The wheel lift-off theory as to the origin of "spikes" in the inclinometry difference plots

The wheel lift-off theory as to the origin of "spikes" in the inclinometry difference plots. Justin Greenhalgh, Jan 25 1999 P/001/21/RJSG (1999)

This note has been assembled from a couple of emails, basically to provide a note for posterity as to how our thoughts were going at the time.

1. Statement of a theory to explain the "spikes" in the inclinometry data.

The antenna is a very stiff structure, and is nominally supported on five points (the central pintle bearing and the four rollers). Because it is so stiff, any variation in the height of the support points, or any thermal distortions in the structure, will have a large effect on the load distribution between the five support points. Study of the figures for stiffness and for thermal distortion show that:

the load on each wheel will vary by about +/- 0.6 tonnes as the antenna goes around the track, based on best available information on track profile.
a credible thermal distortion (that induced by a 1 deg differential between the part of the structure above the observing floor and that below it) reduces the loads on every wheel by around 0.5 tonnes.

The nominal wheel loads, measured by a strain gauge system of dubious accuracy, are as follows:

wheel 1, front right : 0.66 tonnes
wheel 2, back right : 2.1 t
wheel 3, back left : 3.3 t
wheel 4, front right : 0.7 t

Allowing for the known track profile and the location at which the loads were measured, we would expect the load on wheel 1 to decrease to zero at two points around the track in the absence of any thermal effects.

Furthermore, a prediction of the places where the wheels would lose load, and the extent to which they would lift off, matches the patterns seen in the spikes both in location, magnitude, and general form.

The explanation of the "spikes" is that at times the weight of the telescope is removed from the front wheels by unevenness in the track, the effect being exacerbated intermittently by thermal distortions in the structure of the main frame. When the weight comes off a wheel, the relevant corner of the antenna no longer follows the track profile and so a change in measured profile results. The number of spikes and their size depends upon the magnitude of the thermal effects and the current height of the central bearing relative to the track. The overall pattern and relative size of the spikes is given by the track profile.When the weight comes off a wheel, the wheel itself remains in contact with the track and a gap opens up between the flanged bearing (item 13, OR180051) and its mating part (?Bearing housing yoke, item 3 OR180051). The weight of the roller, motor, and yoke is sufficient to keep the roller in contact with the track and prevent it from spinning.

The "asymmetry" would appear whenever the wheel loads were light, because the inclinometry would be dominated by rear-wheel effects which do not repeat at 180 degrees.

2. Possible tests of the theory were:

Study existing data to look for a correlation between spike size and "delta T". The theory predicts a relationship of the form:

S = (dTc - dTn) - W
Where
dTc = delta T when central bearing was adjusted
dTn = delta T now
W = weight offset introduced by central bearing adjustment (or by adding weights)
S = spike height
So we expect to see a set of straight lines of S vs dTn, a different one for each central bearing adjustment.

induce spikes by heating the basement, or by heating one suitable bar - would need FE to decide which one.
put weights on and observe that present spike-free state continues for a long time. (How long?)
start to observe wheel weight (once the strain gauges are wired up) and note daily variations and correlation with spike height over time.

3. Possible solutions to the problem were identified as follows:

Add weight at the front of the telescope
Move existing weight around (though no-one could think of any candidates)
Remove the two front wheels, or at least lift them off the track (we were brainstorming for a while)
Add springs to the front wheels to keep them in contact with the track
Control the temperature in the basement to match upstairs
Measure the temperature difference and predict when wheel contact will be lost; modify track model in real time to suit.
Measure load on front wheels directly and modify track model when wheel lifts off.
Measure load on front wheels, use strategically placed heater on structure to control the load.

General agreement was that the first solution was the most appealing although we should revisit if it turns out to be harder than we thought.

4. Analysis of the "Assumptions, Observation, etc" paper in terms of this theory.

Assumption number 3, the one about the way the antenna interacts with the track remaining constant, is the one that falls and this theory provides an explanation. Note that although the work I did shows that the two A-frames bend and interact a lot, it does not invalidate assumption number 1 (about two rigid independent A frames) provided the wheels stay on the track.
Observations 1 to 4 fit the theory.
5 (CW different to CCW) is not explained at all.
6 is a paradox: pointing is perceived as getting worse and yet attempts to document the trend (IMC's recent work on SCUBA and A2 pointing) have failed. The current theory would not explain any worsening trend unless there were a worsening thermal environment *OR* we can show a relationship with the central bearing adjustments.
7,8,9, and 10 fit
11 (SY differs from LY) is not covered by this theory - but I have found that the SY-LY term is fitted quite well by a suitable sum of track profiles as seen by each wheel, and I hope to verify that the manner in which this happens is consistent with the FE analysis of flexure along the beams.
12 and 13 fit (inclinometers are OK)
14 (spikes getting worse) is not explained by this theory alone - unless we know of something about the thermal environment that is getting worse *OR* we can show a relationship with the central bearing adjustments.
The time histories we have seen are plausibly explained with important caveats. Broadly, I would expect to see big variations in the spikes if the central bearing had a lot of load (rollers lightly loaded), but the spikes should pretty much go away if the rollers were heavily loaded.