Maximum Drawing Ratio

The assumption of a single, maximum allowable limit draw ratio is incorrect. The table values ​​for β₁₀₀ are based on empirical data for a punch diameter of 100 mm and a sheet thickness of 1 mm. In the case of deviating geometries, the limiting drawing ratio β_max should be used.

The following equation represents an empirical approximation valid up to a ratio of d/s₀   = 300 applies. The constant e varies between 0.05 and 0.15, with the smaller value for easily formable materials with low surface friction and the larger for poorly formable and rough sheet metal.8

The limiting drawing ratio can be improved by various measures :36

• Increasing the sheet thickness s₀
• Reduction of the ratio of drawn part height / drawn part diameter h/d_s
• Increasing the die radius steel r_Z ⇒ 10 s₀ and aluminum r_Z ⇒ 16 s₀
• Increasing the punch corner radius r_S
• Reduction of the drawing gap u_z⇒ 0.95...0.99 s₀
• Increase in uniform elongation A_g
• Increase in mean anisotropy   r > 1
• Increase of hardening exponent n
• Reduction of the hold-down pressure p_n
• Reduction of friction on the drawing ring μ_Z
• Increase in friction on the punch μ_St
• improvement of lubrication
• Optimization of the surface structure of the sheet metal
• Optimization of the surface structure of the tool