B. Bland, J. Kissel, R. Lane, J. O'Dell, N. Robertson, T. Sadecki

As was mentioned in Monday's aLOG entry, in order to increase the lowest pitch frequency of the X1 SUS BSFM01, we lowered the M1 Blade Tip heights, such that the measurement between the M1 Base Plate and the Blade Tip break off point is 23.6 mm, (i.e. a d1 = nominal + 3 mm = 4 mm below the COM) as opposed to 26.6 mm ( a d1 = 1 mm below the COM). This *did* increase the pitch frequency, but not as much as predicted by the model -- The pitch frequency moved from 0.44 Hz to 0.46 Hz, where we expect from the model to be at 0.49 Hz.

We are still confused as to why this is the case, and the attachment plots several models with the respect to the two measurements, adjusting parameters to try to explain the pitch transfer function. The conclusion is that, without redesign of the mechanical components of the suspension we cannot increase the lowest pitch frequency to more that 0.46 Hz, which is a reasonable 12% above from the first longitudinal mode at 0.41 Hz. We'll consult with other experts as to whether such a deviation from "requirements" is acceptable (though our first impression is that it is).

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The story (expanded legend) is as follows:
BLUE - Nominal Model. This is what we expect the M1 P to P transfer function to look like. Note here, the lowest pitch mode is 0.488 Hz. This is what we *expect* a measurement to show if the blade tip heights are set to 26.6 mm, which the SolidWorks model claims sets d1 to the nominal 1 mm.
 
PURPLE - 110620 Measurement, with the blade tip heights set to 26.6 mm. One immediately sees that the lowest pitch frequency is lower than expected, at 0.449 Hz.

GREEN - Modified model, *decreasing* d1 by 3 mm, to 2mm above the center of mass. This implies a blade tip height of 29.6 mm. We see that this model nails the first pitch mode, though fails to precisely predict the upper two pitch modes.

Since the 110620 measurement and model imply that the M1 blade tip heights are too high by 3 mm, we then lowered them by 3 mm, to 23.6 mm, ideally setting d1 back to the nominal 1 mm below the center of mass.

YELLOW - 110621 Measurement, with the blade tip heights set to 23.6 mm. Here, we have increased the lowest pitch mode frequency to 0.461 Hz, and better matched the upper two frequencies to the nominal BLUE model.

Confused as to why we didn't get all the way up to 0.48 Hz by adjusting d1 (the M1 blade tip heights), we began exploring other model parameters that might be different from nominal. Norna explored changing all of the d's:
d0 - the suspension point to M1 connection at M1, 
d2 - the M1 to M2 connection at M2, 
d3 - the M2 to M3 connection at M2, 
and d4 - the M2 to M3 connection at M3.
Note that in reality, only d1 may be adjusted "on the fly," to change the remaining d's would require new mechanical parts. However, varying d4 most accurately replicates what has been measured:

RED - Modified model, *decreasing* d4 by 1 mm, to aligned with the center of mass (i.e. d4 = 0 mm). This model implies the prism height, with respect to the center of mass is incorrect. Joe took some physical measurements, and compared them against the solid works model and respective drawings, and while doing so discovered that the prisms (D080583) are version "F" when the production units should be at version "G". Although this needs to be fixed, the difference between version "F" and "G" is only in the distance to which it protrudes from the M3 mass, and therefore does not effect d4, and consequently would not effect the pitch mode.

Interestingly, if we *increase* the nominal d4 by 1 mm (to 2 mm above the center of mass), the model predicts that we might get a much stiffer first pendulum mode, without effecting the frequency of the upper pitch modes:

CYAN - Modified model, *increasing* d4 by 1 mm. This gets us a particularly stiff lowest pitch mode, without compromising the upper pitch mode frequencies.

It turns out, that *flipping M3 upside down* (rotating 180 degrees about the transverse axis) will accomplish exactly this increase in d4, according to Joe's calculations using the SolidWorks model. Thus, in order to confirm that d4 effects this particular transfer function -- and to get another data point -- we will flip M3 over tomorrow (a reportedly simple task), and remeasure the pitch mode. We have no intention of making this change to the production units, as (we believe, though it has not yet been confirmed) it's too late to make such a change to the glass BSs and/or FMs, and given that the "requirements" for this particular mode are defined in away that is merely to get the first pitch mode away from the first longitudinal mode to simplify local damping.

Stay tuned!!

Note that we have strong evidence against two other "problems" 
(1) The modeled M1 blade spring stiffness is incorrect. We measured a separate M1's 4 blades, and their stiffness matches the model within the uncertainty of the measurement. See sub-entry to follow.
(2) The trim mass distribution of M1 is unbalanced. Joe redistributed the trim mass to be more balanced, and a quick transfer function, and subsequent overnight spectra revealed no change in the lowest pitch frequency.