System and method for measuring tension distribution in a web in a roll-to-roll process

Abstract

Provided are systems and methods for measuring web tension distribution in roll-to-roll processes, including roll-to-roll processes used in the manufacture of printed devices, that include a web moving in a longitudinal direction of the web between first and second rollers, creating tension in a longitudinal direction of the web such that tension exists in a flexible substrate of the web between the first and second rollers, and operating the system to determine an average tension and a linear change in tension present in the flexible substrate caused by the tension induced in the web that creates a non-uniform tension distribution in the flexible substrate between the first and second rollers.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority to U.S. Provisional Patent Application No. 63 / 170,568, filed April 5, 2021, the contents of which are incorporated herein by reference.

[0002] (Technical field) The present invention relates to a system and method for manufacturing flexible printed electronics, including but not limited to the manufacture of electronic, optical, and optoelectronic devices such as thin film transistors, supercapacitors, organic light emitting diodes, solar cells, antennas, and sensors, and in particular to a system and method that enables improved quality and yield of printed electronics manufactured by a flexible printed electronics manufacturing method using a roll-to-roll (R2R) process. [Background technology]

[0003] There is an ongoing effort to manufacture and develop relatively low-cost electronic, optical, and optoelectronic devices that can be mass-produced and widely deployed. One such approach is to manufacture such devices using a roll-to-roll (R2R) system (also known as web or reel-to-reel processing). Generally, roll-to-roll processes manufacture devices by printing or otherwise applying components or entire devices onto a flexible substrate (sometimes referred to as a web). For example, plastic film or metal foil is fed into the roll-to-roll system from a roll and then rewound back into a roll at the end of the roll-to-roll process. Although not limited to these, thin-film transistors, supercapacitors, organic light-emitting diodes, solar cells, antennas, and sensors are well known, and roll-to-roll processes have been employed to provide them at low cost, with high throughput and large-scale manufacturing capabilities.

[0004] A barrier to the scalability of roll-to-roll flexible electronics is the low device yield rate during manufacturing, which requires costly post-process product testing to control. Maximizing yield often requires process modeling and control, in-line metrology, in-line characterization, and the effective use of novel materials.

[0005] Stresses in flexible devices fabricated by roll-to-roll processes arise during fabrication from a combination of web tension and process-induced stresses from printing (e.g., inkjet, gravure, screen, slot-die), chemical vapor deposition, laser / thermal annealing, ultraviolet (UV) curing, and / or hot embossing. These combined stresses are prominent in roll-to-roll fabricated devices because the webs on which these devices are fabricated are flexible substrates (non-limiting examples include polyethylene terephthalate (PET), polyethylene naphthalate (PEN), and polyimide (PI)) that can experience large strains, unlike rigid device substrates such as silicon wafers used in integrated circuit fabrication.

[0006] The flexibility of webs commonly used in roll-to-roll processes makes them prone to non-uniform stress induced by uneven friction between the web and rollers, roller-web misalignment, and roller-roller misalignment. When stress-induced webs are split or cut to separate flexible devices during device fabrication, residual stresses remain within the devices due to the stresses present in the web. The performance of printed electronic devices can be affected by residual stresses. Therefore, non-uniform tension distribution within the web can lead to non-uniform device performance across the web and even web wrinkling. Monitoring and correcting non-uniform web tension is an important consideration in determining residual stress, enabling feedback quality control of the roll-to-roll process to maximize device yield.

[0007] Various types of systems and methods have been reported for measuring web tension in roll-to-roll systems. Rollers equipped with instruments for measuring web tension (commonly referred to as "instrumented rollers") are well-known examples of such systems and methods. Assuming uniform tension exists in the web, instrumented rollers often use tension sensors, such as load cells or dancer systems, in conjunction with a speed center to measure and control web tension along with speed. U.S. Patent Application Publication No. 2007 / 0006644 by Schultheis discloses a method for measuring web tension using a pressure sensor wrapped around a roller.

[0008] Disadvantages of using instrumented rollers include the investment required for customized rollers and the need to perform recalibration if the web path is changed. Additionally, measuring web tension in roll-to-roll systems using instrumented rollers assumes that the tension of the web wrapped around the roller does not change due to friction. Furthermore, the sensors used in instrumented rollers are prone to drift and are sensitive to environmental temperature and vibration.

[0009] Other reported approaches to monitoring web tension in roll-to-roll systems utilize fundamental vibration frequency measurements to infer web tension. However, these methods do not take into account the existence of non-uniform web tension distribution across the web and the effect of air loading (damping) on ​​the measurement. Vibration studies of air-coupled web systems have revealed that air significantly modifies the web frequencies and mode shapes. See, for example, Raman et al., "Observations on the Vibrations of Paper Webs," Proceedings of the 11th Annual Symposium on Information Storage and Processing Systems, Santa Clara, CA, June 10-13, pp. 415-429 (2001); Vaughan et al., "Aeroelastic Stability of Axially Moving Webs Coupled to Incompressible Flows," Journal of Applied Mechanics, 77(2) (2010); and Feng et al., "Vibration of Air-Coupled Web Systems," Journal of Vibration and Acoustics, 143(1):0110404 (2021)).

[0010] Linna et al., "Better Productivity by Measuring Web Tension Profile" (Proceedings, 55th Appita Annual Conference, Hobart, Australia, April 30-May 2, 2001, p. 305 (2001)), report the development of a system that uses air film pressure to measure non-uniform web tension. However, this system only works for high web speeds in air roll-to-roll processes and requires recalibration when the web path is changed. Furthermore, this technique works under the assumption that the cross-width web contact stiffness is uniform, which is not the case for systems with finite widths, even if the tension is uniform.

[0011] Jin et al., "Web Tension Estimation by Local Contact Force Measurement in Roll-to-Roll Manufacturing," International Journal of Precision Engineering and Manufacturing, 21(11), pp. 2067-2075 (2020) reported experimentally fitted web tensions and contact forces for a web under fixed web strain. However, this approach is specific to specific web properties, web geometries, and roller configurations, and requires recalibration for each specific web measured. Summary of the Invention [Problem to be solved by the invention]

[0012] From this perspective, there remains a significant challenge to achieve comprehensive, accurate, reliable, and inexpensive tension distribution in roll-to-roll (R2R) processes in order to improve the quality and yield of printed devices manufactured by the R2R process. [Means for solving the problem]

[0013] The present invention provides systems and methods for measuring web tension distribution in roll-to-roll processes, including, for example, roll-to-roll processes used in the manufacture of printed devices, including but not limited to electronic, optical, and optoelectronic devices.

[0014] According to a non-limiting aspect of the present invention, there is provided a system for monitoring tension distribution across the width of a web in a roll-to-roll system. The roll-to-roll system includes a web, at least first and second rollers between which the web moves in a longitudinal direction of the web, tension-inducing means for inducing tension in the web in the longitudinal direction, and manufacturing means for manufacturing printed devices on a surface of a flexible substrate of the web. The system includes means for inducing strain in the web between the first and second rollers. The system is operable to determine the average tension and linear change in tension present in the flexible substrate resulting from a non-uniform tension distribution induced in the flexible substrate between the first and second rollers.

[0015] According to a non-limiting aspect of the present invention, there is provided a method for monitoring tension distribution across the width of a web in a roll-to-roll process, the method comprising: moving the web between first and second rollers in a longitudinal direction of the web; inducing longitudinal tension in the web such that tension is present in a flexible substrate of the web between the first and second rollers; and operating a system to determine an average tension and linear change in tension present in the flexible substrate caused by the induced tension in the web that induces a non-uniform tension distribution in the flexible substrate between the first and second rollers. The system comprises means for inducing strain in the web between the first and second rollers. [Effects of the Invention]

[0016] The technical features of the above-described systems and methods enable monitoring and measuring tension distribution in a web and correcting for uneven tension distribution in a roll-to-roll process of devices whose quality and yield are affected by uneven tension during their manufacture.

[0017] Other aspects and advantages of the present invention will become apparent from the following detailed description. [Brief explanation of the drawings]

[0018] [Figure 1] FIG. 1 is a schematic diagram illustrating why web friction and misalignment can cause uneven tension distribution within the web in a roll-to-roll (R2R) process. [Figure 2] FIG. 2 is a diagram illustrating a web under non-uniform tension distribution with reference to span geometry and coordinate system. [Figure 3] FIG. 3 is a schematic diagram of a system for measuring (monitoring) web tension distribution in accordance with a non-limiting embodiment of the present invention. [Figure 4]Figure 4 shows two resonant frequencies, f11 and f12, as a function of the linear change in stress (denoted in Figure 4 by the dimensionless ratio (σ) of the linear change in tension, which accounts for the discrepancy between the maximum or minimum tension relative to the average tension per unit width (*1)) for a roll-to-roll web operating in air (sometimes simply referred to as "air") and vacuum (where the web is contacted by air or other gases or fluids). The mode shapes corresponding to σ = 0 and 0.5 are shown. The gray bars indicate the contribution of each basis function to the mode shapes. Analytical expressions were developed based on tension plate theory that relate resonant frequencies (e.g., f11 and f12) to the average tension and the linear change for roll-to-roll processes performed in vacuum and air. A representative web was formed from PET with the properties and environmental conditions shown in Table 1 of Figure 11. The average web tension in this example is 150.47 Nm-1. [Figure 5] FIG. 5 is a schematic diagram of a system for measuring (monitoring) web tension distribution, according to another non-limiting embodiment of the present invention. [Figure 6] FIG. 6 shows the contact stiffness profile of a cross-span of a strained web using a measurement system of the type shown in FIG. [Figure 7] FIG. 7 is a graph plotting the frequency response function showing the locally measured transfer function, phase, and single degree of freedom (SDOF) fitted transfer function for the two minimum resonant frequencies, f11 and f12, using a measurement system of the type shown in FIG. 3. [Figure 8] FIG. 8 is a graph plotting several contact force versus strain fits using a measurement system of the type shown in FIG. [Figure 9] 9A and 9B are graphs comparing the tension measurement methods of the measurement systems shown in FIGS. 3 and 5. FIG. [Figure 10]Figures 10A, 10B, and 10C are graphs plotting frequency response functions obtained for a web from a commercial roll-to-roll system using a measurement system of the type shown in Figure 3. Figure 10A shows the frequency response function for a stationary web. Figure 10B shows the frequency response function for a moving web at transport speeds between 0.98 m / min and 1.26 m / min. Figure 10C shows the frequency response function for a moving web at transport speeds between 1.93 m / min and 2.24 m / min. [Figure 11] Figure 11 shows Table 1, which contains the web properties and environmental conditions used for the simulation, experimental validation, and in-line measurements. [Figure 12] FIG. 12 shows Table 2, which contains the results of in-line measurements of web tension distribution in two spans of a commercial roll-to-roll system under the environmental conditions of Table 1 shown in FIG. DETAILED DESCRIPTION OF THE INVENTION

[0019] The intended purpose of the following detailed description of the invention, and the phraseology and terminology used therein, is to describe the illustrated subject matter, including the description of one or more non-limiting embodiments of the invention, and to describe certain, but not all, portions of the illustrated subject matter, including the illustrated embodiments. The following detailed description sets forth considerations related to the illustrated embodiments and identifies certain, but not all, alternative embodiments of the illustrated embodiments. By way of non-limiting example, the present invention encompasses additional or alternative embodiments that may exclude one or more features or aspects shown and / or described as part of a particular embodiment, or that may comprise a combination of two or more features or aspects shown and / or described as part of a different embodiment. Accordingly, it is the appended claims, rather than the detailed description, that are intended to particularly identify the subject matter of the present invention, including certain, but not all, of the aspects and alternatives set forth in the detailed description.

[0020] The following disclosure describes various aspects of systems, apparatus, and methods suitable for monitoring roll-to-roll (R2R) processes. This disclosure particularly describes roll-to-roll systems used in the manufacture of printed devices, and methods and systems for monitoring and measuring tension distribution within a web and correcting for non-uniform tension distribution during the manufacture of printed devices whose quality and yield are affected by non-uniform web tension.

[0021] The following description specifically discusses considerations for fabricating printed devices using roll-to-roll processes, but the present disclosure encompasses other types of devices fabricated using other processes. As used herein, the term "fabricate" and its various forms include, but are not limited to, printing, depositing, coating, patterning, and modifying devices (and their materials) on a surface. As used herein, "printed device" refers to various electronic, optical, and optoelectronic devices, including, but not limited to, thin-film transistors, supercapacitors, organic light-emitting diodes, solar cells, antennas, and sensors, the fabrication of which involves depositing and processing at least one layer of the device using one or more of printing, coating, laser processing, annealing, and other thin or thick film deposition, processing, and / or etching techniques. Specific examples of these techniques include inkjet printing, gravure printing, screen printing, slot-die coating, chemical vapor deposition, laser / thermal annealing, UV curing, and / or hot embossing.

[0022] Additionally, the terms "R2R" and "roll-to-roll" are used to refer to systems and continuous processes that are capable of producing large volumes of printed devices, but that may reduce the reliability of some of the printed devices due to the manufacturing methods used. This disclosure also intends to explain the drawbacks of roll-to-roll and other relatively high-speed processes in order to improve device yield.

[0023] High-quality roll-to-roll manufacturing for flexible printed devices often requires uniform tension in the web comprising the flexible substrate on which the printed device is fabricated. Non-uniform tension distribution can lead to non-uniform performance of the printed device across the width of the web, and excessively non-uniform tension distribution in the web can lead to wrinkling of the web. Non-limiting examples of causes of non-uniform tension distribution in the web include misalignment between rollers in a roll-to-roll system, non-uniform contact and / or friction between the web and rollers, non-uniform roller geometry, and non-uniform process parameters.

[0024] The following description describes the "non-contact resonance (NCR)" method and the "gentle contact stiffness mapping (GCSM)" method, which were developed and tested to measure the web tension distribution of a web, characterized by at least the average tension and its linear change across the web's width. As used herein, "width," "cross-span," "average tension," and "linear change in tension" (or "average stress" and "linear change in stress") refer to the transverse (short-distance) direction relative to the longitudinal direction in which the web moves between a pair of adjacent rollers in a roll-to-roll system. The portion of the web between a pair of adjacent rollers at any given time is referred to herein as the "span" of the web. The NCR method uses the resonant frequency of the web in conjunction with a closed-form equation to obtain its linearly changing tension distribution. The closed-form equation includes the important effect of air loading on the web's vibration through an accurate hydrodynamic function. The GCSM method is based on a nonlinear regression of the contact stiffness at multiple locations on the web.

[0025] Both the disclosed NCR and GCSM methods can be used to complement the in-line metering process of existing roll-to-roll systems operating in air (where the web is contacted by air or other gases or other fluids) or vacuum, and do not require expensive instrumented rollers (which herein refer to rollers with physically embedded tension and / or pressure sensors). Both methods can accurately measure web tension distribution over a wide range of web properties, web paths, web tensions, measurement configurations, and environmental conditions. Both methods are based on first-principles mechanical models of tension plates.

[0026] The NCR method involves the interaction of the plate with the surrounding fluid. These methods were cross-validated using static tests (where the web is statically supported between two rollers) performed on a fixed test stand, and the NCR method was validated using in-line (dynamic) tests performed on a commercial roll-to-roll system (where the web is moved by rollers at speeds within the range typical of commercial roll-to-roll systems). Studies measured cross-span tension variations of up to 35.58% in the web of the roll-to-roll system, and showed that both the mean tension and its linear change vary across different spans of the web in the roll-to-roll system. Reducing cross-span tension variations can improve quality control of the roll-to-roll process for flexible printed devices, potentially increasing device yield.

[0027] 1 is a schematic diagram of a roll-to-roll (R2R) system 10 including a web 12 traveling between a pair of adjacent rollers 14 and a printing apparatus 15 that produces printed devices 16 across the width of the web 12 within the span of the web 12 between the rollers 14. The span is referred to as a tension zone of the system 10 and may include any number of tension zones depending on the process being performed on the web 12. The printing apparatus 15 may include, by way of non-limiting example, an inkjet, gravure, screen, or slot-die printer. The web 12 may also be treated by other processes, such as chemical vapor deposition (CVD), laser / thermal annealing, ultraviolet (UV) curing, and / or hot embossing.

[0028] 1, roller 14 downstream of printing device 15 is a take-up roller and is driven to induce tension in web 12. The tension in web 12 can be controlled using a closed-loop control system 16, which can accelerate or decelerate one or more rollers 14 and / or apply a tensioning force directly to web 12 using mechanisms such as dancers (not shown). One or more feedback devices 17, such as load cells, can be used to provide feedback to control system 16 and close the control loop.

[0029] 1 is a schematic diagram illustrating how friction and misalignment of a web 12 in a roll-to-roll system 10 can result in a non-uniform (i.e., non-constant) tension distribution 18 across the width of the web 12 within the span of the web 12 between rollers 14. Non-uniform tension distribution in the web 12 (e.g., the non-uniform tension distribution shown in FIG. 1 ) can result in non-uniform performance of devices 16 across the width of the web 12 and can even cause wrinkling in the web 12. Therefore, monitoring web tension and correcting non-uniform tension distribution are important considerations in determining residual stress, which can support feedback quality control in the roll-to-roll process and maximize device yield.

[0030] Figure 2 shows a diagram of a web with non-uniform tension distribution, with reference to the span geometry and coordinate system. A two-dimensional (2D) isotropic, linearly elastic, uniaxially tensioned rectangular Kirchhoff plate model was selected to simulate a single span between a pair of adjacent rollers in a roll-to-roll system, as shown schematically in Figure 1. To measure the tension distribution in the web, particularly the average tension and linear variation of tension in the web, the NCR method can distinguish the resonant frequencies of the web, including but not limited to the minimum resonant frequency of the web in the cross-span (width) direction of the web, and the GCSM method can accurately determine the contact stiffness profile of the web in the cross-span (width) direction of the web.

[0031] Because roll-to-roll systems do not impart tension in the cross-span direction, the NCR and GCSM methods use a tension Kirchhoff plate model instead of a linear membrane model to define the spatial dependence of the eigenmodes in that direction, including a very small but finite web bending stiffness. Furthermore, within the operating range of typical roll-to-roll systems used in the manufacture of flexible printed devices, the effect of the web transport speed (reel speed) on the frequency is very small. The partial differential equation of motion for the out-of-plane vibration of a fixed tension plate: Equation (1) is as follows:

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[0032] As shown in Figure 2, x1, x2, and x3 are coordinates along the longitudinal direction (in the plane of the web and in the direction of web movement and web tension), the transverse direction (perpendicular to the surface of the web on which the printed device is fabricated), and the transverse direction of the web (in the plane of the web but perpendicular to the direction of web movement and web tension), respectively. L is the in-span length of the web in the longitudinal direction, b is the cross-span width of the web in the transverse direction, τ is time, w(x1, x3, τ) is the web strain in the transverse direction, ρ webis the web area mass density, D=Eh 3 / [12(1-υ 2 )] is the web bending stiffness, E, h, and υ are the Young's modulus, thickness, and Poisson's ratio of the web, respectively, and ▽ 4 is the biharmonic operator, N 11 (x3) is the uniaxial tension of the web per unit width of the web, and P(x1, x3, τ) is the pressure on the web surface (e.g., the pressure due to the air pressure and contact force on the web in air-coupled web vibration). The non-uniform tension distribution is described as a polynomial function of x3. The first two terms of the polynomial are experimentally defined as Equation (2).

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[0033] where *1 is the average web tension per unit width (N / m), and σ is a dimensionless ratio to the linear change in tension that accounts for the discrepancy between the maximum or minimum tension relative to the average web tension per unit width *1. In particular, *2 indicates the absence of tension at one of the free ends. Therefore, *3 is the significant tension variation associated with a local web wrinkle adjacent to one of the free ends. Substituting equation (2) into equation (1) yields the following equation (3):

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[0034] Because simply supported boundary conditions can accurately predict the linear vibration of a pre-tensioned web passed between finite radius rollers, the following boundary conditions are used for both the NCR and GCSM analyses.

[0035] 1) The web is simply supported by the upstream and downstream rollers.

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[0036] 2) There are no shear forces or bending moments at either free end.

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[0037] [NCR method] 3 is a schematic diagram of a monitoring system adapted to measure (monitor) tension distribution (including the presence of non-uniform tension distribution) in a web during a roll-to-roll process according to the NCR method. In FIG. 3, the monitoring system is shown as being installed in a roll-to-roll system 10 and is shown to include at least one device 20 for inducing strain, more specifically, for exciting vibration, a device 22 for detecting vibration (strain) of the web 12 (a laser sensor or other non-contact motion or proximity sensor, as a non-limiting example), and a processor 24.

[0038] Although device 20 is shown schematically in Figure 3 as an acoustic speaker, other means of inducing vibrations may be employed, particularly when web 12 and device 20 are in a vacuum. Non-limiting examples include inherent vibrations that exist mechanically, thermally, and / or acoustically in or around system 10.

[0039] The processor 24 performs calculations based on the detected vibrations to calculate the average tension (and / or stress) and the linear change in tension (and / or stress) based on the resonant frequency of the vibrations using a tension Kirchhoff plate model to define the spatial dependence of the eigenmodes across the width of the web.

[0040] As shown schematically in Figure 3, a system for measuring web tension distribution includes devices 20, 22 and a processor 24. Processor 24 may be part of control system 16, which is depicted as part of roll-to-roll system 10 in Figure 1. Thus, in combination with control system 16 and feedback device 17 shown in Figure 1, the web tension distribution measurement system shown in Figure 3 can include or form a subsystem consisting of means for controlling the tension induced in web 12 to increase the uniformity of the tension distribution present in web 12. Other features of system 10 shown in Figure 3 will not be described in detail, but its components, functions, etc. are essentially as described for system 10 shown in Figure 1.

[0041] In the non-limiting studies described herein, the eigenmodes 11 and 12 are generally (though not necessarily) symmetric and antisymmetric, respectively, at the lowest transverse resonant frequency f of the web. 11 and f 12 Using the NCR method, we measured *1 and σ. 11 and f 12 The eigenmodes of the vibrations are coupled by the non-uniform tension distribution. To account for both the roll-to-roll process in air and in vacuum in a consistent manner, key results for estimating the influence of aerodynamic loading on the resonant frequencies and eigenmodes of the vibrating web were obtained in the presence of aerodynamic effects. The aerodynamic effects were modeled as an inviscid, incompressible fluid surrounding the vibrating web. The web tension was assumed to vary linearly. The two lowest web frequencies were predicted as follows:

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[0042] where the values ​​of *4 and *5 are determined by the hydrodynamic function, the web dimensions L and b, and the web area mass density ρ. web and air density ρ airIn the vacuum analysis, the air density is set to 0, so *4 and *5 = ρ web , and the following equations (8) and (9) hold.

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[0043] As shown in Figure 4, in roll-to-roll systems operating in air and vacuum, the dimensionless ratio (σ) of the linear change in tension (hereafter simply referred to as "linear change in tension") significantly changes the frequency and corresponding mode shape compared to the case of a uniform tension distribution. In the example shown in Figure 4, the web is a flexible substrate entirely made of PET with the properties and air density shown in Table 1 of Figure 11. The average tension per unit width *1 (hereafter simply referred to as "average tension") in this example is 150.47 N / m. The frequency was calculated using Equations (6) to (9). The corresponding mode shape for σ = 0 was obtained using the Assumed Modes Method (AMM). For roll-to-roll systems in vacuum, *6. The small boxes containing gray bars indicate the basis functions W for the corresponding mode shapes. 11 , W 12 , W 13 and W 14 The basis functions were as follows:

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[0044] The following findings were obtained:

[0045] In both vacuum and air, the resonant frequency (f 11 ) decreases, and the resonant frequency (f 12 ) increases.

[0046] The lowest resonant frequency of the web (f 11 and f12 ) are tightly clustered for the vacuum web system under uniform tension distribution (i.e., linear variation of tension equal to 0), but are split by non-uniform tension distribution.

[0047] The minimum resonant frequency (f) of a web with uniform tension distribution in air 11 and f 12 ) separate due to the different magnitudes of the added air masses.

[0048] From the grey bars with uniform tension distribution (i.e., linear variation of tension equal to 0), eigenmodes 11 and 12 are perfectly symmetric and antisymmetric, respectively. In a web with uniform tension distribution, there is no cross-coupling between the symmetric and antisymmetric basis functions.

[0049] Non-uniform tension distribution (i.e., a linear change in tension other than zero) causes coupling between the symmetric and anti-symmetric basis functions in the mode shapes, modifying the mode shapes both in vacuum and in air.

[0050] minimum resonant frequency f 11 and f 12 To measure the average tension and the linear change in tension due to strain, equations (6) and (7) were rewritten inversely to obtain the closed-form equations (10) and (11) shown below.

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[0051] The NCR method can resolve the linear change in tension, but not its direction. This is because positive and negative values ​​of the linear change in tension (σ) give the same frequency as shown in equations (6) to (9). In a vacuum roll-to-roll system, there is no air load, and equations (10) and (11) can be simplified as follows:

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[0052] Equations (10)-(13) can be applied to a wide range of web properties, web thicknesses, web aspect ratios, web paths, web tensions, measurement configurations, and environmental conditions without the need for recalibration.

[0053] [GCSM method] 5 is a schematic diagram of a monitoring system adapted to measure (monitor) tension distribution (including the presence of non-uniform tension distribution) in a web during a roll-to-roll process in accordance with the GCSM method. In FIG. 5, the monitoring system is shown installed in a roll-to-roll system 10 and includes at least one device 26 for inducing strain in the web 12 (as a non-limiting example, one or more devices 26 that sequentially apply at least two predetermined and constant forces at different levels and positions across the width (cross-span) of the web 12), a device 28 for detecting strain in the web 12 (as a non-limiting example, a laser sensor or other non-contact motion or proximity sensor), and a processor 30.

[0054] 5 as a force meter, other means for inducing a predetermined constant strain in web 12 may be employed. Processor 30 performs calculations based on the sensed strain, such as using a tension Kirchhoff plate model, to calculate the average tension (and / or stress) at multiple locations across the width of web 12 and the linear change in tension (and / or stress) with strain.

[0055] As shown schematically in Figure 5, a system for measuring web tension distribution includes devices 26 and 28 and processor 30, which may be configured as part of control system 16 represented as part of roll-to-roll system 10 shown in Figure 1. Thus, the web tension distribution measurement system shown in Figure 5, in combination with control system 16 and feedback device 17 shown in Figure 1, may include or configure a subsystem of means for controlling the tension induced in the web and increasing the uniformity of the tension distribution present in web 12. A detailed description of other aspects of system 10 shown in Figure 5 will be omitted, but its components, functions, etc. are essentially the same as those described for system 10 shown in Figure 1.

[0056] The GCSM method involves gently applying multiple contact forces at at least two locations along the web's width and measuring the resulting strain. The contact forces are applied gently to ensure the web deforms far below its plastic deformation region. At each contact location, the multiple local contact forces are fitted to the strain with a polynomial equation containing linear and cubic terms to extract the local (linear) contact stiffness. This nonlinear fitting reflects the nonlinear response derived from nonlinear von Karman plate mechanics. The web tension distribution (mean tension *1 and linear change in tension σ) is obtained by nonlinear regression of the local contact stiffness at different locations. Furthermore, plastic deformation can locally damage the web and reduce measurement accuracy. To avoid local plastic deformation and ensure that all work imparted by each contact force is absorbed into the web strain energy in the elastic region, the contact forces are gently applied with a large contact sphere (a standard ping-pong ball).

[0057] To determine the web tension distribution using the linear contact stiffness measured at two locations on the web, assuming that the web strain determined by equation (1) is under quasi-static loading, the linear combination of acceptable basis functions is:

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[0058] where M and N are the numbers of functions along the x1 and x2 directions, respectively. mm and B mm are the amplitudes of the antisymmetric and symmetric components, respectively.

[0059] A mm , B mm Equation (15) describing the relationship between the average tension *1, the linear change in tension σ, and the local contact force F was obtained as follows:

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[0060] X1 is the coordinate of the contact position in the x1 direction. Once the web strain is obtained due to the contact force, the local contact stiffness is solved as in Eq. (16).

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[0061] where X3 is the coordinate of the contact position in the x3 direction, and A' mm =A mm / F and B′ mm =B mm / F. Based on convergence studies of distortions at the center of the web and the center of the free edge, choosing M=51 and N=18 results in M=1E4 and N=1E4 with a 1% error. Alternatively, one can choose to use M=3 and N=5 with a 20% compensation in the calculation.

[0062] Applying the same contact force at different locations results in different local strains. To understand the overall web strain profile versus contact location, we performed calculations. Using the same web properties as in Figure 3, we found that applying the same contact force F = 0.1 N at four different locations along the x1 direction on a PET web resulted in greater strain at the center than at the locations closer to the roller. This is consistent with the constraint of the simply supported boundary condition in Eq. (4). Meanwhile, along the x3 direction, we found that the web was distorted more by the applied contact force at the free edge than at the center. This indicates an edge effect on web stiffness. To understand the spatial variation of the web contact stiffness, we calculated the contact stiffness using Eqs. (15) and (16) based on the same web properties as in Figure 3. Figure 6 plots the corresponding cross-span profile of the web contact stiffness at x1 = L / 2. The following findings were obtained:

[0063] Along the longitudinal direction x1, the contact stiffness close to the simply supported boundaries is higher than in the central region, and at these boundaries the contact stiffness is eventually infinite.

[0064] There was an edge effect near the free end, and in the lateral direction x3, the local contact stiffness near the free end decreased to about half of that in the central region.

[0065] When the web was under uniform tension distribution, its contact stiffness profile was symmetric for both x1 = L / 2 and x3 = 0.

[0066] The non-uniform tension distribution caused the contact stiffness profile to change asymmetrically with respect to x3=0.

[0067] Equation (17) is based on the strain-displacement relationship in the von Karman theory and the relationship between the antisymmetric contact forces on both sides of the web in the transverse direction x2 and the web strain.

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[0068] where k'1 and k'3 are the linear and cubic coefficients for the ratio of strain to web thickness. The web strain is measured under conditions of multiple local contact forces at the same location on the web, and k'1 and k'3 are obtained by least-squares fitting. The local linear contact stiffness in the linear elastic deformation region leads to Eq. (18).

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[0069] After measuring the linear contact stiffness at at least two locations with different X3 values, the mean tension on the web and the linear change in tension, σ, can be determined. While determining the linear contact stiffness from a known mean tension and linear change in tension is easily accomplished using equations (15) and (16), it is not possible to obtain a closed-form solution for determining the mean tension and linear change in tension from the contact stiffness. The mean tension and linear change in tension were determined by nonlinear regression using a trust-region reflex algorithm. The optimization procedure minimized the root-mean-square error between the measured stiffness and the model, as shown in equation (19).

number

[0070] where r is the total number of measured positions. The average web tension at each iteration step and the slope of e with respect to the linear change in tension σ are respectively the currently estimated The average tension in the web and the linear change in tension σ are each selected to be within ±10% of each other.

[0071] [Experimental Procedure] Experimental testing was conducted based on the NCR and GCSM methods described above. As mentioned above, each method was evaluated on a fixed test stand (a web statically supported between two rollers) to allow for cross-validation of the two methods. The NCR method was further evaluated using in-line (dynamic) tests performed with a web transported by rollers in a commercial roll-to-roll system to demonstrate the performance of the NCR method in a manufacturing environment. In the experiments, the fixed test stand and roll-to-roll system were configured with the monitoring systems shown schematically in Figures 3 and 5, and the NCR and GCSM methods were performed, respectively.

[0072] In tests conducted by the NCR method on a stationary test stand and a roll-to-roll system, the monitoring system used a speaker (VISATON® FR10, VISATON GmbH & Co. KG) as device 20 in Figure 3 to excite the web vibrations, and a laser sensor (Microtrak 7000, MTI Instruments Inc.) as device 22 in Figure 3 to measure the response. A data acquisition system and processing means (corresponding to processor 24 in Figure 3) recorded and processed the vibration response detected by the laser sensor. The experiments were conducted on a PET web (film) with properties and dimensions matching those used in the simulations described above. A portion of the PET web was painted white to facilitate measurements by the laser sensor. Tension was applied by hanging a 2.34 kg or 2.85 kg low-carbon steel rod from the end of the web. Careful alignment of the roller and web was performed to minimize unevenness in tension distribution. The speaker was driven by a 1 Hz to 100 Hz chirp signal with an amplitude of 0.005 V and a duration of 200 seconds. The amplitude and phase of the response detected by the laser sensor were calculated using a fast Fourier transform. The transfer function of the web was obtained from the amplitude ratio and phase difference between the measurements on the web and the measurements on the speaker. The resonant frequency was obtained by fitting the transfer function to the half-width value of the power bandwidth of a single-degree-of-freedom system (SDOF).

[0073] In tests conducted using the GCSM method on a fixed test stand, the monitoring system used a force meter (VTSYIQI HF-5 Digital Push-Pull Force Gauge, Vetus Electronic Technology Co.) with a ping-pong ball as the contact head (Device 26, Figure 5) to deform the web and measure the resulting force. The same laser sensor as used in the NCR method (Device 28, Figure 5) and the same data acquisition system and processing means (Processor 30, Figure 5) were used to measure, record, and process the web deformation at the load location. By using a ping-pong ball contact head with a relatively large contact area, local plastic deformation of the web was minimized. Forces of 0.06 N to 0.13 N were applied to the web in increments of 0.004 N to 0.01 N, and the corresponding web deformation varied from 0.55 mm to 1.10 mm.

[0074] In an in-line test using the NCR method on a commercial roll-to-roll system, we measured the web tension distribution in two spans of a DICE web digital inkjet printer roll-to-roll system (Prototype & Production Systems, Inc.). Web tension was applied by torque from a servo motor on the unwind roller of this roll-to-roll system, and the web transport speed was adjusted by torque from a servo motor on the take-up roller. Both rollers had sensors measuring the roll radius to control the applied torque. The DICE web system did not have feedback control, as was the case when testing the dynamics of tension and speed. For these measurements, an opaque PET web with the properties listed in Table 1 in Figure 11 was used. The in-span lengths of the roll-to-roll system, designated as span 1 and span 2, were measured at 292.10 mm and 107.95 mm, respectively. Span 1 was upstream of span 2, which corresponded to the functional area of ​​the inkjet printer. A laser sensor and speaker were installed in each of the two spans. The laser sensor was oriented perpendicular to the direction of web movement.

[0075] Figures 7, 8, 9A, and 9B are graphs containing data from cross-validation experiments between NCR and GCSM. For the NCR data shown in Figure 7, the speaker position remained fixed, and the laser sensor was relocated to seven different positions (X1 = 101.6 mm and X3 = 0 mm, ±22.86 mm, ±45.72 mm, and ±68.58 mm). For the GCSM data shown in Figure 8, the contact head was placed at the same seven locations as for the NCR method. The web was a PET web tensioned with a 2.34 kg hanging mass (Figures 7, 8, and 9A) or a 2.85 kg hanging mass (Figure 9B).

[0076] Figure 7 plots the frequency response function at X1 = 101.6 mm and X3 = -45.72 mm. Figure 8 plots the fit of multiple contact forces and strains at X1 = 101.6 mm and X3 = -45.72 mm using Equation (17). Figure 7 shows the frequency response function between 1 Hz and 100 Hz, including two resonant peaks. A 180° phase shift is observed as the frequency moves across the resonant region. The mean and one standard deviation of the first two resonant frequencies are f 11 =43.89±0.02Hz, f 12 =53.22±0.06Hz.

[0077] Figure 8 shows the results of fitting the contact force and strain of the GCSM method to the von Karman theory. The local contact stiffness in the linear elastic deformation region was extracted using Eqs. (17) and (18). k′1 = 0.007909 ± 0.000223, k′2 = 0.000107 ± 0.000005, and k = 62.27 ± 1.76 N / m.

[0078] Figures 9A and 9B compare the contact stiffness and web tension distribution in the NCR and GCSM methods when the web is subjected to tension from hanging masses of 2.34 kg and 2.85 kg, respectively. The environmental conditions for measuring the data in Figure 9A were an air pressure of 102.67 kPa, a temperature of 21°C, and a relative humidity of 68%, with a calculated air density of 1.208 kg / m. 3The root mean square error between the stiffness of the seven contact locations measured by the NCR method and the GCSM method was 3.00 Nm -1 The NCR method measured the web tension distribution with an average tension of 134.49 N / m and a linear change in tension of ±0.2724, while the GCSM method measured the web tension distribution with an average tension of 139.26 N / m and a linear change in tension of ±0.2619 with a regression error (Equation (19)) e = 2.4594.

[0079] Because the NCR method did not distinguish the sign of the linear change in tension, its value was chosen to have the same sign as the GCSM method in the graph plotted in Figure 9A. The errors in the mean, maximum, and minimum tensions between the two methods were 3.43%, 2.62%, and 4.78%, respectively. The percentage of cross-span tension variation relative to the mean tension (2σ) was 54.48%. This variation can significantly affect the performance of printed electronic devices and existed despite optimal conditions for web alignment. Furthermore, the observations showed an edge effect on contact stiffness, consistent with theory.

[0080] Figure 9B shows a comparison of contact stiffness and web tension distribution using the NCR and GCSM methods with a 2.85 kg hanging mass. The environmental conditions for these measurements were air pressure 101.84 kPa, temperature 21 °C, relative humidity 76%, and a calculated air density of 1.198 kg / m. 3 The measured resonant frequency was f 11 =49.01±0.06Hz, f 12 = 62.16 ± 0.55 Hz. The root mean square error between the contact stiffnesses determined by the NCR and GCSM methods was 15.84 N / m. The mean tension and linear change in tension measured by the NCR method were 176.59 N / m and ± 0.3602, respectively. On the other hand, the mean tension and linear change in tension measured by the GCSM method were 211.84 N / m and ± 0.4542, respectively, with a regression error (Equation (19)) of e = 12.6698. The errors for the mean tension, maximum tension, and minimum tension between the two methods were 16.64%, 28.25%, and 2.34%, respectively.

[0081] On the web, the GCSM method revealed high contact stiffness at X3 = ±45.72 mm. The average stress measured by the NCR method was 139.0 MPa, which was greater than the yield strength of the PET web. The web likely underwent localized plastic elongation along the x1 direction. This localized plastic elongation reduces the local web areal mass density and local web thickness. Equations (6) through (9) revealed that a slight decrease in the overall web areal mass density due to localized plastic elongation slightly increases the resonant frequency. Therefore, the NCR method slightly overpredicted the average tension using equations (10) and (12). The GCSM method used the local contact stiffness extracted by the von Karman theory shown in equations (18) and (19). As the local web thickness decreased, the predicted linear contact stiffness increased, resulting in an overprediction of the web tension. Because contact stiffness was measured in limited locations, the localized plastic elongation affected the GCSM method more than the NCR method in the region where localized plastic elongation occurred. In Figure 9B, without the two abnormally high localized contact stiffnesses, the average tension was 175.33 N / m, the linear change in tension was 0.2894, and e = 2.9621. Compared to the results using the NCR method, when the two abnormally high contact stiffness measurements were excluded, the errors in the average, maximum, and minimum tensions between the NCR and GCSM methods were reduced to 0.72%, 5.88%, and 10.27%, respectively.

[0082] The above tests were performed on a static web, and it is clear that the NCR and GCSM methods can also be used with a moving web as long as the web line speed is much less than the critical line speed. As the web line speed approaches the critical line speed, the resonant frequency drops to zero.

[0083] To demonstrate the performance of the NCR method in a practical manufacturing environment, the NCR method was used in an in-line test conducted on a commercial roll-to-roll system. In this test, measurements were performed at a single position on two different spans of the roll-to-roll system at different conveying speeds. The environmental conditions during the measurements were an air pressure of 102.71 kPa, an air temperature of 21°C, a humidity of 43%, and an air density of 1.212 kg / m. 3 The frequency was swept between 40 Hz and 100 Hz to measure the resonance in span 1, and between 140 Hz and 200 Hz to measure the resonance in span 2.

[0084] In-line testing was performed at conveying speeds of 0 (fixed), 0.98 m / min to 1.26 m / min, and 1.93 m / min to 2.24 m / min in Span 1, and 0 (fixed), 1.07 m / min to 1.31 m / min, and 1.85 m / min to 2.22 m / min in Span 2. All conveying speeds (except for the fixed speed) were within the range of typical conveying speeds used in the manufacturing of flexible printed devices. The normalized conveying speed was defined as the ratio of the conveying speed to the critical conveying speed. The maximum test conveying speed of approximately 2 m / min was much lower than the estimated critical conveying speeds of the web, which were 53.57 m / s and 55.89 m / s for Span 1 and 47.32 m / s and 47.48 m / s for Span 2. This indicates that it is safe to ignore the effect of web conveying speed on the NCR method during testing. The measured static tension of the web in span 1 was significantly smaller than the tension measured when the web was moving. This was hypothesized to be the effect of the unwind and rewind motor movements on the web tension distribution. As the web began to move, the frictional resistance between the web and the roller changed, causing tension fluctuations in some spans.

[0085] Figures 10A-10C show the transfer function and the SDOF fitting used to extract the resonant frequency when the conveying speed was set to 0, 1, and 2 m / min, respectively. When the web was moving, the actual conveying speed varied up to 0.26 m / min. The transfer function for the moving web was noisier than that for the stationary web. Possible causes of this noise were identified. One is the effect of web surface irregularities and roughness on the laser sensor output. As the web moves, imperfections on the web surface can be falsely detected as web distortion. Another possible cause is noise from the motor driving the web being transmitted through the web, causing it to vibrate. Such spurious vibrations can be detected by the laser sensor and captured in data analysis. Another possible source of noise is changes in web tension caused by the rotation of the unwind and rewind motors. Ultimately, noise was not an obstacle to implementing the NCR method, as it did not prevent the NCR method from accurately identifying the resonant frequency of the web.

[0086] Table 2 in Figure 12 shows the results of in-line measurements of the web tension distribution in two spans of the roll-to-roll system. The cross-span linear variation of tension in span 2 is negligible, but in span 1 it varies by up to 35.58%, indicating that tension varies differently across the spans of the roll-to-roll system. The average tension in span 2 is 21.46% to 28.29% smaller than that in span 1. When the linear variation of tension is small, σ 2 had low negative values. This was caused by ignoring higher order tension variations and errors in fitting and measurement. However, negative values ​​of σ 2 This did not have a significant impact on the use of the NCR method, since it is reasonable to approximate the case where the tension distribution is small as being uniform.

[0087] From the above studies and tests, it is clear that uneven distribution of web tension in a roll-to-roll process can lead to uneven device performance across the width of the web. Both the NCR and GCSM methods were implemented to measure the average tension and linear change in tension in the web (which can alternatively or additionally allow for the calculation of the average stress and linear change in stress in the web based on the cross-section of the web). Referring to the roll-to-roll system 10 shown in FIG. 1, the average tension and linear change in tension measurements provided by the NCR and GCSM methods can be used as feedback to the control system 16. This allows the control system 16 to be used to control the tension distribution across the width of the web 12 using a variety of known or yet to be developed techniques, including, for example, accelerating, decelerating, and / or adjusting the position of one or more rollers 14 (e.g., raising, lowering, and / or changing the axial orientation of one or both rollers 14), applying and / or generating additional tension to the web 12 at one or more locations across the width of the web 12, and, by way of non-limiting example, contacting the web 12 with one or more additional rollers 14 positioned upstream, downstream, or between the rollers 14. The NCR and GCSM approaches are inexpensive to implement and can flexibly accommodate different spans of web path without requiring recalibration. From this research and testing, the following conclusions were drawn:

[0088] Increasing the linear change in tension leads to densely clustered resonant frequencies f 11 and f 12 decreases and increases, respectively.

[0089] The linear variation of tension combined symmetric and antisymmetric basis functions.

[0090] The NCR method using closed-form equations measured the average tension and its linear variation with the minimum resonant frequency.

[0091] The local contact stiffness near the free edge of the web is less than the contact stiffness in the central region of the web, so the same contact force will result in more deformation at the edge of the web than in the central region of the web.

[0092] The non-uniform tension distribution causes the contact stiffness profile to vary asymmetrically about the cross center.

[0093] The GCSM method was able to measure the mean tension and its linear change from the local contact stiffness by nonlinear regression.

[0094] The NCR and GCSM methods were experimentally cross-validated, yielding an error of 3.43% for the average tension and 4.12% for the linear change in tension in the absence of local plastic elongation.

[0095] The NCR method was able to measure the tension distribution in the span of a commercial roll-to-roll system inline at three different conveying speeds.

[0096] Different spans in the same roll-to-roll system can have different average tensions and linear changes in tension.

[0097] As noted above, while the foregoing detailed description describes one or more specific embodiments of the present invention and related work, alternative aspects of the invention may be applicable by those skilled in the art. For example, systems in which the present invention may be used may differ in appearance and structure from those shown, the function of a particular component may be achieved by components having different structure but similar (but not necessarily equivalent) function, process parameters may be varied, and suitable materials may be substituted for those described. Thus, as noted above, the present invention is not limited to the embodiments described herein or shown. The parts marked with * (komeji) in the specification are to be filled with symbols or formulas as shown in the image below. *1 TIFF0007777149000021.tif10158※2 TIFF0007777149000022.tif10158※3 TIFF0007777149000023.tif10158※4 TIFF0007777149000024.tif12159※5 TIFF0007777149000025.tif11157※6 TIFF0007777149000026.tif11160

Claims

1. 1. A system for monitoring tension distribution across the width of a web in a roll-to-roll system, comprising: The roll-to-roll system includes: The web and at least first and second rollers between which the web moves in a longitudinal direction of the web; tension inducing means for inducing tension in the longitudinal direction of the web; a manufacturing means for manufacturing printed devices on a surface of the flexible substrate of said web; Equipped with The system comprises: means for inducing strain in the web by exciting vibrations in the web between the first and second rollers without contacting the web; the system is operable to determine the average tension and linear variation of tension present in the flexible substrate resulting from a non-uniform tension distribution induced in the flexible substrate between the first and second rollers; and The system comprises: a second device for detecting resonant frequencies of first and second vibrations in the web in a transverse direction perpendicular to a surface of the flexible substrate, the resonant frequencies being differentiated relative to the linear change in tension; processor means for calculating the average tension and the linear change in tension based on the resonant frequencies of the first and second vibrations; Equipped with system.

2. 2. The system of claim 1, wherein the processor means uses a tension Kirchhoff plate model to define the spatial dependence of eigenmodes across the width of the web and calculates the average tension and the linear change in tension based on the resonant frequencies of the first and second vibrations.

3. The system of claim 1 , wherein the first and second resonant frequencies detected by the second device are two minimum resonant frequencies in the vibration of the web.

4. The system of claim 1 , wherein the web is in contact with a fluid between the first and second rollers.

5. 5. The system of claim 4, wherein the fluid is modeled as an inviscid, incompressible fluid and used to estimate the effect of aerodynamic loading on the first and second resonant frequencies and eigenmodes of the web.

6. The system of claim 1 , wherein the web resides in a vacuum between the first and second rollers.

7. 10. The system of claim 1, further comprising means for controlling the tension induced in the web to increase the uniformity of the tension distribution present in the flexible substrate between the first roller and the second roller.

8. 1. A method for monitoring tension distribution across a web in a roll-to-roll process, the method comprising: moving the web between first and second rollers in a longitudinal direction of the web; creating tension in the web in a longitudinal direction of the web such that tension exists in the flexible substrate of the web between the first and second rollers; operating a system to determine the average tension and linear changes in tension present in the flexible substrate caused by tension induced in the web causing a non-uniform tension distribution in the flexible substrate between the first and second rollers; The system comprises: means for inducing strain in the web by exciting vibrations in the web between the first and second rollers without contacting the web; Activating the system comprises: detecting resonant frequencies of first and second vibrations in the web in a transverse direction perpendicular to a surface of the flexible substrate, the resonant frequencies being differentiated relative to the linear change in tension; calculating the average tension and the linear change in tension based on the resonant frequencies of the first and second vibrations; Including, method.

9. 9. The method of claim 8, further comprising using a tension Kirchhoff plate model to determine the spatial dependence of eigenmodes across the width of the web and to calculate the average tension and the linear change in tension based on the resonant frequencies of the first and second vibrations.

10. The method of claim 8 , wherein the detected first and second resonant frequencies are two minimum resonant frequencies in the vibration of the web.

11. The method of claim 8 , wherein the web is in contact with a fluid between the first and second rollers.

12. 12. The method of claim 11, wherein the fluid is modeled as an inviscid, incompressible fluid and used to estimate the effect of aerodynamic loading on the first and second resonant frequencies and eigenmodes of the web.

13. The method of claim 8 , wherein the web is in a vacuum between the first and second rollers.

14. 10. The method of claim 8, further comprising controlling the tension induced in the web to increase the uniformity of the tension distribution present in the flexible substrate between the first and second rollers.

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