Transfer Line Calculations 9-March-2009 and following

Input 24 DCOPS, with 2 (averaged) values per PG positions of the DCOPS wrt their disk centers Ideal SLM directions Ideal Z positions of DCOPS

Verify DCOPS PG Z on ME+2/3 agree with ideal Z differences

Unknowns 3 disks (x,y) and RZ  9 unknowns 6 lasers (sx,sy)  12 unknowns 24 dV (?)  24 unknowns at 3.8T (0 at 0)

Location Define ideal transformation From Cocoa: CMS = OffSLM + RotSLM*(OffXfer+RotXFer*XFerPos) My local coordinate system: XFerPos = OffJNB+RotJNB*DCPos RotSLM=Rz(θz) Ry(θy) Rx(θx)

Stations ME+1 and ME+2 face the same direction

ME+1 SLM transforms to CMS X Y Z Rx Ry Rz HSLM1 -17.0821 63.7511 6782 -90 15 HSLM2 -63.7511 17.0821 75 HSLM3 46.6690 135 HSLM4 195 HSLM5 255 HSLM6 315

ME+1 TP transforms to SLM X Y Z Rx Ry Rz PT1 7175.83 -48 22.5 -90 PT2 PT3 PT4 PT5 PT6

ME+2 SLM transforms to CMS X Y Z Rx Ry Rz SLM1 -77.64571 289.7777 7998 -90 15 SLM2 75 SLM3 -212.132 135

ME+2 TP transforms to SLM X Y Z Rx Ry Rz TP1/S1 7175.829 -48 -22.5 90 TP4/S1 -7175.833 22.5 -90 TP2/S2 -7175.829 TP5/S2 7175.833 TP3/S3 TP6/S3

ME+3/4 SLM transforms to CMS X Y Z Rx Ry Rz SLM1 -77.64571 289.7777 9642/ 10537 90 15 SLM2 75 SLM3 -212.132 135

ME+3/4 TP transforms to SLM X Y Z Rx Ry Rz TP1/S1 7177.343 -48 22.5 -90 TP4/S1 -7175.803 -22.5 90 TP2/S2 7175.833 TP5/S2 -7175.833 TP3/S3 TP6/S3

Local DCOPS/XFER coordinate X = rφ, phi in x y direction Y = R, radial Z “into page” using right hand rule X=Y=0 = center of DCOPS in ideal system Z=0 = position of Ref DCOPS dowel

Nomenclature (Z always ideal) (δx, δy) = shift in disk from ideal (H,V) = center of DCOPS wrt ideal, PG (ΔH, ΔV) = shift in local DCOPS center (PH,PV) = Profile predictions (0, dV) = cantilevered shift due to bending Indexed by station or disk and by point #

XFer Plate details Ref DCOPS dowel pin is X,Z center of XFer Ref DCOPS dowel is +6.724 shimmed away from Y center of XFer

Transfer Plate Center X Center Y

Transform Center to XFer X (=H) Y Z (=-V) PT1 208.5 73.175 PT2 202.5 PT3 -157.5 PT4 -163.5 PT5 PT6 Rx=-90 Ry=0 Rz=0

Disk and PT: DCOPS to CMS: B=0 C = XC + RC(XT+RT(XD+RD P) C = XA + RA P XA ≡ XC +RCXT+ RCRT XD RA ≡ RCRTRT Above are Ideal positions, XT from PG Shifting (per disk) gives unknown (to be solved for): C’ = XS + RS C RS mostly rotation about Z

Complications w/ B=3.8 The disks bend Bending is not the same at every PT Cannot assume each disk bends the same amount ME+2/ME+3 cantilever by the same angle in different directions Disks have additional rotation about Y (actually about line near the floor)

Laser position/direction Nominal position is same as center of ME+4 XFer DCOPS Each PT has 2 laser slopes

DCOPS data Preprocess to include orientation, average both sides Calibration (scale and offset) not included yet Only 1 laser; only Plus Endcap