Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Y−coordinate [m] Y−coordinate [m] 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 0.1 0.05 0 −0.05 −0.1 Nominal Design PT Design −15 −10 −5 0 5 10 15 X−coordinate [m] (a) −15 −10 −5 0 5 10 15 X−coordinate [m] (c) Y−coordinate [m] Y−coordinate [m] 0.2 0.1 0 −0.1 −0.2 0.2 0.1 0 −0.1 −0.2 −15 −10 −5 0 5 10 15 X−coordinate [m] (b) −15 −10 −5 0 5 10 15 X−coordinate [m] Figure 2-8: Comparison of critical mode shapes for nominal (–) and PT (- -) designs: (a) Mode #1: ACS (b) Mode #3: second bending (c) Mode #2: first bending (d) Mode #4: third bending. 68 (d)
also symmetric as seen in the figure. It is obvious from inspection of the OPD equation (Equation 2.9) that symmetric y-translation of the collectors does not result in OPD. It is only relative motion that is important. The PT design, however, is slightly asymmetric due to the small mass added to the negative-x arm of the interferometer. The mode shapes of the PT design show definite asymmetry resulting in a small relative displacement between the end points and a slight energy accumulation in these modes. The asymmetry is slight however, and does not have a large affect on the total OPD. The final mode of interest is the second observable axial mode, Mode #11, listed in the table. The mode shape is not pictured here because the motion is only axial and difficult to discern on a linear plot. In both designs the positive x-motion of the collectors together with the negative x-displacement of the combiner node increase the OPD (Equation 2.9). The main difference between the two systems is that in the nominal design this mode is much higher in frequency and therefore contributes very little to the overall OPD, while the axial stiffness in the PT case is decreased significantly so that this mode plays a major role in the accumulation of output energy. The increase is only relevant to the distribution of energy; the total PT energy is still much lower than that of the nominal design. In summary, the optimized design achieves better performance by choosing very small truss elements that result in lower natural frequencies overall and move the nodal points of the first two asymmetric bending modes to the ends of the array, where the collector optics are located. The large mass of the collectors on a very flexible truss effectively pin the collectors in place, so that the truss isolates the optics from the disturbances entering at the center. 2.6 Summary In this chapter Performance Tailoring (PT) is introduced and formalized. A sim- ple model of structurally-connected interferometer is presented in detail and used to step through the process of applying the PT formalization to a structural model. The 69
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- Page 73 and 74: through careful and experienced mod
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- Page 79 and 80: Magnitude, OPD/F x [µm/N] Magnitud
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Y−coordinate [m]<br />
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Nominal Design<br />
PT Design<br />
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−15 −10 −5 0 5 10 15<br />
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X−coordinate [m]<br />
Figure 2-8: Comparison of critical mode shapes for nominal (–) and PT (- -) designs:<br />
(a) Mode #1: ACS (b) Mode #3: second bending (c) Mode #2: first bending (d)<br />
Mode #4: third bending.<br />
68<br />
(d)
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