"Two accelerometers, A1 and A2, are placed on the bearing and gearbox housings, respectively."
It is presumed there's enough energy content in both/either A1 and/or A2 transmitted through the mountings of the shaft and gearbox case to be able to find the components' contributions in the overall signals.
In real life(*), this is totally dependent upon construction of the gearbox and quality of accelerometer mountings. Generally it does work at least well enough, but is easy-enough to observe whether the known frequencies are actually contained in the returned waveforms.
That's not to say it is always a trivial exercise by any means. It sometimes isn't all that easy in practice to be able to get sensors in the places they would need to be ideally, and even if is physically possible to get to the location, conditions at that point may be far from ideal for instrumentation or getting a signal from somewhere remote in the bowels of a nearly mile-long paper rolling mill back to a collection point can be a challenge. While at CSi we introduced the first wireless accelerometer...
In the example they're there because the author simulated an ideal gearbox; it would have been instructive to have followed that up with actual data from a real gearbox of the same type -- what we did routinely at CSi to test new instruments, algorithms, etc., etc., ... amongst the lab gear was included the test rig called "The Alligator" that was precisely a set of gears, bearings, and all with known and introducible faults of all kinds.
(*) In former life I was employed by CSi, the leading vendor/pioneer firm in the field...now a part of Emerson.
