Centerless Grinding Through-Feed & Workrest Angle Formula

Setting a centerless grinder workrest blade right on wheel centerline (beta = 0.29°) copies every incoming bump into a constant-width Reuleaux 3-lobe triangle!

**Through-Feed Centerless Grinding** finishes automotive piston pins, hydraulic spool valves, and bearing needles to `< 0.5` um roundness without spindle centers by trapping Workpiece Diameter `d_w` (`mm`) between a fast Grinding Wheel (`D_g` mm), an angled carbide Workrest Blade, and a rubber-bonded **Regulating Wheel (`Diameter D_r` mm, `Speed N_r` RPM)** tilted by **Feed Inclination Angle `alpha` (`1°–6°`)**! Resolving **Regulating Peripheral Velocity `v_r = (pi * D_r * N_r) / 1,000`** (`m/min`) along the workpiece axis fixes **Axial Through-Feed Rate `v_f = pi * D_r * N_r * sin(alpha)`** (`mm/min`)! Crucially, elevating the workpiece center by **Above-Center Height `h_w`** (`mm` above the wheel-centerline chord) creates **Tangency Rounding Angle `beta = arcsin(h_w / ((D_g + d_w) / 2)) + arcsin(h_w / ((D_r + d_w) / 2))`** (`degrees`, ideally **`6°–8°`**): grind on-center (`beta ~= 0°`) and a high spot touching the regulating wheel pushes the opposite side straight into the grinding wheel—generating `3`-lobe or `5`-lobe **odd-harmonic out-of-roundness** that fools two-point micrometers!

Verify on a `24` mm Hardened Wrist-Pin Through-Feed Setup—Regulating_Wheel_Diameter `D_r` = 300 mm (B2), Regulating_Speed `N_r` = 32.0 RPM (B3), Tilt_Angle `alpha` = 3.50° (B4), Grinding_Wheel_Diameter `D_g` = 500 mm (B5), Workpiece_Diameter `d_w` = 24.0 mm (B6), and Above-Center_Height `h_w` = 11.0 mm (B7): Regulating Surface Speed equals `30.16` m/min (E2), Axial Through-Feed Rate equals **`1,841.2` mm/min** (`1.841` m/min in E4), and Tangency Rounding Angle `beta` sits right in the sweet spot at **`6.30°`** (`6°–8°` odd-lobe suppression window! E5)!

Centerless Regulating-Wheel Helix Feed & Dall/Rowe Rounding-Angle Formula

Validate `Regulating_Diameter D_r` in `[100, 600]` mm, `Regulating_RPM` in `[5, 300]`, `Tilt_Angle alpha` in `[0.5, 10.0]`°, `Grinding_Diameter D_g` in `[200, 800]` mm, `Work_Diameter d_w` in `[1, 200]` mm, and `Above-Center Height h_w` in `[0, 0.25 * (D_r + d_w)]` mm!

=LET(dr_m, B2, nr_p, B3, al_d, B4, dg_m, B5, dw_m, B6, hw_m, B7, IF(OR(dr_m < 100, dr_m > 600, nr_p < 5, nr_p > 300, al_d < 0.5, al_d > 10, dg_m < 200, dg_m > 800, dw_m < 1, dw_m > 200, hw_m < 0, hw_m > 0.25 * (dr_m + dw_m)), "Invalid Centerless Input", ROUND(((ASIN(hw_m / ((dg_m + dw_m) / 2)) + ASIN(hw_m / ((dr_m + dw_m) / 2))) * 180) / PI(), 2)))

Dropped Workrest Blade (`h_w = 0.5` mm) + Steep `6°` Feed 3-Lobe Out-of-Roundness Check

Forget to shim the workrest blade after wheel dressing (`h_w` drops to `B7 = 0.50` mm) while steepening tilt to `B4 = 6.0°`: Axial Feed E3 rushes at `3,152.5` mm/min (`3.153` m/min in E4), while Tangency Angle `beta` E5 collapses to **`0.29°`**—guaranteeing `3`-lobed Reuleaux pins that pass `2`-point snap gauges yet seize inside cylindrical bores!

=IF(ISTEXT(E5), E5, ROUND(PI() * B2 * B3 * SIN((B4 * PI()) / 180), 1))

Further reading

• Arte Sheets Lesson — Surface Grinding Specific Energy & Malkin Burn Power Formula
• Arte Sheets Lesson — Lathe Single-Point Turning Theoretical Ra & Rz Roughness