balancing-in-situ

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:

1. Measure initial vibration: A₀ = amplitude [mm/s or mils]; φ₀ = phase [°] (relative to 1× trigger)
2. Add trial weight T at known angle θ_T
3. Measure new vibration A_T; φ_T
4. Calculate influence coefficient α: α = (A_T e^{jφ_T} - A₀ e^{jφ₀}) / T [complex; mm/s per g·mm]
5. 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:

1. Original run: [A₁₀, A₂₀]
2. Add trial T₁ at plane 1: measure [A₁₁, A₂₁]
3. 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).