| name | rotor-balancing |
| description | Rotor balancing — static and dynamic imbalance, ISO G grades, residual unbalance, influence coefficient method, field balancing, two-plane balancing. |
| metadata | {"priority":6,"promptSignals":{"phrases":["rotor balancing","dynamic balance","static balance","ISO G grade","influence coefficient","field balancing","unbalance"],"minScore":4}} |
Rotor Balancing — Complete Skill
Types of Imbalance
Static (force) imbalance: CG not on spin axis → net radial force
Characterized by single correction mass in one plane
Tests with: non-spinning journal supports (cradle)
Couple (moment) imbalance: CG on axis but two equal/opposite masses at different planes
No net radial force but moment couple → vibration at 2 planes
Cannot detect by static test — requires spinning
Dynamic imbalance: combination of static + couple
Requires two correction planes for full correction
Quasi-static: CG off-axis AND couple — two correction planes still needed
Imbalance Quantification
Eccentricity: e = u/M [mm] — distance from CG to geometric axis
Unbalance: U = m_correction × r_correction = M × e [g·mm or oz·in]
Specific unbalance: e = U/M [g·mm/kg = μm] — eccentricity in microns
ISO 1940-1 Balance Grades (G grades)
G_grade = e × ω_max [mm/s] (velocity of CG)
e [mm], ω [rad/s]
| Grade | G [mm/s] | Application |
|---|
| G0.4 | 0.4 | Gyroscopes, grinding spindles |
| G1 | 1.0 | Audio spindles, precision grinders |
| G2.5 | 2.5 | Gas turbines, turbines, aircraft jet engines |
| G6.3 | 6.3 | General industrial machines, pumps, electric motors |
| G16 | 16 | Agricultural machinery, V-belt pulleys |
| G40 | 40 | Crankshafts for single-cylinder engines |
| G100 | 100 | Large crankshafts for slow diesel |
Allowable residual unbalance:
U_per = G × M / ω_max [g·mm]
where M = rotor mass [g], ω_max = max operating speed [rad/s]
Example: G6.3 grade, M = 10 kg = 10,000 g, n = 3000 rpm → ω = 314 rad/s
U_per = 6.3 × 10,000 / 314 = 200.6 g·mm ≈ 200 g·mm per plane
Two-Plane Balancing (Influence Coefficient Method)
Setup:
- Measure vibration (amplitude + phase) at two planes
- Add trial weight in plane 1, measure change → influence coefficients α₁₁, α₂₁
- Add trial weight in plane 2, measure change → influence coefficients α₁₂, α₂₂
Influence coefficient matrix:
{V} = [α]{U}
V₁ = α₁₁U₁ + α₁₂U₂
V₂ = α₂₁U₁ + α₂₂U₂
Solution: {U_correction} = -[α]⁻¹{V₀}
Where V₀ = initial vibration vector (complex, includes phase)
All quantities are complex: V = A∠φ, U = mass × r∠(angle)
Phase measured by keyphasor (once-per-rev trigger) + vibration sensor
Field Balancing Procedure (Single Plane)
- Measure vibration amplitude A₀ and phase φ₀ at speed N
- Add known trial weight W at radius R, at angular position θ_trial
- Measure new amplitude A₁ and phase φ₁
- Compute influence coefficient: α = (A₁∠φ₁ - A₀∠φ₀) / (W×R∠θ_trial)
- Correction unbalance: U_c = -A₀∠φ₀ / α
- Add correction mass: m_c = |U_c|/R at angle = arg(U_c)
Practical rule of thumb: Phase angle reading = location of heavy spot + 180° at supercritical speed
Balancing Machine Types
Hard-bearing machine: rigid supports above ω_n of support; measures bearing forces; direct readout of U in g·mm, no calibration needed per rotor
Soft-bearing machine: supports below ω_n (compliant); measures displacement; requires calibration runs with known trial weights
ISO 2953: specifies balancing machine accuracy
Minimum achievable residual: typically U_residual ≤ 0.5 × U_per per API 670
Rigid vs. Flexible Rotors
Rigid rotor: balanced below critical speed; balance valid at all speeds
Condition: rotor does NOT bow significantly at operating speed
N_operating < 0.75 × N_cr → rigid rotor assumption
Flexible rotor (API 670, ISO 11342):
Balance at or above first critical speed in own bearings
Modal balancing: balance each mode independently using mode shapes
Requires: high-speed balancing facility (balance shop in own pedestals)
Weight-sensitive balancing: at least 3 planes
Vibration Acceptance (API 670)
Baseline: 25 μm (1 mil) peak-to-peak maximum at operating speed
Alert level: 150% of baseline
Danger level: 250% of baseline
API 670: proximity probes (XY pair) at each bearing
Alarm: vibration level × displacement sensor reading × vector analysis
Output
Provide: G grade required, U_per [g·mm per plane], correction mass m_c [g] at radius R [mm], angle position [°], residual vibration amplitude [μm].
