A dynamic balancing machine locates the heavy spot by comparing the phase of the once-per-revolution (1X) vibration signal to a reference pulse from a tachometer, with the angular offset between the two being the heavy spot position [S2][S3].
Unbalance U is reported in gram-millimetres (metric) or ounce-inches (English) as the product of a trial weight w and its radius r, and the centrifugal force it produces scales with the square of running speed, so even a small heavy spot can produce destructive loading at modern rotor speeds [S4].
Why Phase, Not Just Amplitude, Defines the Angle
A bare amplitude reading tells you how much unbalance is on the rotor, but it does not tell you where it is around the circumference; the heavy spot angle lives entirely in the phase relationship between two signals [S2][S3].
The reference signal is generated by a once-per-turn marker: an optical sensor reading a reflective stripe, a magnetic pickup on a keyway or timing tooth, or an encoder pulse. The vibration signal comes from a velocity or displacement transducer mounted on the bearing pillow block, or from a force transducer in a soft-bearing machine. The instrument reads the time gap between the reference pulse and the next 1X peak, multiplies that time by degrees per revolution (360° divided by the running speed in seconds), and outputs a phase angle in degrees. A 0° reference convention can be set to any chosen keyway or scribed line, which is why the operator is asked to mark the rotor before the first run [S3][S5].
How a Hard-Bearing vs Soft-Bearing Machine Reads the Angle
On a hard-bearing balancing machine, the rotor runs on relatively stiff supports, so the unbalance force is measured directly by load cells or piezoelectric force sensors under the bearing blocks. Because the force vector points radially outward from the heavy spot, its phase directly encodes the angle, and no trial run is required to get a first-pass result [S5].
On a soft-bearing machine, the supports are deliberately compliant, and the instrument measures bearing displacement at a known low-resonance speed. The calibration constant (a mass-radius per millimetre of displacement) converts displacement to unbalance, and the phase relationship between the displacement peak and the tachometer pulse gives the heavy spot angle. The Texas A&M training note describes the geometric rule that ties the two together: the reference mark shifts opposite a shift of the heavy spot, and the shift angles are equal in magnitude [S2][S5].
The Influence Coefficient Method: Locating the Heavy Spot With Trial Weights
Field balancers and many shop machines do not rely on a calibrated force constant at all; they find the heavy spot by running the rotor twice, once bare and once with a trial weight of known mass at a known angle, then solving two equations for two unknowns (unbalance magnitude and unbalance angle) [S1][S8].
The procedure, as laid out in the field guides, is: (1) run the rotor at the balance speed and record the 1X amplitude and phase (φ₁) of the vibration; (2) stick a trial weight Wt at a known radius Rt and a known angle θt, then run again and record the new amplitude and phase (φ₂); (3) use the influence coefficient, which is the vector change in the vibration response per unit trial weight, to back-solve the original unbalance. The heavy spot angle is then read from the vector diagram, and the correction angle, the position where the corrective weight must go, is 180° away from the heavy spot in the direction of rotation [S1][S8].
Static, Couple, and Dynamic Unbalance Change What the Angle Means
For a narrow disc-shaped rotor, one angle and one weight correction are enough; this is static unbalance, and the heavy spot rolls to the bottom under gravity on knife edges [S4].
For a longer rotor, couple unbalance appears: two equal and opposite heavy spots in two different correction planes along the shaft, with the principal inertia axis intersecting the rotation axis at the centre of gravity, so the rotor will not roll to a stop but will still shake the bearings in service. A dynamic balancing machine resolves this by measuring the 1X vibration at both ends of the shaft, separating the response into a static component (same angle both ends) and a couple component (opposite angle both ends), and printing two angles and two weights, one for each correction plane [S1][S3][S4].
What Operators Get Wrong: Reference Marks, Strobe Lag, and the 180° Rule
The most common error is sloppy reference-marking: if the scribe line is offset from the true keyway, every subsequent heavy-spot angle is biased by the same amount, and the correction will be wrong even though the magnitude looks correct [S2].
Operators also forget that the displayed angle is the position of the heavy spot, not the position where the correction weight must go. The correction goes 180° away, in the direction of rotation, at the same radius; a 90° error here leaves the rotor in exactly the same imbalance condition. Heavy spot angles are also sensitive to rotor speed: run the rotor at 300 rpm and again at 1500 rpm and the indicated phase can shift slightly because of structural modes, dampers, and sensor-mount resonances, which is why shop balancing at the planned operating speed is preferred when the part can be spun up to it [S7][S8]. The practical rule when the rotor is grossly out of balance, as the ACOEM field guide notes, is that the heavy spot will roll to the bottom under gravity, so place the trial weight on top and let the geometry do the locating for you [S7].
From Heavy Spot to Correction Weight in the Real Shop
The closed-out workflow on a modern dynamic balancing machine reads: enter the rotor mass and the correction radius, run a calibration spin, the instrument prints "add X grams at Y°" (or "remove Z grams at Y°"), and the operator welds, drills, or grinds accordingly. Acceptance is then verified by a final spin that should land the residual 1X amplitude inside the balance grade specified for the rotor class, typically expressed in mm/s RMS velocity or in mm displacement per ISO 1940 balance quality grades for rigid rotors [S3][S5].
For a 1 kg rotor running at 3000 rpm with a measured 5 g·mm of unbalance, the centrifugal force works out to 0.01 × 0.001 kg × 0.5 cm × (3000/1000)² = 0.045 kg, roughly 0.44 N, a load that a healthy bearing will absorb quietly but that an uncorrected fan or motor will announce as a 1X tone the moment the casing is touched [S4]. The same calculation explains why doubling the speed quadruples the force and why balance grades tighten dramatically as line speeds rise in turbo machinery, where a coding machine marking and an angle grinder trim on a coupling are common shop operations performed right at the balance stand. For procurement-side context on how shop balance grades map to other instrumented assets, see the breakdown of pressure transmitter accuracy classes for custody transfer and the alarm delay and signal averaging trade-offs, which run on the same phase-vs-amplitude logic the balancer uses.