CNC Toolholder Balance Calculator: ISO 1940-1 G2.5 & Bearing Load
Under ISO 1940-1 and ISO 21940-11, permissible specific unbalance is eper = (9549.3 × G) / RPM (in µm or g·mm/kg), and permissible residual unbalance is Uper = m × eper (in g·mm). A 1.20 kg HSK-A63 toolholder assembly spinning at 20,000 RPM to grade G2.5 allows eper = 1.19 µm and Uper = 1.43 g·mm (6.3 N radial bearing load).
ISO 1940-1 / ISO 16084 Toolholder Balance Grade (G2.5 / G6.3) & Bearing Force Calculator
Calculate maximum permissible center-of-gravity eccentricity eper = 9549.3·G/n (µm), permissible residual unbalance Uper = m·eper (g·mm), rotating centrifugal bearing load Fc = U·10−6·ω², and runout-induced unbalance.
How Do ISO 1940-1 (G2.5) and ISO 16084 Define Toolholder Unbalance?
In high-speed CNC machining, rotating centrifugal force grows with the square of angular velocity (Fc = U × 10−6 × ω²), where ω = 2π·n / 60 rad/s and residual unbalance U is in g·mm (NIST SI Units Reference). In ISO 21940-11 / ISO 1940-1 (Rotor Balance Quality), the balance quality grade G (such as G2.5 or G6.3) is a physical velocity in mm/s equal to the center-of-gravity eccentricity eper multiplied by angular speed ω. Solving for eccentricity yields eper [µm] = 9549.297 × G / n.
Multiplying that specific eccentricity by the complete rotating assembly mass m (in kg)—which must include the toolholder body, retention knob, collet, nut, and cutting tool—gives the permissible residual unbalance Uper [g·mm] = m × eper. Because very light modular toolholders under 1.0 kg get penalized with sub-micron tolerances under permanent rigid-rotor rules, ISO 16084 (Balancing of Rotating Tools) supplements ISO 1940-1 by linking allowable tool unbalance directly to the dynamic load rating of the machine's front spindle bearings and taper repeatability.
| Spindle Speed n | G2.5 Limit eper (Uper/kg) | G2.5 Radial Force (1 kg) | G6.3 Limit eper (Uper/kg) | G6.3 Radial Force (1 kg) |
|---|---|---|---|---|
| 8,000 RPM (ω=838 rad/s) | 2.98 µm (2.98 g·mm/kg) | 2.1 N (0.5 lbf) | 7.52 µm (7.52 g·mm/kg) | 5.3 N (1.2 lbf) |
| 10,000 RPM (ω=1047 rad/s) | 2.39 µm (2.39 g·mm/kg) | 2.6 N (0.6 lbf) | 6.02 µm (6.02 g·mm/kg) | 6.6 N (1.5 lbf) |
| 12,000 RPM (ω=1257 rad/s) | 1.99 µm (1.99 g·mm/kg) | 3.1 N (0.7 lbf) | 5.01 µm (5.01 g·mm/kg) | 7.9 N (1.8 lbf) |
| 15,000 RPM (ω=1571 rad/s) | 1.59 µm (1.59 g·mm/kg) | 3.9 N (0.9 lbf) | 4.01 µm (4.01 g·mm/kg) | 9.9 N (2.2 lbf) |
| 18,000 RPM (ω=1885 rad/s) | 1.33 µm (1.33 g·mm/kg) | 4.7 N (1.1 lbf) | 3.34 µm (3.34 g·mm/kg) | 11.9 N (2.7 lbf) |
| 20,000 RPM (ω=2094 rad/s) | 1.19 µm (1.19 g·mm/kg) | 5.2 N (1.2 lbf) | 3.01 µm (3.01 g·mm/kg) | 13.2 N (3.0 lbf) |
| 24,000 RPM (ω=2513 rad/s) | 0.99 µm (0.99 g·mm/kg) | 6.3 N (1.4 lbf) | 2.51 µm (2.51 g·mm/kg) | 15.8 N (3.6 lbf) |
| 30,000 RPM (ω=3142 rad/s) | 0.80 µm (0.80 g·mm/kg) | 7.9 N (1.8 lbf) | 2.01 µm (2.01 g·mm/kg) | 19.8 N (4.4 lbf) |
| 40,000 RPM (ω=4189 rad/s) | 0.60 µm (0.60 g·mm/kg) | 10.5 N (2.4 lbf) | 1.50 µm (1.50 g·mm/kg) | 26.4 N (5.9 lbf) |
Why Does Spindle Taper Runout (TIR) Destroy High-Speed Balance?
Even if a shrink-fit chuck is balanced on a Haimer Tool Dynamic or Schunk balancing stand to 0.5 g·mm, any radial runout (TIR) at the spindle taper or collet shifts the assembly's center of gravity off the axis of rotation by eTIR ≈ 0.5 × TIR. On a 1.20 kg tool assembly, a seemingly minor 3.0 µm TIR (e = 1.50 µm) generates 1.80 g·mm of dynamic unbalance and 7.9 N of radial load all by itself—already exceeding the entire 1.43 g·mm G2.5 budget at 20,000 RPM! Stepping down to G6.3 at 20,000 RPM raises allowable unbalance to 3.61 g·mm (15.8 N bearing load).
| Toolholder Assembly | Typical Mass m | Balance Specification | Max Residual Unbalance Uper | Centrifugal Bearing Force Fc |
|---|---|---|---|---|
| HSK-A40 / BT30 High-Speed Finishing | 0.55 kg | G2.5 at 24,000 RPM | 0.55 g·mm (e=0.99 µm) | 3.5 N (0.8 lbf) |
| HSK-A63 Standard Machining Center | 1.20 kg | G2.5 at 20,000 RPM | 1.43 g·mm (e=1.19 µm) | 6.3 N (1.4 lbf) |
| CAT40 / BT40 Dual-Contact Milling | 1.45 kg | G2.5 at 15,000 RPM | 2.31 g·mm (e=1.59 µm) | 5.7 N (1.3 lbf) |
| CAT40 / BT40 Roughing Assembly | 1.80 kg | G6.3 at 12,000 RPM | 9.02 g·mm (e=5.01 µm) | 14.3 N (3.2 lbf) |
| HSK-A100 / CAT50 Heavy Face Mill | 3.80 kg | G6.3 at 8,000 RPM | 28.58 g·mm (e=7.52 µm) | 20.1 N (4.5 lbf) |
Worked Example: 1.20 kg HSK-A63 Assembly at 20,000 RPM
In our default 1.20 kg HSK-A63 setup at 20,000 RPM (ω = 2094.4 rad/s, Grade G2.5), permissible eccentricity is eper = 1.19 µm and maximum residual unbalance is 1.43 g·mm, producing a modest 6.3 N (1.4 lbf) radial bearing force (which quadruples to 25.1 N if speed doubles to 40,000 RPM), as detailed in Machinery's Handbook (31st Ed., Industrial Press) and V-flange standard ASME B5.50 (V-Flange Tool Shanks). Compare taper speed ratings on our CAT40 / BT40 / HSK63A spindle taper chart, check collet nut torque on the ER collet chuck DIN 6499 chart, evaluate cutter overhang in the end mill deflection calculator, and size drawbar stacks on the Belleville disc spring stack calculator.
Cite this page
ToolSpecVault Engineering Data Team. (2026, October 29). CNC Toolholder Balance Calculator: ISO 1940-1 G2.5 & Bearing Load. ToolSpecVault. https://toolspecvault.com/cnc-toolholder-balance-grade-g2-5-unbalance-calculator/