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Research Papers

Boundary Conditions That Govern the Lateral Behavior of Flexible Webs in Roll to Roll Process Machines

[+] Author and Article Information
B. Fu, A. Reddy, S. Vaijapurkar

Research Assistant

R. Markum

Research Engineer

J. K. Good

Professor
Fellow ASME
Mechanical and Aerospace Engineering,
Oklahoma State University,
Engineering North 218,
Stillwater, OK 74078
e-mail: james.k.good@okstate.edu

Keyence Corporation of America, 669 River Drive, Suite 403, Elmwood Park, NJ 07407.

Dassault Systems, Simulia, Rising Sun Mills, 166 Valley St., Providence, RI 02909-2499.

Beta LaserMike Americas, 8001 Technology Blvd., Dayton, OH 45424.

National Instruments Corporation, 11500 N MoPac Expwy Austin, TX 78759-3504.

LabVIEW is a trademark of National Instruments Corporation, Austin, TX.

3M Company, 3M Corporate Headquarters, 3M Center, St. Paul, MN 55144-1000.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 19, 2012; final manuscript received April 3, 2013; published online October 14, 2013. Assoc. Editor: Hiroyuki Sugiyama.

J. Comput. Nonlinear Dynam 9(1), 011010 (Oct 14, 2013) (11 pages) Paper No: CND-12-1181; doi: 10.1115/1.4025278 History: Received October 19, 2012; Revised April 03, 2013

Thin web materials are commonly transported through machinery where a process adds value to the web. The flexible web is supported intermittently by contact with rollers. The friction forces associated with this contact are largely responsible for determining the lateral mechanics and dynamics of the thin web transiting rollers in roll-to-roll process machinery. The investigation focuses on cases where slippage between the rollers and web has become substantial and has resulted in a complex lateral behavior of the web. Two methods are presented for investigating the frictional forces and the resulting lateral behavior. The first method employs explicit finite element (FE) dynamic analysis to study the lateral mechanics of the web after steady state behavior has been achieved. This method allows the direct study of the frictional forces. The second method employs Laser Doppler Velocimetry in a novel experimental noncontact technique to examine internal loads within the web, which were influenced by the frictional forces. Both methods are shown to provide results, which agree with one another and with previous analysis. The analyses are used to form a new friction boundary condition between a web and roller that will benefit other analysis methods.

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References

Figures

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Fig. 1

Lateral deformation and tension distribution before (a) and after (b) web slippage on R2 due to misalignment of R3

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Fig. 2

Schematic of LDV target positions for moment measurement

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Fig. 3

Schematic of test section

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Fig. 4

Roll-to-roll web machine with instrumented test section of Fig. 3. The linear ways (C) and pivot allow the LDVs (A) to infer moments in the web in Spans A and B and on R2. Displacement sensors (B) are used to measure web edge position prior to R2 and after R3.

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Fig. 5

Explicit model of a web transiting four rollers

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Fig. 6

(a) Web lateral displacements at the entry point of each roller. (b) Web lateral velocities at the entry point of each roller.

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Fig. 7

(a) Comparison of lateral displacement of simulations and experiments and the calculated slope curve for a misalignment at R3 of 1.29 mrad. (b) Comparison of lateral displacement of simulations and experiments and the calculated slope curve for a misalignment at R3 of 3.89 mrad. (c) Comparison of lateral displacement of simulations and experiments and the calculated slope curve for a misalignment at R3 of 7.78 mrad. (d) Comparison of lateral displacement of simulations and experiments and the calculated slope curve for a misalignment at R3 of 8.76 mrad. (e) Comparison of lateral displacement of simulations and experiments and the calculated slope curve for a misalignment at R3 of 9.74 mrad.

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Fig. 8

Slope of the elastic axis of the web at the entry and exit of roller R2

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Fig. 9

(a) Moment from simulation and tests for a misalignment of 1.29 mrad at R3. (b) Moment from simulation and tests for a misalignment of 3.89 mrad at R3. (c) Moment from simulation and tests for a misalignment of 7.78 mrad at R3. (d) Moment from simulation and tests for a misalignment of 8.76 mrad at R3. (e) Moment from simulation and tests for a misalignment of 9.74 mrad at R3.

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Fig. 10

Comparison of moments at the entry and exit of R2 from simulations and Good [9]

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Fig. 11

CShear1 stress distribution on R2 for the 7.78 mrad misalignment case

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Fig. 12

CShear 2 stress distribution on R2 for the 7.78 mrad misalignment case

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Fig. 13

Forces of slip between the web and R2 due to a misalignment of 7.78 mrad at R3

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