Why a Machine Is Worse at One Speed Than at a Higher One

Why this matters

A two-speed fan that hums on high and rattles the ceiling grid on low is the single most misread condition in field service. It reads as a fault that only appears at part load, so techs go looking for something that changes with speed: a loose part that seats at high speed, a bearing that only complains when it is cold, a drive that is unstable down low. There is usually nothing wrong with any of it. Shaking is not proportional to force, it is proportional to force multiplied by an amplification factor set entirely by how close the running speed sits to a natural frequency. Below that frequency the machine amplifies. Above it, the machine isolates itself. A shop that knows the shape of that curve stops chasing part-load faults and starts asking a much better question: where is the frequency, and can we get farther away from it?

Before you change a speed to test this

Speed is not a free variable. On a variable-frequency drive, stay at or above the motor's stated minimum continuous speed, because a shaft-mounted cooling fan moves much less air down low and a fully loaded motor held there overheats without ever tripping on current. On a fan, never raise the wheel above its rated maximum speed to find a quieter point: wheel stress climbs with the square of speed and the rated maximum is a burst limit, not a comfort guideline, and a wheel that lets go inside a housing at speed will leave it. If a speed change means swapping a sheave, the machine gets shut down, the disconnect locked and tagged, and the rotor confirmed stopped rather than coasting first, under 29 CFR 1910.147 and its verification-of-isolation step, with the belt guard back on before it is restarted per 29 CFR 1910.219. Take every reading with a magnetic-base sensor on a stationary housing outside an intact guard, no gloves near the shaft line.

Two curves are fighting, and they point opposite ways

The force curve rises with speed. Unbalance force goes with the square of shaft speed, so doubling the speed quadruples the force. That is covered in detail in the companion article on how a small imbalance becomes a large force, and it is the intuition everyone already has.

The amplification curve does not. It depends only on the ratio between the forcing frequency and the structure's natural frequency, and its shape is fixed: it climbs from about 1 at very low ratios, peaks sharply at a ratio of 1, then falls away steeply above it toward zero.

The observed motion is the product of those two. That is the whole article. Everywhere below the peak, raising speed raises both terms and the machine gets worse. Everywhere well above the peak, raising speed raises the force but cuts the amplification faster, and the machine gets better.

The ratio table

Values below are for a single mass on a spring with 5 percent of critical damping, a common assumption for a bolted steel assembly and one that is very rarely measured on an actual machine. The damping figure sets the height of the peak and almost nothing else, so the shape of this table is reliable while the number in the middle row is not.

The row at 1.41 deserves its own sentence. The square root of 2 is where transmitted force exactly equals applied force, and it is one of the few points on the curve that damping does not move at all: below it a flexible support makes things worse than a rigid one, above it a flexible support helps. That is why design practice puts a mount's natural frequency at a third of running speed or lower rather than just "somewhere below", and why an isolator chosen without checking the ratio is a coin flip.

The two-speed fan, worked all the way through

A belt-driven supply fan runs 900 rpm on low and 1,800 rpm on high. On low it rattles the ceiling grid in the space below; on high it is unremarkable. An impact test on the stopped, locked-out unit rings the base and curb assembly at about 870 cpm.

Low speed. Ratio = 900 / 870 = 1.034. That is within about 4 percent of the peak. Amplification at 5 percent damping works out to about 8.0.

High speed. Ratio = 1,800 / 870 = 2.069. Amplification works out to about 0.30.

The force. Doubling the speed multiplies the unbalance force by 2 squared, so the force on high is 4 times what it is on low.

The product. Take the low-speed motion as 1.0 for comparison. High-speed motion = 4 x 0.30, divided by 8.0, which is 0.15, or roughly one seventh of the low-speed motion.

Four times the force, one seventh of the shaking. Nothing on that machine is defective at low speed and healthy at high speed. The rotor's residual unbalance is identical at both speeds, the bearings are identical, the belt is identical. The only thing that changed was where running speed sits relative to 870 cpm.

What a tech who skips the impact test concludes. They observe that the problem appears at low speed and disappears at high speed, and they reason that something is loose and centrifugal force seats it at speed. That is a real mechanism and it does happen, which is what makes this misdiagnosis so durable. They pull the wheel, find nothing, torque everything, and return it with the same behavior. The distinguishing evidence takes twenty minutes: strike the base with a soft-face hammer on the stopped and locked-out machine and see whether it rings near 900 cpm. If it does, the loose-part hypothesis is dead.

What the fix actually is. Not the rotor. Move the frequency or lower the excitation. Stiffening the curb or base raises 870 cpm upward and away from 900; that means shortening unsupported spans rather than adding a member alongside an existing one, because natural frequency rises with the square root of stiffness and a change that feels substantial often is not. If that stiffening is welded on, welding fume is the hazard the mechanical work brings with it: zinc-coated or galvanized curb steel releases zinc oxide fume and stainless releases hexavalent chromium, so it takes local exhaust and respiratory protection under a written 29 CFR 1910.134 program, with 29 CFR 1910.1026 applying where chromium-bearing metal is in the joint. Adding damping at the base lowers the peak without moving it, which helps because the machine sits almost exactly on the peak. Balancing the wheel to a tighter grade reduces the force being amplified, which works but is the most expensive of those three and does nothing about the next excitation that lands there. If the low-speed setpoint is adjustable and 780 rpm is still above the motor's minimum continuous speed, moving it there puts the ratio at 0.90 and the amplification near 4.8 instead of 8.0, and the force down about 25 percent as well, so the motion falls to roughly 45 percent of what it was for the cost of a setpoint change.

Why this pattern is mistaken for an intermittent fault

Three things make it convincing. It is speed-dependent, and most genuine mechanical faults are too. It is repeatable, so it survives the "let us see if it does it again" test that filters out real intermittents. And it disappears at the speed where the machine is easiest to observe, which is usually full speed, because that is where the tech ran it while listening. A machine that only misbehaves at a speed nobody watches it at looks like a control problem or a load problem long before it looks like a structural one.

The tell that separates them: a genuine mechanical fault gets worse as speed rises somewhere in its range, because every mechanical excitation grows with speed. Amplification is the only mechanism that reliably produces less motion at a higher speed.

What changes the answer

A second mode above the first. The table describes one natural frequency. Real assemblies have several, so going faster to escape one can walk you into another. Take the census before you commit to a speed change, using the method in the companion article on why coincidence is the normal case.

The excitation may not be running speed. If the amplified frequency is blade pass or belt pass rather than 1x shaft speed, the ratio has to be computed against that frequency, not against rpm, and the speed change that fixes one may not touch the other.

A rotor's own critical speed behaves differently from a support mode. A shaft passing through its first bending critical is not the same phenomenon as a base rocking, and the response through it is a rotor property rather than a structural one. The companion article on working out whether you are near a critical speed separates the two.

How to verify you got this right

Predict before you measure. Take your natural frequency, take the two speeds, compute both ratios and both amplifications, multiply each by the square of its speed, and write down the ratio you expect between the two readings. Then take the readings. If the measured ratio lands anywhere near the predicted one, the mechanism is confirmed and the fix is structural. If the measured drop is far smaller than predicted, something else is also changing with speed and you have two things going on, not one.

The most common arithmetic slip in this calculation is forgetting the force term and comparing amplifications alone, which in the worked example above would have predicted the high-speed reading at about one twenty-seventh rather than one seventh. Both numbers say "much better on high", so the error hides, right up until someone uses it to size a correction.

References

• 29 CFR 1910.147 for isolation and stopped-rotor verification before a sheave change or an impact test
• 29 CFR 1910.219 for belt and sheave guarding on restart and during running measurements
• 29 CFR 1910.134 and 29 CFR 1910.1026 for respiratory protection and hexavalent chromium exposure where base stiffening is welded onto coated or chromium-bearing steel
• Fan and motor manufacturer documentation for maximum rated wheel speed and minimum continuous motor speed, both of which bound any speed experiment
• See related: How a Small Imbalance Becomes a Large Force; What Resonance Is and Why It Finds Your Machine; How to Work Out Whether You Are Near a Critical Speed