Continuous drawing coefficient and relative drawing height
The continuous drawing coefficient and relative drawing height are two key parameters for measuring the degree of deformation during continuous drawing. The continuous drawing coefficient reflects the proportional change in diameter during each drawing, while the relative drawing height reflects the ratio of part height to diameter. Together, they determine the feasibility and process stability of continuous drawing. Proper control of these two parameters ensures uniform material deformation and avoids defects such as cracking and wrinkling, and is the core basis for continuous drawing process design.
The continuous drawing coefficient ( mₙ ) is the ratio of the diameter after the nth drawing pass to the diameter after the n -1th drawing pass: mₙ = dₙ / dₙ₋₁ , where dₙ is the diameter after the nth drawing pass and dₙ₋₁ is the diameter after the n-1th drawing pass. The initial drawing coefficient m₁ = d₁/D₀ ( D₀ is the blank diameter). The total drawing coefficient mtotal = dₙ / D₀ = m₁ × m₂ ×… × mₙ . The continuous drawing coefficient must be greater than the material’s limit drawing coefficient to prevent cracking. For example, the first limit drawing coefficient for low-carbon steel is 0.5-0.55 , the second is 0.7-0.75 , and the third is 0.75-0.8 . Therefore, if the total drawing coefficient is 0.3 , at least three drawing passes are required (0.55 × 0.7 × 0.8 ≈ 0.308). The smaller the value of the continuous drawing coefficient, the greater the degree of deformation and the fewer drawing passes required, but the higher the risk of deformation.
Relative draw height ( H/d ) refers to the ratio of the height of the drawn part to its diameter, where H is the draw height and d is the drawn diameter. The greater the relative draw height, the greater the deformation difficulty and the more drawing passes required. For example, for a low-carbon steel cylindrical part, the maximum relative draw height for a single draw is H/d ≈ 1.5 , for a double draw is ≈ 3.0 , for a triple draw is ≈ 4.5 , and for a quadruple draw is ≈ 6.0 . The relative draw height is closely related to the continuous drawing coefficient: the smaller mₙ , the greater the H/d . The required number of draw passes should be determined based on the relative draw height during design. For example, a part with H/d = 5.0 requires four draw passes (with draw coefficients of 0.55 , 0.7 , 0.75 , and 0.8 , respectively , for a total coefficient of 0.55 × 0.7 × 0.75 × 0.8 = 0.231, resulting in an H/d of 6.0, which meets the requirement).
The distribution of continuous drawing coefficients must follow the principle of ” gradual increase” The principle of continuous drawing is to minimize the coefficient (maximum deformation) in the first drawing, and gradually increase (decreasing deformation) in subsequent drawing passes. For example, the coefficients for the four drawing passes are assigned as m₁=0.55 , m₂=0.7 , m₃=0.75 , and m₄=0.8 , showing an increasing trend. This distribution fully utilizes the material’s plasticity. The first few drawing passes exploit the material’s superior plasticity for significant deformation, while the subsequent drawing passes reduce deformation due to work hardening, thus preventing fracture. Improper coefficient distribution (e.g., subsequent coefficients are smaller than the previous ones) can lead to excessive material deformation. For example, if m₁=0.6 and m₂=0.55 , the material will be unable to withstand significant deformation during the second drawing due to work hardening, increasing the probability of fracture by over 50% .
Controlling the relative draw height depends on the material’s mechanical properties. The greater the material’s plasticity, the greater the allowable relative draw height. The relative draw height of low-carbon steel (σb = 300-400 MPa) is 50%-100% greater than that of high-carbon steel (σb = 600-800 MPa). For example, the maximum single-draw ratio H/d for high-carbon steel is approximately 0.8, while that for low-carbon steel can reach 1.5. For materials with good plasticity but lower strength, such as aluminum alloys, the relative draw height is similar to that of low-carbon steel. However, care must be taken to prevent wrinkling, so the blank holder force should be appropriately increased. The relative draw height is also related to material thickness. Thick materials (t > 3 mm) can have a relative draw height 20%-30% greater than thin materials (t < 1 mm) because thicker materials are more resistant to wrinkling and can withstand greater deformation heights.
The matching relationship between the continuous drawing coefficient and relative drawing height is key to ensuring process stability and requires adjustment through trial punching. When the relative drawing height exceeds the maximum allowable value for a given drawing cycle, the number of draws must be increased or the drawing coefficient adjusted. For example, a part with an H/d ratio of 4.0, originally planned for three draws (maximum allowable H/d = 3.5), needs to be increased to four. If significant part thinning (thinning rate > 15%) is observed after a particular draw cycle during trial punching, the drawing coefficient for that cycle should be increased (to reduce deformation) and subsequent drawing coefficients should be adjusted. Finite element simulation software (such as Dynaform) can predict the relative draw height and deformation distribution for different coefficient combinations, optimizing coefficient allocation and reducing the number of trial punches. Properly matching the continuous drawing coefficient and relative drawing height ensures efficient, high-quality continuous drawing production.
