g f r o m

    similar

    t es t s

    w i t h d i f f e r e n t mass platens.

    -PARATUS

    AND

    TEST

    PROCEDURE

    Figure 1 i s a photographof he

    t e s t

    apparatusand t e s t t i r e . The appara-

    t u s i s

    shown preparedf o r

    a

    l a t e r a l dynamic

    t es t .

    Test F i x t u r e

    Themain s t r u c t u r e of t h e t e s t f i x t u r e is conf igured as two three-bay

    por-

    t a l frames oinedoverhead by fo ur beams a n dalo ng he loo r by a t h i c k p l a t e .

    The frames,cons t ruc tedsfwelded 10-in. s t e e l H-beams, are nominally 3.0 m

    (10 f t ) deep,2.2

    m

    (7.1 f t ) highand a r e spaced a d i s t a n c eof 2.1

    m

    ( 7 f t )

    a p a r t . The p l a t e l o n g h e l o o r

    i s

    2.5

    c m

    (1

    in . ) h i ck . The

    t i r e rim

    i s

    s u p p o r t e don he ef t by a taperedwelded box s t ru c tu re , c o n s t r u c t e d from

    2.5-cm (1-in. ) t h i c k p l a t e

    s tee l

    which i s su sp e n d e d ru n h eu p p e rp a r t of t h e

    f i x t u r e and s t a b i l i z e d by 0.2-cm (4-in . )

    diameter

    pipe. A v e r t i c a l

    beam a l so

    suspended rom heupper par t o f h e f i x t u r es u p p o r t s h e r i g h t s i d e of t h e

    rim

    and

    clamps it to

    t h e f i x t u r e

    t o

    preven t t i r e r o t a t i o n .

    T h e sp e c i a l f ea tu re o f h ea p p a ra tu s

    i s

    t h e s u p p o r t i n g of t h e t e s t p l a t e n

    by fourcables . Each ca bl e i s 1/2-in.

    s t ee l wire rope

    and i s suspended rom

    a

    force-measuring oad

    ce l l

    connected t o

    a

    h y d r a u l i c c y l i n d e r as shown i n f i g -

    u r e

    1. The cab le ree -sw ing e n g th 8 i s approximately .83 m ( 6 t ) . Ti re

    load ing is accomplished by ene rg iz in g he h y d r a u l i cc y l i n d e r s

    to

    l i f t t h e p l a t e n

    v e r t i c a l l ya g a i n s t h e

    t i r e ;

    i

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