Comparison of experimental and analytical vibration welding meltdown-time profiles for nylon 66 and polypropylene

Comparison of Experimental and Analytical VibrationWelding Meltdown-Time Profiles for Nylon 66 andPolypropylene

P.J. Bates, J. MacDonaldRoyal Military College of Canada, P.O. Box 17000 Stn Forces, Kingston, Ontario K7K 7B4, Canada

V. SidiropoulosCentre for Automotive Materials and Manufacturing, 945 Princess St., Kingston, Ontario K7L 5L9, Canada

M. KontopoulouQueen’s University, Kingston, Ontario K7L 3N6, Canada

This work presents experimental meltdown-time profilesfor nylon 66 and polypropylene and compares them withpredictions obtained by applying the analytical modeldeveloped by Stokes [11] . A methodology is presentedfor obtaining approximate estimates of shear rates andtemperatures developed within the molten polymer dur-ing the process. Use of the corresponding melt viscosityvalues as inputs in the model yielded good agreementbetween experimental data and model predictions. Pre-dictions of melt film thicknesses, maximum melt tem-peratures, and shear rates are also presented. POLYM.ENG. SCI., 45:789–797, 2005. © 2005 Society of Plastics Engi-neers

INTRODUCTION

Vibration welding is a common technique for joininginjection-molded thermoplastic parts. Examples of automo-tive components assembled using this technique include airintake manifolds and resonators. The mechanical propertiesand microstructure of the welded parts are related to theend-use performance of the parts and have been the focus ofmany studies [1–9]. However, meltdown-time profiles,which can be measured continuously during welding andcan provide useful information about the process, have notbeen studied as extensively [10–12].

The purpose of this study was to measure meltdown-timeprofiles of butt-welded plates made of two thermoplastics of

industrial interest, nylon 66 and polypropylene, over a rangeof weld pressures and to compare them with Stokes’ ana-lytical model [11]. A methodology is proposed for theestimation of appropriate shear rates and temperatures thatdevelop inside the melt, which are then used to obtain asuitable viscosity input to the model. The model was furtheremployed to estimate several other useful process parame-ters, such as molten film thickness.

BACKGROUND

The vibration welding process involves bringing twoparts together under pressure (Fig. 1). One of the parts isthen vibrated in the y-direction at a frequency on the orderof 200 Hz over amplitudes on the order of 1 mm.

Stokes [10, 11] divided the vibration welding processinto a series of phases. In Phase I, Coulomb friction heatsthe solid interface from ambient to the polymer meltingtemperature. In the transitory Phase II, energy is generatedby viscous dissipation in the thin melt film created duringPhase I. At this stage, the film thickness is small and the rateof energy generation is therefore high. The thickness of thefilm thus increases until the rate of melting equals the rate atwhich polymer is squeezed from the film. The molten poly-mer is forced from the film primarily in the x-direction asthe two parts come together (meltdown). In Phase III, thefilm thickness and the meltdown rate remain constant.When a preset meltdown distance is reached, the vibrationis stopped and cooling begins. During the cooling, Phase IV,weld pressure is maintained and the melt film between thetwo plates starts to solidify. Some molten polymer issqueezed out of the melt film prior to solidification and thisis referred to as overshoot. A typical plot of the meltdown-time curve is shown in Fig. 2.

Correspondence to: P.J. Bates; e-mail: [email protected] grant sponsors: Queen’s Centre for Automotive Materials andManufacturing, AUTO21 Network of Centres of Excellence.DOI 10.1002/pen.20333Published online in Wiley InterScience (www.interscience.wiley.com).© 2005 Society of Plastics Engineers

POLYMER ENGINEERING AND SCIENCE—2005

For Phase I, Stokes assumed that each plate represents asemi-infinite body exposed to a constant heat flux resultingfrom frictionally dissipated energy at the weld interface. Hethen modeled the time required (t1) for the weld interface toreach the polymer melting temperature using:

t1 ��

� ��Tm � Ta�

2 f poNA � 2

(1)

where � is the polymer thermal diffusivity, � is the polymerthermal conductivity, Tm – Ta is the difference betweenambient and melting temperatures, f is the coefficient offriction, po is the weld pressure, A is the peak-to-peakamplitude, and N is the vibration frequency. Stokes com-pared the experimental values of t1 with those estimated forpolycarbonate (PC) for a range of Tm – Ta values, but the

agreement was unsatisfactory [11]. This was attributed tothe variations coefficient of friction during Phase I as wellas uncertainties in the estimation of the experimental t1.

Taking into account volume, force and energy balanceconsiderations, Stokes further developed expressions thatrelate the steady-state meltdown rate in Phase III (�̇) and thesteady-state thickness of the melt layer between the plates(ho), to measurable welding parameters, such as frequencyof vibration, N, amplitude, A, and weld pressure, po:

�̇2 �8��NA�3�pO �

b�8�� Cp�T1 � Ta��1.5 (2)

hO3 �

�b2�̇

pO(3)

where b is the part thickness, � is the polymer melt density, is the latent heat of melting, Cp is the polymer heatcapacity, � is the melt viscosity, Ta and T1 are the ambientand average melt temperatures, respectively. The meltdown(penetration) rate is related to the velocity of the two solidparts, �o according to:

�̇ � 2�O. (4)

Using experimental meltdown rate data and a range ofNewtonian viscosities for PC, Stokes estimated ho to be inthe 50–200 �m range. No attempt was made to estimatemeltdown rate from physical properties and welding param-eters.

These vibration welding models were further modifiedby Stokes [13] to model the spin-welding process. Usingdata from Crawford and Tam [14], Stokes estimated themelt film viscosity, temperature, and thickness as a functionof spin velocity and pressure. A more complex approachwas subsequently used by Stokes [15] to account for theshear thinning and temperature-dependent behavior of thepolymer melt and differences in physical properties betweenthe melt and solid phases during spin welding. A scalinganalysis was performed on the mass and energy balanceequations to yield a more simplified set of equations thatwas then solved using a finite element method.

An alternative approach is proposed here, whereby theanalytical vibration welding model first proposed by Stokesis used by taking into account the shear thinning and tem-perature-dependent viscosity behavior of polymers. Themeltdown rate estimations of this relatively simple modelare compared to experimental data obtained using poly-amide and polypropylene polymers. In addition, experimen-tally obtained times obtained during Phase I are comparedto model predictions.

MATERIALS AND CHARACTERIZATION

A general-purpose Nylon 66 polymer (Zytel 101) sup-plied by E.I. duPont and a 35 MFR polypropylene (PP1105)

FIG. 1. Schematic representation of the vibration butt-welding of twoplates. The white arrows represent force applied to create the clampingpressure. The two-headed black arrow represents the vibration direction.Axes are shown for reference.

FIG. 2. Schematic meltdown-time plot for vibration welding showing thefour phases of vibration welding.

790 POLYMER ENGINEERING AND SCIENCE—2005

from Exxon Mobil were used in this study. They are re-ferred to as PA and PP, respectively. The polymers wereinjection-molded into 3.2 � 100 � 133 mm plaques usingan Engel 55 ton injection molding machine. The plaqueswere edge gated on the 3.2 � 100 mm face creating apreferential molecular orientation in the part parallel to the133 mm dimension. After molding, all PA parts were vac-uum-sealed in aluminum-lined bags to minimize moisturepickup.

The rheological properties of the polymers were evalu-ated for PA using a Viscotech controlled stress rheometerby Reologica in the oscillatory mode using 20-mm parallelplates over a temperature range of 280–290°C. PP viscos-ities were measured using a Rosand RH2000 dual borecapillary rheometer in the range 180–200°C. Since it iscurrently impossible to obtain measurements of viscosity atthe shear rates encountered in vibration welding using con-ventional testing equipment, the data were fitted to thepower-law model, assuming an exponential temperaturedependence (Eq. 5), and viscosity values at higher shearrates were obtained by extrapolation:

� � mrefe�E�T�Tref��̇n�1 (5)

where mref is the consistency index at the reference temper-ature, n is the power law index, and E is a “temperaturesensitivity” factor. The fitted values of these parameters aresummarized in the Nomenclature section. The referencetemperatures, Tref, were 290°C for PA and 180°C for PP.Figure 3 shows the experimental viscosity data as a functionof shear rate and the power-law model fits at the referencetemperature for both polymers.

A TA Instruments 2010 differential scanning calorimeter(DSC) was used to measure the latent heat of melting of thepolymers () as well as their melting temperatures (Tm) at a

heating rate of 10°C/min. The resulting values are summa-rized in the Nomenclature section.

Equipment and Procedure

A butt-joint assembly was used in this work. Butt-jointsconsist of two identical plates welded together as shown inFig. 1. The plates were prepared by cutting the moldedplaques in half along the 133-mm melt flow direction. Theplates were oriented such that the 133 � 3.2 mm moldedsurface became the weld area. Welding occurred on moldedsurfaces to more adequately represent an industrial weldingprocess. Vibration was parallel to the 133-mm dimension.The fixture, which is described in detail in Ref. 8, allowedone part to vibrate at the prescribed frequency over thedesired amplitude while maintaining alignment with thesecond fixed part. Vibration welding was performed on aBranson Mini II linear vibration welder. The nominal weldpressure (net force at the weld divided by total weld area)was varied from 0.38 to 5 MPa in order to cover the rangeof weld pressures used industrially. The vibration frequencywas set at 210 Hz. This frequency represents the resonantfrequency of the welder and fixture. Most industrial ma-chines operate at the resonant frequency to minimize powerconsumption. The peak-to-peak amplitude was fixed at themaximum available amplitude, which was 1.78 mm.

The meltdown signal from the welder was recorded as afunction of time by a data acquisition system. The electricalcurrent consumption was also recorded in order to accu-rately determine the start and end of the welding cycle.

EXPERIMENTAL RESULTS AND MODELPREDICTIONS

Phase I

Typical meltdown-time profiles for PA and PP butt-welds are shown in Figs. 4 and 5, respectively. The profiles

FIG. 3. Experimentally measured viscosity vs. shear rate for PA 66(temperature 290°C) and PP (temperature 180°C). The solid lines repre-sents the Power-law model predictions for each polymer.

FIG. 4. Meltdown profile for PA butt welds at three different weldpressures.

POLYMER ENGINEERING AND SCIENCE—2005 791

obtained at pressures �1 MPa are similar to the represen-tative meltdown-time profile shown in Fig. 2. The presenceof two steady-state meltdown regions at pressures lowerthan 1 MPa may be attributed to poor mating between thetwo parts, resulting in the formation of a gap along themating surface, which is slowly filling with molten polymer.Under these conditions, substantial meltdown (Phase III)would take place only once the two parts come into perfectcontact with each other. Similar behavior has been observedon several other semi-crystalline and amorphous polymerswelded at low pressure [10].

Figure 6 summarizes the variation of the Phase I time (t1)as a function of weld pressure for welds made at pressuresabove 1 MPa and compares them with the predictions of Eq.1. A fitted value of f between 0.1 and 0.4 seems to offer thebest agreement between model and experiment. These are

reasonable values of the coefficient of friction and thereforetend to support the validity of this model.

Phase III

Figures 7 and 8 show the experimental steady statemeltdown rate (�̇) for butt welds as a function of weldpressure for PA and PP, respectively. The meltdown rateswere measured between 1 and 1.5 mm of meltdown for allruns. The experimental data show a relatively constantmeltdown rate of �0.6 and 0.4 mm/s over the range ofpressures examined for PA and PP, respectively. In order to

FIG. 5. Meltdown profile for PP butt welds at three different weldpressures.

FIG. 6. Predicted time (t1) for the end of Phase I (Eq. 1) as a function ofweld pressure (po) for two coefficients of friction. White diamonds repre-sent the experimental data for PA and black diamonds represent the datafor PP.

FIG. 7. Meltdown rate as a function of weld pressure for butt-welded PAplates. The solid curve represents model predictions. The dotted linesrepresent model predictions for three different constant Newtonian viscos-ities.

FIG. 8. Meltdown rate as a function of weld pressure for butt-welded PPplates. The solid curve represents model predictions. The dotted linesrepresent model predictions for three different constant Newtonian viscos-ities.


obtain insight on the effect of material properties, primarilyviscosity, on the process, the analytical model developed byStokes for Phase III was used to estimate the meltdown rateusing fixed welding parameters and known polymer prop-erties. Given the strong shear rate and temperature depen-dence of viscosity in polymer melts, the procedure outlinedbelow was followed in order to obtain estimates of the shearrates and temperatures encountered during vibration weld-ing.

Shear Rate Estimation

Assuming that the predominant shear deformations are inthe y-direction (�̇zy), due to the vibratory motion, and in thex-direction (�̇zx), due to flow of the molten polymer out ofthe melt film under the action of the weld pressure, the totalshear rate in the melt film (�̇) can be estimated using thesecond invariant of the rate-of-deformation tensor (D v� vT):

�̇ � �12

D:D � ��̇zx2 �̇zy

2 . (6)

The component �̇zy varies in the time domain throughout acycle, due to the oscillating motion of the upper vibratingplate. Nonhof et al. [12] estimated the average value of �̇zy

over one oscillation period as:

�̇zy �2NA

ho. (7)

Similarly, �̇zx varies with position x and z inside the meltfilm. However, based on Stokes’ analysis, the maximumvalue of �̇zx can be shown to be:

�̇zxMAX�

3�̇b

ho2 . (8)

As a first approximation, it is assumed that �̇zy is signifi-cantly higher than �̇zxMAX

2 , over the range of pressures stud-ied in this research, therefore �̇ � �̇zy. The validity of thisassumption will be discussed in Simulation Results (below).It is important to note that, based on Eq. 7, the shear rate canbe assumed to be constant throughout the melt for a givenvibration welding pressure; therefore, no shear rate-inducedviscosity variations would exist throughout the melt.

Estimation of Temperature

Heat generated in the melt film flows out by conductionin the x, y, or z directions or by convection with polymerleaving the melt film. From scaling considerations, conduc-tion in the x or y directions can be neglected [15]. As a firstapproximation, convective losses are assumed to be smalland are neglected. The implications of this assumption willbe discussed further in the Results section.

It can therefore be assumed that the temperature distri-bution is similar to that observed in simple shear flowbetween two parallel plates. Such a system consists of amoving boundary (the vibrating upper part) and a stationaryboundary (the lower part), both of which are at the polymermelting temperature (Tm). The heat generated by viscousdissipation in the melt film is thermally conducted towardsthe two boundaries. It can be shown [16] that the maximumtemperature in the center of the melt film (Tmax) understeady simple shear can be approximated by:

Tmax � Tm ��̇2ho

2

8�. (9)

The average melt temperature in the film (T1) will bebetween Tmax and Tm. As a first approximation, it is assumedthat:

T1 �Tm Tmax

2. (10)

The shear rate estimated from Eq. 7 and the average melttemperature from Eq. 10 can be used to calculate the meltviscosity, using Eq. 5, which is then substituted into Eqs.2–4.

Physical Properties

The differences between melt (�) and solid (�S) densitiesof the polymer must also be considered. Recall that themeltdown rate (�̇) in Eq. 2 was obtained by doubling themelt velocity (�o) off each of the solid faces contacting themolten weld layer (Eq. 4). The meltdown rate measuredexperimentally, however, is based on the velocity of the twosolid parts. By considering conservation of mass for thepolymer entering the molten zone:

�o,solid � vo,melt

�

�S. (11)

Simulation Results

Using the physical property values provided in the No-menclature section, Eqs. 2–11 can be solved simultaneouslyto yield estimates of �̇, �, �̇, ho, Tmax, and T1. The modelestimations of these quantities are given in Tables 1 and 2.

Figures 7 and 8 show the calculated meltdown (solidcurve) and the experimental values as a function of pressurefor PA and PP, respectively. Given the underlying simpli-fications involved in this simulation, the agreement betweenexperimental data and model is judged to be adequate. ThePA model estimates are within 25% of the experimentaldata. The PP data are overestimated by 30–50%. Thesediscrepancies are partly due to the inherent simplificationsin the model and also to uncertainties in the estimation of


melt viscosity at the high shear rates encountered in vibra-tion welding. From Tables 1 and 2 it is noted that theseshear rates are on the order of 10,000–30,000 s–1. It isimpossible to accurately measure viscosities at these highshear rates due to slip effects in capillary rheometers. Inaddition, elastic effects may be present at these high vibra-tion frequencies. Although this phenomenon is complex andthe subject of current research, it could cause deviationsfrom the simple viscous behavior assumed here. In order toassess the effect of changes in viscosity on meltdown rate,a sensitivity study is also shown in Figs. 7 and 8. Thedashed curves in these figures show the model results usinga series of Newtonian viscosities, fixed at a constant valuefor the entire pressure range. As expected from Eq. 2,changes in viscosity have a large effect on the predictedmeltdown rates. This confirms the need for reasonable es-timations of shear-rate and temperature in order to modelthis type of process.

It is instructive to examine the differences between theconstant Newtonian viscosity curves and the experimentaldata for each polymer. For PP, the fit between the constant10 Pa.s curve and the experimental data is good at lowpressures but deviates significantly at higher pressures. Thereason for this discrepancy is the decrease in viscosityassociated with the higher shear rates caused by the highpressure welding conditions (see Table 2). This effect is alsoobserved for PA but to a lesser degree because its power-law index is close to unity, as shown in Table 1.

It is also interesting to note that PP has a lower experi-mental meltdown rate than PA in spite of its lower meltingpoint, lower density, and lower latent heat. The reason forthe lower meltdown rate would therefore appear to beviscosity. The results would suggest that, under vibrationwelding conditions, PP must exhibit lower viscosity that PA

because it is more shear thinning, and therefore dissipatesless viscous energy. This is confirmed by the model thatestimates PA viscosities in the range of 29–32 Pa.s and PPviscosities in the range 11–20 Pa.s.

Figures 9 and 10 show the estimated thickness of themelt film (ho) as a function of pressure for PA and PP,respectively. Again, the model predictions using a constantNewtonian viscosity are shown for each polymer usingdashed curves. It is observed that ho decreases with increas-ing pressure and is 30–60 �m for PA and 30–70 �m forPP. Although it is impossible to obtain experimental esti-mations of ho, it should be noted that this result is consistentwith observations of the heat-affected-zone (HAZ) of PA.Mah and colleagues [7] showed that the thickness of theHAZ decreased with increasing weld pressure and was onthe order of 50 �m. The HAZ thickness and ho are on thesame order of magnitude, as expected. However, it must benoted that the HAZ thickness represents the thickness of thenon-spherulitic region made on a completely solidified sam-ple and, although related, the two thicknesses are not di-rectly comparable.

It is important to test the hypothesis relating the relativemagnitude of �̇zy and �̇zxMAX

. Figure 11 shows the plot of �̇zy

TABLE 1. Model results for PA.

Parameter

Weld pressure (MPa)

0.5 1 2 3 4 5

�̇ (s�1) 11,500 13,900 16,800 18,800 20,300 21,600Tmax � Tm (°C) 5.6 5.5 5.3 5.2 5.2 5.1� (Pa � s) 32.1 31.2 30.4 29.8 29.5 29.2�̇ (mm/s) 0.39 0.46 0.54 0.59 0.63 0.67ho (�m) 65 54 44 40 37 35

TABLE 2. Model results for PP.

Parameter

Weld pressure (MPa)

0.3 1 2.3 4.8

�̇ (s�1) 10,500 15,900 21,300 27,500Tmax � Tm (°C) 10.8 8.6 7.3 6.4� (Pa � s) 20.1 16.0 13.7 11.8�̇ (mm/s) 0.46 0.56 0.63 0.71ho (�m) 71 47 35 27

FIG. 9. Estimated thickness of the nylon 66 molten film as a function ofweld pressure for the shear thinning model with temperature dependencyterm (solid line) and for a constant Newtonian viscosity (dotted line).


and �̇zxMAXas a function of weld pressure for PA. Similar

results were observed for PP. Over the range of pressuresstudied in this research, �̇zy is always larger than �̇zxMAX

, thusjustifying the use of �̇zy to estimate �̇. However, this assump-tion should be viewed with caution as pressure increases be-yond 5 MPa. As pressure increases, the shear rate wouldincrease above that estimated here. This would lower viscosityand cause a leveling off of meltdown rate-pressure curve. Inorder to account for the effect of �̇zx on melt viscosity, a morecomplex analysis is required such as that used by Stokes [15]or using computational fluid dynamics (CFD) [17].

Tables 1 and 2 show the difference between the max-imum temperature (Tmax) and the polymer melt temper-ature (Tm) estimated by the analytical model for PA andPP. It can be seen that Tmax was �5–10°C above Tm forboth polymers for all conditions. The maximum melttemperature was a stronger function of weld pressure forPP than PA. Equations 7 and 9 shed some light onto thissmall temperature increase. In this simulation, the shearrate (�̇) and melt film thickness (ho) are inversely relatedvia Eq. 7. Their effects in Eq. 9 then cancel each otherout, leaving viscosity (�) and thermal conductivity (�) asthe only remaining terms. As pressure goes up, the shearrate increases, causing a decrease in viscosity and adecrease in maximum temperature. The PA viscositydecrease is small because its viscosity is a relativelyweak function of shear rate—its power law index is closeto unity. The viscosity of PP has a stronger shear ratedependency, and therefore changes more drastically withweld pressure, due to increasing shear rate. This smallincrease in melt temperature above the melting point isconsistent with temperature measurements made by in-serting a very thin (25 �m diameter) thermocouple intothe molten weld zone [18]. However, it is significantlyless than the 80°C suggested by Kagan [19] based oninfrared camera measurements. Difficulties in estimatingthe melt emissivity may have been the cause of the highinfrared temperature measurement in that work.

These temperature estimations would suggest that theconvection effects are not large. Convection would decreasethe average temperature below the levels estimated in themodel. Given the current estimations that are only 5–10°Cabove the melting point, the effect of convection is mostlikely significantly smaller than conduction in the z-direc-tion.

FIG. 10. Estimated thickness of the polypropylene molten film as afunction of weld pressure for the shear thinning model with temperaturedependency term (solid line) and for a constant Newtonian viscosity(dotted line).

FIG. 11. Shear rates as a function of pressure in a butt-weld geometry for nylon 66.


CONCLUSIONS

Vibration welding meltdown-time measurements werecarried out using nylon 66 and polypropylene homopoly-mer. Simple analytical models adequately predict the dura-tion of Phase I for pressures larger than 1 MPa. For lowpressures, a second steady-state meltdown region was ob-served. This may be attributed to poor mating of the partsunder low pressures.

In Phase III of vibration welding, the analytical modelsdeveloped by Stokes were used by taking into accountdependency of viscosity on shear rate and temperature.These models were used to adequately model the meltdownrate of nylon 66 and polypropylene. The model predictsmelt film of thicknesses ranging from 30–70 �m and max-imum melt film temperatures of �5–10°C above the poly-mer’s crystalline melting point.

The biggest drawback of this analytical model is itsinability to account for the shear rate contribution from flowout of the melt film, which affects temperature and viscosityestimations. CFD work is required to account for theseeffects.

ACKNOWLEDGMENTS

The PA material and molding were provided by E.I.duPont. The authors thank Mr. Helmut Wieland for the

design and construction of the tooling fixtures and Mr.Eudes Lebaut and Ms. Chelsea Braybrook for generating thePP data.

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NOMENCLATURE

Symbol Description PA PP Comments

A Peak-to-peak amplitude mm 1.78 Welder parameterb Plate thickness mm 3.2 Measured on plateCp Polymer heat capacity J/kg °C 2800 2800 Refs. 20, 21E Temperature sensitivity factor °C�1 0.02 0.02 Fitted parameterf Coefficient of friction 0.1–0.4 Fitted parameterho Thickness of the melt mm — Equation 3N Vibration frequency Hz 210 Welder parametern Power law index 0.84 0.33 Fitted parameterpO Weld pressure MPa 0.4–4.6 Welder parametert1 Total time required for Phase I s — Equation 1Ta Ambient temperature °C 22°C MeasuredTm Melting temperature °C 261 164 Tm

Tmax Maximum melt temperature °C — Equation 13Tref Reference temperature °C 290 180 MeasuredT1 Melt temperature °C — Equation 14�o Melt velocity m/s —�̇ Shear rate, s�1 — Equation 9�̇ Steady state meltdown rate Phase III, mm/s — Equation 2� Polymer thermal conductivity W/m/°C 0.4 0.13 Refs. 18, 22 Polymer latent heat of melting J/g 105 68.2 Measured� Melt viscosity Pa � s — Equation 4mref Power-law consistency index at Tref Pa � s 85 4300 Fitted parameter� Density at melting temperature kg/m3 1000 700 Refs. 23, 22�s Density at ambient temperature kg/m3 1120 900 Refs. 23, 22


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Documents

Comparison of experimental and analytical vibration welding meltdown-time profiles for nylon 66 and polypropylene