these tests (tf, Jh 5) were designed for evaluating cutting resist
ance of rubber-insulated electric conductors. T he m ethods described in these papers are satisfactory for evaluating the cutting resistance of rubber insulating m aterials, b u t fail in some cases to evaluate correctly th e cu ttin g resistance of tire tread stocks. In the m ost recent of these papers, w hich deals specifically with the cu ttin g of tire treads, Clarke (I) using a rubber stock is a v e ry complex function of several interrelated factors, some of which are them selves complex. T he m ost im portant of these factors are hardness, tear resistance, elastic modulus, tensile strength, aging resistance, and tem perature.
At first thought, it m ight seem desirable to determ ine th e functional relationship between cu ttin g resistance and these factors and th u s evaluate cutting resistance in term s of sim pler quantities. T h is procedure has n o t proved practicable in the experim ents perform ed in this laboratory, for it was not found possible to express this relationship as a simple, single- valued function. F o r example, it w as found th a t, in general, c utting resistance increased w ith increasing hardness but, in certain cases, a stock w ith a greater hardness th a n another be, it is desirable to incorporate in it as accurately as possible th e factors existing in service. In th e case of th e cutting T h is expression is only approxim ate for a deform able p neu
m atic tire for, sidewise bulging neglected, only th e extrem e
ANALYTICAL E D IT IO N 69 In E q u atio n 7, co and a are known. T he factor P is sim ply a
function of y or th e sta tic load applied to a cu ttin g edge to cause a deflection y w ith o u t actu ally cu ttin g th e rubber.
In order to determ ine P for various sta tic deflections e, a device was em ployed by m eans of which a 20° steel wedge was pressed ag ain st th e contact area of th e tread of a nor
m ally inflated an d loaded tire. In th is m anner, a load-deflec- tion curve w as determ ined from which th e values of P cor
responding to various values of e = y were directly obtained.
In sertin g th ese values of P into E q u atio n 4, th e im p act force S was calculated. Values of im p act velocity and im pact force, calculated from E q u atio n s 1 and 7, respectively, are given in T ab le I.
Ta b l e I . Im p a c t Ve l o c i t y a n d Im p a c t Fo r c e (H e a v y - d u t y tir e 81 X 15.2 c m .; ro llin g ra d iu s, 3 8 .9 cm .)
O b sta c le H e ig h t O b sta c le H e ig h t O b sta cle H e ig h t 0 .2 5 C m . 0 .0 2 C m . 2 .5 C m . C ar S p e e d V e lo c ity F o r ce V e lo c ity F o r ce V e lo c ity F o r ce
K m ./ h r . C m ./se c . K g ./c m . C m ./se e . K g ./c m . C m ./se c . K g ./c m .
1 6 .1 52 62 79 103 158 7 7 5
3 2 .2 104 124 158 3 2 0 3 1 0 1550
0 4 .4 2 0 8 2 4 8 3 1 6 0 5 2 0 3 2 3 1 0 0
9 0 . 0 31 2 37 2 4 74 9 7 8 9 4 8 4 0 5 0
T he sim plest ty p e of a p p a ratu s which could be used w ith these values of im p act velocity and force appeared to be a steel knife falling freely u nder gravity. F or such a device, th e im pact velocity w ould be determ ined by th e height of free fall and th e im pact force by th e load a ttac h ed to th e falling knife. T he relation betw een th e load, L, on th e knife and the im pact force is obtained dircctly from E q u atio n 2 by re- placing g - by h and ta k es th e formV 2
S = 2 L
(>+S)
(8)w here h is th e height of fall and d is th e d ep th of penetration of th e knife before cu ttin g occurs.
I n th e im pact cu ttin g device, described in detail below, the im p a ct velocities ranged from 300 to 600 cm. per second, and th e im p act forces varied from 360 to 1200 kg. per cm. of knife edge. Com paring these actual values of velocity and force used on th e a p p a ra tu s w ith th e calculated values of T able I, it is seen th a t th e im pact cu ttin g device could be operated u n d er conditions approxim ating those found in road service.
I t is tru e th a t th e tread ru b b er on a tire is m ounted on a pneum atic base, w hereas th e te st piece of the im p act cutting te s t was a rubber block, 12.7 cm. (5 inches) in length, 1.9 cm. (0.75 inch) in w idth, and 3.8 cm. (1.5 inches) in height, m ounted on a heavy steel platen. However, it was tho u g h t th a t th e use of a pneum atic backing for th e te s t block of the im p a ct cu ttin g device would introduce into th e te st a vari
able v ery difficult to control. T hus, th e pneum atic backing of a tire w as sim ulated q u alitatively b y using a ra th e r tall
(3.8 cm .), and therefore highly deform able, te s t block.
A p p a r a tu s a n d A n a ly s is o f R e s u lt s
The im pact cutting device illustrated in Figure 1 consists, mainly, of an accurate vertical slide which guides a loaded knife in approximately free fall. The slide is rigidly suspended from the top end. The knife, which is a 20° wedge of altitude 3.8 cm. (1.5 inches) and has an edge of 7.6 cm. (3 inches), impinges on a rubber test block and produces a cut which can be measured with an ordinary steel scale. The sliding Dowmetal carriage which bears the knife is constructed so as to permit different combinations of weights to be attached to it. The knife is readily detachable and is removed from the machine after each series of tests, oiled, and kept in a closed box until needed again.
The machine is also equipped w ith a vertically movable electro
magnet with which the knife and carriage can be raised to the desired height and released by reversing the current in the coils of the magnet. The magnet is raised and lowered by means of a windlass. The slide is equipped w ith a number of stops (not
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shown in Figure 1) set a t known heights, which can be used by the operator to ascertain when the carriage has been raised to the correct height. Two rubber bumpers a t the bottom of the slide cushion the blow of the carriage and make it impossible for the knife edge to hit the platen face. Blocks of certain stocks deform to such an extent th a t the carriage hits the bumpers be
fore completion of the cut. A trip device (not shown) mounted a t the base of the slide, lights a small lamp when the carriage strikes the bumpers. In cases where the light is thus turned on, the test results are discarded.
The rubber test block, 12.7 X 1.9 X 3.8 cm. (5 X 0.75 X 1.5 inches), is placed in a holder a t the bottom of the slide and rests on the large face of a steel platen 51 X 51 X 10 cm. (20 X 20 X 4 inches). The block rests on its 12.7 X 1.9 cm. (5 X 0.75 inch) face with its long axis perpendicular to the knife edge.
Two cuts are made in each block a t positions 3.2 cm. (1.25 inches) from the ends of the block. The deeper cuts are usually uni
form in depth across the width of the block and can thus be measured with a steel scale after slitting through the rubber remaining a t the bottom of the cut. The shallow cuts are, in general, less regular in depth than the deep cuts. However, with a little practice, the operator can estimate the average depth of the shallow cuts without much difficulty.
The cutting knife is of hardened steel and is carefully ground in the form of a 20° wedge. The feather edge is removed from the knife with a fine abrasive cloth. The sharpness of the knife changed with use but, by always running a control stock simul
taneously with an experimental stock, it was found th a t the rela
tive cutting results were essentially uniform over a period of 2 years. In this study of th e aging of the knife edge, the effect of the aging of the rubber was avoided by using new samples.
In the method of testing adopted as standard, a t least six test blocks of each stock or cure to be tested are cured in a 12-cavity mold in a press, the tem perature of which is very carefully controlled. The blocks are then set aside for 1 week to allow the cutting resistance to come to a stable state. The hardness is then measured with a Firestone 1.36-kg. (3-pound) penetrome
ter (8) a t various points on the 12.7 X 1.9 cm. face of the blocks. Two cuts are then made in each block with the impact cutting machine, as described above. Thus, using six blocks, it is possible to obtain twelve cuts in each stock or cure. These cuts are usually made a t 2 or more loads chosen to give a depth of cut vs. load (D vs. L) curve. The cutting velocity is usually
70 INDUSTRIAL AND E N G IN E ER IN G CHEM ISTRY VOL. 8, NO. 1 T a b l e II. C u t t in g R e s i s t a n c e v s. R e s i s t a n c e t o T e a r
F u n c t io n a l R e la t io n s h ip s
As mentioned above, th e relationship between d epth of cu t and load is linear. T h a t b o th th e slope and load in te r
cept v a ry for different stocks is clearly dem onstrated in Figure 2. T he relationship between dep th of cu t an d velocity a t co n stan t load is n o t linear, however (Figure 3). In general, th e D vs. V curves are convex upw ard, though occasionally a curve which is concave upw ard is found. Unlike th e D vs.
L curves, the D vs. V curves do n o t cross in th e range of ve
locities investigated. T he practice of running te sts a t a singlo velocity is therefore justified.
T h e curves of F igure 4 show th a t La, a m easure of th e cu t
ting resistance, decreases rapidly w ith increasing tem perature.
In m aking these tests, th e te s t blocks were k ep t in an ice box
Vnoc/rr
( CmPe# S ee J
F ig u r e 3. D e p t ii op C u t ps. Im p act V e l o c i t y 2 0 ° k nife
set a t 424 cm. per second (13.9 feet per second). In practically every case the D vs. L curve is linear (Figure 2).
To be very exact, there are two physically independent indexes of cutting resistance—i. e., th e slope of th e D vs. L curve and th e extrapolated load intercept. However, i t is difficult to in te rp re t d ata on th e basis of tw o indexes. Hence, th e load necessary to give a 25-mm. cut, L ,s, has been selected as a single cutting index. T his index, L a , h as been found very satisfactory, in th a t results arrived a t th rough its use agree w ith road test results and w ith results evaluated by means of th e slopes and load intercepts of th e D vs. L curves.
H a n d T ea r
iock L a
G ram s
E s tim a te
A 43 0 0 B e s t
B 4 0 4 0 V er y good
C 41 8 0 V ery good
D 42 3 0 V ery g o o d
E 4 3 5 0 G o o d
F 4 3 9 0 F a ir
G 43 6 0 F a ir
O 13 3 0 4 S SO
T e /w r °C .
F i g u r e 4 . C u t t i n g R e s i s t a n c e v s. T e m p e r a t u r e
2 0 ° k n ife, v e lo c ity 4 2 4 c m . per seco n d
/fCO
L o w (
F ig u r e 2. D e p t h o f C ut-»s. Im p act L oad 2 0 ° k n ife, v e lo c ity 4 8 8 cm . per seco n d
or oven u n til th e center of the blocks had reached th e desired tem perature, as m easured b y a m ercury-in-glass therm om eter inserted in a hole in the block. T he te sts were th e n ru n im
m ediately to m inim ize tem p eratu re changes occurring after rem oval from the oven or ice box. T h is dependence on tem p e ra tu re indicates th e necessity of recording the room tem p era tu re for all tests.
T h e index of cu ttin g resistance, L 25, generally increases w ith hardness [Firestone 1.36-kg. (3-pound) penetrom eter] as is shown in Figure 5. However, in several cases, d istin ct rever
sals occurred—for example, stock I X vs. stock X and stock V II vs. stock V III.
C u ttin g resistance does n o t always correlate w ith te ar resistance. T his fact is clearly shown in T able I I , where two stocks w hich ap p ear to be best from th e cutting sta n d p o in t show up as d istin ctly in
ferior to th e others from th e te a r standpoint.
T he accuracy of th e results of th e im p act cutting te s t depends upon th e num ber of te sts averaged.
F or example, w here six blocks of a given stock were tested, th e m ean deviation was 4 per cent; where tw elve blocks were tested, th e m ean deviation was 3 per cent. In individual cases th e accuracy is m uch greater and can be determ ined in each case—
for example, th e m ean deviations for th e te sts of T able IV were m uch less th a n 3 per cent.
C o m p o u n d in g T r e n d s in R e s is t a n c e t o C u t t in g
T he cutting resistance generally increased w ith th e car
bon black loading, as is shown in Figure 6. T o ob tain these d a ta , th e carbon black content in a commercial m ercapto- benzothiazole tread stock was varied so as to give loadings varying from 38 to 76 p a rts by w eight per 100 p a rts of rubber.
I t m ay be seen th a t th e cutting resistance increased w ith in creasing carbon black loading u p to a loading of 67 per cent and th e n began to decrease. T he existence of this m axim um in c u ttin g resistance w ith respect to carbon black loading has v ery little p ractical significance, since 67 per cent black is considerably above present p ractical com pounding lim its for
3OOO
ANALYTICAL E D IT IO N 71
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Perver^r/OA/ J ¿s. /^mrr/ro/Mere,e) F ig u r e 5. C u t s in g R e s i s t a n c e v s. H a r d n e s s T e n sto c k s; e a c h p o in t a v e r a g e o f 12 t e s t s ; 2 0 ° k n ife: v e lo c it y
4 2 4 cm . p er seco n d
treads. However, th e fact th a t th e cu ttin g resistance increases to th a t poin t indicates th a t, for special ty p es of service where c u ttin g resistance is th e m ajor consideration, th e loading of carbon black should be increased above th e lim its considered satisfactory for o ther ty p es of service.
T he effect upon th e c u ttin g resistance of varying th e am o u n t of carbon black in a m ercaptobenzothiazole tread stock where glue is used is shown in T able I I I . T h e addition of 5 per cent glue had no appreciable effect on th e cutting resistance; furtherm ore, th e cu ttin g resistance increased w ith increasing black loading to a m axim um a t approxim ately 57 p arts b y w eight per 100 p a rts of rubber.
T a b l e III. C u t t in g R e s i s t a n c e a s a F u n c t io n o f C a r b o n B l a c k L o a d in g w i t h G lu e U s e d a s a S o f t e n e r
P e r c e n t b y W e ig h t o n R u b b er
G lu e C arb on b la ck L n
0 4 9 .4 4 6 0 0
5 4 9 .4 46 5 0
5 5 3 .7 4 7 6 0
5 5 7 .0 5000
5 6 0 .0 4 9 9 0
C o m p a r is o n o f I m p a c t C u t t in g w it h R o a d T e s t s G re at care m u st be exercised in com paring th e results of a lab o rato ry c u ttin g te s t w ith road te st results, for m ost so- called cutting te sts on th e road involve cracking as well as
cutting. In fact, it was found necessary to devise a special road cu ttin g te st. In th is te st, half-and-half tires m ounted on a tru c k were ru n a t low speeds over a specially constructed road upon which were strew n sh arp pieces of furnace slag, broken insulators, etc. T he tires were rem oved from th e rims, a fte r 200 to 500 miles of th is service, in a badly cu t and chipped condition. T h e treads were th e n cu t u p in such a m anner th a t th e areas of all th e individual cuts could be m eas
ured. T he am o u n t of cu ttin g sustained by a stock in th e te s t was assum ed to be proportional to th e to ta l area of th e cuts.
Six stock com parisons were m ade in th is m anner. C u ttin g te s t blocks were cured from sections of th e extruded treads which were actually used in th e te st tires and im p act tests were m ade in th e sta n d ard m anner.
T h e results are given in T able IV . T he results of th e im p ac t cu ttin g te st correlated w ith th e road te s t results in all cases.
T a b l e IV. Im p a ct T e s t s vs. R o a d T e s t s (81 X 15.2 c m . tir es)
T ir e S to c k R o a d T e s t E v a lu a tio n L it G ram s
I A S lig h tly b e tte r 3 2 7 0
B 3 2 7 0
II C B e t t e r 3 7 0 0
D 3 2 7 0
I I I E B e tte r 3 2 4 0
F 3 1 5 0
IV G W orse 3 1 8 0
H 3 2 7 0
V I B e tte r 36 0 0
J 3 2 6 0
V I K W orse 3 3 1 0
L 3 5 9 0
F i g u r e 6 . C u t t i n g R e s i s t a n c e v s. C a r b o n B l a c k L o a d i n g 2 0 ° k n ife , v e lo c it y 4 2 4 cm . p e r seco n d
C o n c lu s io n
T h e im pact cutting device described in th is p aper is recom m ended for testing th e cu ttin g resistance of trea d stocks be
cause of its sim plicity and th e accuracy w ith which its results agree w ith road te s t results. T he fac t th a t th e device was designed on sem i-quantitative theoretical grounds gives some additional confidence in its results. I t is possible th a t o ther cu ttin g devices, designed w ith no regard to theory w hatsoever, m ight operate as well as th e im p act device. H owever, i t is felt th a t, since m ost la boratory te sts on ru b b er stocks are necessarily largely em pirical, it is well to a tte m p t to design a testing m achine which will operate in th e ranges of th e variables found in service.
A c k n o w le d g m e n t
T h e au th o r desires to acknowledge th e work of B. A. Jones, who designed th e im p a ct cu ttin g device and perform ed th e prelim inary tests, an d to th a n k N . Joh n sto n and R . J . B onstein for th e ir helpful suggestions, an d N . A. Shepard u n d er whose direc
tion th e w ork was done.
L ite r a tu r e C ite d
(1) Clarke, In st. Rubber In d . Trans., 10, 80 (1934).
(2) Depew, H am m ond, and Snyder, Proc. Am. Soc. Testing Materials, 31, P t. 2, 923 (1931).
(3) H ippensteel, I n d . E n g . C h e m ., 18, 409 (1926).
(4) H o lt, Bur. Standards J. Research, 12, 489 (1934).
(5) Ingm anson and G ray, In d ia Rubber World, 82, 53 (1930).
(6) K en t, "M echanical Engineers’ H andbook,” 10th ed., p. 345, New Y ork, Jo h n W iley & Sons, 1923.
(7) Somerville, In st. Rubber In d . Trans., 6, 150 (1930).
(8) Zim m erm an and Brow n, I n d . E n g . C h e m ., 20, 216 (1928).
R e c e i v e d O c to b er 18, 1 9 3 5 . P r ese n te d b efo r e t h e D iv is io n o f R u b b e r C h e m istr y , A m er ic a n C h e m ic a l S o c ie ty , a t A k ro n , O h io , O cto b er 1, 1935.