Shimming the elevation rails

feb, 2002

     The pitch, roll, and focus errors measured in aug01 can be corrected by rotating the dome by .12 degrees in roll and shimming a linear ramp in pitch of .125 degrees between za=10 and za=20 degrees (see the simulation).

How the shim distances were computed:

    A beam of length 21.5 feet (the distance between the main beams of the dome support) was moved along a radius of 420.75 feet (the radius of the rolling surface). Let y2, y1 be the vertical positions of the two ends of this beam (y2 is the uphill coordinate). The za is just asin((y2-y1)/lenbeam). After shimming we will have yp2, yp1. The change  in pitch is  dpitch=asin((yp2-yp1)/lenbeam)-asin((y2-y1)/lenbeam). To compute the relative shim changes we can set y2,y1=0. So:
    dp=asin((yp2-yp1)/lenbeam )--> yp2=sin(dp)*lenbeam + yp1

The change in pitch we want for our linear ramp as a function of za is :
    dp=(pslope*(za-10))  for za > 10.

Solving for yp2 :
    yp2=sin(pslope*(za-10))*lenBeam + yp1



    The requested pitch change is for the center of the beam. The halfangle of the beam is BmHangle= asin(21.5/2/420.75)=1.464 degrees.  So yp1 is 1.464 degrees below the central za and yp2 is 1.464 deg above the central za.  The computation starts with a vertical offset dy(za)=0. At each za step it looks up dy(za-bmHangle) and then computes dy(za+bmHangle) via yp2 above. These are vertical distances. The shims are radial so the dy's must be multiplited by 1/(cos(za)) to get the shim lengths.
    The figure shows the needed vertical offsets and shim distances.
 The black line is the vertical distance, the red line line is the radial distance or shim lengths needed. The * are the locations of the panel points where the shims are inserted.  The vertical lines are spaced every BmHalfAngle. The discontinuites are spaced by beamlength feet. This is where the trailing wheel starts to see the shim changes caused by the leading wheel. The table at the bottom  shows the shim length and vertical distance for each shim position.

    The pitch, roll, and focus model, as well as the shim locations use the encoder zenith angle reading as the parameter. The support beam is centered on the mechanical center of the dome. The optic axis of the system passes 1.1113 degrees uphill from the mechanical center of the dome. The black and red lines assumed that y2 and y1 were spaced equidistant from the center of the za position. In reality, y2 is 1.464 degrees uphill from the center of the beam while the za optic axis is 1.1113 degrees uphill from the center of the beam suport. The green and blue lines redo the computation recomputing y1 = (-1.464-1.1113) degrees downhill and y2=(1.464-1.1113) degrees uphill from the encoder (optical) za. The bottom most table has the shim values for this computation.

processing: idl/prf/