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ˉcontaining NTP points. Designating the average number number of points per
ˉ

carrier cycle as Navg, then it is useful to .nd the smallest
integer value, NTP, such that: 
min哩 !巳 NT P (|Nr(NT P . 1) + 1 . ˉNavg|)  (8) 
Once NT P is solved, ˉN is determined from: 
ˉN = Nr(NT P . 1) + 1  (9) 

It is convenient to work in units associated with a single TMP consisting of NTP points. The Vibration Separa-tion Vector consists of either Np TMPs of an individual planet gear or Ns TMPs of the sun gear. The length of their corresponding Vibration Separation Vector,缸v, is given by:
缸v = Np,s(NTP . 1)+ 1 (10)

where Np,s is either Np or Ns.
Extraction

The data extracted from each carrier cycle depends on three parameters: planet gear angle θiP, accelerometer an-gle, θAj , and the number of data points to extract,缸E .
Since the 1st carrier cycle is rejected, the analyzed por-tion of the data starts at θc = 2π, as shown in Figure 13.
The ordering of the planets starts with P1. Since the carrier rotates counter-clockwise, the planet numbering is clockwise, so that increasing planet number corresponds with the order in which they reach each accelerometer. The accelerometers, shown in Figure 13, are numbered counter-clockwise from A1 to A5. Their angular accuracy is on the order of 1 of the ring gear’s tooth pitch (≈ 1o). The con-

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vention used is such that, when the planetary system is in its initial orientation at θc = 0, all planet teeth engaged with the ring gear are assigned Tooth ID 1 and increase in the di-rection opposite to the gear’s rotation. In addition, the sun gear’s tooth just above the origin is assigned Sun Tooth ID 1 and has an initial angle given as θ1 = 3.8o .
　
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