RESEARCH AND APPLICATION OF VIBRATION ASSISTED DRILLING

Items Presented for Defense  Mathematical model and modeling results of vibrational cutting process;  Original pre-twisted cantilevers dynamics theory;  SPH method availability for

KAUNAS UNIVERSITY OF TECHNOLOGY

MARTYNAS UBARTAS

RESEARCH AND APPLICATION

OF VIBRATION ASSISTED DRILLING

Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T)

2013, Kaunas

This dissertation was prepared at the Faculty of Mechanical Engineering and mechatronics, Department of Engineering Design, Kaunas University of Technology, during the period of 2009 – 2013

Dissertation Defense Board of Mechanical Engineering Science Field:

Prof Dr Habil Ramutis Petras BANSEVIČIUS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T)-chairman;

Dr Habil Algimantas BUBULIS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T);

Prof Dr Vytenis JANKAUSKAS (Aleksandras Stulginskis University, Technological Sciences, Mechanical Engineering – 09T);

Prof Dr Habil Genadijus KULVIETIS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T); Prof Dr Habil Arvydas PALEVIČIUS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T)

2013, at the public session of the Board of Mechanical Engineering Science Field in the Dissertation Defense Hall at the Central Building of Kaunas University of Technology

Address: K Donelaičio St 73-403, 44029 Kaunas, Lithuania

The summary of the dissertation was sent on 20th of September, 2013

The dissertation is available at the library of Kaunas University of Technology (K Donelaičio St 20, Kaunas)

KAUNO TECHNOLOGIJOS UNIVERSITETAS

Disertacija rengta 2009 – 2013 metais Kauno technologijos universitete, Mechanikos ir mechatronikos fakultete, Inžinerinio projektavimo katedroje

Mechanikos inžinerijos mokslo krypties daktaro disertacijos gynimo taryba:

prof habil dr Ramutis BANSEVIČIUS (Kauno technologijos universitetas, technologijos mokslai, mechanikos inžinerija – 09T) – pirmininkas;

Habil dr Algimantas BUBULIS (Kauno technologijos universitetas, technologijos mokslai, mechanikos inžinerija – 09T);

prof dr Vytenis JANKAUSKAS (Aleksandro Stulginskio universitetas, technologijos mokslai, mechanikos inžinerija – 09T);

prof habil dr Genadijus KULVIETIS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos inžinerija – 09T);

prof habil dr Arvydas PALEVIČIUS (Kauno technologijos universitetas, technologijos mokslai, mechanikos inžinerija – 09T)

Adresas: K Donelaičio g 73-403, 44029 Kaunas, Lietuva

Disertacijos santrauka išsiuntinėta 2013 m rugsėjo 20 d

Disertaciją galima peržiūrėti Kauno technologijos universiteto bibliotekoje (K Donelaičio g 20, Kaunas)

INTRODUCTION

Field of metal cutting is closely linked to different industrial sectors including automotive, construction, aerospace, mechanical engineering, etc Material treatment using cutting is still one of the predominant technological processes for manufacturing high-precision and complex components Metal machining sector has an annual worldwide turnover of more than 506 billion EUR, final finishing operations global annual turnover of about 100 billion US Dollars and loss on this area is about 10 billion US Dollars annually

According The Engineering Industries Association of Lithuania (LINPRA) data, this industry turnover of 6.3 billion LT, and exports at this time make 73 percent

Higher productivity and better surface quality are the prerequisites for current machining industry to be more competitive since modern manufacturing requires shorter production times and higher precision components

Mechanical process industry today is widely studied area To be more competitive, many indicators must be approved Manufacturing requires shorter production time and better surface quality of manufactured parts Cutting force and speed, feed-rate, temperature in the contact zone is those key variables that significantly influence surface quality and tool life Constant pursuit for more effective cutting methods revealed that machining quality can be improved if the tool is assisted with so - called high frequency vibrations, which results in reduction of cutting forces and surface roughness of a workpiece

Constant pursuit for more effective cutting methods revealed that machining quality can be improved if the tool is assisted with high frequency vibrations, i.e small-amplitude (typically 220 m) and high-frequency (typically up to 20 kHz) displacement is superimposed onto the continuous cutting motion of the tool

Important feature of vibration-assisted cutting is that a significant increase

in quality of machined part can be achieved in comparison to conventional cutting This may lead to elimination of surface finish processes such as grinding and polishing as well as other additional machining processes Last but not least advantage is associated with reduced tool wear during cutting Presented factors determine the economy of vibration cutting

In shortly summarizing the achievements in vibration cutting technology,

it should be mentioned that it has already matured to an extent which enabled several limited industrial applications However, the knowledge of fundamental mechanisms governing the associated machining processes is still incomplete Therefore, vibration cutting remains an actively pursued research object in scientific community because considerable work is still needed in the field of development of reliable computational models, which would allow optimization

or adaptation of the vibration cutting processes and tools for the specific materials and operating conditions

Research objective

To investigate physical sense of the best vibrational drilling conditions and adapt it for effective machining of materials

The following tasks are set in order to reach the objective:

1 Numerical investigation of dynamics for a pre-twisted cantilever using adapted finite element method;

2 Study of dynamical peculiarities of pre-twisted cantilever, excited in different vibration modes;

3 Design and implementation of vibrational drilling equipment and research methodology;

4 Development of numerical model for dynamical research of vibration cutting tool in contact with the workpiece;

5 Experimental study of vibrational drilling process, indicating cutting forces, surface quality and cutting regimes;

6 To validate adequacy of the numerical and physical models of vibrational drilling process;

7 To demonstrate vibrational drilling advantages for difficult-to-cut materials

Research methods

The research work was carried out by using both analytical and experimental methods Theoretical research is based on classical theory of vibrations of distributed-parameter mechanical systems and finite element analysis, which was performed by means of commercial softwares SolidWorks and ANSYS

Reliability of modeling results was confirmed by experimental studies that were conducted at the KTU Mechatronics Centre for Research, Studies and Information employing CNC machine-tools, modern non-contact laser Doppler vibrometry and accelerometer sensors Surface roughness tester was used for investigation of machined workpieces PicoScope hardware and software was used for registration and processing of acoustic emission and frequency response measurements

Computational model of vibration cutting tool contact with the workpiece was performed by software LS-DYNA using SPH method Vibrational drilling

experiments were carried out in French industrial mechanical machining centre CTDEC using the newest KISTLER four component platform

Scientific novelty:

1 Numerical model of vibrational drilling tool was developed, all various vibration modes, which influence the best vibrational drilling results (including specific dynamic effects inherent to the twisted structure) are identified;

2 Peculiarities of dynamical behavior of pre-twisted cantilever are uncovered;

3 Computational model of vibration cutting tool contact with the workpiece is developed;

4 Vibrational drilling advantages for machining of difficult-to-cut materials is demonstrated

 Experimental results are beneficial for industrial use

Items Presented for Defense

 Mathematical model and modeling results of vibrational cutting

process;

 Original pre-twisted cantilevers dynamics theory;

 SPH method availability for cutting process simulation of cutting tool contact with workpiece material;

 Results of experiments generated for traditional and difficult-to-cut materials

Publications and approbation of the work: The results of the research

were published in 2 WoS scientific journals and in Proceedings of 7 International conferences Results of the research have been presented in these scientific conferences:

1 International conference „Mechanics – 2009“, Kaunas, 2009

2 International conference „Mechanics – 2010 “,Kaunas, 2010

3 International conference „Mechanics – 2011“, Kaunas, 2011

4 International conference „Mechanics – 2012“, Kaunas, 2012

5 International conference „Mechanics – 2013“, Kaunas, 2013

6 Lithuanian Academy of Sciences „Contest for Young Scientists “, Vilnius,

2013

7 „9th European LS-DYNA user's conference 2013“, Manchester, United

Kingdom

Results of the research have been presented in these scientific projects:

1 Project, supported by Research Council of Lithuania “VibroCut” (MIP – 113), 2011;

2 Scientific work at University Savoy, France, supported by program EGIDE, French Embassy in Lithuania, 2010;

3 Kaunas University of Technology and German Lithuanian

Company “UAB SEBRA” project Nr 101102/8585, 2010

Structure and volume of the work: The dissertation consists of

introduction, five chapters and conclusions, list of 75 references and list of publications on dissertation topic The total volume of dissertation is 113 pages, containing 77 figures and 9 tables

Control of vibrational behavior of different technological tools is a widely applied approach enabling improvement of process efficiency This is particularly true for vibrations of cutting tools generated during machining since the magnitude of induced vibrations has a direct effect on the surface quality of a workpiece Continuous efforts to increase machining efficiency led to the observation that cutting process can be enhanced if the tool is assisted with ultrasonic frequency vibrations, which results in reduced cutting forces and surface roughness This cutting method was termed vibration cutting

The research interest in both conventional and vibration-assisted cutting processes has been active for many years with notable progress both in terms of experimental and numerical efforts

Vibrational turning is fairly widely studied process It was concluded that the highest surface quality is obtained when the second transverse mode of the tool concentrator is excited in the direction of vertical cutting force component This positive effect is attributed to the increased energy dissipation inside the tool material during excitation of the mode, i.e the tool functions as an effective

damper, which reduces influence of deleterious vibrations generated in the machine-tool-workpiece system during turning process

Vibrational drilling is still not widely investigated process.Benefits in drilling performance are observed including faster penetration rates, reduction of tool wear, better surface finish, and, in ductile materials, the reduction or even elimination of burrs on both the entrance and exit faces of plates As a result, vibration drilling leads to improved surface quality and tool life

From the viewpoint of the theory of vibrations the drilling process is an attractive research object since the drill is considered as a pre-twisted cantilever that may be excited in three different directions: torsional, axial and transverse The mechanism of torsional chatter in drilling differs qualitatively and quantitatively from other types of chatter Torsional chatter can be explained by the torsional-axial coupling inherent in a twisted beam: the beam "untwists" and extends in response to an increase in cutting torque The effect of the torsional-axial coupling is opposite to that of traditional cutting in that an increase in cutting forces leads to axial extension and greater chip load

To the best knowledge of the scientists the available scientific literature does not provide unambiguous answer to the question, which types and modes of vibrations of a pre-twisted cantilever are the most beneficial for the practical use, for example, in the case of vibration drilling Therefore clarifications should be sought through joint application of theoretical and experimental investigations by employing accurate numerical models, which are able to provide results that are consistent with experimental findings

2 FINITE ELEMENT ANALYSIS OF DYNAMICS OF A TWISTED CANTILEVER

PRE-Most of the world vibrational drilling research is based mainly on experiments Theoretical research and physical sense are not disclosed This chapter covers the tool, excited high-frequency vibrations theoretical study

2.1 Model formulation

Modeling procedure commenced from formation of a solid model of a twisted cantilever in CAE software SolidWorks (Fig 1(a)) Subsequently, the model was transferred to the FEM software ANSYS, where it was imposed with the appropriate boundary conditions The following material properties were used for the model: density  = 8000 kg/m3, Young's modulus E = 207 GPa,

pre-Poisson's ratio  = 0.3 10-node tetrahedral structural finite element SOLID92 with up to three degrees of freedom at each node was used for meshing SOLID92 has a quadratic displacement behavior and is well suited to model irregular meshes (such as produced from various CAD/CAM systems) The model consists of about 6163 elements SOLID92 and 267 elements COMBIN14

with a total of about 30000 DOFs The model, in general, is based on the Cartesian coordinate system (Fig 1), which was used for modal analysis However, for harmonic and transient simulations it was more convenient to define the coordinates in a cylindrical system with the following degrees of

freedom: displacements z along the rotational axis of the pre-twisted cantilever (axial direction), displacements r orthogonal to the axis (transverse direction) and rotations φ about the rotational axis (torsional direction)

Fig 1 (a) SolidWorks model of a pre-twisted cantilever with the delineated zones where

the structure is imposed with appropriate boundary conditions (b) ANSYS finite element model with the designated zones that are meshed with spring elements

Spring elements COMBIN14 were implemented for modeling of contact interaction in the places where the pre-twisted cantilever is assumed to be fixed

to immovable support: this enables adjustment of boundary conditions to different structural clamping scenarios, for example, those encountered when rotary cutting tools are mounted in a chuck In the FE model the pre-twisted

cantilever is fixed elastically by employing the longitudinal spring elements k r , k z and the torsional spring elements k φ (k r  stiffness in transverse r direction, kz 

stiffness in axial z direction, k φ  torsional stiffness) These one-dimensional link elements are positioned in all directions of the cylindrical coordinate system and are placed at each node of the three zones located on the shank (these zones are marked by the circles in Fig 1(a)) One node of the spring element is superposed with the corresponding node on the zone, while the other link node (further referred to as the "free node") is: (a) connected to the immovable support when running modal analysis; (b) left unconstrained but is imposed with the kinematic (base) excitation in axial direction (when running harmonic and transient simulations)

Zones for imposing boundary conditions

x

z

y

Zones of spring elements

2.2 Modal analysis

The purpose of the numerical modal analysis was to determine vibration modes of the pre-twisted cantilever that are excited at particular resonant frequencies For these simulations the free nodes of the elastic link elements were constrained in all directions The dimensions of the modeled cantilever are:

l = 132 mm, d = 10 mm Table 1 presents results of the simulations, which were

carried out in ANSYS using "Block Lanczos" mode extraction method in a frequency range of 022 kHz In total, 5 transverse modes in two different planes, three torsional modes and one axial vibration mode are detected in the considered frequency range A harmonic analysis is subsequently performed to reveal additional peculiarities of dynamic behavior of the pre-twisted cantilever

Table 1

Summary of simulated natural vibration modes of the pre-twisted cantilever

2.3 Harmonic analysis

Harmonic analysis of the pre-twisted cantilever was carried out by applying the following boundary conditions to the free nodes of elastic link elements: displacements in transverse and torsional directions were fully constrained, while an external load in the form of kinematic excitation was imposed on the nodes in the axial direction Fig 2 illustrates the computed

amplitude-frequency characteristics of the cantilever tip in axial z, transverse r

and torsional  directions

Inspection of the frequency responses obtained in axial and torsional directions reveal two predominant peaks located at the frequencies of 8.9 kHz and 11.1 kHz A resonant peak at 19.8 kHz is notably smaller in comparison to the latter Simulation results indicate a larger number of pronounced resonant peaks in the case of the frequency response in transverse direction It is evident that the highest peaks in all the presented frequency responses are observed in the frequency range of 1112 kHz The preceding modal analysis established the mode shapes of the pre-twisted cantilever, which are associated with the particular resonant frequencies They will be used here to interpret the results of the harmonic analysis

(a)

Fig.2 Simulated frequency responses of the pre-twisted cantilever in axial (a), transverse

(b) and torsional directions (c) Numerical values for the latter response are provided in

radians

Fig 2 (a) indicates that the highest resonant peak observed in the frequency response in axial direction corresponds to the first axial mode of the pre-twisted cantilever at 11.1 kHz However, amplitude peak at this particular frequency is also observed in the frequency response in torsional direction (Fig 2(c)) It should be pointed out that modal analysis found no torsional mode at this frequency Computer visualization of the mode shape at 11.1 kHz revealed

"twisting" and "untwisting" motion of the cantilever, which implies that torsional oscillations are induced alongside the prevalent axial vibration mode This coupling of axial and torsional deflections manifests due to the helical geometry

of the pre-twisted cantilever The same effect is also observed in the "opposite" direction: the 2nd torsional mode at 8.87 kHz in Fig 2(c) is accompanied by a corresponding peak in the frequency response in axial direction (a smaller peak

in Fig 2(a)), while computed natural vibration modes in Table 1 indicate no axial mode at 8.87 kHz Thus, in the latter case, torsional vibration of the pre-twisted cantilever leads to a simultaneous axial deflection, i.e elongation and contraction of the structure, which is consistent with Bayly's model [12] Performed harmonic analysis shows that the coupling effect is indeed pronounced since the frequency response in torsional direction (Fig 2(c)) illustrates that the peak at 11.1 kHz, corresponding to the induced twisting motion, is even larger in amplitude when compared to the peak associated with the natural torsional vibration mode of the pre-twisted cantilever at 8.87 kHz Results of harmonic and modal analysis also resolved the resonant peaks observed in the frequency response in transverse direction (Fig 2(b)): the first two peaks represent the 2nd and 3rd modes at 2.61 kHz and 6.461 kHz respectively, while the highest peak corresponds to the 4th transverse mode at 11.688 kHz The preceding smaller peak in a range of 89 kHz is associated with the 2nd torsional mode at 8.87 kHz A group of three smaller peaks in 1820 kHz range correspond to the 5th transverse modes at 18.151 kHz and 18.894 kHz, while peak at 19.843 kHz refers to the 3rd torsional mode

Results of these simulations reveal comprehensive dynamic behavior of the analyzed pre-twisted cantilever indicating diverse types of vibrations that are generated in the frequency range of interest during kinematic excitation of the structure in axial direction: transverse, torsional and axial modes in conjunction with the additional twisting/untwisting and elongation/contraction oscillatory actions, which are attributed to the coupled nature of axial and torsional vibrations inherent to the twisted structure Furthermore, it should be emphasized that all the mentioned types of vibrations are generated as a result of excitation of the considered pre-twisted cantilever only in an axial direction, thus representing

a case of parametric vibrations

2.4 Transient analysis

The purpose of the transient analysis is to additionally examine the effect

of coupling of axial and torsional vibrations of the pre-twisted cantilever, which was previously detected at 11.1 kHz Transient simulations were performed by applying boundary conditions, which are analogous to the case of harmonic analysis, except that the kinematic excitation was imposed on the nodes in the

axial direction in terms of displacement U z =Asin(t), where A  amplitude,  

excitation frequency, t  time

Computed transient response in Fig 3(a) confirms that at the excitation frequency of 11.1 kHz the first mode of axial vibrations is generated in the pre-twisted cantilever since: (a) it is clearly visible that the excitation curve and the tip response curve are out of phase, i.e the cantilever undergoes extension and contraction in axial direction, (b) vibration amplitudes at the tip are significantly larger with respect to the applied excitation In addition, the out-of-phase character of the presented curves of transverse vibrations in Fig 3(b-c), which were registered at two points located at the opposite sides of the cross-section of the cantilever tip, refer to the aforementioned (un)twisting motion, which is induced at its end simultaneously with the prevalent axial vibration mode due to the helical shape of the structure

(a)

(b) (c)

Fig 3 (a) Simulated transient axial vibrations at the cantilever tip (red dashed line) as a

response to harmonic kinematic excitation (blue solid line) at 11.1 kHz (b-c) Transient transverse vibrations at the two points located at the opposite sides of the cross-section of

the cantilever tip ((b) in y direction, (a) in x direction)

3 Four types of vibrations are observed: natural vibrations modes in axial, torsional and two transverse directions supplemented by the dynamic effects induced due to the coupling of axial and torsional deflections in a helical-shaped structure, namely, twisting/untwisting of the helical end of the cantilever during natural vibration mode in axial direction as well as elongation/contraction during torsional mode

3 EXPERIMENTAL STUDY OF DRILLING TOOL DYNAMICS

3.1 Measurement of frequency responses

The highest effectiveness of the vibration drilling is expected when the drill-tip is excited with the largest amplitude, which is achieved during resonant operation of the device Therefore, a series of frequency response measurements were carried out in order to determine dynamic characteristics of the vibration drilling tool Experimental setup was performed using laser Doppler vibrometer for registration of the frequency responses The piezoelectric transducer of the vibration drilling tool was driven harmonically by using function generator ESCORT EGC-3235A Measurements were conducted in the excitation

frequency range of 2.522 kHz The obtained signal was converted and transmitted to the computer via analog-digital converter (digital oscilloscope PICO 3424) PicoScope software was used for the processing of measurement results

Frequency responses in the axial direction were recorded for three different cases (Fig 7): measurement at the drill-tip as well as at concentrator-tip with and without the drill bit mounted in the vibration drilling tool Comparison

of the responses at the concentrator-tip in Fig 7(a) reveals nearly coincident characteristics for the cases with the drill bit inserted in the tool and without it Thus, it may be safely assumed that the drill bit dynamics has negligible influence on the axial vibrations generated by the vibration drilling tool This result justifies the modeling approach that was employed in this research work, i.e excitation generated by the vibration drilling tool is represented as an equivalent kinematic excitation of the drill bit, which is imposed on zones where the drill bit is actually clamped in the chuck by the bolts In addition, the considered system is linear, therefore the adopted modeling approach allows to judge about dynamic behavior of the vibration drilling tool by simulating a single drill bit with accurately reproduced actual boundary and excitation conditions

Frequency response registered at the drill-tip (Fig 7(b)) reveals two pronounced resonances at the excitation frequencies of 11.2 kHz and 16.6 kHz when using twist drill bit of 10 mm and length of 132 mm Comparison of this frequency response with those registered at the concentrator-tip (Fig 7(a)) indicates that the resonant peak at 16.6 kHz corresponds to the axial mode of the vibration drilling tool itself but not the drill bit This statement is supported by the simulation results in Fig 7(c), which indicate that the drill bit has no axial vibration mode at 16.6 kHz Meanwhile, the peak at 11.2 kHz, on the contrary, refers to the excitation of the first axial mode of the drill bit since: (a) this peak is not present in the frequency responses of the vibration tool measured at concentrator-tip (Fig 7(a)), (b) simulation results in Fig 7(c) confirm that this measured peak corresponds to the numerically determined first axial mode of the drill bit at 11.1 kHz (Table 1)

3.2 Time responses to harmonic excitation  study of axial vibrations

Several series of time response measurements in axial direction were performed by exciting the tool harmonically The main goal of these experiments was to evaluate the dynamic interaction between the vibration tool and the drill bit, i.e to determine how the tool generates and transfers vibrations to the drill bit at two excitation frequencies: 16.6 kHz and 12 kHz (the latter was selected arbitrarily for comparison purposes as a frequency which is close in value to the

4th mode of transverse vibrations of the pre-twisted cantilever determined from the simulations (Table 1))

Fig 4(a) provides a schematic representation of the experimental setup, which is based on application of accelerometers for the registration of time responses These dynamic measurements were conducted with the tool placed on

a vibration-isolation table Piezoelectric transducer of the vibration drilling tool was driven harmonically by using function generator ESCORT EGC-3235A A constant excitation voltage of approximately 100 V was maintained by power amplifier PIEZO SYSTEMS EPA-104

(a)

(b)

Fig 4 (a) Experimental scheme for accelerometric measurements of transient vibrations

generated at the drill-tip (Position A) and concentrator-tip (Position B): 1 – vibration drilling tool; 2 – power amplifier PIEZO SYSTEMS EPA-104; 3 – signal generator ESCORT EGC-3235A; 4 – analog-digital converter PICO 3424”; 5 – computer (b) Vibration drilling tool with two acceleration sensors mounted on the drill-tip Vibrations were registered by using two single-axis piezoelectric charge-

mode acceleration sensors METRA KD-91 (sensitivity k=0,5 mV/(m/s2)): one sensor was fixed on the drill-tip (position A) with the measurement axis aligned

Acceleration sensor, Position A

along the tool and the other one  at concentrator-tip, near the place of drill bit mounting (position B) for measuring axial vibrations generated by the vibration tool itself The recorded acceleration signal was converted and transmitted to the computer via analog-digital converter (digital oscilloscope PICO 3424) PicoScope software was used for data processing

Measurement results provided in Fig 5(a) indicate that at the excitation frequency of 12 kHz vibration amplitude of the drill bit reaches moderate values and the amplitude at the concentrator-tip is relatively low In contrast, at the excitation frequency of 16.6 kHz (Fig 5(b)), the registered time responses of the drill-tip and concentrator-tip are of comparable amplitude Moreover, these dynamic measurements indicate that at the excitation frequency of 16.6 kHz vibration responses of the drill bit and the vibration tool reach their peak values, i.e maximal achievable amplitudes of axial vibrations are observed both at the drill-tip and at concentrator-tip This implies that at this particular frequency the piezoelectrically-excited tool transfers the highest energy to the drill bit, which leads to the boost of axial vibration amplitude at the drill-tip As a consequence, this creates the conditions to achieve the largest positive impact of the superimposed high-frequency vibrations on the cutting process In addition, examination of the vibration curves in Fig 5(b) reveals that at 16.6 kHz there exists a 180 phase difference between the time responses at the concentrator-tip and the drill-tip The observed out-of-phase character of vibration curves indicates that the drill-tip oscillates in one direction, while the concentrator-tip at the same time oscillates in the opposite direction, i.e simultaneous extension and contraction of the tool in the direction parallel to its axis is induced at 16.6 kHz Thus, the aforementioned amplitude amplification and presence of phase difference at 16.6 kHz between the two sensor signals confirm that the observed vibrations are attributed to the axial resonant vibrations of the vibration drilling tool itself

Simulations analogous to the aforementioned vibration measurements were carried out in order to compare the results with the experimental findings It is evident from the presented numerical results that the FE model of the drill bit reproduces the measured vibrational character of the tool fairly well: simulated time responses in Fig 5(c-d) closely match the corresponding experimental responses in Fig 5(a-b) in terms of generated amplitudes and phase differences between the excitation and the drill-tip curves (experimental vibration curves for the concentrator-tip in Fig 5(a-b) correspond to the applied kinematic excitation

in Fig 5(c-d))

Fig 5 Measured (a-b) and simulated (c-d) axial vibrations at the drill-tip (red dashed line) and

concentrator-tip (blue solid line) during harmonic excitation at 12 kHz (a,c) and 16.6 kHz (b,d)

3.3 Time responses to harmonic excitation  study of transverse and torsional vibrations

Another series of time response measurements were performed at the tip in order to gain a more comprehensive view on the dynamic behavior of the vibration drilling tool at 16.6 kHz

drill-The arrangement of acceleration sensors during the following measurements was as follows: two accelerometers were mounted on the drill-tip

so as their measurement axes lie perpendicular to the axis of the drill bit (Fig 7(b) The sensors were fixed by gluing them on the small and thin plate, which was directly attached to the tip and thereby facilitated the repositioning of the sensors Each sensor in this case measured the oscillations in transverse direction Furthermore, this particular arrangement of a pair of sensors enabled to differentiate whether transverse or torsional vibrations are observed in the registered time responses

Fig 6(a-b) illustrates the fragments of time responses received during tool excitation at 12 kHz It is obvious from Fig 6(a) that signal curves are essentially concurrent in phase, thereby indicating purely transverse vibrations,