Ripple in Inclinometry no longer a cause for concern ?

SUMMARY
Although a problem with one of the antenna wheels may still be a reality, concern about a worsening of the condition is revealed to be an artifact of the data analysis. Fourier transform analysis of all 1997 and 1998 inclinometry data show the amplitude of the problem crested last autumn.

There was, and still is , an 8.8 degree ripple
Analysis of recent inclinometry data shows a `ripple' reminiscent of a problem seen during 1996. The diagnosis then - following an earlier catastrophic wheel failure - was a faulty wheel on the rear right corner of the antenna. However, after that wheel had been replaced and examined, no physical damage was discovered. The new ripple has again been determined to lie within the right A-frame structure and again the rear right wheel looks to be the culprit.

Difference Data
During the routine creation of a track model from inclinometry data, comparison is made with previous datasets. The comparison of data from 980222 and 971214 lead to the current concern. Previous pairs of data also showed the ripple, and we had to go back to the consecutive pair of 971104 and 971031 before the ripple vanished. So : "When had it appeared ?", and "Was it growing in amplitude ?"

Fourier Transform employed
The individual inclinometry data, and even sometimes difference data, are not amenable to an eyeball inspection for given frequencies due to the presence of many component frequencies and large amplitudes. This was especially true of the data taken during the Azimuth Track Upgrade (joint welding) Program that took place between April and June 1997. Fourier transform methods must be employed, and so a (NAG) FFT subroutine was used, first on the difference data (971104-971031) through (980222-971031). A movie of these FTs shows (*) a strong spike emerging on 980124 at a frequency corresponding to 8.8 degrees - the circumference of the antenna wheels. The spike continues growing and, in the last frame (980222) has 6 units of power (**), which, by inspection of the data, corresponds to an amplitude of about 1".

A growing problem seems indicated.

[ (*) - The information content of the FT resides on the left half of the movie screen and is simply replicated on the right.
(**) - The power in the FT plots is related to the amplitude of the effect in arcseconds, but at the moment the conversion I'm using is entirely empirical.]

Radial Arm Inclinometry
The radial arm inclinometer was duly set up on 980301 to monitor the rear right wheel, and several radial arm datasets have been taken since. A graphical comparison of each of these data with those of 980301 seems to confirm that the 8.8 degree ripple emanates from the rear right wheel, with an amplitude that has increased to 1" presently. The FT movie of these differenced data shows a change in the power at 8.8 degrees of a factor of ~2.

( There is much more power, and variation, at 25.7 degrees, or k=15 in the FT movie. It is also easily discernible in the graphical comparison . We identify this as the mean track segment length, 360/14. The variation in behaviour of the track joints from one inclinometry run to another is not fully understood, but might be ascribed to changes in temperature, humidity or loading.)

However, the FT movie of the individual radial arm data shows only insignificant variations in the strength of the 8.8 degree feature. Justin suggested that this could all be explained by a change in the phase of the feature. In the current scenario this could be caused by slippage of the wheel(s), and it is clear that, with slippage, eccentric wheels, rather than flawed wheels, would produce similar observations.

The appearance of a problem
Some of the analyses above suggested a growing problem, but the picture is not clear. However, the interpretations are fraught with enough difficuties without those introduced by using differenced data. The strength of the 8.8 degree feature in differenced data is not accompanied by its sense or sign (or phase). We should examine rather the power and phase of this component in individual datasets. The datasets of 971031 and 980411, for instance, (those highlighted in the analysis above) show power at 8.8 degrees of 11 and 5 units, respectively - i.e. the amplitude of this ripple has diminished over this interval by these 6 units !

The FT campaign
Accordingly, I have FT'd the 33 individual inclinometry runs (A-frame configuration) since the beginning of 1997 (that's all the data available on disk just now), and present the power movie here . It shows the 8.8 degree feature appearing first during April/May 1997, attaining maximum amplitude in October/November 1997, and diminishing - though not disappearing - thereafter. The apparent zero amplitude of the feature in the consecutive pair of 971104 and 971031 is thus explained as the subtraction of two equally strong features. However, a time sequence of the power and phase of the 8.8 degree feature shows that the rise and fall of the power is not accompanied by any significant phase change, implying that the ripple is not generated by a slippage of the wheel(s).

The phase is -1.0 +- 0.8 degrees throughout the period where power > 3 units (= 0.5" ?), with only the 3 degrees of phase change at day 400 (Feb 1998) seeming potentially significant. This amounts to about 5mm of wheel circumference. If a mechanism for inducing a phase change is postulated (a burr on the wheel, an object on the track ?), could the return of the phase to its previous average value be explained satisfactorily ?

Phase loss (in the absence of defects) is possible in rotating systems, but the studies uncovered by Ian mainly concern uni-directional motion. The back and forth nature of the motion of (the wheels of) JCMT probably ensure phase stability.

Conclusions

• Neither my understanding of, nor analysis of, this phenomenon is complete, but the results so far are presented in order to stimulate further discussion and understanding. The cause of the 8.8 degree ripple presumably resides within the wheel, (or housing or motor), but I feel that our (my) early concerns about its structural integrity are allayed. The magnitude of the problem has certainly abated since the peak amplitude was reached last autumn.

• It is also probably true that no structural damage was found in the wheel in 1996 because there was none - and that analysing differences only - as is convenient to do in order to monitor changes - can lead to misinterpretation.

• Interpreting the FTs is complicated, and I cannot claim at this stage to have extracted all the relevant information from this method. The above conclusion removes somewhat the immediate concern of catastrophic failure, but will need continuous reinforcement.

• This phenomenon can at least be monitored and placed in the context established above, but to continue the movie(s) sensibly into the future requires a resolution of about a week. This is still best met by our current weekend inclinometry schedule, and - as if in passing - is also necessary to maintain a current track model for the business of achieving the best possible pointing.

How I made the movies