# Phase Measurement on Turbomachinery

Phase is one of five key measurements fundamental to vibration analysis on large, critical, rotating machinery. Along with vibration amplitude, frequency, form, and shaft position, phase is a vital measurement that should always be acquired for diagnostics purposes, and is also valuable for long-term trending.

A generic definition of phase is “relative timing between two events”. To have relevance in the context of machinery vibration analysis, these two events must be periodic and occur at the same frequency. The two events can be two vibration signals, which might be measured at either end of a rotor, from which relative phase can be obtained after filtering the signals to the frequency of interest.

Figure 1:  Relative Phase Lag Between Two Signals: B Lags A by 90 Degrees

Figure 1 displays two such filtered vibration signals, “A” and “B”, on a common time axis from left to right. The two signals are occurring at the same frequency, but they are also offset in time and hence have a phase difference. As can be shown in the graph, each positive peak in signal B lags that of signal A by approximately ¼ cycle or 90°, given 360° for a full cycle. By convention, relative phase is expressed as phase lag in values between 0° and 180°.

Absolute phase is a timing measurement similar to relative phase, with the main difference being that one of the two signals is from a fixed reference. A once-per-turn tachometer pulse or “Phase Trigger” can be generated from a fixed proximity transducer observing a slot or keyway on a rotating shaft. The resulting pulse can serve as both a speed and phase reference. An optical or laser sensor observing a strip of reflective tape on a shaft can similarly be used to generate a once-per-turn pulse.

As shown in Figure 2, a proximity type transducer observing a keyway produces a negative-going pulse whenever the keyway passes beneath the sensor. Analysis instrumentation typically can be programmed to use the midpoint voltage, on the slope defined by the user, as the trigger threshold.

Figure 2:  Phase Trigger Reference Pulse

In the time domain, this trigger point defines T=0 for measurement of absolute phase. The absolute phase of a vibration signal filtered to 1X running speed frequency, therefore, is derived from the time lag from trigger point on the reference pulse to the first positive peak of the filtered vibration signal. As shown in the example in Figure 3, this time lag is approximately 3/8 of a rotation cycle or 135°. Absolute phase is expressed as a lagging angle with values between 0° and 360°.

Figure 3:  Absolute Phase Lag of Vibration Signal

Also shown in Figure 3 are timing marks superimposed on the vibration signal which are coincident with the trigger points on the Phase Trigger signal. These timing marks, shown in a blank-bright sequence, eliminate the need to show the actual phase reference signal when displaying vibration waveforms.

Another way to understand absolute phase measurement is to go through the process of identifying the measured “high spot” on a rotating shaft, as determined by the phase angle. This can be accomplished by physically indexing the rotor with phase lag values. First, the keyway or reflective tape used to generate the Phase Trigger pulse must be placed directly under the tachometer sensor to define T=0, and a value of 0° is then marked on the rotor directly under the vibration sensor being used. Next, phase angle values of increasing lag are marked on the rotor – against rotation – from the vibration sensor. In the example shown in Figure 4, a phase angle measurement of 135° to the peak of the vibration signal corresponds to a high spot on the rotor which is 135° against rotation from the vibration sensor – when the keyway and tachometer sensor are aligned. Another way to say this is to state that the positive peak of the signal or high spot on the rotor passes under the vibration sensor 135° after the Phase Trigger pulse fires.

Figure 4:  High Spot Identification with Absolute Phase

With this basic understanding of relative and absolute phase measurement, the analyst is better prepared for analysis and interpretation of data displayed in various formats which use phase. Shaft orbits and timebase waveforms can be filtered at 1X running speed and displayed with timing marks to show phase. When graphed along with vibration amplitude, such as in bode and polar graphs, phase angle values are presented as vector quantities. Phase measurement of signals filtered at higher orders of running speed can also be performed by synthesizing higher integer orders of the once-per-turn Phase Trigger pulse and filtering the vibration signal to the higher order.

Phase measurements captured and presented in such a manner are used to identify a variety of machine characteristics such as resonances and mode shapes, and are also used to evaluate malfunctions such as unbalance, misalignment, rotor-to-stationary part rubs, rotor bow, coupling wear, and shaft cracks. When performing diagnostics on a large machine, or when trending measurements over time, phase is a critical measurement that should always be included in the data set.

-Robert Bloomquist, Product Manager, SignalCalc Turbo