the dynamics of fabric forming on the loom at high weaving...

Indian Journal of Fibre & Textile Research Vol. 19, September 1994, pp. 125-138

The dynamics of fabric forming on the loom at high weaving rates

Stanislav Nosek

Department of Weaving Technology, University of Liberec, Czech Republic

The problems arising with the increase in weaving machines outputs and their speed are discussed. The main problem is the decrease in the weavability of higher fabric densities. It is shown that the loss of weavability related to fabric is caused by an increase in the frictional and deformation work of woven-in threads due to increase in the velocity of weft sliding into the fabric. This causes then an increase in the weaving resistance, beat-up force, lift of the reed in contact with the cloth fell, and in the angle of duration of beat-up. All these variables are functions of the time of the beat-up pulse of reed, f[y (/)l, and vary progressively with weaving speed. There exists nevertheless one parameter, the impulse of the beat-up force (or force of weaving resistance R)/= ItT )R(/)·dl, which remains constant for the given fabric and weave at today's usual loom speed (about 500 rpm and higher). This parameter can be taken as the detennining variable for the given weave and fabric density, and the weavability can be measured by it.

The machine related problems are caused by the compliance of the light-built fast running mechanims of the loom, which may not be able to deliver the necessary 'active' impulse of the beat-up force to the fabric; the active impulse is imparted due to forces of the elastic deformation of the beat-up mechanism as of a "press", and due to its momentum as of a "hammer".

Further complications arise due to the superposition of forces arising during the beat-up in the warp as a result of shedding and backrest oscillations. These forces get added to the beat-up force of the reed, but they may vary rather significantly even with small random variations in the ratio of weaving frequency to eigen frequency of the backrest system, so that the intensity of beat-up may be unstable in the course of weaving. However, the effect of backrest oscillations may be, under certain conditions, exploited for improving the weavability of the given loom.

Keywords: Beat-up mechanism. Fabric structure, Weavability

1 Introduction Increase in new inventions in mechanics, elec

tronics, chemistry, machinery, etc. is mainly the result of contemporary business competition. With today's possibilities of information transfer, new inventions in all branches of industry and science affect each other strongly. This leads to the development of principally new and still more sophisticated constructions of production systems.

The most important features of the modem production devices are:

- high machine outputs (realized mostly through high working rates),

- high applicability (i.e. high flexibility of basic types of devices or their deeper specialization), and

- high comfort for machine attendants (using computer monitoring, computer control, servomechanisms and robotics, self-teaching systems, etc.).

Of all these directions of development, the tendency to increase machine output still prevails.

At first sight, the main reason for making the textile machines more productive seems to be the aim of machine producers to show, as often as possible, new "FORMULA ONES" of their devices. But the main effect of increasing the machine productivity lies in the fact that to achieve high working rates of machines, it is necessary to secure simultaneously the higher reliability of mechanism, better and more scientifically based designs, and more effective controlling systems, which lead to the application of original new techniques and high-tech technologies in the manufacturing of devices, including the textile ones.

Nevertheless, the high working rates, especially of textile machines, bring along a further row of problems concerning stability of product forming (of yarn, fabric .... ) and the quality of the produced goods. In the manufacture of textiles, difficulties arise in (i) achieving the required structure and

126 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 1994

standard properties of products, (ii) keeping at a sufficiently low level the tendency of increasing the number of machine stops during winding, warping, sizing, weaving and knitting, and (iii) maintaining good weavability of denser and more difficult fabrics made from fine yams.

The aim of this paper is to discuss some problems of the weavability and dynamics of fabric forming on a loom at todays high machine revolutions as the most important barrier against increasing productivity.

2 Weavability of Fabric Structures Weavability is the capability of the system loom

textile material to produce a fabric with a given weave, structure and qUality. Each part of this system brings its own set of specific conditions to the problem of weavability of fabrics.

2.1 Conditions orWeavability Related to Fabric

To achieve a certain fabric structure with a given set of guidelines (weft density, threads waviness, ... ), the given fabric style during the process of its formation on the loom consumes a set of input quantities (with values corresponding to the required structure), e.g. the path of reed lift in contact with cloth fell at the beat-up; beat-up force and time duration of beat-up pulse of reed or, in a complex form, the impulse of beat-up force (i.e. the time integral of force acrOss the beat-up duration); basic tension in the warp ends and tension in weft direction; etc. These quantities consumed by the woven fabric are different for each fabric style. They also depend on weaving frequency, which is different for each style-thanks to individual speed-dependent frictional and deformation resistances against beating-in of various textile fibres into various fabric weaves.

2.2 Conditions orWeavability Related to Loom

The set of required input quantities is delivered by the loom. But the quantities delivered to the fabric by the loom are also variable with the fabric structure and weaving frequency as a result of construction and dynamic behaviour of the machine.

The system 'loom-fabric' works in fact as a power source and receiver. It permanently maintains an equilibrium between the delivered and consumed quantities, and produces fabric structure in correspondence with this equilibrium. The equilibrium parameters can be found at the intersection point of certain loom (source) characteristics and fabric (loading) characteristics.

The object of the study described here was to find some of these characteristics. An attempt has therefore been made to form simple relations for equilibrium conditions of the weaving process to get a better view of fabric forming. This oUght to enable the prediction of the weavability of various fabric densities (structures), and to open a search for ways of improving the weavability if it is reduced due to increased machine revolutions.

3 Weavability Related to Fabric

3.1 Static Weavability and Weaving Resistance or a Fabric

The problem of weavability was studied originally in the static domain (in fact at low machine speeds) probably first by Greenwood et aL I. They found then relatively simple mathematical relations between warp and fabric deformation (cloth fell displacement) x, beat-up force Fp, weaving resistance R, and fabric density in weft D2 (or pick spacing A= lID 2 ). The idea was as follows:

In every moment of the beat-up process, i.e. of the period of weft sliding in the fabric, there is an equilibrium between beat-up force produced by the reed and the weaving resistance caused by the sliding or wavering of picks among the warp ends2·4:

... (1)

Beat-up force (F p) is the force developed by· the pushing of the reed upon the last pick. For the purpose of the theory of the beat-up process, the force F p was replaced by the difference between reactions QI and Q2 ofthe system 'warp-fabric':

Fp= QI- Q2=(Q+ C1 'x)-(Q- C2 'x)

=(C1 + C2 )'x ... (2)

Weaving resistance (R) is a function of immediate pick spacing A in the cloth fell or, in other words, of the achieved path ~(At.: - A) of weft sliding into the fabric during beat-up from the initial (inserting) position Au to standard position A:

R= R(~) le.g. R= k/(Au - A lim - n according to Greenwood et al. I } ... (3)

Warp elongation x and weft sliding path (slip) ~ are components of the total beat-up pulse y imparted to the fabric by the reed:

y=x+~ ... (4)

These four static relations yield the equation of the "height" of beat-up pulse y, which is necessary

NOSEK: DYNAMICS OF FABRIC FORMING 127

for achieving a given weft density D2 = 1 I A. in common form it holds

... (5)

where

The same equations also yield the static beat-up force and weaving resistance F p = R as functiom ofy.

The determining quantity for achieving the demanded weft density D2 is consequently the height of beat-up pulse (or the cloth fell distance). Its value is continuously and automatically adjusted by the system loom-fabric-warp (by shifting the cloth fell forward or backward) so that the resulting pick spacing on an average corresponds with the stroke of the take-off motion.

3.2 Dynamic Beat-up Process

With an increase in loom speed from 400 rpm to more than 1500 rpm during the last four decades, the static relation comprised in Eq. (5) be~ came more complex. The original Eq. (5) gives the beat-up pulse y that must be imparted to the fabric to obtain the given density D2 = l1A= 1 I(Au - ~) for a known instant value of the weaving resistance R( ~) corresponding to the given fabric density. But it does not say anything about the influence of machine speed and beat-up velocity on the weaving resistance, and thus on the complete beat-up duration and weavability.

As per the common experience with weaving it can be stated that with the increase in weaving frequencies, the weavability generally slackens.

To make this statement about the dependence of weavability on machine speed more exact, we may define the t.erm weavability (WA) by a measurable quantity of weft slip (~) into the fabric during beat-up. The deeper the weft can be pushed into the fabri~ the denser the pick spacing arise, and the weavability is higher. So, the weavability corresponds with the weft slip:

Weaving resistance arises as a result of energy losses during fabric forming. One part of the beatup energy gets lost as heat due to the frictional work of the weft sliding among the warp ends. The second one dissipates in the form of deformation work of yams getting crimped during the weaving-in of weft into the fabric. It can be proved that the latter is significantly lower than the former and can, therefore, be practically neglected (This concerns textile materials and does not hold good for metallic fibres.). Moreover, deformation losses depend on beat-up velocity in a similar mathematical form as friction (i.e. ex· vH If it is necessary, they can be added to the frictional losses, forming thus a slightly higher effective friction.

Weaving resistance R (A, f) can be then simply calculated on the basis of frictional conditions in the cloth fell (Fig. 1), where friction depends on beat-up velocity. The resulting dependence of weaving resistance R on pick spacing A and varying friction coefficient f and on various fabric structures (= on various thread wavinesses e 1.2) is then

... (8)

where v (= d/A) is the linear covering of fabric by weft; and e2 (= H/d), the relative weft waviness. The resulting curves of weaving resistance are plotted in Fig. 1.

For further applications, it is more convenient to use a linearized form of weaving resistance which is true in the vicini.ty of the working point P of resistance curves of studied weave. By differentiation of R(A, f)

aR aR R(A f)=R 1--. (A -A)+-· f

, 0 aA () af Jdyn

... (9)

WA""'~ ... (6) where(Au-A)=~.

The dynamic weft slip into the fabric, which is substituting now weavability, yields from the dynamic dependence of weaving resistance R on weft density at varying weaving speed, represented by the beat-up frequencyS-7. The beat-up frequency will be defined later.

The weaving resistance obtains an approximate form of a linear combination of the influences of weft slip into the fabric, and of the dynamic coefficient of friction fdyn'

The dynamic coefficients of friction fdyn in this equation can vary considerably with the speed Vp


.... '1

.JV~ ~ t::::~ V

fa 1.0{ ~

J ~;.; f-OS{

le.- ~ ~ L---"

f-ll2< ~ - r. _

A=10.d • A IS.d

II _._.-it- .-.--__ ..... fi

-'-'1i·-~"-"'iiiIII'" _·_·t·_· I

I

/ 1

/ !) 'P

1\:':

fYJ , '~ /J 'j (J ~ VI) Itl

05

~ r;J/ II, V lkJ , .---:

~ l/;V ! .... $r-r

-

Fig I-Weaving resistance R calculated from frictional forces and geometry of yarns in the cloth fell If- coefficient of friction; eu(=Hl.2ld)-relative waviness of warp and weft respectively; A-pick spacing; Au-fictitive insening distance of Oth pick; Alim-c1osest pick distance; ~-pick slip (sliding path of pick) in the fabric from insening position Au to normal distance A at the

beat-up]

of the weft sliding along the warp threads. Let us express it in the simplest fonn:

f= fo + fdyn = fo + lPk' vp(t) ... (10)

(This simplified expression neglects the transition friction at the left side of Fig. 2 (ref. 2). Yet a study of this phenomenon would exceed the extent of this paper).

Substituting now the static value of weaving resistance R (A) from Eq. (3) (which was only a function of immediate pick spacing) by these last dynamic equations of R [A, fdyn], we obtain from Eqs (1), (2), (4), (9) and (10) a set of equations of dynamic beat-up at high weaving speed:

in the time domain

Fp(t)-R(t)=O

Fp(t) =(CI + C2 )' x(t)

R(t) =a' ~(t)-rp' lPk'd~/dt

y(t) =x(t)+~(t)

in L-operator fonn

Fp(p)-(Rp )=0

Fp(p) =(C I + C2 )' x(p)

R(pl =(a+p, lPk' p)'~(p)

y(p) =x(p)+ ~(p) ... (11)

(For further use, it is more purposeful to write the equations in the operator form, where p-+- d/dt, ~(p) -+- ~(t), p' ~(p) -+- d~/dt+ ~o, etc.)


't,-21T1S·0pQl 4 04 8 08

1.6 '6 32 32 ~

t

.. ',5

',0

0.5

o o

xft

Ums) .:.....----:----.

Vy =300 msl,,::v. Tz = 20ms T1 = 1 ms

fo =025 -3-1 I.l'Ic = 5/3.10 m.s

Fig. 2-30 representation of friction coefficient f[ v(t)] as a function of sliding speed v(t) and time t since the start of sliding. On the left: C-conventional representation of I( v) as a function of speed only (as known from the literature); L-linearized friction function of speed v; T -transition curves of friction coefficient during the establishment of steady speed. v y (t)-process of speed

increase up to steady value

From Eq. (11), analogical to the static case, we can obtain-now in the operator form-the relations between dynamic beat-up quantities:

Y(P)=c 1+c2 +a'(1+ p , fJ'qJk ).~(P) C 1 +C2 C 1 +C2 +a

1 =i( . (1 + P' TI )' ~(p) ... (12)

~

From here, we obtain dynamic weft slip ~, dynamic beat-up force Fp, and dynamic weaving resistance R as

1 ~(p)= K~' . y(p)

l+p' ~

1 + p' T2 Fp(p)=K~' a' . y(p)

l+p' ~

R(p)= a'(l + p' T2 )' ~(p)

... (13)

[= R(p)]

... (14)

... (15)

where

If the form of beat-up pulse y(t) is given by the machine construction (using p.e. crank- or camtype slay drive), we can find from here the duration of weft sliding into the fabric ~(t) and the courses of weaving resistance R(t) and beat-up force Fri.t). On the other hand, if we know the necessary maximum slip of weft into fabric I ~I,we can find the necessary height of pulse for achieving the given density D 2 (given I ~ I) and the corresponding maximum weaving resistance I RI. 3.3 Response of Pick Sliding ~(I) on a Half-sinusoid form of

Beat-up Pulse y(l)

The beat-up pulse is represented by the reed lift in the period of contact with cloth fell. On a conventional loom with a swinging reed driven by a crank or cam mechanism, the beat-up pulse is a section of the reed swing (usually a section of a


full sinusoid). For the purpose of this study, the real reed movement can be substituted by a halfsinusoid with the amplitude I yl and half period TF ( = duration of beat-up pulse):

y(t) = Iyl' sin Wp t; Wp

y(p) = I y I . 2 + 2 P Wp

... (16)

where

Wp = nlTp = nl (tpp' T d = n' n/(60' tpp) is the beat-up frequency; Tc = (60In), the duration of a a weaving cycle; and tpp, the relative exploitation of the weaving cycle for the beat-up pUlse.

Inserting this into Eqs (13) and (14) and using the inverse Laplace transform from operator tables, we get for the weft sliding into the fabric ;(t) and for the beat-up force (weaving resistance) F p ( t) [ = R (t)1, the following expressions:

... (17)

... (18)

Time functions ;(t) and Fp(t)=R(t) are responses on the idealized half-sinusoid form of the beat-up pulse. The courses are shown in Fig. 3. It is observed that the relative movement of weft on the warp ends follows the reed movement [beat-up

(0 )

I ~Iyl Jf

/ ,/ '" ~ ~ -...............

I II U-

1/ l XY /?, I

./ V / \ ~ ,

1

f til,

f-

~ / l)-< I ~ ~\

I I

V I

1\ 4 I

I

\ / I I

'" I

r 20 ......L..tl, J t 10~

1: ='1Vc.J ..

o

pulse y(t)] with a small phase delay - tp~ of the maximum 1;1 after the peak Iyl, whereas the maximum of beat-up force IF pi = I R I arises with a phase lead + tp R sooner than the peak Iyl ..

The quantities Tl and T2 are certain time constants of the process, arising during the calculation and representing, in fact, the properties of warp and weft, and the friction between them.

3.4 Dynamic Weavability of Fabrics and Its Dependence on the Beat-up Frequency wp

The maximum values of 1;1 and IFpl = IRI are important quantities. I; I represents the total path of the weft sliding into the fabric (lets call it TWS-Total Weft Sliding). After reaching the maximum amount of sliding into the fabric, the weft halts in the achieved position or slightly returns due to the shearing forces of the crossing of the shed. We take the TWS as a measure of weavability.

The maximum beat-up force F p or maximum weaving resistance (MWR) arising during the beatup shows the difficulty in achieving the given weft density D2 corresponding with TWS as shown before.

The maximum values of weft sliding into the fabric ~(t) and weaving resistance R(t) yield from the Eqs (17) and (18). As the transition parts of these equations, compnsmg expressions exp( - tiT), fade down very rapidly, they are practically 0 before reaching the maximum. The values of these maximum quantities for given height of beat-up pulse Iyl are approximately

... (19)

( b) yIIyl----,------,----r-,----,

I

20: I -,.r:tJ .1 ._

=" to)

Fig. 3-Time course of (a) sliding path ;(t) of the weft into the fabric and (b) weaving resistance R{t)-both as a response on an idealized half-sinusoid form of beat-up pulse y{t)=lyl·sin{n·tITp ); here nITp=wp=n/{lPp'60In) is the beat-up frequency.

The faster (shoner) i~ the beat-up pulse y{t), the lower is the resistance IRI


and

... (20)

or for the case of given I ~ I (given weft density D2 )

ly(wp)I=I~lo ~oh+w~o~ K~

... (21)

and

IFp(wp)1 = 1~lo a o h + w~o I; ... (22)

The characteristics of weft sliding I ~ I at a given beat-up pulse Iyl [Eq. (19)] are shown in Fig. 4a. It is observed that the weft sliding remains approximately constant at low beat-up frequencies wp!5; Wp . = 1/ T1.2. Yet, at high frequencies, it starts to cdecrease down to zero. The pick simply has not enough time to slip into the fabric due to the increase in friction with speed.

At steady machine run, the weft density D2 and the corresponding weft sliding I ~ I are given rather then Iyl. The questions then arise, how much be the amplitude of beal-up pulse at the given beatup frequency Wp so that the weft density would

lU .

10~r;:::IJ::r:;:g~;!!!!!!!~( Cg)~lTmmr"A"'LD~ 1,\1 = crll,l. -11+ u~ T, = B'9I./(C,+CI +cr)

be achieved, and what would be the magnitude of weaving resistance at this situaton. This can be understood from the characteristics of I y ( W p, ~) I and IR(wp, ~)I (Figs 4b and 4c) [Eqs (21) and (22)].

The characteristics show the values of Iyl and I RI consumed by the fabric for producing the desired weft density D2 "'" I H

The characteristics represent a certain portrait of natural properties of the system "warp and fabric" on the loom, independent from the type and construction of the loom itself (except of free lengths of warp and fabric, which affect their elasticity constants C I 2 = E I 2 ° AI Ll 2). Except for these two, all the c~efficients at" warp and fabric behaviour consist only of the values of the parameters of the textile materials and the weave of the fabric.

3.5 The Impulse fFpdt or Beat-up Force as a Variable Determining the Weavabilty

In order that a cloth with a given density and structure be properly fanned on a loom, the loom has to deliver to the fabric the necessary beat-up pulse y; (t) and develop the necessary beat-up force IF pi to overcome the arising weaving resistance.

1~T~~~~ntt~ .. ~.~~~~~~~ . -. _ .. -- ... ---

Fig. 4-Characteristics of (a) maximum weft sliding I~I into the fabric at a steady height of the beat-up pulse Iyl; (b) maximum weaving resistance IR~I; (c) necessary height of the beat-up pulse Iyl at a requested slip 1~I=Au -A of weft for a given weft

density D z = II A. The argument of the characteristics is the beat-up frequency Wp; (d) impulse of beat-up force J~ = rPFp(t)o dl, consumed by the presently woven fabric at a given weft slip I ~ I 0


Theoretically, a certain type of loom is able to weave a certain cloth with a known weaving resistance. However, the weaving resistance and the beat-up force depend on the beat-up frequency. After a change in machine revolutions, the equilibrium with the same fabric gets shifted to another point. Therefore, the weaving resistance and beatup force cannot be used as a determining quantity to achieve a certain fabric density.

It would be advantageous to find another parameter of the weaving process which would be a function of the fabric density only and independent of beat-up frequency Wp or machine revolutions. This quantity is the intensity of beat-up, expressed as the impulse of the beat-up force

Tp

1= f Fpdt. o

The fabric with a given structure consumes during its forming a corresponding impulse of beat-up force. The eqUilibrium lies at a certain set of machine parameters at which the loom produces the necessary beat-up intensity. The impulse of beatup force can be calculated first from the fabric side from the process of weft pushing into the fabric.

Tp Tp j1 + w~. ~ 1-;= f Fp(t)'dt= fR(t)'dt=I~I'a' T1' • T

o 0 Wp I

... (23)

The index "1; at the symbol for the impulse II; indicates that the impulse belongs to a given weft slip I~I'" D2• '

Here T3 is a further time constant of the beatup process, yielding from the material properties of warp and weft.

The impulse II; 'of beat-up force is a determining parameter for the value of fabric density in the weft. At low weaving rates, it still varies (decreases) with illcreasing beat-up frequency wp. But at higher beat-up frequencies, the impulse necessary for the requested density D2 does not depend on beat-up frequency any more. Fig. 4d shows that the curves I I; (wp ) remain flat to the right from a certain critical beat-up frequency Wp . = 1/ T3•

enl

4 Weavability Related to Loom 4.1 Delivered Impulse or Beat-up Force Imparted to the

Fabrk by the Relatively Rigid Beat-up Mechanism or the Loom

The II; (Wp) curves represent a type of loading characteristics of fabric for the loom's beating me-

chanism. The load is put periodically on the loom by the fabric's consumption of beat-up impulse during each beat-up. The loom has to produce the same amount of active beat-up impulse on account of the momentum and pressure of its mechanisms to meet the needs of the fabric.

The impulse II;' which is necessary for a given weft density D 2, has to be met by an equally high beat-up impulse H imparte.d to the fabric by swinging reed. The imparted 'active' impulse develops firstly on account of the slay's own momentum m' vp (thus the slay with the reed acts as a hammer) and secondly, on account of deformation of the mechanism Cp' xp; the mechanism acts then as a press:

Tp

H(n, Tp)=kI'(m'vp)+ki' f Cp·xp(t)·dt . ... (24) a

where m' vp is the tramsmitted momentum of the slay, reed and attached mechanism; and Cp' xI'> the product of the elasticity constant of the beatup mechanism multiplied by its deformation (deformation force).

For active beat-up impulse H, it holds at the steady run of the loom

Now, the quantity Iyl involved in this equation can be expressed as a part of approximately harmonic reed movement in the form

Iyl= Izl'(l-coswp tp ) ... (26)

or

Iyl = Izl' [1- COS.7l 2 • n/(60 '1/Jp )] . .. (27)

where 1/Jp is the relative duration of the beat-up pulse.

Putting this in the Eq. (25), we obtain the levels of active beat-up impulses, either at constant beatup duration Tp= 1/Jp' Tc [i.e. H1/I(wp)] or at constant machine revs n [i.e. H n (wp)J. These levels are also plotted in Fig. 5. They represent frequency characteristics of relevant parameters of the machine as a source of an exciting signal for the loading system "warp-weft-fabric".

In Fig. 5, the following parameters are plotted: Hili -the active impulse of beat-up force deliv

ered by the loom at constant duration 1~ = 1/Jp . T c of the half-sinusoid beat-up pulse, i.e. usually delivered at the steady state of weaving process


Fig. 5-Characteristics of active impulses (H n , H",) of beat-up force delivered by the loom to the fabric, in comparison with the impulses I~ consummed by the fabric in order to reach a requested weft density

when the relative duration (beat-up angle) remains constant or, on the contrary, at rather rapid changes of machine revolutions with practically no time to change the cloth fell position Iyl and thus the beat-up duration 1/Jpo Here, T c is the absolute length of the weaving cycle.

H n -the active impulse delivered to the fabric at constant machine revolutions n= 60/ Tc (in Fig. 5, delivered by a relatively rigid beat-up system of the loom, i.e. by rotating reed of rigid lamellae). For compliable, high-speed beat-up mechanisms, the curves in the area of higher beat-up frequencies would be a little different.

I ~ -the passive, consumed impulse of beat-up force, which must be in equilibrium with the impulse H~ or Hn (both delivered by the loom) respectively.

We can find out a set of parameters of the process of fabric forming for a freely given working point P, defined e.g. by the given values of weft sliding I ~ I corresponding to prescribed densities D2 and machine revolutions n. From here, we find the necessary impulse of force I ~ = H 11" relative beat-up duration 1/Jp= Tp/Te, beat-up frequency Wp, and the height of the beat-up pulse Iyl. We can then read, what occurs after a change in machine revolutions or in beat-up duration (after a change of cloth fell position) and even the course of variation of the weft slidings into the fabric after stopping and restarting the loom (see marked path P-S-A-B in Fig. 5).

In Fig. 5, the marked loop BA between the steady working point P and a further point S with the same relative beat-up duration 'lip (= 1/ 12· Tc'" 30°), but with decreased revolutions ns (= 100), represents the process of braking (line B) and new acceleration (line A) of the loom if it stops fully,e.g. in the course of two beat-ups. At the time of rapic braking, the cloth fell has no time to shift itself against the reed and change the relative beat-up duration 1/Jp and, therefore, the weft slip and weft density D2 slightly increase due to increased absolute beat-up duration T po During loom restart, the system accelerates more slowly in the course of several steps of revolutions, whereas the values 1/Jp follow a dynamic transition process. The weft slips I ~ I and density D2 now often significantly decrease and show thus a stop-bar in the fabric.

This all is true for comparatively rigid beat-up mechanisms without compliances in the links and without backlashes in the bearings. For compliable mechanisms, the active beat-up impulses H n and H~ are different, depending on the system configuration. This needs then special studies on concrete cases.

4.2 Innuence orDeal-up Mechanism Compliance

If the beat-up mechanism is not rigid enough (and that is usually the case of todays's lightweight high-speed weaving machines), the course of beating pulse y(t) gets distorted due to the ad-

134 INDIAN J. FIBRE TEXT. RES., SEPTEMHER 1994

ditional vibrations of the beat-up mechanism. Then the simple Eqs (26) and (27) ate not satisfactory any more and must be substituted by much more complicated ones. A general situation for this alternative is drawn in Fig. 6a,b which shows the distribution of main compliances, elasticities, and masses of the driving mechanism, links and reed in the mechanic chain on one side, and the model of weaving resistance with warp and fabric elasticities on the other side. Furthermore, an inner autocontrol feedback works in the system changing the cloth fell position I Y.I automatically, and, consequently, changing the actual value of active beat-up impulse so that the weft density D2 is held close to the standard level i52 according to the fabric take-up. This feedback is nonlinear and makes the problem a little complicated. In fact, it can sometimes bring the weaving process ihto a sort of instability or even a little chaotic behaviour (periodically or even randomly varying weft den-

DISTRBJTION IF INERTIA MASSES A ~I:~'~r.

ON TIE LOOM

SIMPLIFIED KINEMATIC CHAIN WITH FEED-BACK M CLOTH FELL [lSPlACEMENT TO cr. POSITION

a..FHL

sities, or fluctuating the weft weaving-in, or causing instability of fabric borders, etc.). The problem of nonlinear reed vibrations can be solved on the basis of a fictitive circuit with the flow of forces in the loops instead of currents, and deformations in knotting points as potentials (Fig. 6c). The circuit consists of two loops, one of them represent the excited swingings of the reed and the other one represents the loading of the 1st loop by the beatup resistance. The load is applied periodically in short time sections, which are, of course, controUed by a feedback from the actually achieved weft density.

4.3 Practical Solutions or Beat-up Intensity Improvement at High Weaving Frequencies

Light and, therefore, usually compliable beat-up mechanisms designed for today's high machine revolutions (1000-1600 revs min - 1) can fulfill, only with difficulties, the requirement for maintaining

CORRESPONDING ELECTRIC MODEL Iz."lyl

. '''"'''--- ~

MEo-t.OF" BEAT-UP I LOADING 'BY WITH THE Q.OTH FELL

MODELUNG IMPEDANCES IN THE CIRCUIT d zJp)-~

F.ItI.I~.b4r~lzJtl- z.JtD +KJpI.. F.(PI 1 1 b • ""~=-.-- ; T. .. ...3-C. 1·p.T. • C.

KJ!I=-' .~ m .. p

IC ",. 1 1 . T. _ ~ . .,.... (t·1.p.T,3 I a- cr

~~ .. + = _1_ C,+ C.

Fig. 6-(a) The layout of main compliances and masses or a beat-up system in the loom, including the compliance of the magnetic field (magnetic slip) of the electric motor, compliance of motion transmission, and compliance of elastic reed

(b) Model of a kinematic chain of compliable masses in the beat-up system (the left half of the chain) and the mojel of the beatup resistance R of an elastic warp and fabric (the right half of the chain). Y is the lift of the reed and/or the cloth fell respect-

ively at the beat-up (c) The analogue model of we oscillations of a damped elastic beat·up mechanism loaded on one side permanently by its own mass rnA (left circuit). On the other side, for periods of beat-up, the mechanic circuit is loaded aditionally by contact with the fabric (with cloth fell, represented here by the model of weaving resistance R).K A , KM , Kp and Kc are mechanic impedances of

blocks representing individual resistances against the flow of deformation signal


rather high beat-up intensities for higher fabric densities. The natural struggle of the inner autocontrol abilities of the 'machine-fabric' system, when it is trying to manage this task, goes usually on account of the increase in beat-up lift of reed lyl, and of enlarging the cloth fell distance. The increased beat-up lift can then create a suitable beat-up force Fp and a sufficient impulse H y• Yet, on the other side, it causes sometimes a higher number of end-downs and the machine efficiency decreases.

The top types of weaving machines shown in the last International Textile Machines Exhibition ITME (lets call these machines "Formula 1") solved this problem by weaving only light articles with low densities or by using positive backrests, improving (with effort) the beat-up process.

4.4 Effect and Possible Exploitation or Backrest Resonance Vibrations on Beat-up Intensification

A conventional spring-hanged backrest (SBR) swings in the rhythm of the loom's weaving cycles around a certain level given by the average deflection of the beam caused by basic warp tension Q. With increasing weaving frequency WI' the amplitude of swingings increases until reaching the resonance Q s. At the same time, the swings get phase shifted (delayed) as can be seen in Fig. 7b. At low frequencies, the swinging proceeds in the same phase as the reed. The SBR deflections then make the warp ends loose at the period of beat-up and, consequently, the beat-up weakens.

Above the resonance frequency WI> Q s the SBR gets into opposite swingings according to the reed. Beat-up intensity should then increase.

Yet, the problem is not as simple as it was described now. The real backrest behaviour can be followed in Fig. 7a. The response Ys of SBR on warp tensioning splits into two parts-response y sb on practically harmonic warp elongation caused by shed opening, and response y sp on periodic pulses of the reed Y(/). Whereas the transfer function of the first response is quite conventional,

A( . ) Ysb(j· WI) j"w =

I Xb (j. w,)

... (28)

the response on beat-up pulses IS more complicated. Ater each beat-up, the SBR gets into faded vibrations on it's own frequency Q s. Each new cycle starts new vibrations, with the addition of some residual swingings from the previous beatups.

The resulting transfer function of beat-up pulses represents a transfer of a whole history of foregoing oscillations of SBR, caused by previous beatups. It has a fonn:

where Ks and E 1 are certain constants given by the actual SBR design, and E2 is a function of immediate weaving frequency.

The characteristics of this impulse transfer function are shown in Fig. 7c. The function has a nonconventional wavering course caused by composition of residual oscillations from previous beat-ups. These residual oscillations come to the start of a new beat-up, either in phase or out of phase, depending on the immediate beat-up duration 1/Jp (or on immediate weaving frequency Wp ).

According to this, they will then be either added or distracted, alternately or even randomly in accordance to the fluctuations of loom speed.

The beat-up force F p is caused by the sum of all warp elongations occurring at the moment Ip of beat-up when the cloth fell is in contact with the reed (Fig. 8). The sum of elongations is (without writing the sings of absolute value):

xl(tpi=Y(tpj+Xb(/p~-[ySb(/pr+Ysp(tpil ... (30) I

swings of SBR as response to beat-up pulse y(t)

swings of SBR as response to shedding elongation y(t)

shedding elongation of warp x h (I)

warp elongation caused by the beat-up pulse y(/)

Individual elongations y(t), xb(t), Ysb (I), Ysp(t) are simple harmonic functions with frequencies either

Tc w, (weaving frequency) or Wp=-- w, (beat-up

2 Tp

frequency). The elongations show phase shiftings at the instance of beat-up. The quantities along the Eq. (30) have, therefore, to be added together vectorwise.

As the amplitudes Ix .. I, IY .. I and their phase angles vary with the weaving frequency w,, the resulting vector x 1 varies too. The hodographs of


BACK-REST RESPONSE ON EXCITING SIGNALS AT THE TIME OF BEAT-UP

,.=Yn+y., ~ ~ 1i Jh t, .. _.~. J ~. C Q ~ Auf --. J

g I"~~y"'~ ® i""". .

1+ Q lI'T

r~~ \t;;.~ ) TQ!AL WARP ELONGAT!QN

AT THE BEAT - UP : IX11t,l = yltJ·x,It,J- l~bfttJ·y,P ftpJll

- CCRRESP. BEAT-UP FCR:E:

I F,I = 01- Q,= CT X1ft',). Cay ItpJ

HERE: BACK-REST DEFLECTIONS y. ta.P CAUSED -BY SHEDDING x .. lt) :

bel y.~lt ) = KiT -{1- A~.cos[Utt • t,lut )))

-BY BEAT -UP PULSE ylt): )J,Ilt) = KilyI.E~iJ. E,,,-\,'&' exp[-I·~i(t-t,l)J.

t .sin( iiV1-1lt- t~-tj~1 IRAN~FER CHARACIEBISIICS (TQ BACK-BESI) OF SHEDDING xblt) OF BEAT -UP PULSE ylt)

K •. m Ki~ lm I~ t ~D y,;!y

~ , ",." .. .' \ I

i I I! I iii K,.10 I

~v ~ 't "V.v, ......

A ~ I

." \ ." ,It ~ ')I~ ~~ \1 " ! i. KiElI

Ka·~ 19 , \

~ ~

10 m ~ I ...... • .. ~ 90· I' 0.1 1 ( .v ~ ~ ~0.1 't-f.1 0• - rl.=lJ ~Ul )5 I

~p 0 It! ...

v '" \/' ~~ ., " ~,

-90· I" -r-

-180" -90" -r-

::J

Fig. 7-(a) Schematic representation of a spring-hanged and damped backrest, excited by shed opening and ~t-up pulses of reed. The elongations XI (Ip) of warp at the moment of beat-up comprise elongations caused by shedding Xb (Ip), beat-up pulse

y( I p), and by warp releasing caused by backrest oscillations excited by shedding [ - Y.b (I p) 1 and beat-ups [ - Y Ii> (I p ) 1 (b) Amplitude and phase characteristics of amplification of harmonic backrest oscillations caused by shedding (el Amplitude and phase characteristics of amplification of backrest oscillations caused by a set of half-sinusoid beat-up pulses

y(l) (a nonlinear problem)


Fig. 8-The superposition of warp elongations caused by beat-up pulse y(t), shed opening xb(t), releasing of warp due to backrest following the shedding motion [-Y,b(t)), and releasing due to damped backrest swingings excited by beat-up pulses [-Y,p(t)]. Resulting elongation of warp is x.(t). The highest elongation is the real beat-up. It needs not occur just in the moment of the

beat-up pulse of the reed .but later (see arrow), and can be higher than the original beat-up pulse

this vector XI (tp , w,/Q.) are shown in Fig. 9 for two different relative dampings. After proper tuning of eigen frequency Q. and damping of the backrest, the total warp elongation at the beat-up can show very interesting values-at several weaving frequencies significantly higher, but at others, dangerously lower than the elongation Iyl provided solely by the beat-up pulse.

The deciding part of the vector X I is its real part Rex I (in Fig 9, the horizontal component), which represents the effective warp elongaton at the beat-up. It is practically proportional to the beat-up force. The beat-up elongation of warp has been plotted separately in Fig. 10 from which it is clear that there are weaving situations where the vector of total warp elongation in the moment of beat-up is significantly higher than that arising without the influence of excited backrest swinging. The exploitation of this effect could basically improve the weaving process, without the need of 2

positive backrest driving mechanism. Nevertheless, it is important to emphasize that

with other combinations of WI and Q., the swingings of the backrest can coincide with the beat-up. This means that the backrest would move at the same time in the same direction as the reed, releasing thus the warp tension. This would then weaken the action of reed, may be even to zero. When not under control, this inverse effect of resonance depressions of warp elongation at the beat-up may worsen either the fabric forming process or the fabric quality.

( b)

Fig. 9-Vector characteristics (phase ponrait) of total warp elongation x I at beat-up. Its real pan Rex. (horizontal component) shows the alternating improvement and deterioration of maximum beat-ups due to influence of shedding elongation and backrest motions which depend on immediate ratio of weaving frequency and backrest natural frequency (w,l Q ,)

[(a) at small natural damping ~, and (b) more realistic at higher damping ~ of the system, including artificially controlled

damping]

138 INDIAN J. FmRE TEXT. RES., SEPTEMBER 1994

REAL WARP ELONGATION ReXt AT THE BEAT-UP - VAR~_ EFFECT OF DAMP~G I-T. EFFECT CF E£AT-LPTlMlNG

J.lyll----1--"-M--+--+---t-~

Fig. IO-Amplitude characteristic of improvement (heightening) of beat-up warp elongation I x ,I caused by resonance

swingings of backrest (deduced from Fig 9)

The problem of exploitation of automatic backrest resonance has not yet been solved technically in a sufficient way. But at least, this short analysis of backrest behaviour may have brought a new view into the complex weaving process. It may also have given some explanation of the effects of sudden improvement or worsening of weaving, without any clear reasons, noticed sometimes in practice. It may also have shown some new ways of designing and studying the weaving systems in order to obtain higher and better properties of weaving machines in future.

References 1 Greenwood K, Cowhing W T, Vaughan G M, The position

of the cloth fell in power looms, J Text Inst, 47 (1956) 241, 255,274.

2 Nosek S, Problems of friction in textile processes, paper presented at the International Conference on Textile Science '94, Liberee, 1994.

3 Stein F, Melliand Textilber, 8(6) (1927) 994.

4 Watzel S, Backmann R, Faserforsch Texdltech, 16(1) (1966) 1~.

5 Nosek S, Cloth forming process, Veda Vyzk Prum Textilnim, 5 (1966) 70 (in English).

6 Nosek S, Dynamiclui setkatelnost tkanin (Dynamic weavability of fabrics), Research Report of the Research Institute of Cotton Industry (VUB), Usti nad Orlic!.

7 Nosek S, Factors controlling weavability with regard to beat-up motions in modem looms, Veda ~vzk Prum TextiJnim, 15 (1976) 65 (in English).

8 Nosek S, Teorie tkani (Theory of Weaving), Vols I-III (Dum techniky, Pardubice), 1988-89,790.

the dynamics of fabric forming on the loom at high weaving...

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