PROJECT REPORT

ON

VIBRATION IN CUTTING TOOL

(MEASUREMENT AND ANALYSE)

Submitted in partial fulfillment of the

Requirement for the award of the

Degree of

B. Tech

in

MECHANICAL ENGINEERING

PROJECT GUIDE: Submitted by:

MR. DHANIRAM SHKRAWAL VIJAY KUMAR (7ME131L)

PREETAM KR. (7ME118L)

KARISHAN KR. (7ME113L)

PARVEEN KR. (7ME117L)

SANDEEP KR. (7ME134L)

SESSION: 2010-11

Department of Mechanical Engineering

LINGAYA’S INSTITUTE OF MANAGEMENT & TECHNOLOGY.

FARIDABAD

LINGAYA’S INSTITUTE OF MANAGEMENT & TECHNOLOGY.

FARIDABAD

ACKNOWLEDGEMENT

“SUCCESS IS NOURISHED UNDER THE KIND COMBINATION OF PERFECT

GUIDANCE, CARE AND BLESSING”

First and foremost, we, VIJAY KUMAR (7ME131L), PREETAM KUMAR (7ME118L), PARVEEN KUMAR (7ME117L), KARISHAN KUMAR (7ME113L) and SANDEEP KUMAR (7ME134L) are thankful to Dr. N.J. Dembi, Head of department MECH. ENGG., LIMAT for the kind support that they extended to us for making this project.

We would like to express our sincere gratitude to our project guide, Mr. Dhaniram

Shakrawal. We were privileged to experience a sustained enthusiastic and involved interest

from his side. This fuelled our enthusiasm even further and encouraged us to boldly step into

what was a totally dark and unexplored expanse before us.

We are also thankful to Mr. Sukesh Babu, (Mechanical Deptt.), Mr. Murli Karishan (Mechanical Deptt.) and Mr. R.K. Singh (Mechanical Deptt.) for their co-operation, kindness and general help extended to us during the completion of this work.

We would also like to thank our seniors who were ready with a positive comment all the time, whether it was an off-hand comment to encourage us or a constructive piece of criticism.

Last but not least, we would like to thank the mechanical staff members and the institute, in

general, for extending a helping hand at every juncture of need.

With due respect,

VIJAY KUMAR (7ME131L)

PREETAM KR. (7ME118L)

KARISHAN KR. (7ME113L)

PARVEEN KR. (7ME117L)

SANDEEP KR. (7ME134L)

CERTIFICATE

This is certified that the project report titled “VIBRATION IN CUTTING TOOL

(MEASUREMENT AND ANALYSIS)” submitted by VIJAY KUMAR (7ME131L),

PREETAM KUMAR (7ME118L), PARVEEN KUMAR (7ME117L), KARISHAN

KUMAR (7ME113L) and SANDEEP KUMAR (7ME134L) in partial fulfillment of the

requirements for the award of Degree of Bachelor of Technology (Mechanical) of M.D.

University Rohtak is record of bonafide work carried out under my supervision and has not

been submitted anywhere else for any other purpose.

DR. N.J. DEMBI MR. DHANIRAM SHAKRAWAL

(HEAD OF DEPTT. MECHANICAL) (PROJECT GUIDE)

ABSTRACT

Machining is a complex process in which many variables can deleterious the desired results. Among them, cutting tool vibration is the most critical phenomenon which influences dimensional precision of the components machined, functional behavior of the machine tools and life of the cutting tool. In a machining operation, the cutting tool vibrations are mainly influenced by cutting parameters like cutting speed, depth of cut and tool feed rate.

In this work, the cutting tool vibrations are measured by the use of Digital Vibration meter, which can measure displacement, velocity, acceleration and frequency. Experiments were conducted on a lathe machine tool. The cutting tool vibration signals were collected through a data acquisition system supported by RS-232 software. The sensor was attached with the tool post for sensing the vibration of tool during turning operation. The signal provided by sensor is shown in digital form on the screen of vibration meter. The vibration meter transfer these signal to computer where with the help of RS-232 software the data is recorded.

Three different materials were used for the collecting data at various parameters like depth of cut, speed, feed rate etc. A no. of data was recorded by varying the above parameters. On the completion of experimental work MATLAB is used to analyze the result for vibration in metal cutting tool and also to predict the behavior of the system under any cutting condition within the operating range

TABLE OF CONTENTS

Chapter Pages

CHAPTER 1……………………………………………………………1

INTRODUCTION

1.1 Units of vibration………………………………...…...………….21.2 Characteristics of vibration……………………………………....21.3 Relationship between the vibration parameters…………………31.4 Types of Vibration…………………………………………….....3

1.4.1 Free Vibration………...…………………………………….31.4.2 Forced Vibration…………………………………………....41.4.3 Self-excited vibration……………………………………....4

CHAPTER 2…………………………………………………………….6

VIBRATION IN MACHINE TOOL SYSTEM

2.1 SOURCES OF VIBRATION EXCITATION………………….....7

2.1.1 Vibration due to Inhomogeneities in the workpiece………7

2.1.2 Vibration due to cross-sectional variation

of removed material………………………………….…..8

2.1.3 Disturbances in the workpiece and tool drives……………9

2.1.4 Impacts from massive part reversals……………………....14

2.1.5 Vibration transmitted from the environment……………...15

2.1.6 Machine-tool chatter…………………………………….….16

2.2 The effect of vibration on tool life………………………………..19

2.3 Free Vibrations in the Machine-tool System………………………19

2.4 Forced Vibrations in the Machine-tool System……………………23

2.5 Disadvantage of Vibration in the Machine Tool System…………26

2.5.1 Chatter Occurring in the Machine Tool System……………26

2.5.2 Types of Chatters………………………………………......27

2.5.3 Machining Instability……………………………………......28

CHAPTER 3……………………………………………………………...29

VIBRATION CONTROL IN MACHINE TOOLS3.1 Stiffness…………………………………………………………29

3.2 Damping…………………………………………………….…..38

3.3 Tool Design…………………………………………………......42

3.4 Variation of Cutting Conditions………………………….…….43

CHAPTER 4………………………………………………………………45

VIBRATION MEASUREMENT

4.1 Measurement of Vibration……………………………………..45

4.2 Effect of the transducer on the vibrating structure……………46

4.3 Vibration Transducers…………………………………………..46

4.3.1 The Stroboscope Method………………………………46

4.3.2 The Reed Vibrometer…………………………………..47

4.3.3 The Seismic-Mass Transducer…………………………48

4.4 Comparison of Vibration-Measuring Systems……..…………..49

CHAPTER 5………………………………………………………………50

MACHINE DATA

5.1 EQUIPMENT……………………………………………………50

5.1.1 Machine Tool…………………………………………..50

5.1.2 Vibration Meter………………………………………...51

5.1.3 USB-232 Data Cable and Software……………………53

5.1.4 Computer……………………………………………….54

5.2 Block Diagram of Set up………………………………………...55CHAPTER 6………………………………………………………………56

APENDIX

APENDIX A………………………………………………………...56

6.1 Aluminium……………………………………………………....56

APENDIX B………………………………………………………...60

6.2 MILD STEEL…………………………………………………...60

APENDIX C………………………………………………………...64

6.3 Low Grade alloy steels………………………………………....64

CONCLUSIONS AND FUTURE WORK……………………………....68

BIBLIOGRAPHY………………………………………………………...69

LIST OF TABLE

Table Pages

1. Comparison of vibration-measuring systems……………………….….49

2. Techanical Data………………………………………………………...52

3. General Properties of Aluminium……………………………………....56

4. Analysed data of Aluminium Specimen………………………………..59

5. Analysed data of Mild Steel Specimen………………………………....63

6. Analysed data of Low Grade Alloy Steel Specimen…………………..66

LIST OF FIGURES

Figure Pages

1. Schematic illustrating the inuence of the delay on the cutting process….1

2. Free Vibration………………………………………………………………………4

3. Turning Opertion…………………………………………………………7

4. (A) Turning process with material defects,

( B) Single DOF free vibration system…………………………………20

5. (A) Internal grinding process,

(B) Single DOF forced vibration system……………………………….25

6. Poorly machined surface resulted from chatter…………………………26

7. Load transmission between column and bed.(A) Old design, relatively

flexible owing to deformation of flange.(B) New design, bolt placed in a

pocket (A) or flange stiffened with ribs on both sides of bolt (B)……...31

8. Successive stages in the improvement of a flange connection…………31

9. Torsional stiffness of box columns with different holes in walls………32

10. Influence of cover plate and lid on static stiffness of box column.(A)

Column without holes,(B) one hole uncovered,(C) hole covered with

cover plate, and (D) hole covered with substantial lid, firmly

attached……...………………………………………………………….33

11. Mounting schemes of a jig borer……………………………………….34

12.Deflection of machine-tool spindle and bearings. A machine-tool spindle

can be regarded as a beam on flexible supports. The total deflection

under the force P consists of the sum of (A) the deflection X1 of a flexible

beam on rigid supports and (B) the deflection X2 of a rigid beam on

flexible supports………………………………………………………..35

13. Effect of bore diameter on stiffness of hollow spindle where k1 =

stiffness of solid spindle, k2 = stiffness of hollow spindle, D =outer

spindle diameter, d = bore diameter, J2 =second moment of area of

hollow spindle, and J1= second moment of area of solid spindle. The

curve is defined by k2/k1 = J2/J1 = 1 − (d/D)…………………………....36

14. Load-deflection characteristics for flat, deeply scraped surfaces (overall

contact area 80 cm2).1,no lubrication;2,lightly lubricated(oil content 0.8 ×

10−3gram/cm2);3,richly lubricated (oil content 1.8 × 10−3gram/cm2)…..38

15. Influence of various components on total damping of lathes. The major

part of the damping is generated at the mating surfaces of the various

components…………………………………………………………......39

16. Auxiliary mass damper with combined elastic and damping element. The

combined element lies between two retainer rings, of which one (3) is

attached with bolt 1 to the machine structure. The other ring (2) takes the

weight of the auxiliary mass. (A) Arrangement when auxiliary mass is

being supported.(B) Arrangement when auxiliary mass is being

suspended.(C) Application of both types of arrangements to a hobbing

machine…………………………………………………………………40

17. Lanchester damper for the suppression of boring bar vibration……..41

18. The Stroboscope Method………………………………………………47

19. The Reed Vibrometer…………………………………………………..47

20. Seismic Mass Transducer………………………………………………49

21. Lathe Machine tool used for experiment……..……………………….51

22. Vibration sensor mounted on tool post………………………………..52

23. Digital Vibration Meter………………………………………………...53

24. Vibration meter and Computer………………………………………..54

25. Block Diagram of set up……………………………………………….55

26. Aluminium graph of Freq. vs Magnitude with depth of cut 0.5 mm and

speed 750 rpm………………………………………………………….57

27. Aluminium graph of Freq. vs Magnitude with depth of cut 1 mm and

speed 750 rpm…………………………………………………………..58

28. Aluminium graph of Freq. vs Magnitude with depth of cut 1 mm and

speed 750 rpm…………………………………………………………..58

29. Mild Steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and

speed 750 rpm…………………………………………………………..61

30. Mild Steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and

speed 1250 rpm………………………………………………………..61

31.Mild Steel graph of Freq. vs Magnitude with depth of cut 1 mm and

speed 750 rpm…………………………………………………………..62

32. Mild Steel graph of Freq. vs Magnitude with depth of cut 1 mm and

speed 1250 rpm…………………………………………………………62

33. Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 0.5

mm and speed 450………………………………………………………65

34. Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 0.5

mm and speed 750………………………………………………………65

35. Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 1

mm and speed 750………………………………………………………66

CHAPTER 1

INTRODUCTION

Vibration is a repetitive, periodic, or oscillatory response of a mechanical system.

The rate of the vibration cycles is termed “frequency.” Repetitive motions that are somewhat

clean and regular, and that occur at relatively low frequencies, are commonly called oscillations,

while any repetitive motion, even at high frequencies, with low amplitudes, and having irregular

and random behavior falls into the general class of vibration.

With the modern trend of machine tool development, accuracy and reliability are gradually

become more prominent feature. To achieve higher accuracy and productivity it is not enough to

design the machine tools from static consideration without considering the dynamic instability of

the machine tools. If there be any relative vibratory motion present between the cutting tool and

the job, it is obvious that the performance of the machine tool not be satisfactory. Moreover

machine tool vibration has detrimental effect on the tool life, which in turn, lowers down the

productivity and increase cost of production.

Figure 1.1: Schematic illustrating the inuence of the delay on the cutting process.

During operations machine tools are subjected to static and dynamic loads. These forces may act

in either of the following manners:

(1) Dynamic behaviour caused by entirely by the load acting during the action of the load

(forced vibration),

(2) Dynamic behaviour initiated by a load but persisting after load has caused to act (free

vibration),

(3) Dynamic behaviour through an interaction between the structure and cutting process

(self-exited vibration).

While analysing dynamic behaviour of machine tools, rigidity and stability are two

important characteristics to be considered. Dynamic rigidity is defined as the ratio of amplitude of

vibratory force considered harmonic to the vibratory displacement at a given frequency. It is the

measure of structure’s resistance to vibration.

1.1 Units of vibration

The units of vibration depend on the vibrational parameter, as follows:

a) Acceleration, measured in g or [m/s2;

b) Velocity, measured in [m/s];

c) Displacement, measured in [m].

1.2 Characteristics of vibration

Vibration may be characterised by:

a) The frequency in Hz;

b) The amplitude of the measured parameter, which may be displacement, velocity, or acceleration.

This is normally referred to as the vibration amplitude when expressed in units, but vibration level

when expressed in decibels.

1.3 Relationship between the vibration parameters

Assuming that the vibration is simple harmonic motion, then

Displacement (x) = A sin ωt

Velocity (v) = Aω cos ωt

Acceleration (a) = -Aω2 sin ωt

Where

ω = 2πf rad/s

f = frequency of vibration in Hz

Note that the frequencies are the same in each case, although there is a phase shift. The amplitudes

of the above parameters are thus

Displacement amplitude= A

Velocity amplitude = Aω

acceleration amplitude = Aω2

1.4. Types of Vibration

1.4.1. Free vibration

Free vibration occurs when a mechanical system is set off with an initial input and then

allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing

and then letting go or hitting a tuning fork and letting it ring. The mechanical system will then

vibrate at one or more of its "natural frequency" and damp down to zero.

Figure 1.2: Free Vibration

1.4.2. Forced vibration

Forced vibration is when an alternating force or motion is applied to a mechanical system.

Examples of this type of vibration include a shaking washing machine due to an imbalance,

transportation vibration (caused by truck engine, springs, road, etc.), or the vibration of a

building during an earthquake. In forced vibration the frequency of the vibration is the frequency

of the force or motion applied, with order of magnitude being dependent on the actual

mechanical system.

1.4.3. Self-excited vibration

Steady input force is modulated into vibration at the system natural frequency.

Examples include:

Whistle -steady air flow produces acoustic vibration

Violin -bow across string produces vibration at frequency that depends on string length chatter in

machining -steady excitation of teeth impacting work leads to large tool vibrations at system

natural frequency.

CHAPTER 2

VIBRATION IN MACHINE TOOL SYSTEM

Machining and measuring operations are invariably accompanied by relative vibration between

workpiece and tool. These vibrations are due to one or more of the following causes:

1. Inhomogeneities in the workpiece material

2. Variation of chip cross section

3. Disturbances in the workpiece 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 tolerable level of relative vibration between tool and workpiece, i.e., the maximum

amplitude and to some extent the frequency is determined by the required surface finish and

machining accuracy as well as by detrimental effects of the vibration on tool life and by the noise

which is frequently generated.

This chapter discusses the sources of vibration excitation in machine tools, machine-tool chatter

(i.e., self-excited vibration which is induced and maintained by forces generated by the cutting

process), and methods of control of machine-tool vibration.

Vibrations in the machine-tool system are a well-known fact in causing a number of

machining problems, including tool wear, tool breakage, machine spindle bearings wear and

failure, poor surface finish, inferior product quality and higher energy consumption.

Vibrations can be classified in a number of ways according to a number of possible

factors. For instance, vibrations can be classified as free vibrations, forced vibrations and self-

excited vibrations based on external energy sources. It is useful to identify vibrations types in

machine tools.

Figure 2.1 –Turning Opertion

2.1 SOURCES OF VIBRATION EXCITATION

2.1.1 Vibration due to Inhomogeneities in the workpiece

Hard spots or a crust in the material being machined impart small shocks to the tool and

workpiece, as a result of which free vibrations are set up. If these transients are rapidly damped

out, their effect is usually not serious; they simply form part of the general “background noise”

encountered in making vibration measurements on machine tools. Cases in which transient

disturbances do not decay but build up to vibrations of large amplitudes (as a result of dynamic

instability) are of great practical importance, and are discussed later. When machining is done

under conditions resulting in discontinuous chip removal, the segmentation of chip elements

results in a fluctuation of the cutting thrust. If the frequency of these fluctuations coincides with

one of the natural frequencies of the structure, forced vibration of appreciable amplitude may be

excited.

However, in single-edge cutting operations (e.g., turning),it is not clear whether the segmentation

of the chip is a primary effect or whether it is produced by other vibration, without which

continuous chip flow would be encountered. The breaking away of a built-up edge from the tool

face also imparts impulses to the cutting tool which result in vibration. However, marks left by

the built-up edge on the machined surface are far more pronounced than those caused by the

ensuing vibration; it is probably for this reason that the built-up edge has not been studied from

the vibration point of view. The built-up edge frequently accompanies certain types of vibration

(chatter), and instances have been known when it disappeared as soon as the vibration was

eliminated.

2.1.2 Vibration due to cross-sectional variation of removed material

Variation in the cross-sectional area of the removed material may be due to the shape of the

machined surface (e.g., in turning of a non round or slotted part) or to the configuration of the

tool (e.g., in milling and broaching when cutting tools have multiple cutting edges).In both cases,

pulses of appreciable magnitude may be imparted to the tool and to the workpiece, which may

lead to undesirable vibration. The pulses have relatively shallow fronts for turning of non-round

or eccentric parts and steep fronts for turning of slotted parts and for milling / broaching. These

pulses excite transient vibrations of the frame and of the drive whose intensity depends on the

pulse shape and the ratio between the pulse duration and the natural periods of the frame and the

drive. If the vibrations are decaying before the next pulse occurs, they can still have a detrimental

effect on tool life and leave marks on the machined surface. In cylindrical grinding and turning,

when a workpiece which contains a slot is machined, visible marks frequently are observed near

the “leaving edge” of the slot or keyway. These are due to a “bouncing” of the grinding wheel or

the cutting tool on the machined surface. They may be eliminated or minimized by closing the

recess with a plug or with filler.

When the transients do not significantly decay between the pulses, dangerous resonance

vibrations of the frame and/or the drive can develop with the fundamental and higher harmonics

of the pulse sequence. The danger of the resonance increases with higher cutting speeds.

Simultaneous engagement of several cutting edges with the workpiece results in an increasing dc

component of the cutting force and effective reduction of the pulse intensity, while run out of a

multi-edge cutter and inaccurate setup of the cutting edges enrich the spectral content of the

cutting force and enhance the danger of resonance. Computational synthesis of the resulting

cutting force is reasonably accurate.

2.1.3 Disturbances in the workpiece and tool drives

Forced vibrations result from rotating unbalanced masses, gear, belt, and chain drives, bearing

irregularities, unbalanced electromagnetic forces in electric motors, pressure oscillations in

hydraulic drives etc.

2.1.3.1 Vibration Caused by Rotating Unbalanced Members

Forced vibration induced by rotation of some unbalanced member may affect both surface finish

and tool life, especially when its rotational speed falls near one of the natural frequencies of the

machine-tool structure. This vibration can be eliminated by careful balancing, or by self

centering due to resilient mounting of bearings.

When a new machine is designed, a great deal of trouble can be forestalled by placing rotating

components in a position in which the detrimental effect of their unbalance is likely to be

relatively small. Motors should not be placed on the top of slender columns, and the plane of

their unbalance should preferably be parallel to the plane of cutting. In some cases, vibration

resulting from rotating unbalanced members can be eliminated by mounting them using

vibration-isolation techniques

Grinding and boring are most sensitive to vibration because of the high surface finish resulting

from the operations. In cylindrical grinding, marks resulting from unbalance of the grinding

wheel or of some other component are readily recognizable. They appear in the form of equally

spaced, continuous spirals with a constant slope. From these marks, the machine component

responsible for their existence is found by considering that its speed in rpm must be equal to

πDn/a, where D is the workpiece diameter in inches (millimeters), a is the pitch of the marks in

inches (millimeters), and n is the workpiece speed in rpm. An analogous procedure also can be

applied to peripheral surface grinding. The speed of the responsible component in

rpm is equal to the number of marks (produced in one pass) which fall into a distance equal to

that traveled by the workpiece (or wheel) in 1 min.

Since centrifugal force magnitudes are proportional to the square of rpm, high-speed machine

tools are more sensitive to unbalance of tool holders and small asymmetrical tools (e.g., boring

bars).Lathes may be sensitive to workpiece unbalance due to asymmetrical geometry or the

nonuniform allowance (e.g., forged parts).

2.1.3.2 Marks Caused by Inhomogeneities in the Grinding Wheel

Although grinding marks usually indicate the presence of a vibration, this vibration may not

necessarily be the primary cause of the marks. Hard spots on the cutting surface of the wheel

result in similar, though generally less pronounced marks. Grinding wheels usually are not of

equal hardness throughout. A hard region on the wheel circumference rapidly becomes glazed in

use and establishes itself as a high spot on the wheel (since it retains the grains for a longer

period than the softer parts).These high spots eventually break down or shift to other parts of the

wheel; in cylindrical grinding, this manifests itself as a sudden change in the slope of the spiral

marks. Marks which appear to be due to an unbalanced member rotating at two or three times the

speed of the wheel and which are non-uniformly spaced are always due to two or three hard

spots.

2.1.3.3 The Effect of Vibration on the Wheel Properties

If vibration exists between wheel and workpiece, normal forces are produced which react on the

wheel and tend to alter the wheel shape and/or the wheel’s cutting properties. In soft wheels the

dominating influence of vibration appears to be inhomogeneous wheel wear, and in hard wheels

inhomogeneous loading (i.e., packing of metal chips on and in crevasses between the

grits).These effects result in an increased fluctuation of the normal force, which produces further

changes in the wheel properties. The overall effect is that a vibration once initiated tends to

grow. When successive cuts or passes overlap, the inhomogeneous wear and loading of the

wheel may cause a regenerative chatter effect which makes the cutting process dynamically

unstable.

2.1.3.4 Drives

Spindle and feed drives can be important sources of vibration caused by motors, power

transmission elements (gears, traction drives, belts, screws etc.), bearings, and guide ways.

Electric motors can be sources of both rectilinear and torsional vibrations. Rectilinear vibrations

are due to a non-uniform air gap between the stator and rotor, asymmetry of windings,

unbalance, bearing irregularities, misalignment with the driven shaft etc. Torsional vibrations

(torque ripple) are due to various electrical irregularities. Misalignment and bearing-induced

vibrations of spindle motors are reduced by integrating the spindle with the motor shaft.

Gear induced vibrations can also be both rectilinear and torsional. They are due to production

irregularities (pitch and profile errors, eccentricities etc), assembly errors (eccentric fit on the

shaft, key/spline errors and backlash), or distortion of mesh caused by deformations of shafts,

bearings, and housings under transmitted loads. Tight tolerances of the gears and design

measures reducing their sensitivity to misalignment (crowning, flanking) should be accompanied

by rigid shafts and housings and accurate fits. All gear faults, eccentricities, pitch errors, profile

errors etc., produce non-uniform rotation, which in some cases adversely affects surface finish,

geometry, and possibly tool life. In precision machines, where a high degree of surface finish is

required, the workpiece or tool spindle usually is driven by belts or by directly coupled motors.

In some high-precision systems, inertia drives are used, in which the energy is supplied to the

flywheel between the cutting operations,but the cutting process is energized by the flywheel

disconnected from the motor/transmission system. Such a system practically eliminates

transmission of drive vibrations into the work zone.

Belt drives, used in some applications as filters to suppress high-frequency vibrations (especially

torsional), can induce their own forced vibrations, both torsional and rectilinear. Any variation of

the effective belt radius, i.e., the radius of the neutral axis of the belt around the pulley axis,

produces a variation of the belt tension and the belt velocity. This causes a variation of the

bearing load and of the rotational velocity of the pulley. The effective pulley radius can vary as a

result of eccentricity of the pulley or variation of belt profile or inhomogeneity of belt material.

Another source of belt-induced vibrations is variation of the elastic modulus along the belt

length, which may excite parametric vibration. Flat belts generate less vibration than V belts

because of their better homogeneity and because the disturbing force is less dependent on the

belt tension.

Grinding is particularly sensitive to disturbances caused by belts. Seamless belts or a direct

motor drive to the main spindle is recommended for high-precision machines. Vibration is

minimized when the belt tension and the normal grinding force point in the same direction. The

clearance between bearing and spindle is thus eliminated. Large amplitudes of vibration may

arise when the normal grinding force is substantially equal to the belt tension and/or the

peripheral surface of the wheel is non-uniform. Tests indicate that vibration due to the

centrifugal force is likely to be caused by an unbalance of the wheel. The spindle pulley should

preferably be placed between the spindle bearings and not at the end of the spindle , unless the

pulley is “unloaded”(supported by its own bearings). Chain drives have inherent non-uniformity

of transmission ratio and are a significant source of vibration, even when used for auxiliary

drives.

2.1.3.5 Bearings

Dimensional inaccuracies of the components of ball or roller bearings and/or surface

irregularities on the running surfaces (or the bearing housing) may give rise to vibration trouble

in machines when high-quality surface finish is demanded. From the frequency of the vibration

produced, it is sometimes possible to identify the component of the bearing responsible. For

conventional bearings frequently used in machine tools, the outer race is stationary and the inner

race rotates. In some cases, a disturbing frequency can be detected. This is the frequency with

which successive rolling elements pass through the “loaded zone” of the bearing, which is

determined by the direction of the load. These disturbing frequencies are less pronounced with

bearings having two rows of rolling elements, each unit of which lies halfway between units of

the neighboring row. Because of the importance of spindle bearings’ influence on accuracy of

machining and on vibrations in the work zone, especially for precision and high-speed machine

tools, both races and rolling bodies of spindle bearings must have high dimensional accuracy.

From the point of view of vibration control, both stiffness and damping of bearings should be

maximized. Stiffness can be maximized by using roller bearings (with tapered or cylindrical

rollers), by using rollers with two rows of rolling elements, by preloading the bearings in the

radial direction, and by improving fits between bearings and shafts/housings. Preloading

eliminates clearances (play) in bearings, besides increasing their stiffness. However, increased

preload is accompanied by decreased damping, as well as by an increase in heat generation and a

likely decrease in bearing life. Optimal preload values are recommended by bearing

manufacturers. Roller bearings usually have higher damping than ball bearings. Sliding, and

especially hydrostatic, bearings have a greater damping capacity than antifriction bearings and

are therefore superior with respect to vibration. Machine tools with hydrostatic bearings have

extremely high chatter resistance.

2.1.3.6 Guideways (Slides)

The uniformity of feed motions is often disturbed by a phenomenon known as stick-slip. When

motion of a tool support is initiated, elastic deformations of the feed drive elements increase until

the forces transmitted exceed the static frictional resistance of the tool support. Subsequently, the

support commences to move, and the friction drops to its dynamic value. As a result of the drop

of the friction force, the support receives a high acceleration and overshoots because of its

inertia. At the end of the “jump” the transmission is wound up in the opposite sense; before any

further motion can take place, this deformation must be unwound. This occurs during a period of

standstill of the support. Subsequently, the phenomenon repeats itself. The physical sequence

described falls into the category generally known as “relaxation oscillations”. The occurrence of

stick-slip depends on the interaction of the following factors:

1. The mass of the sliding body,

2. The drive stiffness,

3. The damping present in the drive,

4. The sliding speed,

5. The surface roughness of the sliding surfaces,

6. The lubricant used.

It is encountered only at low sliding speeds; slide drives designed for stick-slip-free motion have

small moving masses and high drive stiffness. Excellent results also may be achieved by using

cast iron and a suitable plastic material as mating surfaces. By keeping the oil film between the

mating surfaces under a certain pressure (hydrostatic lubrication),the possibility of mixed dry

and viscous friction is eliminated, and stick-slip cannot arise. High damping is another advantage

of hydrostatic slides.

Rolling friction slides do not exhibit stick-slip but may generate high-frequency vibrations

because of the shape and dimensional imperfections of the rolling bodies. These can be reduced

by increasing their dimensional accuracy and by introducing damping. Rolling friction slides

have very low damping and as a result can amplify vibrations from other sources if their

frequencies are close to resonance frequencies of the slide. High-precision systems require

extremely low friction as well as the absence of vibration.

2.1.4 Impacts from massive part reversals

Some machine tools have reciprocating massive parts whose reversals produce sharp impacts

which excite both low-frequency solid-body vibrations of the machine (the system “machine on

its mounts”) and high-frequency structural modes. Such effects occur both in machine tools,such

as surface grinders, and in high-speed computer numerically controlled (CNC) machining centers

and coordinate measuring machines(CMM). In the CMMs the working process is associated with

start-stop operations; in machining centers it is associated with changing magnitude and/or

directions of feed motions of heavy tables, slides, spindle heads etc., with accelerations as high

as 2g. The driving forces causing such changes in magnitudes and directions of momentum of

the massive units have impulsive character and cause free decaying vibrations in both solid-body

and structural modes. These vibrations excite relative displacements in the work zone between

the workpiece and the cutting or measuring tool.

Reduction in the adverse effects of the impulsive forces can be achieved by enhancing the

structural stiffness and natural frequencies, thus reducing the sensitivity of the machine to

impulsive forces and accelerating the decay. A similar effect results from an increase in “solid-

body frequencies” (the natural frequencies of the machine on its mounts) in the direction of the

impulsive forces and from decoupling of vibratory modes in the vibration-isolation system, e.g.,

by increasing the distance between the mounts in the direction of acceleration. Increase of

structural damping as well as damping of mounting elements (vibration isolators) also results in a

reduction in the decay time.

2.1.5 Vibration transmitted from the environment

Shock and vibration generated in presses, machine tools, internal-combustion engines,

compressors, cranes, carts, rail and road vehicles etc., are transmitted through the foundation to

other machines, which they may set into forced vibration. Vibration of the shop floor contains a

wide frequency spectrum. It is almost inevitable that one of these frequencies should fall near a

natural frequency of a particular machine tool. Although the amplitudes of the floor vibration

usually are small, they may adversely affect precision machine tools and measuring instruments.

The undesirable effects include irreversible shifts in structural joints of machine tools and their

mounts, shape and surface finish distortions of machined parts, erroneous readings of measuring

instruments, and chipping of cutting inserts. Vibration transmitted through the floor may be

reduced by vibration isolation i.e., the stationary machines which generate the vibration are

placed upon vibration isolators. However, precision machine tools and measuring instruments

are isolated to provide further reduction.

When applying vibration isolators to machine tools, some care must be exercised. The

foundation constitutes the “end condition” of the machine-tool structure. Any alteration of the

end condition affects equivalent stiffness and damping, and thus the natural frequencies and

vibratory modes of the structure.

If vibration isolators are not properly selected and located, the machine tool may become more

susceptible to internal exciting forces, and its chatter behavior also may be affected in an

undesirable way, usually at the lower modes of vibration. Many undesirable effects can be

eliminated or significantly reduced by using vibration isolators having a natural frequency that is

independent of weight loads on isolators (“constant natural frequency” isolators); by using

isolators with high damping; by assigning the mounting points locations that enhance the

effective stiffness of the machine-tool frame; by increasing the stiffness of isolators and the

distance between them in the directions of movements of heavy reciprocating masses and by

reducing modal coupling in the isolation system. In general, machine-tool structures which are

very stiff by themselves (i.e., without being bolted down) can be placed on vibration isolators

safely (milling machines, grinding machines, and some lathes).

2.1.6 Machine-tool chatter

The cutting of metals is frequently accompanied by violent vibration of workpiece and cutting

tool which is known as machine-tool chatter. Chatter is a self-excited vibration which is induced

and maintained by forces generated by the cutting process. It is highly detrimental to tool life and

surface finish, and is usually accompanied by considerable noise. Chatter adversely affects the

rate of production since, in many cases its elimination can be achieved only by reducing the rate

of metal removal. Cutting regimes for non attended operations (such as computer numerically

controlled machine tools and flexible manufacturing systems) are frequently assigned

conservatively in order to avoid the possibility of chatter.

Machine-tool chatter is characteristically erratic since it depends on the design and configuration

of both the machine and the tooling structures, on workpiece and cutting tool materials, and on

machining regimes. Chatter resistance of a machine tool is usually characterized by a maximum

stable (i.e., not causing chatter vibration) depth of cut. Forced vibration effects in machine tools

are more frequently detected in the development stage or during final inspection, and can be

reduced or eliminated. The tendency for a certain machine to chatter may remain unobserved in

the plant of the machine-tool manufacturer unless the machine is thoroughly tested. If this

tendency is encountered at the user facility, its elimination from a particular machining process

may be highly time-consuming and laborious. A distinction can be drawn between regenerative

and non regenerative chatter. The former occurs when there is an overlap in the process of

performing successive cuts such that part of a previously cut surface is removed by a succeeding

pass of the cutter. Under regenerative cutting, a displacement of the tool can result in a vibration

of the tool relative to the workpiece, resulting in a variation of the chip thickness. This in turn

results in a variation in the cutting force during following revolutions. The regenerative chatter

theory explains a wide variety of practical chatter situations in such operations as normal turning

and milling. An important characteristic feature of regenerative chatter is a “lobing” dependence

of the maximum stable depth of cut on cutting speed (rpm of tool or workpiece).

There is an area of absolute stability below the lobes’ envelope. The position of this envelope

depends on the material and geometry of the cutting tool as well as the workpiece material. The

lobing shape indicates that some speeds are characterized by much higher stability.

Non regenerative chatter is found in such operations as shaping, slotting, and screw-thread

cutting. In this type of cutting, chatter has been explained through the principle of mode

coupling.

If a machining system can be modeled by a two degree of freedom mass-spring system,with

orthogonal axes of major flexibilities and with a common mass, the dynamic motion of the tool

end can take an elliptical path. If the major axis of motion (axis with the greater compliance) lies

within the angle formed by the total cutting force and the normal to the workpiece surface,

energy can be transferred into the machine-tool structure, thus producing an effective negative

damping. The depth of cut for the threshold of stable operation is directly dependent upon the

difference between the two principal stiffness values, and chatter tends to occur when the two

principal stiffnesses are close in magnitude.

2.1.6.1 Dynamic stability

Machine-tool chatter is essentially a problem of dynamic stability. A machine tool under

vibration-free cutting conditions may be regarded as a dynamical system in steady state motion.

Systems of this kind may become dynamically unstable and break into oscillation around the

steady motion. Instability is caused by an alteration of the cutting conditions produced by a

disturbance of the cutting process (e.g., a hard spot in the material). As a result, a time-dependent

thrust element dP is superimposed on the steady cutting thrust P. If this thrust element is such as

to amplify the original disturbance, oscillations will build up and the system is said to be

unstable. This chain of events is most easily investigated theoretically by considering that the

incremental thrust element dP is a function not only of the original disturbance but also of the

velocity of this disturbance. Forces which are dependent on the velocity of a displacement are

damping forces; they are additive to or subtractive from the damping present in the system (e.g.,

structural damping or damping introduced by special anti vibration devices).When the damping

due to dP is positive, the total damping (structural damping plus damping due to altered cutting

conditions) also is positive and the system is stable.Any disturbance will then be damped out

rapidly. However, the damping due to dP may be negative, in which case it will decrease the

structural damping, which is always positive. If the negative damping due to dP predominates,

the total damping is negative.

Positive damping forces are energy absorbing. Negative damping forces feed energy into the

system; when the total damping is negative, this energy is used for the maintenance of

oscillations (chatter). From the practical point of view, the fully developed chatter vibration

(self-induced vibration) is of little interest. Production engineers are almost entirely concerned

with conditions leading to chatter (dynamic instability).The build-up of chatter is very difficult to

observe, and experimental work has to be carried out mainly under conditions which are only

indirectly relevant to the problem being investigated. Experimental results obtained from fully

developed chatter vibration may, in some instances, be not really relevant to the problem of

dynamic stability.

The influence of the machine-tool structure on the dynamic stability of the cutting process is of

great importance. This becomes clear by considering that with a structure (including tool and

workpiece) of infinite stiffness, the cutting process could not be disturbed in the first place

because hard spots, for example, would not be able to produce the deflections necessary to cause

such a disturbance. Further-more, it is clear that were the structural damping infinite, the total

damping could not become negative and the cutting process would always be stable. This

discussion indicates that an increase in structural stiffness and/or damping always has beneficial

effects from the point of view of chatter.

In practically feasible machines, the interrelation between structural stiffness, damping, and

dynamic stability is of considerable complexity. This is because machine-tool structures are

systems with distributed mass, elasticity, and damping; their vibration is described by a large set

of partial differential equations which can be analyzed using simplified models or more precise

large finite-element models. Stiffness and damping play similar roles in determining the stability

of a machine tool. The maximum stable depth of cut is proportional to a product of effective

stiffness and effective damping coefficients. The cutting angles and the number and shape of the

cutting edges of the cutting tool are important.

2.2 The effect of vibration on tool life

As much as the cutting speed and the chip cross section vary during vibration, it is to be expected

that vibration affects tool life. The magnitude of this effect is unexpectedly large, even when

impact loading of the tool is excluded. Elimination of vibration may significantly enhance tool

life. Ceramic and diamond tools are especially sensitive to impact loading. The life of face-mill

blades may suffer considerably owing to torsional vibration executed by the cutter. The torsional

vibration need not necessarily be caused by dynamic instability of the cutting process but may be

forced vibration, because of resonance caused by one of the harmonics of impact excitation from

interrupted chip removal, by tool runout etc. Judiciously applied forced vibration of the tool

and/or the workpiece may also significantly enhance tool life by reducing cutting forces, leading

to enhanced dynamic stability.

2.3 Free Vibrations in the Machine-tool System

If an external energy source is applied to initiate vibrations and then removed, the

resulting vibrations are free vibrations. In the absence of non-conservative forces, free vibrations

sustain themselves and are periodic.

The vibrations of machine tools under pulsating excitations can be regarded as free vibrations.

The origins of pulsating excitations in machine tools include:

• Cutter-contact forces when milling or flying cutting

• Inertia forces of reciprocating motion parts

• Vibrations transmitting from foundations

• Imperfects of materials

For instance, taking a single-point diamond turning a part as an example, the part has

some material defects such as cavities, as shown in Figure 2.2a. If the cutting tool is taken as the

object to be investigated, it can be simplified as a single DOF mass-spring free vibration system

as shown in Figure 2.2b, although this is an idealized model and the real system is far more

complicated.

Firstly, consider the case of an undamped free vibration system.

The general form of the differential equation for undamped free vibrations is:

Mx + Kx = 0 (2.1)

Figure 2.2. (a) Turning process with material defects,( b) Single DOF free vibration system

Where M and K are the mass and stiffness which are determined during the derivation of the

differential equation. Equation 2.1 is subject to the following initial conditions of the form:

x (0)=x 0

x(0) = x 0

The solution of Equation 2.1 is:

(2.2)

where x is displacement at time t:

x0 is the initial displacement of the mass

is the undamped natural frequency.

There is a slight increase in system complexity while a damping element is introduced to the

spring-mass system. Here only viscous damping is taken into account. The general form of the

differential equation for the displacement of damped free vibrations becomes:

Mx+ cx+ Kx= 0 (2.3)

Where c is the damping of the system.

Dividing Equation 2.3 by M gives:

(2.4)

The general solution of Equation 2.4 is obtained by assuming:

(2.5)

The substitution of Equation 2.5 into Equation 2.4 gives the following quadratic equation for a:

(2.6)

The quadratic formula is used to obtain the roots of Equation 2.6:

(2.7)

The mathematical form of the solution of Equation 2.4 and the physical behavior of the system

depend on the sign of the discriminant of Equation 2.7. The case when the discriminant is zero is

a special case and occurs only for a certain combination of parameters. When this occurs the

system is to be critically damped.

For fixed values of K and M, the value of c which causes critical damping is called the critical

damping coefficient, cc:

(2.8)

The non-dimensional damping ratio, z, is defined as the ratio of the actual value of

c, to the critical damping coefficient:

(2.9)

The damping ratio is an inherent property of the system parameters. Using Equations 2.8 and

2.9,Equation 2.7 is rewritten in terms of z and wn as:

(2.10)

Therefore, the general solution of Equation 2.4 is:

(2.11)

where C1 and C2 are the arbitary constants of integration. From Equation 2.11, it is evident that

the nature of the motion depends on the value of z; Equation 2.4 then becomes:

(2.12)

This is the standard form of the differential equation governing the free vibrations with damping.

There are different conditions of damping: critical, overdamping, and underdamping.

2.4 Forced Vibrations

If vibrations occur during the presence of an external energy source, the vibrations are called

forced vibrations. The behavior of a system undergoing forced vibrations is dependent on the

type of external excitation. There are a few types of external forces including harmonic, periodic

but not harmonic, step, impulse and arbitrary force, etc. If the excitation is periodic, the forced

vibrations of a linear system are also periodic.

Considering the internal grinding process in which the spindle is out of balance, the resulted

unbalance force is assumed in a harmonic form, Fsin(wt+j). This force will vibrate the grinder

relative to the work piece and result in forced vibrations.

Again, an undamped mass-spring system under harmonic forces is considered. The differential

equation for undamped forced vibrations subjected to an excitation of harmonic force is:

(2.13)

If excitation frequency w is not equal to wn the following equation is used to obtain the

particular solution of Equation 2.13:

(2.14)

The homogeneous solution is added to the particular solution with the initial conditions applied,

yielding:

(2.15)

In a damped forced vibration system with harmonic excitation the standard form of the

differential equation is:

(2.16)

The particular solution of Equation 2.16 is:

(2.17)

Equation 2.17 can be rewritten in the following alternative form:

(2.18)

A is the amplitude of the forced response and f is the phase angle between the response and the

excitation.

Figure 2.3 (a) Internal grinding process, (b) Single DOF forced vibration system.

Forced vibrations in machine tools can be generated from two kinds of energy sources, which are

internal and external vibration sources. External vibration sources, such as seismic waves,

usually transfer vibrations to the machine tool structure via the machine base. The design and use

of effective vibration isolators will be able to eliminate or minimize forced vibrations caused by

external vibration sources. There are many internal vibration sources which cause forced

vibrations. For instance, an unbalanced high speed spindle, an impact force in machining

processes, and inertia force caused by a reciprocal motion component such as slide ways, etc.

2.5 Disadvantage of Vibration in the Machine Tool System

2.5.1 Chatter Occurring in the Machine Tool System

Apart from free and forced vibrations, self-excited vibrations exist commonly in

machine-tool system. A self-excited vibration is a kind of vibration in which the vibration

resource lies inside the system. In machining self-excited vibrations usually result in machine

tool chatter vibration. It should be noted that chatter vibration can also be caused by the forced

vibration, but it is usually not a major problem in machining because the external force or the

dynamic compliance of the machine structure can be reduced to reasonable levels when the

external force causing the chatter is identified.

Figure 2.4. Poorly machined surface resulted from chatter (Courtesy: GE Company)

Chatter occurs mainly because one of the structural modes of the machine tool workpiece

system is initially excited by cutting forces. Chatter is a problem of instability in the machining

process, characterized by unwanted excessive vibration between the tool and the workpiece, loud

noise, and consequently a poor quality of surface finish. It also has a deteriorating effect on the

machine and tool life, and the reliability and safety of machining operation. The problem has

affected the manufacturing community for quite some time and it is a popular topic for academic

and industrial research. Therefore, it is very important to identify and to get a better

understanding of the machine structural dynamic performance at both the machine design and

production stage. Figure 2.4 shows a poorly machined surface resulting from chatters.

2.5.2 Types of Chatters

There are mainly three forms of self-excited chatters. The first one is the velocity

dependent chatter or Arnold-type chatter, named after the man who discovered it, which is due to

a dependence on the variation of force with the cutting speed. The second form is known as the

regenerative chatter, which occurs when the unevenness of the surface being cut is due to

consequent variations in the cutting force when on the previous occasion the tool passed over

that location, causing detrimental degeneration of the cutting force. Depending on the phase shift

between the two successive wave surfaces, the maximum chip thickness may exponentially grow

while oscillating at a chatter frequency that is close to but not equal to the dominant structural

mode in the system. The growing vibrations increase the cutting forces and produce a poor and

wavy surface finish. The third form of chatter is due to mode coupling when forces acting in one

direction on a machine-tool structure cause movements in another direction and vice versa.

This results in simultaneous vibrations in two coupling directions. Physically it is caused by a

number of sources, such as friction on the rake and clearance surfaces and mathematically

described by Wiercigroch.

Most of the chatters occurring in practical machining operations are regenerative chatter,

although other chatters are also common in some cases. These forms of chatters are

interdependent and can generate different types of chatter simultaneously. However, there is not

a unified model capable of explaining all chatter phenomena observed in machining practice.

2.5.3 Machining Instability

In the previous sections, many aspects of self-excited machine tool vibrations or chatters have

been briefly discussed. In practice, however, many problems of poor work surface finish are due

to forced vibrations and the methods of reducing forced vibrations should thus well be

understood. Forced vibrations are usually caused by an out-of-balance force associated with a

component integrated with, or external to, the machine tool, whereas a self-excited vibration is

spontaneous and increases rapidly from a low vibratory amplitude to a large one; the forced

vibration results in an oscillation of constant amplitude. An exploration into chatter vibrations

enables a better understanding of machining instability in practice. From the machining point of

view, with the designed machining conditions, a desired surface finish will be produced under a

stable machining process. But as a complicated dynamic system, various mechanisms inherent in

the machining process may lead the innately stable machining system to work at a dynamically

unstable status which invariably results in unsatisfactory workpiece surface quality. For instance,

a variety of disturbances affect the machining system such as self-excited vibration, thermo

mechanical oscillations in material flow, and feed drive hysteresis, but the most important is self-

excited vibrations resulting from the dynamic instability of the overall machine-tool/machining

process system. However, sometimes the machining process is carried out with a relative

vibration between the workpiece and the cutting tool, especially in heavy cutting and rough

machining, in order to obtain high material removal rates.

The relative vibration is not necessarily a sign of the machining instability for the

designed machining conditions and prescribed surface finish. The surface generated may be

unsatisfactory because of the disturbance, even though the machining system itself operates in

the stable state. Therefore, the machining instability is related to the level of the surface quality

required and the designed machining conditions.

CHAPTER 3

VIBRATION CONTROL IN MACHINE TOOLS

Vibration in metal cutting is familiar to every machine tool operator. This phenomenon is

recognized in operations such as internal turning, threading, grooving, milling, boring and

drilling, to which there are several reasons why this problem occurs. Some are related to the

machine tool itself, to the clamping of the tool, the length and diameter of the tool holder and the

cutting data to be used.

The vibration behavior of a machine tool can be improved by a reduction of the intensity of the

sources of vibration, by enhancement of the effective static stiffness and damping for the modes

of vibration which result in relative displacements between tool and workpiece, and by

appropriate choice of cutting regimes, tool design, and workpiece design. Abatement of the

sources is important mainly for forced vibrations. Stiffness and damping are important for both

forced and self-excited (chatter) vibrations. Both parameters, especially stiffness, are critical for

accuracy of machine tools, stiffness by reducing structural deformations from the cutting forces,

and damping by accelerating the decay of transient vibrations. In addition, the application of

vibration dampers and absorbers is an effective technique for the solution of machine-vibration

problems. Such devices should be considered as a functional part of a machine, not as an add-on

to solve specific problems.

3.1 STIFFNESS

Static stiffness ks is defined as the ratio of the static force Po, applied between tool and

workpiece, to the resulting static deflection As between the points of force application. A force

applied in one coordinate direction is causing displacements in three coordinate directions; thus

the stiffness of a machine tool can be characterized by a stiffness matrix (three proper stiffness’s

defined as ratios of forces along the coordinate axes to displacements in the same directions, and

three reciprocal stiffness’s between each pair of the coordinate axes).Frequently only one or two

stiffness’s are measured to characterize the machine tool.

Machine tools are characterized by high precision, even at heavy-duty regimes (high magnitudes

of cutting forces).This requires very high structural stiffness. While the frame parts are designed

for high stiffness, the main contribution to deformations in the work zone (between tool and

workpiece) comes from contact deformations in movable and stationary joints between

components (contact stiffness). Damping is determined mainly by joints (log decrement ∆≅ 0.15), especially for steel welded frames (structural damping ∆≅ 0.001).Cast iron parts

contribute more to the overall damping (∆≅ 0.004), while material damping in polymer-concrete

(∆≅0.02) and granite (∆≅ 0.015) is much higher. While the structure has many degrees of

freedom, dangerous forced and self-excited vibrations occur at a few natural modes which are

characterized by high intensity of relative vibrations in the work zone. Since machine tools

operate in different configurations (positions of heavy parts, weights, dimensions, and positions

of workpieces) and at different regimes (spindle rpm, number of cutting edges, cutting angles

etc.), different vibratory modes can be prominent depending on the circumstances.

The stiffness of a structure is determined primarily by the stiffness of the most flexible

component in the path of the force. To enhance the stiffness, this flexible component must be

reinforced. To assess the influence of various structural components on the overall stiffness, a

breakdown of deformation (or compliance) at the cutting edge must be constructed analytically

or experimentally on the machine. Breakdown of deformation (compliance) in torsional systems

(transmissions) can be critically influenced by transmission ratios between the components. In

many cases the most flexible components of the breakdown are local deformations in joints i.e.,

bolted connections between relatively rigid elements such as column and bed, column and table

etc. Some points to be considered in the design of connections are illustrated in Fig.3.1

To avoid bending of the flange in Fig.3.1A, the bolts should be placed in pockets or between

ribs, as shown in Fig.3.1B. Increasing the flange thickness does not necessarily increase the

stiffness of the connection, since this requires longer bolts, which are more flexible. There is an

optimum flange thickness (bolt length), the value of which depends on the elastic deformation in

the vicinity of the connection. Deformation of the bed is minimized by placing ribs under

connecting bolts.

Figure 3.1: Load transmission between column and bed.(A) Old design, relatively flexible owing to deformation of

flange.(B) New design, bolt placed in a pocket (A) or flange stiffened with ribs on both sides of bolt (B).

. Figure 3.2 shows the results of successive stages of a model experiment in which the effect of

the design of bolt connections on the bending rigidity (X and Y directions) and the torsional

rigidity of a column were investigated. The relative rigidities are shown by the length of bars.

Figure 3.2: Successive stages in the improvement of a flange connection.

In the design of Fig.3.2A, the connection consists of 12 bolts (diameter of 5⁄8 in.) arranged in

pairs along both sides of the column. In the design of Fig.3.2B, the number of bolts is reduced to

10, arranged as shown. With the addition of ribs, shown in succeeding figures, the bending

stiffness in the direction X was raised by 40 percent, which in the direction Y by 45 percent, and

the torsional stiffness by 53 percent, compared to the original design.

Openings in columns should be as small as possible. Smaller holes result in relatively smaller

decreases of stiffness and natural frequency than larger ones. The torsional rigidity k sθ of a box

type column is particularly sensitive to openings, as shown in Fig.3.3.

Figure 3.3: Torsional stiffness of box columns with different holes in walls

Lids or doors used for covering these openings do not restore the stiffness. The influence of

covers depends on their thickness, mode of attachment, and design, as shown in Fig.3.4.

However, covers may increase damping and thereby partly compensate for the detrimental effect

of loss of stiffness.

Welded structural components are usually stiffer than cast iron components but have a lower

damping capacity. Some damping is generated because welds are never perfect; consequently,

rubbing takes place between joined members. A considerable increase in damping can be

achieved by using interrupted welds, but at a price of reduced stiffness. Welded ribs may be

necessary not so much to increase rigidity as to prevent “drumming”(membrane vibration) of

large unsupported areas.

Figure 3.4: Influence of cover plate and lid on static stiffness of box column.(A) Column without holes,(B) one hole

uncovered,(C) hole covered with cover plate, and (D) hole covered with substantial lid, firmly attached.

Not all deformations in machine tools are objectionable, but only those which influence relative

displacements in the work zone between the tool and the workpiece. The magnitude of the

relative displacement in the work zone under external or internal forces (weight, cutting force,

inertia force) determines effective stiffness.

Effective stiffness of machine-tool frames is significantly influenced by their interaction with the

supporting structures (foundations).For large, low-aspect-ratio machine-tool frames, a rigid

attachment to a properly dimensioned foundation substantially improves dynamic stability.

Medium- and small-size machine tools are usually attached to the reinforced floor plate by

discrete mounts (rigid wedge or screw mounts or vibration isolators). A rational assignment of

number and location of mounts noticeably enhances the effective stiffness of machine tools and

in some cases may allow direct mounting of rather large machine tools on vibration isolators.

Figure 3.5: Mounting schemes of a jig borer.

Examples of influence of number and location of mounts on the effective stiffness are given in

Fig.3.5, which shows three schematics of a mounting for a jig borer on rigid wedge mounts. The

table of the jig borer is in the lower end of the illustration. Relative displacements in the work

zone when the table travels from right to left for the scheme in Fig.3.5C are three times smaller

than for Fig.3.5A and 1.5 times smaller than for Fig.3.5B, notwithstanding the fact that in the

latter case there are seven mounts vs. three mounts in Fig.3.5C. In the case shown in Fig.3.5A,

the large weight of the moving table creates a twisting of the supporting frame about the single

front mount, while the column is rigidly positioned by two mounts. In case of Fig.3.5C, the front

end is well supported, but the column can tilt on its single mount and follow small deformations

of the front part, thus resulting in smaller relative deformations and higher effective stiffness. For

example, in the case of a precision grinder having a bed 3.8 m long, it was found that mounting

the grinder on seven carefully located (offset from the ends) vibration isolators resulted in higher

effective stiffness than installation on 15 rigid mounts.

The effective static stiffness of a machine tool may vary within wide limits. High stiffness values

are ensured by the use of steady rests, by placing tool and workpiece in a position where the

relative dynamic displacement between them is small (i.e., by placing them near the main

column, etc.), by using rigid tools and clamps, by using jigs which rigidly clamp (and if

necessary support) the workpiece, by clamping securely all parts of the machine which do not

move with respect to each other etc., and by the optimization of mounting conditions mentioned

above.

The static and dynamic behavior of machine tools is influenced significantly by the design of the

spindle and its bearings. The static deflection of the spindle consists of two parts, X1 and X2,as

shown in Fig.3.6.The deflection X1 corresponds to the deflection of a flexible beam on rigid

supports, and X2 corresponds to the deflection of a rigid beam on flexible supports which

represent the flexibility of the bearings.

Figure 3.6: Deflection of machine-tool spindle and bearings. A machine-tool spindle can be regarded as a beam on

flexible supports. The total deflection under the force P consists of the sum of (A) the deflection X1 of a flexible

beam on rigid supports and (B) the deflection X2 of a rigid beam on flexible supports.

The deflection of the spindle amounts to 50 to 70 percent of the total deflection, and the bearings

30 to 50 percent of the total, depending on the relation of spindle cross section to bearing

stiffness and span. The stiffness of antifriction bearings depends on their design, accuracy,

preload, and the fit between the outer race and the housing (responsible for 10 to 40 percent of

the bearing deformation).

It is often important to consider the dynamic behavior of a spindle before establishing an

optimum bearing span. Maximizing the stiffness of a spindle at one point does not establish its

dynamic properties. Care must be taken to investigate both bending and rocking modes of the

spindle before accepting a final optimum span. For example, a large overhang on the rear of a

spindle could produce an undesirable low-frequency rocking mode of the spindle even if the

“optimum span” as defined previously were satisfied. The optimum bearing span for minimum

deflection as well as the dynamic characteristics of spindles may be computed with the help of

available computer programs.

The influence of the ratio of bore diameter to outside diameter on the stiffness of a hollow

spindle is shown in Fig.3.7.

Figure 3.7: Effect of bore diameter on stiffness of hollow spindle where k1 = stiffness of solid spindle, k2 = stiffness

of hollow spindle, D =outer spindle diameter, d = bore diameter, J2 =second moment of area of hollow spindle, and

J1= second moment of area of solid spindle. The curve is defined by k2/k1 = J2/J1 = 1 − (d/D).

A 25 percent decrease in stiffness occurs only at a diameter ratio of d/D = 0.7, where D is the

outside diameter and d the bore diameter. This is important for the dynamic behavior of the

spindle. A solid spindle has nearly the same stiffness, but a substantially greater mass.

Consequently, the natural frequency of the solid spindle is considerably lower, which is

undesirable. A stiff spindle does not always assure the required high stiffness at the cutting edge

of the tool because of potentially large contact deformations in the tool holder/spindle interface.

Measurements have shown that in a tapered connection, these deformations may constitute up to

50 percent of the total deflection at the tool edge. These deformations can be significantly

reduced by replacing tapered connections by face contact between the tool holder and the

spindle. The face connection must be loaded by a high axial force.

A significant role (frequently up to 50 percent) in the breakdown of deformations between

various parts of machine tool structures is played by contact deformations between conforming

(usually flat, cylindrical, or tapered) contacting surfaces in structural joints and slides.

Contact deformations are due to surface imperfections on contacting surfaces. These

deformations are highly nonlinear and are influenced by lubrication conditions. Figure 3.8 shows

contact deformation between flat steel parts as a function of contact pressure for different

lubrication conditions in the joint. Joints are also responsible for at least 90 percent of structural

damping in machine-tool frames due to micro motions in the joints during vibratory processes.

Contact deformations for the same contact pressure can be significantly reduced by increasing

accuracy (fit) and improving the surface finish of the mating surfaces. The non-linear load-

deflection characteristic of joints, Fig.3.8, allows enhancement of their stiffness by preloading.

However, preloading reduces micro motions in the joints and thus results in a lower damping.

This explains why in some cases old machines are less likely to chatter than new machines of

identical design. The situation may result from wear and tear of the slides, which increases the

damping and effects an improvement in performance. Also, in some cases chatter is eliminated

by loosening the locks of slides. However, it would be wrong to conclude that lack of proper

attention and maintenance is desirable. Proper attention to slides, bearings (minimum play),

belts, etc., is necessary for satisfactory performance. It would be wrong also to conclude that a

highly polluted workshop atmosphere is desirable because some new machines exposed to

workshop dirt for a sufficiently long time, even when not used, appear to improve in their chatter

behavior. The explanation is that dirty slides increase the damping.

When the rigidity of some machine element is intentionally reduced, but this reduction is

accompanied by a greater damping at the cutter, the increase in damping may outweigh the

reduction in rigidity. Although a loss of rigidity in machine tools is generally undesirable, it may

be tolerated when it leads to a desirable shift in natural frequencies or is accompanied by a large

increase in damping or by a beneficial change in the ratio of stiffness’s along two orthogonal

axes, which can result in improved non-regenerative chatter stability.

Figure 3.8: Load-deflection characteristics for flat, deeply scraped surfaces (overall contact area 80 cm2).1,no

lubrication;2,lightly lubricated(oil content 0.8 × 10−3gram/cm2);3,richly lubricated (oil content 1.8 × 10−3gram/cm2)

A very significant improvement in chatter resistance can be achieved by an intentional measured

reduction of stiffness in the direction along the cutting speed (orthogonal to the direction of the

principal component of cutting force).The benefits of this approach have been demonstrated for

turning and boring operations.

3.2 DAMPING

The overall damping capacity of a structure with cast iron or welded steel frame components is

determined only to a small extent by the damping capacity of its individual components. The

major part of the damping results from the interaction of joined components at slides or bolted

joints. The interaction of the structure with the foundation or highly damped vibration isolators

also may produce a noticeable damping. A qualitative picture of the influence of the various

components of a lathe on the total damping is given in Fig.3.9.The damping of the various modes

of vibration differs appreciably; the values of the logarithmic decrement shown in the figure

correspond to an average value for all the modes which play a significant part.

The overall damping of various types of machine tool differs, but the log decrement is usually in

the range of from 0.15 to 0.3.While structural damping is significantly higher for frame

components made of polymer-concrete compositions or granite (see above), the overall damping

does not change very significantly since the damping of even these materials is small compared

with damping from joints.

A significant damping increase can be achieved by filling internal cavities of the frame parts

with a granular material, e.g., sand. For cast parts it can also be achieved by leaving cores in

blind holes inside the casting. A similar, sometimes even more pronounced, damping

enhancement can be achieved by placing auxiliary longitudinal structural members inside

longitudinal cavities within a frame part, with offset from the bending neutral axis of the latter.

The auxiliary structural member interacts with the frame part via a high viscous layer, thus

imparting energy dissipation during vibrations.

Figure 3.9: Influence of various components on total damping of lathes. The major part of the damping is generated

at the mating surfaces of the various components.

Damping can be increased without impairing the static stiffness and machining accuracy of the

machine by the use of dampers and dynamic vibration absorbers. These are basically similar to

those employed in other fields of vibration control. Dampers are effective only when placed in a

position where vibration amplitudes are significant. The tuned dynamic vibration absorber has

been employed with considerable success on milling machines, machining centers, radial drilling

machines, gear hobbing machines, grinding machines, and boring bars.

A design variant of this type of absorber is shown in Fig.3.10. In this design a plastic ring

element combines both the elastic and the damping elements of the absorber. The auxiliary mass

may be attached to the top of a column (Fig.3.10C), as shown in Fig.3.10A. Alternatively, the

auxiliary mass may be suspended on the underside of a table (Fig.3.10C), using the design shown

in Fig.3.10B. In either case, several plastic ring elements may support one large auxiliary mass,

as shown in Fig.3.10C. In a boring bar, shown in Fig.3.11A, elastic and damping properties are

combined in O-rings made of a high-damping rubber. Tuning of the absorber can be changed by

varying the radial preload force on the O-ring. The natural frequency of this absorber can be

varied over a range of more than 3:1.

Figure 3.10: Auxiliary mass damper with combined elastic and damping element. The combined element lies

between two retainer rings, of which one (3) is attached with bolt 1 to the machine structure. The other ring (2) takes

the weight of the auxiliary mass. (A) Arrangement when auxiliary mass is being supported.(B) Arrangement when

auxiliary mass is being suspended.(C) Application of both types of arrangements to a hobbing machine.

A variation of the Lanchester damper is frequently used in boring bars to good advantage. This

consists of an inertia weight fitted into a hole bored in the end of a quill. To ensure effective

operation, a relatively small radial clearance of about 1 to 5 × 10 −3d must be provided, where d

is the diameter of the inertia weight. An axial clearance of about 0.006 to 0.010 in. (0.15 to 0.25

mm) is sufficient. A smooth surface finish of both plug and hole is desirable. The clearance

values given refer to dry operation, using air as the damping medium. Oil also can be used as a

damping medium, but it does not necessarily result in improved performance. When applying oil,

clearance gaps larger than those stated above have to be ensured, depending on the viscosity of

the oil. In general, Lanchester dampers are less effective than tuned vibration absorbers.

Figure 3.11: Lanchester damper for the suppression of boring bar vibration.

Since the effectiveness of both Lanchester dampers and tuned vibration absorbers depends on the

mass ratio between the inertia mass and the effective mass of the structure (Chap.6),heavy

materials such as lead and, especially, machinable sintered tungsten alloys are used for inertia

masses in cases where the dimensions of the inertia mass are limited (as in the case of boring

bars in Fig.3.11).The mass ratio and the effectiveness of the absorber can be significantly

enhanced by using a combination structure. In such a structure the overhang segment of the

boring bar or other cantilever structure, which does not significantly influence its stiffness but

determines its effective mass, is made of a light material, while the root segment, which

determines the stiffness but does not significantly influence the effective mass, is made from a

high Young’s modulus material.

Dynamic absorbers can be active (servo-controlled).Such devices can be designed to be self-

optimizing (capable of self-adjustment of the spring rate to minimize vibration amplitude under

changing excitation conditions) or to use a vibration cancellation approach. The self-optimizing

feature is achieved by placing vibration transducers on both the absorber mass and the main

system. A control circuit measures the phase angle between the motions and activates a spring-

modifying mechanism to maintain a 90° phase difference between the two measured motions. It

has been demonstrated that the 90° phase relationship guarantees minimum motion of the main

vibrating mass. In the vibration-cancellation devices, the actuator applies force to the structure

which is opposite in phase to structural vibrations.

Dynamic analysis of a machine tool structure can identify potentially unstable natural modes of

vibration and check the effectiveness of the applied treatments. In another approach, transfer

functions between the selected points on the machine tool are measured and processed through a

computational technique which indicates at which location stiffness and/or damping should be

modified or a dynamic vibration absorber installed in order to achieve specified dynamic

characteristics of the machine tools.

3.3 Tool Design

Sharp tools are more likely to chatter than slightly blunted tools. In the workshop, the cutting

edge is often deliberately dulled by a slight honing. Consequently, a beveling of the leading face

of a lathe tool has been suggested. This bevel has a leading edge of −80° and a width of about

0.080 in.(0.2 mm).Tests show that the negative bevel does not in all cases eliminate vibration

and that the life of the bevel is short. Appreciably worn cutting edges cause violent chatter.

Since narrow chips are less likely to lead to instability, a reduction of the approach angle of the

cutting tool results in improved chatter behavior. With lathe tools, an increase in the rake angle

may result in improvement, but the influence of changes in the relief angle is relatively small.

Reduction of both forced and chatters vibrations in cutting with tools having multiple cutting

edges (e.g., milling cutters, reamers) can be achieved by making the distance between the

adjacent cutting edges non equal and/or making the helix angle of the cutting edges different for

each cutting edge. However, such treatment results in non-uniform loading of the cutting edges

and may lead to a shortened life of the more heavily loaded edges as well as deteriorating surface

finish as a result of different deformations of the tool when lighter or heavier loaded edges are

engaged.

Reduction of cutting forces by low-friction (e.g., diamond) coating of the tool or by application

of ultrasonic vibrations to the tool usually improves chatter resistance.

3.4 Variation of Cutting Conditions

In the elimination of chatter, cutting conditions are first altered. In some cases of regenerative

chatter, a small increase or decrease in speed may stabilize the cutting process. In high-speed or

unattended computer numerically controlled machine tools, this can be achieved by continuous

computer monitoring of vibratory conditions and, as chatter begins to develop, a shifting of the

spindle rpm toward the stable area.

Cutting with a variable cutting speed (constant speed modulated by a sinusoidal or other

oscillatory component) acts similarly with regard to undulations in the positioning of the cutting

edges (see above) and results in increased chatter resistance.

An increase in the feed rate is also beneficial in some types of machining (drilling, face milling,

and the like).For the same cross-sectional area, narrow chips (high feed rate) are less likely to

lead to chatter than wide chips (low feed rate), since the chip thickness variation effect results in

a relatively smaller variation of the cross-sectional area in the former (smaller dynamic cutting

force).

After identifying chatters occurring in the machine-tool system, a number of approaches for

reducing chatters have been proposed. Classical approaches usually use the stability diagrams to

avoid the occurrence of chatters. The following approach formulates some general methods for

the reduction of chatters both on the design and the production stage:

• Selecting the optimal cutting parameters

• Selecting the optimal tooling geometry

• Increasing the stiffness and damping of the machine tool system

• Using the vibration isolator as necessary

• Altering the cutting speed during the machining process

• Using a different coolant

More recently, modern control and on-line chatter detection techniques were applied to suppress

chatters. Furthermore, a change of tool geometry is also an industrial feasible approach to chatter

control, for instance, through the application of cutting tools with irregular spacing or variable

pitch cutters.

CHAPTER 4

VIBRATION MEASUREMENT

4.1 Measurement of Vibration

The choice of the best parameter to be measured depends on a number factors, including

a) the type and size of the transducer available,

b) the mass of the vibrating structure, and

c) the frequency and amplitude characteristics of the vibration.

If the velocity, acceleration, and displacement amplitudes measured at various

frequencies, the resulting graphs of amplitude vs. frequency are referred to as the vibration

spectra, and the shape of graphs are referred to as the spectral shapes. With instrumentation

based on accelerometer transducers and integrator amplifiers, the user is free to choose between

acceleration, velocity and displacement as the measurement parameter. The typical vibration

spectra are displays of the three parameters of a machine’s vibration.

Although they each have different average slopes their peaks occur at the same frequencies. In

the example shown the amplitude range required to display the velocity spectrum is the smallest

and thus occupies the least dynamic range. In addition it means that all the frequency

components on this curve need a smaller relative change before they begin to influence the

overall vibration level.

The low frequency acceleration and high frequency displacement components of the spectra need

to exhibit much larger changes before they influence the overall vibration level. In general it is

therefore advisable to display in turn each of the three parameters and choose the one which has

the flattest spectrum. This will enable one to detect machine faults, which produce an increase in

vibration level, at an early stage. In practice the velocity-frequency spectra of many industrial

machines are shaped this way, i.e. they are quite flat over a wide range of frequencies. Since it is

also a measure of vibrational energy present, the velocity parameter is the one in most common

use.

4.2 Effect of the transducer on the vibrating structure

In general, the larger the mass of the vibration transducer, the greater its sensitivity.

Unfortunately, the addition of the transducer's mass (m1) to the mass (m0) of the vibrating

structure changes the resonant frequency of the vibrating system as follows:

where

f1 = resonant frequency of the structure with the mass added

and f0 = resonant frequency of the structure before the transducer is added.

4.3 Vibration Transducers

4.3.1 The Stroboscope Method

The fixed pointer or stud, shown in Figure 4.1, is attached to the vibrating surface and is used to

give an indication of the displacement only. By using the light of a stroboscope to “freeze” or

“slowly move” the stud, quite high-frequency small-amplitude vibrations may be measured. The

typical upper range of frequency is quoted at 500 Hz for direct measurement.

Figure 4.1: The Stroboscope Method

4.3.2 The Reed Vibrometer

The variable-length reed vibrometer shown in Figure 4.2, is used to measure the main frequency

component of the vibration. In practice the length l is adjusted until the maximum reed vibration

occurs, when its resonant frequency is the same as the frequency of the vibrating mechanism or

structure. The length l is calibrated directly in Hz. A small mass may be added to the cantilever if

the vibrometer is to be used for very-low frequency investigation, but the scale readings would

then need to be corrected for the additional mass. The range of measurement is quoted as 5 Hz to

10kHz.

Figure 4.2: The Reed Vibrometer

4.3.3 The Seismic-Mass Transducer

In instrumentation, seismic pickups are used to measure the motion of the surfaces to which they

are fixed. They are sensitive to motion along one axis only, so if the motion is three dimensional,

three seismic pickups are needed to determine the components of the motion along three

mutually perpendicular axes. The principal features of a seismic pickup are shown

diagrammatically in Figure 4.3. The essential component is the seismic mass. This is a body of

metal, suspended from a resilient support. This is a support whose deflection is proportional to

the force applied to it. The inertia of the seismic mass causes it to lag behind the motion of the

casing when the casing is accelerated, causing a deflection in the support. This deflection forms

the input to a transducer, which produces a proportional output signal. In Figure 4.3 the

transducer is represented by a potentiometer, but any suitable type of transducer may be used.

The damping shown in Figure 4.3 may consist only of the hysteresis of the support material, or it

may be increased by filling the casing with a silicone fluid of suitable viscosity for example.

By choosing suitable values for the mass, the stiffness of the support and the damping, and by

using an appropriate transducer, the same basic arrangement of seismic pickup can be designed

as a displacement pickup, a velocity pickup or an acceleration pickup (accelerometer). The

seismic pickup is essentially a damped spring-mass system, and will have a natural frequency of

vibration given by:

where

ωn is the natural angular frequency (rad/s)

λ is the spring stiffness (N/m)

m is the mass (kg).

Figure 4.3: Seismic Mass Transducer

4.4 Comparison of Vibration-Measuring Systems

Table 4.1 compares some features of complete vibration-measuring systems and reveals that the

accelerometer system, although the most expensive, covers the widest range of frequencies and

vibration levels.

Table 4.1: Comparison of vibration-measuring systems

CHAPTER 5

MACHINE DATA

5.1 EQUIPMENT

We measure and analyze the vibrations produced in the machine tool at

different cutting speed, depth of cut, feed rate etc. during the cutting operations on the machine

tool on three different materials. The different parameters like speed, depth of cut, feed rate give

the different results for the vibration in the tool. We measure the frequency, amplitude of the

vibration in the tool.

For measurement of the vibration following elements were used:

1. Machine tool,

2. Vibration meter,

3. RS-232 data cable,

4. Software,

5. Computer,

6. Material for Turning on machine.

5.1.1 Machine Tool:

We has to choose a machine tool for perform operation and collect data for analyzing

vibration. We choose the lathe machine for our project from the college workshop. A lathe is a

machine tool which rotates the work piece on its axis to perform various operations such as cutting,

sanding, knurling, drilling, or deformation with tools that are applied to the work piece to create an

object which has symmetry about an axis of rotation. Lathes are used in woodturning,

metalworking, metal spinning, and glass working. The material can be held in place by either one

or two centers, at least one of which can be moved horizontally to accommodate varying material

lengths. Other work holding methods include clamping the work about the axis of rotation using a

chuck or collets, or to a faceplate, using clamps or dogs.

Figure 5.1: Lathe Machine tool used for experiment

5.1.2 Vibration Meter:

Vibration meter is the device which is used for measuring various vibration

parameters like frequency, amplitude, time period etc. The vibration meter can also measure

acceleration, velocity, displacement. These parameters give us information about the vibration

Figure 5.2: Vibration sensor mounted on tool post

produced in the tool. These parameters when fed to the computer with the help of data cable

provide us the frequency mode of vibration. The vibration meter we choose for our project is

digital vibration meter VB-8205 HTC.

Sensor

Cutting Tool

` Figure 5.3: Digital Vibration Meter

5.1.3 USB-232 Data Cable and Software:

The cable which is used for the transmitting data from the vibration meter to

computer is RS-232 USB data cable. It is high speed data transmission data cable. Software is

used for the process of vibration measurement. The software receive data from the vibration

meter through data cable and show them in the form of displacement, velocity, acceleration or

frequency as per requirement. These collected data from vibration meter used for plotting graph

of various parameters like frequency-time, amplitude-frequency etc., in MATLAB.

5.1.4 Computer:

Computer which receives signals from vibration meter through RS-232 data

cable, process the signals in the software and show on the screen.

Figure 5.4: Vibration meter and Computer

Vibration Meter

5.2 Block Diagram of Set up

Machine Tool

Sensor

Vibration Meter

Computer

MATLAB

CHAPTER 6

APENDIX A

Aluminium

Aluminium (Al) is the most abundant metal on this planet which is silvery-whitish in

appearance. There are several aluminum properties that makes aluminum, one of the most

heavily used element. Aluminium is a silvery white member of the boron group of chemical

elements. It has the symbol Al and its atomic number is 13. It is not soluble in water under

normal circumstances. Aluminium is the most abundant metal in the Earth's crust, and the third

most abundant element, after oxygen and silicon. It makes up about 8% by weight of the Earth's

solid surface. Aluminium is too reactive chemically to occur in nature as a free metal. Instead, it

is found combined in over 270 different minerals. The chief source of aluminium is bauxite ore.

.General Properties of aluminium:

Name, symbol, number aluminium, Al, 13

Density 2.70 g·cm −3

Crystal structure face-centered cubic

Thermal expansion (25 °C) 23.1 µm·m−1·K−1

Young's modulus 70 GPa

Shear modulus 26 GPa

Bulk modulus 76 GPa

Brinell hardness 245 MPa

Poisson ratio 0.35

Aluminium is remarkable for the metal's low density and for its ability to resist corrosion due to

the phenomenon of passivation. Structural components made from aluminum and its alloys are

vital to the aerospace industry and are very important in other areas of transportation and

building. Its reactive nature makes it useful as a catalyst or additive in chemical mixtures,

including ammonium nitrate explosives, to enhance blast power

During machining of aluminium following data was recorded with the help of vibration meter:

Figure 6.1: Aluminium graph of Freq. vs Magnitude with depth of cut 0.5 mm and speed 750

rpm

Figure 6.2: Aluminium graph of Freq. vs Magnitude with depth of cut 1 mm and speed 750 rpm

Figure 6.3: Aluminium graph of Freq. vs Magnitude with depth of cut 1 mm and speed 750 rpm

After analyse and calculation following data was obtained :

Table 6.1:

Analysed data of Aluminium Specimen

Result:-

Best method for machining Aluminium

Depth of cut:- 0.5mm

Speed: 1650rpm

Feed:- 175 mm/min.

Sr.

No.

Depth of cut

(mm)

Speed

(rpm)

Avg.

Magnitude

(mm)

Max

Magnitude

(mm)

Log10

1 0.5 750 .0028 .02 -1.699

2 0.5 1250 .0025 .021 -1.678

3 0.5 1650 .0038 .011 -1.958

4 1 750 .0038 .282 -0.549

5 1 1250 .004 .o13 -1.886

APENDIX B

MILD STEEL

Mild steel is the most common form of steel because its price is relatively low while it provides

material properties that are acceptable for many applications. Low carbon steel contains

approximately 0.05–0.15% carbon and mild steel contains 0.16–0.29% carbon, therefore it is

neither brittle nor ductile. Mild steel has a relatively low tensile strength, but it is cheap and

malleable; surface hardness can be increased through carburizing .

It is often used when large quantities of steel are needed, for example as structural steel. The

density of mild steel is approximately 7.85 g/cm3 (0.284 lb/in3) and the Young's modulus is

210,000 MPa.

Low carbon steels suffer from yield-point runout where the material has two yield points. The

first yield point (or upper yield point) is higher than the second and the yield drops dramatically

after the upper yield point. If low carbon steel is only stressed to some point between the upper

and lower yield point then the surface may develop

Mild steel has a density of .248 pounds per cubic inch.

Mild steel is very strong due to the low amount of carbon it contains. In materials science,

strength is a complicated term. Mild steel has a high resistance to breakage. Mild steel, as

opposed to higher carbon steels, is quite malleable, even when cold. This means it has high

tensile and impact strength. Higher carbon steels usually shatter or crack under stress, while mild

steel bends or deforms. Both the BHN and VHN for steel range from 150 to 190. For all

structural steels, the modulus of elasticity can be taken as 205,000 MPa

During machining of aluminium following data was recorded with the help of vibration meter:

Figure 6.4: Mild Steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and speed 750 rpm

Figure 6.5: Mild Steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and speed 1250

rpm

Figure 6.6: Mild Steel graph of Freq. vs Magnitude with depth of cut 1 mm and speed 750 rpm

Figure 6.7: Mild Steel graph of Freq. vs Magnitude with depth of cut 1 mm and speed 1250 rpm

After analyse and calculation following data was obtained :

Table 6.2:

Analysed data of Mild Steel Specimen

Result:

Best method for machining mild steel

Depth of cut:- 1mm

Speed:-750rpm

Feed:-125mm/min.

Sr.

no.

Depth of cut

(mm)

Speed

(rpm)

Avg.

Magnitud

e

(mm)

Max

Magnitude

(mm)

Log10

1 0.5 250 .0083 .065 -1.187

2 0.5 750 .0071 .028 -1.553

3 0.5 1250 .0099 .022 -1.657

4 1 750 .0087 .015 -1.824

5 1 1250 .0122 .023 -1.638

APENDIX C

Low Grade alloy steels

Low alloy steels are usually used to achieve better hardenability, which in turn improves its other

mechanical properties. They are also used to increase corrosion resistance in certain

environmental conditions.

With medium to high carbon levels, low alloy steel is difficult to weld. Lowering the carbon

content to the range of 0.10% to 0.30%, along with some reduction in alloying elements,

increases the weldability and formability of the steel while maintaining its strength. Such a metal

is classed as a high-strength low-alloy steel. hey have a carbon content between 0.05–0.25% to

retain formability and weldability. Other alloying elements include up to 2.0% manganese and

small quantities of copper, nickel, niobium, nitrogen, vanadium, chromium, molybdenum,

titanium, calcium, rare earth elements, or zirconium. Their yield strengths can be anywhere

between 250–590 MPa.

During machining of aluminium following data was recorded with the help of vibration meter:

Figure 6.8: Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and speed 450

rpm

Figure 6.9: Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 0.5 mm and speed 750

rpm

Figure 6.10: Low grade alloy steel graph of Freq. vs Magnitude with depth of cut 1 mm and

speed 750 rpm

After analyse and calculation following data was obtained :

Table 6.3: Analysed data of Low Grade Alloy Steel Specimen

Sr.

no.

Depth of

cut (mm)

Speed

(rpm)

Avg.

Magnitude

(mm)

Max

Magnitude

(mm)

Log10

1 0.5 450 .0044 .012 -1.921

2 0.5 750 .008 .022 -1.657

3 0.5 1250 .0073 .014 -1.853

4 1 750 .0089 .02 -1.698

5 1 1250 .0388 .066 -1.180

Result:

Best method for machining Aluminium

Depth of cut:- 0.5mm

Speed:-450 rpm

Feed:-80 mm/min.

CONCLUSIONS AND FUTURE WORK

CONCLUSIONS

This paper has a detailed description of the effect of cutting tool vibration

on surface roughness of workpiece. The surface roughness of machined parts is predicted by

using the vibration data. For this purpose, a series of experiment were conducted on a lathe

machine. It is well known that the vibration amplitude increases with the progression of tool

wear. The conclusion of our work is that the vibration of machine cutting tool increase with

speed and depth of cut for the hard to machined material as in our case the vibration amplitude

also increase with increase in speed and feed rate. On the other hand for soft material the

vibration is much less at higher speed then slow speed. Vibration also increase in the tool due to

whirling of the job mounted between two stock of lathe machine. With the increasing feed rate

the surface roughness of work piece will increase. The feed rate can be considered as a main

cutting factor in the machining operation.

FUTURE WORK

Micro-electric mechanical system has been used in the future. Therefore

required precision method of machining. Vibration can be controlled by using some damper

material like lather. Some improved technique also develop to reduce vibration like piezoelectric

materials.

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