To measure the error in the azimuth encoder rack gear, jon hagen built a proximity sensor. It consisted of two plates of a capacitor. One plate was mounted on the azimuth encoder mounting bracket (this is fixed relative to the azimuth arm). The second plate was mounted on the spring loaded mechanism that pushes the encoder into the encoder rack gear (this part moves). Measuring the voltage as the distance between these two plates changed gives the radial distance that the encoder rack gear is moving. The device was calibrated by mounting it in a milling machine in the lab and measuring the inches per ohm (.000425 inches/ohm).
We measured the run out error by moving at .02 deg/sec azimuth velocity (using the encoder arc length) and sampling the voltage at a 5 hz rate.
To convert from radial error to angular we need to define some terms:
ds : The differential arclength the encoder covers as it moves.
R_avg is the average radius of 127/2=63.5 feet. R_T: The true radius when the encoder moves through the length ds (actually it is the average true radius along ds). dR = R_T - R_avg. Error in radius at each point (actual - ravg).
dTh_M: The differential angle theta measured by the encoder as it moves though the arc ds. The computation used is: dTh_M= ds/R_avg . dTh_T: The true angle we moved through when the encoder moved along the path ds. dTh_T=ds/R_T = dTh_M * R_avg/R_T = dTh_M * R_avg/(R_avg + dR)
To compute the az encoder runout error:
The measurement used a clockwise azimuth spin from 70 to 710 degrees followed by a counter clockwise spin from 710 down to 340 degrees.
The plots (.ps) (.pdf) show the results of the runout measurement:
The 2nd page shows the frequency spectrum of the runout (.ps) (.pdf):
Top: shows the resistance versus azimuth. The dark lines are the clockwise spin while the red lines are the counter clockwise spin. The measurement technique is repeatable. Middle: converts the resistance measurements to dr. We've subtracted off the average resistance from each spin and then mulitplied by the inchesPerOhm factor. It is negative since an increasing resistance gave a shorter radius.Between az = 140 and az=160 degrees the rack gear moves in and out radially by over 1 inch. The other oscillation corresponds to the length of the rack gear segments (i think they are every 10 or 15 degrees). There is a bracket holding the two pieces together forcing them to have the same radius at that point. This bows the sections between the connection points. Bottom: The azErr vs azimuth (azTrue - azMeasured). The units are arc seconds at the encoder. The green line is an eleventh order harominc fit to the data (saved in coefIRunout.sav). The idl routine fitsinneval() can evaluate this fit for you.
The measured azimuth errors were applied to the pointing error residuals from model11 but they did not reduce the residual errors (this needs to be looked into).
Another check would be to look at the difference in the azimuth encoders (from both sides of the azimuth arm). Their difference should equal the difference in the error at the two positions.
processing : x101/000121/doit.pro. the analyz code is in x101/phil/analzy/anz.21jan00t