How to characterize warp?

Let us first consider some different situations of warped boards and identify them by name (Fig. 1)

warp_fig_1_small
Figure 1. Naming conventions for warped board

In the following let us only consider warp in cross-machine direction (up or down warp). Sign conventions say that up-warp has positive values and consequently down-warp has negative values.

There are two accepted ways of defining degree of warp.

 

Warp definition, %

The most common way is to measure the arc height and relate that to the width of the sheet. Fig. 2 gives an example where warp must not exceed 4 %.

Note that in this case is the value of the warp is directly related to the width of the sheet dimension

A US voluntary standard express acceptable warp as shown in Fig. 3. Maximum arch height is set to ¼” ( 6mm) for a blank length of 12” (305 mm).

warp_fig_2_small warp_fig_3_small
Figure 2. Scandinavian standard for acceptable warp. Figure 3. US standard for acceptable warp.

 

Warp definition, 1/R

warp_fig_4_small
Warp=1/R= (8•u)/L² [m-1]
Figure 4. Correlation between Blank Width, Arch Height and Radius

An alternative way to characterize the degree of warp is to calculate the radius (R) of the arch (Fig. 4). In order to have a value for warp of zero when the board is flat the inverse radius (1/R) is used to denote the degree of warp.

Assuming that the arch is a segment of a circle, the radius can be calculated from L and u. If the warp is less than 15 % the radius can be calculated with good approximation from the equation given in Fig. 4.

What does Warp–i calculate?

Warp – I determines locally (in cm-scale) the curvature of the blanks in the stacker across the width of the corrugator (approx. 100 separate readings). From this information we can calculate the exact profile representing the curvature of the different “outs”. (The profile is aviable live in real time).

From the so obtained results, it possible to express the warp in terms of any of the basic alternatives above;

  • % related to actual blank width (Scandinavian convention)
  • % related to specific blank width (US convention)
  • 1/R
warp_fig_5_small
Figure 5. Illustration of blanks with rills.

Both values are available to the operator on the screen as complementary information and can be used as input to a control loop. All information is stored in a data base for later retrospective search of information.

We believe that 1/R is a good alternative since it gives a solid average warp value over the full width of the machine – or for each out.

Sometimes, when there are rills in the blanks, we can have a situation as illustrated in Figure 5. Here the board itself does not show any warp – the three flaps are flat – and no correction is needed. If the determination of warp is done without considering this situation, false indication of warp can be obtained.

Warp–I Monitoring System can handle this situation and will not give false information of warp.