Periodic error

I am using a very nice program called PEMPro to minimize the periodic error in my mount. I have to say, this is a great program, and also helps you do a nice drift alignment. I highly recommend it

The figure below is the periodic error just after HyperTuning. Sadly, I did not check the periodic error before HyperTuning. Figure 2 shows that there is a major fundamental at 1, and a minor one at about 2.7.

Periodic error

Figure 1. Periodic error in the CGEM.

 

Before Fundamentals

Figure 2. CGEM fundamentals. The peak occurring at 1 represents the worm gear (1 cycle every turn of the worm gear). There is another non-integer fundamental near 3 (approx. 2.7). Non-integer fundamentals cannot be corrected by PEMPro.

Below is the periodic error after correction (Figure 3). The curve generated by PEMPro in Figure 1 was inverted before sending it to the mount. Then another analysis was run with PEC on to give Figure 3.The was still some error caused by the first fundamental (Figure 4) which was removed by a further refinement of the curves. Notice that as in Figure 1, there does seem to be some addition periodicity (i.e. some curves are overlaid with each other).

Correction on

Figure 3. Periodic error after correction in the CGEM.

 

After fundamentals

Figure 4. CGEM fundamentals after correcting the periodic error.. The peak occurring at 1 is reduced. That non-integer peak around 3 is now the major fundamental.

In Figure 5, I have expanded the middle portion of Figure 3 to illustrate that at least with my mount, there is an additional repeat every 3 worm gear rotations.That is, the periodic error in turn 1 of the worm gear is almost identical to the periodic error in turn 4 of the worm gear. This is interesting, because what it implies is that the actual worm gear cycle in the CGEM is not one worm gear rotation (about 8 min.), but but actually 3 worm gear rotations. In some Meade mounts,, 3 worm gear rotations are used for periodic error corrections.The reason for this is that there is an 8th fundamental in these mounts which cannot be corrected with a single cycle of PEC data because it repeats 2 2/3 times in a single worm period, and is thus not periodic over only one cycle. In three cycles it will repeat exactly 8 times. Note that in the fundamentals graphed in Figures 2 and 4, there is indeed a fundamental at about 2 2/3.

I suggest that if Celestron would use 3 worm cycles instead of 1,worm cycle the periodic error could be modeled more accurately in this mount. A good suggestion by Ed Thomas is that this error could arise from the gearbox (see below for evidence that it is the gearbox).Periodicity

Figure 5. The middle of the periodic error curve from Figure 3. The worm gear cycles are numbered.1 through 6. Also shown are the left hand side (LHS) and right hand side (RHS) of the graphs showing the end and beginning of each curve. Notice how closely the end of one curve lines up with another curve.

 

What I did next was use a worm period of 3 cycles (1436.07 s) and used the data from PEC on analysis. I had thought I would have to edit the data file, but the author of PEMPro (Ray Gralak) mentioned that all I would have to do is alter the worm period time. Have I mentioned that this is a great program?

Three Cycle

Figure 6. The data from Figure 3 but with a 1436.07 s worm period.

Below is the frequency spectrum showing new peaks near 3 (for three turns of the worm gear) and near 8. What I do not know if the peak is near enough near 8 to be considered an integer.

Frequency Spectra

Figure 7. Frequency spectrum for the data from Figure 6.

However, PEMPRo is able to model the data with the smallest RMS error I have ever gotten.

Curve

Figure 8. Suggested curve predicted by PEMPro.

Ed Thomas posted the information on gearing in the CGEM on the CGEM yahoo site.
Here are the gears in the CGEM starting from the motor:

1 - 8 teeth (pinion gear)
2 - 23 teeth to 12 teeth
3 - 30 teeth to 12 teeth
4 - 30 teeth to 12 teeth
5 - 32 teeth
6 - 47 teeth (motor spur)
7 - 47 teeth (worm spur)

Ratios are:
1 - 23:8 or 2.875:1
2 - 30:12 or 2.5:1
3 - 30:12 or 2.5:1
4 - 32:12 or 2.67:1
5 - 47:47 or 1:1

There is indeed a gear which could cause a a periodic error every 3 turns of the worm gear (ratio 4). It is right next to the gear ratio for the worm gear. So the two major sources of periodic error in the CGEM are from the worm gear and the 32:12 gears.

The error could be corrected for using PEMPRo if there were a way to program the mount. According to the author of PEMPro "Celestron mounts only have 88 PEC cells because of a limitation in non-volatile storage memory. If that limit is still in place there may not be any more internal permanent memory available to add more PEC cells to cover three worm cycles. The only possibility might be for Celestron to try to programatically compress a 3-cycle curve into the 88 bytes, assuming that is all that is available."

The other option would be to improve the gearing and motor.