Polymers for Fibers and Elastomers - American Chemical Society

23 M o d e l i n g the M e l t S p i n n i n g Process HENRY H. GEORGE

Downloaded by FUDAN UNIV on December 14, 2016 | http://pubs.acs.org Publication Date: August 29, 1984 | doi: 10.1021/bk-1984-0260.ch023

Celanese Research Company, Summit NJ 07901 Melt spinning is, today, a major commercial process for the formation of synthetic fibers. Two of the major commercial fibers, nylon and polyester (PET), are produced by melt spinning. During the late 1950's and early 1960's, the mathematical modeling of melt spinning began to develop. This early activity is summarized by Ziabicki(1). Since then, there have been numerous models published until today we have models that can predict spun yarn physical properties from a knowledge of the process conditions and polymer properties, dynamic models that predict spin-line stability and simulate the effects of process disturbances. A typical melt spinning process is shown in Figure 1. The key features are a source of molten polymer, in this case, from an extruder, a metering pump, and a spin pack that contains the spinneret and filter media. The spinneret is, in effect, a plate with a number of holes, one for each filament. The number can range from one to several thousand, and their diameter is typically of the order of tens of thousandths of an inch.There is a considerable body of technology extant dealing with the design and construction of spinnerets. When the polymeric filament leaves the spinneret, it enters a gaseous environment that is usually air at a temperature below the melting point of the polymer. The spin line generally contacts some guide surface before going onto the godet rolls which control the linear velocity of the process. The temperature of the spin line must be below its melting point before touching any surface. The linear density or denier (grams/9000 meters) is positively controlled by the metering pump and the godet rolls. On the other hand, the denier of the individual filaments is determined by the hydraulic split between the individual holes in the spinneret, which points up the need for precise control of the hole diameter and entry shape. There are many objectives in modeling the melt spinning process; the three most pertinent are: - Relating spun yarn properties to process variables. - Evaluating process uniformity and robustness. - Process stability. 0097-6156/84/0260-0355S06.00/0 © 1984 American Chemical Society

Arthur et al.; Polymers for Fibers and Elastomers ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

356

POLYMERS FOR FIBERS AND ELASTOMERS


The triangle shown in Figure 2 shows the i n t e r r e l a t i o n between the process, the structure of the resulting product, and physical properties. In a modeling s i t u a t i o n , one generally starts with a knowledge of the process conditions from which i t is desired to determine structural and physical properties. A studyU) of s p i n ning Poly(ethylene terephthalate) (PET) w i l l be discussed where i t was possible to use a model to calculate the stress at the s o l i d i f i cation point, and then relate this to spun yarn t e n s i l e properties. In a typical commercial spinning s i t u a t i o n , there can be hundreds of filaments which experience s l i g h t l y different h i s t o r i e s as they proceed from the spinneret to the godet. A model can be useful in determining the product differences that r e s u l t . A successful process should be insensitive to minor fluctuations in the operating conditions to avoid excessive defective product. A model can be used to estimate this robustness of the process. In any of the situations mentioned above, the model can be used i t e r a t i v e l y to help determine an optimum set of operating conditions. The question of s p i n - l i n e s t a b i l i t y is an important one, and there is considerable l i t e r a t u r e in t h i s area, but i t is beyond the scope of t h i s presentation. In most models, the calculations deal with the filament from the moment i t leaves the spinneret until i t reaches a guide surface. Figure 3 shows schematically in some detail what is involved in the model of a single filament. Polymer exits from the spinneret at X = 0 at a temperature above i t s melting point, and immediately swells to some extent as i t undergoes e l a s t i c recovery from the recent deformation history experienced in the spinneret hole and entry. It also is now exposed to a quenching or cooling gas, t y p i c a l l y a i r , which is usually blown perpendicular to the spin l i n e . In the past, when spinning speeds were r e l a t i v e l y slow (500-1000 meters/min), the c r o s s - v e l o c i t y component increased the overall heat transfer c o e f f i cient. At the higher take-up v e l o c i t i e s in current use, the effect on the heat transfer is f a i r l y small, and the most important effect of the cross-flow of a i r i s to provide aerodynamic s t a b i l i t y to the spin l i n e . Another result of the cross-flow v e l o c i t y is to bend spin line at a slope, S. The spin line i s accelerating a l l the way down to the freeze point where i t reaches i t s s o l i d i f i c a t i o n temperature and the velocity of the godet or other take-up device. Published s p i n - l i n e models are generally phenomenological, r e l y ing on correlations only for such engineering parameters as heat transfer and aerodynamic drag c o e f f i c i e n t s . In general, they a l l make recourse to equations of continuity; conservation of mass, force, and energy; and a constitutive equation for the polymer. In order to have a tractable set of equations, some assumptions are usually made, either of mathematical necessity or for convenience and conservation of computing resources. The assumptions shown in Table 1 are from George's(2) work, and are f a i r l y t y p i c a l . The f i r s t two reduce the equations from second-order p a r t i a l d i f f e r e n t i a l to f i r s t - o r d e r ordinary d i f f e r e n -


GEORGE

Modeling the Melt Spinning Process

POLYMER

EXTRUDER

0

METERING PUMP SPIN PACK


QUENCH AIR SOURCE

LUBE APPLICATORGODET ROLLS TO WIND-UP OR FURTHER PROCESSING

Figure 1 Schematic View of Melt Spinning Process Reproduced with permission from Ref. 2. Copyright 1982

PROCESS

PROPERTIES

STRUCTURE Figure 2 Process/Property/Structure Interrelation Reproduced with permission from Ref. 2. Copyright 1982




Table 1 STEADY MAJOR •

STATE

MODEL

ASSUMPTIONS

NO RADIAL T E M P E R A T U R E GRADIENT NO

A X I A L CONDUCTION

•

EXTENSIONAL VISCOSITY « 3 x SHEAR VISCOSITY

•

ELASTIC E F F E C T S A R E NEGLIGIBLE

•

S U R F A C E TENSION E F F E C T S A R E NEGLIGIBLE

•

CRYSTALLIZATION E F F E C T S (THERMAL & RHEOLOGICAL) ARE NEGLECTED



23.

GEORGE

359


t i a l ones. The radial gradient assumption is v a l i d , except at very high speeds, as has been shown by Knox and Frankfort(3). The assumption of a Troutonian type extensional v i s c o s i t y was made in the absence of any data and the generally recognized d i f f i c u l t y in measuring i t . Assuming no e l a s t i c effects allows the use of a powerlaw type constitutive equation, which again simplifies the mathematics; and, based on the shear v i s c o s i t y data a v a i l a b l e ^ ) , is quite reasonable for PET. The inclusion of a Barris effect at the top of the spin line takes into account the e l a s t i c effects experienced in the spinneret where the deformation rates are about an order of magnitude larger than experienced in the draw-down region of the spin line. Surface tension effects are negligible for polymers with t h e i r high v i s c o s i t y . Surface tension must be considered in glass s p i n ning. The c r y s t a l l i z a t i o n assumption is made because we don't know how to deal with i t in a non-isothermal, transient stress s i t u a t i o n . Fortunately, for many commercially important polymers, c r y s t a l l i z a tion is not encountered at normal process conditions. This is true for PET, through i t will c r y s t a l l i z e at high speeds( 5

The system of equations shown in Figure 4 are Georgev ), except for the addition of the s p i n - l i n e terms, S, the slope of the spin l i n e with respect to the and Y, the distance from the v e r t i c a l axis through the hole. Both these terms are i l l u s t r a t e d in Figure 3. 2

those of deflection vertical, spinneret

An important step in any model development process is validation or confidence building. As a f i r s t step, one attempts to predict some of the primal properties; in t h i s case, v e l o c i t y and temperature p r o f i l e s with respect to p o s i t i o n . Figure 5 compares experimental and calculated v e l o c i t y p r o f i l e s . The agreement is good in general, though the 3000 meter/minute profiles do show a substantial d i f f e r ence. These data can be brought into line by increasing the heattransfer coefficient by about 25% at the expense of the low-velocity data. Gagan and Dennw) have analyzed the same data using more complex constitutive equations to r e f l e c t some e l a s t i c i t y . They show that, with the more complex constitutive equations, they can achieve a better f i t . However, considering the imprecise nature of the heat transfer and e l a s t i c i t y data, i t is not clear which situation is correct. The temperature profiles shown in Figure 6 show excellent agreement and i l l u s t r a t e the fact that, at a constant flow rate, the take-up v e l o c i t y has v i r t u a l l y no effect on the temperature p r o f i l e . The model predicts a very weak dependence of temperature with v e l o c i ty. This observation was found to be most useful in some studies of high-speed spinningw). H i s t o r i c a l l y , temperature and v e l o c i t y profiles have been shown as functions of p o s i t i o n , as in Figures 5 and 6. It is instructive to plot these profiles as functions of time, as in Figures 7 and 8. From t h i s type of plot, we gain a sense of the time involved and the magnitude of the rates of change. The time plotted in these two figures starts at the instant an element of polymer leaves the s p i n neret hole and ends when the freeze point is reached. Typically, t h i s t r a n s i t time is a few hundred milliseconds but, as can be seen




360

Figure

4

Steady State Spinline Model Equations

0.675 IV PET 2.5 gm/min/hole 0.025 cm CAPILLARY DIA.

0

Figure

5

20

40 60 80 100 120 140 DISTANCE FROM SPINNERET, cm

160

Comparison of Calculated and Measured Spinline Velocity Profiles Reproduced with permission from Ref. 2.

Copyright 1982.


23.


GEORGE

361


0.675 IV PET 2.5 gm/min/hole 0.025 cm CAPILLARY O 3000 meters/min. A 2000 • 1000

20

Figure

40 60 80 100 120 DISTANCE FROM SPINNERET, cm

140

160

Comparison of Calculated and Measured Spinline Temperature

6

Profiles

Reproduced with permission from Ref. 2.

Copyright 1982.

3000 0.67 IV PET SPINNERET DIA. 0.010 in. 8.6 DPf TAKE-UP VELOCITY 3000 m/min SPIN TEMP. 310°C 6 2000 E

u

0 _J UJ

> UJ

z 1

IOOO-

0.1

Figure

0.2 0.3 TIME (Seconds)

0.4

0.5

7 Calculated Spinline Velocity as a Function of Residence Time


362


here, most of the deformation and cooling occur over a much shorter period of time and near the end of the time i n t e r v a l . In other words, the polymer spends most of the time in a hot, slow-moving state.


In

some

early

models

(8,9).

i t was further assumed that the s p i n - l i n e tension was constant along i t s length. This is approximately correct at low speeds, but is seriously in error at the higher speeds in use today. For example, spinning PET at 3000 meters/min. is i l l u s t r a t e d in Figures 9 and 10. In the f i r s t figure, the veloci t y and temperature profiles are compared and, while different, do not suggest any profound differences. However, in Figure 10, a comparison of the stress profiles shows a difference in the stress at the freeze point of about 70%. This terminal stress is one of the most important properties that models of t h i s type can compute, because i t is the key property that enables us to estimate structural and, f i n a l l y , physical properties of the spun yarn. In Figure 11, the calculated stress at the freeze point is p l o t ted versus the measured birefringence of as-spun fibers for several IV levels of PET. The three lines represent various other workers' measurements of the s t r e s s - o p t i c a l coefficient by various techniques, and are a l l in excellent agreement with the model c a l c u l a t i o n s . This plot demonstrates the bridge between process conditions and polymer properties and developed structure as measured by birefringence. It is interesting to note that this curve is e s s e n t i a l l y linear over the entire range of experimental conditions in spite of the fact that s p i n - l i n e c r y s t a l l i z a t i o n begins to occur at a s p i n - l i n e stress of about 0.08 grams per denier(^). The f i n a l link in getting from predeterminate operating conditions to spun yarn physical properties is presented in Figures 12, 13, and 14, which show the correlations between tenacity, elongation to break, and i n i t i a l modulus as a function of birefringence for PET. With this link established, we are now in a position to deal with more r e a l i s t i c situations involving multifilament spinning and trying to minimize the filament to filament differences that occur in a spinning process. Looking back to Figure 1, i t can be seen that the quench a i r blows across the spin line in such a way that some filaments are upstream of others. The upstream filaments are quenched by fresh a i r that is heated as i t cools the filament. Consequently, the next f i l ament i s cooled by s l i g h t l y warmer a i r and i s , therefore, produced by a s l i g h t l y different process. In a case where the filament count i s high, the a i r can pass through many rows of filaments. In m u l t i f i l a ment spinning, one also has to become concerned with the tendency of the filaments to pump a i r down the spinway which alters the a i r v e l o c i t y and convects heat downward. Matsuo, et. al (14) have published a methodology for dealing with multifilament problems, including a i r heating and pumping, in which they solve for the conditions of the upstream filament and calculate the temperature and flow rate of a i r leaving the filament



23.

GEORGE


I 0

i 0.1

l 0.2

363

i 0.3

1 0.5

1

0.4

TIME (Seconds)

Figure

8

Calculated Spinline Temperature as a Function of Residence Time

I

1 1 1 TUS = 3000 m/m DPF = 5.0 CAPILLARY DIA. =0.04 cm

1

1

DISTANCE FROM SPINNERET, cm

Figure

9

Comparison of Constant and Variable Tension Models; Velocity and Temperature


Copyright 1982.




364

0.04

20 40 60 80 100 DISTANCE FROM SPINNERET, cm

Figure 10 Comparison of Constant and Variable Tension Models; Tension and Stress


Copyright 1982.

100 •

0 . 6 7 5 IV

o 0 . 7 4 5 IV

o

a 0 . 9 1 0 IV 80 HAMANA, et.ol.

©

GARG-SHRINKAGE FORCE 'INNOCK 8 WARD LGARG- ON-LINE AT FREEZE POINT

60

o z

©

UJ

QC m 40 o

UJ

cr Z>

2 ^

^cP


AO

J 6

*7

8

J 20 30 BIREFRIGENCE, A n x 1 0

L 9 10

I 40

I 50

I 60

I L 70 80

3

Figure 12 Spun Yarn Tenacity as a Function of Spun Yarn Birefringence

Reproduced with permission from Ref. 2. Copyright 1982.

500r-

2

400

• • o o

or CD

£

• 0.675 IV O 0.745 IV A 0.910 IV

300

z

g o 200 o -j LU

100

J 2

3

4

5

6 7 8 910

15

20

BIREFRINGENCE, A n x 1 0

30

40

50 60 70 80 100

3

Figure 13 Spun Yarn Elongation as a Function of Spun Yarn Birefringence

Reproduced with permission from Ref. 2. Copyright 1982.


366



which, in turn, become process conditions for the next filament. Their approach is shown schematically in Figure 15. The extent of t h i s upstream/downstream effect is shown graphically in Figure 16, which deals with a case where there were 7 rows of filaments. The cross-sectional area p r o f i l e shows some deviation along i t s length, but f i n a l l y reaches the same value as would be expected from the material balance. The tension (or stress) at the freeze point is different; consequently, the properties w i l l be different. The real u t i l i t y of the model in t h i s situation i s that a number of approaches to reducing the spread in stress can be evaluated quickly and cheapl y , and only the most promising pursued in the p i l o t plant. Also, the use of these models allows one to t r y solutions that would not be evaluated in the p i l o t plant due to cost or low likelihood of success. Matsuo, et. a l U 4 ) also published an interesting table (Figure 17) that relates several commonly observed spinning i n s t a b i l i t i e s which should be useful to any spinner. In their paper, they are not clear how t h i s table was developed, but i t i s interesting to note that they show the relevant calculable variables. It is not unreasonable that one can obtain s t a b i l i t y information from a steady-state model. For example, Kase(^) develops a linearized transient model which can be expressed in terms of time and position-dependent deviation variables and position-dependent but time-independent parameters derived from the steady-state solution. Thus, the s t a b i l i t y of the system of deviation equations is determined solely by the values of functions of the steady-state solution only.

The objective of this review has been to provide an insight into the considerations involved in constructing s p i n - l i n e models and some of the ways in which they can be used. Like any area, the task is never complete and the development is continuing. There are many areas in which the models can be improved and made more useful. Some of the main areas that need attention: -

Development models that handle radial temperature g r a d i ents. With the ever-increasing a v a i l a b i l i t y of computing resources, this should not be too formidable a challenge.

-

Continue work on transient models.

-

Develop models that deal with s p i n - l i n e c r y s t a l l i z a t i o n .


23.

367


GEORGE

o f t .0 o

v4'

JD 4

CO


=J o o

00

3

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Polymers for Fibers and Elastomers - American Chemical Society

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