Aspects of the GEO 600 Style Triple and Quadruple Pendulum Suspension Systems
4 October 2002
Mentor : Dr Calum I. Torrie
California Institute of Technology
T030150-00
By
John Veitch
University of Glasgow
Caltech SURF Programme 2002
Caltech UID: 0001467336
Contact:
Advanced LIGO Suspension Research
John Veitch
Introduction 2
LIGO Suspensions 2
Experiments 3
Properties of Suspension Wire
Determination of Breaking Stress 4
Determination of Young’s Modulus 10
Blade Height Adjustment 13
Single Pendulum Experiment 16
References 19
Acknowledgements 18
Appendix 20
The work described in this report was undertaken as part of a SURF project for the LIGO group at Caltech during the summer of 2002. The project was supervised by Dr C. Torrie and
1.1 Introduction
Gravitational waves are a prediction of Einstein’s General Theory of Relativity, which describes the influence of gravity as a curvature of space-time. Gravitational waves produce a curvature in such a way as to stretch, then shrink space in the directions perpendicular to their propagation. The Laser Interferometer Gravitational wave Observatory (LIGO) project is a facility whose goal is to detect these gravitational waves and study them to gain information about the cosmos. [1] In order to detect these strains of space, and therefore gravitational waves, the LIGO project has developed, and continues to develop, highly sensitive interferometers situated in Louisiana and Washington state, which act in unison to eliminate local noise sources. A typical gravitational wave is expected to produce a strain of the order 10-21 or lower, producing a change in length of roughly 10-18 meters in the 4km arms of the detectors, a distance roughly one thousandth the diameter of a proton, so the interferometers must be extraordinarily sensitive. Such a sensitive instrument will be extremely susceptible to noise from non-gravitational sources, including photon shot noise, seismic noise and thermal noise in the suspension wires and mirrors that make up the interferometer. [2] The first generation of LIGO is already installed and is expected to begin taking scientific data in the near future. The next generation of LIGO, known as Advanced LIGO, is expected to come online in 2006.
1.2 LIGO Suspensions
In order to isolate against seismic noise, LIGO employs several stages of isolation. The active seismic isolation system removes most of the external vibrations. This is complemented by the passive seismic isolation system, which removes most of the low-frequency noise. To further reduce noise, especially at higher frequencies, the optics in Initial LIGO are suspended as single pendulums on metal wire. This design will be extended to include triple and quadruple pendulums to meet the more stringent isolation requirements in Advanced LIGO.
When the optics are suspended in this manner, the pendulum acts as a filter, which has a transfer function that falls as 1/f2 above its resonant frequency f0, as shown in figure 1. Initial LIGO is designed to detect gravitational waves of frequencies from a few tens of Hz up to a few kHz. Therefore a LIGO pendulum with f0=~1Hz will provide an isolation factor of 104 at 100Hz. To further improve isolation, a system of multiple pendulums in series, as used in Advanced LIGO, has a transfer function that falls off as 1/f2n, where n is the number of pendulums. Therefore a quadruple pendulum system for a main optic in Advanced LIGO provides an isolation factor of 1016 in the horizontal direction at 100Hz. In the vertical direction, however, the pendulum has a much higher resonance frequency caused by the stiffness of the wire, and due to unavoidable cross-coupling between the horizontal and vertical modes, the limiting factor is the vertical isolation. [3] To reduce the frequency of the vertical oscillations, Advanced LIGO will employ cantilever blades, which act as springs with a low spring constant, lowering vertical resonant frequencies and thus enhancing isolation in the detection band of the interferometer.
This project will investigate aspects of both the cantilever blades and the wire by which the pendulums are suspended, and an analysis of a single pendulum suspension will be performed.
2 Experiments
Over the course of the work conducted for the SURF project, several experiments were performed, in which various aspects of the suspension system were analysed. These included the measurement of the physical properties of suspension wire and comparison between types of wire and different clamping methods. Over the course of the summer, Dr C. Torrie developed a library of clamps for adjusting the height of the cantilever blades in the suspension, and this aspect was tested on different blades. For a single pendulum system with both single and double loops of suspension wires, and symmetric and antisymmetric crossed blades, the frequencies of oscillation were measured.
In addition to the experiments described above, Dan Mason of the Rensselaer Polytechnic Institute conducted a computer analysis of the cantilever blades and their deflection under load, wrote a mathematical simulation of the bending of the upper pendulum stage caused by the mass of the stages below, and performed an investigation into the phenomenon of cold welding. [4]
Properties of Suspension Wire
2.1 Breaking Stress
2.1.1 Introduction
The suspension wire used in LIGO and advanced LIGO for the upper stages of the pendulum is an important part of the pendulum assembly. Suitable wires must be chosen for each pendulum. Due to the large 40kg masses to be suspended in Advanced LIGO, it is important that the wire be able to bear its load safely. To ensure this safety, the wires are only ever loaded with 1/3 of their breaking stress. The method that is used to clamp the wire onto the pendulum can also affect its strength. In this experiment comparisons were made of the breaking stress of wires across three manufacturers, different types of wire and different clamping methods.
2.1.2 Theory
The breaking stress of a material can be measured directly by applying stress to the material until it yields. In this experiment the wire to be tested was used to suspend a platform, upon which mass could be loaded. The weight of the mass under gravity, then, provided the force with which to stress the wire. If we equate the equations for breaking stress:-
where F is the force on the wire and r is the radius, and weight:-
Where m is the mass and g the acceleration due to gravity, the expression for Breaking Stress below is easily obtained:-
Equation 1
Three types of clamp were tested in this experiment. The simple clamp was designed to be the simplest possible version of a clamp, with no special measures taken to reduce the damaging effects of the clamp, such as crushing of the wire. It consisted simply of two metal plates which bolted together with the wire in between.
The machined clamp was designed to improve upon the basic clamp. This was achieved by reducing the tolerances of the hole seperation and diameter, having the faces fly-cut to ensure that they were perfectly parallel and placing a groove through the centre of the clamp to better define the position of the wire. The machined clamp is similar to the clamps used in certain parts of GEO 600.
The third clamp was designed to minimise the deformation of the wire as it is clamped, since the more the wire is crushed the smaller its cross-section and the easier it is to break. This was achieved by wrapping the wire round a cylinder before clamping it, where the cylinder takes up most of the load.
2.1.3 Procedure
In the Breaking Stress experiment, music wire and stainless steel wire of diameters ranging from 0.2mm to 0.85mm were tested. The sources of wire were the Malin Wire Company, the California Fine Wire Company and the Knight Precision Wire Company. For this experiment, a length of wire was cut using wire cutters and clamped at both ends. Care was taken to ensure that the wire ran through the middle of the clamp, so that the angle at which the wire leaves the clamp is the same on each occasion. The upper clamp was then attached to a small 5-tonne capacity crane [see Picture 1], and a clear plastic cylinder attached around the assembly to ensure safety against the snapped wire recoiling and harming someone. For wires with diameters less than 0.3mm, mass in kilograms was added to the lower clamp in the form of cylindrical known weights on a hook (see Picture 1). For thicker wires of diameter >0.3mm a greater mass was required, and this was provided in the form of lead bricks of known mass, which were added to a metal platform suspended from the clamp. Both the hook and the platform were weighed beforehand, and their masses included in the calculation. Mass was added at first in large units, and as the theoretical breaking stress was approached, the units were made smaller, using the cylindrical masses in range 200g-2kg and finally the very small weights in range 5g-100g until the wire finally failed. This allowed the point at which the wire reached its ultimate tensile stress to be measured to a high degree of accuracy. The final mass suspended was recorded in a spreadsheet. The broken wire was then removed from the clamp, and the clamp inspected to ensure that the breaking of the wire had not damaged it. A new length of wire was cut from the spool and the procedure repeated until the spreadsheet had sufficient data to calculate an average result and standard error on the result. Wires that showed inconsistent breaking points were tested more often to reduce the overall error in the result.
2.1.4 Results & Analysis
Wire from the three manufacturers mentioned in section 2.1.3 was tested in this experiment. The California Fine Wire Company provided 0.2mm and 0.34mm diameter “Elgiloy” wire [Graph 1].
The Malin Wire Co. provided a range of music wire, which was tested along with music wire from the California Fine Wire company [Graph 2]. It was found that, although the manufacturers’ specifications were similar, in tests the Malin wire outperformed the California Wire at 0.3mm diameter. At 0.35mm diameter, however, both wires gave similar results for the basic clamp, but the California Wire had a higher breaking stress when used with the round clamp.
The third company to provide wire was Knight Precision wire manufacturers. They provided music wire and Stainless Steel wire [Graph 3]. The results show that the Knight wire always performed below the manufacturer’s specifications. Wire from Knight Precision was already used in suspension systems at the GEO 600 gravitational wave detector in Germany and at the MIT Quad, which is in development. However, there is no risk to these existing installations due to the safety precaution of only loading wires to one third of their breaking stress, which is still well below the breaking stress determined in these experiments.
The Effect of Clamping on Breaking Stress
In all three sets of data, it can clearly be seen that the type of clamp used has a strong effect on the results of the breaking stress experiment. In every case, the use of the round clamp improves the breaking stress value over the simple clamp. The machined clamp shows an improvement from the simple clamp, as would be expected with the addition of the precautions described in section 2.1.2.
The lower performance of the simple clamp is attributed to compression of the wire in the clamp, decreasing its cross-sectional area, and therefore reducing its ability to bear weight. This effect is reduced in the round clamp, as described in section 2.1.2.
Effect of “Kinks” on Breaking Stress
When working with fine wire, i.e. diameter 0.22mm, caution must be taken to avoid bending the wire and causing a kink. Experiments were performed on two types of kink which are common in the laboratory when working with wires. The first was a kink caused by the wire being bent, for example over the sharp edge of a table, and pulled straight again. It was found that such a kink dramatically reduces the breaking stress of the wire. [Graph 4] The second type of kink occurs frequently when working with spools of wire, whereby the wire is caught in a loop and the loop pulled closed, resulting in the pinching of a small section of wire into a circle. When this type of kink was tested, it was found that the wire was so weakened that the addition of any significant mass caused the wire to break at the kink. These results indicate that kinked wires should not be used when assembling pendulums, as they cannot provide the safety margin that is required.
2.1.5 Conclusions
This experiment has shown that the choice of clamp used when suspending the pendulums can have an effect on the breaking stress of the wires used. Based on the results of this experiment, a new clamp was designed by Dan Mason to combine the benefits of the machined and round clamps. This involved combining the small size of the machined clamp with the rounded surface of the round clamp [Fig 5]. This clamp will be produced and tested by Dr Calum Torrie in the winter of 2002.
This experiment has also demonstrated the need for testing of wires prior to their use in the suspension systems, since the values of breaking stress supplied by the manufacturer are not always accurate. This inaccuracy is compounded by the choice of clamp in suspending the wire. It was found that the Malin Music wire performed well, having both a comparatively high breaking stress, and results with the round clamp showing an agreement with the manufacturer’s value to within 20% at maximum, and a much smaller margin in the cases of 0.22 and 0.3 diameter wires. Further work may be conducted to compare this to the performance of California Fine Wire Co. music wire.