Low Speed Balancing Procedure

This is the fourth article in a series on the topic of rotor balancing. The article on low speed balancing machines described the tool. This article covers operating it — the balancing procedure, from setup through correction, ending with the verification test that proves the result. It covers:

• setting up the rotor and the machine,
• the measure-and-correct cycle,
• correction methods, including splitting a correction between available positions, and
• the residual unbalance verification test.

Setup

The balance tolerance is established first. The permissible residual unbalance per plane follows from the rotor weight, service speed, and the selected criterion, as described in the article on single-plane balancing. It is essential to confirm that the balancing machine’s minimum achievable residual unbalance (Umar), as defined in the article on low speed balancing machines, sits comfortably below the balance tolerance specified for the rotor. A machine with an Umar value that is greater than or equal to the tolerance cannot verify a balance to that tolerance.

One assembly convention deserves particular attention during setup. Rotor components are commonly keyed to the shaft, and whether the key is included or excluded during balancing deserves consideration. If a keyway is left empty on the balance stand but will carry a key in service, the mass of the key should be accounted for by other means. For example, where only half the keyway exists on the component being balanced, the typical practice is to fill it with a half-key, thereby simulating the mass distribution of the fully-assembled rotor.

A rotor with its own journals is set directly into the machine’s roller carriages. A rotor without journals is mounted on an arbor. The arbor’s runout must be checked before any balancing begins, because arbor eccentricity is indistinguishable from rotor unbalance in the measurement. The operator enters the correction radius for each plane, which the machine will need when converting an unbalance into a correction mass. A hard-bearing machine also takes the rotor geometry — the axial distances from each correction plane to each pedestal. A soft-bearing machine requires calibration of the setup with trial masses. The rotor is first run to record a baseline, then run again with a trial mass of known unbalance attached. Relating the change in response between the two runs to the trial mass’s known unbalance determines the machine’s sensitivity and phase reference for that rotor.

The Measure-and-Correct Cycle

The first run establishes the as-found condition. The machine reports an unbalance vector in each correction plane, along with the correction mass each vector calls for at the entered radius. The operator stops the rotor, applies the corrections, and runs again. The fraction of the unbalance that is removed with each correction cycle depends in part on the machine’s unbalance reduction ratio (URR), as defined in the article on low speed balancing machines. The cycle ends when the reported residual in each plane sits inside the tolerance.

Correction Methods

Correcting unbalance may be accomplished by adding or removing mass.

Common methods of mass addition include weld-on or bolt-on weights, washers stacked at existing fasteners, clips, or set screws in tapped holes provided for the purpose. Every added mass must be judged for retention at service speed and in service conditions. A correction mass that departs the rotor in service becomes a projectile and takes the balance with it.

Mass removal may be accomplished by removing discrete items intended for balancing purposes, such as those mentioned above in the discussion of mass addition. However, mass removal is more commonly accomplished by grinding in plant rotor work. Grinding takes material in shallow, distributed passes, leaves a smooth surface, and, unlike the mass addition techniques, doesn’t carry the risk of coming loose in service. Material is removed at the correction radius, away from high-stress regions such as blade roots and bore keyways, and the removal is spread rather than concentrated so that no sharp pocket results. Some applications employ drilling to remove mass. However, a drilled hole is a geometric discontinuity and a potential crack initiation site, so drilling is generally avoided on components subject to harsh service conditions.

The correction angle depends on which method is used. The machine reports the heavy spot, the angular location of the unbalance. Mass removal corrections are applied at that angle, in phase with the heavy spot. Mass addition corrections are applied at the opposite angle, 180° away from the heavy spot. A balancing machine usually lets the operator select whether corrections add or remove mass and then displays the correction angle resolved for that choice.

Correction Splitting

The correction the machine calls for lands at whatever angle the unbalance dictates, and a rotor may not offer a correction location at exactly that angle. Obstructions and design features may restrict where mass can be added or removed, making it necessary to adjust the correction position. When the required angle falls between two available positions, the correction is split into components at the two nearest positions, given by the following equations:

m1 = m · sin(θ2 − θ) / sin(θ2 − θ1)

m2 = m · sin(θ − θ1) / sin(θ2 − θ1)

where:

• m = required correction mass at the required angle (g)
• m1, m2 = component correction masses at the two available positions (g)
• θ = required correction angle (degrees)
• θ1, θ2 = angles of the two available positions, with θ1 < θ < θ2 (degrees)

The two masses together produce the same effect as the required correction (Figure 1). The equations apply to mass additions and mass removals alike. Both corrections m1 and m2 must sit at the same radius as the original correction m. The split costs mass: the components together weigh more than the single correction they replace, and the penalty grows as the available positions sit further from the required angle. Splitting between positions 30° apart costs little. Splitting between positions 90° apart requires up to roughly 40 percent more total mass than the direct correction.

Residual Unbalance Verification Test

The residual unbalance reported by the machine depends on its calibration. To circumvent any error in the calibration, the verification test described below measures the residual unbalance using the machine only as a comparator. It is the standard means of proving a balance rather than accepting the machine’s direct reading of it.

The procedure uses a test mass of known unbalance. A mass mt attached at radius rt produces the test unbalance:

Ut = mt · rt

where:

• Ut = test unbalance (g·mm or oz·in)
• mt = test mass (g or oz)
• rt = radius at which the test mass is attached (mm or in)

The test mass is sized to produce a test unbalance several times the tolerance, which guarantees it dominates whatever residual remains. The test mass is attached in the correction plane at each of several equally-spaced angular positions in turn, and the rotor is run once per position, recording the unbalance vector the machine reports for each run. Eight or twelve positions are common (Figure 2). The test is run on one correction plane at a time, not both at once.

Each unbalance reading during the verification test is the sum of two vectors: the measured residual unbalance, which is fixed to the rotor and never moves, and the measured test unbalance, which steps around the rotor with the test mass. As the test mass visits the positions, the tips of the reported vectors trace a circle. The circle’s radius Rr is the measured test unbalance, and its center Rc is the measured residual unbalance vector. Plotted on polar axes, the recorded vectors form that circle directly (Figure 3).

With equally spaced positions, the test unbalance contributions cancel in the average of the readings, so the average locates the circle’s center. The radius follows as the mean distance from the readings to that center:

Rc = ( R1 + R2 + … + RT ) / T

Rr = ( |R1 − Rc| + |R2 − Rc| + … + |RT − Rc| ) / T

where:

• Rc = center of the plotted circle, a vector in the machine’s reported units (g·mm or oz·in, magnitude and phase)
• Rr = radius of the plotted circle, in the machine’s reported units (g·mm or oz·in)
• R1 … RT = unbalance vectors reported by the machine with the test mass at each position (g·mm or oz·in, magnitude and phase)
• T = number of equally spaced test positions

When the balance machine’s calibration is accurate, Rc is equivalent to the residual unbalance Ures, and Rr is equivalent to the test unbalance Ut. An error in the machine’s calibration manifests as a multiplier that affects every unbalance reading and the values of Rc and Rr that are calculated from them. Therefore, the ratio of Ures to Ut is equivalent to the ratio of Rc to Rr. The residual unbalance Ures may be calculated from the following formula:

Ures = Ut · Rc / Rr

where:

• Ures = residual unbalance vector in the plane under test (g·mm or oz·in, magnitude and phase)
• Ut = test unbalance (g·mm or oz·in)
• Rc = center of the plotted circle (g·mm or oz·in, magnitude and phase)
• Rr = radius of the plotted circle (g·mm or oz·in)

The test carries its own consistency check. The distance from each plotted point to the center should equal Rr, within measurement scatter. The spread of those distances about Rr quantifies the machine’s run-to-run consistency. Expressed as a percentage of Ut, the largest deviation is a few percent for a machine in good order. Points that refuse to sit on a common circle indicate a problem, such as a loose test mass, a shifting setup, or thermal drift.

The residual unbalance determined by the verification test (Ures) can also be compared with the residual unbalance the machine reported during its final correction run, Urep. The two describe the same quantity by different routes: the machine’s reading depends on its calibration, and the test result does not. Approximate agreement in magnitude and angle confirms the machine’s reading. A disagreement in magnitude with agreement in angle points to a calibration scale error. A disagreement in angle points to a setup or plane-separation problem.

As a worked example, consider the 50 lb impeller from the first article in this series, with a correction radius of 7 in (178 mm) and a permissible residual unbalance of 40 g·mm per plane under the API criterion. A test mass of 1 g at the correction radius produces a test unbalance of 178 g·mm, roughly four and a half times the tolerance. Suppose the eight runs return eight vectors that plot as a circle of radius Rr = 183 g·mm centered at Rc = 28.5 g·mm at 119°. The radius differs slightly from the test unbalance, revealing a small calibration error in the machine, and the formula corrects for it: Ures = 178 · 28.5 / 183 = 27.7 g·mm at 119°. The plane passes: 27.7 g·mm sits inside the 40 g·mm tolerance, with the verification standing independent of the calibration error. Suppose the machine reported a residual of Urep = 30 g·mm at 116° on its final correction run. The verified residual agrees in angle within a few degrees and sits close in magnitude, so the machine’s reading is confirmed. The magnitude gap between 30 g·mm and 27.7 g·mm reflects the same calibration scale error the circle radius revealed, together with run-to-run scatter.

Companion Calculators

Two calculators accompany this article.

The correction splitting calculator resolves a required correction into components at two available positions: enter the required correction mass and angle and the two available angles, and it returns the two component masses and the total mass penalty.

The verification calculator performs the residual unbalance verification test’s arithmetic: enter the test mass and its radius, the unbalance vector reported at each test position for each plane, the tolerance, and, if desired, the machine’s reported residual from the final correction run (Urep). It returns the residual unbalance vector per plane (Ures), the calibration scale check from the circle radius, the run-to-run consistency as per-point deviations, the comparison against the tolerance, and the comparison against Urep.

Next in the series: At-Speed Balancing: The Fundamentals — why a low-speed balance can be insufficient for flexible rotors whose bending modes are excited at operating speed, and how at-speed balancing supplements it rather than replacing it.