The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure

Gross, Michael

Leifer, Joel

English

NASA Technical Reports Server

N88- 1361 4
Non-Linear Shipboard Shock Analysis of the
TOMAHAWK Missile Shock Isolation System
Joel Lei fer
Michael Gross
The identification, quantification, computer
modeling and verification of the TOMAHAWK
non-linear liquid spring shock isolation system
in the surface ship Vertical Launch System (VLS)
are discussed. The isolation system hardware and
mode of operation is detailed in an effort to
understand the non-linearities. These
non-linearities are then quantified and modeled
using the MSC/NASTRAN finite element code. The
model was verified using experimental data from
the Naval Ordnance Systems Center (NOSC) MIL-S-901
medium-weight shock tests of Aug. 1986. The model
was then used to predict the TOMAHAWK response to
the CG-53 USS MOBILE BAY shock trials of May-June
1987. Results indicate that the model is an accurate
mathematical representation of the physical system
either functioning as designed or in an impaired
condition due to spring failure.
INTRODUCTION
This paper presents the analysis and predicted response of the
TOMAHAWK CG53/VLS shock isolation system during shipboard shock. The
analysis was complicated by the need to identify and quantify several
non-linearities. The heart of the shock isolation system analyzed is
an assembly of liquid springs. The function of each assembly was non-
linear due to geometric clearance (gapping) and loading as a non-
linear function of displacement and velocity. These springs work in
conjunction with the sixteen friction pads that are attached to the
MK-14 canister and grip the AUR.
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97
https://ntrs.nasa.gov/search.jsp?R=19880004232 2020-03-20T09:22:53+00:00Z
The VLS is a modular construction consisting of eight cells.
Seven of the cells contain eight encanistered missiles each. The
eighth cell contains five encanistered missiles and a strikedown
crane. The missiles are TOMAHAWKcruise, Standard Missile Two and
Vertical Launch ASROC. The isolation system study applies only to the
TOMAHAWKmissile in the MK 14 Canister.
LIQUID SPRING HARDWARE
The liquid spring system considered in this paper is designed to
isolate the TOMAHAWK missile in the surface ship Vertical Launch
System from shipboard shock caused by nearby underwater explosions.
Each missile/All-Up Round (AUR) configuration has its own integral
shock isolation system containing four liquid spring assemblies. Each
assembly has a primary and secondary liquid spring working in opposite
directions. The secondary spring has the ability to isolate itself
from the system during the initial pulse by lifting off of its bearing
surface (gapping). Each spring has a resetting spring force that is a
quadratic function of the relative displacement and a damping force
(that varies depending on whether the spring is in compression or
extension). This damping force is a function of the velocity to a
power of .7 as specified on the procurement drawings.
MODE OF OPERATION
The liquid spring assembly experiences four distinct conditions
or modes of operation as it performs its job. These conditions are :
I) Primary in compression and compressing,
secondary gapped - condition 1
2) Primary in compression but extending,
secondary gapped - condition 2
3) Primary in compression but extending, secondary in
compression and compressing - condition 3
4) Primary in compression and compressing, secondary in
compression but extending - condition 4
A plot of a typical spring assembly response is shown in Figure 1
with the occurrence of each condition labeled. The four conditions
are discussed in more detail in the following paragraphs.
The secondary spring is preloaded by pressurizing the cylinder.
This forces the piston to its full one inch displacement. The two
springs are then loaded into the strut and the primary spring is
preloaded by torquing the bolt that bears on the secondary spring (see
Figure 2) to a one inch displacement. The two springs are in series,
but, since the secondary is so much stiffer than the primary, it acts
as a semi-rigid bar and transfers most of the load (and hence the
deflection) into the primary spring. The AUR is then installed,
reducing the preload in the primary spring by an amount equal to its
weight of 3600 ibs. This is the steady state condition.
Condition 1 (see Figure 3) commences when the system is subjected
to a transient excitation in the vertical or X direction. The
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FIGURE 2 LIQUID SPRING ASSEMBLY GEOMETRY
PRELOAD BOLT
GRID 1
MK-14 CANISTER
GRID 2 SECONDARY SPRING
SPRING STRUT
ROD
PRIMARY SPRING
AUR
GRID 3
GRID 4 AUR BASEPLATE
i00
FIGURE 3 PRIMARY IN COMPRESSION AND COMPRESSING,
SECONDARY GAPPED
• % • •
i01
resulting load path is from the MK-14 Canister, thorough the liquid
spring assemblies and into the AUR. Initially, the MK-14 Canister
will move in the X- direction (see Figure 2 for coordinate system
definition), compressing the primary spring. The secondary spring
will gap when the compression force generated in the primary spring
overcomes the remaining primary preload. This remaining preload is
the difference between the initial preload caused by the one inch
compression and the weight of the AUR.
When the acceleration in the X+ direction is of sufficient force
to overcome the momentum in the opposite direction the relative
displacement will have peaked and will begin to decline. This signals
the start of condition 2 (see Figure 4). At this time the primary
spring (which has been compressed) will start to extend. The spring
force stored in the primary spring will add to the acceleration
generated force. The secondary spring will remain gapped until the
primary spring releases its stored spring force by extending to its
original length. The gap will close at the same condition it opened
at, ie, when the force generated in the primary spring by the applied
load is equal to the remaining preload.
The momentum continues in the same direction as in the previous
condition causing the primary to pass to its equilibrium position and
try to extend. At its equilibrium position, however, the secondary
will have closed its gap and will attempt to bear the load. At this
point (the start of condition 3, Figure 5) any compression of the
secondary is accompanied by an equal extension of the primary. The
total load on the secondary is the sum of the applied force and the
stored spring force in the primary. For this analysis, any impact
forces generated by the gap closing are ignored.
At the start of condition 4 (Figure 6) the momentum has shifted
to the X- direction, and the extension in the primary and compression
in the secondary have peaked. The secondary will start to extend,
releasing its stored spring energy in the form of a force which adds
to the acceleration developed force. The sum of these forces is
absorbed by the compressing of the primary spring.
FINITE ELEMENT MODEL
The MSC/NASTRAN [i] finite element computer code was used to
analyze the missile response. MSC/NASTRAN employs the finite element
method to assemble a mathematical model based on user supplied
parameters describing the structure and loading. This model is solved
using a numerical integration technique that steps through time. The
code requires the user to define physical hardware locations (grid
points) and connections (elements) that will result in a mathematical
model representing the system under analysis. The associated geometry,
element selection, and loading are discussed in the following
paragraphs.
The grid points are located using the geometry shown in Figure 2.
Grid point one is located on the end of the preload bolt above the
secondary spring. Grid point five is at the end of the secondary
102
FIGURE 4 PRIMARY IN COMPRESSION BUT EXTENDING,
SECONDARY GAPPED
I
103
FIGURE 5 PRIMARY IN COMPRESSION BUT EXTENDING,
SECONDARY IN COMPRESSION AND COMPRESSING
104
FIGURE 6 PRIMARY IN COMPRESSION AND COMPRESSING,
SECONDARY IN COMPRESSION BUT EXTENDING
I I
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spring piston. Its geometric location is identical to grid point one.
Grid point two is located on the plate that bolts the two springs
together. Grid point three is located at the intersection of the
primary spring and the MK-14 Canister. The base plate adapter is
represented by grid point four.
The grid and element numbering system is shown schematically in
Figure 7. The X axis is positive downward, and the origin is located
at grid point one. The orientation of the Y-Z axes is immaterial for
this model.
The gap element is used to simulate the ability of the secondary
spring (at grid point 5) to separate from the MK-14 Canister (at grid
point i). When the gap is closed (which occurs at steady state and
conditions 3 and 4), the element acts like a rigid bar and causes the
secondary spring to work. During conditions 1 and 2, the gap is open,
and the secondary spring is isolated. The gap condition during
operation is illustrated in Figures 3 through 6.
The rod element is used to model the linear part of the static
spring force. The non-linear part is handled as a non-linear load
(see further discussion below). The static spring force is used as a
reset mechanism to return the assembly to its original position. As
such, it will absorb force when it is being compressed and release the
force when it is extending from the compressed position. The
stiffness is set equal to the linear part of the spring force for both
the primary and secondary springs.
For simplicity, a viscous damper element is used to characterize
the coulomb damping resulting from the MK-14 Canister pads contacting
the AUR. The correct value was determined using an iterative process
of running the model and comparing the results to the experimental
data.
The non-linear load applied to the model consists of the non-
linear static spring force and the velocity dependent spring damping.
The non-linear static spring force consists of a preload and a term
that is a function of the spring displacement squared. The damping is
a function of the velocity to .7 power.
The preload for both springs is ignored. This could be done
since the model was constructed at the steady state assembled
condition.
The squared term for the primary spring is input according to the
liquid spring drawing specifications. The squared term for the
secondary spring is ignored. This is done since the anticipated
secondary spring displacement is about one inch and after squaring and
scaling the resulting force is negligible.
The primary spring damping acts in compression and extension and
removes force from the system in either case. The force was generated
as a function of the relative velocity of the end points of the spring
in accordance with the liquid spring drawing specifications. It was
106
FIGURE 7 LIQUID SPRING ASSEMBLY FINITE ELEMENT MODEL
t IJ--SPRINGODELEMENT
GRID 1 (MK-14CANISTER,
-,- _ POINT OF APPLIED
i EXCITATION)
,_.._ GAP ELEMENT
GRID 5 (TOP OF SECONDARY SPRING)
SECONDARY
I SPRING VISCOUSDAMPER
PRIMARY SPRINC-_ROD ELEMENT
GRID 2 (AUR LOCATION AND POINT OF
APPLICATION OF NON-LINEAR
LOADS)
..L
GRID
PRIMARY
SPRING
VISCOUS
DAMPER
ELEMENT
3 (BOITOM OF
PRIMARY SPRING)
GRID 4 (AUR)
107
anticipated that a spring failure would result in the loss of
extension damping and so the model was constructed to be able to zero
this term. The damping of the secondary spring was ignored. This was
done since the damping force range specified in the liquid spring
drawing is negligible.
The excitation consisted of the MK-14 Canister acceleration.
response in the X or vertical direction was used since it was the
primary load direction.
The
RESPONSE TO NOSC MIL-S-901 MEDIUM-WEIGHT MACHINE SHOCK TESTS
Tests 75 through 86 corresponding to the second canister Launch
Test Inert Vehicle (LTIV) series [2] were chosen to validate the
finite element model. Selected displacement results are shown in
Figures 8 and 9. Model parameters indicate a degradation of the
primary compression damping occurring over tests 75 and 76 (see Table
i) with zero effective primary extension damping. This is an
indication that the springs were malfunctioning. The post test
inspection revealed that three of the four springs had sustained a
tension failure at the attachment of the piston rod to the damper
plate.
The presence of the compression damping can be explained when one
considers how the springs operate as detailed in the preceding
section. At the initial pulse the primary spring is compressed, hence
the compression damping. As the spring starts to expand, the damper
plate (which has broken off from the piston rod, see Figure 2) will be
suspended in the fluid as the piston moves away resulting in zero
extensional damping. At the conclusion of the test the damper plate
will settle onto the piston rod as gravity and time take effect. This
provides compression damping at the start of the next test.
Table 1 Optimized Model Parameters for each Test
test
no
extension compression initial primary
damping damping gap viscous
damping
(-) (-) (in) (ib/in-sec)
secondary
viscous
damping
(ib/in-sec)
75
76
77
78
79
8O
81
82
83
84
85
86
5 -2200 0.02 200
5 -1800 -0.02 i00
5 -1800 -i.i i00
5 -1800 -0.9 200
5 -1800 -0.3 200
5 -1800 -1.6 400
5 -1800 -i.0 150
5 -1700 -2.2 20
5 -1700 -0.5 200
5 -1700 -i.0 i0
5 -1700 -i.0 i0
5 -1700 -0.5 150
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Test 77 (Figure 8) provides an ideal response in that it is
relatively easy to divide the MSC/NASTRANgenerated curve into the
four conditions described previously. Condition one occurs between
time zero and fifteen msec and peaks at 1.05 inches. This is a
primary spring displacement (the secondary having gapped and so
isolated itself at this time) and results in a stored force of 6000
ibs for four springs. The velocity at this time is 0.518 fps which
translates into 6500 ibs of force reduced by the springs. Additional
force is removed by the friction pads.
Condition 2 occurs between 15 and 42 msec. At 42 msec the 6000
ib spring force has been returned to the MK-14 Canister and the
secondary spring gap has closed. No additional force has been removed
from the system by the springs. All damping is due to the friction
pads.
Condition 3 occurs between 42 and 78 msec. The 0.25 in. peak
displacement at this time is an extension of the primary spring and an
equal compression of the secondary spring. The deviation from the
experimental data during this and the next condition is due to the
modeling of the friction pads (coulomb damping) as a viscous damper
element. At low velocities, the viscous damper removes less energy
while the friction pads ,in reality, are removing more energy due to
higher forces.
Condition 4 starts at 78 msec and continues until the
displacement returns to zero. This analysis was stopped at 120 msec
when most of the energy from the shock had been dissipated. This
condition corresponds to a resetting of the spring in preparation for
the next test. The system does not return to the pretest condition.
This can be seen from Table 1 which shows an initial gap corresponding
to the system condition at the end of the previous test. This gap is
caused by the friction pads.
RESPONSE TO CG-53 SHOCK TRIAL
After NOSC test validation the model was used to predict TOMAHAWK
response to the CG-53 shock trial loading. Predictions and validation
were done for TOMAHAWK test missiles designated IOM-A (Inert
Operational Missile), IOM-B, IOM-C, LTIV-I, AND LTIV-3.
After the first shot, the procedure was to validate the model using
the previous shot data (MK-14 Canister and AUR baseplate accelerations
and relative displacement across the liquid springs), scale up this
data by a ratio obtained from analysis of the YORKTOWN shock test
series to make a prediction for the next shot and, at the conclusion
of the next shot, compare predictions with actual data. The YORKTOWN
test series was analyzed due to the ship's similar specifications and
identical shock geometry to the MOBILE BAY's. The procedure was
performed for shots 2 through 4.
Figures i0 through 13 compare the model predictions and
subsequent validations with test data. These results are
representative of the results for all TOMAHAWK test vehicles. The
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model parameters indicated that the springs provided adequate shock
isolation with only a slight degradation of primary spring extensional
damping.
Figure i0 is a plot of model verification for shot 4 IOM-B
relative displacement. Note that conditions 3 and 4 are not as
pronounced as in the NOSC tests. This is due to the availability of
extensional damping (since the spring is not broken) on the primary
spring. Conditions 3 and 4 can be considered as occurring after i00
msec when the system is settling down after its response to the shock.
Figure ii is a plot of the fast fourier transform of the gross
acceleration (experimental and model prediction) for shot 2 LTIV-3
model verification. Figure 12 is a plot of the shock spectrum of the
gross acceleration (experimental and model prediction) for shot 4 IOM-
B model verification. These figures demonstrate that the majority of
energy is concentrated below 50 Hz and the model response is valid to
50 Hz. Therefore, the experimental data is low-pass-filtered at 50
Hz. and compared to the model response (Figure 13) for verification.
Based on Figures I0 thru 13 it is concluded that the finite element
model accurately represents the physical system.
Figure 14 compares the prediction made for shot 4 with the actual
shot results for LTIV-I relative displacement. This model was first
verified for shot 3 before being used for the shot 4 prediction. This
comparison indicates that the scaling ratio obtained from analysis of
the YORKTOWNtest series is reasonable.
Displacement and acceleration predictions agree well with
experimental results indicating that the model can successfully track
the actual TOMAHAWKperformance and that the response from shot to
shot is a linear function of the previous shot.
CONCLUSIONS
Successful analysis of non-linear systems is a three step
process. First the non-linearities must be identified and quantized.
Step two is the selection of an analysis technique and/or computer
code that addresses the identified non-linearities. The final step is
the validation of the model using system data and the subsequent use
of the model in prediction and validation of test results. This
technique was illustrated using the TOMAHAWK shock isolation system
and MSC/NASTRAN finite element computer code with excellent agreement
between model and test results.
REFERENCES
i. MSC/NASTRAN USER'S MANUAL version 65, November 1985.
2. QUICK LOOK REPORT, VLS CANISTER/MISSILE CONFIDENCE SHOCK TEST,
TEST 75-86, NOSC, August 1986.
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Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system

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