Gear & Spline Production Machining, Internal Pull-Broaching Pitch, RPT & Tonnage
Internal Pull-Broaching Engaged Teeth & Tonnage Formula
Calculate Simultaneous Engaged Broach Teeth Ze, Total Instantaneous Uncut Chip Cross-Section (mm²), Peak Hydraulic Pull Force (kN), and Machine Pull Tonnage (metric tf).
Pulling a 12.5-mm-pitch spline broach through a longer 95 mm gear hub engages 7.6 teeth at once—packing chip gullets solid and snapping a $9,500 M42 HSS broach shank!
**Internal Hydraulic Pull Broaching** cuts `24`-tooth involute gear hubs and keyways in a single `6`-second stroke because every stepped cutting ring stands higher by **Rise Per Tooth `RPT` (`a_z` mm/tooth, `0.04–0.09` mm roughing)**—yet because chips CANNOT escape until each tooth exits the far face of **Workpiece Bore Length `L_w` (`mm`)**, **Tooth Pitch `p` (`mm`, sized via `p ~= 1.75 * sqrt(L_w)`)** MUST keep **Simultaneous Engaged Teeth `Z_e = L_w / p` inside `3.0 <= Z_e <= 6.0`** (`< 2.5` chatters; `> 6.5` overloads shank root area and packs spiral chips solid inside gullets)! Multiplying **Total Instantaneous Chip Area `A_{chip} = Z_e * b_{perim} * RPT`** (`mm²` across Total Cut Perimeter `b_{perim}` mm) by Specific Cutting Pressure `k_c` (`MPa` = `N/mm²`) gives **Broaching Pull Force `F_b = (A_{chip} * k_c) / 1,000`** (`kN`, or **`F_b / 9.80665` metric ton-force `tf`** against pull-head shank tensile rating)!
Verify on a `10`-Ton Vertical Spline Pull-Broaching Machine Cutting Alloy Steel (`k_c = 2,420` MPa)—Hub_Length `L_w` = 56.0 mm (B2), Broach_Pitch `p` = 12.5 mm (B3), Summed_Spline_Cut_Perimeter `b_{perim}` = 78.5 mm (B4), Roughing_Rise_Per_Tooth `RPT` = 0.065 mm (B5), and Specific_Cutting_Force `k_c` = 2,420 MPa (B6): Simultaneous Engaged Teeth `Z_e` equals **`4.48`** (`ideal 3–6 window!` E2), Active Chip Cross-Section equals `22.86` mm² (E3), Peak Pull Force equals **`55.32` kN** (E4), requiring **`5.64` tf** (`56%` of `10`-tf press rating! E5)!
| Internal Pull-Broaching KPI (Pitch p=12.5 mm, Cut Perimeter=78.5 mm, kc=2,420 MPa) | Formula | Verified Output |
|---|---|---|
| Simultaneous Engaged Teeth Ze | Workpiece_Bore_Lw_mm / Tooth_Pitch_p_mm | 4.48 IDEAL (7.60 > 6 GULLET JAM!) |
| Total Active Chip Area (mm²) | Engaged_Ze * Perimeter_mm * RPT_mm | 22.86 mm² (56.68 mm² heavy step) |
| Peak Broach Pull Force (kN) | (Active_Chip_Area_mm2 * Specific_kc_MPa) / 1000 | 55.32 kN (137.16 kN shank overload!) |
| Machine Pull Tonnage (tf) | Broach_Pull_Force_kN / 9.80665 | 5.64 tf safe (13.99 tf > 10-tf STALL!) |
Internal Pull-Broaching Engaged Teeth, Chip Area & Hydraulic Tonnage Formula
Validate `Bore_Length L_w` in `[5, 600]` mm, `Tooth_Pitch p` in `[2, 50]` mm, `Cut_Perimeter b_{perim}` in `[2, 800]` mm, `Rise_Per_Tooth RPT` in `[0.005, 0.400]` mm, and `Specific_Force k_c` in `[400, 5,000]` MPa!
=LET(lw_m, B2, pt_m, B3, pw_m, B4, rp_m, B5, kc_m, B6, fk_n, ((lw_m / pt_m) * pw_m * rp_m * kc_m) / 1000, IF(OR(lw_m < 5, lw_m > 600, pt_m < 2, pt_m > 50, pw_m < 2, pw_m > 800, rp_m < 0.005, rp_m > 0.4, kc_m < 400, kc_m > 5000), "Invalid Broach Input", ROUND(fk_n / 9.80665, 2)))Stacked Double Gear Blanks (`L_w = 95` mm) + Heavy `0.095` mm RPT Broach-Snap Check
Stack two hubs (`B2 = 95.0` mm) on a coarse `B5 = 0.095` mm/tooth broach without widening pitch: Engaged Teeth E2 climbs to **`7.60`**, Active Chip Section E3 jumps `2.48x` to `56.68` mm², and Pull Load E5 spikes to **`13.99` tf (`137.16` kN in E4)**—stalling a `10`-ton cylinder or snapping the pull-neck tang!
=IF(ISTEXT(E5), E5, ROUND(((B2 / B3) * B4 * B5 * B6) / 1000, 2))Try the example
Use the original values or change them to test your understanding.