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Metal Additive Manufacturing, Laser Powder Bed Fusion (LPBF/SLM) & Melt-Pool QA

LPBF Metal 3D Printing Volumetric Energy Density Formula

Calculate Linear Energy Density P/v (J/mm), Volumetric Energy Density VED = P/(v*h*t) (J/mm³), Theoretical Laser Melt Build Rate (cm³/hr), and Lack-of-Fusion vs Keyhole Porosity Window.

Too little J/mm³ leaves unmelted Lack-of-Fusion voids—while too much J/mm³ drills vapor Keyhole bubbles!

In Selective Laser Melting / Laser Powder Bed Fusion (LPBF) of Ti-6Al-4V, Inconel 718, and 316L stainless steel, four scan parameters govern 99.9%+ full metallurgical density: Laser Power P (W), Scan Velocity v (mm/s), Hatch Spacing h (mm between adjacent tracks), and Powder Layer Thickness t (mm)! Dividing Laser Power by swept voxel volume rate v * h * t yields Volumetric Energy Density VED = P / (v * h * t) (J/mm³), while Swept Melt Rate equals BR_th = (v * h * t * 3,600) / 1,000 cm³/hr! Below ~45 J/mm³ in 316L/Inconel, shallow melt pools fail to remelt underlying tracks ("Lack-of-Fusion" sharp crack-initiating defects); above ~105 J/mm³, metal recoil vapor pressure punches a deep unstable cavity whose collapse traps spherical gas pores ("Keyhole Porosity")!

Verify on an Aerospace Inconel 718 / 316L Single-Laser Parameter Set—Laser_Power P = 285.0 W (B2), Scan_Speed v = 960.0 mm/s (B3 -> Linear Energy Density = 0.297 J/mm in E2), Hatch_Spacing h = 0.11 mm (B4), and Layer_Thickness t = 0.040 mm (40 um, B5): Volumetric Energy Density VED lands squarely at 285 / (960 * 0.11 * 0.04) = 67.47 J/mm³ (E3), Theoretical Single-Laser Build Rate hits 15.21 cm³/hr (E4), and Process Window Check confirms "DENSE PROCESS WINDOW" (E5)!

LPBF Melt-Pool KPI (P=285 W, v=960 mm/s, Hatch h=0.11 mm, Layer t=0.04 mm)FormulaVerified Output
Linear Energy Density LED (J/mm)Laser_Power_W / Scan_Speed_mm_s0.297 J/mm (0.570 @ v = 500 mm/s)
Volumetric Energy Density (J/mm³)P_W / (v_mm_s * Hatch_mm * Layer_mm)67.47 J/mm³ (129.55 @ v = 500 mm/s!)
Theoretical Build Rate (cm³/hr)(v_mm_s * Hatch_mm * Layer_mm * 3600)/100015.21 cm³/hr (7.92 @ v = 500 mm/s)
Porosity Defect Window (45–105)<45 Lack-of-Fusion; >105 KeyholeDENSE PROCESS WINDOW (KEYHOLE @ 500!)

LPBF Volumetric Energy Density (VED) & Defect Regime Classification Formula

Validate Power P in [20, 2000] W, Scan_Speed v > 10 mm/s, Hatch_Spacing h in (0.01, 1.0] mm, and Layer_Thickness t in (0.005, 0.30] mm!

=LET(pw_w, B2, vs_m, B3, ht_m, B4, lt_m, B5, IF(OR(pw_w < 20, pw_w > 2000, vs_m <= 10, ht_m <= 0.01, ht_m > 1, lt_m <= 0.005, lt_m > 0.3), "Invalid LPBF Input", LET(vd_j, pw_w / (vs_m * ht_m * lt_m), IF(vd_j < 45, "LACK-OF-FUSION RISK", IF(vd_j <= 105, "DENSE PROCESS WINDOW", "KEYHOLE POROSITY RISK")))))

Over-Slowed Corner Scan Keyhole Vapor-Pore Check (Set Scan Speed v = 500.0 mm/s)

Slow Scan_Speed B3 from 960.0 mm/s down to 500.0 mm/s without ramping down laser power at acute part overhangs: Build Rate E4 drops to 7.92 cm³/hr while Volumetric Energy Density E3 spikes to 129.55 J/mm³, triggering "KEYHOLE POROSITY RISK" in E5!

=IF(ISTEXT(E3), E3, ROUND((B3 * B4 * B5 * 3600) / 1000, 2))

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