Modeling of Tool Wear in Vibration Assisted Nano Impact-Machining by Loose Abrasives

Vibration assisted nano impact-machining by loose abrasives (VANILA) is a novel nanomachining process that combines the principles of vibration assisted abrasive machining and tip-based nanomachining, to perform target specific nanoabrasive machining of hard and brittle materials. An atomic force microscope (AFM) is used as a platform in this process wherein nanoabrasives, injected in slurry between the workpiece and the vibrating AFM probe which is the tool, impact the workpiece and cause nanoscale material removal. The VANILA process are conducted such that the tool tip does not directly contact the workpiece. The level of precision and quality of the machined features in a nanomachining process is contingent on the tool wear which is inevitable. Initial experimental studies have demonstrated reduced tool wear in the VANILA process as compared to indentation process in which the tool directly contacts the workpiece surface. In this study, the tool wear rate during the VANILA process is analytically modeled considering impacts of abrasive grains on the tool tip surface. Experiments are conducted using several tools in order to validate the predictions of the theoretical model. It is seen that the model is capable of accurately predicting the tool wear rate within 10% deviation.


Introduction
Well-known tip-based nanomachining processes such as nanoscratching and nanoindentation involve direct tool contact with the workpiece and result in high tool wear.Vibration assisted nano impact-machining by loose abrasives (VANILA) process, a noncontact vibration tip-assisted nanomachining process that uses loose abrasives, has been investigated and can be used to perform target specific impact-based machining of nanoscale features on hard and brittle materials, such as glass and ceramics materials [1,2].This process uses an AFM platform in which a slurry of nanodiamond abrasive particles is introduced between the tool and the workpiece.The machining is conducted in tapping mode where the tool vibrates at resonance within the slurry of abrasive nanoparticles.The impact of the tool along with the acoustic field generated moves the abrasive grain towards the workpiece surface causing a high velocity impact and material removal.A schematic of the VANILA process is shown in Figure 1.
The feasibility of nanoscale machining using the VANILA process was successfully demonstrated on hard and brittle materials such as borosilicate glass and silicon.Patterns of nanocavities were successfully machined to demonstrate the controllability and repeatability of the process as shown in Figure 2 [2].
The VANILA process uses an AFM probe as the vibrating tool to impact the nanoabrasive grains which causes material removal at nanoscale.Earlier studies using scanning electron microscopy (SEM) imaging have shown that tool wear in the VANILA process is comparatively lower than that in other nanomachining processes such as nanoscratching and nanoindentation involving direct tool contact with the workpiece (Figure 3) [2].The accuracy and precision of any tip-based nanomachining process is limited by the tip's sharpness, material, and geometry [3].The level of precision of the nanomachined features continuously degrades during the machining process as the probe tip inevitably wears resulting in an increase of contact diameter and forces acting on it [3].Establishing the point at which the tool is considered worn is important, since, after this point, machining results are no longer acceptable [4].Thus quantification of tool wear to predict the tool life is of great significance.This study aims to develop a theoretical model to predict the tool wear in the VANILA process.

Mechanism of Tool Wear during VANILA Process
The nanoscale wear of AFM tip often refers to the volumetric wear of the tip due to the height loss and varying tip radius.
The AFM probes, in general, have a sharp pyramidal tip of the order of few nanometers.The wear during operation causes tip to become blunt with larger tip.Studies have found that the tip shape and geometry significantly influence its deformation behaviors at nanoscales [5][6][7].A review of the available literature reveals that that AFM tip wear occurs through multiple wear mechanisms [8,9] such as abrasive and adhesive wear [10], low-cycle fatigue and material fracture [10], plastic deformation [11], coating failure, corrosive wear, and tribochemical wear [11], and thermochemical wear [12].Recently, abrasive wear of AFM tips has been studied at atomic scales and it is found that the damaged surface is smoothly modified [13].This basic abrasive-wear mechanism is often termed as gradual wear due to atom-by-atom attrition [14], whereby single atoms or cluster makes up the wear debris.
During the VANILA process, the resonating tool tip repeatedly impacts the nanoabrasive grains suspended in the slurry.The tool tip wear caused by these nanoscale impacts in rapid succession would lead to considerable size effects both in the length and in the time scales.Decohesion forces or pull-out forces become significant which may lead to gradual removal of atoms from the tool tip.This phenomenon is further supported by the fact that, at such lesser tool dimensions, the energy required to break the atomic bonds decreases due to bond stretching [14].Based on the literature study, it is understood that, although several mechanisms could be involved, wear due to gradual atom-by-atom loss would be the most relevant wear mechanism causing the tool wear in the VANILA process [14].Thus, based on this information, a wear model is developed to predict and quantify the tool wear during the VANILA process.Other wear mechanisms that could affect the tool wear process are ductile mode plastic deformation and nanoscale cracking [15].However, these mechanisms would be more relevant when the tool tip size is considerably larger than the abrasive grain size.

Modeling of Tool Wear in VANILA Process
During the VANILA process, the tool tip and workpiece surface are maintained at a distance.The tool wears due to the impact of nanoabrasive grains.For the purpose of analytical modeling of tool wear, the following simplification assumptions are made.(1) The abrasive grains are assumed to be spherical and rigid and remain intact throughout the machining process.
(2) Abrasive nanoparticle and tool material are electrically and chemically neutral and the electrostatic effects during impact are neglected.
(3) The effects of surface adhesion and interactions outside the region of contact are not considered in this study.
(4) For the theoretical modeling, the tool tip is assumed to be flat.The change in profile of the tool tip during the machining process is not considered in this study.
(5) The effects of abrasive grain impact on the sides of the tool tip are not considered in this study.(6) The collisions between the abrasives grains are assumed to be perfectly elastic.

Impact Velocity and Forces.
During the VANILA process, the abrasive grains moving in the slurry medium impact the tool which is excited at resonance.The resultant velocity of impact (V I ) has two components: (a) velocity of vibrating tool (V t ) and (b) velocity of abrasive grain (V a ).The motion of tool tip can be expressed as    (+/2) .The phase associated with the total force can be considered as /2 due to the fact that machining is conducted at resonance frequency and since on resonance the oscillations of the cantilever follow the total force with a phase delay of /2 [16].Average velocity of the tool tip (V t ) can be expressed as The velocity of the nanoabrasive grain within the fluid medium can be considered to be equal to the velocity of the fluid molecule.The acoustic streaming motion generated by the acoustic field near the tool tip results in the motion of the fluid slurry between the tool tip and the workpiece surface.The nanoparticle within the slurry is transported along with the streaming fluid molecules and causes impact with the International Journal of Manufacturing Engineering where   is the vibration intensity of the acoustic waves generated at the tool tip and can be calculated by dividing the acoustic power by the area of the radiating surface which is the tool tip surface area [18]: The acoustic power generated at the tip which is excited at its resonant frequency can be found as [19] The impact velocity V I can be expressed as According to the law of conservation of momentum, the impact force (  ) on the tool tip surface due to the impact with the abrasive nanoparticles can be expressed as [20] where  is the angle of impact and Δ is the response time defined as The response time can be considered as the time scale over which the particles respond to changes in flow conditions [20].Also, the mass term in the expression for   only International Journal of Manufacturing Engineering considers the abrasive grain mass since the tool tip mass is much larger than the grain mass.

Establishing Threshold Criteria.
When the impact force   is larger than the critical pull-out force   , the tool atoms are able to pass through a critical energy barrier resulting in gradual atom-by-atom attrition [14].The critical pull-out force can be expressed as [21] where  is the Dupré energy of adhesion and  * is effective tool tip radius which is given by [21] The effective radius term would enable modeling the tool wear in the VANILA process at various instants of wear.This formulation of  * is commonly used in classical Hertzian contact theory to determine the contact radius between the impacting bodies.

Estimation of Tool Wear Rate.
Tool wear rate TWR is proportional to the product of volume of tool removed   by single impact, the total number of active abrasive grains   , and the frequency of vibration   : Introducing a proportionality factor  termed as wear coefficient, the tool wear rate can be determined as TWR =  *   *   *   . (11)

Volume Removed by Single Impact.
Since the wear happens at atomistic scales, the classical theories of mechanics may not be applicable.A quantum mechanism based approach is thus used to estimate the volume   removed by single impact of the abrasive grain.The tool volume removed   due to interaction with single nanoabrasive grain can be deduced by the D' Acunto model [13,22,23]: where  atom is the number of atoms passing through the energy barrier,  atom is the transition rate, and vol atom is the individual atomic volume.Δ corresponds to the time of interaction between the abrasive grain and the tool which is described in earlier section of this paper.The term ( atom *  atom ) can be calculated using the well-known Arrhenius kinetics [24] as follows [22]: where Δ is the effective activation energy barrier,   is the Boltzmann constant,   is the surface atomic density of the tool tip,   is the area of contact between the tool and abrasive grain which is circular region having diameter  * ; that is, The term  atom corresponds to the attempt frequency or oscillation frequency.The activation energy barrier for the atoms to be removed from the tool is considerably reduced by the bond stretching due to impact of the abrasive grain.Thus the effective activation energy barrier Δ is the difference of the activation energy  act of the tool material and the energy of impact I of the abrasive grain (Δ = E act − E i ).

Number of Active
Abrasives.  is the number of active abrasive grains in the machining zone which can be derived as follows.The vibrating tool impacts the abrasive grains within the volume of an imaginary cylinder having diameter equal to tool tip diameter and height equal to the amplitude of vibration of the tool as shown in dotted line in Figure 3.It is to be noted that this figure is not drawn to the actual scale and its purpose is to show the method of determining the active abrasive grains.The volume of active abrasive particles within this imaginary cylinder can be expressed as where Area  is the cross-sectional area of tool tip given by Area  =  2  ,   is the slurry volume concentration, and   is the amplitude of tool vibration.
The volume of active abrasive particles within the imaginary cylinder can also be expressed as the product of the number of abrasive nanoparticles (  ) within the imaginary cylinder and volume of a single grain: Using the above equalities,   can be calculated as

Experimental Verification
The VANILA process experiments are performed using several commercially available tapping mode AFM probes and 10 nm sized nanodiamond abrasive grains suspended in deionized water-based slurry.The tools used are made of commercially available tapping mode probes (NSC16 series MikroMasch make) made of n-type silicon having a tip diameter in the range of 8-10 nm and is excited at its resonance frequency (5-10 KHz range).The tool tip is vibrated at its resonance frequency using the cantilever tuning operation in the Nanoscope IIIa software of the AFM.Representative drive amplitude versus frequency curve during the cantilever tuning for VANILA process is shown in Figure 4(b).The resonance frequency is chosen from the peaks shown during the cantilever tuning.
The maximum vibration amplitude of the tool (  ) is approximately 200 nm with a quality factor (  ) ranging from 1to 50 and spring constant (  ) 0.5-45 N/m.Properties of deionized water that are considered in this study are dynamic viscosity (]  ) = 0.00078 Kg/m⋅s, density (  ) = 1000 Kg/m 3 , and speed of sound in water () as 1500 m/s.AFM (Veeco Dimension 3100 with Nanoscope III) is used to perform experiments along with a direct drive fluid cantilever holder (DDFCH) for holding the tool.The tool tip is vibrated at its resonant frequency.Polished silicon wafers are used as the workpiece substrate and the abrasive slurry is introduced on the workpiece surface using a syringe.The tool tip is maintained at a distance of 100-200 nm above the substrate surface to avoid contact, while the amplitude of vibration is approximately 100 nm.The machining set-up used for the VANILA process is shown in Figure 4(a).Figures 4(c  VANILA process.The common experimental conditions are listed in Table 1. Each tip is used to machine several nanocavities before it is analyzed using scanning electron microscope (SEM) images (make -FEI XL30 ESEM).In order to determine the wear volume with nanoscale precision, SEM images are analyzed and relevant tool dimensions such as its tip length and radius are estimated as shown in Figure 5.Using this information, three-dimensional computer models of the tool tips are created using 3D modeling software SolidWorks in Figure 5(c).The model is sliced at a specified length which is obtained from the SEM images of the worn tip as In these calculations, the surface atomic density of the tool tip   is taken as 10 16 atoms/cm 2 [25], the response time is approximately 10 −12 seconds, and the attempt frequency  atom has typical values of 10 13 cps for silicon [26].The atomic volume of silicon (vol atom ) is taken as 0.02 nm 3 with an activation energy  act value of 0.9 eV [14].Based on the experimental conditions, the impact velocity is approximately in the range of 2-3 m/s and the impact force is estimated in the range of 20-50 nN assuming the angle of impact to be normal.The Dupré energy of adhesion for silicon is taken as 4 mJ/m 2 [27] and the critical pull-out force   is estimated to be 0.19 nN which is lower than the force of impact and thus the wear could progress.The duration of machining for the tools is varied between 100 s and 1200 s where the tool is used to machine multiple nanoscale cavities on the workpiece.Figure 6 shows the plot between the theoretically predicted TWR and the experimental TWR for machining durations ranging from 100 s to 1200 s for a  value of 9500.
From the study, it is seen that during the VANILA process, the typical tool wear rates are in the order of 10 3 nm 3 /s compared to the material removal rates (MRR) from the workpiece which is in the order of 10 5 nm 3 /s [28].From the plot, it is seen that the TWR model is capable of predicting the tool wear rates within 10% accuracy.It is seen that the tool wear increases gradually with the machining duration.This could be due to the fact that, as the machining duration increases, the number of active abrasive grains which affect the tool wear process increases resulting in increased tool wear rates.For the theoretical calculation of TWR, final tool tip radius value (from the SEM images of worn tool tips) is used to calculate the  * value.

Conclusion
In this study, the tool wear involved in the VANILA process is studied using analytical modeling and experimental methods.Tool wear rates are estimated to be in the order of 10 3 nm 3 /s during the machining process for tool tips made of silicon.In order to validate the model, experiments are performed with different tools for varying machining durations.Reasonably good quantitative correlations (within 10%) are obtained between the model predictions and the corresponding experimental observations.

3. 1 .
Simplification Assumptions.The simplification assumptions made in developing the theoretical model are listed as follows.

Figure 2 :Figure 3 :
Figure 2: Pattern design and AFM image of nanocavity pattern machined using the VANILA process (a) on silicon substrate [2] and (b) on borosilicate glass substrate.
) and 4(d) show the tool tip (and enlarged view) used for the

Figure 5 :
Figure 5: SEM images and solid model of tool tip used for VANILA process.

RFigure 6 :
Figure 6: Plot showing tool wear rates from experiments versus theoretical predictions for varying machining duration.

Table 1 :
Experimental conditions for VANILA process.