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Sun Tooth Mesh Schedule
In order to match extracted dynamics with the correct sun tooth region, the sun tooth meshing shedule is needed. As the carrier rotates, the angle of sun Tooth ID 1, θ1(i, j)
s is tracked. When Pi is aligned with Aj, the clockwise angle
between θi, j and Aj is used to determine the region of the
s1 sun tooth that is aligned. The angle θ1(i, j) is given by:
s
θ1(i, j)=(1 + NNpr )(θij + m(2π)+ θˉ1) (23)
s sep s
where the identity:
Nr
θs =(1 +)θc (24)Ns
is used. The clockwise angle to Aj, corresponding to in-creasing Sun Tooth ID number, is given by
θj = mod(mod(θi j s1,2π) . θAj ),2π) (25)
s
ˉ
where θ1 is the initial angle of Tooth ID 1. The Sun Tooth
s
ID is found by counting the number of sun tooth pitches in θsj. Since the sun tooth pattern repeats, it is possible to tab-ulate the sun tooth mesh schedule for both systems. Table 3 shows the tooth meshing schedule in term of the approx-imate tooth ID for Mv = 9. Sun Tooth ID values are used
Table 3. Sun Tooth Meshing Schedule OH-58C Mv = 9
instead of angular values to make the tables more intuitive. During implementation however, the actual angle is used.
Looking at Table 3, each column represents a carrier cy-cle and each row represents one of the .ve accelerometers. There are only three carrier cycles, since the pattern repeats, Table 3 represents a complete set. The highlighted columns within each block represent the closest sun tooth associated with Ni j ... Each row contains Mv = 9 tooth ID numbers rep-resented per extraction. Figure 21 is a graphical representa-tion of the .rst box of Table 3 for which the lightly shaded sun tooth represents Sun Tooth ID 1 and the darker tooth is the one represented in the table and indicated on top of each plot.
When P2 aligns with A1, the sun gear is in mesh between teeth 10 and 11. The chart’s value of 10 is rounded to the closest tooth for clarity. Data is extracted that corresponds to when sun teeth 6 through 14 are in contact with P2 as P2 passes A1. This is then repeated when the next planet, P3, arrives at A1 and data associated with teeth 10 to 18 are extracted. As shown in Table 3, extractions associated with six consecutive planet passes are needed to get full tooth representation: four from the current cycle and two from the subsequent cycle.
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