Rooftop chiller, 31.5 Hz, and a rigidly mounted rail
A rooftop air-cooled chiller serving a 12-storey apartment building sits on steel rails above the top-floor penthouse. Since commissioning, the occupants report a continuous low 'drone' and say the floor and bed frame hum. A one-third-octave measurement in the bedroom shows the 31.5 Hz band at 58 dB(Z) (51 dB(C), 38 dB(A)); with the chiller switched off but the supply and extract fans still running, that band falls to 32 dB(Z). Accelerometers show 0.6 mm/s RMS at 31.5 Hz on the roof slab beside a chiller foot, and 0.18 mm/s at the same frequency on the penthouse floor slab. The chiller, 2,800 kg, sits on 10 mm neoprene pads bolted to a shared steel rail fixed directly to the roof slab; the refrigerant pipework is rigidly bracketed to the same rail. The compressor runs at 1,740 rpm and the manufacturer's data sheet notes a fundamental at that speed.
1. Diagnose the transmission path and state what test would confirm it.
Read the worked answer
Structure-borne transmission dominates. The evidence is the 26 dB collapse in the 31.5 Hz band when the chiller alone is stopped while the fans keep running: that isolates the chiller as the source, and the bedroom level is therefore not coming from the fans or from unrelated building services. The vibration data supply the second half of the argument - 0.6 mm/s on the roof slab beside a foot and 0.18 mm/s on the penthouse floor at the same frequency, meaning the slab is being driven and is radiating into the room below.
The installation gives the mechanism. Neoprene pads on a rail bolted directly to the slab is a short-circuit: the pads deflect only a millimetre or two under load, giving a natural frequency around 12-14 Hz, which is far too close to the 29 Hz running speed to isolate it. The rigidly bracketed pipework is a second short-circuit path straight past the pads. The 29 Hz fundamental also sits squarely in the 31.5 Hz one-third-octave band, so the band level is a tone, not broadband.
Confirmatory test: measure accelerometer-to-microphone coherence at 31.5 Hz, and run the chiller briefly on temporary springs or on its own isolated frame. If the bedroom band drops with the temporary isolation while the pipe brackets are left in place, the residual identifies the pipe path.
2. Design the isolation and show the numbers that size it.
Read the worked answer
Target: a system natural frequency well below 29 Hz. For a spring-mounted system, fn = 15.76/sqrt(deflection in mm). With 25 mm static deflection, fn = 15.76/5 = 3.15 Hz, so f/fn = 29/3.15 = 9.2 and the undamped transmissibility is T = 1/(9.2^2 - 1) = 1/83.6 = 0.012, i.e. about 38 dB of theoretical isolation. In the field, with damping, rail flexibility and residual pipe paths, expect 15-25 dB - still a large reduction in the 31.5 Hz band.
By contrast, 10 mm neoprene pads deflecting 1-2 mm give fn of roughly 11-14 Hz, f/fn of about 2.2-2.6, and T of 0.17-0.26, which is marginal at best and becomes amplification if the pads stiffen with age or cold.
Design: replace the pads with springs selected for the actual load per mount, typically six mounts, each rated within its working range and checked for lateral stability and wind/seismic restraint. Add an inertia base of the same order as the machine mass (1-3 times; more for reciprocating plant) to control starting torque and lower the system frequency. Replace the rigid pipe brackets within the plant area with flexible connectors and isolation hangers, and isolate conduit and duct connections. Verify at commissioning that no bracket or cable tray has re-short-circuited the springs.
3. The contractor proposes to verify success using the overall dB(A) in the bedroom. What is wrong with that, and what would you specify instead?
Read the worked answer
A-weighting at 31.5 Hz is about -39.4 dB. The chiller's contribution to the bedroom dB(A) total is therefore almost nil, and even a 20 dB reduction at 31.5 Hz would move the overall dB(A) by little more than a decibel - the metric would show 'no significant change' while the complaint was actually solved. Using it as the acceptance test invites a dispute in which the acoustics is right and the paperwork says failure.
Specify instead: one-third-octave measurements from 20 Hz upward, reported as dB(Z), with dB(C) as a cross-check, at the same bedroom position, height and orientation before and after. The acceptance target should be framed against the plant-off condition at the same band - for example, the chiller-related 31.5 Hz level at or below the 32 dB(Z) measured with the chiller off, or a stated absolute band limit agreed with the occupants and the building owner.
Add three safeguards. Check the 63 Hz band and any new tone introduced by the springs or by changed fan speed. Repeat the measurement with the chiller cycling to catch start-up transients. And keep dB(A) in the report only as a secondary descriptor, clearly labelled, so that no one later mistakes it for the design criterion.