Free Engineering Tool · #007
Centrifugal Force from Unbalance
Calculate the centrifugal force generated by residual unbalance in a rotating part. Enter unbalance and speed to instantly see force results.
Results
Centrifugal Force from Unbalance
When a rotor has residual unbalance U (mass × eccentricity), rotation generates a centrifugal force:
- F — centrifugal force (N)
- U — unbalance in kg·m (= g·mm × 10⁻⁶)
- ω — angular velocity = 2πn/60 (rad/s)
- n — rotational speed (RPM)
Speed Dependence
Since force depends on ω², the relationship with RPM is quadratic:
Doubling the speed quadruples the centrifugal force. This is why high-speed machinery (turbines, turbochargers) requires much tighter balance tolerances.
Equivalent Static Load
The equivalent static mass is the mass that, placed at rest on a bearing, would produce the same load as the rotating unbalance force:
Practical Example
Given: Unbalance U = 1000 g·mm, Speed n = 3000 RPM
ω = 2π × 3000 / 60 = 314.16 rad/s
U (SI) = 1000 × 10⁻⁶ = 0.001 kg·m
F = 0.001 × 314.16² = 98.7 N
Equivalent static load: 98.7 / 9.81 = 10.06 kg
Typical Unbalance Forces
| Unbalance (g·mm) | Speed (RPM) | Force (N) | Application |
|---|---|---|---|
| 100 | 10 000 | 109.7 | Turbocharger |
| 1 000 | 3 000 | 98.7 | Electric motor |
| 5 000 | 1 500 | 123.4 | Centrifugal pump |
| 10 000 | 750 | 61.7 | Large fan |
| 50 000 | 300 | 49.3 | Crusher |
⚠️ Note: This calculation assumes a rigid rotor below the first critical speed. Above the first critical speed, the dynamic response is more complex and requires a rotor-dynamics analysis.
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.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Reduce unbalance forces on-site with our portable balancing instruments. Achieve ISO 21940-11 compliance and extend bearing life.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
