DIN 509 Undercut Chart & Calculator: Form E, F, G & H
Under DIN 509:2006-12 and ISO 18388, shaft relief undercuts allow turning tools and grinding wheels to clear a 90° shoulder without corner interference. A standard Ø25 mm shaft uses DIN 509 - F 0.8 x 0.3 with radius r = 0.8 mm, depth t1 = 0.3 mm, root diameter 24.40 mm, and width f = 2.5 mm.
DIN 509:2006-12 Undercut Dimensions & Grinding Allowance Calculator (Form E, F, G, H)
Lookup standard DIN 509 relief groove callouts (r × t1), groove width f, shoulder recess t2 × g, turned root diameter d1 − 2t1, and grinding transition offsets (15-degree entry-ramp geometry assumed on this page) a1 = z2·cot(15°) and a2 = z1·cot(15°).
When Should You Specify DIN 509 Form E, Form F, Form G, or Form H?
Every single-point carbide turning insert and vitrified grinding wheel carries a finite nose radius (typically 0.4 mm or 0.8 mm). If a blueprint calls for a bearing inner ring or gear hub to seat flush against a vertical shaft shoulder without an undercut, the mating bore chamfer must be oversized or it will ride up on the tool nose radius and cock out of square. The German standard published by DIN German Institute for Standardization and harmonized in International Organization for Standardization (ISO) ISO 18388 defines four distinct relief geometries tailored to specific downstream finishing operations:
• Form E (Cylindrical Surface Grinding Only): Recessed exclusively into the cylindrical diameter d1 by depth t1 over length f with a 15° entry ramp. Select Form E whenever the cylindrical bearing journal is precision ground to an ISO 286 k6 or m6 shaft fit while the vertical shoulder face remains as-turned.
• Form F (Cylindrical + Planar Shoulder Grinding): Combines the radial groove t1 × f with a secondary axial undercut t2 × g cut into the vertical shoulder face so an angled plunge or traverse wheel in our cylindrical grinding wheel calculator can dress both surfaces crisp to the corner.
• Form G & Form H (Indexable Turning Insert Reliefs): Form G (R0.4 × 0.2) provides the smallest possible footprint for thin-walled parts, whereas Form H uses a 30° transition and larger radius (R0.8 or R1.2) to minimize the torsional notch factor Kt modeled in our shaft torsional shear stress calculator.
| Diameter Range d1 | Normal Load Designation | Radius r & Radial Depth t1 | Width f & Form F Shoulder (t2, g) | High Alternating Fatigue Series | Counter-Angle |
|---|---|---|---|---|---|
| >1.6 to 3 mm | DIN 509 - F 0.2 x 0.1 | R0.2 mm / t1=0.1 mm | f=1.0 mm / t2=0.1 mm / g=0.9 mm | — (no fatigue series below Ø18) | 15° entry ramp |
| >3 to 10 mm | DIN 509 - F 0.4 x 0.2 | R0.4 mm / t1=0.2 mm | f=2.0 mm / t2=0.1 mm / g=1.1 mm | — (no fatigue series below Ø18) | 15° entry ramp |
| >10 to 18 mm | DIN 509 - F 0.6 x 0.2 | R0.6 mm / t1=0.2 mm | f=2.0 mm / t2=0.1 mm / g=1.4 mm | — (no fatigue series below Ø18) | 15° entry ramp |
| >18 to 50 mm | DIN 509 - F 0.8 x 0.3 | R0.8 mm / t1=0.3 mm | f=2.5 mm / t2=0.2 mm / g=2.3 mm | DIN 509 - F 1.2 x 0.2 (R1.2 × 0.2) | 15° entry ramp |
| >50 to 80 mm | DIN 509 - F 0.8 x 0.3 | R0.8 mm / t1=0.3 mm | f=2.5 mm / t2=0.2 mm / g=2.3 mm | DIN 509 - F 1.6 x 0.3 (R1.6 × 0.3) | 15° entry ramp |
| >80 to 125 mm | DIN 509 - F 1.2 x 0.4 | R1.2 mm / t1=0.4 mm | f=4.0 mm / t2=0.3 mm / g=3.4 mm | DIN 509 - F 2.5 x 0.4 (R2.5 × 0.4) | 15° entry ramp |
| >125 mm | DIN 509 - F 1.2 x 0.4 | R1.2 mm / t1=0.4 mm | f=4.0 mm / t2=0.3 mm / g=3.4 mm | DIN 509 - F 4.0 x 0.5 (R4.0 × 0.5) | 15° entry ramp |
How Do Grinding Allowances z1 and z2 Shift Pre-Turned Undercut Widths?
When rough-turning a shaft prior to heat treatment and cylindrical grinding, leaving radial grinding stock z1 (per side) and axial shoulder stock z2 raises the rough surfaces above the finished datum planes. Because the undercut entry ramp slopes at 15° (or 30° on Form H), the rough-turning tool engages the outer diameter and face earlier by the trigonometric offset of the 15-degree entry-ramp geometry assumed on this page (general reference: Machinery's Handbook (31st Ed., Industrial Press); not a tabulated DIN 509 value):
a1 = z2 · cot(15°) = 3.73205 · z2 and a2 = z1 · cot(15°) = 3.73205 · z1
Therefore, the CNC lathe programmer must program the pre-grind axial groove length to fmach = f + a1 and the radial shoulder relief to gmach = g + a2 so that after the grinding wheel removes z1 and z2, the finished undercut lands exactly at nominal f and g.
| Grinding Stock z1, z2 | Form F/G Offset (15°) | Compensated F 0.8×0.3 Widths | Form H Offset (30°) | Pre-Grind OD (Ø25 Nominal) |
|---|---|---|---|---|
| z1 = z2 = 0.05 mm | +0.19 mm (z·cot 15°) | fmach = 2.69 mm / gmach = 2.49 mm | +0.09 mm (z·cot 30°) | Ø25.10 mm → Ø25.00 mm |
| z1 = z2 = 0.10 mm | +0.37 mm (z·cot 15°) | fmach = 2.87 mm / gmach = 2.67 mm | +0.17 mm (z·cot 30°) | Ø25.20 mm → Ø25.00 mm |
| z1 = z2 = 0.15 mm | +0.56 mm (z·cot 15°) | fmach = 3.06 mm / gmach = 2.86 mm | +0.26 mm (z·cot 30°) | Ø25.30 mm → Ø25.00 mm |
| z1 = z2 = 0.20 mm | +0.75 mm (z·cot 15°) | fmach = 3.25 mm / gmach = 3.05 mm | +0.35 mm (z·cot 30°) | Ø25.40 mm → Ø25.00 mm |
| z1 = z2 = 0.25 mm | +0.93 mm (z·cot 15°) | fmach = 3.43 mm / gmach = 3.23 mm | +0.43 mm (z·cot 30°) | Ø25.50 mm → Ø25.00 mm |
| z1 = z2 = 0.30 mm | +1.12 mm (z·cot 15°) | fmach = 3.62 mm / gmach = 3.42 mm | +0.52 mm (z·cot 30°) | Ø25.60 mm → Ø25.00 mm |
| z1 = z2 = 0.40 mm | +1.49 mm (z·cot 15°) | fmach = 3.99 mm / gmach = 3.79 mm | +0.69 mm (z·cot 30°) | Ø25.80 mm → Ø25.00 mm |
| z1 = z2 = 0.50 mm | +1.87 mm (z·cot 15°) | fmach = 4.37 mm / gmach = 4.17 mm | +0.87 mm (z·cot 30°) | Ø26.00 mm → Ø25.00 mm |
Worked Examples: Programming DIN 509 Reliefs on Bearing Journals
Worked Example 1 (Ø25 mm Bearing Seat with Form F): A Ø25k6 bearing journal requires both cylindrical and shoulder grinding with z1 = 0.15 mm radial stock and z2 = 0.10 mm face stock. Our engine selects DIN 509 - F 0.8 x 0.3: turn the pre-grind journal OD to Ø25.30 mm, plunge the undercut root to Ø24.40 mm with an R0.8 mm nose insert, and extend the rough axial width to fmach = 2.87 mm (2.5 + 0.37 mm) and shoulder height to gmach = 2.86 mm.
Worked Example 2 (Ø40 mm Form E vs Ø60 mm Fatigue Series): For a Ø40 mm journal ground only on the diameter (z1 = 0.20 mm), DIN 509 - E 0.8 x 0.3 specifies root diameter Ø39.40 mm and width f = 2.5 mm. For a heavily loaded Ø60 mm gearbox shaft under alternating bending, switching to the fatigue series selects DIN 509 - F 1.6 x 0.3 (R1.6 × 0.3, root Ø59.40 mm). For threaded shoulders, use the DIN 76 thread undercut calculator, and for circlip grooves see the DIN 471/472 retaining ring groove chart.
The DIN 509 relief dimensions in the tables above follow DIN German Institute for Standardization, and the shaft diameter tolerances in the worked examples follow International Organization for Standardization (ISO) ISO 286. In precision CNC turning and 5-axis milling setups, holding consistent feature geometry across production lots requires verifying both the nominal target dimension and the upper and lower inspection limits before releasing the first article from quality control. Machinists can export the active readout card directly to a blueprint PNG or pin multiple calculations into a combined shop traveler sheet.
Before taking a finish pass on the machine, always verify that your measuring instruments—including pitch micrometers, optical comparators, cylindrical plug gages, and dial test indicators—are thermally stabilized near the standard reference temperature of 20°C (68°F). When cutting high-strength alloy steels, titanium, or work-hardening austenitic stainless grades, tool nose wear and radial cutter deflection can shift finished dimensions by several hundredths of a millimeter over a single batch, making in-process gaging essential for zero-scrap manufacturing.
Cite this page
ToolSpecVault Engineering Data Team. (2026, November 2). DIN 509 Undercut Chart & Calculator: Form E, F, G & H. ToolSpecVault. https://toolspecvault.com/din-509-undercut-dimensions-chart-calculator/