Coherent Phasor Sum and Difference Worksheet
Combine two documented same-frequency phasors, preserve the signed phase relation and choose the subtraction order explicitly. This worksheet does not diagnose a fault or calculate a balancing correction mass or angle.
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| Vector | x component | y component | Πλάτος | Φάση |
|---|---|---|---|---|
| V1 | – | – | – | – |
| V2 | – | – | – | – |
| V1 + V2 | – | – | – | – |
| Selected difference | – | – | – | – |
Equations and sign convention
These are general complex-plane relations, not balancing formulas issued by ISO 21940. For each phasor with amplitude A and entered phase phi:
A positive signed result means V2 is positive relative to V1 under the convention selected above: “lead” if positive angles are lead, “lag” if positive angles are lag. The smallest unsigned separation is the absolute value and intentionally discards direction.
Independent examples: 3 at 0 degrees plus 4 at 90 degrees gives 5 at 53.1301 degrees. For the same inputs, V2 minus V1 gives 5 at 126.8699 degrees. Equal opposing phasors have a zero sum with undefined phase; identical phasors have a zero difference with undefined phase.
Balancing and diagnostic boundary
The difference between a baseline response and a trial-run response can represent the measured response change only when the records are comparable. It is not by itself a correction weight. A balancing solution additionally needs the trial mass, radius, angular location, consistent measurement conventions, a valid influence coefficient and applicable safety/procedure controls.
Source and standards boundary
| Αριθμός ταυτότητας | Πηγή | Verified public information | Use on this page |
|---|---|---|---|
| S1 | ISO 21940-13:2012, Edition 1 | Published and confirmed in 2023; replaces ISO 20806:2009. It addresses criteria, instrumentation, safety, reporting and records for in-situ balancing of medium and large rotors. The public abstract explicitly says it does not provide methods for calculating correction masses from vibration data. | Balancing safety/scope boundary only; not the source of the phasor equations. |
| S2 | Dewesoft Order Analysis Manual V26-1 | Public manual pp. 14, 18-19 and 33-34: absolute order phase needs zero-angle information; phase reference may be the frequency-source/keyphasor position or the first order; extracted harmonics are complex channels with magnitude, phase, real and imaginary parts. | Evidence for reference identity and complex-channel representation. |
| S3 | Dewesoft Orbit Analysis Manual V26-1 | Public manual pp. 69-70 documents application-specific phase conventions: Order Analysis uses a leading zero-crossing convention while Orbit Analysis uses a lagging peak convention. | Evidence that phase values from different modes are not interchangeable without conversion. |
| S4 | Fluke, Phase in Vibration Analysis | Official technical article describes balancing with a rotational-rate response relative to tachometer, a known trial weight/angle and a subsequent program calculation. | Public evidence that a response-vector difference alone is not a correction mass/angle method. |
Corrections made in this audit
Signed and unsigned phase are no longer conflated
The former page reduced every phase relation to 0-180 degrees, losing which phasor led or lagged. The replacement reports signed V2 minus V1 in [-180, 180) and the unsigned separation separately.
Subtraction order is explicit
V2 minus V1 and V1 minus V2 have the same amplitude but phases separated by 180 degrees. The user must now select which operation is intended, and the result/table label states it.
Zero-vector phase is undefined
The old engine called atan2 on floating residue for exact cancellation and could display a meaningless phase. The replacement uses a scale-aware numerical cancellation check and reports undefined phase.
Measurement comparability is required
Amplitude unit/scaling, coherent component, phase reference, sign/peak convention, sensor polarity, operating condition and measurement quality are now visible evidence gates.
Balancing and diagnostic shortcuts were removed
The old FAQ mapped 0/90/180-degree observations to specific faults and implied a simple phase shift supplied a correction angle. Those claims were removed; the page does not calculate a correction mass or diagnose a fault.
Input and runtime integrity were rebuilt
Defaults, presets, automatic calculation, browser history, clipboard export, dynamic HTML and external equation rendering were removed. Decimal point/comma are accepted separately; mixed separators, zero/negative amplitudes, non-finite/overflow inputs and incomplete records are rejected.
