| name | balancing-in-situ |
| description | In-situ (field) balancing — influence coefficient method, trial weight, single-plane/two-plane, vibration measurement, ISO 1940 balance quality grades, residual unbalance acceptance. |
| metadata | {"priority":7,"promptSignals":{"phrases":["field balancing","in situ balancing","influence coefficient","trial weight balancing","rotor balancing","single plane balancing","two plane balancing"],"minScore":3}} |
In-Situ Rotor Balancing — Complete Skill
Unbalance Fundamentals
Static unbalance: mass off-center; vibration at 1× running speed (synchronous); force in one plane
Couple unbalance: equal and opposite masses in two planes; no net force but creates moment
Dynamic unbalance: combination; requires two-plane correction for complete balance
Unbalance force:
F_u = m_u × e × ω² [N; m_u = unbalance mass [kg]; e = eccentricity [m]; ω = angular speed [rad/s]]
Or: F_u = U × ω² [N; U = unbalance = m_u × e [kg·m]]
ISO 1940 residual unbalance (specific unbalance e_per):
e_per = G × 1000 / ω [g·mm/kg; G = balance grade; ω in rad/s]
U_per = e_per × M_rotor / 1000 [g·mm; M_rotor in kg]
Balance grades (ISO 1940-1):
| Grade | e_per × ω [mm/s] | Application |
|---|
| G 0.4 | 0.4 | Precision gyroscopes |
| G 1 | 1 | Machine tools, gas turbine rotors |
| G 2.5 | 2.5 | Marine turbines, pumps |
| G 6.3 | 6.3 | Process plant fans, pumps |
| G 16 | 16 | Agricultural tractors |
| G 40 | 40 | Crankshafts, single cylinders |
Example: G 6.3 fan, 1500 RPM (ω = 157 rad/s), mass 50 kg
e_per = 6.3 × 1000 / 157 = 40 μm
U_per = 40 × 50 / 1000 = 2 g·mm residual per plane
Single-Plane Balancing (Static)
Method:
- Measure initial vibration: A₀ = amplitude [mm/s or mils]; φ₀ = phase [°] (relative to 1× trigger)
- Add trial weight T at known angle θ_T
- Measure new vibration A_T; φ_T
- Calculate influence coefficient α:
α = (A_T e^{jφ_T} - A₀ e^{jφ₀}) / T [complex; mm/s per g·mm]
- Correction mass and angle:
T_corr = -A₀ e^{jφ₀} / α [complex weight; magnitude = mass; angle = placement angle]
Vector diagram (graphical method):
Draw A₀ vector; draw trial-run result A_T; difference = effect of trial weight W
Required correction = A₀ vector × (W / |W_effect|) in opposite direction
Two-Plane Balancing (Dynamic)
Influence coefficient matrix:
[A₁] = [α₁₁ α₁₂] [U₁]
[A₂] [α₂₁ α₂₂] [U₂]
A₁, A₂ = vibration at planes 1 and 2 (complex vectors)
U₁, U₂ = unbalance corrections at planes 1 and 2 (complex)
α_ij = influence coefficient: vibration at i due to unit unbalance at j
Measurement procedure:
- Original run: [A₁₀, A₂₀]
- Add trial T₁ at plane 1: measure [A₁₁, A₂₁]
- Remove T₁; add trial T₂ at plane 2: measure [A₁₂, A₂₂]
Influence coefficients:
α₁₁ = (A₁₁ - A₁₀) / T₁; α₂₁ = (A₂₁ - A₂₀) / T₁
α₁₂ = (A₁₂ - A₁₀) / T₂; α₂₂ = (A₂₂ - A₂₀) / T₂
Solution for corrections:
[U₁] [α₁₁ α₁₂]⁻¹ [-A₁₀]
[U₂] = [α₂₁ α₂₂] × [-A₂₀]
Instrumentation
Vibration transducer:
Proximity probe: measures shaft displacement [mil p-p or μm p-p]; required for fluid-film bearings (API 670)
Accelerometer: measures housing vibration [m/s²]; useful for rolling element bearings
Phase reference:
Keyphasor: optical or magnetic pickup on shaft; triggers once per revolution
Phase angle: degrees from keyphasor to vibration peak (measured counter to rotation)
Analyzer:
Single-channel: basic; measure 1× amplitude and phase with phase ref
Multi-channel: simultaneous two-plane measurement; faster
Trial Weight Calculation
Trial weight guideline:
T_trial = U_per / 5 to U_per / 10 [to get measurable change without overloading bearing]
Or: T_trial [g] ≈ 6350 × rated_kW / (N_RPM²) × (D_correction / D_shaft) [for turbines]
Place at known radius r_T; create U_T = T_trial × r_T [g·mm]
Placement accuracy:
±5° angular error acceptable; ±5 mm radial position error acceptable for most applications
Acceptance Criteria
ISO 10816-3 (vibration severity):
Zone A (< 2.3 mm/s): new machine; acceptable
Zone B (2.3–4.5 mm/s): acceptable for continued operation
Zone C (4.5–7.1 mm/s): restricted operation; alarm condition
Zone D (> 7.1 mm/s): danger; shutdown required
Residual unbalance verification (ISO 1940-2):
After balancing: measure 1× vibration amplitude; check against allowable
Or: spin rotor with calibrated unbalance; verify response within tolerance
API 670 (machinery protection systems):
Alert: 1× amplitude > 0.4 × (12,000/N)^0.5 mils pp [typical; site-specific]
Trip: 2× alert level
Balancing Below Critical Speed vs. At Speed
Rigid rotor (N < 0.7 N_critical):
Two-plane static + dynamic balance sufficient; balance at low speed
Modal shapes not relevant
Flexible rotor (N > N_critical):
Modal balancing or influence coefficient at multiple speeds required
Balance at running speed using in-situ influence coefficient method
May need 3+ planes for multi-mode rotors
Standards
| Standard | Scope |
|---|
| ISO 1940-1 | Balance quality grades for rigid rotors |
| ISO 1940-2 | Verifying residual unbalance |
| ISO 21940 | Vocabulary and rotor balancing procedures |
| ISO 11342 | Flexible rotor balancing methods |
| API 670 | Machinery protection systems (vibration limits) |
| ISO 10816 | Mechanical vibration — evaluation criteria |
Output
Provide: balance grade (ISO 1940 G-number), allowable residual unbalance U_per [g·mm] per plane, single or two-plane procedure, trial weight mass [g] and radius [mm], measured amplitude and phase before/after correction [mm/s and °], influence coefficients α_ij (complex), correction mass and angle at each plane, post-balance vibration [mm/s vs. ISO 10816 zone], and applicable standard (ISO 1940, ISO 21940, API 670).
