Digital Sampling Resolution and Phase Angle Precision

I'm hoping to initiate a series of articles dealing with various topics in the Machine Condition Monitoring space. The intent is to keep most of these pretty short, and as entertaining as possible

When machine guys talk about Phase, it's a little different than what the Structural Dynamic guys are talking about. In the MCM environment, Phase is always associated with the rotation of a shaft in the machine. By convention, rotation is always discussed from the perspective that the observer (you) are looking at the machine train from the Driver end to the Driven end. For example, if you have a horizontal motor-pump you imagine yourself standing behind the motor, viewing the system from the motor down the machine train toward the pump.

Again by convention, Zero degrees is agreed to be at the 12 o'clock position on the machine. Rotational direction is expressed as Clockwise, or Counterclockwise. ANGLE is not associated with rotational direction! The most typical referencing for Angle is XX degrees RIGHT (clockwise from zero) or XX degrees LEFT (counterclockwise from zero). In this convention it is not typical to talk about angles of more than 180 degrees... as far as sensor placement is concerned. In the InsightCM environment this convention has not been maintained. Position angles are expressed in positive degrees (clockwise from zero) or negative degrees (-XX counterclockwise from zero). This is a little confusing to the old-time MCM guys, but just bear in mind that 45 degrees Right is +45, and 45 degrees Left is -45.

When selecting Analysis Frequency it is important to recognize that this directly relates to sample rate. In the example below, the Analysis Frequency selected is 500 Hz. This results in an acquisition rate of 1280 samples per second. (Analysis Frequency X Nyquist)

If monitoring a 3600 RPM machine, this configuration would result in only 21 sample points per revolution of the shaft. (1280 / 60 = 21.333) The angular resolution will therefore be 360 degrees / 21 samples or only 17 degrees.

To have at least 1 degree of precision in the angular domain, the acquisition must be configured to provide a minimum of 360 samples per shaft revolution. In order to accomplish this, the Analysis Frequency must be increased to 10,000 Hz. The resultant angular precision will therefore be:

10,000 X 2.56 = 25600 samples per second

25600 samples per second / 60 Hz = 426.66 samples per revolution

360 degrees / 426 samples per rev = 0.84 degrees

A quick reference of Analysis Frequency vs. Angular Precision follows:

This phenomenon is not restricted to IOtech analysis products. Any acquisition system that utilizes the base acquisition clock to determine phase information will be subject to these same resolution issues. For this reason the InsightCM Turbine Monitoring cRIO configuration and the ZonicBook 618e utilize high speed timer / counter inputs for their dedicated tachometer input channels. Since these channels utilize a high frequency internal clock as the timing reference they are not subject to acquisition rate restrictions which limit angular resolution.

In InsightCM, Balance of Plant (BOP) cRIO systems are subject to this same concern, however phase measurements are not usually required of BOP systems and tachometer signals are usually only monitored to determine rotational speed. In the Turbine Monitoring cRIO configurations based on the 9024 cRIO platform, the first slot is dedicated to tach or keyphasor inputs. This module is highly oversampled at a rate independent of the user-selectable sample rate for all other channels, insuring acceptable phase angle precision.