Short range alignment strategy

in CLEX and first results

CLIC Workshop 2015

26-30 January 2015

on behalf of : Hélène Mainaud-Durand,Mateusz Sosin Mathieu DuquenneVivien RUDE

Contents :• CLIC alignment

requirements• CLEX area• Alignment strategy• Results

CLIC alignment requirements

Table 1: CLIC alignment requirements.

Components need to be pre-aligned

Strategy:• Fiducialisation of components and girders• Initial alignment of the components on the girders Mateusz Sosin’s presentation• Determination of the position of the girder axes in the global coordinate system• Adjustment of the position of the girders thanks to actuators

To achieve ultra-low emittance and nanometer beam size

CLEX

CLEX

CALIFE

TBTS

TBL

X (longitudinal)

Y (radial)

Z (vertical)

𝑹𝑪𝑳𝑬𝑿Drive Beam

Main Beam

Module T0 (CLIC)

Drive Beam :• 2 PETS• 2 Drive Beam Quads• 2 BPM

Main Beam :• 2 Superstructures

2

Module T0 (CLIC)

𝑹𝑪𝑳𝑬𝑿

Dmitry Gudkov

Module T0

Drive Beam

Main Beam

Goal : Alignment of girder axes (module T0) in the general coordinate system (R CLEX) in real time and remotely with an accuracy of few microns

CLEX

Drive Beam :• 2 PETS• 2 Drive Beam Quads• 2 BPM

Drive Beam Girder

Main Beam :• 2 Superstructures

Main Beam Girder

3

Mateusz Sosin

Motorization

Girder

MA

ST

ER

CR

.

SLA

VE

CR

.

Girder

MA

ST

ER

CR

.

SLA

VE

CR

.

Girder

MA

ST

ER

CR

.

SLA

VE

CR

.

ARTICULATION POINTS

3DO

F

5DOF

3DO

F

Y

X

Z (blocked)

σ – roll (around Z)

η – yaw (around Y)

θ – pitch (around X)

LONGITUDAL BLOCKADE MECHANISM

(a) (a) (a)

(b) (b) (b) (b) (b) (b)

(c)

Each girder is equipped with two side interfaces called Master and Slave cradles. • Motorization is installed on the Master cradle (3 Degrees of freedom). • The Slave cradle is driven by the adjacent girder (ball joint) thanks to the

articulation Point (+ 2 Degrees of freedom).

Vertical actuator

Radial actuator

Connection joint

4

Fiducialisation

x

y

zC1

C2 xy z

The different components have been measured in the CERN metrological laboratory with a uncertainty of according to the component coordinate system.

The CMM provides in the component coordinate system the coordinates of :• The mean axis of the V shape support of the girder;• The centers of the ceramic balls on the cradles (suporting plate for the sensors);• The centers of the reflectors on the girder and the cradles.

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

5

cWPS (capacitive Wire Positioning System)

Varia

tion

verti

cal (

mm

)Va

riatio

n ve

rtica

l (m

m)

In order to align these girders, a straight reference will be used. The stretched wires measured by WPS sensors areactually one of the most accurate systems.

cWPS sensors :• Range : +/- 5 mm• Long term Stability : < 1 μm / 15 days• Repeatability system: +/- 1 μm• Precision : 1 μm• Linearity : 2 μm/mm Relative calibration• Accuracy : 5 μm Absolute calibration• Resolution : << 1 μm

Cone

Plan

Slot

6

SensorCoordinate system

CenteringCoordinate system

ComponentCoordinate system

CLEXCoordinate system

Calibration

CMM measurement

Absolute calculation

Coordinates systems

Transformation : FROM Component system TO CLEX system

Modeling the straight reference (Wires)

x

y

zC1

C2

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

𝑹𝑪𝑳𝑬𝑿

X

Y

Z

𝑹𝑪𝑳𝑬𝑿

7

A

B

𝑋 𝐴

𝑌 𝐴

Horizontal model:

Longitudinal (X)

Radial (Y)

D

ΔY M

l

𝑌𝑀=∆𝑌𝐷

∗𝑙+𝑌 𝐴

A

B

𝑋 𝐴

𝑍 𝐴

Longitudinal (X)

Vertical (Z)

D

M

Vertical model :

f

𝑓 =𝑔∗𝑞∗𝐷2

8∗𝑇

𝑍𝑀=𝑍𝐴+4∗ 𝑓 ∗𝑙2

𝐷2 +(∆𝑍−4∗ 𝑓 )∗𝑙

𝐷

l

ΔZ

The wires, projected on an horizontal plan, are considered as straight lines.

The wires are modeled by a catenary and can be approximated by a second order polynomial.(Freddy Becker, Hélène Mainaud-Durand, Thomas Touzé)

Modeling of the stretched wires

𝑌𝑀=𝑎∗𝑙+𝑏

𝑹𝑪𝑳𝑬𝑿 𝑹𝑪𝑳𝑬𝑿

Linear mass

Tension

[ 𝑋𝑌𝑍 ]= 𝑓 (𝑙)

𝑹𝒕𝒖𝒏𝒏𝒆𝒍

8

Linear function

Transformation of Coordinates systems

x

y

z

12

34

X

Y

Z

𝑇 𝑋

𝑇 𝑌

𝜃𝑍

[ 𝑋𝑌𝑍 ]=𝑇+𝑅∗ [𝑥𝑦𝑧 ]

[𝑇 𝑋

𝑇 𝑌

𝑇 𝑍]

𝑅=𝑅𝑍∗𝑅𝑌 ∗𝑅𝑋

Linearization of the rotating matrix(θx, θy, θz <1 mrad)

𝑅=[ 1 −𝜃𝑍 𝜃𝑌

𝜃𝑍 1 −𝜃𝑋

−𝜃𝑌 𝜃 𝑋 1 ]

C1C2

𝑹𝑪𝑳𝑬𝑿

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

𝑹𝑪𝑳𝑬𝑿 𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

To know the position of the components in the general system, the transformation from the component system to the general system () has to be determined.

9

XY

Z

xy

z

12

34

A

ΔY

Modeling of stretched wires Transformation of Coordinates system

[𝑋

∆𝒀𝐷

∗𝑙+𝒀 𝑨

𝒁 𝑨+4∗ 𝑓 ∗𝑙2

𝐷2+

(∆ 𝒁−4∗ 𝑓 )∗𝑙𝐷

]¿

B

[ 𝑋𝑌𝑍 ]=¿

Observation equation

D

C1C2

𝑹𝑪𝑳𝑬𝑿

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

l

[ 𝑋𝑌𝑍 ]= 𝑓 (𝑙)=𝑇+𝑅∗[ 𝑥𝑦𝑧 ]𝑹𝑪𝑳𝑬𝑿

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

4 unknowns / wire 5 unknowns / component 2 observations/sensor 10

Method of least squares and results

Method to determine the values of the unknowns Principle : Minimize the sum of the squared residuals

Unknowns : 13Observations : 16

A priori accuracy of cWPS : 5 μm

Results :

Conclusion :There are some mistakes on the observations

• Residuals : 30 μm• Statistical test (Pearson’s chi-squared test) : 57

(3 degrees of freedom / Probability threshold : 95% Limit : 0.07 and 3.12)

11

Link girder-cradles :

Measurement Deformation of these links since the CMM measurement

xy

z

Fiducialisation between the cradles and the girder

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

• Roll higher than 200 microradians;• Radial and vertical translations higher than 50 microns.

Fiducialisation in-situ

12

Results

Unknowns : 13Observations : 16

A priori accuracy of cWPS : 5 μm

Results with new fiducialisation :

• Residuals : 3 μm for the Main Beam 6 μm for the Drive Beam

• Statistical test (Pearson’s chi-squared test) : 1.4 for the MB 4.2 for the DB (3 degrees of freedom / Probability threshold : 95%)

Limit : 0.07 and 3.12

Precision of the position of the girder in the general coordinate system12 μm in radial / 17 μm in vertical

X (longitudinal)

Y (radial)

Z (vertical)

𝑹𝑪𝑳𝑬𝑿

DB

MB

13

CLEX

CALIFE

TBTS

TBL

X (longitudinal)

Y (radial)

Z (vertical)

𝑹𝑪𝑳𝑬𝑿

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

𝑹𝒄𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕

Comparison with an other methodCalculation of the transformation to go from Rcomponent to RCLEX with a best-fit between common points.

Max Residuals : 10 μm

Precision of the position of the girderin the general coordinate system : 17 microns in radial / 8 microns in vertical

14

Difference between the 2 methods

Difference Radial (μm) Vertical (μm)

DB (C1) 7 27

DB (C2) -7 52

MB (C1) 15 32

MB (C2) 7 33

Goal : Alignment of girder axes (module T0) in the general coordinate system (R CLEX) in real time and remotely with an accuracy of few microns

The links between the girders and the cradles have to be improved if we want to achieve our goal.

15

Summary

• The link girder-cradles has to be improved or the sensors have to be installed directly on the girder

• CMM measurements are necessary to provide precise and accurate component fiducialisations

• The short range alignment strategy proposed is good to achieve our goal (for distances <10m)

• The stretched wire measured by WPS sensors is curently the most suitable systems to meet the expectations

• Some comparisons have to be done with beam based alignment method (Wilfried Farabolini).