Measurement of web tension using ambient vibrations in roll-to-roll manufacturing of flexible and printed electronics

Web tension measurement and control are important for the quality control of flexible and printed electronics fabricated by roll-to-roll (R2R) manufacturing. The distribution of tension within a R2R web can be calculated from the values of the web’s mechanical resonance frequencies. Typically, such measurements require an active external forcing to be generated and applied to the web. In this work, we show it is possible to obtain the web’s resonance frequencies from forcing due to ambient noise present in the test environment. This result broadens the applicability of noncontact resonance methods for computing web tension as currently available methods of active external forcing cannot be applied to all web materials and all R2R operating environments. We validate the ambient excitation method by comparing it to speaker-based acoustic excitation at atmospheric pressure and find the two methods agree within 0.5%. A calculation of the experimental motion of the web due to finite temperature effects suggests the observed vibration is generated from air-borne or structure-borne noise in the test environments. To show the effectiveness of the approach, we demonstrate the use of ambient excitation at five externally applied tensions, on three different web materials, and at both atmospheric and vacuum pressures.

In-span and between-spans tension variation can lead to variation in device quality [15], registration errors [16], and web wrinkling [8].Accurate measurements of the web tension and its non-uniformity assists with the quality control of R2R processes needed to maximize yield.
Existing web tension measurement methodologies include contact methods utilizing load cells or dancers [17][18][19] and non-contact methods utilizing the vibrational characteristics of the web.Noncontact methods have an advantage in that they do not need to account for the friction between the web and roller to accurately measure the web tension.However, they require an external source of excitation such as impact excitation [20], eddy current excitation [21], or acoustic excitation [8,22,23] to be applied to the web.The excitation source is often a limiting factor in the application of a noncontact web tension method to a particular R2R system.Impact excitation risks damaging delicate features on the web surface.Eddy current excitation requires a conductive web.Acoustic excitation requires air to transmit the excitation from the source to the web and thus is not applicable to in vacuo processes.The exclusion of acoustic excitation from in vacuo process is especially limiting as important R2R processes, such as chemical vapor deposition, occur in vacuo.Currently, a noncontact web tension excitation method compatible with both in air and in vacuo R2R processes and all types of web materials does not exist.
In this work, we investigate ambient excitation as a universal excitation source for non-contact web tension measurements in R2R systems at both atmospheric pressure and under vacuum.This approach leverages random noise from the environment instead of an active external excitation source.At atmospheric pressure, we compare the ambient excitation approach to acoustic excitation with a speaker and find that the two methods agree within 0.5%.Under vacuum, we show that there can be sufficient ambient excitation to obtain a measurable vibration response of the web.These results broaden the applicability of vibration based non-contact tension methods as they prove a meaningful measurement signal can still be achieved even without an active external excitation source.
For atmospheric pressure testing, the web was placed in the stationary test stand shown in figure 1(a).The span length of the section where tests were performed was 0.3 m.Hanging masses with weights of 2.65 N, 4.90 N, 11.76 N, 22.93 N, and 27.93 N were used to provide a controlled tension.The tested webs were 0.2 m wide, 50.8 µm thick PET coated with either 100 nm of copper (copper-PET) or 50 nm of aluminum (aluminum-PET).A laser sensor (Microtrak 7000, MTI Instruments Inc., Albany, NY) was used to measure the web response.We place the laser spot at the center along the longitudinal direction of the web to maximize the signal from modes 11 and 12.To avoid node locations of modes 11 and 12 the lateral laser spot location on the web was placed as shown in figure 1(b).A data acquisition system (NI PXIe-1071, NI PXIe-8102, NI PXIe-6124, NI BNC-2120, National Instruments™, Austin, TX) was used to record the response of the laser sensor.For the atmospheric pressure acoustic excitation tests, a speaker (VISATON ® FR 10, Art No. 2020, 20 Watt, 4 Ω, VISATON GmbH & Co. KG, Berlin, Germany) driven with a 0.1 V amplitude chirp was used.For vacuum testing, the web was placed in an Applied Materials SmartWeb TM R2R system, similar to the one shown in figure 2(c).The web was advanced at a rate of 1 m min −1 while the applied tension was controlled with the built-in tensioning system.This rate of web advancement is far below the speed at which the web resonance frequency shifts due to transport effects [8,24].The tested web was an uncoated 125 µm PET film.As shown in figure 2(d) the web was 0.8 m wide and the span in which the test was performed was 0.475 m long.A confocalDT 2421/2422 confocal light sensor (Micro-Epsilon, Ortenburg, Germany) with an integrated data acquisition system was used to measure the web response.The measurement laser spot was placed 34 mm from the edge of the web and 50 mm from the roller.
Figure 2(a) shows a comparison of acoustic and ambient excitation methods for the copper-PET film for the 2.65 N hanging weight.A fast Fourier transform was used to convert the speakerbased acoustic excitation 10 Hz to 16 Hz chirp time series signal into a frequency-dependent amplitude and phase transfer function.A Welch method power spectral density (PSD) analysis was used to convert the ambient excitation random time series from the out-of-plane transverse vibration of the axially stationary web into a transfer function.Resonance frequencies were obtained by fitting a Lorentzian (equation (S1), supplementary materials) in the vicinity of the eigenmode.For speakerbased acoustic excitation, we observed that phase shifts by 180 • across the selected peaks, confirming these are resonances of the web.The locations of the observed resonance peaks of the two lowest frequencies differ by 0.37% and 0.41% between the acoustic and ambient excitation methods.This demonstrates that speaker-based acoustic excitation and ambient excitation can generate identical measurement results.Figure 2(b) shows the results of using the ambient excitation method to measure the lowest symmetric transverse resonance frequency f 11 (Hz) and the lowest antisymmetric transverse resonance frequency f 12 (Hz) of the copper-PET film and the aluminum-PET film.Measurements were done at atmospheric pressure with five different hanging weights (2.65 N, 4.90 N, 11.76 N, 22.93 N, and 27.93 N).
Previously, solving for the contribution of the air mass loading to the web vibration required computationally expensive simulations for each specific web material, web length-to-width ratio, surrounding fluid density, and the distribution of cross-width web tension.However, based on a fully 3D potential flow model [8,23], we have developed and experimentally validated a semi-analytical, closed-form solution for the air-coupled web vibrations valid for arbitrary web areal mass density ρ web , web tension, density of the surrounding fluid ρ air , and a web length-to-width ratio κ from 0.1 to 10.The combination of the web mass and the added air mass, M 11 and M 12 , for the first two modes are: where L is the in-span length of the web in the longitudinal direction, F ijmn (κ) ′ s are the hydrodynamic functions (equations (S2.1)-(S2.6),supplementary materials).F ijmn (k) are expressed in terms of the nondimensional ratio κ, enabling the values to be calculated for webs of different dimensions.
The measurements are compared to the theoretically predicted frequencies of a uniformly tensioned Kirchhoff plate with air mass loading and combined simply supported/free boundary conditions [8,23], where N ave 11 is the average web tension distribution.In the case of uniform tension, theory predicts that f 11 and f 12 are slightly different due to the effect of air mass loading.The theoretical predictions match closely with the measured values.The differences that arise are likely due to either non-uniform tension within the web or friction between the web and the rollers changing the average in span tension.
While figures 2(a) and (b) show that the ambient vibration method works for our tested measurement conditions, they do not provide insight into the underlying source of web vibration.One hypothesis is that the vibrations arise due to the finite temperature of the web.A second is that the vibrations arise due to background noise in the room that is transmitted through the air and floor.This can be investigated by calculating the thermally induced fluctuations of the web and comparing this to the experimentally observed motion (equations (S5)-(S7), supplementary materials).We calculate the thermal fluctuationinduced mean square displacement (MSD) is on the order of 10 −22 -10 −23 m 2 .As shown in table 1, the experimentally observed MSD values are on the order of 10 −9 -10 −12 m 2 .This is significantly larger than MSD predicted from thermal fluctuations alone, therefore the experimentally observed excitation is not caused by thermal fluctuation and must be due to either air-borne noise or structure-borne noise.To predict the tension and its linear variation from the noise-based vibration spectrum, we calculate N ave 11 and its linear variation σ from the measured f 11 (Hz) and f 12 (Hz) as [8]: Note that when a web is in vacuo, the density of the surrounding fluid/air ρ air = 0 yields M 11 = M 12 = ρ web , which is the web areal mass density.For the atmospheric pressure experimental setup shown in figure 1(b), L = 0.3 m and κ = 1.5.The web areal mass density for the copper-PET film is 71.858 ± 0.025 g m −2 and the aluminum-PET film is 65.964 ± 0.003 g m −2 .Air density is assumed to be 1.208 kg m −3 .Calculated values of N ave 11 and σ are as shown in table 2. The real part of 2σ gives the ratio of cross-width tension variation to average tension [8].The calculated values of N ave 11 are slightly smaller than the corresponding average tension calculated from the hanging weight, which is likely due to the friction between the rollers and the web.The linear variation of cross-width web tension (2σ) varies between 0 and 0.82.This variation is due to the difficulty of mounting the web in our test stand with uniform cross-width tension.
To test the ambient web vibration method both in vacuo and on a moving web we performed a series of measurements on a PET web mounted in an Applied Materials SmartWeb TM system.SmartWeb TM is a high-performance R2R system capable of in vacuo techniques such as physical/chemical vapor deposition enabling processes such as display manufacturing to transition from batch processing to a R2R approach [5].During the measurements, we increased the applied tension from 75 N to 400 N while measuring the web position for ten 10 s segments with a sampling frequency of 1 kHz and computed the PSD. Figure 3(a) shows the average web PSD for six different web tensions.The observed signals are comparable in magnitude to the atmospheric pressure tests; however, there is a considerably greater amount of high-quality factor background noise which significantly complicates the identification and fitting of the resonance peaks.To obtain a non-subjective curve fitting result we first calculated the predicted f 11 from equation (3) and then cropped the frequency range of the PSD such that f 11,predicted /3 < frequency < 3f 11,predicted .We then fit a simple harmonic oscillator to the cropped data range (supplementary material, figure S3).The resonance frequencies extracted from this analysis are compared to the resonance frequencies predicted by our model in figure 3(b).
The 150 N, 300 N, and 400 N tensions fit our model well while the 75 N, 100 N, and 200 N tensions deviate from expected behavior.For the 75 N and 100 N tensions, the problem is a strong background signal in the data at a frequency of 13.9 Hz.This peak is visible in most of the tested tensions and is likely associated with the motors or rollers of the R2R system.However, for the 75 N and 100 N data sets in particular this 13.9 Hz background signal is close to the web's resonance frequency and is amplified such that it is the largest peak in the cropped frequency range.For the 75 N data set this causes a relatively poor curve fitting result compared to the other tensions and in the 100 N data set this peak is misidentified as the web resonance by our curve fitting procedure.It is less clear why the 200 N data point is an outlier.This could also be due to peak misidentification; however, there is not an obvious stationary peak at the other web tensions near this frequency.A second possibility is that the disagreement may be due to the external tension control being far removed from the span where the non-contact web tension measurement was performed, thus allowing friction or processing effects to change the in-span tension relative to the monitoring load cell.If this is the case, the tension difference between the load cell and measurement span would need to be greater for the 200 N test than at the other applied tensions.Ultimately, we lack sufficient data to make a definitive determination regarding why the 200 N data point deviates from theory.Due to the challenges with peak identification, we have not attempted to identify secondary resonance peaks (i.e.f 12 ) in the vacuo data set.Improved signal-tonoise through additional averaging and better identification or suppression of high-quality factor spurious background peaks is needed for confident identification of resonance frequencies of moving webs in vacuo.Nevertheless, these measurements do illustrate a clear trend of increasing resonance frequencies with increasing web tension indicating that the ambient web vibration method can be applied to in vacuo systems.
We have proposed and demonstrated the approach of using ambient excitation for vibration based non-contact web tension measurements at both atmospheric and vacuum pressures.The atmospheric pressure tests showed the difference in measured resonance frequency between the ambient excitation method and speaker-based acoustic excitation is less than 0.5%.We observed that the experimentally measured mean square deflection is around ten orders of magnitude greater than the mean square deflection calculated from finite temperature effects, therefore the cause of the observed signal must be due to background noise present in the environment.We demonstrate the ambient excitation method by measuring the resonance frequencies of three different webs, with five different applied tensions, and at both atmospheric and vacuum pressures.The average web tension distribution and its linear variation can be extracted from the measured frequencies.This work validates the use of the ambient excitation method on R2R webs, opening the possibility of vibration based noncontact web tension measurements being utilized in a wider range of R2R systems.

Figure 1 .
Figure 1.(a) Schematic for the atmospheric pressure experimental setup with 1: (a) laser displacement sensor head, 2: web span where the measurement was made, and 3: a hanging weight to provide tension.(b) Drawing of web span geometry and the measurement location for the atmospheric pressure test.(c) Picture of a Smartweb TM system, similar to the one used for vacuum testing [25].(d) Drawing of web span geometry, measurement location, and web movement direction for the in vacuo testing.

Figure 2 .
Figure 2. (a) Comparison of frequency response functions under acoustic and ambient excitation for the copper-PET film with a 2.65 N hanging weight.(b) Ambient excited frequencies of the copper-PET film and the aluminum-PET film with five different hanging weights (2.65 N, 4.90 N, 11.76 N, 22.93 N, and 27.93 N) and the theoretically predicted frequencies with the hanging weights from 2.5 N to 30 N under the assumptions of no friction between the rollers and the web and no cross-width tension non-uniformities.

Figure 3 .
Figure 3. (a) PSD frequency response at different externally applied tension captured with ambient excitation of a PET web in vacuo.The web material is a 125 µm thick PET film.(b) Extracted resonance frequencies at each applied force value.

Table 1 .
MSD from the measured PSD frequency response functions.The predicted thermal fluctuation-induced MSD is on the order of 10 −22 -10 −23 m 2 .

Table 2 .
Average web tension distribution N ave 11 and its linear variation σ.