Aero-Elasticity of a Paper Web
Paper sheet transport is a time-varying process, in part due to:
⦁ the unsteadiness of the supply and spooling mechanisms,
⦁ the frictional force of mechanical elements in contact with the sheet, and
⦁ the aerodynamic instabilities and induced aero-elastic forces, i.e., flow induced vibrations.
ESI was commissioned to evaluate how the relative motion of a paper sheet relates to:-
i) the external mechanical forces placed on a paper sheet during the manufacturing process,
ii) the speed range in which a paper sheet can be transported through manufacturing web, and
iii) the conditions likely to produce failure of the sheet,
using flow visualization, thermal anemometry, and load cell measurements.
Figure 1: Lateral Movement of the Paper Sheet Caused by a Low Pressure Region
Flow induced instabilities can produce unsteady forces that result in paper sheet oscillation along and normal to the paper sheet; a condition that can result in greater unsteady loading, and ultimately leading to sheet failure. Figure 1 depicts a local low pressure region on a paper sheet undergoing a medium speed production operation.
However, when a large-scale paper web underwent very high speed production processes, aero-elastic effects were observed with oscillations reaching as high as +/- 2.7 inches, but were reduced by 20% when preliminary flow conditioning was used.
Typical oscillations in the unsupported paper web are shown in Figure 2 and when flow conditioning was installed.
Figure 2: Aero-Elastic Oscillations of the Paper Web
During High Speed Production
An FFT analysis of acquired load-cell data indicated that the energy contained in these oscillations varied between 37 to 40 Hz. The 85 to 100 Hz ranges and were due to excitation and vibration of the system, Figure 3.
Figure 3: Spectrum of the Energy Associated with
the Paper Oscillations