Free Engineering Tool
Machine Tool Spindle Unbalance Calculator
Calculate permissible spindle + toolholder unbalance, eccentricity (nm), centrifugal force, and equivalent tool deflection per ISO 21940.
Results
Permissible Spindle Unbalance (ISO 21940)
- G — balance quality grade (mm/s)
- m — spindle + toolholder assembly mass (kg)
- ω = 2π·n/60 — angular velocity (rad/s)
Eccentricity (Specific Unbalance)
For high-speed spindles, eccentricity is often expressed in nanometers (1 μm = 1000 nm).
Centrifugal Force & Tool Deflection
The centrifugal force from unbalance acts on the spindle bearings, causing a deflection at the tool tip. The deflection estimate uses a simplified spindle stiffness model (≈ 20 N/μm typical for HSK-63).
Balance Grades for Machine Tools
| Grade | Application | Typical Speed |
|---|---|---|
| G0.4 | Ultra-precision grinding, optical | > 60,000 RPM |
| G1.0 | Grinding machines, high-speed milling | 15,000–40,000 RPM |
| G2.5 | General machining centers, lathes | 5,000–24,000 RPM |
Practical Example
Given: Mass = 2 kg, Speed = 24,000 RPM, Grade = G2.5
ω = 2π × 24000 / 60 = 2,513.3 rad/s
Uper = 2.5 × 2 × 1000 / 2513.3 = 1.99 g·mm
eper = 2.5 × 1000 / 2513.3 = 0.995 μm = 995 nm
F = 1.99 / 1e6 × 2513.3² = 12.6 N
⚠️ Note: Tool deflection estimate uses a simplified stiffness model. Actual deflection depends on bearing preload, spindle design, tool overhang, and clamping. Use this as a rough guide only.
Professional field balancing instruments for machine tool spindles and rotating assemblies. Achieve ISO 21940-11 compliance on-site.