LETTER (Sanitized)

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B04770A002900010012-8
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 35
• Document Creation Date: December 28, 2016
• Document Release Date: June 8, 2005
• Sequence Number: 12
• Publication Date: June 30, 1965
• Content Type: REPORT

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im
illil
Task II
Item 1. Submicron Measurement
Error Analysis
3rd Preliminary Technical Report
11111lli~~
Declass Review by NGA.
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25X1
3P30 1965
5X1
25X1
used are five copies of the third p limit
I of Task Ti o the sub j+ t contract.
lad " b cran Masurenont Irtor Analys
he subject contrast.
V truly yours,
25X1
t is submitted in # rdanne tit tno
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25X1
June 30, 1965
5X1
Task. II, Item 1, 3rd Preliminary Technical Report
Item 1. Submicron Measurement Error Analysis
WORK STATEMENT
Evaluate the physical and metallurgical properties
of materials used in measuring engine construction
.to determine comparative suitability to submicron
measuring. Materials to be considered are: Meehanite,
steel, granite, aluminum, magnesium, and glass, and
other materials that may be particularly suitable.
Evaluate physical properties and structural concepts
appropriate to achievement of vibration levels and
structural rigidity compatible with submicron
measuring requirements. Evaluate methods of measuring-
the small vibration levels expected in a high
performance structure.
Reports No. 1 and No. 2 dealt with the physical and metal-
lurgical properties of materials. This report, No. 3, deals
with structural rigidity and vibration control.
Submitted by:
25X1
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25X1
Task II, Item 1, 3rd Preliminary Technical Report
1. Summary
1.1 Introduction
1.2 Summary of report
1.3 Conclusions and recommendations
2. The major base block
2.1 Composite or homogeneous construction
2.2 Weight and rigidity
2.3 Principal elastic mode of vibration
2.4 Vibration isolation of the block
2.5 Interaction with the floor slab
3. The microscope objective support
3.1 Microscope depth of field
3.2 Some structure criteria
4. The moving platen
4.1 General size and construction consideration
4.2 Air bearing normal transmissibility and pulsation
4.3 Air bearing lateral transmissibility and pulsation
5. The outer structure
5.1 Some structure criteria
5.2 Vibration isolation of the structure
5.3 Some criteria for the drives, pumps and blowers
6. Detail analysis of the structure following preliminary design
6.1 Analytical approach
6.2 The computer program for structural dynamic analysis
6.3 Isolation system servo loop simulation
7. Methods of measuring structure peeformance
7.1 Floor dynamic environmental data
7.2 Granite damping characteristics
7.3 Tests of critical items
Appendix
Free vibration analysis of 20?x20? floor slab by IBM 7094
computer program
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25X1
Task II, Item 1, 3rd Preliminary Technical Report
LIST OF FIGURES
Figure 1
Figure 2
Figure 2a.
Figure 3
Figure 4
Figure 5
Figure 6a
Figure 6b
Figure 7a
Figure 7b
A General Arrangement of Major Structural
Components
An Alternate General Arrangement of Major
Structural Components
Composite of Vibration Frequency Data
Major Base Block Construction
Estimated Theoretical Transmissibility of
Air Bearing
Machinery Vibration Limit for Very Smooth
Running
Major Base Block Mechanical System
Pneumatic Isolator Servo-Control System
Floor Slab Grid Framework
Section A-A of Floor Slab
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1. SUMMARY
1.1 Introduction
This report is intended to provide some guidelines
for the preliminary design of a structure for a precision
.stereo comparator. The general major structural components
of a stereo comparator for submicron measurement are:
a. The major base blocks
b. The moving platens
co The microscope objective lens supports
d. The film drive and roller support structures
e. The microscope eyepiece lens support
f. The operator s work station
The film will be carried on the moving platen there-
fore inadvertent relative movement between the moving platen
.and the microscope objective must be avoided. To minimize
undesired motion the structure supporting the microscope
objective should be rigidly anchored to the base block. It
is assumed that the microscope and the operator will remain
in a fixed position and the moving platen carrying the film
format will move to permit viewing different parts of the
format with the microscope.
One advantageous, arrangement is to place the
operator's work station between the two moving platens (see
Fig. 1). Such an arrangement imposes certain restrictions
on the machine and its structure. For example, the two base-
blocks should be independently supported since a structure
which would tie the two blocks together with the required.
stiffness appears to be impractical. The microscope eyepiece
must be supported independently from the base blocks. Thus
there will be relative movement between the two microscope
objectives and between the objectives and the eyepiece. The
microscope optics must, therefore, incorporate a pivoted link
(similar to a stereo arm)-which permits the above relative
movements without adversely affecting the image observed by
the operator. The relative movement to be accommodated will
be small.-
An alternate arrangement of major structural com-
ponents is shown in Fig. 2. This arrangement uses one base
block, approximately 6 ft x 6 ft to support both moving platens.
It is a much less desirable arrangement for operating ease
and efficiency, but it places the microscope optical system
in one rigid structural unit. The optical relay.path length
is approximately 3 ft longer than the first arrangement which
minimizes the optical relay path length.
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i
Mechanism
Support Structure
It
4 ~
--Microscope Eyepiece
Operator's Work Station
Microscope Objective
~t ti t t
y;' Y I I I V. `1
Floor Slab
IZFT:
A General Arrangement of Major Structural Components
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Support Structure
'_ j j--Moving Platen
Fig.
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Columns for overhead support of mechanism
support structure
Major base block
Moving platen
Microscope support structure
-G FT.
2.. FT
Obj ective
Eyepiece
operator's
station
Work station and control console
An Alternate-General Arrangement of Major Structural.Components_
Plan View) Fig.. 2
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Other general considerations of the structure are:
(a) the operator's work station must be structurally isolated
from the major base block; (b) the mechanism support structure
which supports the film rolls and drives, vacuum pump, blowers,
etc., must be structurally isolated from the major base
blocks; (c) ideally, the natural resonant frequencies of
structural components should be widely separated and well
damped. Items of concern are:
a. The vibration isolator supports
b. The floor slab
c. The free-free mode of the major base block
d. The free-free mode of the moving platen
e. The moving platen air bearing
f. The microscope objective support structure
g. The microscope eyepiece support structure
h. Every beam, post and bracket in the mechanism
support structure
i. The operator's work station
(d) input disturbances should be minimized by dynamic balancing
of motor rotors, film rollers, pumps and fans.
A detail analysis of the structural dynamics of the
submicron measuring engine can be performed by an existing
computer program when the preliminary design of the structure
is established. The analysis will provide data for the detail
structural design. Section 6 of the report indicates the pre-
liminary design data needed for the computer analysis.
1.2 Summary of Report.
A homogeneous granite major base block will have a
fundamental dynamic frequency of about 410 cps which is satis-
factory. Two blocks will weigh about 3400 lbs each. They
can be readily supported by the floor with a simple support
design.
Cast iron major base blocks will be much more rigid
and lighter weight. The fundamental dynamic frequency will
be about 765 cps and weight about 2,000 lbs each (including a
2-in. granite cap).
A fabricated steel major base block will be even
more rigid. The fundamental dynamic frequency will be 1,710
cps which is excellent. The weight would also be about 2,000'
lbs each (including a 2-in. granite cap). Special.precautions
would be required in the design to insure a well damped structure
and to insure that all webs have a high fundamental mode. If
the suggested two major base blocks are combined into one,
the above weights will-double.
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Calculations of the floor slab stiffness indicate
it will have a fundamental mode of 20 to 65 cps. It is
estimated floor excitation will be between 10-2g and 10-3g.
The floor slab vibration characteristics should be measured.
The microscope depth of field will be approximately
2 to 8 microns; therefore, the structure which supports the
microscope objective lens must be rigidly attached to the
major base block. If possible the microscope eyepiece should
be independently supported in order to obtain the most effective
operating arrangement. The microscope relay lens structure
should be vibration isolated so as not to transmit vibration
from the eyepiece to the major base block.
The moving platen, if made of 1-1/2-in. thick glass,
will have a"_120 cps fundamental mode which is too close to the
estimated theoretical fundamental mode of 115 cps of the air
bearing. A test of the normal transmissibility of the air
bearing is needed. Low frequency pressure pulsations in the
air bearing should not be allowed to exceed 1% or 2%. The
lateral transmissibility of vibration across an air bearing is
extremely low. Under worst conditions it should not exceed
1 to 2 millimicrons which is excellent for measuring resolutions
of 1/10 micron.
Ideally there should be no mechanical connection
between the moving platen and the major base block which could
provide a vibration path bypassing the air bearing. Practically,-
special attention should be paid to minimizing electrical
cables, hoses, drive and film loop connections to the moving
platen and to designing the required connections for minimum
transmission of vibration to the moving platen. Pneumatic
and electromagnetic drives should be given special attention
for this reason.
The outer'structure should house all sources of
vibration and shock associated with machine operation. The
outer structure should be physically structurally separate from
the major base block and the optical support structure. Simple
conventional vibration pads are adequate for vibration iso-
lation of the outer structure from the floor. Bolted con-
struction and other damping techniques such as sand filling
should be employed. After preliminary design, the elements
of the outer structure should be computer analyzed for
resonance interactions.
Rotating members of drives, pumps, and blowers
should be balanced to achieve a close coincidence of the center
of mass to the center of support. Recommended maximum
eccentricity versus speed is given.
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Fig. 2a is a composite chart of the vibration fre-
quency data. The chart shows peak-to-peak amplitudes of
vibration in microinches vs frequencies at various vibration
g: levels. The data may serve as design guidelines in sizing
the structural components. The actual responses of the
structural elements must be calculated by analyzing the structure
as a dynamic model.
1.3 Conclusions and Recommendations
The principal conclusions of this report are:
a. A granite major base block will be satisfactory
and least expensive. A superior composite
.steel structure with a granite or glass cap
could be designed but would be more expensive.
b. The major base block or blocks should be sup:
ported on three pneumatic isolators of about
8 cps natural frequency. Automatic level
recovery time should be no more than 2 sec.
c. The principal elastic mode of the floor is.
estimated to be in the range of 20 to 65 cps
and should be measured.
0
d. The microscope objective lenses should be
rigidly fixed to the major base blocks.
e. The microscope eyepiece should, if possible,
be separately supported.
f. The operator?s work station should be struc-
turally separated from other structure and
need not be vibration isolated from the floor.
g? An outer structure should house all machine
sources of vibration and shock and should be
structurally separate from the major base block.
Conventional vibration pads can be used.
h. Air bearings will provide excellent isolation
.of horizontal vibration. Transmissibility
should be well below the 1/10 micron measuring
resolution desired.
i. Transmissibility of vertical vibration by
the air bearings may have an undesirable
characteristic and should be measured.
At this stage recommendations are principally con-
cerned with filling gaps in our information:
a. Measure floor resonance and damping..
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b. Measure natural damping of granite.
C, Measure transmissibility of an air bearing
normal to the air cushion.
We suggest that the customer have the above measure-
ments made during the preliminary design. phase so that the
data will be available for the detail analysis of the structure.
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2. THE MAJOR BASE BLOCK
2.1 Composite or Homogeneous Construction
The basic structural dynamic requirements of the
major base block are as follows:
a. The fundamental bending frequency of the
free-free structure should be well above
300 cps.
b.. The weight of the block must be such that
the loads transmitted through the'supports.
to the floor will not exceed the allowable
design loads of the floor.
c. The material and construction of the block
should provide high damping to minimize
vibration loads.
Three methods of the major block construction have
been considered. Each of the methods is described below..
The first construction method is simply_a solid
granite block (see Fig. 3a) supported by a number of isolators-
along the fundamental mode node line of the block. This is
an homogeneous construction. The surface of the granite can
be smoothed and polished. The surface is relatively free of
corrosion and easy to keep clean. The material damping of
granite is high; however, the flexural rigidity per distributed
weight of the homogeneous granite'is low compared to cast iron
or steel structures. The cost of the homogeneous granite block
is lower than other construction methods.
The second method is also a homogeneous construction.
The block will be cast to form a waffle-like cast iron structure
(see Fig. 3b). With this type of construction the distributed
weight, M (lb/in.), along the length dimension is lower than
granite. Assuming an 18-in. depth block, the EI/M will be
somewhat higher than granite which results in higher bending
frequency. Cast iron also has good damping characteristics.
One of the disadvantages is that-the surface would require
protection from rust and corrosion. Care must be exercised
in sizing the webs such that the natural'frequencies of the
webs are well above the fundamental block bending frequency.
The third construction is a composite type made
of a bolted steel framed structure 18 in. high with,a granite
or glass top (see Fig. 3c). The steel-framed structure could
be of sandwich type. The compartments.can be filled with
sand to provide damping. A bolted instead of welded structure
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(a) Homogeneous granite block
(b) Cast iron block with waffle pattern bottom
(c) Composite steel block with granite or glass top plate
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is preferred because of higher structural damping. Of the
methods considered, the composite type of construction
generally will yield highest EI/M. The total weight of the
block is also the lowest.
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2.2 Weight and Rigidity
As stated in 2.1 the weight requirement of the block
is'that the support load should not exceed the allowable floor
load. Since the support is of point load nature and the floor
is of concrete slab construction, the punching shear load,will
be the criterion in calculating the internal stresses of the
floor slab. By providing a steel base plate under the support
.the loading may be considered a distributed load.
Preliminary estimates of weights for the,three types
of block construction have been made. The granite block would
weigh approximately 3400 lbs. The weight of the cast iron or
the steel-framed blocks is approximately 2,000 lbs (including
a 2-in.-thick granite or glass surface plate).
Assuming the moving plate and the associated equip-
ment would weigh around 200 lbs, the gross weight to floor for
the granite block (worst case) will not exceed 3,600 lbs which
will be distributed among three supports. If one of the
supports receives 1,800 lbs and the support base is 10 in. in
diameter, the shear load along the perimeter would not exceed
60 lbs/in. Assuming the support rests on a 10-in. concrete
slab, the concrete shear stress would be 6 lbs/in.2 which is
well within the allowable.
2.3 Principal Elastic Mode of Vibration
The fundamental free-free bending frequenicies of
the three block structures have been calculated and listed
below:
Block Type
M(lbs/ft)
EI(in.2/lb)
f(cps)
Granite
570
2 x 1010
410
Cast Iron
330
4 x 1010
765
Steel-framed
330
20 x 1010
1710
The calculations; were based on 6 ft-span free-free
beams.
2.4 Vibration Isolation of the Blocks
To minimize floor excitations to the major base block,
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is desirable to support the block on isolators.
The mass-spring resonance frequency of the isolators
should be well below the fundamental mode of the floor slab.
It is undesirable that the isolators be too soft since the
moving platen would then cause tilt of the base block. If
the moving platen is 10% of the weight of the base block,
the tilt could be as much as 10% of the static deflection of
the isolators. To eliminate permanent tilt of the major base
block, a self-leveling pneumatic type isolator such as the
Barry Controls SERVA-LEVL should be used. The very soft
standard 2 cps SERVA-LEVL has a.level recovery time of 15
to 20 sec which is too. long. To prevent interaction of the
level recovery system and the vibration isolation action.
the level recovery time constant must be long compared to the
vibration isolator time constant. Probably an 8 cps mount
with a 1 to 2 sec level recovery time would be a good compromise.
2.5 Interaction with the Floor Slab
In general, if the floor structure is of reinforced
concrete construction, the-fundamental bending frequency will
be above'15 cps. A preliminary estimate of the bending
frequency of the floor where the.submicron measuring system
will be located is somewhere between 20 and 65 cps.
The criteria set forth in 2.1 and 2.4 were generated
C~ 2 i 2 ~lz ? a cOIS f
J..
r -Cw >aj a * c 2 , )2 ,~ - C '?
L. w 1L e
from the knowledge of the floor structure.
The relative displacement transmissibilities con-
sidering a system indicated in Fig.. 6a can be expressed by
the following equation:
where
w~ = Floor. excitation resonant frequency.
~B = Isolation system frequency
= Major base block resonant frequency
= Damping ratio of the isolation system
Damping ratio of the base block
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Sections 6 and 7 will discuss further analytical,
and experimental work to determine the over-all structural
dynamic performance of the submicron measuring system. The
floor excitations and interaction with the measuring system,
are of major consideration.
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3. THE MICROSCOPE OBJECTIVE SUPPORT
3.1 Microscope Depth of Field
The allowable relative movement of the film platen
and the microscope objective support is governed by the micro-
scope depth of field.
DF = 2 n2 - (NA)2
(NA)2
where
= Wave. length of light ='0.5 x 10-6 meters
n = Index of refraction of air = 1.
.NA = Numerical aperture'which varies from 0.25 to 0.5
The DF range varies from 80 to 320 microinches (2 to 8 microns).
3.2 Some Structure Criteria
The microscope objective support structure criteria
a. 'The resonant frequency should be at least
.twice that of the major base block.
b. The relative peak-to-peak movement should be
less than 80 microinches (2 microns) under
any excitations.
C, The optical linkage components connecting the
eyepieces,should not transmit appreciable
vibration load to the microscope objective
structure. ..
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4. THE MOVING PLATEN
4.1 General Size and Construction Considerations
The required observable format size for each platen
is 10 in. x 20 in. The glass plate can therefore be assumed
to be approximately 1 ft x 2 ft. To obtain adequate flatness
(approaching an optical flat) it will need to be at least 1 in.
thick and may need to be 2 in. thick. The weight of the plate
only will, therefore,. be from 25 to 50 lbs. Additional thick-
ness will be required for vacuum slots. In addition, structure
will be required for supporting the glass plate, for air
bearings, for the ways, for the X-axis measuring engine, for
the intermediate ways and for the Y-axis measuring engine.
The total weight will probably not exceed 200. lbs for each
moving platen of the stereo pair.
4.2 Air Bearing Normal Transmissibility and Pulsation
The air bearings which will support the moving
platen on the base blocks will help to isolate the platen ,
from vibrations in the base. The air bearing will act as a
damped spring and with the supported. mass will have a frequency
response characteristic dependent on the spring-mass constants..
Amplification at the resonant frequency will depend upon the
damping. As a first approximation of transmissibility we
assumed the air bearing would follow the same principles as
an air bearing isolator in which the natural resonant frequency
is determined by the air column height. The air column height
was assumed to be the thickness of the air cushion in the air
bearing. The resonant frequency is therefore estimated to be:
fn
= Resonant frequency, cps
= Gravity constant = 386 in./sec2
= Ratio of specific heats of air = 1.4
Thickness of air cushion = 0.002 in. (assumed)
= 1 V//. 386 (1.4)
AIr 0.002
= 82.5 cps
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The curve of Fig. 4 illustrates the estimated theoretical
transmissibility of the air bearing. Note that below 25 cps
a 0.002-in, thick air bearing will transmit vibration at 1:1.
Between 25 cps and 150 cps an 0.00_24--in. thick air bearing
will amplify vibration as much as 1.4:1. Above 150 cps it
attenuates vibration and at 300 cps the transmissibility is
0.3. Transmissibility is defined as the output amplitude
divided by the input amplitude.
For an 0.001-in. thick air bearing f = 115 cps.
The curve will be similar but shifted to the right as shown.
The actual''response of an air bearing to vibration
inputs may differ appreciably from the estimated theoretical
transmissibility shown here. A more realistic theoretical
analysis immediately becomes exceedingly complex and no dynamic
analysis of an air bearing has been found in the literature.
A measurement of the frequency response of a typical air
bearing is recommended since it appears that the air bearing
will amplify vibration in the frequency range of the floor
inputs and at the fundamental mode of the glass platen.
Pressure pulsations in the air bearing, if they are
.of low frequency, will change the air cushion thickness. If
the air cushion is 0,001-in. thick then a.10% pressure variation
will cause the platen to move 2-1/2 microns which is unaccept-
able for the depth of the field of the best microscopes. A
1% pulsation would cause only 1/4 micron movement of the
platen which is acceptable.
4.3 Air Bearing Lateral Transmissibility and Pulsation
For horizontal vibration the air bearings will be
a highly effective isolator. Motion will be transmitted across
the bearing by shear in the air cushion. The shear force is
given by:
F = AP dV
dy
= Force on supported member, lbs
A = Area of supporting air cushion, ft2
}1 Viscosity of air = .04 x 105 lb sec/ft2
dV = Velocity gradient of the air across the
ay thickness y of the air cushion in ft/sec/in.
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By assuming some fairly extreme worst case conditions, we can
demonstrate that lateral transmissibility across the air
cushion is negligible.
Assume a base vibration of 300 microinch amplitude
and about 65 cps (i.e., 400 rad/sec), then peak velocity of
the base will be 0.12 in. /sec. The force transmitted to the
supported member will be:
F = 40 x 0.4 x 10-5 x .12 = 1.33 x 10-3 lbs
14 .00
for A = 40 in.2 = 40/144 ft2
p = 0.4 x 10-5 lb sec/ft2
dV = 0.12 in./sec
dy = 0.001 in. air cushion thickness
For a 200-lb supported weight this is less than 10-5g which
corresponds to approximately 1-1/2 millimicrons amplitude.
Such amplitude is negligible compared to the 1/10 micron
resolution desired.
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5. THE OUTER STRUCTURE
5.1 Some Structure Criteria
The outer structure will support the film drive
system and other operating equipment. Although the outer
structure will be isolated from the floor and the major block,
any excitation of the outer structure to the floor will be
transmitted to the major base block. The criteria of the
outer structure design are listed below:
a. The resonant frequencies of all the components
and their mountings to the outer structure
should be well separated from,the resonant
frequencies of the floor slab, block isolation
system, and the first elastic mode of the
major base block.
b. Bolted structure is preferred to welded
structure for higher structural damping.
5.2 Vibration Isolation of the Structure
The purpose of the isolation of outer structure
from the floor is to minimize floor.excitation. With a proper
conventional design of mounting pad the goal can be achieved.
It is not necessary to incorporate a pneumatic isolation
system as required for the major block. Care must be exer-
cised in designing the isolation mount such that the isolation
frequency is not near the floor resonant frequency.
5.3 Some Criteria for the Drives, Pumps and Blowers
To minimize the sources of vibration in the outer
structure, good balancing of the rotating components of the
drives, pumps, and blowers are essential.
The criteria to achieve good balancing are as
follows:
a. The permissible unbalance tolerances for
these items in terms of millimeter-grams of
permissible residual unbalance per kilogram
of rotor weight should be in the order of
0.5. This is equivalent to center of gravity
displacement of 20 x 10-6 in.
b. The bearing displacement versus speed of the
rotating equipment should be in the shaded
area of Fig.5.
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6. DETAIL ANALYSIS OF THE STRUCTURE FOLLOWING PRELIMINARY DESIGN
6.1 Analytical Approach
One'of the main factors that affect the performance
of the submicron measuring system is the understanding of
the structural dynamic behavior of the system.
The dynamic response of the major base block will
be of chief concern. Block vibration loads will be transmitted
to the moving platen and the measuring system as well as the
microscope supports. When the preliminary machine design is
established, a detail study of the block structure under floor
excitations can be made. Dynamic behavior of other structural
and mechanical components can also be analyzed to obtain the
over-all performance limits of the submicron measuring system;
An existing IBM 7094 computer routine is available
for detail analysis of the structural dynamic responses of the
major base block. The capabilities of the routine will be
described in 6.2.
The performance of the block isolation system should
.also be well understood. The pneumatic system is a non-linear
system. The stability and. response characteristts of the servo-
control loop should be simulated by an analog or digital
computer.
6.2 The Computer Program for Structural Dynamic Analysis
An IBM 7094 computer pro ram named LESAR (Linear
Elastic Structural Analysis Routine) has been developed
recently by Ying-Nien Yu. A brief description of the routine
is given below.
LESAR performs static and dynamic analyses of any
linear structure which can be idealized as one of the following
frameworks:
Type 1 Three dimensional pin-jointed frame-
work (examples of structures which can
be so idealized--spaceframes, membranes,
box beams).
Type 2 - Three dimensional rigid-jointed frame-
work (e.g., spaceframes, shells, box
beams, curved beams).
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Type 3 - Two dimensional rigid-jointed frame-
work, loaded in-plane (e.g., bars,
curved planar beams, rings, planar
frames).
Type 4 - Two dimensional rigid-jointed frame-
work loaded normal-to-plane, also called
a two dimensional grid (e.g. lates,
planar frames, arches, beams .
A framework is defined as a system of uniform
weightless bars connected together at joints to form a stable
structure.. At the joints, inertias are lumped and loads are
applied. The bending, torsional, and axial.stiffnesses of the
bars simulate the elastic properties of the corresponding
structure. The lumped inertias and loads represent the actual
distributed inertias and applied forces.
The framework and its environment can be described
by the following quantities:
a. Coordinates of joints
b. Geometry and elastic properties of bars
connecting the joints
c. Lumped inertias at joints
d. Restraints at joints
e. Loads applied at joints
Given these quantities as input LESAR will perform
computations to provide the following output:
1. Stiffness matrix for the structure
2. Up to 12 Eigenvalues and Eigenvectors
(modes and frequencies)
3. Response to loading conditions:
a. Deflections and internal loads (moments,
shears,. torques, and axial forces)
within the structure for static loads.
b. Time history of deflections and internal
loads for transient excitations.
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c. Deflections and internal loads as a
function of frequency for harmonic
excitation.
4. Summary of the maximum design loads occurring
at joints.
The program is versatile as far as the structural
types and excitations are concerned. The only limitation is
in the total number of degrees of freedom which is 102. For
the base block analysis, Type 4 structure will be used. The
maximum number of degrees of freedom is not expected to
exceed 80.
The use of this routine will provide structural
dynamic analysis of the submicron measuring engine structure
to a sophisticated degree. Computer time will normally not
exceed 5 minutes per set of input conditions.
In the present study, LESAR was used to analyze the
free vibration of the floor slab.
In future structural dynamic analysis of the major
base block, the block-support system will be organized as a
mechanical system as given in Fig. 6a,
Considering vertical motion only, the following
data will be generated:
1. Three rigid body frequency modes (1 vertical,
2 rotational with respect to block surface).
2. Up to 9 elastic modes and frequencies.
3. Static and dynamic deflections and stresses
to given loading conditions.
Similar models can be established for motion side-
ways to yield other rigid body modes, but this is not believed
necessary. The stiffness of the block in the plane direction
is high, and it is not necessary to carry out the elastic
motion computation of the block. Knowing the isolation stiff-
ness horizontally, the rigid body modes can be hand computed
without resorting to computer routine.
6.3 Servo-Control Loop of the Isolation System
The isolation system stiffness requirement will
depend on the dynamic behavior of the major base block. The
level recovery time requirement of the system will be derived
from the following considerations:
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1. The moving platen will be free of oscillations
or unstable motions throughout the slew rate
range of the measuring engine.
2. Should a two-base-blocks system be chosen,
the relative motions of the blocks should be
small and the recovery time should be such that
the motion disturbances of the eyepieces.will
be at a practical minimum;
As indicated in 2.4, an 8 cps mount with a 1 to 2
sec. level recovery time may be desirable for the pneumatic
isolation system. The position-sensing valve design of SERVA-
LEV would probably not permit the fast response requirements.
In general, a fast response pneumatic system would
require an electro-pneumatic controller which actuates a servo
valve through error signals received from displacement and/or
velocity sensors.
Fig. 6b shows a typical servo-control loop mechanism
of the pneumatic isolation system.
Since the pneumatic transfer functions are non-
linear, the servo-control system will involve a set of non-
linear differential equations relating the parameters Pl., P2,
V1, V2, P1 T , P2 T -1 Ps, Al) A2, Xa, Xb, and the controller
transfer function. The solutions of the equations can. be
programmed for either a digital or analog computer.
The degree of sophistication in the servo-control
loop is dependent on the requirements derived after prelim-
inary structural dynamic design of the complete submicron
measuring system.
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Plan Grid Framework
(Type 4 Structure)
.A:
-rloo.r .slab
Elevation
Major. Base. ,Block Mechanical _ System ._..
Fig.. 6a -.
-Major. base block-
Supply
gas
ontroller
DampingTTchambers.
Pneumatic Isolator Servo-Control System
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);77 r2 V2 //7
;'. Floor. slab
Isolation-support .
Fig. 6b
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7. METHODS OF MEASURING STRUCTURE PERFORMANCE
7.1 Floor Dynamic Environmental Data
For detail structural dynamic analysis of the
.design of the submicron measuring system, the dynamic environ-
mental data of the floor where the system will be located
will be needed.
The data of interest are the following:
a. Fundamental resonant frequency
b. Damping characteristics
c. Acceleration environment
These data will be used to determine the isolation
requirements of the outer structure and the major base blocks.
The resonant frequency and the damping character-
istics of the floor slab can be measured by simply applying
a hammer blow (using a lead hammer) and recording of acceler-
ation-time history. In general, the fundamental resonant
frequency and the damping ratio can be obtained simultaneously
from the acceleration-time history record by measuring the
period and calculating the decay rate. However, should the
noise level of the floor be higher than the hammer blow or
if more than one frequency is excited, the data will be
difficult to reduce.
An alternate measuring method is to attach a small
vibration exciter (such as an electrodynamic shaker with.
sweep frequency range of 5 cps to 100 cps) to the floor
supplying the excitations. The accelerometer response will
again be recorded. At resonant frequency, a survey on adjacent
points should be made so that the damping ratio can be
determined.
To measure the acceleration environmental condition
of the floor a portable acceleration recorder will be employed..
The sensitive ies of the recorder should be in the order of
10-3g and 10- in. Measurements should be made. in all three
directions.
7.2 Granite Damping Characteristics
Having obtained the floor-environmental data, the
major block and isolation system design can proceed. One of
the factors in choosing the major block construction technique
is the damping characteristics of the three types of construction
considered.
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Damping data are available for cast iron and steel-
framed structures.. Research will be needed to obtain the
material damping data of the granite. In the event that data
are either not existant or not complete, a resonant survey
of'a specimen granite block should be performed on an electro-
dynamic shaker.
The material damping energy is generally a function
of internal stresses; thus in performing the resonant. survey,
the input acceleration level of the shaker should be comparable
to the level of floor acceleration environment.
7.3 -Tests of Critical Items
It may be necessary to perform vibration level tests
on critical items of the submicron measuring system for the
following reasons:
a. Items which are either moving parts (rotors,
fans, etc.) or parts transmitting motions
(gear, linkage, etc.) will generate vibration
sources. These parts must be properly balanced
or tested to be sure that the frequencies are
well separated from other major items of the
system.
b. Items which directly affect the measurements
of the film coordinates (measuring engine,
moving platen, etc.) should also be tested-
to insure structural integrity.
Specific determination of which items are critical
can be made during preliminary design of the submicron
measuring instrument.
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Free Vibration Analysis of 20'x20'
Floor Slab by IBM 7094 Computer Program
0
The floor structure is made of a non-uniform two dimen-
sional plate. Hand calculations of the modes and frequencies
will be laborious and inaccurate. A computer analysis of the
free vibration of the 20?x20 concrete floor slab has been.
carried out.
In this Appendix section we shall be concerned with the
structural dynamic model of the floor slab. In a subsequent
report, the input/output of the computer run and the results
of the computation will be discussed.
Figure 7a. shows the grid framework of the floor slab.
Figure 7b shows a cross section of the floor slab.
A number of assumptions of the floor slab model are
given below:
(1) The effective. depth of the members adjacent
to the columns is 32".
(2) The effective depth of the remaining members
is 8".
(3) The concrete strength is 2000 psi which results
in Ec= 2,000,000 psi.
(4) The distributed weight of the slab is 125 psf.
(5) Members 3-26,11-27, 15-28, and 23-29 in Figure'.-.'7a
are dummy members simulating the stiffness of
the adjacent floor bays. Joints 1, 5, 21, 26,
27, 28, and 29 are restrained in. all directions.
The input data will then be organized based on the
model. The input and output data of the LESAR run will be
tabulated in the future report.
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Figure 7a Floor Slab Grid Framework
Figure 7b Section.A- A. of Floor Slab
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Item 1.
3rd Preliminary Technical Report
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Submicron Measurement
Error Analysis