When a machine looks calm at its running speed, its steady-state trends can hide the most important thing about it: how it behaves passing through its critical speeds on the way up and down. Bode and polar plots are the paired diagnostic views that capture exactly that. Both show the running-speed vibration vector as the machine changes speed, one laid out against a speed axis and the other wrapped onto a phase-referenced circle, and together they make a critical speed unmistakable. This guide explains what each plot shows, how an amplitude peak and a phase shift identify a resonance, and why capturing the startup and shutdown transients matters even when steady-state monitoring looks quiet.
Bode and Polar Plots in one line: A Bode plot and a polar plot are two ways of showing the same running-speed vibration data as a machine changes speed during a runup or coastdown. The Bode plot draws the 1x amplitude and the 1x phase each against shaft speed on separate graphs, while the polar plot draws the 1x vector as amplitude and phase on a single circular plot. A resonance or critical speed appears as an amplitude peak accompanied by a phase change of about 180 degrees, which both plots make clear.
Both plots are built from the same underlying data: the running-speed vibration vector, meaning its amplitude and phase, captured as the shaft speed changes during a startup or shutdown. The difference is only in how that data is displayed. A Bode plot uses speed as the horizontal axis and stacks two graphs above one another, the upper one showing how the 1x amplitude changes with speed and the lower one showing how the 1x phase changes with speed. Reading the two together, you follow the vibration up through the speed range and watch both its size and its timing evolve.
A polar plot takes the same amplitude-and-phase pairs and places them on a single circular diagram. Distance from the center represents the 1x amplitude and the angular position represents the 1x phase, so each measured speed contributes one point, and as the machine sweeps through its speed range the points trace a curve on the circle. The speed itself is not an axis on the polar plot; instead it is a parameter that moves you along the traced curve, often marked with speed labels at intervals. The polar view compresses the amplitude and phase into one picture where the shape of the traced loop is itself diagnostic.
The two are complementary rather than redundant, which is why analysts capture both. The Bode plot makes it easy to read a value at a specific speed and to see exactly where in the speed range something happens, since speed is an explicit axis. The polar plot makes the combined behavior of amplitude and phase easier to grasp as a single evolving vector and is particularly good at revealing how many resonances the machine passes through and how they are oriented. Looking at the same transient in both forms gives a fuller reading than either alone.
A critical speed is a rotational speed at which the shaft coincides with a resonance of the rotor system, and it has a distinctive twin signature that both plots are designed to expose. As the machine approaches the critical speed the 1x amplitude rises to a peak, because the rotor is being driven at its resonance and responds strongly, and then falls again as the speed moves past it. On the Bode amplitude graph this is a clear hump centered on the critical speed, and on the polar plot it shows as the traced curve swinging out to a larger radius as it loops through the resonance.
The amplitude peak alone is not conclusive, and this is where the phase is essential. Passing through a resonance, the phase of the response shifts by roughly 180 degrees, a hallmark of a system moving from below to above its natural frequency. On the Bode phase graph this appears as a marked change in phase across the speed range where the amplitude peaks, and on the polar plot it appears as the curve executing a loop. The combination of an amplitude peak together with a phase change of about 180 degrees at the same speed is what confirms a genuine critical speed rather than some other cause of a high reading.
This paired signature is also what lets an analyst distinguish a true resonance from a merely large forced response. A rotor could show high amplitude at some speed simply because of severe unbalance without any resonance, but that would not be accompanied by the characteristic 180-degree phase transition. When the amplitude peak and the phase shift occur together, the machine has passed through a critical speed, and identifying where those critical speeds sit relative to the operating speed is fundamental to understanding the machine's behavior and its safe operating margin.
The crucial point about Bode and polar plots is that they require the machine to be changing speed, which means they can only be captured during a startup or a shutdown, not while the machine sits at its steady running speed. Steady-state monitoring, the everyday trends an operator watches, holds the machine at one speed and therefore never sweeps through the critical speeds where this behavior appears. A machine can look perfectly calm in its steady-state SCADA trends while carrying a critical speed uncomfortably close to its operating range, and only a transient capture would reveal it.
This is why a good machinery-monitoring practice captures the runup and coastdown transients and preserves them, rather than only trending the steady-state condition. A cloud monitoring platform can record the 1x amplitude and phase against speed through each startup and shutdown so that the Bode and polar views can be reconstructed afterward. Merobix can log the running-speed vector together with the shaft speed during these transients, so a reliability engineer can review how a machine behaved passing through its critical speeds even long after the event, from wherever they happen to be.
Keeping a baseline transient capture is especially valuable because it gives something to compare future startups against. If a machine's critical-speed response changes over time, for example the resonance peak growing or shifting, that change can indicate a developing problem such as a cracked shaft altering the rotor's stiffness, and it is visible only by comparing transients rather than steady-state readings. Storing the Bode and polar data from a known-good runup means that when a machine is next started, its behavior can be checked against how it behaved when it was healthy, adding a dimension of insight that steady-state trends, however continuous, cannot provide on their own.
They display the same 1x amplitude and phase data from a runup or coastdown in two forms. A Bode plot uses speed as the horizontal axis and shows amplitude and phase on two stacked graphs, making it easy to read values at a specific speed. A polar plot places the amplitude and phase on a single circular diagram where radius is amplitude and angle is phase, so the vibration vector traces a curve as speed changes. Analysts use both because each makes different features easier to see.
A critical speed shows a twin signature: the 1x amplitude rises to a peak as the machine passes through the resonance, and the phase shifts by about 180 degrees across the same speed. On a Bode plot this is a hump in the amplitude graph with a marked phase change in the phase graph, and on a polar plot it is the curve looping outward. The amplitude peak together with the 180-degree phase shift is what confirms a genuine critical speed rather than another cause of high vibration.
Because Bode and polar plots require the machine to be changing speed, they can only be captured during a startup or shutdown, not at steady running speed. A machine can look calm in its steady-state trends yet carry a critical speed close to its operating range that only a transient sweep would reveal. Capturing runup and coastdown data also gives a baseline: comparing future startups against a healthy one can expose a changing critical-speed response that signals a developing problem.
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