2. Rotating Machinery

Introduction

The sounds in our environment carry a great deal of information.  The sense of hearing in most mammals is highly developed to allow them to extract useful information from sound and humans are no exception.  We are constantly monitoring the noisy environment we live in, extracting information we need or want from it and discarding the rest.

We can also analyze sounds mathematically to extract very detailed information about the sources of sound.  In the following example we will analyze the sound of a vacuum cleaner to introduce the ideas of spectrum analysis of rotating machinery.

Discussion of the theoretical model

A vacuum cleaner is a commonly available rotating machine.  An upright vacuum cleaner usually has one electric motor with a main suction fan and a shaft extension which drives the agitator brush roll via a rubber drive belt.  There are variations; sometimes there is a separate motor driving the brush roll.  Sometimes there is a small additional fan on the main motor to provide ventilating air to keep the motor cool.

As long as the load on the motor is steady the motor will run at constant rotational speed usually specified in revolutions per minute (rpm).  When working with sound it is more convenient to think about the rotational speed in revolutions per second to easily relate it to frequency in Hertz (cycles per second).  The trivial conversion between the two is

If the vacuum has an attachment hose the air load on the suction fan can be reduced by sealing the end of the hose with your hand.  This will result in increased the motor speed.   Contrary to popular opinion, a vacuum cleaner does less work if you seal off the hose.  Vacuum cleaner motors typically will operate in the 20,000 to 30,000 rpm range (333 to 500 revolutions per second) but some may operate as low as 12,000 rpm (200 rps) to as high as 40,000 rpm (667 rps).  The motor generates sound at equivalent frequencies due to the forces of slight mechanical unbalance left over from the manufacturing process so we should expect to see a spectral peak due to the motor speed in our analysis.

The main suction fan is also rotating at that speed and generates a pulse of sound at  its blade passing frequency, just the number of blades on the fan multiplied by the rotational speed in revolutions per second.  Common suction fans may have 5, 6, or 9 blades.

Acquiring the Spectrogram

Setup Raven Lite to record from the input device you want to use and start recording to memory.  Power on the vacuum cleaner and then operate it quickly through several modes: idling in the storage position, with the nozzle and brush roll on carpet, in the tool cleaning mode with no obstruction or tool on the end of the hose and then briefly with the end of the hose sealed with your hand.  Then turn off the vacuum cleaner.  Stop the recording when the vacuum has completely stopped and save it to disk.

Interpreting the Spectrogram

The spectrogram for the vacuum cleaner I recorded is shown:

The horizontal axis is the time axis running from left to right and the vertical axis is the frequency running from low frequencies at the bottom to higher frequencies at the top.  The amplitude of the sound is denoted by the brightness of the display with the brighter colors representing higher amplitudes.

Horizontal bright bands are the features of interest.  These are the tones that we hope to relate back to the rotating components in the vacuum cleaner.  When the vacuum cleaner is energized (at the far left part of the green band) you can see a “knee” on the motor band as it comes up to speed.  In this first operating mode, idling, the fan noise is very faint but visible.  The next operating mode is with the nozzle dropped down onto the carpet.  You can see the motor speed dropped just a little bit due to the load of the brush roll now brushing the carpet.  In this mode you can see a yellow line due to the brush roll rotation and the motor but no fan noise.  Its noise is too low to see on this vacuum cleaner in this mode.  The cleaner is briefly returned to the idle mode and then the end of the hose is sealed by hand.  You can see the motor speed increase.  The amplitude of noise has generally increased and you can see the fan noise in this mode.  Finally, at the far right portion of the green area you can see the motor speed drop off after the vacuum is switched off.

I used the mouse pointer to pick out the following frequencies.

Component	Idling	Carpet	Hose Open	Hose Sealed
Motor	402 Hz	390 Hz	402 Hz	450 Hz
Brush	n/a	154 Hz	n/a	n/a
Fan	2035 Hz	1999 Hz	2046 Hz	2295 Hz

The motor frequency indicates that this vacuum cleaner motor rotates at speed ranging from 23,400 to 27,000 rpm.  The ratio between the fan blade passing frequency and the motor rotational frequency ranges from 5.06 to 5.13 indicating that the suction fan has five blades on it.

The brush roll shows up at a frequency of 154 Hz.  Because there are two rows of brushes on the brush roll the dominant frequency is twice the rotational frequency indicating that the brush roll is turning at about 77 revolutions per second or 4620 rpm.  If the brush roll has more than two rows of brushes it most likely will brush continuously and not appear as a distinct frequency.

You can often see harmonics of the discrete tones described here.  If you look closely you can see harmonics of the brush rotation.

Updated Notes and Images on this Project

Commenter Tim’s suggestion to increase the brightness and contrast settings to enhance the discrete frequency components resulted in doing just that. I have appended Raven images with those settings applied below and also make a couple of additional observations.

The spectrogram shown below is roughly the same view as the original spectrogram shown above but with the brightness and contrast values increased. The fan blade passing tone is much easier to see although it is somewhat concealed by broadband noise in the sealed hose condition. Another component of interest is apparent in the enhanced display, that of the 120 Hz hum, the second harmonic of the actual 60 Hz power line frequency.

I have also now included a view of the same spectrogram that is zoomed in to show the lower frequency components. This view shows the speed transitions at startup, between operating modes, and at shutdown much more clearly than before. The harmonic nature of the brush roll noise on carpet is also much easier to see in this view. Notice the regular spacing of lines above the line labelled “Brush” at intervals equal to its distance above the 0 Hz line. I picked frequencies of 158, 319, 479, 637, and 796 Hz corresponding to the first, second, third, fourth, and fifth harmonic of the “Brush” tone. Keep in mind that the line labelled “Brush” is the 2nd harmonic of the brush roll rotation frequency because the brush has two rows of bristles on it. Thus all of odd harmonics of the brush rotation are suppressed while the even harmonics of 2,4,6,8, and 10 of the rotation frequency are present. The odd harmonics would show up on this style of brush roll if it was severely out of balance.

The last spectrogram shows an additional feature that I had overlooked in the original analysis. This is a dim, low amplitude but high frequency tone related to the 22 bar commutator and appearing as the 22nd harmonic of the motor rotation. Of note here is the fact that changes in motor speed are magnified by the harmonic multiplier. In other words a change of 100 Hz in the motor speed would show up as a change of 2200 Hz in the commutator tone.

The zoomed spectrograms allow for better selectivity in reading the frequency values when the number of lines chosen for the spectrogram calculation is large. A new set of values is shown below which along with the calculation of the number of fan blades and commutator bars shows the effect of the increased precision.

Component	Idling	Carpet	Hose Open	Hose Sealed
Brush		158 Hz
Motor	406 Hz	397 Hz	406 Hz	459 Hz
Fan	2032 Hz	1984 Hz	2041 Hz	2301 Hz
Commutator	8948 Hz	8780 Hz	8987 Hz	10129 Hz

Calculated values for the number of fan blades and commutator bars using measured frequencies from the table above and dividing by the motor rotation frequency are shown in the table below.

Component	Idling	Carpet	Hose Open	Hose Sealed
Fan Blades	5.00	5.00	5.03	5.01
Commutator Bars	22.04	22.12	22.14	22.07