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I'm being annoyed by a pulsating hum which comes from my neighbor's HVAC system. I read up a little on the design of HVAC systems and I came to a tentative conclusion that what I'm hearing is a compressor being driven by an AC induction motor. A frequency spectrum shows a spike at 120 Hz and another at 117 Hz; which of course produces a 3 Hz beat. The 117 Hz spike actually moves around between say 117 and 118 Hz. I guess what I'm hearing is called a "slip frequency beat"? I'm in the US, where the mains frequency is 60 Hz; so 120 Hz is the audible hum produced from magnetic fields in motors, transformers, and so on.

According to this document (p. 3), the "slip frequency", defined as "per-unit slip times line frequency" is the "actual frequency of current in the rotor conductors". Per-unit slip is proportional to torque and is commonly 0.03 - 0.05. This means 3 Hz could be a typical slip frequency, and I guess 117 Hz could be a slip-frequency sideband of 120 Hz. But there is no 123 Hz spike, and in fact the rest of the spectrum is pretty quiet except for spikes at 59 Hz and 29 Hz. There are harmonics at 234 Hz and 240 Hz, but the harmonic at 352 Hz is stronger than that at 234 Hz. All the harmonics have much less energy than the 117 Hz and 120 Hz fundamentals (say >20 times less). The 29 Hz and 59 Hz spikes don't seem to vary much when the compressor turns on and off, and neither does the 120 Hz spike. Only the 117 Hz spike and its harmonics show an "on-off" square wave in a time-series plot, corresponding to compressor activation at 10-minute intervals.

I can't provide decibel-calibrated sound pressure levels (and since I don't have access to the equipment, I can't measure the actual vibration intensity). I would say the sound is not loud enough to be annoying unless you have to live next to it.

I have calculated that the sound amplitude in the 117 Hz "spike" is 3 times higher than that in the 120 Hz spike. I don't know if this reveals anything significant.

I've read that the speed of an AC motor is 120 Hz / (number of poles), and that the minimum number of poles is 2, so I'm concluding that the motor cannot be turning at just under 120 Hz (7200 RPM) but rather must be going at some slower speed like 60 Hz (3600 RPM). This seems to imply that the 117 Hz vibration is not mechanical vibration from the rotor - but I'm not sure what else it could be. The linked document mentions certain faults producing vibrations at 2 x RPM, but it seems these should be concurrent with vibrations at 1 x RPM. But, as I said, the 59 Hz spike doesn't vary with compressor activation.

Here's a time-series plot of various spectral amplitudes, taken over 6 hours at night. The spectral bands shown here are 58-59 Hz, 116-118 Hz, 174-177 Hz, etc. You can see that compressor activation doesn't seem to affect the 59 Hz spike, but there is a clear signal at 117 Hz and 3x117 = 351 Hz. (I also appended a spectrum plot)

Harmonics of 59 Hz, 6-hour time-series, plus spectrum

According to the linked document, some amount of vibration is normal and the surest way to diagnose a developing fault is to take spectral readings over time and see if anything is getting worse. The neighbor's HVAC system is 20 years old, but I only have readings for the past six months, and there seems to be a lot of fluctuation just from weather conditions and diurnal temperature variations influencing the propagation of sound across the property line. Because of this I can't say that there has been an obvious trend upwards in sound amplitude over this time period.

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    $\begingroup$ Just curious, are you trying to help your neighbour fix his HVAC? Or is it just bugging you so much that you started to do in depth analysis of the situation? I'm picturing the second one and it's making me laugh a bit. $\endgroup$
    – JMac
    Feb 27, 2017 at 11:45
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    $\begingroup$ @JMac hey, the world is full of us engineering analysis nerds. We jump at any chance to play with our toys. $\endgroup$
    – Carl Witthoft
    Feb 27, 2017 at 16:15
  • $\begingroup$ A 20-yr-old system that's still working is a miracle :-) . But before pronouncing this one dead, maybe someone should check the coolant volume. Possibly a nearly-empty system is running "smoothly" when there's no load, and shifting to a different speed when there is a load (i.e. material to compress) $\endgroup$
    – Carl Witthoft
    Feb 27, 2017 at 16:16
  • $\begingroup$ @Carl_Witthoft thanks for the idea! Will try to read up on that. Sounds like you know something about HVACs. The device is a rooftop "forced air" type of unit, as I've heard from a local technician. I'm wondering if the compressor is always running, and there's a solenoid valve that shunts the coolant through a constriction to get the cooling effect? But the guy said that the rattle I'm hearing when the compressor starts up is from an AC motor spinning up from zero...? The spectrum when the unit is "off" contains a very little spike at 118 Hz - but maybe this is from a fan? $\endgroup$
    – Metamorphic
    Feb 27, 2017 at 19:58
  • $\begingroup$ The 3600rpm you have for the motor is going to be the "no load speed". Under load, it should be something like 3450rpm which would be ~115Hz $\endgroup$
    – DLS3141
    Feb 28, 2017 at 13:34

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A 3Hz pulsating hum-- noise that is getting louder and softer at 3Hz. Yes, I agree that would be quite annoying.

Since this is a residential unit in the US, both the compressor and the fan are run with single phase asynchronous motors. Almost certainly, they are four pole with an 1800 RPM synchronous speed, running about 1750 RPM or so, depending upon load. The peak you are seeing at 116.8 Hz is consistent with this since that corresponds to the second harmonic of a 1752 RPM rotation rate. The big peak you see at 120Hz is interesting. I wonder if this is due to a loose winding in one of the motors.

The compressor is inside the A/C unit, in this case, on top of the house. The fan has to be exposed to the outside. My experience is the fan is what you hear most of the time.

From the graphs, it looks like everything is working correctly. The compressor or fan is cycling in and out every 20 minutes which is to be expected. The duty cycle is less than 50% which means it is properly cooling so I guess the coolant levels are adequate. The sounds are probably caused by a combination of loose sheet metal and maybe a loose winding. If it were my unit, I would put my hand here and there to try to guess where the noises are coming from and make sure everything I can get to was bolted down securely. Recognizing that it is not your unit and you don’t have access to it, much less permission to go monkeying around, this won’t do you much good. If it is not running in heat pump mode and it is running at close to 50% duty cycle in February, (when this question was originally posted), it won’t be able to keep the house cool when it starts to get hot and your neighbor will get it fixed, hopefully with a replacement unit.

After reading the linked document, I think you should go over there in the dark of night and do a “power trip test” if for no other reason than to get some peace and quiet.

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    $\begingroup$ Thank you for your answer. I had forgotten that I had asked this question here. The problem was eventually solved, by (1) gently threatening to sue the neighbor, (2) which resulted in them authorizing their facilities manager to work on it, (3) he installed two compressor blankets over the compressor, (4) he placed a number of buckets of sand on the roof to dampen the vibration, adjusting their positions using feedback from a web-based realtime plot of the sound levels in the 117 Hz and 120 Hz bands, which I had developed for this purpose. $\endgroup$
    – Metamorphic
    Sep 13, 2018 at 20:32
  • $\begingroup$ I saw the question and typed up a long winded answer and only then noticed WHEN the question was posted, oh well. If it is a business, it will be a bigger unit and there is a good chance it will be a three phase motor but it sounds like you got things pretty much under control. Beat Frequency: I stand corrected, you did say "pulsating hum" which is what I assumed. I'll have to come up with some appropriate edits. $\endgroup$
    – user1683793
    Sep 14, 2018 at 18:09
  • $\begingroup$ Thanks, the answer looks better now. I just marked it as accepted. Can you also provide a link for the claims in the second paragraph though? Sorry I forgot to ask for that before. $\endgroup$
    – Metamorphic
    Sep 15, 2018 at 19:49
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    $\begingroup$ With motors, you don't want too slow or too fast. It happens that 1750 or so RPM is a good middle point. Practically all the equipment I have access to runs at that speed. But you wanted a link. I went to Grainger’s web site and looked up motors. They have a surprising number (568) of six pole, 1101-1200 RPM motors. Most (1610) of their motors are four pole, 1701-1800 RPM. They have a goodly number (948) of two pole between 3001 and 3600 RPM. $\endgroup$
    – user1683793
    Oct 1, 2018 at 22:52

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