COMPOSITES FOR MACHINE TOOL BEDS Department of Mechanical Engineering ROURKELA (INDIA)

COMPOSITES FOR MACHINE TOOL BEDS Department of Mechanical Engineering ROURKELA (INDIA)
COMPOSITES FOR MACHINE TOOL BEDS
THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF TECHNOLOGY
IN
PRODUCTION ENGINEERING
By
B.SRIKANTH
209ME2208
Department of Mechanical Engineering
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA (INDIA)
2011
COMPOSITES FOR MACHINE TOOL BEDS
THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF TECHNOLOGY
IN
PRODUCTION ENGINEERING
By
B.SRIKANTH
209ME2208
Under the supervision of
Prof. B.K.NANDA
Department of Mechanical Engineering
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA (INDIA)
2011
Dedicated to my parents & guide
*
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA
CERTIFICATE
This is to certify that work in this project report entitled, “COMPOSITES FOR MACHINE
TOOL BEDS” by B.SRIKANTH has been carried out under my supervision and guidance in
partial fulfillment of the requirements for the award of Master of Technology Degree in
Mechanical Engineering with “Production Engineering” specialization during session 20092011 in the Department of Mechanical Engineering, National Institute of Technology, Rourkela.
To the best of my knowledge, this work has not been submitted to any other university/ institute
for award of any Degree or Diploma.
Date
(Dr. B.K.NANDA)
Dept. of Mechanical Engineering
National Institute of Technology
Rourkela-769008
i
ACKNOWLEDGEMENT
It gives me immense pleasure to express my deep sense of gratitude and regards to my guide Dr.
B.K. Nanda, Dept of Mechanical Engineering, NIT Rourkela for kindly providing me to
work under his supervision and guidance. I extend my sincere indebtedness to him for his
valuable guidance, constant encouragement & kind co-operation throughout period of work
which has been instrumental in the success of thesis.
I am thankful to Dr. R. K. Sahoo, Professor and Head, Dept. of Mechanical Engineering for
extending all possible help in carrying out the dissertation work directly or indirectly.
I further cordially present my gratitude to Mr.Kunal Nayak for his indebted help in carrying
out experimental work and valuable suggestions.
Special thanks to my parents & elders without their blessings & moral enrichment I could not
have landed with this outcome.
I am greatly thankful to all the staff members of the department and all my well wishers,
classmates and friends for their inspiration and help.
Date
B.SRIKANTH
209ME2208
ii
ABSTRACT
In general, machine tool structures like lathe, milling, broaching, and grinding machines, etc. are
subjected to regular unwanted vibrations. These machine tool vibrations or chatter are
deleterious to machining operations. It results in degraded quality on the machined parts, shorter
tool life, and unpleasant noise, hence are to be necessarily damped out. The important
characteristics of the machine tool structures for metal cutting are high damping and static
stiffness which ensure manufacture of work pieces of the required geometries with acceptable
surface finish at the required rate of production in the most economical way. The unwanted
vibrations must be arrested in ordet to ensure higher accuracy along with productivity.
In the present work, the chatter vibrations on a slotted table Horizontal Milling Machine have
been damped out using composite structure as a substitute for the base of the work piece. Glass
Fiber Polyester and Glass Fiber Epoxy plates are fixed on to the slotted table as a secondary bed
material and the workpiece is mounted on this bed for feeding to the rotating milling cutter.
Initially four holes are drilled on each plate of the composite and a set of five plates of each type
of composite are mounted for conducting the experiments. A mild steel specimen of similar
dimension of the composite plate is placed on the pile of the composites and the setup is fixed to
the slotted table using bolts and nuts. An up milling operation is carried out and the vibration
signal is recorded on the screen of the digital phosphorus storage oscilloscope. The signal and
RMS amplitude, frequency and time period of vibrations are recorded. The experiment is
repeated for different sets of composite plates by decreasing the number and the corresponding
readings are recorded and tabulated. Moreover, experiments are also conducted without any
composite material below the mild steel specimen. It is observed that the vibration amplitude
decreases with increase in number of layers of sheets of composites and then increases with
increase in number of plates. Moreover, the optimum number of composites are also
experimentally determined. The design of the experimental setup has been modeled using
CatiaV5R15.
Apart from total damping of the system, emphasis has also been focused to find out the material
damping of the composite materials so as to select the same for effective damping of the
structures. An energy balance approach has been used for calculating the material damping of the
fiber reinforced composites used in the experiment.
iii
CONTENTS
Page
no.
i
Description
Certificate
Acknowledgement
ii
Abstract
iii
Contents…
iv
List of figures
vi
List of tables
viii
Nomenclature
ix
Chapter 1 Introduction
1.1 Machine tool vibrations and their adverse effects
1
1.2 Main objective of the research work
1
Chapter 2 Literature Review
2.1 Introduction Introduction to machine tools
2
2.2 Damping overview
3
2.3 Review on Research done in Damping of Composite materials
4
2.4 Review of the previous work done on the machine tool structures
6
Chapter 3 Composites
3.1 Composite Materials
8
Chapter 4 Milling Machine
4.1 Milling Machine
4.1.1 Horizontal knee-and-column mill
4.2 Milling Operation
10
10
11
4.2.1 Up Milling
12
4.2.2 Down Milling
12
4.3 Vibrations in Machine Tools
13
4.4 Chatter in Milling Machine
14
iv
Chapter 5 Damping
5.1 Definition of damping
15
5.2 Types of Damping
16
16
16
16
17
5.2.1 Material damping
5.2.2 Structural damping
5.2.3 Fluid damping
5.3 Damping Mechanisms in Composite Materials
5.4 Damping in machine tools
17
18
Chapter 6 Material damping
6.1 Energy balance approach
6.1.1 Two phase model
6.1.2 Three phase model
6.1.3 Modified three phase model
6.2 Calculating material damping of Glass fiber polyester
23
6.3 Calculating material damping Glass fiber epoxy
6.4 Material damping of sandwich plates Glass fiber epoxy and polyester
Chapter 7 Experimentation
7.1 Experimental set-up
28
7.2 Instrumentation
29
7.3 Experimental procedure
Chapter 8 Results and Discussion
8.1. Experimental results
37
8.2 Discussions
Chapter 9 Conclusion
51
Chapter 10 Scope for future work
52
References
53
v
LIST OF FIGURES
Title
Figure no.
pPage no.
3.1
Types of fiber reinforced materials
8
4.1
Horizontal Knee and Column Milling Machine
11
4.2
Up milling or Conventional milling
12
4.3
Down milling or climb milling
12
5.1
Mass spring damper system
15
6.1
RVE loaded in 1-direction,Voigt model: matrix(m) and fibers(f) are
19
connected in parallel
6.2
RVE with three phases: the matrix(m) and fibers(f) and the interphase (i)
22
6.3
Three phase model with strain and stress distributions for UD beam in
25
bending vibration
7.1
Glass fiber epoxy , Glass fiber polyester and Mild steel
29
7.2
Digital Storage Oscilloscope of Tektronix 4000 series and Vibration
30
pickup
7.3
Five layers of Glass fiber polyester bolted to the slotted table milling
32
machine
7.4
Three layers of Glass fiber polyester bolted to the slotted table milling
32
machine
7.5
Four layers of Glass fiber epoxy bolted to the slotted table milling
33
machine
7.6
Two layers of Glass fiber epoxy bolted to the slotted table milling
33
machine
7.7
Ten layered sandwich plates of Glass fiber epoxy and polyester bolted to
34
the slotted table
7.8
Six layered sandwich plates of Glass fiber epoxy and polyester bolted to
the slotted table
vi
34
7.9
Six layered sandwich plate of Glass fiber epoxy and polyester bolted to
35
the slotted table
7.10
Mild steel bolted to the slotted table milling machine
35
8.1
Vibration signal for five layers of Glass fiber polyester plates
36
8.2
Vibration signal for four layers of Glass fiber polyester plates
37
8.3
Vibration signal for three layers of Glass fiber polyester plates
37
8.4
Vibration signal for two layers of Glass fiber polyester plates
38
8.5
Vibration signal for single layer of Glass fiber polyester plate
38
8.6
Vibration signal for five layers of Glass fiber epoxy plates
39
8.7
Vibration signal for four layers of Glass fiber epoxy plates
40
8.8
Vibration signal for two layers of Glass fiber epoxy plates
40
8.9
Vibration signal for single layer of Glass fiber epoxy plate
41
8.10
Vibration signal for ten layers sandwich plates of Glass fiber epoxy and
42
polyester
8.11
Vibration signal for eight layers sandwich plates of Glass fiber epoxy and
42
polyester
8.12
Vibration signal for six layers sandwich plates of Glass fiber epoxy and
43
polyester
8.13
Vibration signal for four layers sandwich plates of Glass fiber epoxy and
43
polyester
8.14
Vibration signal two layers sandwich plates of Glass fiber epoxy and
44
polyester
8.15
Vibration signal for the mild steel plate
vii
44
LIST OF TABLES
Table no.
Title
Page no.
5.1
Typical damping Values of different materials
18
6.1
Material damping of composite layers
28
6.2
Material damping of the Sandwich plates
28
7.1
Specimen details
29
8.1
Experimental Frequency and Amplitude data for Glass fiber polyester
36
8.2
Experimental Frequency and Amplitude data for Glass fiber epoxy
39
8.3
Experimental data for the sandwich plates
41
8.4
Experimental data for the Mild steel plate
44
8.5
Optimum no. of plates and Height of machine too bed
viii
45
NOMENCLATURE
Fs
Oscillatory force
Fd
Damping force
Ftotal
Strain rate
m
Mass
a
Acceleration
q&
Relative displacement at the joint
C
Friction parameter
sgn
Signum function
ω
Frequency
η
Loss factor
η1
Longitudinal loss factor
η2
Transverse loss factor
η12
Shear loss factor
Wf
Strain energy of fiber
Wm
Strain energy of fiber
E
Young’s modulus
G
Rigidity modulus
Sfict
Static moments of different phases
ν
Poisson’s ratio
mV
milli volts
ρ
Density
ix
Chapter 1
INTRODUCTION
1.1 Machine tool vibrations and their adverse effects
Machining and measuring operations are invariably accompanied by relative vibrations between
work piece and tool. These vibrations are due to one or more of the following causes:
(1) inhomogeneities in the work piece material;
(2) Variation of chip cross section;
(3) Disturbances in the work piece or tool drives;
(4) Dynamic loads generated by acceleration/deceleration of massive moving components;
(5) Vibration transmitted from the environment;
(6) Self-excited vibration generated by the cutting process or by friction (machine-tool chatter).
The adverse and undesirable effects of these vibrations include reduction in tool life, improper
surface finish, unwanted noise and excessive load on the machine tool. A machine tool is expected
to have high stiffness in order to avoid such effects. Hence the machines are to be made of robust
structured materials through passive damping technology to suppress the chatter vibrations and
thereby increasing the production rates.
1.2 Main objective of the research work
The main objective of the work is to study passive damping techniques in machine tool structures
using composite materials and to reduce vibrations in the milling machine during cutting processes
by using these materials as the base of the work piece which act like a bed absorbing vibration
forces and record the vibration curves using digital storage phosphorous oscilloscope. Composites
can be used in machine tool structures because of its inherent damping characteristics which reduces
the undesirable effects of the vibrations. Passive damping technology has a wide variety of
engineering applications, including bridges, engine mounts, and machine components such as
rotating shafts, component vibration isolation, novel spring designs which incorporate damping
without the use of traditional dashpots or shock absorbers, and structural supports.
1
Chapter 2
LITERATURE REVIEW
2.1 Introduction to machine tools
The function of machine tool is to produce a workpiece of the required geometric form with an
acceptable surface finish at high rate of production in the most economic way [1]. In fact, general
purpose machine tools, CNC lathes and machining centres are designed to cope with low cutting
speeds with high cutting forces as well as high cutting speeds with low cutting forces. Machine Tool
Structure must possess high damping, high static and dynamic stiffness. High cutting speeds and
feeds are essential requirements of a machine tool structure to accomplish this basic function.
Therefore, the material for the machine tool structure should have high static stiffness and damping
in its property to improve both the static and dynamic performance..The static stiffness of a machine
tool can be increased by using either higher modulus material or more material in the structure of a
machine tool. However, it is difficult to increase the dynamic stiffness of a machine tool with these
methods because the damping of the machine tool structure cannot be increased by increasing the
static stiffness. Sometimes high specific stiffness is more important than stiffness to increase the
natural frequency of the vibration of the machine tool structure in high speed machining [2]. Often
the most economical way of improving a machine tool with high resonance peaks is to increase the
damping rather than the static stiffness even though it is not easy to increase the damping of the
machine tool structure. The chatter is a nuisance to the metal cutting process and can occur on any
chip producing tool. Chatter or Self-excited vibrations occurs when the width of cut or cutting speed
exceeds the stability limit of the machine tool [3, 4]. The effects of chatter are all adverse, affecting
surface finish, dimensional accuracy, tool life and machine life [5].When the machine tool is
operated without any vibration or chatter, the damping of the machine tool plays no important role
in machining. However, the machine tool structure has several resonant frequencies because of its
continuous structural elements. If the damping is too small to dissipate the vibrational energy of the
machine tool, the resonant vibration occurs when the frequency of the machining operation
approaches one of the natural frequencies of the machine tool structure. Therefore the material for
the machine tool structure should have high static stiffness and damping in its property to improve
both the static and dynamic performance.
2
2.2 Damping overview
The three essential parameters that determine the dynamic responses of a structure and its sound
transmission characteristics are mass, stiffness and damping. Mass and stiffness are associated with
storage of energy. Damping results in the dissipation of energy by a vibration system. For a linear
system, if the forcing frequency is the same as the natural frequency of the system, the response is
very large and can easily cause dangerous consequences. In the frequency domain, the response near
the natural frequency is "damping controlled". Higher damping can help to reduce the amplitude at
resonance of structures. Increased damping also results in faster decay of free vibration, reduced
dynamic stresses, lower structural response to sound, and increased sound transmission loss above
the critical frequency. A lot of literature have been published on vibration damping. ASME
published a collection of papers on structural damping in 1959 [6]. Lazan's book published in 1968
gave a very good review on damping research work, discussed different mechanisms and forms of
damping, and studied damping at both the microscopic and macroscopic levels [7]. Lazan conducted
comprehensive studies into the general nature of material damping and presented damping results
data for almost 2000 materials and test conditions. Lazan's results show that the logarithmic
decrement values increase with dynamic stress, i.e., with vibration amplitude, where material
damping is the dominant mechanism. This book is also valuable as a handbook because it contains
more than 50 pages of data on damping properties of various materials, including metals, alloys,
polymers, composites, glass, stone, natural crystals, particle-type materials, and fluids. About 20
years later, Nashif, Jones and Henderson published another comprehensive book on vibration
damping [8]. Jones himself wrote a handbook especially on viscoelastic damping 15 years later [9].
Sun and Lu's book published in 1995 presents recent research accomplishments on vibration
damping in beams, plates, rings, and shells [10]. Finite element models on damping treatment are
also summarized in this book. There is also other good literature available on vibration damping
[11-13].Damping in vibrating mechanical systems has been subdivided into two classes: Material
damping and system damping, depending on the main routes of energy dissipation. Coulomb (1784)
postulated that material damping arises due to interfacial friction between the grain boundaries of
the material under dynamic condition. Further studies on material damping have been made by
Robertson and Yorgiadis (1946), Demer (1956), Lazan (1968) and Birchak (1977). System damping
arises from slip and other boundary shear effects at mating surfaces, interfaces or joints between
distinguishable parts. Murty (1971) established that the energy dissipated at the support is very
small compared to material damping.
3
2.3 Review on Research done in Damping of Composite materials
Bert [14] and Nashif et al.[15] had done survey on the damping capacity of fibre reinforced
composites and found out that composite materials generally exhibit higher damping than structural
metallic materials. Chandra et al. [16] has done research on damping in fiber-reinforced composite
materials.
Composite damping mechanisms and methodology applicable to damping analysis is described and
had presented damping studies involving macromechanical, micromechanical and Viscoelastic
approaches. Gibson et al.[17] and Sun et al.[18,19] assumed viscoelasticity to describe the behavior
of material damping of composites.
The concept of specific damping capacity (SDC) was adopted in the damped vibration analysis by
Adams and his co workers [20-21], Morison [22] and Kinra et al [23].
The concept of damping in terms of strain energy was apparently first introduced by Ungar et.al
[24] and was later applied to finite element analysis by Johnson et.al [25]. Gibson et.al [26] has
developed a technique for measuring material damping in specimens under forced flexural
vibration. Suarez et al [27] has used Random and Impulse Techniques for Measurement of Damping
in Composite Materials. The random and impulse techniques utilize the frequency-domain transfer
function of a material specimen under random and impulsive excitation. Gibson et al [28] used the
modal vibration response measurements to characterize, quickly and accurately the mechanical
properties of fiber-reinforced composite materials and structures.
Lin et al. [29] predicted SDC in composites under flexural vibration using finite element method
based on modal strain energy (MSE) method considering only two interlaminar stresses and
neglecting transverse stress.
Koo KN et al. [30] studied the effects of transverse shear deformation on the modal loss factors as
well as the natural frequencies of composite laminated plates by using the finite element method
based on the shear deformable plate theory.
4
SINGH S. P et al. [31] analyzed damped free vibrations of composite shells using a first order shear
deformation theory in which one assumes a uniform distribution of the transverse shear across the
thickness, compensated with a correction factor.
Polymeric materials are widely used for sound and vibration damping. One of the more notable
properties of these materials, besides the high damping ability, is the strong frequency dependence
of dynamic properties; both the dynamic modulus of elasticity and the damping characterized by the
loss factor [30-35].
Mycklestad [32] was one of the pioneering scientists into the investigation of complex modulus
behavior of viscoelastic materials (Jones, 2001, Sun, 1995). Viscoelastic material properties are
generally modeled in the complex domain because of the nature of viscoelasticity. Viscoelastic
materials possess both elastic and viscous properties. The typical behavior is that the dynamic
modulus increases monotonically with the increase of frequency and the loss factor exhibits a wide
peak [8, 33].
It is rare that the loss factor peak, plotted against logarithmic frequency, is symmetrical with respect
to the peak maximum, especially if a wide frequency range is considered. The experiments usually
reveal that the peak broadens at high frequencies. In addition to this, the experimental data on some
polymeric damping materials at very high frequencies, far from the peak centre, show that the loss
factor–frequency curve ‘‘flattens’’ and seems to approach a limit value, while the dynamic modulus
exhibits a weak monotonic increase at these frequencies [34-38]. These phenomena can be seen in
the experimental data published by Madigosky and Lee [34], Rogers [35] and Capps [36] for
polyurethanes, and moreover by Fowler [37], Nashif and Lewis [38] for other polymeric damping
materials.
The computerized methods of acoustical and vibration calculus require the mathematical form of
frequency dependences of dynamic properties. A reasonable method of describing the frequency
dependences is to find a good material model fitting the experimental data.
5
2.4 Review of the previous work done on the machine tool structures
In recent years many efforts have been made to increase the material damping of the machine tool
structures.
Rahman et al. [37] have made attempts to review and summarize the key developments in the area
of non-conventional materials for machine tool structures over the last decades. They have
compared many beneficial properties of the machine tool structural materials with the conventional
cast iron. For supporting the ever rising working speeds made possible by the development of tools
and machining processes, the increasing requirements concerning the surface finish of the machined
workpieces and the fabrication cost of the machine tool structures exerted the impetus to find
alternatives to cast iron. Based on the results of previous studies they have stated that composite
materials may be the choice to replace conventional materials.
Lee et al. [38] have improved the damping capacity of the column of a precision mirror surface
grinding machine tool by manufacturing a hybrid column by adhesively bonding glass fiber
reinforced epoxy composite plates to a cast iron column. For optimizing the damping capacity of the
hybrid column they have calculated the damping capacity of the hybrid column with respect to the
fiber orientation and thickness of the composite laminate plate and they have compared with the
measured damping capacity. From experiments they have found out that the damping capacity of
the hybrid column was 35% higher than that of the cast iron column.
Kegg et al. [39]
have used composites for the massive slides for CNC milling machine in
machining moulds and dies because presence of these massive slides do not allow rapid acceleration
and deceleration during the frequent starts/stops encountered in machining moulds and dies. They
have constructed the vertical and horizontal slides of a large CNC machine by bonding high
modulus carbon-fiber epoxy composite sandwiches to welded steel structures using adhesives.
These composites structures reduced the weight of the vertical and horizontal slides by 34% and
26%, respectively and increased damping by 1.5 to 5.7 times without sacrificing the stiffness.
6
Okuba et al. [40] have improved the dynamic rigidity of machine tool structures by studying the
mode shape animation based on the results of modal analysis. This technique was successfully
applied to a machining cell, an arm of automatic assembling machine and a conventional cylindrical
grinder. The examples on a vertical milling machine, an NC lathe and a surface grinder show
effectiveness of the software approach in suppressing the chatter and improving the surface finish.
Chowdhury [41] used epoxy resin as a bonding material between structural components of a milling
machine to increase joint damping. It was reported that the bonded over arm of milling machine
performed much better than those of welded and the cast iron.
Haranath et al. [42] have done attempts experimentally to establish that improvement can be
attained by applied damping treatment using viscoelastic layers. They have done theoretical study
on the vibrations of machine tool structures with applied damping treatment by using a conventional
beam element. Models of milling machine, radial drilling machine and lathe have been analysed for
their natural frequency and loss factors. They have found out the influence of layering treatment on
the natural frequencies and loss factors.
Wakasawa et al. [43] have improved the damping capacity of machine tool structure by ball
packing. In structures closely packed with balls, various damping characteristics appear in
correspondence with the ball size and other conditions. The effect of ball size is the most significant
factor in these structures. Excitation of structure is required to achieve an optimum packing ratio
where the maximum damping capacity is obtained. For a 50% packing ratio, this excitation process
is not necessary to obtain a stable damping capacity. Therefore, they have investigated the effects of
magnitude of impulse, packed ball material, and structure size on the damping capacity at a 50%
packing ratio. Finally, they have constructed actual machine tool structure models and the
effectiveness of the balls packing for the damping capacity improvement has been investigated.
7
Chapter 3
COMPOSITES
3.1 Composite materials
Composite materials, often shortened to composites, are engineered or naturally occurring materials
made from two or more constituent materials with significantly different physical or chemical
properties which remain separate and distinct at the macroscopic or microscopic scale within the
finished structure. The constituents are combined in such a way that they keep their individual
physical phases and are neither soluble in each other nor form a new chemical compound. One
constituent is called reinforcing phase which is embedded in another phase called matrix. The most
visible applications is pavement in roadways in the form of either steel and aggregate reinforced
Portland cement or asphalt concrete.
Mostly fibers are used as the reinforcing phase and are much stronger than the matrix and the matrix
is used to hold the fibers intact. Examples of such composites are an aluminums matrix embedded
with boron fibers and an epoxy matrix embedded with glass or carbon fibers. The fibers may be
long or short, directionally aligned or randomly orientated, or 'some sort of mixture, depending on
the intended use of the material. Commonly used materials for the matrix are polymers, metals,
ceramics, carbon and fibers are carbon (graphite) fibers, aramid fibers and boron fibers.
Fiber-reinforced composite materials are further classified into the following
a) continuous fiber-reinforced
b) discontinuous aligned fiber-reinforced
c) discontinuous random-oriented fiber-reinforced.
Fig 3.1 Types of fiber reinforced materials
8
Composites used in the work are Glass fiber epoxy and Glass fiber polyester.
Fiberglass is made from extremely fine fibers of glass. It is used as a reinforcing agent for many
polymer products; the resulting composite material, properly known as fiber-reinforced polymer
(FRP) or glass-reinforced plastic (GRP), is called "fiberglass" in popular usage. Uses for regular
fiberglass include mats, thermal insulation, electrical insulation, reinforcement of various materials,
tent poles, sound absorption, heat- and corrosion-resistant fabrics, high-strength fabrics, pole vault
poles, arrows, bows and crossbows, translucent roofing panels, automobile bodies, hockey sticks,
surfboards, boat hulls, and paper honeycomb.
Epoxy is a thermosetting polymer formed from reaction of an epoxide "resin" with polyamine
"hardener". Epoxy has a wide range of applications, including fiber-reinforced plastic materials and
general purpose adhesives. The applications for epoxy-based materials are extensive and include
coatings, adhesives and composite materials such as those using carbon fiber and fiberglass
reinforcements (although polyester, vinyl ester, and other thermosetting resins are also used for
glass-reinforced plastic). The chemistry of epoxies and the range of commercially available
variations allows cure polymers to be produced with a very broad range of properties. In general,
epoxies are known for their excellent adhesion, chemical and heat resistance, good-to-excellent
mechanical properties and very good electrical insulating properties. Many properties of epoxies can
be modified (for example silver-filled epoxies with good electrical conductivity are available,
although epoxies are typically electrically insulating). Variations offering high thermal insulation, or
thermal conductivity combined with high electrical resistance for electronics applications, are
available.
Polyester is a category of polymers which contain the ester functional group in their main chain.
Although there are many types of polyester, the term "polyester" as a specific material most
commonly refers to polyethylene terephthalate. Depending on the chemical structure polyester can
be a thermoplastic or thermoset, however the most common polyesters are thermoplastics.
Polyesters are used to make "plastic" bottles, films, tarpaulin, canoes, liquid crystal displays,
holograms, filters, dielectric film for capacitors, film insulation for wire and insulating tapes.
9
Chapter 4
MILLING MACHINES
4.1 Milling machine
A milling machine is a machine tool used to machine various materials. Milling machines are often
classed in two basic forms, horizontal and vertical, which refers to the orientation of the main
spindle. Both types range in size from small, bench-mounted devices to room-sized machines.
Unlike a drill press, which holds the workpiece stationary as the drill moves axially to penetrate the
material, milling machines also move the workpiece radially against the rotating milling cutter,
which cuts on its sides as well as its tip. Workpiece and cutter movement are precisely controlled to
less than 0.001 in (0.025 mm), usually by means of precision ground slides and lead screws or
analogous technology. Milling machines may be manually operated, mechanically automated, or
digitally automated via computer numerical control (CNC). They can perform a vast number of
operations, from simple to complex (slot and keyway cutting, planing, drilling to contouring,
diesinking). Cutting fluid is often pumped to the cutting site to cool and lubricate the cut and to
wash away the resulting swarf. The different types of milling machines are
1) Bed mill
2) Box mill
3) Gantry mill
4) Horizontal boring mill
5) Turrent mill
6) Knee and Column mill
4.1.1 Horizontal knee-and-column mill
The most distinguishing characteristic type of milling machine is the knee and column
configuration. This type of milling machine is unique in that the table can be moved in all three
directions. The table can be moved longitudinally in the X-axis as well as in and out on the Y-axis.
Since the table rides on top of the knee, the table can be moved up and down on the Z-axis. There
are several different types of knee and column type milling machines, but they all have the same
characteristic. The knee slides up and down on the column face.
10
.
Fig 4.1 Horizontal Knee and Column Milling Machine
4.2 Milling Operation
Milling is the process of cutting away material by feeding a workpiece past a rotating multiple tooth
cutter. The cutting action of the many teeth around the milling cutter provides a fast method of
machining. The machined surface may be flat, angular, or curved. The surface may also be milled to
any combination of shapes. The work piece is mounted on the table with the help of suitable
fixtures. The desired contour, feed and depth of cut for the job are noted down. A suitable milling
cutter for the specified job is selected and mounted on the arbor. The knee is raised till the cutter just
touches the work piece. The machine is started. By moving the table, saddle and the knee, for the
specified feed and depth of cut, the desired job may be finished. The machine may then be switched
off. The different methods of milling are
1) Up milling
2) Down milling
11
4.2.1 Up Milling
Up milling is also referred to as conventional milling. The direction of the cutter rotation opposes
the feed motion. For example, if the cutter rotates clockwise , the workpiece is fed to the right in up
milling.
Fig 4.2 Up milling or Conventional milling
4.2.2 Down Milling
Down milling is also referred to as climb milling. The direction of cutter rotation is same as the feed
motion. For example, if the cutter rotates counterclockwise , the workpiece is fed to the right in
down milling.
Fig 4.3 Down milling or climb milling
The chip formation in down milling is opposite to the chip formation in up milling. The figure for
down milling shows that the cutter tooth is almost parallel to the top surface of the workpiece. The
cutter tooth begins to mill the full chip thickness. Then the chip thickness gradually decreases.
12
4.3 Vibration in Machine Tools
The Machine, cutting tool, and workpiece from a structural system have complicated dynamic
characteristics. Under certain condition vibrations of the structural system may occur, and as with
all types of machinery, these vibrations may be divided into three basic types:
1. Free or Transient vibrations: resulting from impulses transferred to the structure through its
foundation, from rapid reversals of reciprocating masses, such as machine tables, or from the
initial engagement of cutting tools. The structure is deflected and oscillates in its natural
modes of vibration until the damping present in the structure causes the motion to die away.
2. Forced vibration: resulting from periodic forces within the system, such as unbalanced
rotating masses or the intermittent engagement of multitooth cutters (milling), or transmitted
through the foundations from nearby machinery. The machine tool will oscillate at the
forcing frequency, and if this frequency corresponds to one of the natural frequency of the
structure, the machine will resonate in the corresponding natural mode of vibration.
3. Self-excited vibrations: usually resulting from a dynamic instability of the cutting process.
This phenomenon is commonly referred to as machine tool chatter and, typically, if large
tool-work engagements are attempted, oscillations suddenly build up in the structure,
effectively limiting metal removal rates. The structure again oscillates in one of its natural
modes of vibration.
4. The sources of vibration excitation in a machine tool structure are vibration due to inhomogeneities in the work piece , cross sectional variation of removed material,
disturbances in the vibration of tool drives , rotation unbalanced members guide ways ,
gears, drive mechanisms and others .
13
4.4 Chatter in the Milling machine
The milling operation is a cutting process using a rotating cutter with one or more teeth. An
important feature is that the action of each cutting edge is intermittent and cuts less than half of the
cutter revolution, producing varying but periodic chip thickness and an impact when the edge
touches the work piece. The tooth is heated and stressed during the cutting part of the cycle,
followed by a period when it is unstressed and allowed to cool. The consequences are thermal and
mechanical fatigue of the material and vibrations, which are of two kinds: forced vibrations, caused
by the periodic cutting forces acting in the machine structure and chatter vibrations, which may be
explained by two distinct mechanisms, called “mode coupling” and “regeneration waviness”,
explained in Tobias (1965), Koenigsberger & Tlusty (1967) and Budak & Altintas (1995).
The mode coupling chatter occurs when forced vibrations are present in two directions in the plane
of cut. The regenerative chatter is a self excitation mechanism associated with the phase shift
between vibrations waves left on both sides of the chip and happens earlier than the mode coupling
chatter in most machining cases, as explained by Altintas (2000). In milling, one of the machine tool
work piece system structural modes is initially excited by cutting forces. The waved surface left by
a previous tooth is removed during the succeeding revolution, which also leaves a wavy surface due
to structural vibrations. The cutting forces become oscillatory whose magnitude depends on the
instantaneous chip dynamic thickness, which is a function of the phase shift between inner and outer
chip surface. The cutting forces can grow until the system becomes unstable and the chatter
vibrations increase to a point when the cutter jumps out of the cut or cracks due the excessive forces
involved. These vibrations produce poor surface finishing, noise and reduce the life of the cutter. In
order to avoid these undesirable effects, the feed rate and the depth of cut are chosen at conservative
values, reducing the productivity.1
14
Chapter 5
DAMPING
5.1Definition of Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory
system, particularly the harmonic oscillator. In mechanics, friction is one such damping effect. In
engineering terms, damping may be mathematically modeled as a force synchronous with the
velocity of the object but opposite in direction to it. If such force is also proportional to the velocity,
as for a simple mechanical viscous damper (dashpot), the force F may be related to the velocity v by
F= -cv , where c is the viscous damping coefficient, given in units of newton-seconds per meter.
Fig 5.1 Mass spring damper system
An ideal mass-spring-damper system with mass m (kg), spring constant k (N/m) and viscous damper
of damping coefficient c (in N-s/ m or kg/s) is subject to an oscillatory force and a damping force,
Treating the mass as a free body and applying Newton's second law, the total force Ftot on the body
Since Ftot = Fs + Fd, then =>
This differential equation may be rearranged into
,
ω0, is the (undamped) natural frequency of the system and ζ, is called the damping ratio.
15
5.2 Types of Damping
Three main types of damping are present in any mechanical system:
1) Internal damping (of material)
2) Structural damping (at joints and interfaces)
3) Fluid damping (through fluid-structure interactions)
5.2.1 Material (Internal) damping
Internal damping of materials originates from the energy dissipation associated with microstructure
defects, such as grain boundaries and impurities; thermoelastic effects caused by local temperature
gradients resulting from non uniform stresses, as in vibrating beams; eddy current effects in
ferromagnetic materials; dislocation motion in metals; and chain motion in polymers. Several
models have been employed to represent energy dissipation caused by internal damping. This
variety of models is primarily a result of the vast range of engineering materials; no single model
can satisfactorily represent the internal damping characteristics of all materials.
5.2.2 Structural damping
Rubbing friction or contact among different elements in a mechanical system causes structural
damping[49]. Since the dissipation of energy depends on the particular characteristics of the
mechanical system, it is very difficult to define a model that represents perfectly structural damping.
The Coulomb-friction model is as a rule used to describe energy dissipation caused by rubbing
friction. Regarding structural damping (caused by contact or impacts at joins), energy dissipation is
determined by means of the coefficient of restitution of the two components that are in contact.
Assuming an ideal Coulomb friction, the damping force at a join can be expressed through the
following expression:
f = c . sgn( q& )
where:
f = damping force,
q& = relative displacement at the joint, c= friction parameter
and the signum function is defined by:
sgn (x) = 1 for x ≥ 0
sgn (x) = -1 for x < 0
16
5.2.3 Fluid damping
When a material is immersed in a fluid and there is relative motion between the fluid and the
material, as a result the latter is subjected to a drag force. This force causes an energy dissipation
that is known as fluid damping.
The damping phenomenon can be applied to the machine tool systems in two ways :
1. Passive damping
2. Active damping
Passive damping refers to energy dissipation within the structure by add on damping devices such as
isolator, by structural joints and supports, or by structural member's internal damping. Active
damping refers to energy dissipation from the system by external means, such as controlled actuator.
5.3 Damping mechanism in composite materials
Damping mechanisms in composite materials differ entirely from those in conventional metals
and alloys [23]. The different sources of energy dissipation in fiber-reinforced composites are:
a) Viscoelastic nature of matrix and/or fiber materials
(b) Damping due to interphase
(c) Damping due to damage which is of two types :
(i) Frictional damping due to slip in the unbound regions between fiber and matrix .
(ii) Damping due to energy dissipation in the area of matrix cracks, broken fibers etc.
(d) Viscoplastic damping
(e) Thermoelastic damping
17
5.4 Damping in machine tools
Damping in machine tools basically is derived from two sources--material damping and interfacial
slip damping. Material damping is the damping inherent in the materials of which the machine is
constructed. The magnitude of material damping is small comparing to the total damping in
machine tools. A typical damping ratio value for material damping in machine tools is 0.003. It
accounts for approximately 10% of the total damping. The interfacial damping results from the
contacting surfaces at bolted joints and sliding joints. This type of damping accounts for
approximately 90% of the total damping. Among the two types of joints, sliding joints contribute
most of the damping[44].Welded joints usually provide very small damping which may be
neglected when considering damping in joints.
Table 5.1 Typical damping values of different materials
Systems/Materials
Loss Factor
Welded Metal structure
0.0001 to 0.001
Bolted Metal structure
0.001 to 0.01
Aluminium
0.0001
Brass, Bronze
0.001
Beryllium
0.002
Lead
0.5 to 0.002
Glass
0.002
Steel
0.0001
Iron
0.0006
Tin
0.002
Copper
0.002
Plexiglas TM
0.03
Wood, Fiberboard
0.02
18
Chapter 6
MATERIAL DAMPING
6.1 Energy balance approach [50]
The loss factor η is commonly used to characterize energy dissipation, due to inelastic behaviour, in
a material subjected to cyclic loading. Assuming linear damping behavior, η is defined by
Vantomme[50] as;
η=
where ∆W is the amount of energy dissipated during the loading cycle and W is the strain energy
stored during the cycle.
Now considering η1, η2 and η12 :
η1 – normal loading in fibre direction of UD lamina ( longitudinal loss factor)
η2 – normal loading perpendicular to fibres (transverse loss factor )
η12—inplane shear loading ( shear loss factor)
6.1.1 Two phase model
Fig.6.1 RVE loaded in 1-direction,Voigt model: matrix(m) and fibers(f) are connected in parallel
19
Longitudinal loss factor (η1) is calculated by the following method : (loading in direction 1 )
The total energy dissipated comprises the sum of that lost in the fibres and matrix. These amounts
are proportional to the fractions of elastic strain energy stored in the fibres and matrix respectively;
i.e.
……….(1)
ηfE and ηmE are the loss factors for fibres and matrix, associated with σ – ε tensile loading.
Using the expressions for the strain energy,
…………………..(2)
with
………………….(3)
gives:
………………………(4)
Introduction of (4) into (2), with W = Wf + Wm, gives:
………….(5)
20
Transverse loss factor (η2) is calculated: (loading in direction 2)
As before, η2 is expressed as
………………(6)
The strain energy contributions are derived in an analogous manner as for η1, but now with the
assumption that the same transverse stress σ2 is applied to both the fibres and the matrix. This
development leads to
………….(7)
Shear loss factor (η12) is calculated: (loading in shear direction )
……………………..(8)
where ηfG and ηmG are the loss factors for fibres and matrix associated with shear loading. The strain
energy fractions are worked out in the same way as for η2, as it is assumed that the shear stresses on
the fibres and matrix are the same. This leads to:
……………..(9)
Equation (9) indicates that damping for a UD lamina, for shear loading, is again matrix-dominated,
because the stiffness Gf is usually much larger than Gm. The similarity of equations (9) and (7),
combined with the fact that ηmE = ηmG, leads to the conclusion that η2and η12 should be very similar.
The coefficients
ηfE,ηmE,ηfG,ηfG
are calculated from the graphs given in the book “Damping of
materials and members in structural mechanics” by Benhamin J. Lazan . These graphs are plotted
with E’ & E” , G’ & G” .
21
E’ : Storage modulus of elasticity
E “ : Loss modulus of elasticity
G’ : Storage modulus of rigidity
G “: Loss modulus of rigidity
ηE = E”/E’ , ηG= G”/G’ , For each type of fibre phase and matrix phase material the respective
coefficient values are taken from the graphs oriented as slopes of these lines .
6.1.2 Three phase model
Fig6.2 RVE with three phases: the matrix(m) and fibers(f) and the interphase (i)
Using the energy balance approach, the elastic strain energy is now divided into three terms, giving
the following expression for energy dissipation, analogous to equation mentioned before :
…………..(10)
where ηi represents the loss factor of the interphase layer.
The elastic strain energies Wf, Wm and Wi may be evaluated as previously described, resulting in the
following expressions for η1, η2 and η12, for the UD laminae:
….……….(11)
22
………..(12)
…………(13)
This model does not explain the experimental increase η1 as compared with the values from the
graphs .In order to introduce the interphase effect into equation (11), it may be better to consider the
elastic strain energy that is associated with the shear stress-strain cycle, when longitudinal bending
is considered. Normally, this strain energy is negligible compared with the strain energy associated
with the tension or compression cycle, but possibly the presence of a layer with very low stiffness
properties may change the energy balance significantly[47].
6.1.3 Modified three phase model
Taking into account the strain energy associated with the shear cycle for the interphase layer only,
and allowing for the fact that ηiE does not affect ηl, see equation (15), the following strain energy
partition may be adopted:
…………..(14)
The strain energy fractions in equation (14) are developed for the three-phase model ,in which the
strain and stress distributions along the cross-section are represented, assuming that a plane crosssection remains plane, and that the adhesion between interphase and matrix, and interphase and
fibres, is perfect.
The strain energy fractions Wfσ-ε, and Wmσ-ε are defined for the total volume of the beam
specimen
as:
23
The introduction of Hooke's law, and the relationships between the stresses for fibres and matrix at
an arbitrary level and the maximum stress in the matrix σm max (which are based on strain
linearity), lead to the expressions [48]:
where Ω represents the cross-section.
The relation between σ m max and the internal M is given by
where Ifict is equal to a combination of the moments of inertia for the different phases:
Finally we get
………..(15)
The integrals in equation (15) may be evaluated for the first bending mode of the free beam
specimen; this requires an equation for M(x), which can be developed from the first mode shape
deflection equation for a prismatic beam with free end conditions, in transverse vibration given by
…………………(16)
where
L = the length of the beam specimen;
C3 = an arbitrary constant;
E = the Young's modulus in the 1-direction, for the three-phase compositematerial;
I = the moment of intertia for the rectangular crosssection of the beam
24
Fig6.3 Three phase model with strain and stress distributions for UD beam in bending vibration
Finally, after substituting the expressions obtained for the strain energy components into
equation(16), and with simplifications, the following expression for η1
where
‘b’ is the width of the rectangular cross-sectio and Sfict is a combination of the static moments of the
different phases in the cross-section between the level on which shear is considered, z=-h/2:
25
6.2 Calculation of material damping of Glass fiber polyester
In this reinforced composite material there are different matrix and fibre phases :
Reinforcing material --- E-Glass fiber
Matrix ---polyester
Ef = 80Gpa
υf = 0.22
Gf = 32.7Gpa
Em = 3.5Gpa
υm = 0.25
Gm = 1.4Gpa
From graphs given in the book “Damping of material and members in structural mechanics” by
LAZAN
ηmE & ηfE
are taken ; ηmE = 0.05 ,ηfE = 0.01
.
η1 =
.
.
=
ηmG
.
= 0.0118
= 0.0545
= 0.01 ,ηfG = 0.015
=
.
.
= 0.0101
Applying all the stresses, assuming for a cycle of operations in a system of forces, the net material damping
according to Koo & Lee [45] is given by
1 2 12
ηav =
= 0.0012
26
6.3 Calculating material damping of Glass fiber epoxy
Reinforcing material --- E-Glass fiber
Matrix ---epoxy
Ef = 80Gpa
υf = 0.22
Gf = 32.7Gpa
ηmE
Em = 3.5Gpa
υm = 0.25
Gm = 1.4Gpa
= 0.03 ,ηfE = 0.01 ;
η1 =
.
.
= 0.0109
.
=
ηmG
.
= 0.0328
= 0.02 ,ηfG = 0.015
=
.
.
= 0.0198
The net material damping for a single fiber epoxy plate according to Koo & Lee is given by
1 2 12
= 0.0010
ηav =
For a single plate of glass fiber polyester and epoxy material damping is 0.0012 and 0.0010
For ‘n’ number of plates:
Loss factor for two plates
η2 = η1
+ η2
, where W1 and W2 are the weights of the plates
27
Considering W1= W2 (homogenous plates)
η2 = 2 η1
which implies ηn = n η1
Table 6.1 Material damping of the composite layers
Number
of plates
Glass fiber polyester
1
0.0012
0.0010
2
0.0024
0.0020
3
0.0036
0.0030
4
0.0048
0.0040
5
0.0060
0.0050
Glass fiber epoxy
6.4 Material damping of sandwich plates Glass fiber epoxy and polyester
In the sandwich plates the weights of the epoxy and polyester are different which means the plates
are non-homogenous [46] ;
η2 = η1
+ η2
η4 = η1
+ η2
η4 = 2 [ η1
+ η3
+ η2
η8 = 4 [ η1
, (GF Polyester) W1 = 0.43 kg, (GF epoxy) W2= 0.37 kg
+ η2
+ η4
, W1= W3, W2= W4
]
η6
]
η10 = 5 [ η1
=3[
η1
+ η2
+ η2
Table 6.2 Material damping of the Sandwich plates
Number of
plates
Sandwich plates
2
0.0011
4
0.0022
6
0.0033
8
0.0044
10
0.0055
28
]
]
Chapter 7
EXPERIMENTATION
7.1 Experimental set-up
Table 7.1 Specimen Details
Material No
Name of the Material
Cross section (mm)
1
Glass Fiber Polyester
210x210x6
2
Glass Fiber Epoxy
210x210x5
3
Mild steel
210x210x10
Fig 7.1 Glass fiber epoxy , Glass fiber polyester and Mild steel (clock wise starting from top left)
29
7.2 Instrumentation
The following equipment is needed in recording the amplitude, frequency, period of the vibrations
during the machining operation
(1) Power supply unit
(2) Vibration pick-up
(3) Digital Storage Oscilloscope
Fig 7.2 Digital Storage Oscilloscope of Tektronix 4000 series and Vibration pickup
Digital Storage Oscilloscope Tektronix 4000 series
Display: - 8x10 cm. rectangular mono-accelerator c.r.o. at 2KV e.h.t. Trace rotation by front panel
present. Vertical Deflection: - Four identical input channels ch1, ch2, ch3, ch4.
Band-width:- (-3 db) d.c. to 20 MHz ( 2 Hz to 20 MHz on a.c.)
Sensitivity: - 2 mV/cm to 10 V/cm in 1-2-5 sequence.
Accuracy: - ± 3 %
Variable Sensitivity:- > 2.5% 1 range allows continuous adjustment of sensitivity from 2-1(mV/cm).
Input impedance: - 1M/28 PF appx.
Input coupling: - D.C. and A.C.
Input protection: - 400 V d.c.
Display modes: - Single trace ch1 or ch2 or ch3 or ch4. Dual trace chopped or alternate
modes automatically selected by the T.B. switch.
30
7.3 Experimental procedure
The work specimen of 210mm x 210mm x10mm is a mild steel square plate. Four holes of 18mm
diameter are drilled on the specimen at the corners. The glass fiber epoxy and polyester composite
plates are thoroughly cleaned and polished. Plates are fixed on to a bench vice and the edges are
filed to clear off the irregularities. All the plates are made to the exact dimensions for the ease of the
further operations. Four holes are drilled on each plate and these holes are needed to be coaxial
when the plates are placed upon one another and also with the mild steel. A right hand cut twoflutes drill bit of size 18mm is used to make holes. All the plates are carefully made homogenously
similar to avoid interfacial vibrations and slipping. The work piece is then mounted onto the layered
sheets of composites and tightly bolted to slotted table of the milling machine using square head
bolts.
Initially five glass fiber polyester plates each of 6mm thickness are placed upon the bed along with
mild steel. A contact type magnetic base vibration pickup connected to a digital phosphor storage
oscilloscope of Tektronix 4000 series is placed on the mild steel during the machining operation.
The response signals with respect to amplitude, time period, RMS amplitude and frequency are
recorded and stored on the screen of the storage oscilloscope. Then the numbers of layers are
reduced to four layers and the observations are recorded. In this way, the experiments are repeated
by decreasing the number of layers of various composites. The experiments are conducted for
5,4,3,2,1 number of layers respectively. The whole process is again repeated using glass fiber epoxy
plates each of 5mm thickness and also with the Sandwich plates (both fiber epoxy and polyester)
combination of 10,8,6,4,2 layers respectively. Finally mild steel plate alone is machined with no
layer under it and the readings are noted and compared.
An Upmilling cutting operation with constant feed of 16mm/min and depth of cut of 0.02mm is
performed during all the experiments. An oil-water emulsion made from animal fat is used as a
cutting fluid.
31
Fig 7.3 Five layers of Glass fiber polyester bolted to the slotted table milling machine
Fig 7.4 Three layers of Glass fiber polyester bolted to the slotted table milling machine
32
Fig 7.5 Four layers of Glass fiber epoxy bolted to the slotted table milling machine
Fig 7.6 Two layers of Glass fiber epoxy bolted to the slotted table milling machine
33
Fig 7.7 Ten layered sandwich plates of Glass fiber epoxy and polyester bolted to the slotted table
Fig 7.8 Six layered sandwich plates of Glass fiber epoxy and polyester bolted to the slotted table
34
Fig 7.9 Six layered sandwich plates of Glass fiber epoxy and polyester bolted to the slotted table
Fig7.10 Mild steel bolted to the slotted table milling machine
35
Chapter 8
Results and Discussion
8.1 Experimental Results
Table 8.1 Experimental Frequency and Amplitude data for Glass fiber polyester
Depth of
Feedrate
Number of
Signal
Time
Frequency
RMS
cut (mm)
(mm/min)
layers
Amplitude(mV)
Period(µs)
(KHz)
Amplitude(mV)
1
0.02
16
5
49.6
292.0
3.425
9.99
2
0.02
16
4
46.4
339.0
2.786
10.2
3
0.02
16
3
23.2
978.7
1.022
5.10
4
0.02
16
2
30.4
510.0
1.961
6.75
5
0.02
16
1
52.4
902.5
1.108
13.4
Sl.no
Fig 8.1 Vibration signal for five layers of Glass fiber polyester plates
36
Fig 8.2 Vibration signal for four layers of Glass fiber polyester plates
Fig 8.3 Vibration signal for three layers of Glass fiber polyester plates
37
Fig 8.4 Vibration signal for two layers of Glass fiber polyester plates
Fig 8.5 Vibration signal for single layer of Glass fiber polyester plate
38
Table 8.2 Experimental Frequency and Amplitude data for Glass fiber epoxy
Depth of
Feedrate
Number of
Signal
Time
Frequency
RMS
cut (mm)
(mm/min)
layers
Amplitude(mV)
Period(µs)
(KHz)
Amplitude(mV)
1
0.02
16
5
67.2
421.9
2.37
16.8
2
0.02
16
4
51.2
558.1
1.792
13.2
3
0.02
16
3
40.0
537.5
1.860
9.04
4
0.02
16
2
28.8
441.7
2.264
7.61
5
0.02
16
1
20.8
845.0
1.183
5.26
Sl.no
Fig 8.6 Vibration signal for five layers of Glass fiber epoxy plates
39
Fig 8.7 Vibration signal for four layers of Glass fiber epoxy plates
Fig 8.8 Vibration signal for two layers of Glass fiber epoxy plates
40
Fig 8.9 Vibration signal for single layer of Glass fiber epoxy plate
Table 8.3 Experimental data for the sandwich plates of Glass fiber epoxy and polyester
Sl.no
Depth of
Feedrate
Number of
Signal
Time
Frequency
RMS
cut (mm)
(mm/min)
layers
Amplitude(mV)
Period(µs)
(KHz)
Amplitude(mV)
1
0.02
16
10
39.2
740.0
1.351
9.56
2
0.02
16
8
49.6
716.7
1.395
11.7
3
0.02
16
6
33.6
692.5
1.444
8.06
4
0.02
16
4
59.2
502.3
1.99
13.5
5
0.02
16
2
65.6
437.5
2.286
14.1
41
Fig 8.10 Vibration signal for ten layers sandwich plates of Glass fiber epoxy and polyester
Fig 8.11 Vibration signal for eight layers sandwich plates of Glass fiber epoxy and polyester
42
Fig 8.12 Vibration signal for six layers sandwich plates of Glass fiber epoxy and polyester
Fig 8.13 Vibration signal for four layers sandwich plates of Glass fiber epoxy and polyester
43
Fig 8.14 Vibration signal two layers sandwich plates of Glass fiber epoxy and polyester
Table 8.4 Experimental data for the Mild steel plate
Sl.no
1
Depth of
Feedrate
Number of
Signal
Time
Frequency
RMS
cut (mm)
(mm/min)
layers
Amplitude(mV)
Period(µs)
(KHz)
Amplitude(mV)
0.02
16
1
59.2
618.6
1.617
15.6
Fig 8.15 Vibration signal for the mild steel plate
44
8.2 Discussions
The above graphs show the variation of signal amplitude with respect to number of layers for
different combinations of composites. It is observed that when the numbers of layers are
increased, the signal amplitude has decreased for both the composites to a certain extent and then
increased abruptly. The maximum amplitude is obtained when no composite material was used
indicating that the presence of composite materials decreases the vibration amplitude and
increases the counter vibration characteristics of the system. This shows that with increase in the
plates the damping can be increased but only to a certain limit and it would have a negative effect
with much of progress. Hence optimum level of plates is to be decided to profitably damp out the
vibrations. This optimum number of plates is different for glass fiber polyester and glass fiber
epoxy.
Table 8.5 Optimum no. of plates and Height of machine too bed
Type of composite
Optimum no. of plates
Height of the machine bed
Glass fiber polyester
Three
18 mm
Glass fiber epoxy
Two
10mm
Sandwich plates
Six
33mm
45
Chapter 9
CONCLUSION
1) Use of composite materials reduces the vibrations of the system as desired which is
justified from the experimental observations. With increase in number of layers of
composites at an optimum level the vibrations are decreased considerably.
2) Effective damping can be obtained only by proper fixation of the composites to the bed
and the work piece. With improper nut and bolt joint there is a danger of additional slip
vibrations between the plates. Hence a proper and intact joint is preferably necessary. On
the contrary the optimum number of plates is decided and a single plate of optimum
thickness is used as the bed material.
3) Extensive experiments with different layer combinations along with sandwich plates are
carried out to determine vibration response of work specimen with specified machining
parameter, i. e., depth of cut and feed rate. The experiments are duly carried out at small
feed, low depth of cut and low cutter speed to primarily investigate the scope of damping
phenomenon in composite materials.
4) Abrupt increase in vibration amplitude has also been observed with increase in number of
layers of composites above an optimum limit interposed between the table and work piece
5) The results obtained are compared with respect to each other. Out of the two materials,
signal amplitudes obtained are less for Glass fiber epoxy material. Therefore, it can be
concluded that Glass fiber epoxy material can be used for machine tool structures to
reduce the undesirable effects of vibrations.
6) The density of the matrix phase plays an important role in damping the vibrations. With
same fiber phase, lower the matrix phase density more is the damping ability. Though
both the thermosets polyester and epoxy have same material properties like Young’s
modulus, Rigidity modulus and Poisson’s ratio, epoxy has more damping ability than
polyester because of its low density.
46
Chapter 10
SCOPE OF FUTURE WORK
As the forces in the milling machine are bidirectional the total damping (in terms of loss factor)
cannot be calculated from the oscilloscope single amplitude readings alone. In addition to
oscilloscope, dynamometer and FFT analyzer has to be used. In each experimental step for each
vibration curve, the single amplitude and frequency at various disturbance zones are to be taken
and total damping (in terms of loss factor) is calculated from the graph plotted between
frequency and amplitude which on whole is a tedious method. Hence, FFT analyzer is connected
to oscilloscope on a circuit basis to get the final FFT curve for each experimental step.
Dynamometer is used to calculate the cutting forces during the experiments which has
reasonable effects on the vibration curves.
By testing suitable damping materials for structures according to the design requirements one
can use the findings of the present work in various vibration problems. Experimental technique
used in this report can be applied to achieve vibration isolation in different machine tool
structures.
The present work can be extended for other types of polymer and metal matrix composites with
fibers like carbon, boron with different types of fiber orientation.
47
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