Indian Journal of Fibre & Textile ResearchVol. 15. December 1990, Pp. 145-153

Computer simulation of melt spinning of poly( ethylene terephthalate) using asteady-state model

• Y C Bhuvanesh & V B GuptaDepartment of Textile Technology, Indian Institute of Technology, New Delhi 110 016. India

Received 16 October 1990; accepted 31 October 1990

A steady-state model for melt spinning has been used to carry out analytical simulations and subse-quently provide information on the velocity, diameter, force and temperature profiles along the spinningway for poly(ethylene terephthalate). The model uses a variable spin line force as against a constant forceused by some earlier workers, as the former brings out the effect of processing parameters on the spinn-ing process more realistically and in greater detail. The simulations were carried out using a fourth andfifth order approximation with a Fehlberg modification of the Range Kutta technique. These were thenused to carry out sensitivity analysis which provides useful information on the effect of process condi-tions on product properties. The primary variables subjected to sensitivity analysis were melt tempera-ture, intrinsic viscosity, throughput rate, cooling air temperature and velocity. The process sensitivity ofeach of these parameters and their relevance with reference to industrial spinning was considered. Thedependence of the filament acceleration and its rate of cooling on take-up speed is also brought out in thepresent work. On-line measurements of surface temperature and filament diameter were attempted andthe data so obtained were compared with the results obtained by simulation. The results achieved wereparticularly helpful in gaining good insight into some aspects of the dynamics of melt spinning.

Keywords: Freeze line, Melt spinning. Poly(ethylene terephthalate), Sensitivity analysis, Simula-tion, Steady-state model. Variable force model

1 IntroductionThe urnfonnity and mechanical properties of

melt-spun filaments are governed by various physi-cal phenomena like fluid rheology, heat transfer,aerodynamics, etc. Due to the complexity of thesephenomena taken individually and their interac-tions, it becomes rather difficult to carry out an ana-lysis of the spinning process by oridinary methods.Development of a process simulation tool by using amathematical model to explain the various physicalphenomena involved in the melt spinning processmakes it easier to identify the most critical parame-ters from among the variables affecting the spinningprocess. Information on the sensitivity of the pro-cess to changes in any parameter would facilitate insetting up norms for production.

Attempts to develop an analytical model werefirst made by Andrews' and Ziabicki 2-4 , who as-sumed that the rheology of the polymer is adequate-ly represented by a Newtonian relation and the for-ce in the spinline is constant throughout. Later, Kaseand Matsuo=' suggested some modifications to in-

elude the effects of air drag, acceleration and gravityon the process dynamics. This model has since beenused by a number of workers":" by incorporating afew improvements, but by and large retaining themain assumptions of the model which still remainvalid. The use of a variable force model incorporat-ing the effects of gravity, inertial drag and air dragleads to more realistic predictions since the use of aconstant spinline force grossly underestimates theproperties of the spun filaments. Any other differ-ences observed while using a variable spinline force,as against a model which assumes constant force,are highlighted in the discussion of results. Themodel is limited to amorphous or to slowly crystal-lizing polymers spun at speeds where no crystalliza-tion takes place. The model has been applied topoly(ethylene terephthalate) (PET) in the presentwork. Further, an analysis of the sensitivity of theprocess to various parameters is also carried outwhich helps in identifying the most critical parame-ters of the melt spinning process. The present workuses a steady-state model which assumes that thereis no variation in any of the variables with time.

145

INDIAN J. FmRE TEXT. RES., DECEMBER 1990

2 Theoretical Background The force acting on the spinline, which was as-2.1 Steady-State Model sumed to be constant and dependent only on the

The model has been developed by making the fol- rheology of the polymer in some earlier works re-

lowing assumptions: portedl-3.12-14, has been suitably modified in the(i) The molten polymer filament is circular in present work to include the contributions due to air

cross-section. drag, gravity and inertial drag of the filament.(ii) Temperature is uniform across a particular Hence, the spinline force changes along the spinline

cross-section. due to these contributions. The effect of surface ten-(ill) Heat conduction in the longitudinal direction sion on the spinline force will be too small in com-

(x-direction, Fig. 1) is negligible. parison with the other contributiom and has hence(iv) Tensile viscosity of the molten filament is de- been neglected.

pendent on local temperature alone with anArrh~nius type. temperature depe~dence: .2.2 Differential Equations

(v) ~lastic elo.nganon.of the filament IS negligible The considerations described in the previous sec-m companson to VISCOUS flow. tions lead to the following set of differential equ-

(vi) The die swell effect is small and can be neg- ations5:lected.

(~) Density is depe~dent on tempera~re .alone. 2.2.1 Equation of Continuity(Vlll) A purely extensIonal flow field eXIsts, I.e. there

is a uniform distribution of axial velocity ac- W= Avp ...(1)ross the filament.. where W is the mass throughput rate; A, the local

Though some of these assu :nptions may not con- cross-sectional area. ~ the velocity. and p the dens-form to the present thinking, they are quite valid ity of the filament. ' , "

over the speed range that has been analyzed. At veryhigh spee.ds of sp~~, th~re is a variation in te.m- 2.2.2 Constitutive Equationperature m the radIal directIon and the deformatIonof the polymer no longer remains purely viscous. dv F.The problem of die swell at the spinneret exit in- -= ~ ...(2)volves a relaxation and consequent disorientation of dx A 1/ethe molecules due to the release in the strain energy .".immediately after leaving the spinneret. Such an ef- v-:here F rheo IS the net rh~ologtc.a1 fo~ce m the spm-fect on the filament diameter and its variation with line; and 1/e, the elonganonal VISCOSIty of the poly-uptake speed has not been taken into account in the mer.present work.

2.2.3 Equation of Momentum or Force Balance

dFrheo dFinertial aFairdru aFOTRvitv (3)~ ~ -= c + ~ -~---J ...~ ~ dx dx ax ax

T.u.D r0 0 0

.Cool1nc a1.. where Finenial is the inertial drag force; Faird'8.l' the~ 1---+ , drag on the filament due to air resistance; and l'gravity'

.the gravitational pull.L ..T.u.D +- .~~= W!!.!: (4)

.dx dx.F z.11-T .v aF.9 airdr8R=PaCdv2nD ...(5)

ax

~=-.!& ...(6)ax vT8k.-up I I

Fig. 1 -Schematic diagram of melt spinning where D is the filament diameter; Cd, the coefficient

146

BHUV ANESH & GUPTA: COMPUTER SIMUlA'I10N OF MELT SPINNING OF PET

of air drag; g, th~ acceleration due to gravity; and Pa, tricted to 3000 m/rnin. Since up to this speed it can

the density of th~ ambient air. be safely assumed that no stress induced crystalliza-

tion is occurring during spinning. The onset of crys-

2.2.4 Equation of Heat Balance tallization complicates the process dynamics whichrequires a more complex mathematical approach. A

!!I = nDh( T -T.) ( nume~cal technique that could solve the differentialdx wc ...7) equatIons 1-7 as a boundary value problem was

P used.

where Cp is the heat capacity of the polymer; and h, ..the heat transfer coefficient. 2.5 Boundary ~ondltions ..

The folloWIng boundary conditIons were taken:

2.3 Parameter Correlations 110) = 285°C,

To estimate the properties of the polymer (PET) --0like density'p', heat capacity 'Cp' and elongational 11L)- Tg-69 C,and

viscosity '17e' at different teII!Peratures, the following v(L) = winder velocity

relations were used19 (all units in CGS units): ..L 1S the freeze line d1stance from the spinneret,

p= ~.356 -(5 x 10-5 T) ...(8) the freeze line being defined as the point at which

C = 995 + (3.375 x T) ...(9) the t~~perature of the filament is equal to its glassp trans1tIon temperature ( Tg).

( 6802 ) The simulation was then carried out to find the

17e = 0.2787 X {I.V.)5.056 x exp ...(10) value of initial force F, which satisfies the boundaryT+ 273 conditions. At the spinneret (x= 0), the rheological

contribution Frheo(O) is the only source of tension in

where I. V. is the intrinsic viscosity of the polymer. the spinning line. To calculate this value, a simple

To include the effects of the cross-flow air, the rel- model, assuming temperature-dependent Newtoni-

ations for the convective heat transfer coefficient' h' an viscosity and convection~controlled heat trans-

and the coefficient of air drag 'Cd' were used assug- fer, was considered1O. The result reads:

gested by Kase and Matsu05:f "'-Rh* 1 .

Cd=0.41 x Re-0.61 ...(11) Frheo(0)=617e(To) ~dv C ( L '7"') ...(14)

"0 v p p1P 0, ~L

where Reis the Reynold's number and is given bywhere

Re=vxD/17k ...(12)

where 17k is the kinematic viscosity of air. -'fTO dT

For the convective heat transfer coefficient 'h', a 1/J( To, TL) -1J e( To, TL) ( T- T~) (T ) (15)... al I . hi h al . I th TL 17e

seInlempmc re atIon,w C so mc udes e heat

loss due to radiation, was used. h . th . nal ..'7"' thwere 17e 1S e extens10 ViSCOS1ty; ~o, e temper-

[ ( ) 2) ature; TL, the filament temperature at the freeze line

h=0.473 x 10-4 (pV2/W) 1+ ~ ...(13) which is equal to To; Too, the temperature of the

v cooling air; R, the filament radius; h*, the convective

heat transfer coefficient which is calculated assum-

where Vy is the velocity of cross-flow cooling air. ing constant filament density throughout the spin

line; ", the filament velocity; p, the filament density;

2.4 Data for Simulation and C p' the specific heat of the filament.

The following data were used to carry out simul-

ations for PET14: 2.6 Differential Equation SolverMelt temperature = 285°C A Range Kutta technique was used for the numer-

Intrinsic viscosity of the PET polymer = 0.61 dVg ical solution of the set of differential equations be-

Spinneret capillary diameter = 0.05cm cause it is quicker than other methods. But an ordi-

Cooling air temperature = 25°C nary version is not enough to deal with the above

Cooling air velocity = 80 cm/s highly non-linear set of differential equations, since

The uptake speeds used were 1000, 2000 and a stable solution which satisfies the boundary condi-3000 m/rnin. The maximum speed taken was res- tions cannot be obtained. This problem is further

147

INDIAN J. FIBRE TEXT. RES., DECEMBER 1990 ..

aggravated by the consideration that force also va- (vii) If the velocity achieved is more than the up-ries along the spinning way. Hence, a modification take velocity the initial force is decrementedof the Range Kutta technique, which uses the fourth and incremented if the case is vice versa. r

and fifth order approximation to compute the values (viii) The cycle is continued till a suitable value ofat the next step1ength, was used. The Fehlberg mod- the initial force is obtained which satisfies theification of the Range Kutta method was opted for boundary conditions.since it is quicker due to the special selection of the (ix) When the boundary conditions are finally ful-constants used in the computation of the values at filled the simulation is stopped.the next step length15. Also, the method is capable ofhandling some amount of stiffness arising in the so- 3 Experimental Procedurelution of the differential equations and thereby gives In making on-line measurements, it is preferablegood results with minimum computational time. To not to contact the filament for two reasons. First, theminimize the error of computation, an algorithm filament close to the spinneret is in a fluid like statewhich automatically adjusts the step length was in- and second, any contact made during measurementscorporated11. can disturb the spinline. Hence, non-contact tech-

niques are most suited tb obtain data on parameters2.6.1 Algorithm for Steady-State Solution like temperature, velocity, diameter, birefringence,

The algorithm is outlined briefly discussing the ~tc.various steps involved in carrying out the simula- On-line techniques have been used by Kase andtion: .,. Matsu05 and more recently by Zierninski et ap2. In

(i) Supply data for the pnrnary vanables: Spm- the present work, only temperature and diameterneret diameter, uptake lelocity, intrinsic vis- were measured on slow-speed machines.cosityof polymer, cooli.lg air velocity, coolingair temperature, melt temperature and 3.1 Spinning Unitsthroughput rate. 3.1.1 Fuji Machine

(ii) Specify initial conditions: The initial values of Measurement of surface temperature was carriedvelocity, diameter, birefrigence, temperature out on a Fuji melt spinning machine on which PET \and force (which includes the rheological, in- multifilament yams were spun. The following condi- '

ertial, air drag and gravity force) are to be tions were maintained during spinning:specified for the simulation to be carried out. Polymer throughput rate = 0.28 girnin

Remarks: The initial rheological force requires Melt temperature = 285°Cmost attention. The other initial values a,re known Polymer intrinsic viscosity = 0.611 dl/gbeforehand and the gravity, inertia and airdrag force Spinneret diameter = 0.05 cmare taken as zero. To avoid undue wastage of time it Ambient air temperature = 30°Cis vital to make a good approximation of the initial Uptake velocity = 75 rn/rninforce. The other components of the spinline force atthe spinneret are taken to be zero. The initial condi- 3.1.2 Miniature Spinning Machinetions are: For measurement of diameter, a laboratory-scaleF. = 0 0 monofilament melt spinning facility was used.

3lrdrag .Spinning was done under the following conditionsFinertial = 0.0 with PET:F ' = 0 0 Polymer throughput rate = 0.0129 gis

graV1ty .Polymer intrinsic viscosity = 0.63 dl/g(ill) Using these initial values, the values at the next Melt temperature = 278°C

step length are approximated using the differ- Ambient air temperature = 25°Cential equation solver:. Capillary diameter = 0.06 cm

(iv) The polymer properties as specified from Eqs Uptake velocity = 24 rn/rnin(8) to (13) are calculated to solve the set of si-multaneous equations. 3.2 Measurement of Surface Temperature

(v)The step length is incremented till the temper- Surface temperature of the filament spun on theature reaches below the glass transition tem- Fuji machine was measured as a function of the spin-perature. line distance with the help of an infrared camera

(vi)The velocity obtained at the freeze line is (AGA Thermovision). This camera measures thechecked whether it is more or less than the wavelength of the radiation emitted by the source ofspecified uptake velocity. which the temperature is to be measured. The radia-

148

..BHUVANESH & GUPTA: COMPUfER SIMUlATION OF MELT SPINNING OF PET

tion emitted by a body depends on its temperature more rapid decrease (Fig. 3) and then stabilizesand is described by the Stefan-Holtzman's law of ra- asymptotically. The rate at which the filament un-diation, viz. dergoes deformation increases with the uptake;. = sr ...(16) speed when the other parameters are unchanged.

where;' is the wavelength of the radiation source; S,the Stefan-Holtzman constant; and 1; the tempera- 0.06

ture of the body in K. The camera has an aperturewhich filters out all radiation except the infrared ra- 0.05

diation. The object is then displayed digitally on a 0.04cathode.ray tube as a thermal image in the form of Eisotherms. :~ 0.03

...0-...:E3.3 Diameter :5 0.02 (a) 1000 m/min.. b d o (b) 2000 m/mln

lThe on-line dIameter measurements can e ma e (c) 3000 m/mineither with the help of a microscope or by taking 0.01grab samples and measuring their diameter later us- .ing a microscope. In this work, 1 cm long samples 0.00were grabbed at specific points of the filament spun 0 20 4D eon the miniature laboratory spinning unit using a DISTANCE, cmspring loaded clip and simultaneously freezing it by Fig. 3 -Change in diameter of the filament along the spinningspraying silicone oil. Their diameters were later waymeasured using a microscope. 300

4 Results and Discussion 2404.1 Steady-State Simul.ation

The set of partial differential Eqs 2-6 were sub- .u 180jected to simulation to solve the boundary condi-.;; (a) 1000 m/min.. d .. 2 5 . al ~ (b) 2000 mlmintions mentione m section. usmg a person 'C (c) 3000 m/mincomputer (XT) with the data given in section 2.4. ~ 120

The velocity profiles for the three spinning speeds § -were calculated keeping all the other variables con- 60stant except the winding speed ( VL) which was vari..ed. The velocity variation along the spinning way is 0plotted in Fig. 2. It is observed that the filament 0 20 40 60reaches the uptake speed asymptotically and the DlSTANCE,cmcurve has a sigmoidal shape. The diameter shows a Fig. 4 -Change in surface temperature of the filament along the

spinning way

S 400

3000",/min4 h300 ~ ; ~m/min 2000 m/min

3 .£ ../

E ~ 200 /-->- /E min " -'>" 2 .,; in0- u

-a:~ 0~ 1000 m/min IL 100> I

0 00 20 4D ~ 0 20 40 60

DISTANCE,cm DISTANCE ,omFig. 2 -Change in velocity of the filament along the spinning Fig. 5-Change in the spinline force with distance from the

way spinneret

149

.INDIAN J.FIBRETEXT,RES.;pECEMBER 1990 .'.'

On the other hand, the surface temperature profiles the spinline force due to ineitial and aerody~(Fig. 4) do n(j; differ much for the three speeds. The namic drag are small compared to the initial rheo-force profiles (Fig. 5) indicate differences in the for- logical force (Fig. 6). The initial rheological forcece for the three speeds. The compositions of the increases with increase in take-up speed. For 3000spinline force for the three speeds are shown in m/min, the air drag component is the largest con-Figs 6-8. For 1000 m/min, the contributions to tributor and the inertial drag is also larger than the

400 initial rheological force at the end of the spinline( (Fig. 8). The other components dominate the rheo-I " logical component of the force at speeds of 3000

300 m/min and above. Hence, a constant force system" ..would grossly underestimate the spinline force at

~ :, such speeds. Though the aerodynamic drag force~ 200 ;;; continues to increase even after solidification point~ j (freeze point), its effect on the filament deformation~ Rheo:..~-~~\.. 'c is small. Hence, the simulations have been limited to

100 the region only up to the freeze poin~.

4.2 Acceleration and Cooling Rate0 Figs 9 and 10 show the filament acceleration and

0 20 40 50 its cooling rate against the time taken by the filamentDISTANCE, cm after leaving the spinneret for the speeds 1000,

Fig. 6 -Rheological, inertial, air drag and gravitational forcealong the spinning way for a take-up speed of 1000 m/min 450 00 rn/mi

400 400

M 350I0.-..JOO..3DD -~ 250...

~ al ~ 200>- -~ ...

.-c'" 200 ffi 150u -'« '"0 u...u 100

-C

100 50

aa 0.04 0.08 0.12 0.16 0.20 0.24' 0.28

GravitY00 20 40 50 TIME AFTER LEAVING SPINNERET, S

DISTANCE ,cm. Fig. 9-Filarnent acceleration vs. time taken after leavingFig. 7 -Rheological, inertial, air drag and gravitational force spinneret

along the spinning way for a take-up speed of 2000 m/min13

400 17 3000rn Imln

11Rheological 10

0-r c:' I// ~ OOOm/..in

/ ..S.. / ~..u 7c °.~ '" 6~ ..tJ « 5« ~~,.. ! 4: 0'

3, 0( u; 2: 1; a'. 0 " a C.04 0.08 0.12 U.16 0.20 0.24 0.28

0 20 40 50 TIME AFTER LEAVING SPINNERET,sOISTANCE,cm

Fig. 8 -Rheological, inertial, air drag and grav;itational force Fig. 10-Filament cooling. rate VS. time wen after leavingalong the spinning way for a take-~p speed of 3000 m/min spInneret

150

BHUVANESH & GUPTA: COMPUTER SIMUlATION OF MELT SPINNING OF PET

2000 and 3000 m/min, It is interesting to note thatthe acceleration and cooling rate peaks lie close toeach other for any particular set of spinning condi-tions. This closeness clearly brings out the inter-re-lationship of the two important physical processesof melt spinning, viz. heat transfer and mass flow. Italso indicates the possibility of controlling the de-formation rate by adjusting the cooling conditions,and thereby making attempts to minimize filamentbreakages during spinning. The filament accelera-tion is related to the rate of deformation of the fila-ment (Fig. 9) while the cooling rate curves (Fig. 10)indicate the severity of quenching to which the fila-ment is subjected.

4.3 Sensitivity AnalysisThe steady-state solution described in section 4.1

was used to analyze the sensitivity of the process tochanges in the various primary variables, viz. polym-er melt temperature and intrinsic viscosity, coolingair velocity and temperature, spinneret capillary di-ameter, uptake speed and the throughput rate of thepolymer. The sensitivity of the process to these var-iables has been judged in terms of some secondaryand resulting variables like initial force (at spinner-et), stress at freeze and the freeze line distance.Their effect on each of these process variables andeventually on the spun filament properties are dis-cussed in the succeeding paragraphs.

4.3.1 Freeze Line StressThe filament birefringence '!l.ri is related to the

spinline stress' a' by the relation

!l.n=Cop,xa ... (17)

where Cop is the stress optical coefficient.Birefringence is known to be the single most im-

portant resulting variable which decides the pro-perties of the spun filament". The fibre-line proces-sability in terms of drawability and level of brokenand fused filaments is determined by the orientationof the as-spun filaments. Also, the final product pro-perties such as tensile strength, elongation, shrin-kage, dyeability, etc. are influenced by the as-spunfilament properties like orientation, etc. which are,in turn, dependent on the birefringence of the spunfilament. Since birefringence is directly related tothe spinline stress, it follows that the parameterswhich significantly affect the freeze line stress arethe critical process variables. The process sensitivityin terms offreeze line stress is illustrated in Fig. II.The figure clearly indicates that the most criticalprocess parameter is the melt temperature followedby the intrinsic viscosity of the polymer, both ofwhich control the melt viscosity. The polymer rheol-

ogy thus plays a crucial role in deciding the spun fi-lament properties. Hence, it is imperative to moni-tor closely and accurately the melt characteristics,more so, for a multifilament, multiposition meltspinning plant. These parameters become evenmore critical at much higher speeds of spinning anddemand greater attention in ensuring uniform meltproperties. The uptake velocity is the next most cri-tical process parameter. Even though uptake veloc-ity is not the most critical parameter, but is still themost amenable to change. The spinneret capillarydimensions and melt throughput rate have a moder-ate effect on the stress at freeze while the cooling airtemperature and velocity have the least effect on thefreeze line stress.

On comparing the present results with those ob-tained from a constant force model!", it is observedthat the sensitivity levels differ, apparently becausethe constant force model underestimates the freezeline force and as a result the sensitivity values interms of freeze line stress become exaggerated.

To get a more thorough insight into the effect ofthe different parameters on the spinning process,sensitivity analysis for the initial force (Fig. 12) andfreeze line force (Fig. 13) were also carried out. Atthe spinneret, only the rheological force is believedto be acting on the filament. The filament is weakestnear the spinneret and hence the analysis on the in-itial force might throw some light on the conditionof the filament near the spinneret. But if the effect ofchange in any parameter is to be fully understood interms of the spinline force, it is useful to have similarresults for the freeze line force also. The melt tem-perature and intrinsic viscosity were found to havethe most effect. The throughput rate and spinneret

50,-------------,--------------,x

40 \wN 30w!I!u,

20...""

~ 10

~...(J)

:5 -10

i -zo f'"' -30

-40

-50-60 -40 -20 20 40 60

"1.CHANOC IN PARAMETER

Fig. II - Sensitivity analysis for stress at freeze: ( + ) melt tem-perature. (~) intrinsic viscosity. (x) polymer throughput rate,(0) spinneret capillary diameter, (V) temperature of cooling air.

and (0) velocity of cooling air

151

INDIAN J. FffiRE TEXT. RES., DECEMBER 1990

100 50

80 40

~ 60 ~ 30

...II):i 40 25 20

-~I- -! 20 oJ 10

1:1~ ~ 0I 0 ...z -10-20 -

I'!I -20

-40-30..

-60 -40

-80 -50-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

x CHANGE IN PARAKTER % CHANGE IN PARAKTER

Fig. 12 -Sensitivity analysis for initial force: ( + ) melt tempera- Fig. 14 -Sensitivity analysis for freeze line distance: (0) velocityture, (A) intrinsic viscosity, ( x ) polymer throughput rate,{ <> ) of cooling air, (+ ) melt temperature, ( <> ) polymer throughputspinneret capillary diameter, (V) temperature of cooling air, and rate, and (A) temperature of cooling air

(0) velocity of cooling air ..., f inlin.. high}SltlV1ty m terms 0 sp e stress gives a y exag-

50 gerated value. However, the hierarchy of process40 parameters predicted is similar to the one predicted

by Nadkarni and coworkers14.17-19 using a constant30 force model.

~ 20 4.3.2 Freeze Line Distance...10 The freeze line r~esents an important transition~ 0 point and its location is therefore useful. It also gives~ some idea about the rate of cooling or the severity of~-10 quenching to which the filament is subjected. The1-20 rate of filament defomlation is also dependent~ on the cooling rate. If the freeze line is shifted closer~~JO to the spinneret by changing only the cooling condi--40 tions and without altering the throughput and up-

take speed, it is easy to imagine that the distance and-50_60 -40 -20 0 20 40 60 ~~ available for the fil~ent todefoml and stab~-

me IS also shortened. This means that the filament ISrx: CHAN<*: IN PARAKTER subjected to a more severe defomlation rate. Hence,

Fig. 13 -Sensitivity analysis for uptake force: ( + ) melt tempera- a sensi~vity ~~dy on the fr~ze line ~o.cation can beture, (A) intrinsic viscosity, ( x ) polymer throughput rate, «» useful m optlmIzmg the cooling conditions also. Thespinneret capillary diameter, (V) temperature of cooling air, and filament above freeze line is weakest. Hence, any

(0) velocity of cooling air disturbance or turbulence above the freeze line hasdimensions again show moderate effect while the to be avoided. One direct use of the location of thecooling air temperature and velocity show the least freeze lin~ is in ascertaining that the take-up is mucheffect. The effect of change in any parameter has a below the freeze line so that the filament is fully so-similar effect on both the initial force and freeze line lidified before it is wound onto the take-up. The spinforce except due to change in polymer throughput. finish is also preferably applied below the freezeThe initial force decreases with increase in through- line. It can be observed from Fig. 14 that the meltput (Fig. 12) whereas the freeze line force shows an throughput rate and melt temperature show theincrease (Fig. 13). This is due to the accompanying maximum effect on the freeze line location. If thechange in the denier of the filament due to change in denier is doubled by increasing the throughput ratethroughput rate. On the whole there is a reduction in without altering other parameters, the freeze linethe stress at freeze. But, the constant force model14 distance is also approximately doubled. These andshows a reduction in the spinline force due to in- other factors have to be kept in mind while design-crease in melt throughput rate and the process sen- ing the spin line. The cooling conditions also affect

152

BHUVANESH & GUPTA: COMPUTER SIMUlAll0N OF MELT SPINNING OF PET

300 en while spinning multifilaments. Also, small errors

in judging the distance at which the measurements240 were made could lead to quite significant differ-

ences when comparing with simulated data.

.u 180

~- 4.4..2 Diameter~ The diameter measurements (Fig. 16) were made~ 120 on grab samples. The diameter profile of the simu-

~ lated data stabilizes asymptotically. The experimen-60 tal data also shows a similar trend. But the fit is not

very good which may again be due to errors in judg-0 ing the points at which the samples are to be

0 20 ~ grabbed.

DISTANCE,cm

Fig. 15 -Temperature profile: ( -) simulated, and (+) experi- Acknowledgementmental data The authors are grateful to Prof. M. Gopal and

0.052 Prof. O.P. Chawla of lIT, Delhi, for their useful ad-0.048 vice and assistance.

0.044References

0.04 1 AndrewsEH,BrJAppIPhys, 10(1960) 39,

E 0.036 2 ZiabickiA& KedzierskaK, Ko/loid-Z, 171(1960) 51.~ 3 Ziabicki A, Ko/loid-Z, 175 (1961) 14.~ 0.032 4 Ziabicki A, High speed melt spinning(Wiley, London) 1981,'"~ 0.028 5.0 5 KaseS&MatsuoT,JPolym$c~3A(1965)2541.

0.024 6 Kase S & Matsuo T, J Polym Sc~ 38 (1966) 251.0.02 7 DuttaA,JChernEng,29(2}(1985) 1050.

8 Gagon D K & Denn M M, Poiym Eng Sc~ 21 (13) (1981)0.016 884.

0 20 40 60 9 Denn M M, In Computers in polymer processing, edited by

DISTANCE, om J R A Pearson & S M Richardson (John Wiley & Sons, Lon-Fig. 16 -Diameter profile: ( -) simulated, and ( + ) experimental don) 1980,57.

data 10 Ziabicki A, Fundamentals of fibre formation (Wiley, Lon-th fr }in . Th fr }in I ..don) 1976.

e e~ze ~ .location.. ~ .ee~e ~ ocatlon IS 11 Aiken R, Stiff computation (Oxford University Press) 1985,almost msensItlve to the mtrtnsic VISCOSIty of the po- 179.Iymer and the capillary diameter. Hence, the corre- 12 Zieminski, Kenneth F Spruiell & Joseph E, J Appl Polymsponding data has not been included. Obviously, Sci, 35(8)(1988) 1119. .they do not affect the cooling rate of the filament. 13 George~H,Po!ymEngScI,22(1982)291. ..

14 Nadkarni V M, In Man-made fibres: productIon, processing,4.4 Comparison or On-line Measurements with Simulated structure, properties and applications, Vol. 1, edited by V 8

Data Gupta & V K Kothari (Department of Textile Technology,lIT, New Delhi) 1988, 15.

4.4.1 Temperature 15 Collan L, The numerical treatment of differential equationsThe temperature was measured using an infrared (Sp~ger-Verlag, New York) 1966,95.

camera (AGA Thermovision) as explained in sec- 16 Fibre and yam processing, Appl Polym Symp, (25) (1975)

tion 3.3. Fig. 15 shows the data obtained by mea- 17 ~1.surements and the simulated profile. The match is utta A & Nadkarni V~, Text Res J,54 (1984) 35.

..18 ShenoyAV&NadkarntVM,TextResJ,54(1984)165.not very good s~ce the sln1~lated data was for a 19 Shenoy A V & Nadkarni V M. Fibre World, Sep. 1985.52-monofilament while the expenmental data was tak- 58.

153