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Machine Tool Spindle Unbalance Calculator

Calculate permissible spindle + toolholder unbalance, eccentricity (nm), centrifugal force, and equivalent tool deflection per ISO 21940.

ISO 21940-11 HSK / BT / CAT G0.4 – G2.5
Quick presets

Results

Permissible Unbalance
Eccentricity
Centrifugal Force
Equivalent Tool Deflection Estimate
Angular Velocity ω

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

GradeApplicationTypical Speed
G0.4Ultra-precision grinding, optical> 60,000 RPM
G1.0Grinding machines, high-speed milling15,000–40,000 RPM
G2.5General machining centers, lathes5,000–24,000 RPM

Practical Example

Example — HSK-63 Toolholder at 24,000 RPM

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.

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Professional field balancing instruments for machine tool spindles and rotating assemblies. Achieve ISO 21940-11 compliance on-site.
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