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Research Papers

Dynamical Models of a Wire Scanner

[+] Author and Article Information
Ana Barjau

Universitat Politècnica de Catalunya,
Diagonal 647,
Barcelona 08028, Spain
e-mail: ana.barjau@upc.edu

Juan Herranz

Universitat Politècnica de Catalunya,
Diagonal 647,
Barcelona 08028, Spain;
CERN,
Geneva 23 CH-1211, Switzerland;
Proactive R&D,
Diagonal 429,
Barcelona 08036, Spain
e-mail: juan.herranz.alvarez@cern.ch

Bernd Dehning

CERN,
CH-1211 Geneva 23, Switzerland,
e-mail: Bernd.Dehning@cern.ch

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 16, 2015; final manuscript received April 21, 2016; published online June 17, 2016. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 138(5), 051012 (Jun 17, 2016) (17 pages) Paper No: VIB-15-1439; doi: 10.1115/1.4033568 History: Received October 16, 2015; Revised April 21, 2016

The accuracy of the beam profile measurements achievable by the current wire scanners at CERN is limited by the vibrations of their mechanical parts. In particular, the vibrations of the carbon wire represent the major source of wire position uncertainty which limits the beam profile measurement accuracy. In the coming years, due to the Large Hadron Collider (LHC) luminosity upgrade, a wire traveling speed up to 20 m s−1 and a position measurement accuracy of the order of 1 μm will be required. A new wire scanner design based on the understanding of the wire vibration origin is therefore needed. We present the models developed to understand the main causes of the wire vibrations observed in an existing wire scanner. The development and tuning of those models are based on measurements and tests performed on that CERN proton synchrotron (PS) scanner. The final model for the (wire + fork) system has six degrees-of-freedom (DOF). The wire equations contain three different excitation terms: inertia forces associated with the fork rotation, parametric terms associated with the fork tips approaching/separating motion, and terms associated with the wire stiffness (Duffing terms). Though forced, parametric, and Duffing oscillators have been treated in the literature, it is the first time that a model containing all those terms is treated through a purely analytical model. The model has been run for different rotation patterns, and the results show the same trends as the measurements. From the simulations, we conclude that fork flexibility is the main cause of the wire vibration.

Copyright © 2016 by ASME
Topics: Wire , Vibration
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References

Figures

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Fig. 4

Detail of the PS fork, the flexible region on each tip is indicated as “flexible hinge”; R/L stand for “right/left”

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Fig. 3

Schematics of the rotating parts and vibrating elements studied in this paper. (a) Shaft bending and (b) fork tips and wire vibrations.

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Fig. 2

Schematics of the PS scanner scan cycle from OUT to IN (left) and from IN to OUT (right) positions

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Fig. 1

Schematics of the wire scanner instrument

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Fig. 5

Coordinate system used to formulate the wire dynamics

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Fig. 6

Lumped-parameter model (DM) in a general configuration. Points Q1R and Q1L are the fork endpoints.

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Fig. 7

DM in a general configuration with (down) and without (up) deflection in the fork tips

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Fig. 8

Detail of the wire fixation system

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Fig. 9

Flexible fork tip (left) and its representation through a hinged joint (right)

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Fig. 10

Forces and torques on the fork tips. F is the wire tension, which is not constrained to the fork plane in general.

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Fig. 12

Experimental curve of tangential force F versus wire elongation ΔL=L−Lu

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Fig. 13

(a) Detail of the fork tip and (b) schematics of the wire fixation system

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Fig. 11

Alternative representation for the fork model

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Fig. 14

Experimental curve of tangential force F versus tangential displacement Δz (top) and total momentum M(O) versus rotated angle Δφ (bottom)

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Fig. 15

Free response of the right fork tip associated with the first Z-vibration mode

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Fig. 22

Fork modified model

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Fig. 17

Free–fixed measurement (with zL=0): (a) right tip displacement zR, (b) wire elongation ΔL, and (c) normalized spectrum amplitude of the wire elongation |FFT(ΔL)|

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Fig. 18

Displacement of the left tip (zL) in a free–free measurement: (a) time evolution and (b) normalized spectrum

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Fig. 19

Wire elongation (ΔL) associated with the free–free measurement in Fig. 18: (a) time evolution and (b) amplitude of the normalized spectrum

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Fig. 20

Displacement of the right tip (zR) in a free–free measurement: (a) time evolution and (b) amplitude of the normalized spectrum

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Fig. 21

Wire elongation (ΔL) associated with the free–free measurement in Fig. 20: (a) time evolution and (b) amplitude of the normalized spectrum

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Fig. 16

Free–fixed measurement (with zR=0): (a) left tip displacement, (b) wire elongation ΔL, and (c) normalized spectrum amplitude of the wire elongation |FFT(ΔL)|

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Fig. 29

Results obtained with the hybrid approach during the OUT-to-IN phase of the scan cycle in Fig. 27, and for a wire tension of 0.1 N: (a) wire transverse vibration, (b) wire elongation, and (c) comparison between the active and the passive wire elongations

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Fig. 23

Displacement of the left tip (zL) in a free–fixed simulation (zR=0) : (a) time evolution and (b) normalized spectrum

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Fig. 31

Displacement (a) and acceleration (b) of the right fork tip obtained through combination of a quasi-static test and the angular pattern in Fig. 27(a)

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Fig. 24

Displacement of the left tip (zR) in a free–fixed simulation (zL=0) : (a) time evolution and (b) normalized spectrum

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Fig. 25

Displacement of the right tip (zR) in a free–free simulation: (a) time evolution and (b) normalized spectrum

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Fig. 26

Wire elongation (ΔL) associated with the free–free simulation in Fig. 25: (a) time evolution and (b) normalized spectrum

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Fig. 27

Time evolution of the angle (a), the angular velocity (b) and the angular acceleration, and (c) of the shaft during a real OUT-to-IN scan cycle

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Fig. 28

Measured behavior of fork tips and wire during the OUT-to-IN phase of the scan cycle in Fig. 27: (a) right tip deflection, (b) left tip deflection, and (c) wire elongation

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Fig. 30

Results obtained with the hybrid approach during the OUT-to-IN phase of the scan cycle in Fig. 27, and for a wire tension of 0.013 N: (a) wire transverse vibration, (b) wire elongation, and (c) comparison between the active and the passive wire elongations

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Fig. 33

Results obtained with the analytical approach during the OUT-to-IN phase of the scan cycle in Fig. 27, and for a wire tension of 0.1 N: (a) wire transverse vibration and (b) wire elongation

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Fig. 34

Results obtained with the analytical approach during the OUT-to-IN phase of the scan cycle in Fig. 27, and for a wire tension of 0.013 N: (a) wire transverse vibration and (b) wire elongation

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Fig. 32

Oscillation of the right (a) and left (b) fork tips obtained with the analytical approach. The inertia forces considered in the simulation are those associated with the scan cycle shown in Fig. 27 and the hinge acceleration shown in Fig. 31(b).

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