Precision Abrasive Machining, Surface/Creep-Feed Grinding & Malkin Grinding Burn
Surface Grinding Specific Energy, MRR & Burn Power Formula
Calculate Volumetric Grinding Removal Rate Qw (mm³/s), Specific Removal Rate Per Wheel Width Q'w (mm³/(mm·s)), Grinding Spindle Power (kW), and Workpiece Heat-Partition Burn Load (kW).
Abrasive grinding consumes 10x more specific energy per mm³ than milling—and 65%–80% of that heat flows straight into the steel!
Unlike sharp positive-rake carbide milling (`u ≈ 2–4` J/mm³, where `>80%` of cutting heat leaves harmlessly in thick steel chips!), abrasive aluminum-oxide or CBN grinding grit has steep negative rake, plowing and sliding wear flats that drive Specific Grinding Energy `u` up to `30–70+` J/mm³! At Wheel Contact Width `b_w` (mm), Downfeed Depth of Cut `a_e` (mm), and Worktable Traverse Speed `v_w` (m/min -> `v_w * 1,000 / 60` mm/s), Volumetric Removal Rate is `Q_w = b_w * a_e * (v_w * 1,000 / 60)` (mm³/s), Specific Removal Rate per mm of wheel width is `Q'_w = Q_w / b_w` (`mm³/(mm·s)`), Net Grinding Spindle Power is `P_grind = (u * Q_w) / 1,000` (kW), and Stephen Malkin’s Heat Partition Ratio `epsilon_w` (`~0.65–0.80` in shallow conventional steel grinding!) conducts `Q_work = epsilon_w * P_grind` kW directly into the ground surface—risking white-layer untempered martensite ("grinding burn") and tensile residual cracks when wheel dressing is overdue!
Verify on a Hardened Bearing-Raceway Surface Grind—Wheel_Contact_Width `b_w` = 18.0 mm (B2), Downfeed `a_e` = 0.025 mm (B3), Table_Speed `v_w` = 16.0 m/min (B4 -> `Q_w = 120.00` mm³/s in E2 & `Q'_w = 6.67` mm³/(mm·s) in E3), Sharp-Dressed_Specific_Energy `u` = 42.0 J/mm³ (B5 -> Spindle Power = `5.040` kW in E4), and Workpiece_Heat_Partition `epsilon_w` = 0.72 (B6): Heat Conducted Into Steel equals `3.629` kW (E5)!
| Malkin Surface Grinding KPI (bw=18 mm, ae=0.025 mm, vw=16 m/min, u=42 J/mm³) | Formula | Verified Output |
|---|---|---|
| Volumetric Removal Rate Qw (mm³/s) | bw_mm * ae_mm * ((vw_m_min * 1000) / 60) | 120.00 mm³/s |
| Specific Removal Q'w (mm³/mm·s) | ae_mm * ((vw_m_min * 1000) / 60) | 6.67 mm³/(mm·s) |
| Grinding Spindle Power (kW) | (Specific_Energy_J_mm3 * Qw_mm3_s) / 1000 | 5.040 kW (8.160 kW @ glazed dull wheel!) |
| Workpiece Thermal Burn Flux (kW) | Spindle_Power_kW * Heat_Partition_eps_w | 3.629 kW (5.875 kW triggers temper burn!) |
Specific Removal Rate Q'w, Grinding Power & Malkin Thermal Partition Formula
Validate `Width b_w > 0` mm, `Downfeed a_e > 0` mm, `Table_Speed v_w > 0` m/min, `Specific_Energy u >= 10` J/mm³ (always `>= 13.8` J/mm³ adiabatic melting energy of iron in fine grinding!), and `Heat_Partition epsilon_w` in `(0, 1]`!
=LET(bw_m, B2, ae_m, B3, vw_m, B4, us_j, B5, ep_w, B6, IF(OR(bw_m <= 0, ae_m <= 0, vw_m <= 0, us_j < 10, ep_w <= 0, ep_w > 1), "Invalid Grinding Input", LET(qw_s, bw_m * ae_m * ((vw_m * 1000) / 60), pg_k, (us_j * qw_s) / 1000, ROUND(pg_k * ep_w, 3))))Glazed Undressed Wheel Wear-Flat Burn Spike Check (Set Specific Energy u B5 = 68.0 J/mm³)
Skip diamond wheel dressing until grit wear flats drive Specific Energy `u` B5 from `42.0` up to `68.0` J/mm³: Material Removal E2 stays `120.00` mm³/s, yet Spindle Power E4 jumps `+61.9%` to `8.160` kW and Workpiece Heat Input E5 surges to `5.875` kW—explaining why operators monitor spindle-load kW meters to trigger automatic diamond dressing before grinding burn ruins hardened gears!
=IF(ISTEXT(E5), E5, LET(qw_s, B2 * B3 * ((B4 * 1000) / 60), ROUND((B5 * qw_s) / 1000, 3)))Try the example
Use the original values or change them to test your understanding.