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

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Correction unbalance

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Trial unbalance

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Vibration change ΔV

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Response coefficient α=ΔV/Uₜ

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Effect ratio |ΔV|/max(A₀,A₁)

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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

De 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.