A study on the mechanism of wool felting

A STUDY ON THE MECHANISM

OF WOOL FELTING

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECHNISCHE HOGESCHOOL TE DELFT, OP GEZAG VAN DE RECTOR MAG-NIFICUS DR O. BOTTEMA, HOOGLERAAR IN DE AFDELING DER ALGEMENE WETEN-SCHAPPEN, VOOR EEN COMMISSIE UIT DE

SENAAT TE VERDEDIGEN OP WOENSDAG 1 JUNI 1955, DES NAMIDDAGS TE 4 UUR

DOOR

ANNE KLAAS VAN DER VEGT

NATUURKUNDIG INGENIEUR

GEBOREN TE UTRECHT

DIT PROEFSCHRIFT ES GOEDGEKEURD DOOR DE PROMOTOR:

The work presented in t h i s t h e s i s was c a r r i e d out at the Fibre Research I n s t i t u t e and the Central Laboratory of the Organization for Applied S c i e n t i f i c Research in The Netherlands (T.N.O.). The author i s much indebted to the Directors of these I n s t i t u t e s for the opportunity given to perform t h i s i n v e s t i g a t i o n , as well as for t h e i r consent to publish the r e s u l t s in t h i s t h e s i s .

C O N T E N T S

1. Introduction 7 1.1. Wool as a t e x t i l e fibre 7

1.2. P r o p e r t i e s of the wool fibre 8 1.21. Geometry and s t r u c t u r e 8 1.22. The d i r e c t i o n a l f r i c t i o n a l effect 9

1.23. The s t r e s s - s t r a i n diagram 10

1.3. Theories of f e l t i n g 12 1.4. Factors which influence f e l t i n g 13

1.41. C l a s s i f i c a t i o n 13 1.42. Structure 14 1.43. Fibre p r o p e r t i e s 14 1.44. Time of f e l t i n g 17 1.45. Mechanical action 18 1.46. Medium 18 1.5. Scope of the present study 19

2, Measurement of shrinkage 20 2. 1, Discussion of the method 20 2,2, Description of the apparatus 21 2. 3, Performance of the measurements 23 2.4, Parameters of shrinkage-time behaviour 24

2 . 5 , Influence of the quantity of l i q u i d 28

3, Influence of forces 30 3, 1, Effect of shaking r a t e 30

3.2, Effect of shaking amplitude 31 3.3, Relation between forces, shaking r a t e and amplitude 33

3.4. Effect of y a m twist 34 3.5. Discussion of the r e s u l t s 39

4. Measurement of friction 44 4 . 1 , Discussion of the method 44

4.2, The apparatus for measuring f i b r e f r i c t i o n 46 4 . 3 , Derivation of the expression for /x^ 50 4.4, Derivation of the expression for/x,^ 55 4.5, Performance of the c a l c u l a t i o n of c o e f f i c i e n t s of

f r i c t i o n 57 4.6, Preliminary measurements 59

5. Measurement of Young's modulus 61 5 . 1 , P r i n c i p l e of measurement 61 5.2, Description of the method 63 5.3, Preliminary measurements 65

6. Felting and friction 70 6 . 1 , Materials used 70 6.2, F e l t i n g of t r e a t e d yarns 71

6.3. F r i c t i o n of f i b r e s from the t r e a t e d yarns 73 6.4. Relation between f e l t i n g and f r i c t i o n 73

7. Felting and elasticity 77 7 . 1 . I n v e s t i g a t i o n s on t r e a t e d yarns 77

7.2. Fibre e l a s t i c i t y in some aqueous s o l u t i o n s 79

7 . 3 . Shrinkage experiments in s o l u t i o n s 82 7.4. Relation between f e l t i n g and e l a s t i c i t y 84 8. Structure and mechanical properties of felted yarns 86

8 . 1 . I n v e s t i g a t i o n of s t r u c t u r e 86 8.2. Mechanical p r o p e r t i e s of f e l t e d yarns 89 8 . 3 . Discussion 90 Summary 92 Samenvatting 94 References 97

1. I N T R O D U C T I O N

1. 1. WOOL AS A TEXTILE FIBRE

?lbol was probably the f i r s t f i b r e used by man on c l o t h i n g . I t was worn f i r s t in the form of a skin o r p e l t , l a t e r the f i b r e s were matted or f e l t e d i n t o a f a b r i c . The next step in i t s devel-opment was t h e formation of the f i b r e s i n t o y a r n s , from which fabrics were constructed by weaving or k n i t t i n g .

The importance of wool as a t e x t i l e f i b r e i s shown hy the fact t h a t i t was not only one of the f i r s t f i b r e s used but t h a t wool s t i l l belongs to the most s u i t a b l e m a t e r i a l s for t a y l o r e d gar-ments and many household f a b r i c s . Though d u r i n g t h e l a s t few decennia several synthetic f i b r e s have been developed and produc-ed, wool will probably maintain i t s unique p o s i t i o n , s i n c e i t p o s s e s s e s a combination of c e r t a i n h i g h l y d e s i r e d p r o p e r t i e s , which i s not found in o t h e r t e x t i l e f i b r e s . Some of the s p e c i a l features of wool will be mentioned.

F i r s t l y a wool f a b r i c shows a high amount of wrinkle r e s i s t -ance and s t a b i l i t y of shape which i s due to the e x c e l l e n t recov-ery from deformations of the f i b r e .

Secondly wool p o s s e s s e s an o u t s t a n d i n g thermal i n s u l a t i n g power. This i s p a r t l y due to the n a t u r a l c u r l i n e s s of the f i b r e which causes a r a t h e r bulky cloth with much a i r in i t . Further-more, a very important c o n t r i b u t i o n to the thermal behaviour i s

formed by the great water absorbing power of wool, together with i t s l a r g e h e a t of w e t t i n g g i v i n g r i s e to a p r o t e c t i o n a g a i n s t sudden changes in temperature and r e l a t i v e humidity.

Thirdly the f e l t a b i l i t y has to be mentioned. A s l i g h t degree of f e l t i n g c o n v e r t s a woven f a b r i c i n t o a t h i c k e r and u t t e r l y more compact s t r u c t u r e which can be a p p l i e d in garments and b l a n k e t s . When f e l t i n g i s continued, wool f e l t i s obtained which i s of considerable importance for several i n d u s t r i a l purposes.

Beside these and other advantages wool shows some serious de-f e c t s .

Wool i s s u b j e c t to b i o l o g i c a l a t t a c k ; the f i b r e i s r e a d i l y eaten by moth l a r v e s and some o t h e r i n s e c t s , a fact which causes l a r g e economic l o s s e s .

A second defect of wool i s i t s s h r i n k a g e , t h i s being an un-wanted decrease of the dimensions of a fabric during i t s use. Now two d i f f e r e n t kinds of shrinkage must be sharply d i s t i n g u i s h e d , namely the shortening of the f i b r e s themselves and the migration of the f i b r e s with respect to each o t h e r .

The f i r s t form of shrinkage i s c a l l e d relaxation shrinkage and i s shown by nearly a l l kinds of t e x t i l e f i b r e s . Generally i t r e -s u l t -s from the previou-s treatment, for i n -s t a n c e in the following way: when a cloth i s wetted and put under a c e r t a i n small tension i t gets an elongation which recovers in most cases when the t e n -sion disappears. When, however, the cloth i s dried without having the p o s s i b i l i t y of r e t r a c t i n g , i t r e t a i n s i t s deformation. In p r a c t i c e the f i n i s h i n g of the t e x t i l e f a b r i c s often gives r i s e to the occurrence of t h i s phenomenon. When, during washing, wetting takes place again, the quasi permanent deformations recover, a l l fiJDres are shortened, and the shrinkage- i s a fact.

The f e l t i n g shrinkage, on the contrary, i s only met in assem-b l i e s of animal f i assem-b r e s . In f e l t i n g the length of the i n d i v i d u a l f i b r e s i s n o t a f f e c t e d , but they m i g r a t e with r e s p e c t to each o t h e r . During t h i s migration a f i b r e which l i e s o r i g i n a l l y s t r e t c h e d i n the y a m of which the f a b r i c i s composed, undergoes displacements and a t t a i n s a looped and curled p o s i t i o n . In t h i s way i t s c o n t r i b u t i o n to the length of the yarn decreases, which i s accompanied by shrinkage of the c l o t h . The yarn and the fab-r i c , howevefab-r, incfab-rease in thickness.

The s p e c i a l f e a t u r e of animal h a i r f i b r e s by which they and only they show f e l t i n g power, i s t h e i r s c a l i n e s s which gives r i s e to a d i f f e r e n c e in f r i c t i o n in the two d i r e c t i o n s along the f i -b r e . Thus i r r e v e r s i -b l e d i s p l a c e m e n t s occur, whereas for f i -b r e s w i t h o u t s c a l e s t h e t o t a l d i s p l a c e m e n t under the i n f l u e n c e of forces d i r e c t e d a t random i s zero.

This f e l t i n g phenomenon which, as h9,s been pointed out, pos-s e pos-s pos-s e pos-s i t pos-s good and i t pos-s bad- a pos-s p e c t pos-s , w i l l be the pos-subject of the present study.

1.2. PROPERTIES OF THE WOOL FIBRE 1.21. Geometry and structure

The dimensions of the wool f i b r e show a very l a r g e v a r i e t y . They depend l a r g e l y upon the geographical o r i g i n and the kind of sheep from which the wool i s o b t a i n e d . Fibres of 3 cm in length

are found as well as those of 30 cm; the diameters of high q u a l i ty wool and very coarse kinds may amount to 10 and 60 urn r e s p e c t -ively.

Generally the f i b r e s are crimped: they p o s s e s s a number of c u r l s and waves which are most pronounced in short and t h i n f i -bres.

E s s e n t i a l l y a wool f i b r e c o n s i s t s of two components, the cor-tex and the s c a l e l a y e r . A t h i r d component, the medulla, i s gen-e r a l l y prgen-esgen-ent in animal h a i r s but not always in wool f i b r gen-e s . In f i g . l a schematic representation of a longitudinal cross-section i s given from which i t can be seen t h a t the cortex c o n s i s t s of s p i n d l e - s h a p e d e l e m e n t s , and t h e o u t e r l a y e r of o v e r l a p p i n g s c a l e s with the edges p o i n t i n g in the d i r e c t i o n of the t i p of the f i b r e . Recent i n v e s t i g a t i o n s have shown t h a t the s c a l e s are cov-ered with a very thin (0.01 ^im) and very r e s i s t a n t membrane, the e p i c u t i c l e ; a s i m i l a r membrane, the s u b c u t i c l e seems to be p r e s -ent between the s c a l e s and the cortex.

Pig. 1. s t r u c t u r e of a wool fibre

1.22. The directional frictional effect (d.f.e.) As mentioned above (section 1.1) the s c a l i n e s s of the won] f i bre i s responsible for the f e l t i n g phenomenon. Due to tliis s c a l -iness the f i b r e e x h i b i t s a higher f r i c t i o n when i t moves with i t s t i p forward than in the r e v e r s e d i r e c t i o n . Though the p r e s e n t study only d e a l s with t h i s e f f e c t in i t s r e l a t i o n to the f i b r e migration, some of the t h e o r i e s which have b e e n ' e s t a b l i s h e d to account for the d . f . e . will be summarized.

E s s e n t i a l l y two d i f f e r e n t o p i n i o n s have been presented. The f i r s t of these s t a r t s from the geometry of the s c a l e s , the second from a molecular c o n s t e l l a t i o n .

i n t e r l o c k i n g of s c a l e s , has encountered several d i f f i c u l t i e s on being examined e x p e r i m e n t a l l y . Martin ^^'> showed t h a t a d . f . e . s t i l l e x i s t e d when a wool f i b r e was rubbed a g a i n s t a p o l i s h e d g l a s s surface though no i n t e r l o c k i n g or ploughing action of the s c a l e s was to be expected in t h i s case. Viewing these and o t h e r o b j e c t i o n s Rudall ^*) proposed a model with f l e x i b l e s c a l e t i p s ; t h i s model i s a l s o able to explain the decrease of d . f . e . a f t e r various chemical a n t i - s h r i n k processes, in terms of softening or even a removal of the s c a l e t i p s . Makinson ^3) performed a theo-r e t i c a l i n v e s t i g a t i o n of t h i s model and found simple theo-r e l a t i o n s between the f r i c t i o n a l c o e f f i c i e n t s and t h e angle of f r i c t i o n , the average a n g l e of c o n t a c t of the s u r f a c e s and the s h e a r i n g force required to separate two a s p e r i t i e s in contact. Lincoln ' ' ' applied a purely geometrical treatment on t h i s problem, assuming t h a t the real areas of contact are formed by e l a s t i c deformation of the s c a l e m a t e r i a l . In t h i s way he was able to p r e d i c t the v a r i a t i o n of f r i c t i o n with load, swelling, f i b r e diameter, s c a l e d i s t r i b u t i o n and roughness of the second surface.

A d i f f e r e n t explanation was proposed by Martin -^^^ who assumed the d . f . e . to o r i g i n a t e not from the microscopic s t r u c t u r e but from an asymmetric molecular f i e l d a t the surfaces of the s c a l e s . Some experimental evidence appeared to be present for t h i s theo-ry. However, Thomson and Speakman *^'> covered some wool f i b r e s with a very t h i n (0.03 ^.m) l a y e r of s i l v e r or gold and showed experimentally t h a t , though the s c a l e s were e n t i r e l y coated, the f i b r e s s t i l l showed a d . f . e . Martin's^ theory i s , t h e r e f o r e , gen-e r a l l y r gen-e j gen-e c t gen-e d .

1.23. The stress-strain diagram

A f i r s t impression of the e l a s t i c p r o p e r t i e s of the wool f i b r e can be o b t a i n e d from the s t r e s s s t r a i n diagram. In f i g . 2 d i a -grams are reproduced for a wool f i b r e in dry and in wet condi-t i o n .

The f i r s t part of the diagrams (OA) i s characterized by a slow i n c r e a s e of the s t r e s s . This i s due to the crimp of the f i b r e , the removal of which r e q u i r e s a small f o r c e . When the f i b r e i s s t r e t c h e d completely a region follows in which Hooke's law i s v a l i d (AB). The slope of t h i s s t r a i g h t l i n e i s the Young's mod-ulus E of the f i b r e . At B an apparent y i e l d point can be noticed; the slope of the curve decreases sharply. When the deformation i s continued, the slope of the diagram i n c r e a s e s somewhat j u s t

be-/ D l

tension y^

/ / / - D J

v/ y y

o E^ elongation Fig. 2. S t r e s s s t r a i n diagrams for a wool

fibre in dry and in wet condition

fore the f i b r e breaks a t D. When, however, a t C the strain' d i r e c -tion i s reversed the f i b r e i s allowed to recover. The f i r s t p a r t of the recovery curve runs p a r a l l e l to the p a r t AB of the loading curve, but afterwards i t s slope d e c r e a s e s . In wet condition the fibre recovers immediately to i t s o r i g i n a l length. The dry fibre, however, r e t a i n s a defonnation OEj which recovers only slowly and not always completely, dependent on the t o t a l s t r a i n applied.

Several parameters of the diagram appear to depend on the r a t e of elongation; e s p e c i a l l y the p o s i t i o n of B, the apparent y i e l d point, i s r a t h e r time s e n s i t i v e .

Between the diagrams of the f i b r e in wet and in dry condition the p r i n c i p a l differences are found in the slope of the s t r a i g h t p a r t AB and in the recovery. These differences can be i n t e r p r e t e d by the following simplifying reasoning.

The molecular chains possess several points of i n t e r a c t i o n be-tween each o t h e r . The most important of t h e s e l i n k a g e s are the hydrogen bonds, the s a l t linkages and the d i s u l f i d e bonds. These i n t e r a c t i o n s t o g e t h e r c o n t r i b u t e to the t o t a l s t i f f n e s s of the f i b r e in dry c o n d i t i o n . When, however, the f i b r e i s swollen in water, the s a l t l i n k a g e s and the hydrogen bonds a r e broken or weakened, whereas the d i s u l f i d e bonds remain unaffected.

During deformation of the dry f i b r e the s a l t and the hydrogen bonds are ruptured and are reformed on o t h e r s p o t s ; the d i s u l phide bonds, however, remain unbroken. The r e t r a c t i o n of the f i -bre during recovery, i s p a r t i a l l y prevented by these newly formed i n t e r a c t i o n s . In the wet f i b r e , however, only the d i s u l p h i d e bonds are present, which cause a complete r e t r a c t i o n .

These f a c t s account for the smaller s t i f f n e s s of the wet f i b r e and for i t s b e t t e r recovery power.

1. 3. THEORIES OF FELTING

The e a r l i e s t t h e o r i e s of f e l t i n g date from the beginning of the 19th century. The s c a l e s t r u c t u r e of the wool f i b r e not y e t being discovered, the f e l t i n g was mainly a t t r i b u t e d to the tend-ency of wool fibres to curl and thus to become entangled.

The f i r s t i n v e s t i g a t o r who took n o t i c e of the influence of the s c a l i n e s s on f e l t i n g was Bowman (1885) ^>. He introduced the i n -t e r l o c k i n g s c a l e -theory in which -the f i b r e s are supposed -to lock i n t o each o t h e r by means of t h e i r s c a l e s and to form in t h i s way an i r r e v e r s i b l e s t r u c t u r e . This theory met the c r i t i c i s m t h a t the scale geometry i s not r e g u l a r enough to enable such i n t e r l o c k i n g over a number of consecutive s c a l e s and t h a t microscopically t h i s phenomenon I s never observed. The theory was, therefore, modified in t h i s r e s p e c t t h a t only few p o i n t s of i n t e r l o c k i n g will occur on each f i b r e . Though the i n t e r l o c k i n g scale theory has generally been r e j e c t e d during the l a s t few decennia, some i n v e s t i g a t o r s are inclined to believe t h a t i t s t i l l comprises much of the t r u t h . Ditzel (1891) ^^) was the f i r s t who drew the a t t e n t i o n to the r o l e played by the r o o t ends of t h e f i b r e . His experiments on wool l o c k s , arranged in two ways, v i z . with root ends and with t i p ends f a c i n g each o t h e r , c l e a r l y showed the u n i d i r e c t i o n a l nature of the fibre movements towards the root end.

These i d e a s were taken up in 1944 by Martin ^^^ who prepared some locks of wool by removing the s c a l e s from e i t h e r the r o o t ends o r the t i p ends. Shrinkage experiments on k n i t t e d f a b r i c s made from these fibres also showed the importance of the root end in f e l t i n g .

In o r d e r to e x p l a i n the mechanics of t h e f i b r e m i g r a t i o n , Arnold ' ) supposed the wool f i b r e s to move by a s e r i e s of a l t e r -n a t e elo-ngatio-ns a-nd c o -n t r a c t i o -n s , somewhat i-n the same way as a worm c r a w l s . Under the i n f l u e n c e of ejjternal action the f i b r e s are preferably extended in the d i r e c t i o n of t h e i r root ends. When r e l e a s e d , the f i b r e s recover from t h i s e l o n g a t i o n and c o n t r a c t again in the root d i r e c t i o n . A r e p e t i t i o n of extension and recov-ery cycles may cause a considerable displacement of the f i b r e .

S h o r t e r ^*) assumed a d i f f e r e n t migration mechanism. He em-phasized the o c c u r r e n c e of f i b r e entanglements. In a complete entanglement no f i b r e movement i s p o s s i b l e a t a l l ; in a p a r t i a l e n t a n g l e m e n t t h e f i b r e can only move in t h e r o o t d i r e c t i o n . Shorter showed t h a t these spots give r i s e to a t i g h t e n i n g up of the network and to the formation of l o o p s in the f i b r e s when

randomly d i r e c t e d forces act on the f a b r i c under s u i t a b l e condi-t i o n s . T h i s mechanism r e q u i r e s a low f l e x u r a l r i g i d i condi-t y of condi-the s i n g l e f i b r e s in order to enable loop formation.

Martin ^^) paid special a t t e n t i o n to the compression which he considered necessary for the occurrence of f e l t i n g . During wash-ing or m i l l i n g the fabric i s subjected to many deformations, most of which have a compression component in one d i r e c t i o n or an-o t h e r . The recan-overy fran-om the can-ompressian-on tan-o which the f a b r i c i s subjected i s hindered by the f i b r e s which migrate into the open-ings.

Though each of the ideas summarized above assumes a d i f f e r e n t mechanism of f e l t i n g , i t remains quite well possible t h a t in more than only one way f i b r e migration t a k e s p l a c e and t h a t s e v e r a l mechanisms cooperate t o g e t h e r . Which of t h e s e predominates may depend on t h e ' l o c a l fibre c o n s t e l l a t i o n s and on the nature of the mechanical a g i t a t i o n applied.

1.4. FACTORS WHICH INFLUENCE FELTING

1.41. Classification

From the r e s u l t s of the research of many i n v e s t i g a t o r s i t has been e s t a b l i s h e d t h a t f e l t i n g depends upon a large number of fac-t o r s . In afac-tfac-tempfac-ting fac-to a r r i v e a fac-t a sysfac-temafac-tic, c l a s s i f i c a fac-t i o n of these f a c t o r s , i t appears t h a t they can be divided i n t o two p r i n -cipal c l a s s e s , viz. those which are inherent in the material and those a r i s i n g from the external conditions under which the f e l t -ing occurs.

Consequently the following scheme can be made:

S

fabric s t r u c t u r e yarn s t r u c t u r e / f r i c t i o n f i b r e p r o p e r t i e s < e l a s t i c i t y ! time 'geometry mechanical action medium

This scheme i s , however, not e n t i r e l y s a t i s f a c t o r y since sev-e r a l f a c t o r s msev-entionsev-ed arsev-e n o t indsev-epsev-endsev-ent of sev-each o t h sev-e r . Thsev-e various s i n g l e f i b r e p r o p e r t i e s are, for instance, often mutually c o r r e l a t e d . The medium may influence the f e l t i n g t h r o u ^ the f i

-bre f r i c t i o n or f i b r e e l a s t i c i t y as well as through the f o r c e s which the l i q u i d a c t s on the f a b r i c . (Consequently, a sharp d i s -tinguishment i s often d i f f i c u l t .

The most important conclusions from the l i t e r a t u r e about the effect of the various f a c t o r s will be b r i e f l y summarized.

1. 42. Structure

Johnson ^®) i n v e s t i g a t e d the i n f l u e n c e of weave s t r u c t u r e of wool f a b r i c s on f e l t i n g . He found t h a t the t i g h t e r the weave and the g r e a t e r the concentration of threads in the f a b r i c , the l e s s the f a b r i c will shrink. Bogaty and co-workers ^'> performed a sim-i l a r sim-i n v e s t sim-i g a t sim-i o n and came to analogous r e s u l t s namely t h a t the compactness of the cloth i s the most important factor.

This r e s u l t i s u n d e r s t a n d a b l e s i n c e , when the s t r u c t u r e i s made t i g h t e r , the f i b r e s are packed t o g e t h e r more c l o s e l y thus

being hindered in t h e i r migration.

An exception i s sometimes met in very loosely k n i t t e d f a b r i c s which during washing extend r a t h e r than s h r i n k . Presumably, in t h i s case the d i s t a n c e s between the y a r n s in the k n i t t e d s t r u c -t u r e are -too grea-t -to be overcome by -the migra-ting f i b r e s so -t h a -t no tightening action can take place.

1.43. Fibre properties

The influence of f i b r e dimensions on f e l t i n g was i n v e s t i g a t e d by various workers by comparing the shrinkage of i d e n t i c a l types of f i b r e assemblies composed of d i f f e r e n t wool f i b r e s .

As to the r e l a t i o n between f e l t i n g and f i b r e diameter, contra-d i c t o r y r e s u l t s are r e p o r t e contra-d . Some i n v e s t i g a t o r s founcontra-d a higher

f e l t i n g power for finer f i b r e s ' ' i ) ; o t h e r s , however, reported the same for the c o a r s e r ones * ^ \ whereas a t h i r d group ^7)39) ^j^^ not find any c o r r e l a t i o n between these two q u a n t i t i e s . Probably t h i s discrepancy i s brought forth by o t h e r f a c t o r s which cannot be kept constant, e.g. f r i c t i o n a l p r o p e r t i e s and yarn s t r u c t u r e ; furthermore the d i f f e r e n c e between the f e l t i n g methods used may give r i s e to contradictory r e s u l t s .

The influence of f i b r e length on f e l t i n g is studied by Speakman

et al. *^) and by Sookne et al. • " ) , who both ascertained a higher

amount of f e l t i n g for longer f i b r e s .

Since the d i r e c t i o n a l f r i c t i o n a l e f f e c t i s considered tcr be the most important f a c t o r in f e l t i n g , many i n v e s t i g a t i o n s have

been performed on che r e l a t i o n between f e l t i n g and the f r i c t i o n a l c o e f f i c i e n t s of the wool f i b r e . In most c a s e s a comparison i s made between unmodified wool and wool which has undergone an a n t i - s h r i n k t r e a t m e n t . The majority of t h e s e t r e a t m e n t s modify the f r i c t i o n a l c o e f f i c i e n t s . Sometimes the lower of the two, /Xj (the " w i t h - s c a l e " c o e f f i c i e n t ) , i s r a i s e d ; sometimes the h i g h e r one, /x ( t h e " a n t i - s c a l e " c o e f f i c i e n t ) , i s lowered; sometimes both are r a i s e d . Since the difference of the two c o e f f i c i e n t s i s important in f e l t i n g , the tendency e x i s t s to reduce t h i s d i f f e r -ence, but i t has appeared t h a t an equal i n c r e a s e of both /Xy and /Xj i s also e f f e c t i v e in reducing the shrinkage.

Several combinations of /Xj and /j,^ have been proposed as para-meters which are s i g n i f i c a n t for f e l t i n g , namely

'"^"'^1 41) ^2-/^1 31) 6)22)40) J L 19) and — " ) '

/ X j ' /X2+/Xi ' 2 ^ - 1 • fly fl2 ' ' " » ' ^ ^ 2

Most of these combinations are purely empirical and are not r e l a t e d to the mechanism of f e l t i n g . Lindberg ' ' \ however, i n t r o -duced the expression (1//Xj - I//LX2) ° " ^ t h e o r e t i c a l b a s i s . His reasoning, was as follows: Consider an i d e a l i z e d system of f i b r e s in which each fibre can move i n t o two opposite d i r e c t i o n s and i s subjected to a c e r t a i n normal pressure N. A force a c t s on a f i b r e a l t e r n a t i v e l y in both d i r e c t i o n s during short periods and t r a n s f e r s to the f i b r e energy quants of an average value E. The d i s -placements of the fibre in both d i r e c t i o n s are Zj and l^, respec-t i v e l y . Thus

E = N ij.y ly = N /j.^ l^ (1)

and the r e s u l t i n g movement which is a measure for the shrinkage i s

ly -l2=^ ( - - — ) . (2)

This theory i s , however, e s s e n t i a l l y wrong, because of the as-sumption t h a t the transferred energy i s equal in both d i r e c t i o n s . When, for instance, the forces are too small to cause a movement in the a n t i - s c a l e d i r e c t i o n , no energy will be transferred a t a l l . Recently, Lindberg ^"^ put forward another theory in which the volume shrinkage i s r e l a t e d to the f i b r e f r i c t i o n . Now he s t a r t s from the expression

in which Q i s the energy t r a n s f e r r e d to the m a t e r i a l , X i s the t o t a l length of a l l the f i b r e d i s p l a c e m e n t s , W i s the average normal pressure between the f i b r e s , and /x^^^ and fXj^ are the

coef-f i c i e n t s ocoef-f k i n e t i c coef-f r i c t i o n .

Equation (3) i s written in the form

dk i 2

For the volume decrease Lindberg assumes the equation

(4)

In order to r e l a t e eq. (4) to eq. (5), the following proportion-a l i t i e s proportion-are postulproportion-ated:

dQ {:) dt (6)

dV (:) dk (7)

and L (:) V . (8)

W

Substitution leads to the expression 2

(9)

Which r e l a t e s the f r i c t i o n to the r a t e of shrinkage. Some experi-ments seem to confirm t h i s r e l a t i o n s h i p . Nearly a l l the assump-t i o n s made a r e , however, very d i s p u assump-t a b l e . If, according assump-to eq. (7), k denotes the t o t a l resulting f i b r e migration, the expres-sion for Q in eq. (3) cannot be v a l i d s i n c e Q, the t o t a l amount of t r a n s f e r r e d energy, i s used for displacements in both d i r e c t i o n s . Furthermore, i t i s not probable t h a t the load on the f i -b r e s should -be i n v e r s e l y p r o p o r t i o n a l to the volume (eq. ( 8 ) ) . The most s e r i o u s e r r o r i s the assumption of eq. (6), because the t r a n s f e r r e d energy depends on the d i s t a n c e s over which the exert-ed forces are able to move the f i b r e s . When f e l t i n g i s completexert-ed the f i b r e s have ceased to migrate and the work per u n i t time per-formed by the e x t e r n a l l y a c t i n g forces, has become zero.

Various o t h e r i n v e s t i g a t o r s have t r i e d to c o r r e l a t e f r i c t i o n and f e l t i n g . None of the functions of /Xj and /x^ mentioned above, can, however, be favoured as being s i g n i f i c a n t for f e l t i n g since t h e s p r e a d i n g of the t e s t r e s u l t s i s , in g e n e r a l , high. Sookne and co-workers ^"^ e s t a b l i s h e d an empirical r e l a t i o n s h i p between

the shrinkage of wool tops and/Xj -/J-^. They, however, admit t h a t the a p p l i c a t i o n of one of the o t h e r combinations of the c o e f f i -c i e n t s of f r i -c t i o n gives r i s e to an equally good -c o r r e l a t i o n .

The r e s u l t s obtained by d i f f e r e n t i n v e s t i g a t o r s are often con-t r a d i c con-t o r y . This may be due con-to differences in mecon-thods of f e l con-t i n g , in external circumstances or in the m a t e r i a l s used.

The i n f l u e n c e of e l a s t i c p r o p e r t i e s has not obtained so much a t t e n t i o n as the f r i c t i o n , because t h e d i r e c t i o n a l f r i c t i o n a l effect i s more spectacularly involved in the f e l t i n g process than the e l a s t i c i t y .

Speakman, S t o t t and CJiang *^'> were the f i r s t to point out the importance of easy e x t e n s i b i l i t y and recovery power of the f i b r e . They derived t h i s statement from t h e i r measurements of shrinkage and e l a s t i c p r o p e r t i e s a t v a r i o u s temperatures and pH-values of the medium.

Menkart and Speakman ^9) t r e a t e d wool with mercuric a c e t a t e and with benzoquinone. These agents enlarge the f i b r e s t i f f n e s s by c r o s s - l i n k i n g the molecular c h a i n s . Both t r e a t m e n t s reduced the shrinkage though the f i b r e f r i c t i o n was not affected.

Bogaty, Sookne and H a r r i s *'> s t u d i e d the r e l a t i o n between f e l t i n g and e l a s t i c i t y by using a number of d i f f e r e n t s a l t s o l u -t i o n s as media. They e s -t a b l i s h e d a c o r r e l a -t i o n be-tween f e l -t i n g and work for e x t e n s i o n as well as between f e l t i n g and r e s i l i -ence • ) . The exist-ence of these two c o r r e l a t i o n s which are based on the same s e r i e s of experiments suggests t h a t the work for ext e n s i o n and ext h e r e s i l i e n c e are muextually r e l a ext e d . I ext i s , ext h e r e -fore, not p o s s i b l e to a s c e r t a i n which of the two parameters i s the one important in f e l t i n g .

1.44. Time of felting

In nearly a l l the f e l t i n g experiments the mechanical a g i t a t i o n i s a p p l i e d d u r i n g a fixed p e r i o d a f t e r which the shrinkage i s measured. Some i n v e s t i g a t o r s studied the shrinkage as a function of time, and found, in general, a decrease of the r a t e of shrink-age with i n c r e a s i n g time.

Creely en Le Oompte ^'^ expressed t h e shrinkage of y a r n s in the form

*) Ibe r e s i l i e n c e i s the r a t i o of work recovered to t h a t required for 20% extension.

f = - c l (11)

in which I i s the yarn length. The s o l u t i o n of t h i s equation i s

I = l y * . (12)

Since, according to (12), I approaches to zero, eq. (11) can only be v a l i d for not too h i ^ values of shrinkage.

Johnson ^®) derived from h i s shrinkage t e s t s on wool f a b r i c s , for the area shrinkage, a, the equation

^ = fe (X - a) (13) which leads to a = x {1 - e~^^) . (14)

This formula i s a b e t t e r r e p r e s e n t a t i o n of the real shrinkage behaviour than eq. (12), since i t allows the shrinkage to proceed to any l i m i t x between 0 and 1.

1.45. Mechanical action

The i n t e n s i t y of the applied mechanical a g i t a t i o n i s a factor which h a s , in general, been overlooked. Shrinkage t e s t s are in most c a s e s performed in a commercial o r a l a b o r a t o r y washing machine which runs at a c o n s t a n t speed. Some i n v e s t i g a t o r s have noted the importance of the e f f e c t of the mechanical action on s h r i n k a g e , which u s u a l l y led to s p e c i a l e f f o r t s beijig made to keep the mechanical conditions a s constant as possible ii)33)37)_ C a r t e r and Grieve ^ ^ in t h e i r experiments with the s o - c a l l e d wash weel, paid more a t t e n t i o n to the forces involved, by examin-ing the effect of the quantity of water, of the r a t e of shakexamin-ing, and of the s i z e of the b a l l s used for applying impulses to the c l o t h . They, however, did not e s t a b l i s h a systematic r e l a t i o n s h i p between shrinkage and mechanical a c t i o n , presumably because the method they used, was r a t h e r complicated.

1.46. Medium

I t i s a well-known f a c t t h a t wool f e l t s only in moist o r in wet c o n d i t i o n , which demonstrates c l e a r l y the importance of the medium. In s e c t i o n 1.41 i t has already been mentioned t h a t the e f f e c t of the medium can l a r g e l y be reduced to the influence of

other f a c t o r s , f i b r e f r i c t i o n and fibre e l a s t i c i t y being probably the most important ones in t h i s r e s p e c t . For a f i b r e in dry con-d i t i o n the f r i c t i o n a l con-d i f f e r e n c e ancon-d the e x t e n s i b i l i t y are both much smaller than for the fibre swollen in water.

Several i n v e s t i g a t o r s studied the shrinkage as a function of temperature and pH of the medium or they performed t h e i r e x p e r i ments in various s o l u t i o n s . In so far as the r e s u l t s of these i n v e s t i g a t i o n s f a l l within the scope of t h i s chapter, they have a l -ready been discussed in section 1.43.

I t may be p o s s i b l e t h a t a l s o t h e v i s c o s i t y of the medium influences f e l t i n g since the hydrodynamic forces which act during shaking may depend on the v i s c o s i t y . Preston •'*> observed a de-crease of f e l t i n g with i n c r e a s i n g v i s c o s i t y . In h i s experiments, however, the thickened l i q u i d was a g i t a t e d to form a foam from top to bottom before the f a b r i c s were i n s e r t e d . This makes the i n t e r p r e t a t i o n of the observed phenomenon r a t h e r d i f f i c u l t .

1.5. SCOPE OF THE PRESENT STUDY

In the foregoing s e c t i o n s i t has appeared t h a t a great number of f a c t o r s may influence f e l t i n g . The aim of the p r e s e n t i n v e s -t i g a -t i o n i s -to s e p a r a -t e -the e f f e c -t s of several of -these f a c -t o r s and, in p a r t i c u l a r , to study q u a n t i t a t i v e l y the r o l e played by the forces which are responsible for the f i b r e migration.

B e s i d e s , i t w i l l become c l e a r t h a t knowledge about the i n -fluence of the forces leads in a n a t u r a l way to a b e t t e r under-standing of f e l t i n g in r e l a t i o n to the s i n g l e f i b r e p r o p e r t i e s .

2. M E A S U R E M E N T O F S H R I N K A G E

2 . 1. DISCUSSION OF THE METHOD

Most i n v e s t i g a t o r s determine the shrinkage capacity of wool by shaking a p i e c e of f a b r i c with a l i q u i d in a commercial washing machine or in a laboratory shaking equipment.

Sometimes e x t r a mechanical means are used, e.g. s t e e l or rub-ber b a l l s . A f t e r a c e r t a i n p e r i o d of shaking the s h r i n k a g e in area o r in one of the dimensions i s measured. Instead of a fabric, o t h e r workers use a yarn io)3o) QJ. ^ top * ) , prepared in a spe-c i a l manner ^K

In the p r e s e n t i n v e s t i g a t i o n i t was decided to use a k n i t t i n g y a r n as the m a t e r i a l to be t e s t e d . This choice was made on t h e

b a s i s of the following considerations:

a. The experiments on yarns need l e s s material than t e s t s on fab-r i c s ofab-r tops fab-r e q u i fab-r e . This i s of p a fab-r t i c u l a fab-r impofab-rtance when a chemical t r e a t m e n t on l a b o r a t o r y s c a l e has to be a p p l i e d in order to modify the s i n g l e f i b r e p r o p e r t i e s .

b. F e l t i n g t e s t s are performed more simply on yarns than on fab-r i c s o fab-r tops in t h a t a smallefab-r t e s t i n g machine and a smallefab-r amount of l i q u i d can be used.

c. The measurement of yarn shrinkage only c o n s i s t s of a simple determination of the length of the yarn; fabric shrinkage in area or in length i s more d i f f i c u l t to perform reproducibly. Though in p r a c t i c e f e l t i n g takes place in cloth, there are no reasons to suppose t h a t the mechanism of f i b r e migration in y a m s will d i f f e r e s s e n t i a l l y from t h a t in more complicated s t r u c t u r e s . The m a t e r i a l being chosen, the problem remains how to b r i n g about the f e l t i n g of the yarns. In p r i n c i p l e each kind of mechan-i c a l a g mechan-i t a t mechan-i o n wmechan-ill serve the purpose, but a s u mechan-i t a b l e method has to meet the following requirements: The r e p r o d u c i b i l i t y should be as h i ö i as possible; the forces applied to the fibres in the y a m have to b e . a d j u s t a b l e within wide l i m i t s ; preferably the

magni-tude of these forces should be known.

•) A top i s the product of one of the f i r s t stages of the spin-ning process; i t i s t w i s t l e s s and c o n t a i n s a large number of f i b r e s in the c r o s s - s e c t i o n .

Concerning t h i s l a s t requirement i t was considered t h a t the simplest form of mechanical action in which the forces are known i s a p e r i o d i c a l longitudinal s t r e t c h i n g . Thouöi shrinkage of the y a r n s as a r e s u l t of a repeated s t r e t c h i n g and r e l e a s i n g i s not very p r o b a b l e , n e v e r t h e l e s s soiie experiments in t h i s d i r e c t i o n were made. A number of y a r n s were suspended in water, each of them being s t r e t c h e d with a moderate weigjit which was p e r i o d i c a l -ly l i f t e d . Sometimes a small amount of shrinkage was observed, e s p e c i a l l y when the weights were l i f t e d higher so t h a t the y a m became more slack. If an unbalanced t w i s t i n the yarn gave r i s e to c r i n k l i n g during the unloading period, the shrinkage appeared to be g r e a t e r . Prom these observations i t becomes c l e a r t h a t not the repeated s t r e t c h i n g i t s e l f i s the important factor but r a t h e r the movements of the yarn during r e l e a s e , and t h a t the shrinkage i s e s p e c i a l l y favoured by a p e r i o d i c t o r s i o n .

After t h i s f i r s t attempt a p e r i o d i c t w i s t i n g and u n t w i s t i n g of the yarn was t r i e d . The shrinkage obtained in t h i s way, how-ever, was r a t h e r small. Besides, the magnitude of the mechanical a c t i o n could n o t be r e g u l a t e d within wide l i m i t s , s i n c e , a t a h i g h e r t w i s t , very soon u n c o n t r o l l e d c r i n k l i n g of the yarns o c -curred.

A t h i r d attempt consisted of a mechanical rubbing of the yarns between two f l a t s u r f a c e s under a d j u s t a b l e normal p r e s s u r e . In t h i s case a considerable amount of f e l t i n g took place indeed. The r e p r o d u c i b i l i t y was, however, very poor due to the uncontrollable position of the yarn between the surfaces. An improvement of t h i s method could not be r e a l i z e d .

F i n a l l y t h e y a r n was i n s e r t e d i n t o a tube p a r t i a l l y f i l l e d with l i q u i d and the tube was shaken. The shrinkage which occurred was s a t i s f a c t o r y but not quite well reproducible. When, however, t h e y a r n was a t t a c h e d to both extremes of t h e t u b e , i t s more homogeneous d i s t r i b u t i o n gave r i s e to a b e t t e r r e p r o d u c i b i l i t y . The mechanical a g i t a t i o n could be varied considerably by changing the r a t e of shaking, though the actual magnitude of the forces was unknown. Despite of t h i s disadvantage i t was decided to use t h i s method for the determination of the f e l t i n g power of y a m s .

2 . 2 . DESCRIPTION OF THE APPARATUS

The shaking movement of the tubes i s derived from a r o t a t i o n in order to avoid l a r g e i n e r t i a l f o r c e s . Fig. 3 and f i g . 4 r e

-cc

N T % 33

3E

« F H CC N T ^ , 33 CM (REE j (MOTORJ B M

Pig. 3. Scheme of the apparatus for yarn shrinkage p r e s e n t a schematic view and a photograph of the arrangement. A r o t a t i n g arm, G, i s driven by a synchronous motor, M, v i a a s h a f t , D, a t r a n s m i s s i o n , C, and a continuously v a r i a b l e speed c o n t r o l , B. The arm i s provided with two clamping blocks, N, each of which can hold 8 tubes, and which are attached to the s h a f t s L. By means of a s t a t i o n a r y bevel gear wheel, E, and the transmis-sion elements F, H, J and K, the shafts L are made to r o t a t e in a d i r e c t i o n opposite to t h a t of the main shaft D. Consequently, the movement of the blocks, N, with the tubes, T, c o n s t i t u t e s only a t r a n s l a t i o n , so t h a t during the r o t a t i o n of the arm each tube r e -mains in a fixed d i r e c t i o n .

As a r e s u l t of t h i s movement the l i q u i d in the tubes streams a l t e m a t i v e l y from one side to the o t h e r , thus e x e r t i n g hydrody-namic forces on the f i b r e s in the y a r n . These forces can be va-r i e d in two ways. With the aid of t h e c o n t va-r o l , B, the va-r o t a t i o n speed of the arm can be r e g u l a t e d between 20 and 300 r.p.m. In addition, the blocks N can be placed a t three d i f f e r e n t distances from the s h a f t D. The diameter. A, of the c i r c l e described can thus be a d j u s t e d to 60, 45 and 30 cm, r e s p e c t i v e l y . These two f e a t u r e s make i t p o s s i b l e to i n v e s t i g a t e the extent to which the shrinkage i s influenced by the applied forces. In the majority of the experiments only the speed control i s used and the diameter

A i s adjusted to i t s l a r g e s t value, 60 cm.

When s t a r t i n g the r o t a t i o n , the d e f i n i t e speed required can only be a t t a i n e d very slowly owing to the high moment of i n e r t i a of the arm with the tubes. P a r t i c u l a r l y in the case of high speeds when the time i n t e r v a l s a f t e r which the yarn length i s measured, are very s h o r t (10 s for i n s t a n c e ) , t h i s circumstance may give r i s e to i n c o r r e c t r e s u l t s . I t i s therefore, d e s i r a b l e to prevent the shaking of the l i q u i d in the tubes during the speeding up of the arm. For t h i s reason, the bevel gear wheel E has been design-ed so t h a t i t can be disengagdesign-ed. By doing t h i s , the shafts H and L, as well as the tubes, will be s t a t i o n a r y with r e s p e c t to the arm G and no shaking movement will take place. The r o t a t i o n speed of the apparatus can then be slowly raised to the required value; when t h i s speed i s reached the bevel gear wheel E i s engaged by means of a clamping device and, a f t e r the required shaking period has elapsed, i t i s once more disengaged.

A revolution counter i s put i n t o operation when E i s engaged, thus r e g i s t e r i n g the number of r e v o l u t i o n s during which shaking takes place.

2 . 3 . PERFORMANCE OP TOE MEASUREMENTS

The yarn used throughout t h i s i n v e s t i g a t i o n i s an u n t r e a t e d three ply k n i t t i n g yam indicated as EQ. I t i s composed of fibres with an average length of 7.10 cm and an average diameter of 23

|;m.

The metric count of the f i b r e s , Nm, i s 1850, which means t h a t the mass of 1850 meters of the fibre i s 1 gram. The yarn c o n s i s t s of t h r e e t h r e a d s . Each of these contains on the average 115 f i -bres in the c r o s s - s e c t i o n and has a m e t r i c count Nm 16.1. The

s i n g l e thread c o n t a i n s a t w i s t of 1.9 t u r n s per cm; in the com-p o s i t e yarn the t h r e e t h r e a d s are twined round each o t h e r with 0.8 t u r n s per cm in a d i r e c t i o n o p p o s i t e to the s i n g l e t h r e a d twist.

The shrinkage t e s t i s performed as follows: F i r s t a length of yarn of about 110 cm i s cut off and i s soaked for 10 min in the

l i q u i d in which the f e l t i n g will take place. By doing so the r e -l a x a t i o n shrinkage i s e -l i m i n a t e d . Then the yarn i s a t t a c h e d to the rubber stoppers a f t e r i t s length has been adjusted to 100.0 cm, measured under the tension exerted by one of the s t o p p e r s . Fbr t h i s purpose the tube i s clamped in a v e r t i c a l position while one of the stoppers s e a l s off the lower end; the yam i s led over a pulley and the second stopper i n d i c a t e s i t s length on a gradu-ated s c a l e . The tube i s then half f i l l e d with the shaking l i q u i d , t h e yarn i s i n s e r t e d i n t o i t , and the tube i s closed and placed i n t o one of the clamping blocks of the apparatus. After a c e r t a i n p e r i o d of shaking the yarn length i s measured again, whereupon the yarn i s returned to the tube and the shaking i s resumed. In t h i s manner the shrinkage i s determined as a function of time. The way of measuring the yarn length provides the p o s s i b i l i t y to keep the l i q u i d in the tubes during the measurement and to meas-ure the length under a constant tension.

Some of the r e s u l t s of the shrinkage d e t e r m i n a t i o n s are r e -produced i n t a b l e I . This t a b l e r e p o r t s measurements made a t a speed of 100 r.p.m. and a diameter of movement of 60 cm, on the untreated standard sample E^,. In t h i s experiment eight yarns were shrunk simultaneously. The columns Sj to Sg show the shrinkage of each of the yarns as a function of time, expressed as a percent-age; s denotes the mean shrinkage and a the standard deviation of t h i s mean. The standard deviation i s small enough to consider the experiments as being s a t i s f a c t o r i l y reproducible. When the yarns are t r e a t e d with a n t i - s h r i n k agents, sometimes l a r g e r v a r i a n c e s are found, frequently due to non-uniform treatment.

In fig. 5 the average value of the shrinkage, s, i s p l o t t e d as a function of shaking time. In the next section t h i s curve will be discussed.

2 . 4 . PARAMETERS OF SHRINKAGE-TIME BEHAVIOUR

For an e f f i c i e n t comparison of the shrinkage under d i f f e r e n t circumstances i t i s d e s i r a b l e to express the shrinkage dependence

Table I

Shrinkage of e i g h t y a r n s as a function of time

Time (min) 0 1 2 4 6 8 10 12 14 18 22 26 34 Number of completed r e v o l u t i o n s N 0 100 200 400 600 800 1000 1200 1400 1800 2200 2600 3400 S j S j S 3 S4 S 5 Sg S-j Sg (%) (%) (%) (%) (%) (%) (%) (%) 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 13.8 12.4 14.6 15.8 14.9 14.0 12.8 13.7 2 5 . 3 2 2 . 5 2 5 . 1 2 6 . 5 2 6 . 7 2 4 . 1 2 3 . 1 2 4 . 8 4 0 . 5 3 8 . 7 3 7 . 5 4 0 . 5 4 0 . 6 3 7 . 8 3 9 . 2 4 0 . 0 5 1 . 2 4 7 . 6 4 8 . 0 4 9 . 8 4 9 . 8 4 7 . 8 4 8 . 0 5 0 , 2 5 6 . 5 5 5 . 2 5 4 . 3 5 6 . 3 5 5 . 4 5 3 . 9 5 5 . 1 5 5 , 4 6 1 . 0 5 8 . 7 57.9 5 9 . 9 5 9 . 8 57.9 5 8 , 3 5 8 , 8 6 2 . 9 6 1 . 4 6 1 . 4 6 2 . 0 6 1 . 1 6 0 . 5 6 0 . 1 6 1 . 3 6 4 . 3 6 3 . 0 6 2 . 3 6 4 . 0 6 3 . 3 6 2 . 5 6 2 . 9 6 3 . 0 6 5 . 9 6 4 . 8 6 5 . 0 6 5 . 5 6 5 . 3 6 4 . 4 6 4 . 6 6 5 . 2 6 7 . 6 6 6 . 4 6 6 . 0 6 6 . 5 6 6 . 7 6 6 . 2 6 5 . 4 6 7 . 4 6 7 . 7 6 6 . 3 6 6 , 0 6 7 , 2 6 7 , 0 6 6 . 3 6 5 . 7 6 7 . 4 6 8 . 0 6 6 . 3 6 7 . 8 6 7 . 8 6 7 . 6 6 6 . 8 6 7 . 1 6 7 . 9 s a (%) (%) 0 . 0 0 . 0 14.0 1.2 24.8 1.4 3 9 . 4 1.1 4 9 . 0 1.4 5 5 . 3 0 . 9 59.0 1.2 6 1 . 3 0 . 9 6 3 , 2 0 , 7 6 5 . 1 0 , 5 6 6 . 5 0 , 7 6 6 . 7 0 . 7 6 7 . 4 0 . 7 6 5 . 5 ( l - e ' ° - 2 3 5 t ) 0 . 0 13.3 2 4 . 6 3 9 . 9 4 9 . 5 5 5 . 5 5 9 . 2 6 1 . 7 6 3 . 2 6 4 . 7 6 5 . 2 6 5 , 4 6 5 , 5 s N 0 , 1 4 0 0 , 1 2 4 0.099 0 . 0 8 2 0 . 0 6 9 0 . 0 5 9 0 . 0 5 1 to 01

Shrinltagt 7 0 " ' 60 50 O) 30 20 10 °0 5 10 15 20 25 30 35 minutes Pig. 5. Shrinkage, s, as a function of time,

compared with exponential function

on time in a small number of parameters. The most obvious way in t h i s r e s p e c t i s to represent the shrinkage-time curve as a whole by means of a mathematical e x p r e s s i o n . The shape of the curve suggests the v a l i d i t y of an exponential function of the form

s = a ( i - e-*") . (1) I t appears t h a t for the f i r s t h a l f of the time i n t e r v a l the best

f i t i s obtained with

s = 65.5 (1 - e"°-235t)_ (2) For longer times, however, the experimental curve d e v i a t e s from

t h i s exponential one ( t a b l e I and f i g . 5). Presumably the addi-t i o n of a second funcaddi-tion of addi-t h i s kind wiaddi-th much smaller values of a and 6 would be able to account for these deviations; the determination of the four parameters then needed i s , however, r a t h -er complicated and time consuming.

Moreover, even in the case of a s i n g l e exponential function, t h e p a r a m e t e r h i s not of any d i r e c t p r a c t i c a l s i g n i f i c a n c e , though a can be i n t e r p r e t e d simply as the l i m i t of the shrinkage for i n f i n i t e l y increasing time of shaking. I t i s therefore b e t t e r to express the course of the shrinkage with the aid of the quan-t i quan-t i e s

s^ = lim s ( t ) (3) t-oo

which i s the shrinkage l i m i t , and

.j^ actual stvmKage

So = l i m — ( 4 )

t-o dt

which i s t h e i n i t i a l r a t e of s h r i n k a g e . When equation (1) i s v a l i d , i t i s c l e a r t h a t s^ = a and s^ = ab. The use of t h e s e parameters has also the advantage t h a t So can be determined with-out measuring the shrinkage up to the l i m i t .

The use of s^ i s , however, not y e t e n t i r e l y s a t i s f a c t o r y . An i n c r e a s e in the r a t e of shaking not only causes the force to i n -crease but also the number of times t h i s force t r a n s m i t s an im-pulse to the f i b r e s in the yarn. For t h i s reason i t i s preferable to express the i n i t i a l shrinkage not per u n i t of time, but r a t h e r per revolution of the apparatus. At the same time the experiments will then correspond more l o g i c a l l y with those in which the am-p l i t u d e of the shaking movement i s v a r i e d , s i n c e t h i s causes a change in the forces but not in the number of times they act on the yarn. The i n i t i a l shrinkage per turn equals io/n, i f n r e -p r e s e n t s the number of r e v o l u t i o n -per minute. T h i s q u a n t i t y , which will be denoted by 5, can also be defined as

S = lim ^ (5) in which N = nt, the t o t a l number of completed revolutions.

The two parameters s^j, and 5 can be determined g r a p h i c a l l y in a f a i r l y simple manner. The shrinkage l i m i t , Sa,. can be estimated from the graph, i f necessary with the aid of a logarithmic time s c a l e . The quantity 5 can be approximated by p l o t t i n g log(As/AiV), being the logarithm of the r a t i o between the shrinkage i n c r e a s e during a c e r t a i n i n t e r v a l and the number of r o t a t i o n s during "this i n t e r v a l , a g a i n s t A^. By e x t r a p o l a t i n g the curve thus o b t a i n e d towards N = 0, S can be estimated. The same r e s u l t i s , however, reached when s/N i s taken instead of AS/AA', since

1 • * -I • ^^ fdss , „ . l i m — = l i m —77 = i-rrr) . - ( 6 )

The q u a n t i t y s/N i s c a l c u l a t e d more e a s i l y and shows a smaller spreading than AS/AA^. I t i s therefore used in most cases. Fig. 6 shows how from the p l o t of log(s/N) a g a i n s t A', an approximation of S i s obtained. From the data recorded in f i g . 5 and f i g . 6 i t appears t h a t s^, = 69% and 5 = 0 . 158%/turn. These values roughly represent the shrinkage as a function of time.

logs/N

20 10-'%/turn

10 min

Pig. 6. Determination of 5 from the data of t a b l e I

curve f i r s t l y increases, then reaches a maximum, a f t e r which i t d e c r e a s e s in the normal way. I t i s obvious t h a t in t h i s case the maximum slope i s more s i g n i f i c a n t for t h e s h r i n k a g e behaviour than t h e i n i t i a l one. In t h i s case the r a t i o s/N also shows a maximum which h a s , however, not the same values as (ds/dN)^g^. When t h i s phenomenon occurs, for S i s taken the maximum reached by AS/AA^ as a

func-tion of N.

2 . 5 . INFLUENCE OP THE QUANTITY OF LIQUID

lb a s c e r t a i n the extent to which the shrinkage i s affected by the quantity of water p r e s e n t in the tubes, the shrinkage of the standard sample, Eo, was measured with l i q u i d volumes, ƒ, of 1/8, 2/8, 3/8, 4/8, 5/8, 6/8 and 7/8 of the t o t a l volume of the tube a t a speed of 157 r.p.m. With each d i f f e r e n t l i q u i d volume, the shrink-age of four y a r n s was measured; 5 was d e r i v e d from the a v e r a g e r e s u l t s . The values of S with r e f e r -ence to the q u a n t i t y of water are given i n t a b l e I I and f i g . 7. I t was found, t h a t the e f f e c t i s very s l i g h t a t a b o u t ƒ = V2, which i s g e n e r a l l y used, so t h a t measure-ments of 5 a r e not affected by small v a r i a t i o n s in the quantity of l i q -uid. In a l l t h e s e experiments the l i m i t Sco remained unchanged a t about 70%. 075 1 degree of filling P i g . 7. Dependence of 5 on quantity of l i q u i d in the tubes

Table I I

Influence of the quantity of l i q u i d ƒ 1/8 2/8 3/8 4/8 5/8 6/8 7/8 S (10-2%/turn) 15.3 19.0 20.5 21.4 21.4 18.4 15.8

3 . I N F L U E N C E O F F O R C E S

3 . 1 . EFFECT OF aiAKING RATE

The standard sample, E^, was shaken at various r a t e s and the diameter A adjusted to 60 cm. Most measurements were c a r r i e d out on four or eight y a m s at a time. Prom the average shrinkage-time behaviours the parameters S and s^ were determined in the way de-scribed in the preceding chapter. The values found for these para-meters as a function of the r a t e of shaking are recorded in t a b l e III and f i g . 8.

Table III

Effect of shaking r a t ^ on the shrinkage parameters for yarn Eo

n (r.p.m. ) 25 30 40 56 75 100 128 156 S (10-2%/turn) 0 . 0 0 . 8 2 . 4 6 . 7 10. 1 15.4 18.5 19.0 Sco (%) 2 37 69 69 70 69 71 70 1 150 r p.m.

Pig. 8. I n i t i a l shrinkage per turn, S, and shrinkage lijhit, soo, as a function of r o t a t i o n a l speed, n

I t appears from fig. 8 t h a t below a c e r t a i n r a t e of shaking no shrinkage occurs a t a l l . The magnitude of t h i s threshold, n^, i s for the experiment under discussion 25 r.p.m. When n < n^, S and Soo are both zero. For speeds exceeding the threshold, 5 appears to be p r o p o r t i o n a l to (n - rij) up to n = 100 r.p.m. Though the r a t e of s h r i n k a g e i s s t r o n g l y f o r c e d e p e n d e n t , t h e l i m i t of shrinkage i s constant a t approximately 70%, except in the imme-d i a t e neighbourhooimme-d of the t h r e s h o l imme-d , where the curve for Soj takes a very steep course. Apart from t h i s r e s t r i c t i o n , the con-stancy of Soo means t h a t when shrinkage occurs, the yarn always s h r i n k s down to 30% of i t s o r i g i n a l l e n g t h , independent of the applied forces.

3 . 2 . EFFECT OF SHAKING AMPLITUDE

The same experiments as d e s c r i b e d in t h e p r e c e d i n g s e c t i o n were c a r r i e d out again with yarn EQ, but t h i s time also other am-p l i t u d e s , viz. /I = 45 cm and A = 30 cm, and higher r a t e s of shak-ing were applied. In these experiments in most cases only 5 was determined, the measuring of the l i m i t Soo being p a r t i c u l a r l y time consuming.

0 "50 1ÖÖ ÏSB 2 0 0 2 5 0 300 r.pm. Pig. 9. Dependence of 5 on n for three amplitudes, A

Table IV

Effect of r o t a t i o n a l speed, n ( r . p . m . ) , and amplitude, A (cm), on the i n i t i a l r a t e of shrinkage, 5 (10"2%/tum)

n 29 30 30 39 40 46 52 52 5 5 . 5 63 6 5 . 5 7 4 . 5 7 4 . 5 75 8 8 . 5 95 9 5 . 5 9 5 . 5 100.5 A = 5 0 . 8 0 . 8 1.6 3 . 2 2 . 3 5 4 . 6 5.8 5.8 6 . 7 9 . 2 8 . 4 10. 1 10.8 9 . 6 13.0 15.9 1 6 . 5 1 6 . 5 1 5 . 4 60 n 101 1 0 1 . 5 113 115 127 128 128 156 157 186 187 189 207 226 228 246 246 246 260 S 14.0 1 6 . 5 18.0 15.2 1 9 , 2 1 8 , 1 1 8 , 5 19,0 2 0 , 4 19,7 2 1 , 0 2 0 . 0 2 1 . 0 2 1 . 4 2 2 . 0 2 2 . 5 2 4 . 5 2 2 . 7 2 4 . 0 A = n 47 56 75 75 89 96 101 114 1 1 7 , 5 127 141 156 172 189 269 45 5 2 , 8 4 , 6 5 7 , 4 5 7 . 8 9 . 4 1 2 . 1 1 2 . 5 13.0 1 5 . 3 15.2 1 6 . 0 1 9 . 0 18.0 19.0 2 0 . 3 A = n 56 66 7 4 , 5 77 94 103 117 118 127 144 158 176 189 209 224 224 246 246 269 269 30 S 2 . 2 5 3 . 3 4 , 8 5 4 , 0 6, 1 7 , 7 8 , 5 9 , 0 13,6 11,2 1 4 , 1 13,7 15.4 1 6 . 4 1 7 , 3 18,3 17,9 1 7 , 4 2 0 , 0 18,8 The v a l u e s of 5 a t d i f f e r e n t v a l u e s of A as a function of n a r e recorded in t a b l e IV and f i g . 9. The t h r e e curves o b t a i n e d are strongly resemblant and they give the impression of d i f f e r i n g only as regards the s c a l e value for n. When S i s p l o t t e d a g a i n s t log n, i t i s found t h a t the t h r e e curves thus obtained run appro-x i m a t e l y p a r a l l e l . Thus a m u l t i p l i c a t i o n f a c t o r for n can be found for each value of A, so t h a t the curves merge i n t o each o t h e r . I t appears t h a t t h i s f a c t o r can b e s t be approximated by ^o.82_ pj^g_ ^Q shovis t h e r e s u l t of t h i s t r a n s f o r m a t i o n . The curves for A = 45 cm and A = 30 cm have both been superimposed on t h a t of A = 60 cm by t a k i n g n(A/60 cm)''-^^ as the h o r i z o n t a l s c a l e value. I t follows, t h e r e f o r e , t h a t the shrinkage per turn depends s o l e l y upon t h i s combination of the q u a n t i t i e s n and A.

-Pig. 10. 5 as a function of n(A/60 cm)

t i o n ; i t also i n d i c a t e s t h a t the study of f e l t i n g as a function of the force can be performed by using one and the same amplitude and by varying only the speed of r o t a t i o n , application of d i f f e r -ent amplitudes giving no e x t r a information. Consequ-ently the ex-periments described in the following c h a p t e r s are a l l performed with A adjusted to 60 cm.

3 . 3 . RELATION BETWEEN FORCES, SHAKING RATE AND AMPLITUDE The a c t u a l magnitude of the forces exerted by the l i q u i d on the f i b r e s during shaking i s not known, since t h i s magnitude i s dependent upon the r e l a t i v e v e l o c i t y between the l i q u i d and the f i b r e s in the yarn. Even i f the forces exerted on the yam i t s e l f could be measured, which i s already a r a t h e r complicated e x p e r i -ment, then even no knowledge would be p r e s e n t about the f o r c e s which cause the f i b r e s to migrate with respect to each other.

About t h e way in which t h e s e f o r c e s depend on t h e r a t e of shaking a very rough estimation can be made in the following way: When there i s no yam in the tube and the v i s c o s i t y of the l i q u i d i s disregarded, the maximum v e l o c i t y of the l i q u i d occurring i s

which i s p r o p o r t i o n a l to nA. This v e l o c i t y i s , however, modified by the presence of the y a m , the modification being brought about, among o t h e r causes, by the f r a c t i o n of the cross-section occupied by the y a m , by the movement of p a r t s of the y a m with respect to t h e tube, and by c a p i l l a r y forces a c t i n g between glass, l i q u i d , y a r n and a i r . About the n a t u r e of the flow l i t t l e can be s a i d ,

since the flow o r i f i c e s are of very d i f f e r e n t dimensions. I t i s probable t h a t with v e l o c i t i e s which are not unduly high, laminar flow c o n d i t i o n s will occur, e s p e c i a l l y when the l i q u i d flows in between the f i b r e s . In t h a t case, the force on the f i b r e s i s pro-p o r t i o n a l to the v e l o c i t y of the l i q u i d . If, in a f i r s t apro-ppro-pro- appro-ximation, the v e l o c i t y i s assumed to be p r o p o r t i o n a l to nA, i t follows t h a t the force also obeys t h i s law.

I f i t i s a l s o assumed t h a t the s h r i n k a g e per turn depends s o l e l y upon t h e force a c t i n g on the s i n g l e f i b r e s , r e a s o n a b l e agreement i s o b t a i n e d with the r e s u l t s found in the p r e c e d i n g section, namely t h a t 5 i s a function of nA°'^^.

Although the absolute magnitude of the force on the f i b r e s r e -mains unknown, i t i s p o s s i b l e in t h i s way to furnish some approximate information concerning i t s dependence upon number of r e -v o l u t i o n s and amplitude. T h i s will e s p e c i a l l y pro-ve to be useful in s e c t i o n 3.5 in which the influence of the force on f e l t i n g i s discussed more in d e t a i l and in which the hypothesis i s used t h a t the s c a l e for n can be considered as a l i n e a r force s c a l e .

3 . 4 . EFFECT OF YARN TWIST

The o b j e c t of the preceding experiments was to a s c e r t a i n the effect of the e x t e r n a l l y exerted forces on the shrinkage. I t will be i n t e r e s t i n g to i n v e s t i g a t e , however, how the shrinkage changes when the i n t e r - f i b r e f o r c e s are v a r i e d . This v a r i a t i o n may be achieved by using yarns twisted to d i f f e r e n t measures. By i n s e r t -ing e x t r a t w i s t in the yarn the f i b r e s are more closely packed, which gives r i s e to a h i g h e r p r e s s u r e on each o t h e r and, conse-q u e n t l y , to a h i g h e r f r i c t i o n a l f o r c e . At the same time o t h e r f e a t u r e s of t h e s t r u c t u r e a r e a l t e r e d , a s , for i n s t a n c e , the average angle under which the f i b r e s l i e in the yarn and the d i -mensions of the openings through which the f i b r e s can migrate.

t w i s t , the following method was used: The o r i g i n a l 3-ply yarn, Eo, was s e p a r a t e d i n t o i t s components by u n t w i n i n g . A 250 cm length of the s i n g l e y a m was untwisted and afterwards r e t w i s t e d hy giving i t a c e r t a i n number of t u r n s . The number of t u r n s ap-p l i e d , m, was s u c c e s s i v e l y 200, 400. 600. 800, 1000, 1200 and 1600. From t h i s t w i s t e d s i n g l e yarn a balanced 2-ply yarn was made by doubling t h e yarn and l e t t i n g i t t o r d a t e f r e e l y u n t i l equilibrium between twist and twine was reached. The 2ply s t r u c -t u r e s -thus o b -t a i n e d were used as i n i -t i a l m a -t e r i a l for a s e r i e s of shrinkage experiments a t d i f f e r e n t speeds. The shrinkage was proceeded t i l l an estimation of the l i m i t could be made so t h a t the parameters 5 and s^ were both determined. The dependence of

Table V

Influence of y a m t w i s t , m, on shrinkage parameters, 5 (10-2%/turn) and sa, (%)

n 19 29 40 52 76 102 128 158 189 n 19 29 40 52 76 102 128 158 189 m = 200 'S 0 . 5 5 2 . 7 6 . 9 6 3 . 5 9 . 2 6 6 . 5 1 1 . 5 6 7 . 5 13.8 6 7 . 5 16.4 6 7 . 5 17.8 67 18.6 6 7 . 5 m = 1000 5 Sco 0. 11 0 . 3 2 33 0 . 6 0 58 1.38 6 1 1.71 63 2 . 4 63 2 . 7 6 3 . 5 3 . 4 6 3 . 5 m = 400 'S 1.3 3.6 62 5.0 6 5 . 5 6 . 0 6 6 . 5 8 . 3 6 7 . 5 1 0 . 3 6 7 . 5 1 2 . 1 6 7 . 5 12.6 6 7 . 5 m = 1200 S Sco 0. 18 23 0.28 44 0 . 7 7 59 1. 15 60 1. 22 59 1.8 5 9 . 5 2. 1 6 1 m = 600

-s

0 . 7 5 1.8 5 5 . 5 2 . 5 6 3 . 5 3 . 5 65 5 . 0 66 6 . 2 67 6 . 8 6 6 . 5 6 . 7 67 m = 1400 5 Sco 0 . 0 5 12 0. 14 33 0 . 4 2 5 5 . 5 0 . 6 6 57 0 . 8 0 5 6 . 5 1. 15 58 1.33 58 m = 800 'S 0 . 2 3 0 . 8 2 39 1.25 61 1.9 6 3 . 5 2.9 6 4 . 5 3 . 2 5 65 4 . 0 65 4 . 9 65 m = 1600 5 Sco 0 . 0 2 5 4 0 . 0 4 2 21 0 . 2 2 47 0 . 4 1 5 3 . 5 0 . 5 9 5 3 . 5 0 . 8 1 54 0 . 8 5 54

t h e s e parameters on speed and t w i s t are recorded in t a b l e V and in the figures 11 and 12. Each curve r e p r e s e n t s the average be-behaviour of 4 y a m s . "0 5Ö 100 150 200 r p m F i g . 11. 5 versus n f o r d i f f e r e n t t w i s t p a r a m e t e r s , m soo TOJ- % 60 50 4C-X 20 10-0 510-0 100 150 200 r p m F i g . 12. Soo versus n f o r d i f f e r e n t t w i s t p a r a m e t e r s , m

I t i s evident from the r e s u l t s shown in fig, 12 t h a t the upper l i m i t of the values of s^, drops somewhat as the t w i s t I n c r e a s e s , while, moreover, the threshold moves to higher values of n. This s h i f t of the threshold can also be seen in the course of 5 ( f i g . 11), where, in addition to a very pronounced change in the slopes of the S - n p l o t , the i n t e r s e c t i o n of the curves with the n a x i s moves to h i ^ i e r values of n when the t w i s t i n c r e a s e s .

In order to a s c e r t a i n the n a t u r e of these s c a l e changes, each of the two graphs has been p l o t t e d two-side l o g a r i t h m i c a l l y . In both cases the curves for various values of m turned out to be of the same shape; they can, by s h i f t i n g the two axes, be made to merge into each other. For fig. 11 and fig. 12 the m u l t i p l i c a t i o n f a c t o r s in n appear to be the same and can, with s u f f i c i e n t a c -curacy, be represented by the following function of m:

h(m) 0.89'»/200 ^ e- 0. 1165- m/200 (1) The s c a l e f a c t o r s for S and Soo are not e a s i l y expressed mathemat-i c a l l y ; these f a c t o r s are denoted by f(m) and g(m) r e s p e c t mathemat-i v e l y and are recorded numerically in t a b l e VI. The course of the t h r e e functions ƒ(«), g(Bi) and /i(m) i s reproduced in fig. 13.

f(rr»30r Table VI

Scale m u l t i p l i c a t i o n f a c t o r s for 5, Soo and n

m. 200 400 600 800 1000 1200 1400 1600 ƒ(«) 1.56 2.33 3.83 5.90 8.55 11.7 16; 7 23.1 g(«) 1.00 1.00 1.01 1.04 1,06 1,11 1,17 1,25 h(m) 0.89 0.79 0.70 0.63 0.56 0.50 0.44 0.39 0 Pig w o 800 1200 1600 13. The transformation func-t i o n s ƒ(«), g(ii) and h(m) The r e s u l t of the performance of t h e s e t r a n s f o r m a t i o n s i s shown in fig. 14 and fig. 15. In these figures f(m)-S and g(m)'Soo are p l o t t e d , both a g a i n s t h(m)-n. All the curves have thus been reduced to m = 0. Though the spreading of the p o i n t s in f i g . 14

50 100 150 200 r p m Pig. 14. Combination of the data of figure 11 by

means of the functions f(m) and /i(m)

200 r p m Pig. 15. Combination of the data of figure 12 by

means of the functions g(«) and h(m)

i s r a t h e r high, no systematic deviations of the individual curves from the generalized one occur.

If the form of the functions of f i g . 14 and fig. 15 i s r e p r e -sented by P(n) and Q(n) r e s p e c t i v e l y , the r e s u l t s may be combined mathematically into