Automotive Transmission Gear Manufacturing, CNC Cylindrical Gear Hobbing Kinematics
CNC Gear Hobbing Sync RPM, Feed & Cycle Time Formula
Calculate Hob Cutter Spindle Speed (RPM), Electronic-Gearbox Synchronized Worktable Speed (RPM), Axial Saddle Feed Rate (mm/min), and Hobbing Cut Time per Stack (min).
Switching from a 2-start TiAlN carbide/PM-HSS roughing hob to a 1-start finishing hob on a 96-tooth gear slows worktable rotation 5.7x—stretching cycle time from 1.37 to 12.47 minutes!
**Continuous Generating Gear Hobbing** meshes a worm-shaped fluted **Hob Cutter (`Outside Diameter d_h` mm, `Thread Starts z_0 = 1..4`)** spinning at **`N_h = (1,000 * V_c) / (pi * d_h)`** (`RPM` for Surface Cutting Speed `V_c` m/min) with a CNC direct-drive **Worktable (`Gear Tooth Count z_2`)** locked electronically to the exact kinematic **Worm-Wheel Indexing Ratio `N_w = N_h * (z_0 / z_2)`** (`RPM`)! Because involute generating facets form once per full worktable revolution, **Axial Saddle Feed `f_a`** (`mm/work-rev`) advances down the gear blank at **`v_f = N_w * f_a`** (`mm/min`), machining **Total Approach + Face Stroke `L_{tot} = b + L_{approach}`** (`mm`) in **`t_m = L_{tot} / v_f`** (`minutes`)!
Verify on a `48`-Tooth EV Reduction Helical Gear Cut Dry with a `2`-Start Coated Hob—Hob_Diameter `d_h` = 95.0 mm (B2), Cutting_Speed `V_c` = 135 m/min (B3), Hob_Starts `z_0` = 2 (B4), Gear_Teeth `z_2` = 48 (B5), Axial_Feed `f_a` = 2.40 mm/work-rev (B6), and Total_Stroke `L_{tot}` = 62.0 mm (B7): Hob Spindle Speed equals `452.3` RPM (E2), Synchronized Worktable Speed equals `18.85` RPM (E3), Axial Feed Velocity equals `45.23` mm/min (E4), finishing the gear in just **`1.371` minutes** (`82.3` seconds! E5)!
| CNC Generating Gear Hobbing KPI (Hob dh=95 mm, Total Stroke=62 mm) | Formula | Verified Output |
|---|---|---|
| Hob Spindle Speed Nh (RPM) | (1000 * Cutting_Vc_m_min) / (PI() * dh_mm) | 452.3 RPM (318.3 RPM wet HSS) |
| Synchronized Table Speed Nw (RPM) | Hob_Spindle_Nh_RPM * (Starts_z0 / Teeth_z2) | 18.85 RPM (3.32 RPM @ 1-start / 96T) |
| Axial Saddle Velocity vf (mm/min) | Worktable_Nw_RPM * Axial_Feed_fa_mm_rev | 45.23 mm/min (4.97 mm/min fine finish) |
| Generating Cut Time tm (min) | Total_Stroke_Ltot_mm / Axial_Vel_vf_mm_min | 1.371 min (12.466 min = 9.1x slower!) |
Electronic-Gearbox Generating Hobbing Indexing & Cycle-Time Formula
Validate `Hob_Diameter d_h` in `[20, 400]` mm, `Cutting_Speed V_c` in `[15, 450]` m/min, `Hob_Starts z_0` in `[1, 6]`, `Gear_Teeth z_2` in `[6, 500]`, `Axial_Feed f_a` in `[0.2, 12.0]` mm/rev, and `Total_Stroke L_{tot}` in `[5, 1,000]` mm!
=LET(dh_m, B2, vc_m, B3, zs_h, B4, zg_t, B5, fa_m, B6, lt_m, B7, nh_r, (1000 * vc_m) / (PI() * dh_m), vf_m, (nh_r * (zs_h / zg_t)) * fa_m, IF(OR(dh_m < 20, dh_m > 400, vc_m < 15, vc_m > 450, zs_h < 1, zs_h > 6, zg_t < 6, zg_t > 500, fa_m < 0.2, fa_m > 12, lt_m < 5, lt_m > 1000), "Invalid Hobbing Input", ROUND(lt_m / vf_m, 3)))Single-Start AGMA Class-10 Finish Hob on `96`-Tooth Ring (`V_c = 95`, `z_0 = 1`, `f_a = 1.5`) Check
Switch to a single-start (`B4 = 1`) precision hob at `B3 = 95` m/min and `B6 = 1.50` mm/rev to cut a `B5 = 96`-tooth ring gear without lead-crown feed marks: Worktable Speed E3 drops to **`3.32` RPM** (`4.97` mm/min saddle feed in E4), multiplying Cutting Time E5 **`9.1-fold` to `12.466` minutes**!
=IF(ISTEXT(E5), E5, LET(nh_r, (1000 * B3) / (PI() * B2), ROUND(nh_r * (B4 / B5), 2)))Try the example
Use the original values or change them to test your understanding.