ENGINEERING RESEARCH INSTITUTE
THE UNIVERSITY OF MICHIGAN
ANN ARBOR
Technical Report
-VACUUM-BOTTLE SUSPENSION SYSTEMS
44 -e
ERI Project 2254
THE ARO EQUIPMEJNT CORPORATION
BRYAN, OHIO
April 1958

~t ~ I k.. i't'a g ~t [x5'U

The University of Michigan ~ Engineering Research Institute
ABSTRACT
A method is presented for designing suspension systems for'liquid oxygen
containers. These suspension systems have the properties of'relatively high
thermal conductive resistance while at the same time providing an overdamped
spring support. The damping is obtained by proper use of dry friction devices
and limits both the relative motion and imposed acceleration of the inner bottle to acceptably small values. The method is of advantage since it requires
a smaller annular space than is presently used between the two bottles.

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INTRODUCTION
The Aro Equipment Corporation requested a study of possible suspension systems in October, 1957, as part of its program to increase the resistance of its
liquid oxygen containers to vibration and shock environments. This was to be
a broad study since Its immediate-object was to reView any possible designs
which came to mind in an effort to find a satisfactory one,
DEVELOPMENT OF DESIGN
Any successful suspension system such as is required here must contain a
spring element of some form or another. One practical means of limiting the
resonant amplitudes of the sprung mass is the introduction of damping. The
most common way of introducing damping into a system is the use of fluids, but
the extremely low thermal resistance of fluids eliminated them from consideration here. Another reason to reject them is that any suspension system designed for this purpose must undergo the approximately 800'F temperature to
which the bottle is subjected in outgassing. Another method, the use of an
absorber, was not deemed practical here due to the flexibility of the mounting
feet and outer shell; further, small design variations in these elements would;
require changes in the absorber designo In general, the absorber would be too
sensitive to small design changes to be a very effective tool.
Ruling out fluid damping and the absorber, the only other methods of introducing damping are through hysteresis or dry frictiono Hysteresis is an
acceptable method and in general should work provided that enough energy can be
removed from the system per cycle. However,, nonmetallic materials (such as
rubber, nylon, etc.) are the most efficient and these are not capable of standing the 800~F temperature mentioned earlier. For this reason, dry friction was
chosen as the mechanism of damping, since it can be obtained easily between
metallic surfaces which can withstand high temperatures.
A number -of dry friction devices were investigated before a design geometry was selected which appeared to possess all the desired features listed
below:
1. Maximumn thermal resistance..__ _ _ _ _ _.__ _ _ _ _.__ _ _ _ _ -_ _ 1,

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2. Good, controllable spring constant properties in the vertical direction and in any two arbitrary but mutually perpendicular horizontal
directions.
30 Good, controllable dry friction properties in the directions listed in
the previous item.
4. Small thickness, so that the evacuated annular space between bottles
may be kept to a minimum.
5D Ease of manufacturing and assembly of the proposed design.
6. Ability to withstand outgassing temperatures of approximately 800'F.
The proposed design geometry uses' the 5-liter spherical bottle as a numerical
example, although the technique outlined here is applicable to bottles of different weight and size.
Reference to Fig. 1, taken from Den Hartog, indicates that successful operation of a dry friction system through the resonant range depends on obtaining enough dry friction so that F/Po is greater ~than about 0.9, in order for
oscillations to be limited to finite values. F is the friction force and Po
the exciting force. Figure 1 was constructed for the system shown in Fig. 2.
3.0
2.5
0 /06/0.75 J750.6 =F/P0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
22
0 0.2 0.4 0.6 0.8 1\0 i.2 1.4 1.6 1.8 2.0

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From this, it is seen that the equation of motion becomes
mx + f(i) + kx = Po sin Mt, (1)
where f(2) represents the damper force~
The system with which we are concerned is shown in Fig~ 30 The equation
of motion governing it is
mx + f(2) + kx = myo 62 sin nt. (2)
P sin ctl
0 m m
k i: AI Damper f(x) X k,t y~yo sin wt
Fig. 2. Spring-mass system with dry Fig. 3. Spring-mass system with dry
friction damping. friction damping and forced base motion
The solution to Eq. (1) is plotted in Fig. 1, while Eq. (2) is identical
to Eq. (1) upon substitution of Po for- myo, so Fig. 1 may be used to plot
out the solution to Eq. (2). This is especially useful upon introducing the
relation
2
YowU = Maximum Base Acceleration = aB
Thus, the ratio F/P0 now becomes, for the solution of Eq. (2), F/maB, and
Figo 1 indicates that the smallest value of this parameter which can be safely
allowed in the vicinity of resonance is
F = F 0O9 ()
r1y u0 9. (3)
myo maB
It is now desirable to preselect the natural frequency of the inner bottle on its suspension syst-em. This selection is based on the general —idea
that the lower the natural frequency, the more isolation of inner from outer
bottle will be obtained~ High stresses in the suspension-system springs put
a lower limit on the natural frequency of about 10 cps, and this figure will
be used in all subsequent calculations. Any desired value of natural frequerny
# 3 - -.

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which is higher could be chosen, but would result in less isolation.
At resonance an effective force Po exists of magnitude2
P0 = (myo02) - o2 (10x2c)2 x o040
g
(4)
= 04 W = maB
Thus,
F F
P. = 0~9 = o4w
or
F > o036W (5)
Equation (5) states that the magnitude of the dry friction force which
must be generated to prevent motion in any given direction is ~36 times the
weight of the suspended inner bottle. This is one of the two'basic design
conditions, the other being the assumption that natural frequency will be held
to 10 cps,.as previously stated.
Design conditions as outlined above must be satisfied with the bottle in
its full condition, since this is the most critical condition for both damping force and stress in the supporting springso It will be shown later that
the response of the system, under conditions other than full bottle loading,
is more severe but not necessarily destructive to the system.
The principles just stated may be applied to a general spring-support
system~ Some work on this subject indicates that an optimum number of springs,
namely, the number giving a minimum conductive path, must exist~ In general,
this minimum conductive path will be obtained with the minimum number of sprins
as a support system. This minimum number is four, for springs which are designed to take only compression~ Another desirable feature of any design would
be a distribution of spring constants so that the natural frequency of the in-.
ner bottle would be the same for any.direction of motiono This can be nearly
accomplishedby a design in which three springs are placed at 45~ below the
circumferential equator of the spherical or near-spherical bottle, while a
single spring at the topmost point acts as a hold-down device~ Figure 4 shows
the coordinate system used to describe the spring positions in Table I, where
a spherical bottle of radius Ro is implied|
Calculation of the spring constant for vertical motion can be done by observing the geometry shown in Fig0 5o Assuming that one face of the spring
may slip with respect to the inner bottle, then a spring deflection occurs
which is described by
4 4._,

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z
x
Figo 4. Spherical coordinates for spring-position description~
Afn-\N
Fig~ 5o Spring~deflection geometry~

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6 = 6y ~ sin
where 5y is the vertical bottle motion. Hence the restoring force is
F = (kob) sin ~ = k6y sin2 o (6)
Two other identical springs exist so that the total restoring force is
F = 3k6y sin2 2,
or
keg = 3k sin2. o (7)
For this design A s 450 so that
3
keq = k o
TABLE I
Spring Noo r
1 Ro 0o 45o
2 Ro 1200 o45
5 o
3 Ro 240~ 45
4 R o -90~
The friction force will be directed perpendicular to the spring force, ard
will be in magnitude the product of spring force and friction coefficient so
that
Ff = Fs f
The vertically acting component of friction force is the one which is effective
in absorbing energy, and is
Ff ~ cos ~ = Fs f ~ cos o
Since 3 springs exist, the total vertical component of damping force is
3 Ff cos ~ - 3Fs of o cos / o (8)
The average value of the spring force Fs may be computed snlce the total
vertical components of both spring and friction forces must at least equal the
weight, not counting any preload which might be present in the system~ Figure
6 shows this geometry, where it must be assumed that the maximum possible
6

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friction force is developed at the spring
bottle joint. The upward component of
force is
Fs cosO + FF sin0 = Fs cos0 + fFs sineo
For three springs, equilibrium of these
forces with the bottle weight gives
3(cos0 + f sin$) Fs - W
FS't or
F5 = |(cosO + f sing)
The vertical component of the total dampFig. 6. Spring and friction force er force is now, from Eqo (8),
directions.
FF = 3f cos fcos
y I3(cosO + f sin.) coso + f sin (9)
Equation (9) allows the angle 0 to be chosen so that Eq. (5) can be satisfied.
For,a typical copperflashed innerP-bottle surface, friction coefficients
have been -measured by:experiment for stainless, steel.Spring wire in contact
with the copper. Details of those measurements are presented in the Appendix,
but their main result is that an effective friction coefficient f = 0.276 was
found. Using this, it is seen that an angle - 45, for placement of the sprng
results:in Eqo (9) becoming
Fy + 0 ~276 2
2 2
Since a vertical damper force of 0o36W is required, then some preload will
in general be necessary, or else a different angle / must be picked. It is
believed that the technique of adding preload is more satisfactory in the end,
since it is necessary to hold the inner bottle down against upward motiono Thus,
if a vertical preload equal to the weight W were put into the system by means
of spring 4 of Table I, the resulting damping force component in the vertical
direction would be
FF = 2(o216W) = o432W,
which is above the lower limit defined in Eq. (5).
7

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The complete design geometry of the suspension system may now be illus-.trated in Fig~ 7 as a function of weight, because it is possible to determine
[from Eqo (7). the known spring positions, and the assumed natural frequency of
10 cps] the spring constant k of each individual spring in terms of the weight
W, since
(lO x 2 1,
Solving for k, one obtains
K'= 6,80 W
This is independent -of preloado
Prelood = W
W (bottle full)
k:6.8 W
k=6.8W
k=6.8W
Figo 7~ Design geometry~
The spring constant of the top, or preloading, spring should be held to as
low a value as possible. Spring stresses will limit this, but in general the
aim here is to provide a preloading device which will exert a minimum influence
on the spring constant of the remainder of the suspension system~
The exact shape of the springs is a matter in which the designer has some
freedom, since the same spring constant can be obtained with a large number of
different design geometries~ The writer has made a short study of this and
8

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wishes to recommend "wave washers" or their wire equivalents as having a particularly desirable set of properties~ Appreciable spring constants can be
obtained with-very small thicknesses, which means that the annular space between inner and outer bottles can be reduced. Also, the conductive paths, as
measured by the length over area ratio of metal between inner and outer bottle,
are usually quite long, and are of the same order of magnitude as that in the
present "spoke type" suspension. Finally, springs of this type contact the
inner and outer bottles at points which have extremely small cross-sectional
areas, and so provide additional thermal resistance.
With the construction shown in Fig. 7, it can be shown that the spring
constant in any horizontal direction is identical to that in the vertical direction so that all natural frequencies in translation are equal to the nat
frequency previously calculated for vertical motiono
Frequencies of rotational and rocking motion were calculated and found to
be close to those for translation, so that no unexpectedly high natural free
quencies should exist.
Calculations were made from Figo 1 of the displacement response of'a mass
supported by a suspension system designed along these principles. This response is plotted in Fig. 8, based on motion of the system in a vibration environment of Speco Mil. E5272A.
These calculations were checked closely by a synthetic experimental system
shown in Fig. 9, in which acceleration could be measured. Results from this
system are plotted in Fig. 10, and are valuable in indicating the acceleration
levels which will be encountered by the inner bottle. This information cannot
be -obtained by calculation due to the nonharmonic nature of the motion. In
general the system behaved as expected in that relative motion became notices
able only at higher values of forcing frequency.
It should be stated here that so far only generalizations based on a syas
tem composed of a rigid mass, linear spring, and perfect dry friction damper
have been made. Testing of these ideas with actual liquid gas containers and
possible change or supplement of them is certainly in order, since the actual
system is quite elastic, contains some fluid damping properties, and operates
with a friction damper which is almost certainly not of constant friction coefficient as assumed in the analysis.
These principles will now be applied to a numerical example, the design of
a suspension system for a 5-liter.spherical bottle.
9l

.030.i
_JIm 0.25.O o
1+1
0 DISC| ~ ~/~ E8.eboettle Empty
z/ Bottle full: w
o.o~5 /01
~~~~~I Dato based on ossumed design for
jlJ | 5-liter bottle of this report subjected 3
a | | | -to conditions of spec. MIL. E 5272A
10
0- /
0 10 20 30.40 50 60 70 80 90 I00 tf_
FREQUENCY OF EXCITATION ~CPS
Fig. 8 Amplitude of relative-motion of inner to outer bottle vs. frequency of'excitation,

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1Y ]

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0
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12

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NUMERICAL EXAMPLE
For the 5.eiter spherical bottle, weights were calculated as follows:
Liquid Oxygen 12.3 lb
Inner Bottle and Probe 4~ 5 lb
Total 16o8 lb
Keeping the natural frequency at 10 cps, the spring constant may be calculated as
K = 6.80 W = 6.8 x 16.8 = 114 lb/ino
for each individual springs assuming them to lie at an angle / = 45o, The preload must be set equal to about 17 lb, as previously discussed.
A large number of calculations have been run on various sizes of wavewasher springs for this type of service. The generalization which may be drawn
from these calculations is that the three-wave wire washer is probably as good
a geometry as it is possible to find. The Associated Spring Corp. Handbook
give's the following expressions for wave washers:
44
Ed N
K l. 94 D3'
3: PD
a = 4dS3Na 2
where
K = spring constant, lb/in.
E = modulus of elasticity, lb/sq ino
d = wire diam, in.
N = number of waves
D = mean diam of washer, in.
a= stress, bending, psi
P load, lb.
Using these, a spring is calculated having the following properties:
K = 114 lb/in.
D = 3 ino
d =.040 ino
E = 28 x 106 (stainless steel)
N =3
a a 104,000 psi, under a 3306 lb load.
13

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For the upper spring, a two-armed wire form is chosen as shown in Fig~ 11L,, ~d =._080
5.55- l
Fig. 11. Top-spring geometry,
Treating each half as a cantilever beam, one obtains the following design:~
K = 50 lb/ino
d = o.08o
E = 28 x 106 (stainless steel)
a = 100,000 psi for a load of 16-lb total
h - to suit the design.
The thermal resistance of this system may be approximated by computing the
qu'antity
L
R _.A
and summing for the entire system, giving a measure of the conductive thermal
resistance. For this suspension
RB 71,
while for the suspension it replaces,
R 61,
so that the loss of liquified gas by heat leakage should be better here than in
the original suspension~
14

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REFERENCES
1. Den Hartog, J. P., Mechanical Vibrations, 4th ed., McGraw-Hill Book Co.,
New York, 1956.
2. Milo E5272A, Procedure 1, p. 10o
35 Handbook of Mechanical Spring I)esign, published and distributed by Associated Spring Corporation, Bristol, Connecticut,:
APPENDIX
The coefficient of friction between stainlessmsteel wire and the copperflashed inner surface of a liquid oxygen bottle was measured by rotating a
weighted stainless-steel spring with respect to the copper-plated surtface The
couple necessary to cause this rotation was measured. Six trials gave a mean
value of coefficient of friction of 0,276, yielding a probable error of the
mean of.005, and no readings were rejected by Chauvenet's criterion.
15

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3 9015 02827 4242