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

1

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

2

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()

3

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

4

Figure 1: An Example of Stability Chart represented by Tobias and Fishwick [7]

Figure 2: Chatter feedback loop represented by Merritt [10]

5

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

6

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

7

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

8

stiffness of the system) [24].

9

Bibliography

[1] Guillem Quintana and Joaquim Ciurana. Chatter in machining processes: Areview. International Journal of Machine Tools and Manufacture, 51(5):363376, 2011.

[2] F Atabey, I Lazoglu, and Y Altintas. Mechanics of boring processes??parti. International Journal of Machine Tools and Manufacture, 43(5):463476,2003.

[3] Miguelez M.H, Rubio L., Loya J.A., and Fernandez-Saez J. Improvement ofchatter stability in boring operations with passive vibration absorbers. 2010.

[4] Abu-Aesh M.A. An investigation into the self-excited vibrations of boringbars on a centre lathe. Masters thesis, 1982.

[5] Arnold RN. The mechanism of tool vibration in cutting of steel. Proc. of theinstitution of Mechanical Engineers, 1946.

[6] S.A Tobias. Machine-Tool Vibration. Blackie & Son, London,, 1965.

[7] Fishwick W. Tobias S. A. The vibrations of radial drilling machines undertest and working conditions. London,, 1956. The Institution of MechanicalEngineers.

[8] F. Koenigsberger and J. Tlusty. Structure of Machine Tools. Pergamon Press,1971.

[9] JP Gurney and SA Tobias. A graphical analysis of regenerative machine toolinstability. Journal of Engineering for Industry, 84:103, 1962.

[10] He E Merritt. Theory of self-excited machine-tool chatter: Contribution tomachine-tool chatter research?? Journal of Manufacturing Science and En-gineering, 87(4):447454, 1965.

[11] MM Nigm. A method for the analysis of machine tool chatter. InternationalJournal of Machine Tool Design and Research, 21(3):251261, 1981.

10

[12] HM Shi and SA Tobias. Theory of finite amplitude machine tool instabil-ity. International Journal of Machine Tool Design and Research, 24(1):4569,1984.

[13] T Kaneko, H Sato, Y Tani, and M O-hori. Self-excited chatter and its marks inturning. Journal of Manufacturing Science and Engineering, 106(3):222228,1984.

[14] M.A. El Hakim. On the causes of dynamic instability of machine tools. In FirstConference of Mechanical Power Engineering, volume III, Cairo, February1977.

[15] M.A El Hakim. Application of the system theory for the investigation of thestability of machine tools. Cairo,, 1975. National Conference on AutomaticControl.

[16] M. Abdel Salam. An Investigation into the Cutting Prrocess Dynamics inTurning. PhD thesis, Cairo,, 1987.

[17] Y. S. Tarng and E.C. Lee. An investigation of the phase shift between theinner and outer modulation for the control of machine tool chatter. 37(12),1997.

[18] Y Altintas and M Weck. Chatter stability of metal cutting and grinding.CIRP Annals-Manufacturing Technology, 53(2):619642, 2004.

[19] C Brecher, S Baumler, and A Guralnik. Machine tool dynamics-advances inmetrological investigation, modeling and simulation techniques, optimizationof process stability. In Proceedings of the 5th Manufacturing EngineeringSociety International Conference, 2013.

[20] Tatiana Smirnova, Henrik Akesson, Lars Hakansson, Ingvar Claesson, andThomas L Lago. Accurate fe-modeling of a boring bar correlated with exper-imental modal analysis. IMAC XXV, 2007.

[21] Henrik Akesson, Tatiana Smirnova, and Lars Hakansson. Analysis of dynamicproperties of boring bars concerning different clamping conditions. MechanicalSystems and Signal Processing, 23(8):26292647, 2009.

[22] Linus Andren, Lars Hakansson, Anders Brandt, and Ingvar Claesson. Identi-fication of dynamic properties of boring bar vibrations in a continuous boringoperation. Mechanical systems and signal processing, 18(4):869901, 2004.

11

[23] M Sortino, G Totis, and F Prosperi. Modeling the dynamic properties ofconventional and high-damping boring bars. Mechanical Systems and SignalProcessing, 34(1):340352, 2013.

[24] Lonnie Houck III, Tony L Schmitz, and K Scott Smith. A tuned holder forincreased boring bar dynamic stiffness. Journal of Manufacturing Processes,13(1):2429, 2011.

12