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Use the formula F = U × ω², where U is unbalance in kg·m and ω is angular velocity in rad/s.

If your unbalance is in g·mm, convert to kg·m by dividing by 10⁶. Angular velocity ω = 2π × n / 60, where n is RPM.

Example: 1000 g·mm at 3000 RPM → F = 0.001 × 314.16² ≈ 98.7 N

Unbalance is measured in mass × distance:

• g·mm (gram-millimeters) — most common industrially
• oz·in (ounce-inches) — North America
• kg·m — SI unit

1 oz·in = 720 g·mm. To convert g·mm to kg·m, divide by 10⁶.

Centrifugal force F = m × r × ω². Since ω is proportional to RPM, doubling the speed quadruples the force.

This is the fundamental reason why high-speed machines (turbines, spindles, turbochargers) need much tighter balance grades than slow machines.

The unbalance force creates a rotating load vector at 1× RPM. This:

• Increases dynamic bearing load → reduces bearing L₁₀ life
• Generates vibration at 1× RPM frequency
• Causes shaft deflection and seal wear
• Can excite resonances in the support structure

For rolling element bearings, bearing life is inversely proportional to load³, so even a modest increase in force significantly reduces bearing life.

Unbalance force is the excitation; vibration is the response. The vibration amplitude depends on:

• Force magnitude (from unbalance × ω²)
• Machine dynamic stiffness (mass, stiffness, damping)
• Proximity to resonance (critical speeds)

The relationship is: vibration velocity ≈ F / (dynamic stiffness). Near resonance, the response is amplified by the quality factor Q.