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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].

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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

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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

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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

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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

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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

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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

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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.

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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.

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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.

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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

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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.

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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

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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.

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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

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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

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(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.

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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

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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;

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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.

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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.

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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.

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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

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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.

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Fig. 3.5 Fabricated vertical axis test fixture

Fig. 3.6 fabricated horizontal test fixture