Balancing

The pull of a heavy spot.

A heavy spot of mass m at radius r on a shaft turning at angular speed ω pulls outward with the centrifugal force F = m·r·ω². The force rotates with the shaft, so every bearing feels it as a once-per-turn push: the 1X vibration of lesson 2. Speed counts twice: double the rpm and the pull is four times stronger.

U = m · r, and e = U ÷ M.

Unbalance is measured in gram-millimetres: ten grams at 100 mm is 1000 g·mm, and so is one gram at 1000 mm. Divide by the rotor's own mass and you get the specific unbalance e, which has a physical meaning: it is the distance between the rotor's centre of mass and its axis of rotation. For a well-balanced 100 kg rotor that distance is a few tens of micrometres at most, still far less than the width of a hair.

Balanced enough: the G grades.

How small should e be? ISO 21940-11 answers with a single number per machine type, the balance quality grade G, which is simply e × ω, the speed at which the centre of mass orbits the axis, in mm/s. Pumps, fans and small or slow motors are built to G 6.3; larger motors above 950 rpm, turbines and compressors to G 2.5; grinding-machine drives to G 1. For any grade the permissible e falls as speed rises: the faster the rotor, the finer the balance.

The vibration lags the force.

The heavy spot is where the extra mass sits. The high spot is where the shaft actually bulges outward, the point that passes the sensor at the moment of the vibration peak. At low speed they coincide. As the speed approaches the rotor's natural frequency, the response starts to lag the force, 90° right at the critical speed, and above it the high spot is on the opposite side of the shaft from the heavy spot. Run the machine up and watch them separate.

Find the spot.

This rotor has a heavy spot you cannot see. Drag a correction weight around the rim and set its mass. The 1X vibration, and the hum, fall as you get it right. Notice that the best position is not simply opposite the measured phase: there is a lag angle hiding in there. Reveal the heavy spot when you give up, or when you are sure.

Measure, perturb, measure, solve.

Every 1X measurement is a vector: an amplitude and a phase angle from the tach pulse. The method rests on one assumption, that vibration is proportional to unbalance, and goes in four steps. Run the machine and record the original vector O. Add a known trial weight and record O+T. The difference is the effect of the trial weight alone; divide it by the trial weight and you have the influence coefficient, the rotor's response to one gram at that radius, lag angle included. The correction weight is then the one whose effect is exactly −O. Press the buttons in order.

A long rotor can rock as well as shake.

A thin disc has one correction plane and can only be pushed sideways. A long rotor has heavy spots at both ends. If they are on the same side they add up to a sideways push (static unbalance). If they are on opposite sides they cancel as a force but twist the rotor end to end (couple unbalance), and the two bearings move 180° apart. Real rotors have some of each (dynamic unbalance) and need two correction planes: the same method, with a trial weight in each plane and a little more arithmetic.

A rotor on its own bench.

Field balancing corrects a rotor in the machine it lives in. A balancing machine takes the rotor out and spins it on pedestals of its own, in a shop, with its own drive. The pedestals carry transducers, and the instrument's job is to turn what they read into an unbalance for each correction plane. There are two ways to build the pedestals. What separates them is where the balancing speed sits relative to the natural frequency of the rotor on its supports, far above it or far below it; the choice of sensor follows from that.

Soft bearings: above the resonance.

On a soft-bearing machine the pedestals sit on flexible supports whose natural frequency, with the rotor on them, is a few hertz. Balancing speed is far above it, so rotor and pedestals swing almost freely, half a turn behind the heavy spot. The motion is proportional to the unbalance divided by the moving mass and hardly depends on speed, and it is large: easy to measure with a velocity pickup or an accelerometer, which is why soft-bearing machines are sensitive and are built for everything from small armatures to turbine rotors weighing tonnes.

The one thing the machine cannot know by itself is the ratio between motion and unbalance, because it depends on the rotor: its mass, its inertia and where the planes sit. So the instrument establishes the influence coefficients once per set-up. That can be done with trial weights, exactly as in section 5; by recalling the coefficients saved from the last rotor of the same type; or by computing them from a model of the rotor's geometry and mass, with no trial runs at all. Once the coefficients are known, each rotor needs a measuring run and a check run, like any other.

Hard bearings: below the resonance.

A hard-bearing machine does the opposite: stiff pedestals whose natural frequency, rotor included, lies far above balancing speed. The pedestals barely move, and what the transducers measure is the bearing reaction force itself, the U·ω² of section 1, whether they sense it directly with a force transducer or through the tiny deflection of the stiff support. Because that relationship is fixed by the machine rather than by the rotor, a hard-bearing machine is calibrated once, within its specified range of speeds, masses and set-ups. A new rotor needs only its geometry entered: bearing spacing, plane positions and correction radii. The instrument divides the forces by the speed squared, resolves them into the planes, and converts each plane's unbalance into a mass at its radius, m = U ÷ r. It still takes a measuring run, and a check run after the correction.

Plane separation.

Whatever the pedestals measure, a rigid rotor has two correction planes and the machine has two bearings. Each plane's unbalance pulls on both bearings, in proportion to how close it is, so each bearing reading is a mixture of the two planes. The instrument solves the two readings back into two plane values, which is why it must be told the distances. Move the planes and watch the mixing, then switch on a little reading error: the closer the planes, the more the error is magnified.

Tooling, drives and indexing.

The rotor is never alone on the machine. An arbor or mandrel carries it, a universal-joint drive shaft or a belt turns it, and each adds an unbalance of its own that the instrument cannot tell from the rotor's. The cure is indexing: measure, turn the rotor half a turn relative to the tooling, measure again. The rotor's unbalance flips; the tooling's does not; two readings separate them.

The checklist.

Adding weights to a machine whose problem is not unbalance makes a clean rotor dirty and leaves the problem in place. Balance when all of these are true:

• The vibration is dominated by 1X, with little at 2X and above (lesson 3).
• It is mainly radial; a large axial component points to misalignment or a bent shaft.
• The 1X phase is steady from run to run, and horizontal and vertical readings differ by roughly 90° (lesson 8).
• Amplitude grows with the square of speed, without a sudden peak at one speed, which would be a resonance.
• The machine is aligned, the bolts are tight, the rotor is clean (fouled fan blades are the commonest "unbalance" of all) and at operating temperature, so that thermal bow is not what you are chasing.

The second 102 module turns the same measurements toward the other faults: Monitoring & diagnostics →