40
CHAPTER 3
STUDIES ON VIBRATION DAMPING IN EPOXY
GRANITE AND METALLIC BEAMS HAVING EQUAL
STIFFNESS
3.1
INTRODUCTION
In the previous chapter, the methodology adopted in this work and
the main objectives of this study were discussed. Chapter 1 speaks about the
selection of the aggregate in the mineral cast and its importance as the
properties of aggregate selected play a vital role in the properties of the
mineral cast developed. In this study, the selection of aggregate, the aggregate
and resin mixture preparation are discussed. The five different stages of a
processing technique, followed in this work, to fabricate mineral cast
structure, is established.
Studies were conducted on fabricated beams made of cast iron, steel
and epoxy granite having equal stiffness. The dynamic characteristics were
analysed, to study the suitability of mineral cast epoxy granite as alternate
material for machine tool structures.
3.2
AGGREGATE SELECTION
Granite, discussed in chapter 1, was found to be a suitable aggregate
material for fabricating machine tool structures. In this work, commercially
defined granite, available in Tamil Nadu (S India) was selected for analysis.
41
In order to select the granite with better properties, the
commercially available granites were selected and studied. Hardness and
compression strength are two important characteristics required by structural
parts of a lathe bed. Hence, granite having better hardness and compression
strength was selected as aggregate. Ten different granite groups were
identified and selected based on their hardness, as explained in the following
section. These granites were subjected to compression tests. The granite
having better compression strength was selected.
3.2.1
Hardness Test
Moh’s Hardness Scale explained in section 1.5.2.2 was used to
determine the hardness of the granite. The granites having hardness between 6
and 7 in the Moh’s Scale, i.e, harder than orthoclase and softer than quartz
were selected. The selected granites and their commercial names (Daniel
Pivko, 2005) are given in Table 3.1. These granites were subjected to
compression tests, to select the one with higher compressive strength.
3.2.2
Compression Test
The granite slabs having 20 mm and 30 mm thickness were found to
be commercially available. For conducting the compression test, 30 mm thick
granite slabs were selected. The granites selected were cut into small cubes of
30 mm side and subjected to uni-axial compression in a hydraulically
operated conventional compression testing machine. The load was applied
gradually until a visible crack was developed on the granite. The load
corresponding to this initial crack was noted. The compressive strength for the
specimen was then calculated from basic principles.
42
Table 3.1 Granites selected for compression test
Type
Commercial Name of Granite
Properties
1
Khammam
Black
Gabbro group - probably
dolerite
2
Hassan Green
Dolerite (gabbro to diorite
composition)
3
Jhansi Red
Granite
4
Juaprana India
Gneiss group - migmatite
5
Forest Green
Granite
6
Black Pearl
Probably Gabbro group
7
Copper Silk
Probably granite
8
Kuppam Green
Gneiss group - probably
migmatite
9
Imperial White
Gneiss group
10
Platinum White
Gneiss group - granulite
43
The compressive strength data obtained for the granite specimens
selected are shown in Figure 3.1.
It was observed that the compressive
strength lies in the range 150-250 MPa for the granite selected.
Figure 3.1 Compressive strength for commercial granite selected
In this work, the granite, commercially named as Jhansi Red (type
3), which comes under granite group was found to have better compressive
strength (246 MPa) compared to other granite groups selected for analysis.
Hence, Jhansi Red was selected and used as the aggregate material for
preparing the mineral cast specimen.
3.3
PROCESSING TECHNIQUE
In this section, the method used for the fabrication of test specimen
is discussed. The five different stages of fabrication described in the following
sections, 3.3.1 to 3.3.5 were combined to develop a processing method for the
mineral cast structures.
44
The aggregate used is a combination of different sizes of granite
particles and the resin mixture used as binder material is a combination of
epoxy resin and hardener. Epoxy resin is used as the binder, considering its
benefits discussed in chapter 1, compared to polyester resin. In stage 1, the
aggregate mixture and resin mixture were developed as described below.
3.3.1
Aggregate Mixture
The selected granite material was crushed using a crusher and
classified into three different grades using sieve analysis as per ASTM C 13606 standards. The Tyler Mesh Size method explained in section 1.8.1.3 has
been used to classify the particles into coarse particles, medium particles and
fine particles as shown in Figure 3.2.
The aggregate mixture selected consists of three different sizes of
granite particles mixed in the ratio 50:25:25 (Coarse : Medium : Fine). Kim et
al (1995) and Orak (2000) had studied the composition of mixtures and
reported that “the bigger particles selected in higher proportion gives strength
to the structure and the medium and fine particles reduce the void formation
in the structure manufactured.”
The crushed granite particles were washed thoroughly in water to
remove any foreign particles in it. It was then dried in hot air conditions to
remove the traces of water in it. The above process was done for proper
binding of the particles, when resin is added.
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Coarse particles: granite particle size ranging
between 1.4-2.38 mm;
Medium
particles:
particle
size
between
0.5-1.4 mm;
Fine particles: powdered granite particles with size
less than 0.5 mm.
Figure 3.2 Classification of aggregate particles
3.3.2
Resin Mixture
The resin mixture consists of 12% epoxy resin (Araldite LY 556 CS
110KG Q2) by weight and 1% by weight of resin used in the mixture as
hardener (Aradur HY 951 IN 20X 1KG I1), was used as the matrix or binder
material. The characteristics of the resin and hardener supplied by a local
vendor (Huntsman), follows ISO 10474 3.1B standards.
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3.3.3
Preparation of the Wooden Mould
In stage 2, a wooden mould was prepared to the required size and
shape of the specimen. Plywood having 5mm thickness was used to prepare
the mould. The different parts of the moulds were assembled together using
screws.
3.3.4
Specimen Preparation
The test specimen of required and size and shape was prepared in
stages 3, 4 and 5. In stage 3, the aggregate mixture and resin mixture prepared
in stage 1 and selected in required ratio were mixed thoroughly using a
concrete stirrer. The aggregate-resin mixture was poured into the wooden
mould and shaken well using a shaker to which the mould is mounted in stage
4. The shaking of mould while filling the mixture helps to remove the air
bubbles and proper filling of voids (Sridhar et al 2011).
Epoxy resin used as the binder material, is able to act as a lubricant
in its liquid phase. This helps the granular structure to form itself into
minimum space. When the particles are shaken well, it is possible to establish
good stone to stone contact minimizing the influence of resin material. Hence,
after curing, the structure provides characteristics close to the granite, which
is used as the aggregate material.
3.3.5
Curing
In stage 5, the test specimen was cured. Curing is the time between
pouring of material into the mould and the concrete attaining its full strength.
The curing time, for the epoxy granite specimen with 1% by weight of
hardener mixed with resin is given as 24 hours by the resin supplier.
47
Vipulanandan et al (1993) reported that, the compressive strength
and modulus are optimum when the polymer concrete structure was cured for
21 days. Hence, in this study the fabricated specimen was cured for three
weeks, at room temperature for better results.
The five different stages in the fabrication of epoxy granite
specimens, followed in this work, are shown in Figure 3.3.
Crush the granite and
classify into different sizes
using sieve analysis.
Wash the aggregate
thoroughly using water to
remove the foreign
particles and dry it out to
remove the traces of water
Epoxy resin +
Hardener
STAGE-1
Curing at room
temperature for three
weeks.
STAGE-5
The aggregate and resin
mixture are shaken well
for degassing, while
filling the mould.
STAGE-4
Preparation of wooden
mould with all inserts
STAGE-2
Mix the aggregate and
resin mixture
thoroughly using a
stirrer and poured into
the mould.
STAGE-3
Figure 3.3 Processing sequence for the preparation of the test specimen
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3.4
FABRICATION OF BEAMS HAVING EQUAL STIFFNESS
It has been observed from available records that many studies were
done to find out the suitability of polymer concrete materials in replacing the
conventional materials. However, no studies have been found that compares
the material properties when the parts possess equal stiffness. A study of
structures having equal stiffness will provide a better comparison of size,
weight, damping properties for the machine tool structure manufactured using
alternate composite materials.
3.4.1
Fabrication
In this study, epoxy granite, steel and cast iron structures exhibiting
equal stiffness were fabricated. Cast iron and steel are the conventional
materials for machine tool structures and the epoxy granite is the polymer
concrete material used in this work for evaluation. A rectangular beam was
selected for analysis to simulate the machine tool components such as the bed
and column. The stiffness equations for bending beams reported by Thomson
(1981) were used in this analysis to arrive at the dimensions for beams
selected.
From first principles, for a beam subjected to bending loads, the
deflection (y) is proportional to the load (F) applied and the cube of the length
(L) of the beam and inversely proportional to its flexural rigidity (EI) as given
in Equation (3.1) below,
y
FL3
EI
(3.1)
From this, the stiffness, k, defined as force per unit deflection was obtained as
in Equation (3.2).
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Stiffness, k
F
y
EI
(3.2)
Hence, for beams having equal stiffness, (i.e., the beams deflect
equally when subjected to same load), their flexural rigidity ‘EI’ will be
constant. The Young’s modulus [E] is a material property, which represents
the material stiffness and the moment of inertia (I) is a structural property
which gives geometric stiffness.
The properties of cast iron (FG 250), steel (C15) and polymer
concrete (epoxy granite) materials selected for analysis are given in Table 3.2.
Table 3.2 Material properties for analysis
Density
), kg/m3
Young’s
modulus (E),
GPa
Poisson
ratio,
)
Specific
weight
(E/ )
7100
100
0.3
0.011
Steel (C-15)
7850
210
0.25
0.027
Epoxy Granite
2300
30
0.25
0.015
Material
Cast
Iron
(FG-
250)
In this study, the aspect ratio, that is, the depth (d) to breadth (b)
ratio and the length for the beams were taken as a constant. For analysis and
fabrication purposes, the aspect ratio for the beams in this study was taken as
2. The breadth and width for the beam are shown in Figure 3.4.
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Figure 3.4 Representation of breadth and width for the beam section
Hence from Equation (3.2, it is evident that the depth is inversely
proportional to (E) 1/4.
i.e, d
1
(3.3)
1
E4
Now, calculating the depth ratio for the specimens made of different
material we obtain,
d EpoxyGranite
1.35 dCastIron
(3.4)
d EpoxyGranite
1.63 d Steel
(3.5)
This indicates that, in order to obtain equal stiffness, the breadth or
depth of epoxy granite beam have to be increased by 35% as compared to cast
iron beam and 63% as compared to steel beam. The dimensions for equal
stiffness, for the beams selected for analysis are shown in Figure 3.5. The
dimensions for steel beam are fixed at 10x20x500 mm and those of cast iron
and epoxy granite beams were obtained using Equation (3.4) and Equation
(3.5).
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Figure 3.5 Dimension for the specimens
The dimensions for epoxy-granite 16x32x500 mm meets the
requirements as per DIN 51290 section-3, standards. In this code the lower
limit values are given such that, the smallest test samples are not allowed to
be less than three times the biggest grain size in case granulated aggregate is
used.
3.4.2
Deflection Analysis
To determine the deflection characteristics experimentally for the
specimen prepared was developed. A schematic and photograph of
experimental setup developed are shown in Figure 3.6 (a) and Figure 3.6(b)
respectively. The experimental set up consists of two L-shaped cast iron end
blocks connecting a split type cast iron module at the centre. The three
cavities in the central module were used to hold the test rods prepared. The
end blocks and the central module were well fastened using screws.
The hanger at the end of the rod, used to carry the weights, was
made of cast iron. A V-shaped plug in the hanger block match with the Vgroove made in the specimen. This helps in exact application of load at the
52
point desired. The weight of the specimen prepared was found out using a
common balance.
Figure 3.6(a) Schematic diagram for experimental setup used for
measuring stiffness
L-Block
Hanger
Steel
Cast Iron
Epoxy
Granite
Dial Gauge
Weight
Figure 3.6(b) Experimental setup for measuring stiffness.
The epoxy granite, cast iron and steel test specimens of required size
were manufactured as single pieces and fixed into the test set up as shown
above in Figure 3.6(b). To obtain the deflection characteristics for the
53
specimen developed, a load of 10 N was applied in the hanger (Load applied
includes the weight of the hanger) attached at the end of the beam. The
deflections were obtained using a Baker make, plunger type dial gauge having
least count of 10 micron. The deflections noted down from the dial gauge and
weights of the specimen manufactured are given in Table 3.3.
Table 3.3 Deflections obtained from experiment
Weight
(kg)
% change in
weight
compared to
Epoxy Granite
beam
7260
1.045
34.95 (+)
103
7700
0.771
11.8 (+)
104
2350
0.680
-
Density of
Stiffness fabricated
beams
N/mm
(kg/m3)
Specimen
Deflection
(mm)
Cast Iron
(FG-250)
0.094
106
0.097
0.096
Steel
(C-15)
Epoxy
Granite
It was observed that, the deflections obtained for all the three loads
vary within 2%. The variation could be due to the round off values taken for
dimensions while fabricating and are in acceptable limits.
The weights for the beams fabricated were found out using a
common balance. The weights obtained are given in Table 3.3. It was
observed that the weight of the mineral cast epoxy granite beam is about
34.95% less than that of a cast iron beam, and about 11.8% less than that of a
steel beam having same stiffness.
Even though the area of cross section of the epoxy granite beam is
1.77 times more than that of cast iron beam and 2.56 times more than that of
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steel beam, the weight of the epoxy granite beam, having equal stiffness, was
found to be lesser. The reduction in weight can be attributed to the lesser
density, about one-third of the cast iron, for the epoxy granite material
developed.
3.5
DETERMINATION OF DAMPING CHARACTERISTICS
The main elements of the machine tool structures are bed support,
column and the head. In this study, machine tool structures are represented by
simple rectangular beams. The damping characteristics of these beams made
of epoxy-granite, cast iron and steel having equal stiffness as explained in the
previous section are examined.
3.5.1
Experimental Setup
An experimental setup similar to the one devised by Wakasawa et
al, (2004) was developed for determining the damping characteristics. Figure
3.7 shows the schematic representation of experimental setup used in this
study for measuring frequency response.
Figure 3.7
Schematic diagram of the experimental apparatus used for
measuring frequency response
55
The test specimen was suspended by stainless steel wires at the
position of the nodes of the fundamental vibration mode and the center was
impacted by an impulsive hammer.
The output signals from the accelerometer were conditioned in a
signal conditioner connected to a Data Acquisition System (DAQ). The
signals were given as input into a personal computer, programmed with Lab
VIEW. The LabVIEW Programme code developed for this analysis is given
in Appendix I.
3.6
RESULTS AND DISCUSSIONS
The frequency response curves obtained were captured using Lab
VIEW.
The outputs obtained for the epoxy granite, cast iron and steel
specimens having equal stiffness are shown respectively through Figures 3.8
to 3.10. The wide frequency response curves for the epoxy granite indicate a
higher damping ratio. The half-bandwidth relationship given by Thomson
(1981) and Rao (2009) explained in Appendix 3, was used to determine the
damping ratio, from the frequency response curves obtained experimentally.
The damping ratio, damping time and the fundamental natural
frequencies obtained for the beams are given in Table 3.4.
Figure 3.8 Frequency response curve for Epoxy Granite specimen
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Figure 3.9 Frequency response curve for Cast Iron specimen
Figure 3.10 Frequency response curve for Steel specimen
Table 3.4 Damping Characteristics for the fabricated specimens
Sl.No
Material
Damping
Ratio
Natural
Frequency
Damping
Time
( )
(Hz)
(Seconds)
1
Epoxy Granite
0.032
310, 790
0.05
2
Cast Iron
0.017
290, 790
0.38
3
Steel
0.002
290, 780
0.8
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It was observed that, the epoxy granite beam has a higher damping
ratio, 1.9 times higher than that of cast iron beam and an order higher than
steel beam, for the same stiffness. The fundamental frequency for the epoxy
granite beam was found to be shifted towards right compared to the cast iron
and steel beams having equal stiffness.
Fundamental frequency is a function of structural rigidity (EI) and
mass density ( A). In this study, the structural rigidity for the beams was kept
constant. Hence, the fundamental frequency depended on mass density. The
mass density for the epoxy granite beam is lesser than that of steel and cast
iron; hence there is a shift in natural frequency towards right.
The time taken to dissipate the vibration into infinitesimally small
amplitude is known as damping time. It was observed that the damping time
for epoxy granite beam was much smaller than the other two beams having
equal stiffness. The outstanding material damping could be due to the
granular materials used in the fabrication of epoxy granite beam.
Figure 3.11 Comparison of damping properties
58
A comparison of the damping ratio of the epoxy granite material
developed with the commercially available granite epoxy materials is made
and is shown in Figure 3.11.
Harcrete is a proprietary polymer composite from Hardinge
developed harcrete with epoxy and 93% granite. American ITW Philadelphia
Resins Polymer Casting Division developed Zanite (www.zanite.com), a
composite with epoxy and 91-93% weight of granite. Orak (2000) had
reported a damping ratio of 1.7% for a polyester concrete developed with
polyester resin and white quartz. Comparing the damping ratio of these
materials with the developed one, it was observed that, the material developed
is better compared to solid harcrete and polyester concrete, but inferior to
Zanite.
3.7
CONCLUSIONS
In this chapter, the selection of aggregate material from the
commercially available granites is discussed. The aggregate particles, their
classification based on particle size and the mixture ratio are discussed. An
overview of the processing technique developed for the fabrication of mineral
cast test specimen is discussed. This method is used to fabricate the test
specimen of required size and shape, used in this work.
The deflection analysis carried out on the fabricated beams
indicated equal stiffness for all beams along with considerable weight
reduction of about 34.95% compared to cast iron beam and 11.8% compared
to steel beam.
From the vibration characteristics studied for the beams, it is found
that, the damping ratio for the epoxy granite beam is 1.9 times more than that
of cast iron beam and an order higher than that of steel beam. The damping
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time for the epoxy granite beam is observed to be much smaller compared to
cast iron and steel beams. The fundamental frequency of the epoxy granite
beam was observed to be shifted towards right compared to the cast iron and
steel beams having equal stiffness.
Based on this analysis, to determine the suitability of epoxy granite
as alternate material for machine tool structures, the mechanical and thermal
characteristics has been evaluated as discussed in the next chapter.