One plane · one measurement point · one speed/state

Documented Single-Plane Influence-Coefficient Calculator

Compute a replacement correction after removing the trial mass. Trial angle and mass radius are part of the complex unbalance vector; phase convention, synchronous quantity and unchanged run conditions are mandatory records.

Trial angle retainedm·r unbalance basisNo residual prediction

Balance job / run identifier

Machine, rotor and correction plane

Measurement point / sensor / mounting

Common run speed (r/min)

Synchronous vibration quantity, unit and amplitude basis

Phase reference, positive direction, viewing side and instrument convention

Initial run — no trial mass

Initial synchronous amplitude A₀

Initial phase φ₀ (degrees)

Trial unbalance and trial run

Mass unit

Radius unit

Trial mass mₜ

Trial radius rₜ

Trial angle θₜ (degrees)

Correction interpretation

Trial-run synchronous amplitude A₁

Trial-run phase φ₁ (degrees)

Correction location and applicability

Correction radius r꜀ (same selected radius unit)

Repeatability, linearity, rotor behaviour, runout, thermal state, trial attachment, ratings, guarding and safety review

Applicability gate: one suitable balance plane and one measurement point, stable synchronous response, identical speed/configuration/thermal state, unchanged phase convention, linear response and securely engineered trial/correction masses. Stop, isolate and follow the machine/tool procedure before changing weights. This arithmetic does not authorize a trial mass, prove rotor rigidity, set an acceptance limit or predict the measured residual.

Replacement correction result

Added correction mass and angle

Correction unbalance

Trial unbalance

Vibration change ΔV

Response coefficient α=ΔV/Uₜ

Effect ratio |ΔV|/max(A₀,A₁)

Implemented complex-vector model

V(A,φ)=A[cosφ+i sinφ]
Uₜ=mₜrₜ[cosθₜ+i sinθₜ]
ΔV=V₁−V₀
α=ΔV/Uₜ
U꜀=−V₀/α=−V₀Uₜ/ΔV
m꜀=|U꜀|/r꜀

α is a vibration-response coefficient per unbalance. Some references use its reciprocal; the convention must always be stated. The output is an added replacement mass after the entered trial mass is removed. Removal corrections, retained-trial corrections, fixed-hole decomposition, multiple measurement points/planes/speeds and least-squares balancing are outside this calculator.

Published numerical example

Na stránkách Texas A&M Turbomachinery Laboratory Rotor Balancing Tutorial (2016) gives V₀=5.6 mil pk-pk∠135°, V₁=3.3 mil pk-pk∠238° and trial unbalance 74 oz·in∠315°. Using the printed polar inputs gives ΔV=7.110850∠288.116° and U꜀=58.277138 oz·in∠341.883971°, consistent with the tutorial’s rounded 58.24 oz·in∠341.9°. The former code omitted θₜ from U꜀ and would have reported approximately 26.9°.

Independent method sources

A peer-reviewed review of rotor balancing methods defines influence coefficients using trial mass, radius and phase. The official Schenck SmartBalancer 4 manual describes the initial/trial-run method and limits its instructions to rotors behaving rigidly at balance speed.

ISO scope/status

ISO 21940-13:2012, edition 1, is Published and confirmed; it covers criteria, instrumentation, safety, reporting and records for in-situ balancing of medium/large rotors, and its official abstract explicitly says it does not guide correction-mass calculations. ISO 21940-11:2016 with Amendment 1:2022 covers procedures/tolerances for rigid behaviour and is under systematic review. ISO 21940-12:2016, confirmed in 2025, covers flexible behaviour. This page’s complex arithmetic is not labelled an ISO formula; exact clauses remain NEEDS_LICENSED_SOURCE.

Required engineering checks

Confirm that unbalance is the dominant cause and the chosen plane can control the relevant response. Review 1× repeatability, runout compensation, phase sign/viewing convention, sensor orientation and integration convention, speed/thermal/configuration equality, structural resonance/nonlinearity, trial centrifugal force and attachment, rotor/bearing/driver limits, clearance, overspeed and guarding. Verify the result with a controlled run; do not treat the algebraic cancellation as a residual-vibration forecast.