Flatness (crossbow / concavity)

Depending upon the application, users may also need to specify flatness and camber. There are no industry standards for flatness per ASTM. A standard flatness tolerance used in the past was 0.003 inches per inch (.076 mm/25.4 mm) of strip width (i.e. .003" PIW). This tolerance is not an accurate measure of flatness for the wider widths, as flatness does not vary in direct proportion to the width. Flatness is best described as an arc and the flatness tolerance increases exponentially.

However, it is not always a true arc and therefore is very difficult to utilize a standard formula. The type of edge, condition, thickness and width of material all play a role in determining a suitable tolerance for flatness. A more accurate determination for a No. 1 edge material is one which uses the PIW formulas as shown in table below. Flatness on No. 3 and No. 5 edge material will be slightly higher due to toe-down. In measuring flatness on slit material, it is imperative to remove any burr to eliminate the burr height from the flatness measurement.

Theis Flatness / crossbow PIW formulas A,B
  This table is applicable only for
hardened and tempered with finished edge
  Width in Inches (mm)  
Specified Up to 1" 1 to 4" Over 4 to 9.5"
thickness (25.4 mm) (25.4 to 101.6 mm) (101.6 to 241.3 mm)
inches (mm) excl. incl. incl.
  PIW flatness tolerances, in. (mm) maximum
(Multiply actual width by value below)
Under 0.010 0.003 0.003 0.003
(0.25) (0.08) (0.08) (0.08)
0.010 to 0.025 0.002 0.003 0.003
(0.25 to 0.635) (0.05) (0.08) (0.08)
0.025 to 0.050 0.0015 0.002 0.003
(0.635 to 1.27) (0.04) (0.05) (0.08)
0.050 to 0.125 0.001 0.0015 0.003
(1.2 to 3.18) incl. (0.025) (0.04) (0.08)

     A.  Tolerances apply only to strip with No. 1 edge
     B.  For tighter tolerances, consult your Theis representative

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