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Literature Review
1 Introduction
Machining processes involve removal of material from workpieces
whatever whichmechanism material removal is used. Then machining as
a manufacturing processis evaluated by two main aspects;
productivity and product quality. Usually theproductivity of
machining processes is measured by material removal rate (MRR),and
product quality is measured by surface roughness.
To achieve these main claims of machining, there are many
constrains. Oneof the major constrains is mechanical vibrations
that affects the whole MFTW(Machine-Fixture-Tool-Workpiece)
system.
2 Machine tool vibrations
Vibrations in metal cutting can be classified into three main
categeories; freevibrations, forced vibrations and self-excited
vibrations [1] .The three types ofvibrations can be very obviously
differentiated with respect to the equation ofmotion represented as
follows
mx+ cx+ kx = F
In case of having zero external forces (F = 0) provided a damped
structure(c > 0), then free vibrations occur and diminish in
short time due to the dampingdissipation of energy. In case of
having an external force (F 6= 0) while theoverall damping is
positive (c > 0) forced vibrations occur, which have an
ampli-tude according to the force amplitude and frequency equal to
the force frequency.Finally, in case of having negative damping (c
< 0) an exponential increase in thevibration amplitude occurs
which may lead to high damaging results and this iscalled
self-excited vibrations.
Self-excited vibrations in machining known as chatter is the
most damagingwhile being the least controllable. Chatter in
machining is caused by the inter-action between the MFTW system and
the cutting process, this interaction givesnegative damping to the
vibrating MFTW system and therefore causes high am-plitudes and
alot of negative effects.
Effects of chatter phenomenon on the cutting process have its
impacts on theworkpiece shown by having poor surface quality and
inaccurate dimensions. Alsoits effects on the tool can increase
till its total damage, this can be extended alsoto any element in
the machine tool . Chatter and its effect can be avoided byhaving
small depth of cut which therefore decreases the material removal
rate and
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thus decreasing productivity. It can be concluded then, that
chatter is an obviouslimitation to the machining processes
productivity and thats why it is studiedextensively through a whole
century.
Although the other machining processes such as milling, turning
and drillinghave been studied relatively broader and deeper, there
were only a few attemptsto model the cutting forces and stability
in boring [2].
The enlargement of holes is achieved via boring operations. The
hole diameteris either enlarged with a single insert attached to a
long boring bar, or with aboring head which has a diameter equal to
the diameter of the hole to be enlarged.Long boring bars statically
and dynamically deform under the cutting forces dur-ing boring
operations. Excessive static deflections may violate the
dimensionaltolerance of the hole, and vibrations may lead to poor
surface, short tool life andchipping of the tool.
The problem of vibration becomes more significant when a
flexible tool isused,as in the case of internal turning operations.
[3]. Boring bars have gener-ally high length to diameter ratio in
order to generate internal surfaces.Thatswhy boring process is a
very specific case for machine tool chatter that need amore
comprehensive work.
Due to the insufficient rigidity of boring bars, chatter is more
likely to occurin boring than in any other machining operation,
which results in a poor surfacequality, shorter tool life and
limited production rate. Extensive investigations havebeen carried
out to avoid chatter vibrations. Several types of vibration
dampershave been suggested by previous investigators. However, due
to the complexity,high expenses, and size limitations of such
dampers they have found only lim-ited practical applications. More
satisfactory results can still be attained by anadequate selection
of cutting conditions as was proved by previous
investigationscarried out into chatter in turning. [4]
Research in machine tool vibrations has involved two main paths.
The firstone involved the investigation of the chatter behaviour
itself and the parametersaffecting it. The second one involved
researching different methods for suppressing,avoiding or
eliminitating chatter.
This chapter summarizes the literature in the context of a)
vibrations thatexist in machine tools and its effects on the metal
cutting process, b) the chatterbehaviour and the theories regarding
its explanation and modeling, and c) thesuppression methods in the
case of boring bars.
3 Modeling of machine tool chatter
The first observation of chatter was in 1907 by F.Taylor stating
chatter behaviourand its negative effects, he also tried to explain
these vibrations by variable periodic
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shearing forces as the metal was removed. The first thorough
investigation ofchatter return back to 1945,when Arnold studied the
chatter vibrations in thedirection of cutting speed. Due to the
negative slope of variation between cuttingforces and the relative
cutting speed, the vibrating tool may undergo dynamicinstability
which leads to chatter vibrations. [5]
Tobias discussed in the 1960s the chatter behaviour and its
modeling. Heexplained the initiation of the machine tool self
excited vibrations to be due toany disturbance to the MFTW dynamic
system such as material hard spots. Hereturned the cause of the
dynamic instability to the regeneratiion effect.
The regenerative effect occurs due to the chip thickness
variation when thecutting edge of the tool traverses a surface on
the workpiece that experienced aprevious cut. When overlapping
occurs between the previous undulations on theworkpiece and the
current cut undulations, regeneration effects takes place whichmay
increase the amplitudes exponentially with respect to time. [6]
Tobias and Fishwick modeled the chatter behaviour by putting the
equation ofmotion of the whole MFTW system. They introduced
variable acting forces thatare function of vibration velocity and
displacement, so in case of having negativedamping (negative
coefficient of velocity) present ,dynamic instability occurs.
[7]
The stabilty measure set in Tobias and Fishwick research is
considered theeffective amplification factor Qe which represents
the damping effect on the struc-ture, therefore minimum Qe at a
specific rotational speed means more tendency tochatter and vice
versa [6]. The effective amplification factor for any single
degreeof freedom system can be presented as
Q =0
=1
2
where is the damping ratioThis means that the presented system
needs a higher damping or a lower Qe to
achieve stability, therefore the stability of the system can be
measured by plottingthe effective amplification factor against the
rotational speed. The plotted stabil-ity chart would have
successive lobes that have some local minima at certainrotational
speed called the stability lobes.
Several authors researched the stability borderline of chatter
thoroughly in the60s, Tlusty [8] considered a single degree of
freedom system for the MFTW systemsubjected to cutting dynamics,
his analysis is done -unlike Tobias- in the complexdomain. Through
this analysis, he could present a mathematical model for thechatter
stability borderline by taking the widthof cut as a measure of
stability.The presented model is as simple as follows
blim =1
2k1G()
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where k1 is the cutting stiffness that represents the relation
between the chipthickness and the cutting force, while G() is the
real part of the MFTW systemtransfer function.
Tlusty and Polacek also presented another theory for chatter
which is themode-coupling, this means that the system has a higher
tendency for chatter incase of have more than one degree of freedom
[8].
Several models representing regenerative chatter are put to
identify the chatterborderline of stability. Tobias represented
some method for determining the sta-bility border line using
analytical methods [6] and graphical methods [9]. AlsoMerrit [10]
modeled the chatter phenomenon using the feedback control theory.He
modeled the interdependance of cutting dynamics and structural
dynamics asa closed loop that has an input of a given uncut chip
thickness and an ouptut ofthe actual chip thickness.
Nigm [11] criticized Merritts graphical method to determine the
stability bor-derline. He pointed to the limitation of that method
in not accounting for the metalcutting dynamics, also he pointed to
the complexity of using it due to the needof using a specially
prepared chart before plotting the transfer function. Instead,he
proposed both a graphical method and a corresponding analytical
method thataccounts for the dynamics of the metal cutting process.
This method uses also thefeedback control theory but having much
more simpler approach graphically, anda very simple analytical
solution for the stability borderline equation.
Shi and Tobias [12] further investigated the possible causes of
chatter. Thispaper represents the finite amplitude instability
theory, which puts the non-linear forces (if present) as an
initiation cause for the chatter behaviour providedthat the width
of cut is within a specific range. Non-linear forces existence
isexplained by large hammer force or interrupted cutting. This work
concludes thatbelow a certain limit of the width of cut no chatter
occurs even if non-linear forcesare subjected to the system, while
above a certain limit of the width of cut chatteroccurs even if no
non-linear forces existed. Finally, it concludes that within
theupper and lower limites of the width of cut chatter occurs if
non-linear forcesexcited the system.
Kaneko et al [13], represented the workpiece as supported by two
perpendicularsupports (vertically and horizontally) having
stiffness and damping, thus providinga two degrees of freedom
system. This work assumed in its model having theresisting force
inversly proportional to the cutting speed and directly
proportionalto the vibration velocity which is in contradiction
with the research done by otherauthors [6, 14]. The application of
multiple regenerative effect is also used in themodel which was
introduced in a previous paper by one of this paper authors.
El Hakim has criticized the regenerative theory of chatter as
being a non suf-ficient theory to describe its behaviour [14]. He
claimed that chatter often starts
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Figure 1: An Example of Stability Chart represented by Tobias
and Fishwick [7]
Figure 2: Chatter feedback loop represented by Merritt [10]
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in the first revolution before any chatter marks can have any
regenerative effects,also chatter occurs in thread cutting when
overlapping does not exist.
In contrast, he explains the chatter behaviour as being due to
the effect of thevibrational energy itself. Since the vibrational
energy affects the friction forces,they have a significant effect
on the cutting forces which may lead to dynamicinstabiity that
results in chatter. He concluded from the presented analysis
thatthe cutting forces have a negative slope with respect to the
vibrational velocitywhich leads to a negative damping condition and
thus, dynamic instability [14].
He then represented a mathematical model depends on the system
controltheory similar to Merrits feedback loop [10]. The new
modification due to thetheory of the vibrational energy is
repersented in that loop by having an extrafeedback loop
representing the negative damping coefficient [15].
M.Salam investigated the start of chatter in the first workpiece
revolution.Moreover, he modified the modeled presented by El Hakim
[15] to include the flankdamping effect and other dynamic effects
as the variation of rake and clearanceangles. He also included the
effect of penetration resistance into the model [16].
Tarng and Lee [17] investigated the effect of the phase shift
between the innermodulation (the waviness of the new cut) and the
outer modulation ( the wavinessof the previous cut) on the
regenerative chatter. They then applied a controlstrategy to search
for a better spindle speed corresponding to certain phase shiftat
which chatter tendency is low and the limiting width of cut is
higher.
Altintas and Weck [18] presented a review on the chatter
modeling theories andcontrol strategies. Regarding the case of
turning and boring, they have concludedthat because the spindle
speed to chatter frequency ratio is small this lets thecomplexity
of the behaviour be much higher. The complexity of chatter
modelingin that case comes from the the significant effect of
process damping on chatterand also the non linearities in the
cutting process. For this reason, they explainwhy most of the
research work in turning and boring is not well modeled andcompared
to experimental results.
Brecher et al [19] presents a review on the current advances in
the modeling ofchatter and machining stability. They stated that
the main issue that is targetedin the present time is how to model
the machine tool damping characteristicsaccurately. They presented
a method for automatic modal analysis of the machinecenter using
laser interferometers and extract the damping properties from
theexperimental modal analysis to match the damping ratio in the
proposed model.
From the presented theories to explain the chatter behaviour and
the numerousmathematical and numerical models to obtain a suitable
model for it, it can beconcluded that chatter is a very complex
phenomenon. The complexities is causedby the mutual interaction
between the structural dynamics of the MFTW systemand the cutting
process dynamics.Also, another source of complexity is from the
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dependancy of stability on the damping properties of the
structure which is not afully understood issue till now in
structural dynamics field of research. And finallythe effect of non
linearities on the behaviour is also a significant factor.
The mentioned research problem has really affected the path of
research throughthe past 50 years. Research in chatter have changed
gradually from focusing onthe explanation and modeling of the
complex chatter phenomenon into proposingnew and promising control
techniques (passive or active) for the sake of
chattersupression.
4 Modeling and Control of boring bar vibrations
Numerous research work has been done for the reduction of
vibrations ,especiallychatter, for the boring bar case. Techniques
for reducing or supressing boring barvibrations can be classified
into two groups as presented by Quintana [1]. The firsttype is by
online or oine change of cutting parameters to fall inside the
stabilityzone in the stability lobes diagram according to Tobias
theory. The second groupfocused on changing the system parameters
either by passive or active techniques.
Modeling of the boring bar dynamic performance is of special
importance forboth the two techniques. Some research work is spent
in obtaining the boring bardynamic behaviour either is a general
case or after introducing special designedboring bar.
One of the examples is the comparison done by Smirnova et al
[20] between nu-merical, analytical models and the experimental
modal analysis results. The mainfocus for that paper is to model
the boring bar in free-free boundary conditionsusing the finite
element (FE) method. The FE model is then verified using
ex-perimental modal analysis and analytical solution using
Euler-Bernoulli theorem.The verification process was concerned with
the first two modes of vibrations byassuming that the chatter
behaviour occur at the low-order bending modes.
Akesson et al [21] discussed the effect of different clamping
conditions of boringbars on its dynamic performance. They examined
different clamping conditionsall related to screw clamping on 4 or
6 points on the boring bar body except forone condition that is
performed by press fitting a boring bar circular cross sectioninto
the clamping house bore without clamping screws.
The investigation concluded that all parameters of clamping
cause significantvariation in the dynamic properties; these
parameters include number of bolts,tightening torques and the order
of tightening of bolts. Also they found that bychanging the
excitation level the dyanmic properties are slightely varied due
tonon linearities of the joints.
The most stiff configuration and the nearest to the analytical
Euler-Bernoullimodel was the case of press fitting the boring bar
inside the clamping house. Also
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several analytical models are investigated to describe the
clamping using screws,the most successful is by assuming that the
point of contact between the pressingscrew and the boring bar has
both torsional and linear springs (in the direction ofthe
bolt).
Andren et al [22] investigated the vibration signal pattern of
the boring barunder steady cutting process (i.e. constant cutting
variables). They concludedthat, although the cutting conditions are
constant, but the vibration signal cant beconsidered to be
stationary. The highest vibration level is measured in the
cuttingspeed direction and is composed of the first two boring bar
natural frequencies.Also, they found that the natural frequencies
of the boring bar is altered at differentfeed rates and cutting
speeds, they explained that by the variation of the boringbar
boundary conditions at the contact between the cutting edge and the
workpiece.
Sortino et al [23] proposed a hybrid model using both analytical
Timoshenkobeam model and emperical transfer functions. The model
aimed to find the com-pliance of the boring bar clamping house and
the actual Youngs modulus of ahigh-damped comercial boring bar.
Also the authors introduced other empericalformula to describe the
damping coefficient different from Rayleighs and they gotthrough
their limited investigation better results.
After completing the model, the receptance of the boring bar and
the naturalfrequency is compared to the experimental results and
statistical analysis is appliedwhich concluded having an acceptable
fitting of data. One of the most importantconclusions, that they
compared the Euler-Bernoullis model with Timoshenkomodel with
respect to the experimental data and found only slight
difference.They then concluded that Euler-Bernoullis model can be
used for slendernessratio of more than 3 which is in contradiction
with most of authors [21].
One popular example of passive change of system paremeters to
control chatter,is by using adjustable vibration absorber. Houck et
al [24] proposed a new toolholder, inwhich the holder acts as the
vibration absorber for the clamped boringbar. In contradiction to
the normal use, the holder is designed to be more flexiblethan the
boring bar but having the same natural frequency of the
clamped-freeboring bar case. By adjusting the holder mass and
stiffness, it can match the caseof clamed-free boring bar and thus
by being assembled to the boring bar, the peakresponse of the
clamped-free boring bar is reduced to zero.
Also another two peaks appear that corresponds to an
approximately 2 de-grees of freedom system (the holder and the
boring bar). Experimental techniquesshowed a reduction in the
response peak height, where the peaks in comparisonare the one of
the clamed-free boring bar and the highest peak in the new
system.The Receptanc Coupling Substructure Analysis (RCSA) is used
In order to modelthis reduction in response maximum amplitude
(which corresponds to the dynamic
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stiffness of the system) [24].
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