Determination of blank size for simple rotating body drawing
Determining the blank dimensions for simple rotational drawn parts (such as cylindrical, spherical, and conical shapes) is a fundamental step in drawing process design. Its core principle is the principle of volume invariance during plastic deformation, which states that the blank’s volume equals the volume of the drawn part (ignoring the effects of thickness variations). Due to the symmetry of rotational parts, the blank is typically circular. After determining the diameter through calculation, adjustments must be made based on the material’s plasticity, the number of draws, and the required part precision to ensure a smooth drawing process and acceptable part dimensions.
For cylindrical drawn parts, the blank diameter calculation requires considering the volumes of the barrel, bottom, and fillet. The formula is: D = √(d² + 4dh + 6.28r (d + 2r) + 8r²), where D is the blank diameter, d is the inner diameter of the cylindrical part, h is the height of the cylindrical part, and r is the radius of the bottom fillet. This formula, based on the law of conservation of volume, decomposes the cylindrical part into the cylindrical portion, the bottom fillet, and the flat bottom. The volumes of each portion are calculated separately, then combined to obtain the blank volume, which is then converted to the diameter of the circular blank. For example, for a cylindrical part, d=50mm, h=80mm, and r=5mm, substituting into the formula we can get D≈√(50²+4×50×80+6.28×5×(50+2×5)+8×5²)=√(2500+16000+6.28×5×60+200)=√(18500+1884+200)=√20584≈143.5mm.
For cylindrical drawn parts with flanges, the flange volume must be added to the blank diameter calculation. The formula is adjusted to: D = √ (d₁²+4d₂h+6.28r₁(d₂+2r₁)+6.28r₂(d₁+2r₂)+8 (r₁²+r₂²)) , where d₁ is the flange diameter, d₂ is the barrel diameter, r₁ is the fillet radius between the barrel and the flange, and r₂ is the fillet radius of the barrel bottom. When calculating the flange volume, it is important to ensure that its thickness matches the barrel body. Therefore, the difference in area is reflected in the formula by the difference between the flange and barrel diameters. For example, for a flanged part with d₁=100mm , d₂=50mm , h=60mm , r₁=8mm , r₂=5mm , the billet diameter D ≈√ (100²+4×50×60+ 6.28×8×(50+16)+6.28×5×(100+10)+8×(64+25))≈√(10000+12000+6.28×8×66+6.28×5×110+8×89)≈√(22000+3315.84+3455+712)=√29482.84≈171.7mm.
Calculating the blank dimensions for spherical and conical drawn parts requires a more complex volumetric formula. The blank diameter D for a spherical part is 1.13√(d³/2h) (d is the sphere’s diameter, h is its height), or by flattening the sphere into a roughly circular shape and applying empirical corrections. Conical parts are categorized as shallow (half-cone angle > 45°) or deep (half-cone angle < 45°) based on the angle of the taper. The blank diameter for shallow tapers can be approximated using the formula for cylindrical parts. For deep tapers, the slope of the taper must be considered, and the blank diameter is determined by integrating the volume. For example, for a hemispherical part with a diameter of 100mm and a height of 50mm, the blank diameter D is ≈ 1.13×√(100³/(2×50)) = 1.13×√(1000000/100) = 1.13×100 = 113mm. In actual production, a 1%-2% margin should be added to prevent underdrawing.
Correction of blank dimensions must account for the effects of material thinning and springback. Material thinning is inevitable during the drawing process (especially at the barrel wall, where thinning can reach 10%-20%). Therefore, the calculated blank diameter needs to be appropriately increased (by 0.5%-1%) to compensate for the resulting undersize. For high-precision parts, a correction factor must be determined through test punching. For example, after the initial test punching, measure the actual height and diameter of the part. If the height is less than the designed value, increase the blank diameter by 0.5-1mm. Furthermore, material springback can increase the diameter of the part’s mouth. For parts requiring strict control of mouth dimensions, the blank diameter can be appropriately reduced, or a post-drawing shaping step can be added for correction.
After the blank size is determined, it is necessary to verify whether it meets the requirements of the drawing process. The ratio of the blank diameter to the finished product diameter (i.e., the total drawing coefficient) must be greater than the material’s limit drawing coefficient; otherwise, multiple drawing passes are required. For example, the calculated blank diameter is 140mm, the finished product diameter is 50mm, and the total drawing coefficient is 0.357. If the material is low-carbon steel (with an initial limit drawing coefficient of 0.5), at least three drawing passes are required. If the total drawing coefficient is too small, the blank diameter needs to be adjusted (appropriately reduced) or the part structure needs to be modified (such as increasing the fillet radius) to ensure the feasibility of the drawing process. By combining theoretical calculations with trial punching corrections, the blank size of simple rotating body drawn parts can be accurately determined, laying the foundation for subsequent drawing processes.
