brett.shapiro@LIGO.ORG - posted 18:47, Monday 03 March 2014 - last comment - 23:50, Monday 03 March 2014(10476)
Quad model wire length study
I have been investigating the wire length values used in the matlab model since the model fitting code results on ETMY from https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=10089 found a discrepancy in the UIM to PUM wire length. The value given by the model parameter file quadopt_fiber.m for this length is
330.8 mm.
However, the model fitting code converged to
340.0 mm +- 2 mm.
About 9 mm longer.
I started investigating this discrepancy by looking at the drawings of the wire jig and the PUM assembly. Since the UIM to PUM wire is a loop, the equivalent length between the UIM and PUM needs to be backed out from these drawings. From these drawings, I calculate the length of wire between the UIM blade tip clamp and the PUM prism is
337.61 mm.
The attached pdf, PUMwireLoopLength.pdf, contains the calculations and references for this number. The limiting assumption for this calculation is likely to be that the wire has an infinitely sharp bending radius going around the prism. In reality, a finite bending radius exists, which will tend to make this calculation a slight overestimate.
Still, the value is close but not quite there. Upon further investigation of the other wire lengths given by the model, I noticed that all the wire lengths are a few mm off from the values determined by the wire jig in D060516. My assumption has always been that the parameter file requires values referenced from the wire clamps (given by the wire jig), as it does for the d's. Thus, either all these values are out of date, or my understanding is incorrect. In particular, quadopt_fiber.m gives the top two stages of wire lengths as
pend.ln = 449.192 mm
pend.l1 = 308.585 mm
In contrast, the wire jig gives these as
pend.ln = 453.0 mm
pend.l1 = 305.8 mm
Since the model predicts the measured longitudinal modes very well with the UIM-PUM fitting correction, I made the assumption that pend.ln and pend.l1 are correct as listed in the parameter file. Therefore, my previous assumption that the model file requires clamp-clamp lengths is wrong. So I searched for an algorithm (by guess and check more or less) that would take the clamp-clamp wire jig lengths and convert them to the listed numbers in the parameter file. What I found was this:
pend.ln = (wire jig length) + pend.dm/pend.cn = 449.208
pend.l1 = (wire jig length) + (pend.dn + pend.d0)/pend.c1 = 308.521
The pend.d values are the distances from the wire clamps to the centers of mass. The pend.c values are the cosines of the wire angle from the vertical. With this, both lengths are within 10s of microns from the current quadopt_fiber.m values. Thus, this algorithm means that the wire lengths as given by the parameter file reference the center lines of the masses rather than the wire clamp positions.
Following this center line to center line convention for the UIM to PUM length, rather than clamp to prism we get:
pend.l2 = (clamp to prism length) + (pend.d1 + pend.d2)/pend.c3 = 337.61 + (pend.d1 + pend.d2)/pend.c3 = 338.924 mm
This value is about 1.1 mm from the value determined by the model fitting code, and it fits quite comfortably in the fitting code's +-2 mm error bar.
So, the good news is that the value determined by the model fitting code is consistent with the other metal wires under the assumption that the parameter file is working with center line to center line distances rather than clamp to clamp distances.
However, ssmake4pv2eMB5f_fiber.m, which compiles the parameter file appears to be assuming the values are in fact clamp-clamp. For example, near the bottom of the ssmake script, the pend.stage2 corrections have
ln = ln - 2*flexn/cn;
l1 = l1 - 2*flex1/c1;
l2 = l2 - 2*flex2/c2;
l3 = l3 - 2*flex3/c3;
where flex is the distance between the wire clamp and the effective flexure point and ln is equal to pend.ln (and so forth). Thus, it seems these corrections are assuming the parameter file references the clamp positions, not the center line positions. Additionally, higher up in the script around line 285 the vertical heights of the masses are calculated as
pend.tln = sqrt(pend.ln^2 - (pend.nn0-pend.nn1)^2) + pend.dm;
pend.tl1 = sqrt(pend.l1^2 - (pend.n0-pend.n1)^2) + pend.dn + pend.d0;
pend.tl2 = sqrt(pend.l2^2 - (pend.n2-pend.n3)^2) + pend.d1 + pend.d2;
pend.tl3 = sqrt(pend.l3^2 - (pend.n4-pend.n5)^2) + pend.d3 + pend.d4;
where the tl's are the 'true' vertical heights of the centers of mass, the n parameters represent the horizontal distance from the centers of mass of the wire clamps, and the d's again represent the clamp to center of mass distances. So for the top wire for example,
sqrt(pend.ln^2 - (pend.nn0-pend.nn1)^2)
gives the vertical length of the top wire, and
+ pend.dn + pend.d0
accounts for the clamp to center line distances for the stage above and below the wire. Thus, it seems again that the ssmake file is expecting clamp-clamp wire lengths from the parameter file.
However, putting clamp-clamp lengths into the parameter file does not provide the correct frequencies. So, the wire length mystery goes on...
Non-image files attached to this report
Comments related to this report
The intent for the ssmake file is very definitely that, when pend.stage2=1, all wire lengths are interpreted as clamp-to-clamp, and all d distances are interpreted as "physical" d's, i.e., COM-to-clamp. (The current quadopt_fiber.m that is under discussion does set this flag correctly.) Moreover this behaviour has been checked against the equivalent Mathematica model both for this parameter set specifically and more generally.
