chapter - 3 design and analysis of vibration test fixtures
Transcript of chapter - 3 design and analysis of vibration test fixtures
54
CHAPTER - 3
DESIGN AND ANALYSIS OF VIBRATION TEST FIXTURES
Vibration testing requires a test fixture to interface the
specimen and vibration shaker. Vibration test fixtures simulates
mounting interface for both the specimen and vibration shaker on
either side. The purpose of a test fixture is to couple mechanical
energy from a shaker into a test specimen. During the vibration
testing, the effects caused by the fixture are important. Vibration
test fixtures [202] exhibit resonant frequencies in the test
frequency range due to the mass/stiffness characteristics. The
resonant frequencies causes significant problem when conducting
vibration tests. However, vibration controller controls the shaker
input through a feedback accelerometer and controls the level of
vibration input into the test specimen. But, the control
accelerometer controls the level of vibration where the control
accelerometer is bonded. This indicates that the resonant behavior
of the vibration fixture is dependent on the fixture itself. Thus
launch vehicle structures vibration testing poses a challenge to
design and realize a good vibration fixture [170].
55
3.1 TEST FIXTURES DESIGN
3.1.1 Basic Concepts
As a vibration test fixture designer, the following inputs of test
article and test equipment are to be considered prior to designing a
fixture [203].
Details of the shaker table such as pattern of the attachment
holes, bolt size and thread sizes are to be known to which
the fixture attaches.
Size and configuration of the test article
Weight and centre of gravity of test article
Details of the test specimen such as the mounting interface
PCD, its dynamic characteristics
Details of the dynamic test specifications
Test axis for which fixture is designed
Mass that can be attached to the shaker table without
possibly causing damage.
Available shaker rating.
Necessary pre load between the table and fixture.
Awareness of the possibilities of the shaker resonances
Anticipated/repeated usage of the fixture
56
Test article size and configuration are preliminary information
required to size and configure the fixture. Weight of the test item
and its C.G at least an estimate of its location are required to
calculate the combined C.G of the test specimen and the fixture to
fall as close as possible to the centre line of the shaker. The axis of
motion such as X, Y or Z should be defined relative to the test item
or to the assembly into which the item is attached in normal
service.
The test intensities must be known for two reasons,
The inertia force acting on the test item F=WtA must be with
stood by the bolts or other fasteners connecting the test item
to the shaker
There is a limit to fixture weight that can be allowed without
exceeding the force rating of the shaker, since Wa and Wt are
fixed.
3.2 DYNAMIC CHARACTERISTICS OF TEST
FIXTURES
3.2.1 Mechanical Impedance
The concept of mechanical impedance helps explain the
interaction between vibration shaker, fixture and specimen [39]. A
57
simple definition of mechanical impedance is that it is the force
required to produce a desired motion to the specimen. Launch
vehicle equipments are exposed to random vibration excitations
during launch and is functionally designed to survive random
vibration testing. In this testing, the random vibration design
levels are applied at the Vibration shaker-interface. For light
weight aerospace structures, the mechanical impedance of the
equipment and of the mounting structure are typically comparable,
so that the vibration of the combined structure and the load
involves modest interface forces and responses. Where as the
complex space launch vehicle test fixtures will exhibit resonant
and anti-resonant frequencies in the testing frequency band. At
anti-resonant frequencies, force exceeding the capability of
vibration equipment is necessitated to maintain the required test
level. The extra force requirement leads to infinite mechanical
impedance. So, the test fixture has to be designed in such a way
that it should not induce mechanical impedance to the specimen
during testing.
3.2.2 Transmissibility
The fixture must be as stiff as possible so that it is not
deflected by the load and transfers motion with high fidelity. This
58
quality is called transmissibility, which is a comparison of the
output to the input. At a transmissibility of 1.0, the output
faithfully follows input. Ideally, a dynamic test fixture couples the
motion from the vibration shaker table to the specimen with zero
distortion at all amplitudes and frequencies. This ideal is
approached, if the test frequency range is narrow or if the test
specimen is small. Practically, the ideal cannot be met and the
limitation of the fixture must be known. The basic fixture
shortcoming is insufficient stiffness. In theory, with an infinitely
stiff fixture, the natural frequency of the fixture-specimen system
can be made as high as necessary to prevent resonance in the
testing frequency band and to provide a transmissibility of 1.0.
Usually, the natural frequency of the fixture lies within the
test specification range. In this case, the motion delivered to the
test item is higher than the input in the region around resonance
and lower than the input above resonance. Suppose the natural
frequency of a fixture is 400 Hz, and the specification calls for a 5g
vibration from 20 to 2,000 Hz. From fig.4.2 the input to the
specimen is 50g at 400 Hz (F1/Fn = 1.0 and T = 10) and only 0.2g
at 2,000 Hz (F1/Fn = 5.0 and T = 0.04). Most modern test facilities
incorporate automatic amplitude control, so that if the vibration
amplitude is measured at the input to the test specimen, a uniform
59
5g would be applied to the specimen. Thus we might conclude that
stiffness of the fixture is of little consequence in the region of
resonance. But such is not the case; fixture stiffness is still
important. At 2,000 Hz, the shaker has to vibrate at 125g to
provide 5g at the specimen (5/0.04 = 125). Presently, there is no
equipment that can provide this high level of vibration. Therefore,
the test specification cannot be met at high frequencies.
Fig. 3.1 Transmissibility curve for single degree of freedom system
Thus, the most important factor in fixture design is a high
natural frequency above the frequency of interest. However, weight
and cost factors require some design tradeoffs. Weight is a
drawback as it infringes the capability of the vibrator to deliver
enough acceleration to the specimen. Cost considerations influence
whether several single-purpose fixtures or one general purpose
60
fixture will be built. Weight and cost considerations almost always
compromise fixture performance.
3.2.3 Cross axis Response
The armature assembly is designed to move in one direction
and is held centrally by a suspension system. This system is
designed to have high stiffness at right angles to the vibration axis.
If high overturning moments are applied to the armature then the
suspension guide will be compromised. This cross axis force
applied during vibration needs to be understood and kept low so as
not to damage the bearings and armature.
Designing all fixtures to be light and stiff will assist in
preventing unwanted cross axial motion. The centre of gravity
should be precisely calculated and each fixture should be rigidly
coupled to the armature or slip table. If the C. G of the payload is
kept low and aligns with the armature centre then cross axial
stress will be minimized. However if the payload C. G is high or
offset, then a turning moment is introduced during vibration. Each
vibrator has some allowance for cross axis forces and limits the
payloads C. G positional distance to the mounting face.
3.2.4 Fixture-Specimen Resonance
A simple way to model the fixture-specimen dynamic system
is to assume that the test specimen is an ideal, resonant-free mass
61
that loads the fixture. An idea of the fixture design problem in
terms of how stiff the fixture can be obtained from the formula
D = (3.13/Fn) 2,
D = the fixture static deflection caused by the specimen that
produces the desired Fn in inches
Fn = the desired resonant frequency of the specimen-fixture
system.
Preferably, Fn is higher than the test spectrum, but usually
this ideal is impractical or impossible. For instance, many
specifications call for testing up to 2,000 Hz. If, to keep
transmissibility close to 1.0, Fn is targeted for 3,000 Hz, the above
equation shows that the fixture must not deflect more than 1 milli
inch under the weight of the specimen. In most cases, such a stiff
fixture is not feasible. Thus, often it is more convenient to develop
a fixture, compute stiffness, and then solve for Fn using the above
equation. Of course, this approach is crude. But it does provide
order-of-magnitude information. The important factor left out of
the equation is the mass of the fixture itself which acts to reduce
Fn. The amount of reduction varies according to the test
configuration and the ratio of the fixture mass to the specimen
mass.
62
3.3 MATERIAL CHARACTERISTICS
The material should be as low in mass as possible without
detriment to the stiffness. As F=m x a, the material mass will have
an influence on the shakers thrust ability. Often a fixture will be
sculptured and material removed to reduce the mass. The
dynamics of the fixture remain unchanged but the stiffness and
strength may be compromised and should be considered. If the
first resonant frequency can be kept above the test frequency range
the quality of test will be improved. The fixture must be stiff
enough not to influence the test or change during a test. The
fixture will see high stress levels from the applied vibration or the
specimen response and must be strong enough to transmit the
forces and survive the tests. For fixtures with high “Q” resonances,
the control method will require some investigation. If possible it is
preferable to use damping at the fixtures points of influence to
reduce the „Q‟. For example a hollow tube will be damped by filling
it with foam and often clamping or additional supports will prevent
a high „Q‟ response. A fixture needs to be significantly stronger
than the specimen so that it does not fatigue during use. Avoid any
thin brackets, small bolts, sharp corners, overhanging areas and
weak areas that will fatigue quickly improve the quality of the
fixture.
63
3.4 INPUTS REQUIRED FOR TEST FIXTURES
DESIGN
Advanced launch vehicle consists large sub systems such as Heat
shield, CBS, Equipment bay, inter stages ITS, SONC. These
subsystems are to be qualified for the Vibration Environment. By
considering the weights of all sub systems, it is seen that the
maximum weight of the specimen to be tested is 55 kN. The
technical details of the large subsystem are given in table 1&2.
Table 3.1 Large subsystem details
Weight of test specimen 5500 kg
Max dia of specimen at fixture
attachment points
4060 mm
Mounting details of the specimen 13 dia holes, 120 Nos
equispaced on PCD 4030mm
PCD‟s on vibration table for fixture
attachment
1200mm,1000 mm,800
mm,22” ,16” & 8”
Height of C.G of specimen from
fixture interface
1750 mm
Max vibration test acceleration
level
9.6 grms
Instantaneous peak acceleration
level
28.8g
Direction of excitation All three mutually
perpendicular axes.
64
Table 3.2 Dynamic Characteristics
Minimum natural frequency
(fundamental mode)
>100 Hz
Transmissibility at any resonance
frequency
<8
Maximum target weight of fixture <1.5 t
General Configuration Conical shell with
stiffeners / Cylindrical
shell with stiffeners
Flatness at fixture attachment
Interface plane
0.05 mm
3.5 DESIGN OF TEST FIXTURE FOR VERTICAL AXIS
The vertical test setup is made by coupling two
Electrodynamic shakers in vertical axis and a common bare table
is attached to the shakers. The common bare table is called as load
bearing platform (LBP). The LBP acts as a test table in dual shaker
system. The LBP is having a maximum PCD of 1200mm for fixing
the test article/test fixture.
From the technical details of the advanced launch vehicle
sub systems, the sub systems are having interface PCD of
65
4060mm. Where as the LBP is having a max PCD of 1200mm in
vertical mode. Hence, it is not possible to assemble the test
specimen directly on the shaker table. Vibration testing of a sub
system in vertical axis is necessitates an intermediate structure to
connect the test specimen to vibration table. This intermediate
structure is called as vibration test fixture. The test fixture is to be
designed to interface both the PCDs of the test specimen and
shaker table.
It is seen that the maximum weight of the specimen to be
tested is 55 kN. The predicted maximum random vibration test
specification of large subsystems of advanced launch vehicle is 9.6
grms and instantaneous peak acceleration is 28.8 grms (three times
of maximum value). The available force rating of the Dual shaker
system is 300 kN max and 900 kN instantaneous peak.
Fixture Weight = 15kN (assumption)
Large sub system weight =55kN
Instantaneous peak acceleration = 28.8 grms
Force rating required = ((55+15) x28.8)
=2016 kN >900kN (Shaker Capacity)
In view of this, the test accelerations are to be fixed judiciously.
66
By limiting the shaker force to 900 kN,
The peak acceleration the specimen can be subjected
= 900/(55+15) = 12.8grms
Maximum possible „g‟=300/70=4.3g
Static loads on fixture:
Max. test acceleration =9.6 grms
Instantaneous peak acceleration =28.8 grms
Ratio=28.8/9.6=3
max instantaneous force on the fixture due to specimen
=55x4.3x3 =709 kN=710 kN
Load due to self-weight of fixture =15x4.3x3 =193.5 kN
Fig. 3.2 Design calculations in vertical axis
67
After studying number of design configurations with different
parameters of shape, radius, thickness of plates, the test fixture is
configured as an expanding conical structure expands from
1200mm to 4100mm and stiffened with internal and external
radial ribs.
In view of large dimensions and weight, the fabrication method
chosen is welding.
The fixture has overall dimensions of 1460 mm base
diameter and height of 800 mm and at top the flange diameter is
4100 mm. The base plate is 40 mm thick and a tapered conical
shell (tapering from 40 mm to 20 mm thick) of 560 mm height is
an integral part of it (bottom shell). Another tapered conical shell
16 mm thick and height of 247 mm is welded to the bottom shell.
Internally 24 nos of ribs of 16 mm thick are connecting to the
bottom shell and conical shell and externally 30 Nos of 16 mm
thick stiffeners are connecting the bottom shell, tapered conical
shells and top flange. Holes of 13 mm dia (total 81 nos) are
provided on base plate on 22”, 800,1000,1200,1400 mm PCDs to
suit the vibration table. Interfacing of the fixture to the specimen is
through 90 Nos of 13 dia holes provided on 3240 mm PCD and 120
Nos of 13 dia holes provided on 4030 mm PCD on top flange.
68
Fig. 3.3 Vertical axis test fixture modal
3.6 DESIGN OF TEST FIXTURE FOR HORIZONTAL
AXIS
The horizontal test setup is made by coupling two
Electrodynamic shakers in horizontal axis and connected to a large
slip table. The large slip table acts as a test table in horizontal
testing. The large slip table is having a maximum PCD of 2800mm
for fixing the test article/test fixture. From the technical details of
the advanced launch vehicle sub systems, the sub systems are
having interface PCD of 4060mm, where as the slip table is having
a max PCD of 2800mm. Hence, it is not possible to assemble the
test specimen directly on the large slip table. Vibration testing of a
69
sub system in horizontal axis is necessitates an intermediate
structure to connect the test specimen to slip table. The test fixture
is to be designed to interface both the PCDs of the test specimen
and slip table.
The available Max force rating of the shaker = 300kN
Instantaneous Force rating (Dual Shaker mode) = 900kN
Overturning moment of the large slip table = 1600kNm.
Since the test specifications called for testing the specimens
beyond the available full force rating & over turning moment
considerations
Required max force rating: 1872kN
Required overturning moment= 3283kNm (with a CG height of
2.0m from the base),
It was necessary to revisit the test specifications. Accordingly the
specifications are revised.
Design overturning moment capacity of Large Slip Table
= 1600 kNm
Max mass of specimen = 55 kN (cg at 2 m from Large slip table)
Mass of fixture = 0.963 t (cg at 0.14 m from slip table)
Moment due to specimen and fixture @ 1g lateral acceleration
70
(5.5*2 + 0.963*0.14) *10 = 111.34 kNm
Max acceleration for design = 1600/111.34 = 14.37 g
Lateral force applied = 5.5*14.37*10 = 790.35 kN
Moment on the top flange of fixture = 790.35*1.75 = 1383.11 kNm
These loads are applied on the fixture interface for finite element
analysis
Support condition due to tightening torque
Tightening torque considered (T) = 66 Nm
(on all 60+60 Nos of M12 bolts)
Pretension in bolt due to the initial torque P
P = T/ 0.2d = 27.5 kN per bolt
Total load applied at the interface of fixture and slip table
= 27.5*120 = 3300 kN
Area of base plate = 1.672e6 mm2 (OD- 2912 / ID- 2520 mm)
Compressive stress at interface = 2 MPa
Moment = 1600 kNm
I and Z of base plate = 1.55e12 mm4 and 1.064e9 mm3
Bending stress due to moment = 1.5 MPa
Since the compressive stress at the interface is more than
the Bending stress due to overturning moment the surfaces are
always in contact and the entire surface can be considered as
participating.
71
With a target weight < 1.0t, number of design configurations with
different parameters, shapes, radius and thickness of plates are
studied. Finally, the fixture is configured as a cylindrical structure
stiffened with radial ribs.
Fig. 3.4 Horizontal axis test fixture modal
3.7 MATERIAL SELECTION FOR FABRICATION
Materials generally considered for vibration fixtures like
Stainless Steel, Aluminum, Magnesium have similar E/ ρ ratio
(ratio of Young‟s modulus to density) not affecting the natural
frequency of the fixture. However, when the shakers are operating
at their full performance level, like in the present case, weight of
72
the fixture dominates the selection of the material. Composite
materials [176] though are ideal for fixture to test large and heavy
specimen, fabrication of the same is highly difficult. Though
Magnesium is a lighter metal, fabricability issues and availability
of indigenous fabrication techniques have compelled to choose
Aluminum alloy AA6061-T6 as the candidate material. The fixture
is fabricated (an all welded structure) from Aluminum alloy
AA6061-T6 plates (Physical properties: young‟s
Modulus=0.689MPa, Density =2700kg/m3, Fatigue strength:
96.5MPa, yield strength: 276MPa, poison‟s ratio: 0.33) based on
the lightness and fatigue strength requirements of the fixture. The
fixture is cylindrical in shape with top flange having internal and
external ribs.
Alloy 6061 is one of the most widely used alloys in the 6000
Series. This standard structural alloy, one of the most versatile of
the heat-treatable alloys, is popular for medium to high strength
requirements and has good toughness characteristics. This alloy
is having good damping property. Applications range from
transportation components to machinery and equipment
applications to recreation products and consumer durables. Alloy
6061 has excellent corrosion resistance to atmospheric conditions
and good corrosion resistance to sea water. This alloy also offers
good finishing characteristics and responds well to anodizing;
73
Alloy 6061 is easily welded and joined by various commercial
methods. Since 6061 is a heat-treatable alloy, strength in its -T6
condition can be reduced in the weld region. Selection of an
appropriate filler alloy results in the desired weld characteristics.
3.8 FINITE ELEMENT ANALYSIS
Ansys Workbench is a computer based analytic tool for
solving problems related to structures [159]. Both the fixtures are
modeled in work bench as per the finalized configuration. As per
the requirements, drilled holes in the specified PCDs are
incorporated in the top and bottom flanges. The structural design
starts with modeling of the structure by dividing it into an
equivalent system of simple elements (solid elements) such as
quards or triangles, with easily obtained stress and deflection
characteristics [191]. Initially free mesh is used by considering
solid (quard) element. Afterwards element size was modified and
solved to get improvements in the results. Upon specifying the
material, material properties, boundary conditions, and loads, the
analysis is completed by computer programs, utilizing arrays of
matrix equations.
74
FEA allows the determination of free vibration natural
frequencies and the associated mode shapes of a structure [172,
189]. It provides valuable information for use in the design stages
of a program, allowing optimization of the design by varying key
parameters [173]. The major issue with the use of FEA‟s is the
relatively high cost associated with modeling, impute properties
and loads, debugging, running of the computer analysis,
interpreting of results etc.
3.8.1 Vertical Axis Test Fixture Analysis
The following FE Analyses are carried out for the vertical axis test
fixture.
Modal analysis of the fixture:
In this analysis boundary conditions is: Bottom plate is
fixed in all degrees of freedom.
Static analysis of the fixture:
In this analysis boundary conditions are: 1) Bottom plate
is fixed in all degrees of freedom. 2) Load of 710 kN
applied on the top flange of the fixture and load due to
12.8g acceleration on the fixture is applied.
75
3.8.1.1 Vertical Axis Test Fixture Analysis Results
Table 3.3 Modal & Static Analysis Results of vertical fixture
1st Natural frequency mode 123.5 Hz
Max Von mises stress (local) 199.6 to 224.6 N/mm2 (Middle of
the ribs)
Max Von mises stress (general) 25 to 100 N/mm2
Normal stress (SY) 57.3N/mm2 (At some discrete
locations)
3 to 40N/mm2 (general)
Deflection (Y-axis) 4.7mm
Max bolt load 36.4kN
3.8.2 Horizontal Axis Test Fixture Analysis
The following FE Analyses are carried out for the horizontal axis
test fixture.
Modal analysis of the fixture:
In this analysis boundary conditions is: Bottom plate is
fixed in all degrees of freedom.
76
Static analysis of the fixture:
In this analysis boundary conditions are: 1) Bottom
plate is fixed in all degrees of freedom. 2) Vibration
analysis along lateral axis is carried out for a load of
14.34g applied to the specimen and fixture. Lateral load
of 790.37kN and moment of 1383.11kNm applied at the
fixture flange in addition to the self weight of the fixture
3.8.2.1 Horizontal Axis Test Fixture Analysis Results
Table 3.4 Modal & Static Analysis Results horizontal fixture
First Natural Frequency 323Hz
Max von mises stress in bolt location 203 MPa
Von mises stress in other locations < 60 MPa
Max bolt load 100 kN
3.9 FABRICATION OF TEST FIXTURES
The vertical axis fixture is having a conical section and a top flange
with external and internal ribs. The base conical portion wall
thickness is varying. The sections are welded along the hoop and
in radial direction. Welding of Aluminum alloy AA6061 is very
critical and requires very clean finish to attain high welding
77
efficiency. Due to the lengthy weld joints, the weld distortions were
high. Especially, the two conical sections joining were very critical
(to attain the required geometric tolerance). Initially during the
fabrication phase, even after taking adequate precautions, there
was noticeable deformation of top flange and top cone portion. To
overcome the noticeable deformation on top flange, the supplier
filled the top flange with metal deposit thus introducing weld
deformation gone at flange to conical weld region. Full welding of
the external ribs induced few distortions, which was corrected
using jacks. The horizontal axis test fixture is fabricated by taking
necessary precautions to avoid the difficulties faced during vertical
axis fixture fabrication.
78
Fig. 3.5 Fabricated vertical axis test fixture
Fig. 3.6 fabricated horizontal test fixture