On-line Measurement of Fiber Motion During Melt Blowing - Industrial

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On-line Measurement of Fiber Motion During Melt Blowing Jessica H. Beard, Robert L. Shambaugh,* Brent R. Shambaugh, and David W. Schmidtke School of Chemical, Biological, and Materials Engineering, UniVersity of Oklahoma, Norman, Oklahoma 73019

A high-speed camera was used to record the motion of a fiber below both a melt-blowing slot die and a melt-blowing swirl die. These recorded images were processed to determine the frequency and amplitude of fiber motion during melt blowing. The operating variables investigated included polymer flow rate, air flow rate, polymer temperature, and air temperature. A crossover counting method was developed to determine the frequency of fiber motion. The frequencies determined from this counting method favorably compared with frequencies determined by taking fast Fourier transforms of the fiber displacement data. Experimental results for frequency and amplitude were compared to predictions from a three-dimensional mathematical model for the melt-blowing process. 1. Introduction Melt blowing is a rapid, one-step process used to produce fine polymer fibers. These fibers are used in a variety of commercial uses such as filtration, sorbent material, and insulation. In melt blowing, an extruded polymer strand is rapidly attenuated by the impaction of high-velocity gas onto the polymer stream. Fibers with diameters as small as 0.1 µm can be produced with this process; see the paper by Shambaugh.1 A schematic of the melt-blowing process is given in Figure 1. Fiber vibration frequency and amplitude are parameters of interest in the melt-blowing process. These parameters relate to the laydown pattern of the fibers, the fiber size that can be produced, the quantity of hot air needed to produce 1 kg of product, and many other technical and economic considerations in melt blowing. For example, a higher amplitude of vibration gives more overlap of adjacent fibers, which results in a more uniform laydown pattern of fibers. A higher frequency of vibration permits the line speed (laydown belt speed) to be increased without losing laydown quality. In general, higher air throughput causes both higher amplitude and smaller fiber diameter. Previous investigators have considered the parameters of vibration frequency and amplitude. For example, Wu and Shambaugh2 used laser Doppler velocimetry (LDV) to measure the cone diameters and maximum flux of fibers. In other experimental work, Chhabra and Shambaugh3 examined the effects on fiber motion of the four main melt-blowing operating parameters (polymer temperature, polymer flow rate, air temperature, and air flow rate). These experimental measurements paralleled the predictions of the 1-D, 2-D, and 3-D models for melt blowing that were developed, respectively, by Uyttendaele and Shambaugh,4 Rao and Shambaugh,5 and Marla and Shambaugh.6 Bresee and Ko7 took on-line pictures of fibers below a melt-blowing slot die. In this work, they used a high-speed (1000 frames/s) digital camera with pulsed-laser illumination. Fiber velocity and acceleration were obtained from analysis of triply exposed individual images taken at known time intervals. Our research involved measuring fiber vibration frequency and amplitude with a high-speed camera. The camera, with the capability of taking up to 150 000 frames/s, was used to record thousands of pictures of the fiber over small time steps. Analysis * To whom correspondence should be addressed. Tel.: (405) 3256070. Fax: (405) 325-5813. E-mail: [email protected].

Figure 1. Schematic of the melt-blowing process with a common slot die.

of this large data set permitted the determination of vibration frequency and amplitude. Both a melt-blowing slot die and a swirl nozzle were used to produce fibers for on-line recording of motion with the high-speed camera. Of particular interest is how our experimentally measured frequencies and amplitudes validate predictions from previously developed mathematical models. 2. High-Speed Camera and Analysis Procedure 2.1. Camera and Camera Control Software. A Redlake HS-4 high-speed video camera was used in our studies. This camera has the capability of recording images at a frame rate of 5 130 full frames/s or up to 150 000 partial frames/s. Full frames are recorded at a resolution of 512 × 512 pixels. In the limit of the maximum frame rate, the resolution is 16 × 512 pixels. Because 5 000 frames/s or less proved to be adequate (as will be discussed below) to record the fiber motion in our experiments, all of the data given below were recorded at a resolution of 512 × 512 pixels. A Nikon 105 mm macro lens was used in conjunction with the camera. This lens provided the camera with a 4.6° field of view in both the vertical and horizontal directions. Unless otherwise stated, the face of the lens was placed 30 cm away from the fiber that was being

10.1021/ie070588j CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007

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Figure 2. Procedure for acquisition and analysis using the Redlake HS-4 camera. The camera is controlled and images are obtained with a laptop computer using MotionPro Central Software. The images can then be converted to a QuickTime movie or analyzed in VideoPoint or MetaMorph. From there, the results are exported into Microsoft Excel.

observed. With this arrangement, the real image size was 2.4 cm × 2.4 cm. For controlling the camera functions and storing the images, MotionPro Central8 software was used. In MotionPro, the user can specify the frame rate, the exposure, the region of interest, and the recording time. See Figure 2 for a schematic of how the video images were acquired and analyzed. As the figure shows, control information is sent (Path 1) from the control computer (with MotionPro software installed) to the camera. Also, images acquired by the camera are sent to the control computer (Path 2). In order to determine fiber velocity, vibration frequency, and other parameters, further processing of the images is necessary. For this task, the two software options examined in our work were VideoPoint and MetaMorph. 2.2. VideoPoint Software. VideoPoint9 is a software package that can determine velocity, position, kinetic energy, momentum, and other dynamic characteristics of a moving object. In VideoPoint, the user can specify the desired number of points to observe per frame. A scale can also be set in VideoPoint in order to obtain measurements in actual linear units rather than in pixels. The user then advances one frame at a time while manually tracking the desired number of points. VideoPoint can then export the data into Microsoft Excel.10 VideoPoint is a very accurate way to analyze the acquired data. However, using the software is time-consuming when, as in our situation, thousands of frames must be analyzed. VideoPoint, as well as the above-mentioned control software (MotionPro), have limitations on what file types they can handle. For example, in order to analyze multiple frames in VideoPoint, the images acquired in MotionPro as .tif files must be converted to .mov files. Path 3 in Figure 2 shows this conversion. Once the files are converted to .mov files, they are sent (see Path 6) to VideoPoint. After this conversion, operator (human) interaction is required for looking at each individual frame. After

frame-by-frame analysis in VideoPoint, the data can be exported into Excel (see Path 9 in Figure 2). 2.3. MetaMorph. In order to speed up the process of analyzing the frames, MetaMorph software11 was selected to be used in conjunction with VideoPoint. Like VideoPoint, MetaMorph can determine the velocity, position, acceleration, and other dynamic parameters of an object. But, unlike VideoPoint, MetaMorph has automation capabilities. Specifically, MetaMorph allows the user to choose an area of interest (in this case, the fiber), and then the software can be set on “autopilot” such that the software will (in a batch-processing mode) track the object without further operator effort. MetaMorph can be directed to follow the brightest point at a certain vertical pixel value (i.e., the brightest point along a horizontal line). For our work with 512 × 512 images, we chose the horizontal line through the center of the image (i.e., the horizontal pixel line at 256). This software capability is ideal for our experiments because the fiber stands out as a bright image against a dark background. In short, the manual process used in VideoPoint was automated in MetaMorph. Another capability of MetaMorph is that it can open image sequences in the .tif format. Therefore, the image sequences obtained from MotionPro can be opened directly in MetaMorph as shown in Path 5 in Figure 2 (i.e., no file conversion is necessary, as is the case with VideoPoint). Hence, because of automation and file compatibility, MetaMorph can analyze 500 frames of our data in mere seconds. However, MetaMorph can only look at a certain range of intensities. Since the fiber moves in and out of focus, sometimes the intensity of light dips below what MetaMorph will accept, and MetaMorph loses track of the fiber. To overcome this limitation, there is an option in which the user can specify the location of the fiber when MetaMorph cannot. When MetaMorph cannot identify the location of the fiber, the automation stops, and the user manually redirects the area of interest within MetaMorph to be again on the fiber (i.e., the brightest part of the image). MetaMorph will then restart the automation from that point. The loss of the fiber can occur at any point in the data set. Fortunately, we found that MetaMorph lost the image only about once for every 1 000 frames. Thus, for our analysis, MetaMorph was able to analyze complete sets of data (6 000 frames) in just a few minutes. When all frames have been analyzed, MetaMorph can export data into Excel (see Path 10 of Figure 2). Although MetaMorph does have the capability to specify a scale, the MetaMorph data were acquired in pixels. The pixel-to-distance conversion was then completed in Excel. The initial location of the fiber (the brightest part of the frame along a horizontal line) was assigned the x-position of zero in MetaMorph. After the initial frame, MetaMorph returned pixel numbers. If the fiber moved to the left when looking at the x-axis, the pixels were considered negative, and if the fiber moved to the right, the pixels were considered positive. (Our view of the motion is in 2-D, in the x-z plane. However, as has been shown previously in experimental melt-blowing studies,3 the motion in the x-y plane is very similar, so our studies are representative of fiber amplitude and frequency in 3-D.) 2.4. Procedure for Acquisition and Analysis. Since there are benefits and drawbacks to both VideoPoint and MetaMorph software packages, a combination of the two was used in our experiments. Initially, the images were acquired from the Redlake HS-4 camera with MotionPro Central (Path 2 in Figure 2). From MotionPro, the images were converted to QuickTime movies (Path 3), opened as an image set in MetaMorph (Path 5), or opened as single images in VideoPoint (Path 4). We chose

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Figure 3. Melt-blowing equipment and the high-speed camera. The polymer fibers were collected on a screen located 30 cm below the die head. The camera was placed on a stand and connected to a laptop computer for realtime analysis and control.

to open the images as an image set in MetaMorph. A scale was set up in VideoPoint using only the first image in .tif format, and the fiber was marked in the first frame of every set of data. This was done in conjunction with work in MetaMorph (Paths 7 and 8). The fiber placement in the first frame was used as the starting point in MetaMorph. Since only one frame was used in VideoPoint, the data did not have to be converted to a QuickTime movie, so the process was sped up substantially. After using MetaMorph, the data were converted from pixels to position in Microsoft Excel (Path 10). 3. Experimental Details 3.1. Slot Die. A Brabender extruder with a diameter of 19.1 mm and a length of 381 mm was used in our experiments. The extruder barrel had an L/D of 20:1 and a compression ratio of 3:1. From the extruder, the polymer was fed into a modified Zenith pump. Then, the polymer was pumped into a singlehole melt-blowing slot die. The two air slots had widths of 0.65 mm, and the slots were set flush with the nosepiece (zero offset). Each slot had a length of 74.6 mm. The air flow was measured with a rotameter with a maximum capacity of 150 standard L/min (slpm). The fiber was collected on a screen located 30 cm below the die. Figure 3 shows a schematic of the extrusion equipment as well as the Redlake HS-4 camera and computer. For all of the slot die experiments, the slot die was viewed such that the slots were parallel to the axis of the camera lens. Slot dies with multiple polymer holes are used in industry. Our use of a single hole made the observation of vibration a tractable problem. Of course, there are interactions between filaments that are not accounted for in our work with a single-hole die. Our gas rates (in terms of slpm/(m of die length)) are at the low end of commercial production. However, these lower gas rates result in larger fibers, and larger fibers are easier to follow. The results can be extrapolated to higher gas rates. The polymer used was 88 MFR Fina Dypro isotactic polypropylene with an Mw ) 165 000 g/mol and a Mn ) 41 500 g/mol. The base operating conditions were a polymer flow rate (mp) of 1.00 g/min, an air flow rate (ma) of 50 slpm (standard L/min), a polymer temperature (Tf) of 310 °C, and an air temperature (Ta) of 368 °C. When taking pictures, the camera

was positioned at intervals of 2.5 cm along the fiber threadline. Specifically, the center of the camera’s vertical field of view was centered at z ) 2.5, 5.0, 7.5, ..., 20 cm. For our experiments, we used camera working distances (y positions) of 20-45 cm. We used closer distances near the die because the amplitude of fiber oscillations was smaller near the die (and, hence, the fiber stayed in the field of view of the lens). Farther away from the die, larger working distances were needed to keep the fiber within the field of view. In addition, the amplitude of fiber motion (and, hence, the required working distance) changed as a function of operating parameters such as polymer flow rate, etc. For example, at a distance of 2.5 cm below the die, a working distance of 30 cm was selected for a polymer flow rate of 1.00 g/min, an air temperature of 368 °C, a polymer temperature of 310 °C, and an air flow rate of 50 slpm. For a 30 cm working distance, the field of view was 24.1 mm x 24.1 mm, and each camera pixel corresponded to a 0.047 mm × 0.047 mm view of the real object. For all pictures, the f-stop on the Nikon lens was manually set at 4.5. In conjunction with this aperture setting, the frame interval was set (via MotionPro) at a value between 100 and 300 µs. Illumination of the fiber was provided by three light fixtures with 21.6 cm diameter reflectors and standard (tungsten) 100 W light bulbs that each produced 1 750 lumens. These three fixtures were placed at different positions around the threadline to give good illumination of the fiber. When the camera was repositioned in the z-direction, each of the three light fixtures was moved a corresponding amount in the z-direction. A frame rate of 5 000 frames/s was initially chosen; however, using this frame rate over a period of >1 s (of actual time) took a large amount (∼30-40 min for each frame set) of computer time to save on our control computer (a HewlettPackard laptop with a Pentium IV Processor). In order to reduce this time, we used VideoPoint to analyze data taken at frame rates of 500, 1 000, 2 000, and 5 000 frames/s (at 50 slpm gas flow rate). The minimum frame rate that still gave the same trend of fiber position was determined to be 2 000 frames/s. In addition to frame rate, we selected 3 s as a sufficient time over which to collect pictures. Thus, we had 6 000 frames in each data set for data collected at a 50 slpm air flow rate. For the experiments that were run at the higher air flow rate of 100 slpm, 2 000 frames/s was not sufficient for accurately tracking the fiber. (The fiber jumped large x-distances from one frame to another.) Therefore, in order to more accurately depict the fiber motion, a frame rate of 5 000 frames/s was used when the air flow rate was 100 slpm. For 100 slpm, the time for recording was again 3 s; this gave a data set with 15 000 frames. Figure 4a shows an actual frame taken by the Redlake camera during the operation of a slot die. Figure 4b is a sketch of the same frame. Figure 4b illustrates how, within the software programs of VideoPoint and MetaMorph, a horizontal line was drawn at the center of the frame (at a vertical pixel position of 256). Point “A” on the figure, a point at the center of the fiber, illustrates the point that was selected as the point to follow in successive frames in both VideoPoint and MetaMorph. In other words, we followed -x and +x motion at a constant z-position (see coordinate system in Figure 4b). 3.2. Swirl Die. The swirl die experiments were done with the same equipment as described above, with the exception that the slot die was replaced with the swirl die. The swirl die has six air-discharge holes; see Figure 5. Each of these air holes has a diameter of 0.46 mm. A circle drawn through the center of these six air holes has a diameter of 4.77 mm. The centerline of each of the air holes is at an angle


Figure 4. (a) Example of a fiber photograph taken by the Redlake HS-4 camera. This picture was recorded at 10 cm below the melt-blowing slot die. It was recorded at a frame rate of 2 000 frames/s. The operating conditions were a polymer flow rate of 1.00 g/min, an air flow rate of 50 slpm, a polymer temperature of 350 °C, and an air temperature of 368 °C. (b) An illustration of how the fiber in Figure 4a would appear in VideoPoint or MetaMorph. Point A indicates the center of the fiber on the 256 pixel line. If the fiber moves to the left, it moves in the -x direction, and if it moves to the right, it moves in the +x direction.

Figure 5. Schematic of the swirl die. The air outlets are at 60° relative to the die face and are canted at 10° relative to the polymer outlet. For further details, see paper by Marla and Shambaugh.6

of 60° relative to the die face. Also, each air hole is offset at an angle of 10° relative to the center hole of the die. This offset

Figure 6. (a) Photograph of a fiber produced by the swirl die. This is an example of a single frame acquired from the Redlake HS-4 camera. This image was taken at a polymer flow rate of 2.4 g/min, an air flow rate of 7.5 slpm, a polymer temperature of 310 °C, and an air temperature of 325 °C. This image was recorded at a z-distance of 5 cm below the die head at a frame rate of 2 000 frames/s. (b) An illustration of how the fiber in Figure 6a would appear in VideoPoint or MetaMorph. Point A indicates the center of the fiber on the 256 pixel line. If the fiber moves to the left, it moves in the -x direction, and if it moves to the right, it moves in the +x direction.

imparts a spiral motion to the polymer stream. The polymer capillary has a diameter of 2.1 mm. The base conditions used with the swirl die were as follows: polymer flow rate ) 2.4 g/min, air flow rate ) 7.5 slpm, Tf ) 310 °C, and Ta) 325 °C. As with the slot die, the camera was moved in 2.5 cm increments along the threadline (z ) 2.5 cm, 5 cm, etc.) until a position 20 cm below the die was reached. The lighting arrangement for the Redlake camera was also the same as that described above. A frame rate of 2 000 frames/s was again used. Initially, a recording time of 3 s was selected. However, it was determined that the frequency of fiber vibration and the amplitude of fiber vibration for the swirl nozzle could be accurately measured with a recording time of 1 s. The calculated frequency for any individual data set (both for 1 and 3 s) differed from the total average (over all sets) by no more than 5%, and there was no difference between the average frequency for 1 s compared to the average frequency for 3 s. Therefore, only 2 000 total frames (taken over 1 s) were analyzed for our swirl die experiments. Figure 6a shows an actual photograph taken by the Redlake camera during the operation of the swirl die. Figure 6b is a schematic of the frame in Figure 6a. Again, point “A” on the

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figure was the point tracked in successive frames. The movement of the fiber in the -x and +x direction was followed on successive frames on the horizontal line at 256 pixels, as was done previously with the slot die. 4. Results and Discussion 4.1. Slot Die. Each set of x-positions gathered from analysis in MetaMorph were graphed against time in order to determine the frequency of fiber motion. Often, the average fiber position was skewed either left or right of center in the photographic image. (Air currents or precession of the fiber motion could be the cause of this positioning of the fiber.) The data were normalized by taking the average of the x-positions over 3 s. This average was called the center, and the normalized xpositions were determined by subtracting this average from each individual value. One example of a normalized set of data is shown in Figure 7a. This data set shows the entire time span of 3 s. Figure 7b shows a smaller section of the normalized data. This section spans only 0.5 s from t ) 1 s until t ) 1.5 s. Finally, Figure 7c shows a span of 0.05 s from t ) 1.2 s until t ) 1.25 s. The individual data points are much more visible in the figures with expanded scales. Observe that enough data were taken such that there are not large jumps between the individual data points (i.e., the selected frame rate of 2 000 frames/s was adequate for the task). The frequency was determined in a manner similar to determining the frequency of a sine wave. See Figure 8, which is a representation of displacement data. The frequency calculation begins by finding the first maximum that occurs between the first and second zero crossovers; see point (T1, A1) in Figure 8. Next, the plot is followed until (a) a third zero crossover occurs into the negative x region and (b) a fourth zero crossover occurs into the positive x region. The minimum value between the third and fourth crossover is called point (T2, A2). Proceeding in this manner, the third peak (a second maximum) is point (T3, A3), and the fourth peak (the second minimum) is point (T4, A4). The fourth peak might be considered to be point (a, b); however, we added the additional limitation that there must be at least 0.05 mm difference between each minimum and maximum. Thus, point (a, b) is not considered a peak because, although there is a crossover just beyond (a, b), the negative positions just beyond this crossover are not 0.05 mm different in magnitude from point (a, b). Thus, our procedure discounts (a, b) and proceeds to point (T5, A5). This 0.05 mm criterion eliminates the chatter from the data. This criterion corresponds to ∼10% of the total amplitude of fiber vibration at a distance of 2.5 cm below the die. (As discussed below, we also tested criterion values of 0.005 and 0.5 mm.) The procedure illustrated in Figure 8 was performed on data exported into Excel from either VideoPoint or MetaMorph. Frequency is determined by taking the time differences between each successive peak. These differences are then averaged, and the result is multiplied by 2 to determine the period of a cycle. Then, the inverse of this period is the frequency. This procedure is similar to that used to calculate frequency in a model of the melt-blowing process.5,6 Amplitude is determined by averaging the absolute magnitude of each maximum and minimum. 4.1.a. Effect of Polymer Flow Rate. Figure 9 shows a comparison of frequency for the following three polymer flow rates: 0.75, 1.00, and 1.25 g/min. Results from a 3-D model developed by Marla and Shambaugh6 are also included in Figure 9. Experimentally, there is little difference in the frequencies

for the different polymer flow rates. For each of the three flow rates, the frequency is roughly constant at 30 Hz for z values between 2.5 and 7.5 cm. Beyond z ) 7.5 cm, the frequency decreases steadily to about 10 Hz at z ) 20 cm. The model predicts that the frequency remains constant down the threadline. This is expected, since the vibrating fiber, which is a mechanical system, cannot vibrate at different frequencies along its length.5 The frequency predicted is around 70, 62, and 60 Hz for polymer rates of 0.75, 1.00, and 1.25 g/min. The higher frequencies at the lower flowrates are due to the fact that, all else being equal, the finer filaments, which are produced at lower polymer flowrates, vibrate at higher frequencies. (Simply put, the finer filaments are more easily pushed around by the available forces.) The model frequencies are roughly twice the frequencies determined by the experiment. The manner in which frequency is experimentally determined may be the cause of the drop in frequency as a function of distance below the die (as shown in Figure 9). When taking pictures close to the die, the amplitude of fiber vibration is small, and most back-and-forth vibrations are included in the count. However, farther from the die, there is the possibility of backand-forth vibrations that occur totally in the negative x, or positive x, region. (As discussed previously, random air currents could cause the fiber to drift to the -x or +x region.). Since this motion is not included in our frequency algorithm, this kind of motion could account for the decrease in measured frequency as distance from the die head increases. As Figure 9 shows, for a polymer rate of 1.00 g/min, the frequency is 28.7 Hz at 10 cm below the threadline. The abovedescribed “chatter criterion” of 0.05 mm was used for determining this frequency. With chatter criteria of 0.5 and 0.005 mm, the analysis of the same data produced frequencies of, respectively, 28 and 28.3 Hz at z ) 10 cm. Since there was less than a 2.5% deviation in the frequencies calculated with these different criterium, a criterion of 0.05 was deemed sufficient. The amplitude of vibration was also determined for polymer flow rates of 0.75, 1.00, and 1.25 g/min; see Figure 10. The amplitude was defined as the average of the absolute values of the maxima and minima as defined above (i.e., a maximum occurred only when a difference of at least 0.05 mm existed between the maximum and the last minimum, and vice versa for the occurrence of a minimum). Experimentally, the amplitude increases from around 1 to 2.5 mm for each of the polymer flow rates; there is little difference between the amplitudes for each polymer rate. The results from Marla’s 3-D model6 are also shown in Figure 10. Like the model, our experimental results show that amplitude (and, thus, fiber cone size) increases with increasing distance from the die head. However, the model underpredicts the amplitude. Air turbulence, which is not accounted for in the model, may be the cause of this underprediction. In addition, the model predicts an increase in amplitude of vibration as the polymer flow rate decreases. In contrast, our experimental results show little effect of polymer flow rate on amplitude of fiber vibration. 4.1.b. Effect of Air Flow Rate. The frequency of fiber vibration is shown in Figure 11 for air flow rates of 50 and 100 slpm. Model results are also included in the figure. For both air flow rates, the experimental results show a decrease in frequency as the distance from the die head increases. As was discussed above, the reason for this decrease is probably related to the way in which frequency was determined from the data. The experimental frequencies are higher for the higher air flow rate. This parallels the predictions of the model. However, as described above, the model always predicts that the frequency


Figure 8. Schematic that shows the method used to determine frequency and amplitude of fiber vibration. The technique for determining maximum and minimum values is described in the text.

Figure 9. Frequency of fiber vibration in melt blowing for polymer flow rates of 0.75, 1.00, and 1.25 g/min. The other parameters were kept at the base conditions of ma ) 50 slpm, Tf ) 310 °C, and Ta ) 368 °C. The frequency was measured at 2.5 cm increments below the die head until reaching 20 cm. Model results are also shown on the figure.

Figure 7. (a) Typical results showing fiber vibration below a melt-blowing slot die. Each data point corresponds to a fiber position determined from a single camera frame acquired from the Redlake HS-4 camera. The data positions were normalized as described in the text. The frame rate was 2 000 frames/s; 6 000 data points are shown on the figure. The polymer flow rate was 1.00 g/min, the air flow rate was 50 slpm, the polymer temperature was 310 °C, and the air temperature was 368 °C. The distance below the die head was 2.5 cm. The two vertical lines indicate a small subset of the data from 1 to 1.5 s. This subset is shown in Figure 7b. (b) A small time segment of Figure 7a. The time segment taken was from 1 to 1.5 s. The two vertical lines indicate a subset of the data from 1.2 to 1.25 s. This subset is shown in Figure 7c. (c) A small time segment of Figure 7b.

remains constant along the entire threadline. The experimental prediction for 100 slpm differs from the experimental prediction for 50 slpm by a much greater amount than the difference between the model predictions for the two air flow rates. For the same two air flow rates considered in Figure 11, Figure 12 shows the amplitude of fiber vibration as a function of distance from the die head. Both the experimental results and the model show that (a) the amplitude increases as the distance from the die head increases and (b) the amplitude is higher at the higher air flow rate. For the experimental results, at an air flow rate of 100 slpm, the amplitude increases from ∼1 mm at z ) 2.5 cm to ∼11 mm at z ) 20 cm. This is a much more drastic change in the amplitude than that for the lower flow rate (where the amplitude increases from 1 to a little more than 2 mm). Marla’s model predicts the same trends that are exhibited by the experimental data. However, the model underpredicts the amplitude by approximately a factor of 10. 4.1.c. Effect of Polymer Temperature. Figure 13 shows the effect of polymer temperature on the frequency of fiber vibration. The results for the experiments and the model are shown for temperatures of 285, 310, and 325 °C. The experiments show that the frequency of fiber vibration increases when

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Figure 10. Amplitude of fiber vibration for various polymer flow rates. Base conditions for the other parameters were the same as in Figure 9. Measurements were taken at 2.5 cm increments below the die head. Simulation results are also included.

Figure 11. Frequency of fiber vibration for melt blowing with a slot die. Data shown are for air flow rates of 50 and 100 slpm. The polymer flow rate was 1.00 g/min, the polymer temperature was 310 °C, and the air temperature was 368 °C. Frequency was measured from 2.5 to 20 cm below the die. Model predictions are also shown on the figure.

polymer temperature increases. Model results show this trend as well; however, the model predicts higher vibration frequencies compared to the experimental results. As discussed above, the model predicts a constant frequency along the threadline. These constant frequencies are about 55, 65, and 70 Hz, respectively, for 285, 310, and 325 °C. As expected, higher temperatures produce finer filaments that vibrate at higher frequencies. For the experimental measurements, the frequency of vibration (for all three polymer temperatures) ranges from 30 to 50 Hz at 2.5 cm and then shows a decrease to approximately 9-12 Hz at 20 cm below the die. For the same three polymer temperatures, the amplitude of fiber vibration is plotted in Figure 14. Both the experimental results and the model show an increase in amplitude as a function of position along the threadline. Also, the experimental results show higher amplitudes than the model. 4.1.d. Effect of Air Temperature. In Figure 15, the frequencies at four air temperatures (325, 350, 368, and 400 °C) are compared to the model simulations. Again, the model results show a constant frequency along the threadline, while the experimental results show a decrease in frequency as distance

Figure 12. Amplitude of fiber vibration for air flow rates of 50 and 100 slpm. Base conditions were the same as those in Figure 11. The amplitude was measured at the same distances from the die as was the frequency of fiber vibration. Predictions from the Marla model are also included on the figure.

Figure 13. Effect of polymer temperature on the frequency of fiber vibration. Polymer temperatures of 285, 310, and 325 °C were used. The other operating conditions were as follows: mp ) 1.00 g/min, ma ) 50 slpm, and Ta ) 368 °C. The results from the Marla model are also included on the figure.

from the die head increases. However, the experimental results do not show any significant trend in frequency as a function of air temperature. The model results show a minimum in frequency for an air temperature of 368 °C. The experimental frequency near the die ranges (for all air temperatures) from about 30-50 Hz near the die to around 8-12 Hz at a distance of 20 cm from the die head. Figure 16 shows the amplitude of fiber vibration for the same four air temperatures considered in Figure 15. Similar to that discussed above, both the experimental results and the model show an increase in amplitude of fiber vibration as distance from the die head increases. Also, similar to what has been shown above, the model predicts lower amplitudes than the experimentally determined amplitudes. For the experimental results, the data for three of the four air temperatures overlap. However, for Ta ) 368 °C, the amplitude is higher all along the threadline. The Marla model predicts that the amplitude should show a slight increase as the air temperature increases. 4.2. Swirl Die. For the swirl die, the frequency and amplitude of vibration were determined in a manner similar to that used


Figure 14. Amplitude of fiber vibration for polymer temperatures 285, 310, and 325 °C. Base conditions for polymer flow rate, air flow rate, and air temperature were the same as those in Figure 13. The figure also shows simulation results from the Marla model.

Figure 15. Frequency of fiber vibration for air temperatures of 325, 350, 368, and 400 °C. Other conditions were a polymer flow rate of 1.00 g/min, an air flow rate of 50 slpm, and a polymer temperature of 310 °C. The model results are also included on the figure.

with the slot die. The swirl die, like the slot die, can have modes of vibration that are left and right, up and down, and back and forth (i.e., 3-D motion as measured by a Cartesian coordinate system). For the swirl die, use of a cylindrical coordinate system might be useful for analyzing motions such as twisting of the loops about the center (z) axis, oscillation of the loops about the center axis, and longitudinal waves moving along the fiber coils. However, such advanced analysis was not done for our preliminary study. Instead, we limited our analysis to motion in the x direction. The data were normalized for skewness as before. An example of normalized data for the swirl nozzle is shown in Figure 17a. Subsets of Figure 17a are shown in parts b and c of Figure 17. As discussed above in the Experimental Details section, for the swirl die work, we used a frame rate of 2 000 frames/s over a period of 1 s. As was the case for the slot die, a guideline was established to filter out the chatter in the displacement data. A difference of 0.05 mm (the same as for the slot die) was found to be suitable for distinguishing between the last maximum and the next minimum or vice versa. The swirl die produced fibers with less chatter in fiber position than did the slot die.

Figure 16. Amplitude of fiber vibration for air temperatures of 325, 350, 368, and 400 °C. Figure 15 base conditions for polymer flow rate, air flow rate, and polymer temperature were used. Model predictions are also included on the figure.

4.2.a. Effect of Polymer Flow Rate. The swirl die was run at polymer flow rates of 1.7, 2.4, and 3.5 g/min. Figure 18 shows the change in frequency of fiber vibration for these polymer flow rates. There is not much difference between the frequencies for the 1.7 and 2.4 g/min flowrates. However, at the highest polymer flow rate (3.5 g/min), the frequency of fiber vibration is significantly lower than those for the other polymer flowrates. The data for all polymer flowrates show a decrease in frequency for distances farther from the die. This result parallels what was discussed above for the slot die. The method used to count crossovers may again be the cause of this decrease in frequency. A model has not been developed yet for use in predicting results for the swirl nozzle. However, as a first approximation, one can assume that trends will be similar to those predicted for the slot die. The model predicted a decrease in frequency for increasing polymer flow rate (see Figure 9). This prediction compares favorably to our experimental results for the swirl die. The amplitude of fiber vibration was also measured for the same three polymer flow rates. The results are shown in Figure 19. For the slot die, the amplitude of fiber motion increases as distance from the die head increases (see Figure 10). However, as Figure 19 shows, at a distance of 2.5 cm, the final cone diameter has already been reached for all three polymer flow rates. Also, there appears to be no major change in fiber amplitude as polymer flow rate changes. The three polymer flow rates have amplitudes of vibrations of between 8 and 15 mm. These amplitudes are much larger than the 1-3 mm amplitudes shown in Figure 10 for the slot die. A fiber coil is formed by the swirl die, and this coil maintains a fairly constant diameter as a function of distance from the die. This is unlike what happens with the slot die. For the slot die, the fiber occupies a cone of ever-increasing radius (i.e., fiber amplitude). The apex of the cone is at the polymer-discharge hole in the die face. 4.2.b. Effect of Air Flow Rate. Figure 20 shows the frequency of fiber vibration for air flow rates of 6.25, 7.5, and 9.75 slpm. Increased air flow rate resulted in increased frequency of fiber vibration. At the highest air flow rate of 9.75 slpm, the swirl pattern was irregular. This gave an uneven laydown pattern to the swirled fibers. For all the data, the frequency of fiber vibration ranged from about 50 to 120 Hz. Model results for the slot die showed that higher air flow rates resulted in slightly higher fiber oscillations (see Figure 11).

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Figure 18. Frequency of fiber vibration for the swirl nozzle. Polymer flow rates of 1.7, 2.4, and 3.5 g/min were used. The air flow rate was held at 7.5 slpm, the polymer temperature at 310 °C, and the air temperature at 325 °C.

Figure 19. Amplitude of fiber vibration for the swirl nozzle. The polymer flow rates used were 1.7, 2.4, and 3.5 g/min. Base conditions were the same as in Figure 18.

Figure 17. (a) Example of normalized data for the swirl nozzle. The polymer flow rate was 2.4 g/min, the air flow rate was 7.5 slpm, the polymer temperature was 310 °C, and the air temperature as 325 °C. The distance below the die head was 2.5 cm. The frame rate was 2 000/s. The two vertical lines are a subset of data from t ) 0.6-0.8 s that is shown in Figure 17b. (b) A small portion of Figure 17a. This is 0.2 s of the above figure. The two vertical lines indicate a 0.02 s subset that is shown in Figure 17c. (c) A 0.02 s subset of Figure 17b.

The amplitude of fiber vibration is shown in Figure 21 for the same three air flow rates considered in Figure 20. There is little difference between the amplitudes for the 6.25 and 7.5

Figure 20. Frequency of fiber vibration for the swirl nozzle. Air flow rates used were 6.25, 7.50, and 9.75 slpm. The base conditions were mp ) 2.4 g/min, Tf ) 310 °C, and Ta ) 325 °C.

slpm airflow rates: both have an amplitude of ∼14 mm, and this amplitude is constant along the threadline. For the highest flowrate of 9.75 slpm, the amplitude is a smaller 9 mm. The


Figure 21. Amplitude of fiber vibration for the swirl nozzle. The air flow rates and other conditions were the same as those for Figure 20.

Figure 22. Frequency of fiber vibration for the swirl nozzle with polymer temperatures of 285, 310, and 325 °C. The polymer flow rate was 2.4 g/min, the air flow rate was 7.50 slpm, and the air temperature was 325 °C.

irregular swirl pattern at the highest air flow rate is probably the cause of this lower amplitude. The air flow rates for the swirl die (6.25, 7.5, and 9.75 slpm) are low compared to the 50 and 100 slpm flow rates used in our slot die experiments. However, though the air flow rates, as well as the die designs, are different, the extension of the model from the slot to the swirl die is still relevant. The fundamental process of air drag on a filament occurs with both types of dies. 4.2.c. Effect of Polymer Temperature. Figure 22 shows the frequency of fiber motion for polymer temperatures of 285, 310, and 325 °C. As observed previously for the swirl die (and the slot die), the measured frequency decreases as the distance from the die head increases. Both experimental results and model predictions for the slot die (see Figure 13) indicated that a higher polymer temperature would result in a higher frequency of fiber vibration. However, the data in Figure 22 do not indicate any obvious trend that a higher polymer temperature gives a higher frequency. The amplitude of fiber vibration was also determined for the same four polymer temperatures shown on Figure 22. These results are shown in Figure 23. As was the case with Figure 19, the amplitude of fiber vibration does not change as distance from the die head increases. The amplitude of fiber vibration

Figure 23. Amplitude of fiber vibration for the swirl nozzle with the same conditions as for Figure 22.

Figure 24. Frequency of fiber vibration with the swirl nozzle for three air temperatures. The air temperatures used were Ta ) 250, 325, and 360 °C. The polymer flow rate, air flow rate, and polymer temperature were 2.4 g/min, 7.50 slpm, and 310 °C, respectively.

(i.e., the coil radius) is ∼10 mm at 325 °C. The amplitude then decreases with increasing polymer temperature. 4.2.d. Effect of Air Temperature. Frequency and amplitude of fiber vibration were determined for air temperatures of 250, 325, and 360 °C. Figure 24 shows the frequency of fiber motion for these three air temperatures. The frequency decreases as distance from the die increases. Also, the frequency increases as the air temperature increases. In contrast, the experimental results for the slot die (see Figure 15) do not show any significant trend in frequency as a function of air temperature. The model results (for the slot die) show a minimum in frequency for the midrange air temperature of 368 °C. Amplitude of fiber vibration for the three air temperatures is shown in Figure 25. The amplitude increases as the air temperature is increased from 250 to 325 °C, but then the amplitude decreases as the air temperature is further increased to 360 °C. 5. Fast Fourier Transforms As an alternative to determining the frequency by counting crossovers, the use of fast Fourier transforms was examined. Fast Fourier transforms (FFT) allow a user to convert a signal from the time domain to the frequency domain. FFT breaks the

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Figure 25. Amplitude of fiber vibration with the swirl nozzle for three air temperatures. As in Figure 24, the air temperatures were 250, 325, and 360 °C. The polymer flow rate, air flow rate, and polymer temperature were kept at the base conditions used in Figure 24.

waveform into a sum of sinusoids of different frequencies. Fast Fourier transform analysis requires careful sampling. Aliasing becomes a problem when large amounts of data are being examined (as is the case for our research). When aliasing occurs, individual signals become indistinguishable in a large data set.12 Aliasing can be avoided if the Nyquist frequency exceeds the bandwidth. The bandwidth is the maximum frequency of the signal. The Nyquist frequency is half of the sampling frequency.12 In our case, for when the sampling frequency was 2 000 Hz, the Nyquist frequency was 1 000 Hz. Since the maximum frequency we observed (by our counting method) was

On-line Measurement of Fiber Motion During Melt Blowing - Industrial

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