Calibration of clinometers Calibration of clinometers for the alignment of muon for the alignment of muon

chambers in the CMS chambers in the CMS experiment. experiment.

MOSCHOUTIS ThomasMOSCHOUTIS Thomas

FAS meeting – Orlando, 12 March 2004

Global view of the Compact Muon Global view of the Compact Muon SolenoidSolenoid

View of one DiskView of one Disk

Dual-axis clinometers for monitoring orientation of transfer pates:

Calibration benchCalibration bench

CIinometer

sensing Liquid

calibrated Linear mover

Θ

First setupFirst setup

Clinometer’s placeLinear mover

Error calculationError calculation

Error in Error in φφ::• φφ =Tan =Tan-1-1(L/H) (L/H) • ΔφΔφ=(∂=(∂φφ/∂L)*/∂L)*ΔΔL+(∂L+(∂φφ/∂H)*/∂H)*ΔΔH H

=(1/(L+H))*=(1/(L+H))*ΔΔL-2L/(HL-2L/(H22+H*L)*+H*L)*ΔΔHH Using the same formula:Using the same formula:

• ΔΩΔΩ=(1/(L+M))*=(1/(L+M))*ΔΔL-2L/(ML-2L/(M22+M*L)*+M*L)*ΔΔMM Taking Taking ρρ=cos-1(M/K) and M=0=cos-1(M/K) and M=0

• ΔρΔρ==ΔΔM/KM/K So the total error is:So the total error is:

• ΔθΔθ =( =(ΔφΔφ22++ΔΩΔΩ22++ΔρΔρ22))1/21/2

MK

ρρ

φφ

LL

HH

First test curveFirst test curve

Angle vs clinometer voltage output

-5

0

5

10

15

20

25

30

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Response Voltage [V]

An

gle

[D

eg

ree

s]

Zero degree measurementZero degree measurement

Pendulum

clinometer

Long rod to get more precision

Problem induce by the plate Problem induce by the plate thicknessthickness

Second test curve Second test curve

Angle vs clinometer voltage output

0

2

4

6

8

10

12

14

16

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Response voltage [Volts]

An

gle

[D

egre

es]

The 6 different mounting platesThe 6 different mounting plates

Clinometer’s place

Next setupNext setupLinear mover

Adapter

Tilting base

Mounting plate

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