MOLA FEM Error and Correction

In General ...

In December of 1995 and January of 1996 the assembled MOLA instrument was put through as series of environmental tests. These tests included thermal/vacuum chamber tests, electro-magnetic interference tests, and random and sine vibration tests. Unfortunately, due to time and money constraints, a modal survey of the instrument was not performed.

The results of the sine vibration tests showed that the MOLA FEM did not correlate well at all with the actual instrument. So, the search was on for the cause of the differences.

Use this links to jump to specific point on this page.

Test correlation of the instrument and the finite element model (FEM)
Searching for the FEM's error
Finding the error
Correcting the error
Further analysis
Any Questions?

Test Correlation

One of the tests performed on the MOLA instrument is a .25 g ("quarter Gee") sine sweep, sometimes called a signature test. This tests inputs a .25 g load into the instrument before all other vibration tests are performed. A quarter g load is assumed to be low enough not to damage any part of the instrument. The .25 g load is held constant while the displacement varies over a frequency range, say 10 - 1000Hz. Acceleration responses are taken from various points on the instrument. A plot of the response vs. the frequency will show peaks, which is where the natural frequencies are. This test creates the signature.

Then, after the other vibration tests are performed, the same .25 g sine sweep test is again performed and a second signature is obtained. This second signature is compared to the first signature. If something in the instrument broke or came loose, then the two signatures should theoretically be different because the instrument's stiffness would have changed. If all went well, the signatures should look very much alike.

Searching for the error

The problem with the MOLA FEM became apparent when the instrument's signature showed very different natural frequecies than what the FEM was predicting. The FEM predicted the first MOLA mode to be at about 75Hz in the Y direction, the first Z-direction mode to be at 104Hz, and the first X-direction mode to be at about 150Hz (See first table below). The instrument, on the other hand, was showing that the first mode should have been at 75Hz in the X direction, the second mode to be at 85Hz in the Y direction, and the first Z-direction mode to be at 110Hz. Hence, the FEM and the instrument did not correlate at all.

When thinking about what the mode shapes of MOLA should be, it became apparent that the FEM really was not representative of reality. Here's why:

The telescope is essentially a cantilever beam with a generally symmetric cross section;
Symmetric cantilever beams always have orthogonal modes (2 modes at the same frequency in perpendicular axes);
The telescope should therefore have two perpendicular modes that are very close in frequecy;
The MOLA FEM had no orthogonal modes.

The table below shows that there are no modes in the X and Y directions (see the X-WT and Y-WT columns) that have significant mass participation and whose frequencies are close together.

Old MOLA FEM (rev. 07)
MODE FREQUENCY X-WT Y-WT Z-WT I-XX I-YY I-ZZ

# (hz) (LB) (LB) (LB) (LB-IN²) (LB-IN²) (LB-IN²)

1 75.31 0.00 11.31 0.17 2.41E+03 2.39E+00 4.16E-01

2 94.80 0.00 0.29 0.59 5.55E+01 1.22E+00 6.61E-04

3 103.78 0.00 0.61 37.22 4.00E+01 4.23E-01 2.21E-01

- - - - - - - -

7 136.19 0.02 11.61 11.13 2.05E+03 2.52E+00 5.17E+00

- - - - - - - -

11 152.83 36.12 0.52 0.15 2.05E+01 1.69E+03 9.51E+00

**Old MOLA FEM (rev. 07)**
MODE	FREQUENCY	X-WT	Y-WT	Z-WT	I-XX	I-YY	I-ZZ
#	(hz)	(LB)	(LB)	(LB)	(LB-IN²)	(LB-IN²)	(LB-IN²)

1	75.31	0.00	11.31	0.17	2.41E+03	2.39E+00	4.16E-01
2	94.80	0.00	0.29	0.59	5.55E+01	1.22E+00	6.61E-04
3	103.78	0.00	0.61	37.22	4.00E+01	4.23E-01	2.21E-01
-	-	-	-	-	-	-	-
7	136.19	0.02	11.61	11.13	2.05E+03	2.52E+00	5.17E+00
-	-	-	-	-	-	-	-
11	152.83	36.12	0.52	0.15	2.05E+01	1.69E+03	9.51E+00

So now the question became, Why were there no orthogonal modes? Something was much stiffer in the X-direction than the Y-direction. Here are most of the areas I looked at to find and eliminate this additional stiffness.

Reviewed the stiffness of the Ti Support Tube - Checked to verify all element properties were correct and uniform. A minor error in some plate thicknesses was discovered and corrected;
Reviewed the stiffness of the Honeycomb Support Panel - Checked to verify honeycomb properties were modeled correctly. New properties were calculated using a different method and included, although the change in stiffness was minimal and did not affect the mode shapes;
Changed honeycomb stiffness by removing edge supports and/or varying the bending stiffness of the honeycomb;
Changed attachment of front foot of the FEM from two points (representing two bolts) to one point to determine if a single pivot point might allow easier rocking in the X-direction;
Verified ALL rigid elements were correctly attached and constrained;
Replaced the telescope on the honeycomb support panel with a concentrated mass at the telescope's center of gravity on a rigid bar. The modal results of this run showed orthogonal mode shapes, thus indicating that the problem was with the telescope;
Performed normal modes NASTRAN run of the telescope only (from the Ti support tube up). Results again showed no orthogonal modes in the X and Y directions, further indicating that the telescope was the problem;
Banged my head against the wall repeatedly and pulled much of my hair out, still to no avail.

Finding the error

Eventually, I began studying the animated mode shapes of the model. I wanted to look at the first X and Y modes, which were rocking cantilever modes. The first Y-direction mode looked normal; it was rocking back and forth in the Y-direction as if it were rotating about an axis. A GIF animation shows Mode 1 (74k). (You must have either Netscape 2.0 or a viewer that handles animated GIFs.)

However, when I looked at the first X-direction rocking mode, it wasn't rocking freely back and forth; instead, the telescope was sliding back and forth and only the support tube and the honeycomb support panel were rocking. This was the clue I needed to find the problem. A GIF animation shows Mode 11 (74.5k).

NASTRAN users know that plate elements (e.g., CQUAD4) have no rotational stiffness at the corner grids in the direction normal to the element's surface. One negative aspect to this is that bars and beams cannot be directly connected to the corner grid of a plate element in a normal direction without some sort of stiffness being added. This is due to some sort of mathematical problem with the elements that I don't understand. (We now have CQUADR elements that take care of this problem.)

Having no rotational stiffness creates all sorts of problems--called singularities--with the math matrix when NASTRAN tries to solve it. There are several ways to get around the problem. One method is to let NASTRAN constrain these grids by itself using an AUTOSPC line in the data file. This will constrain any singularities.

Another trick that many modelers use is to constrain the offending rotational degree of freedom of the plate grids using an SPC (single point constraint). For example, a plate in the XY plane would have an SPC at each grid constraining the Z-rotational direction. This was the case with the telescope portion of the MOLA model. Another person created the telescope part of the FEM and added the constraints by hand. The model image shown here represents the SPCs as blue triangles. These triangles are located throughout the telescope. Many more triangles would be shown but are hidden behind parts of the model.

I was aware of these constraints, but since I know it's a common trick, I ignored them. I also performed all the basic validity checks, but all the translational checks passed, so I ignored the rotational checks. This was my fatal error. NEVER ignore rotational checks!

The telescope model was created using the Y axis as the optical axis, whereas my model used the Z axis as the optical axis. I imported the telescope into my existing MOLA FEM, rotated the telescope to the proper orientation, and then connected the two models together. Unfortunately, the software I was using rotated the grids and elements only, NOT the SPCs. Thus, the Y-rotational SPCs did not change to become the Z-rotational SPCs, which they should have. The result of this was that all those constrained grids could not rotate in the Y direction, which forced the telescope to slide back and forth along the X-axis.

After seeing the model react this way and realizing that the SPCs were probably the cause, I re-ran the validity checks and this time I went through the rotational degrees of freedom as well. The results clearly showed that rotations were being constrained and causing forces on the model. I had absolutely found my model's error.

Correcting the error

Correcting the problem was fairly simple. I quickly deleted all but the 18 necessary SPCs at the feet, and re-ran the model. The corrected model reacted just as expected: The first mode was in the X-direction and the second mode was in the Y-direction. I had to do some minor stiffness tweaking of the honeycomb support panel and the Ti support tube to bring the frequecies up to match those of the actual instrument, and in the end, my new and improved FEM provided the following modes and mass participation table. (Modes 1,2 and 6 correspond to the first X, Y and Z modes.)

New MOLA FEM (rev. 20)
MODE FREQUENCY X-WT Y-WT Z-WT I-XX I-YY I-ZZ

# (hz) (LB) (LB) (LB) (LB-IN²) (LB-IN²) (LB-IN²)

1 73.52 14.54 0.12 0.13 4.53E+01 2.18E+03 7.72E-01

2 83.93 0.44 9.17 0.13 2.02E+03 3.75E+01 6.87E-01

3 90.10 0.00 2.51 0.03 4.91E+02 2.60E-02 1.01E-01

4 99.32 0.00 0.00 0.00 6.86E-04 2.13E-02 8.47E-02

5 107.38 0.01 0.03 0.53 1.37E+01 4.55E-01 5.67E-04

6 111.06 0.06 0.99 34.24 2.01E+01 2.20E+00 4.08E-01

**New MOLA FEM (rev. 20)**
MODE	FREQUENCY	X-WT	Y-WT	Z-WT	I-XX	I-YY	I-ZZ
#	(hz)	(LB)	(LB)	(LB)	(LB-IN²)	(LB-IN²)	(LB-IN²)

1	73.52	14.54	0.12	0.13	4.53E+01	2.18E+03	7.72E-01
2	83.93	0.44	9.17	0.13	2.02E+03	3.75E+01	6.87E-01
3	90.10	0.00	2.51	0.03	4.91E+02	2.60E-02	1.01E-01
4	99.32	0.00	0.00	0.00	6.86E-04	2.13E-02	8.47E-02
5	107.38	0.01	0.03	0.53	1.37E+01	4.55E-01	5.67E-04
6	111.06	0.06	0.99	34.24	2.01E+01	2.20E+00	4.08E-01

Compare this with test results of first major X, Y and Z modes of the instrument, and the correlation is excellent.

MOLA Test Frequncies
MODE FREQUENCY

X 74.2 Hz

Y 85.0 Hz

Z 110.5 Hz

**MOLA Test Frequncies**
MODE	FREQUENCY

X	74.2 Hz
Y	85.0 Hz
Z	110.5 Hz

Further analysis

Now the task remains to redo much of the analysis that has already been performed to determine if the the old analysis is still valid. Since the major reason for doing random and sine vibration analyses was to create vibration test specifications, those analyses will not need to be repeated. The previous specs were higher than what the revised model would provide and the instrument has already passed the tests using the old specs.

Stress analyses performed on the old model will be repeated and the new results will be be posted.

Questions

If you have any questions about the errors I encountered with this model and during these analyses, feel free to contact me. It is my sincere wish to help others avoid the problems I created for myself. You can e-mail me at the address below.

Back to the MOLA Analysis Home Page.

This page is maintained by Ryan Simmons, at Ryan.Simmons@nasa.gov.
This page was updated on April 10, 1996.