Aluminum & Copper Extrusion Presses, Billet Container Friction & Profile Speed
Hot Extrusion Ratio, Johnson Ram Pressure & Exit Speed Formula
Calculate Extrusion Area Ratio R_ext = A_0 / A_f, Direct-Extrusion Peak Ram Pressure p_ext (MPa), Hydraulic Press Force (MN), and Runout-Table Profile Exit Velocity (m/min).
Why direct billet extrusion needs extra container-wall friction tonnage at stroke start—and shoots profile out 40x faster than the ram!
Pushing a heated 6061/6063 aluminum billet of container diameter D_0 (mm -> area A_0 = (PI()/4)*D_0^2) and remaining billet length L (mm) through a profile die opening of cross-sectional area A_f (mm²) defines Extrusion Ratio R_ext = A_0 / A_f! By incompressible plastic volume continuity, Profile Runout Exit Velocity multiplies ram speed by the full Extrusion Ratio: v_exit = (v_ram_mm_s * R_ext * 60) / 1,000 m/min (limiting ram speed before hot surface tearing / "fir-tree" speed cracking occurs)! Simultaneously, Direct (Forward) Extrusion pushes the entire billet length L sliding along the stationary container liner—adding dead-zone container friction (2 * L / D_0) atop Johnson’s homogeneous+redundant die deformation term (0.8 + 1.5 * LN(R_ext)) to demand Peak Breakthrough Pressure p_ext = Y_f * (0.8 + 1.5 * LN(R_ext) + (2 * L) / D_0) MPa and Hydraulic Press Force F_ram = (p_ext * A_0) / 10^6 MegaNewtons (MN)!
Verify on a 2,000-Ton (20 MN) Architectural Aluminum Extrusion Press—Container_Bore D_0 = 200.0 mm (B2 -> A_0 = 31,415.9 mm²), Extruded_Profile_Area A_f = 785.0 mm² (B3 -> Extrusion Ratio R_ext = 40.02 in E2), Hot_480C_Flow_Stress Y_f = 48.0 MPa (B4), Ram_Advance_Speed v_ram = 12.0 mm/s (B5), and Initial_Billet_Length L = 500.0 mm (B6): Peak Breakthrough Pressure hits 544.04 MPa (E3), Required Press Force equals 17.09 MN (~1,743 metric tons, E4), and Runout-Table Exit Speed reaches 28.81 m/min (E5)!
| Direct Hot Extrusion KPI (D0=200 mm, Af=785 mm², Yf=48 MPa, vram=12, L=500 mm) | Formula | Verified Output |
|---|---|---|
| Extrusion Area Ratio R_ext | ((PI()/4) * D0^2) / Profile_Area_Af | 40.02 (89.76 @ thin Af = 350 mm²) |
| Peak Breakthrough Pressure (MPa) | Yf * (0.8 + 1.5*LN(R_ext) + 2*L/D0) | 544.04 MPa (602.19 @ Af = 350 mm²) |
| Hydraulic Press Force Fram (MN) | (p_ext_MPa * A0_mm2) / 1,000,000 | 17.09 MN (18.92 MN @ Af = 350 mm²) |
| Profile Runout Speed (m/min) | (Ram_mm_s * R_ext * 60) / 1000 | 28.81 m/min (64.63 m/min @ Af=350!) |
Johnson Direct-Extrusion Breakthrough Tonnage & Continuity Runout Formula
Validate Container_Bore D_0 > 30 mm, Profile_Area A_f > 0 with Extrusion Ratio R_ext >= 2.0, Hot_Flow_Stress Y_f > 0, Ram_Speed > 0, and Billet_Length L >= 0!
=LET(db_m, B2, af_m, B3, yf_m, B4, vr_m, B5, lb_m, B6, IF(OR(db_m <= 30, af_m <= 0, yf_m <= 0, vr_m <= 0, lb_m < 0), "Invalid Extrusion Input", LET(az_m, (PI() / 4) * (db_m ^ 2), rx_t, az_m / af_m, IF(rx_t < 2, "RATIO BELOW EXTRUSION MIN", ROUND((vr_m * rx_t * 60) / 1000, 2)))))Thin-Wall Solar Frame 89.8:1 High-Ratio Speed-Cracking Check (Set Profile Area A_f = 350.0 mm²)
Switch to a thin-walled hollow solar frame die of Area A_f B3 = 350.0 mm²: Extrusion Ratio E2 jumps to 89.76, Breakthrough Force E4 climbs to 18.92 MN (near the 20 MN press limit!), and Exit Speed E5 surges to 64.63 m/min—alerting operators to throttle ram speed if alloy 6061 tears above 35 m/min!
=IF(ISTEXT(E5), E5, LET(az_m, (PI() / 4) * (B2 ^ 2), rx_t, az_m / B3, px_m, B4 * (0.8 + 1.5 * LN(rx_t) + (2 * B6) / B2), ROUND((px_m * az_m) / 1000000, 2)))Try the example
Use the original values or change them to test your understanding.