At least in the two plots you've presented I don't see anything in the way of amplitudes that would cause me concern. Having said that I can offer a few ideas as to the source of the particular frequencies of interest. But before I do that I would suggest care in attempting to identify elusive (meaning small in amplitude) components in a gearbox spectrum. That practice will drive you nuts! The perfect gear does not exist so when we mesh a pair we have a great device to create not only the anticipated fundamental frequencies but sum and difference frequencies. Couple that with the bearing related frequencies and the spectrum can be quite a mess. Many years ago I wrote the following as an introduction to a tutorial on gearing that related the aspects of design to dynamics.
The term "odontics" may be selected for that limited but important branch of kinematics that is concerned with the transmission of continuous motion from one body to another by means of projecting teeth. It is a field that for several hundred years has received the interest of both mathematician and engineer; it can be educational, frustrating and entertaining. Thousands of pages have been written on the kinematics of gear teeth, however, little has been exhausted except for the writers and readers.
OK, now to some thoughts as to the source.
Observation 1...As I previously mentioned there is the pecularity in that the frequency of interest of 36960 CPM is an exact integer of the 1st reduction gear speed/2nd reduction reduction pinion which likely are mounted on the same shaft rotating at 660 RPM; in other words 36960 CPM/660 RPM = 56 exactly. So what might generate the 56th order of the 2nd reduction pinion which by coincidence has 14 teeth. 56/14 = 4, where does that leads us? I'm not sure, just the numbers game I suspect.
Observation 2...again, back to the frequency of interest of 36960 CPM being the 56th order of the 2nd reduction pinion shaft. Couple that thought with your statement "It seems quite common over all 80 gearboxes with the amplitude varying in each box" and I become suspicious of what is called a ghost frequency. As you may know the machines that make gears are also full of gears. Hopefully all those gears are as near perfect as possible because any error in them gets "impressed" into the final product. Usually, if this happens, it happens in a final tooth cutting or finishing process. If that 81 tooth gear or that 14 tooth pinion was machined using a 56 tooth index wheel and that index wheel had an error, it would be seen in the final gearbox as a 56th order. You would have to determine with the manufacturer the exact method of manufacturer and the teeth involved in the actual gear cutting machines. This can be an exhaustive process and the gear manufacturer, depending on their level of expertise may think you are crazy. My personal first encounter of "ghost frequency" was in a paper written by Bruel & Kjaer that dates to about 1980. I've attached it here for your use but later found it at http://www.bksv.com/doc/233-80.pdf
. I doubt B&K would mind due to its age and not to my knowledge being on the web. Download it and look at the content on pages 10 & 11. My 2nd encounter with ghost frequency was when the famous Charlie Jackson called me while commissioning a gearbox made by a manufacturer in Texas. He was concerned about a frequency in the spectrum, quite large actually, that was not identifiable by the tooth count. I determined that it was an exact integer (292X) of rotating speed. Some further work using time synchronous averaging determined the exact rotor that had the fault. Consultation with the gearbox manufacturer initially confirmed I was potentially nuts but Charlie prevailed and on investigation it was determined there were 292 teeth on the index wheel of the hobbing machine used to generate the rotor. I am aware of other instances of this issue but in my 17 to 18 years with a gear manufacturer they number about five cases. So it is very rare. Wherever the source the primary concern is amplitude because that represents energy. In the case of the gearbox being commisssioned the amplitude at the ghost frequency of 521,000 cpm was in excess of 20 g's peak while gearmesh was about 2 g's peak. Obviously something here was wrong. The gearset was reground (on a totally different machine) and the frequency was no longer present at any measurable amplitude.
So, if you have a good relationship with the gear manufacturer you might investigate ghost frequency. Do you have an ability to simulate a keyphasor on the shaft with the 81 x 14 tooth combination and perform time synchronous averageing? Those techniques can help identify the actual gear with the fault. But if I was in your shoes, and I say that only having seen the two plots showing low amplitudes, I would chalk this up to academic interest only and a probable ghost frequency.