CHAPTER 3 STUDIES ON VIBRATION DAMPING IN...

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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.

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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.

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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.

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Table 3.1 Granites selected for compression test

Type Commercial Name of Granite Properties

1KhammamBlack

Gabbro group - probablydolerite

2 Hassan GreenDolerite (gabbro to dioritecomposition)

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 GreenGneiss group - probablymigmatite

9 Imperial White Gneiss group

10 Platinum White Gneiss group - granulite

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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.

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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 136-

06 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.

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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.

Figure 3.3 Processing sequence for the preparation of the test specimen

Crush the granite andclassify into different sizesusing sieve analysis.

Wash the aggregatethoroughly using water toremove the foreignparticles and dry it out toremove the traces of water

Epoxy resin +Hardener

STAGE-1

The aggregate and resinmixture are shaken wellfor degassing, whilefilling the mould.

STAGE-4 STAGE-3

Mix the aggregate andresin mixturethoroughly using astirrer and poured intothe mould.

STAGE-2

Preparation of woodenmould with all inserts

Curing at roomtemperature for threeweeks.

STAGE-5

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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,

3FLyEI (3.1)

From this, the stiffness, k, defined as force per unit deflection was obtained as

in Equation (3.2).

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, FStiffness k EIy (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

MaterialDensity), kg/m3

Young’smodulus (E),

GPa

Poissonratio,

)

Specificweight(E/ )

Cast Iron (FG-250)

7100 100 0.3 0.011

Steel (C-15) 7850 210 0.25 0.027

Epoxy Granite 2300 30 0.25 0.015

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, 14

1dE

(3.3)

Now, calculating the depth ratio for the specimens made of different

material we obtain,

1.35EpoxyGranite CastIrond d (3.4)

1.63EpoxyGranite Steeld d (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 V-

groove made in the specimen. This helps in exact application of load at the

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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

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

Weight

SteelCast IronEpoxy

Granite

L-Block

Dial GaugeHanger

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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

Specimen Deflection(mm)

StiffnessN/mm

Density offabricated

beams(kg/m3)

Weight(kg)

% change inweight

compared toEpoxy Granite

beamCast Iron(FG-250)

0.094 106 7260 1.045 34.95 (+)

Steel

(C-15)0.097 103 7700 0.771 11.8 (+)

EpoxyGranite

0.096 104 2350 0.680 -

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

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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 MaterialDamping

Ratio

( )

NaturalFrequency

(Hz)

DampingTime

(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

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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.