Cylindrical drawing coefficient and drawing times
The cylindrical drawing coefficient is a key parameter for measuring the degree of deformation during drawing. It refers to the ratio of the diameter of the part after each drawing to the diameter of the blank (or the previously drawn part) before drawing. It is expressed as m, i.e., m = dn /dn-1 (dn is the diameter after the nth drawing, dn-1 is the diameter before drawing). A smaller drawing coefficient indicates a greater degree of deformation, more intense plastic flow of the material, and a greater susceptibility to defects such as cracking. A larger drawing coefficient reduces deformation, which reduces the risk of cracking but increases the number of drawing cycles and production costs. Properly determining the drawing coefficient is central to drawing process design and requires comprehensive consideration of factors such as material properties, mold structure, and part precision.
There are many factors that affect the drawing coefficient, and material properties are the primary factor. Materials with good plasticity and a small yield strength ratio (such as low carbon steel and brass) can use a smaller drawing coefficient; while materials with poor plasticity and a large yield strength ratio (such as high strength steel and stainless steel) require a larger drawing coefficient. For example, the first limit drawing coefficient of low carbon steel can be as low as 0.5, while the first limit drawing coefficient of stainless steel needs to be ≥0.55. The mold parameters also significantly affect the drawing coefficient. The larger the radius of the die corner, the smoother the material flow, and the drawing coefficient can be appropriately reduced; a reasonable gap between the punch and die (usually 1.1-1.2 times the material thickness) can reduce friction resistance and lower the drawing coefficient. In addition, good lubrication conditions and moderate drawing speed (usually 10-30 mm/s for steel plates) can also help reduce the drawing coefficient.
The limit drawing coefficient refers to the minimum drawing coefficient that a material can achieve under certain conditions without cracking. It is the key basis for determining the number of drawing cycles. The limit drawing coefficients of different materials must be determined through testing. Empirical data for common materials is available for reference: for low-carbon steel, the limit drawing coefficient for the first drawing is m1 = 0.5-0.55, for the second drawing, m2 = 0.7-0.75, for the third drawing, m3 = 0.75-0.8, and for the fourth drawing, m4 = 0.8-0.85. Subsequent drawing coefficients gradually increase. For example, if a cylindrical part with a diameter of 50mm is drawn from low-carbon steel and the blank diameter is 100mm, the first drawing coefficient is m1 = 50/100 = 0.5, which does not exceed the limit value and can be drawn in one cycle. However, if the blank diameter is 150mm, m1 = 50/150 ≈ 0.33 < 0.5, and multiple drawing cycles are required.
The number of deep drawing passes must be determined based on the total drawing coefficient and the limit drawing coefficients for each pass. The total drawing coefficient, mtotal, = dn / D (D is the blank diameter, dn is the final part diameter). The calculation begins with the first deep drawing pass and, using the limit drawing coefficient, extrapolates the diameter after each subsequent drawing pass until the part diameter is reached. For example, if the blank diameter is 150mm and the part diameter is 50mm, the total drawing coefficient, mtotal, = 50/150 = 0.33. For the first deep drawing, using m1 = 0.5, d1 = 0.5 × 150 = 75mm; for the second deep drawing, using m2 = 0.7, d2 = 0.7 × 75 = 52.5mm; for the third deep drawing, using m3 = 0.95 (to approximate the part diameter of 50mm), d3 = 0.95 × 52.5 = 49.875mm, = 50mm. Therefore, three deep drawing passes are required. In actual calculations, the drawing coefficient of each time should be slightly larger than the limit value, leaving a certain safety margin to avoid cracking.
Optimizing the number of deep drawing passes requires balancing production efficiency and part quality. Too few passes may result in excessive deformation and cracking, while too many passes increase process costs. Multiple deep drawing passes can also reduce material plasticity due to work hardening, necessitating additional intermediate annealing steps. For example, a cylindrical part was calculated to require four deep drawing passes. However, by optimizing the die corner radius (increasing it from 8mm to 10mm) and improving the lubrication grade, the initial drawing coefficient was reduced from 0.55 to 0.52, reducing the number of deep drawing passes to three, and thus reducing production costs. For high-precision parts, the number of deep drawing passes can be appropriately increased. Multiple, small-deformation deep drawing passes can improve dimensional accuracy and reduce the effects of springback. Once the number of deep drawing passes is determined, the deformation between each pass must be appropriately distributed. Typically, the initial deformation is greatest, with subsequent passes gradually decreasing, so that the drawing coefficients increase sequentially to ensure full utilization of the material’s plasticity.
