a theoretical and experimental investigation of surface generation in diamond turning of an...

International Journal of Mechanical Sciences 43 (2001) 2047–2068

A theoretical and experimental investigationof surface generation in diamond turning of an Al6061=SiCp

metal matrix composite

K.C. Chan ∗, C.F. Cheung, M.V. Ramesh, W.B. Lee, S. ToDepartment of Manufacturing Engineering, The Hong Kong Polytechnic University, Hung Hom,

Kowloon, Hong Kong

Received 20 October 2000; accepted 10 March 2001

Abstract

In this paper, the surface generation in ultra-precision diamond turning of Al6061=15SiCp metal-matrixcomposites was investigated based on di5erent analytical approaches which include parametric analysis,cutting mechanic analysis, 7nite element method (FEM) analysis and power spectrum analysis. Parametricanalysis was performed to explore the in situ inter-relationships between the process parameters and thesurface roughness. The surface properties of the diamond turned surface were extracted and analyzed bythe power spectrum analysis of the surface roughness pro7les. Di5erent surface generation mechanismswere deduced based on the cutting mechanics and FEM analysis. The results of the theoretical analyseswere veri7ed through a series of cutting tests conducted under various cutting conditions and a goodcorrelation between the theoretical and experimental results was obtained. ? 2001 Elsevier Science Ltd.All rights reserved.

Keywords: Cutting mechanics; Finite element method; Metal-matrix composite; Power spectrum analysis; Surfacegeneration; Swelling; Ultra-precision machining

1. Introduction

In the ultra-precision machining community, it has been generally accepted the premisethat only certain materials are “diamond turnable” [1]. In practice, diamond turnable mate-rials are those where the wear rate is low enough that reasonable areas of surface can beproduced economically. Over the past decades, most of the research work and the applicationsof ultra-precision diamond turning reported in the literature were non-ferrous ductile

∗ Corresponding author. Tel.: +852-2766-4981; fax: +852-2362-5267.E-mail address: [email protected] (K.C. Chan).

0020-7403/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved.PII: S 0020-7403(01)00028-5

2048 K.C. Chan et al. / International Journal of Mechanical Sciences 43 (2001) 2047–2068

Nomenclature

d depth of cutf feed rateFt thrust forcern tool edge radiusR tool nose radiusRa arithmetic roughnessN spindle speedPSD power spectrum densitiess tool feed ratetc chip thicknessHtc undeformed chip thickness�n the threshold of normal stress�s the threshold of shear stressVc cutting speed� stress�n normal stress�s shear stress

materials [2] such as copper [3], aluminum [4] and acrylic (PMMA) [2] which are weak instrength and possess low speci7c modulus. They may not be durable enough for long service lifeapplications such as plastic injection moulding. These limited their practical applications in theindustry. The development of new materials with good machinability and surface quality, andlonger service life are prime importance for further development of ultra-precision machiningtechnology.

Metal-matrix composite (MMC) materials are considered to have great potential industrialapplications due to the fact that these materials possess high speci7c modulus, speci7c strength,wear resistance and high temperature resistance [5]. Some of the researchers have examinedthe surface characteristics of machined Al-SiC MMCs. In the study of Looney et al. [6], theinKuence of tool materials on surface 7nish has been reported. Yuan et al. [5] have carried outside turning experiments to evaluate the surface 7nish in single point diamond turning of Al=SiCwmaterials. By varying percentage and direction of whiskers of SiC in Al matrix materials, theyhave reported that it is possible to achieve a surface 7nish in order of Ra=0:01 �m. El-Gallaband Sklad [7] have further examined the microstructures of chips, and observed the formationof shear bands, where reinforcement particles align themselves. By developing an improvedquick-stop device, Lin et al. [8] were able to examine the cutting mechanisms more e5ectively. Itis well known that the MMC materials are diOcult to be machined to a good surface 7nish. Someresearch work [5] has reported that this is due to di5erent mechanisms underlying the surfacegeneration in diamond turning of MMC materials. They found that pits and cracks were formedon the surfaces after machining. However, the causes of the formation of pits and cracks, therelationships between the process parameters and these material phenomena have to be sought.

K.C. Chan et al. / International Journal of Mechanical Sciences 43 (2001) 2047–2068 2049

A widespread industrial application of these advanced materials will not be possible withoutthe solution of the machining problems [9]. The poor reproducibility of physical properties ofMMC specimens and components is an important hindrance for many possible applications.Moreover, our current understanding on the metal removal process and its relation to the sur-face generation mechanisms in ultra-precision machining of the MMC materials have not wellbeen understood. The surface generation in ultra-precision machining is a5ected by the machinecharacteristics, process parameters, and materials related phenomena such as di5erential elasticrecovery of adjacent grains, inclusions, and fracture [10]. In this paper, the mechanisms of sur-face generation in diamond turning of an Al6061=15SiCp MMC composite were analyzed basedon di5erent analytical approaches. Hence, cutting experiments were conducted under variouscutting conditions so as to explore the relationships between the cutting parameters and thesurface 7nish in diamond turning the composites.

2. Approaches for the analysis of surface generation

Over the past decades, the surface generation in machining has been studied from di5erentapproaches. Traditionally, the generation of machined surface has been studied based on mod-els of cutting mechanics [11,12]. Such macroscopic parameters as the cutting forces, stressand strains were correlated with surface roughness parameters [4,13]. Another approach [14,15]derived the surface properties based on the analysis of surface roughness pro7les. Recently,FEM analysis [16] and molecular dynamic simulation [17,18] have been used to analyze themechanisms of nanoscale cutting. However, most of these studies were focused on ductile ma-terials such as copper and aluminum. Although some research work has been found on studyingthe surface generation in brittle materials [19,20] such as silicon, the use of the captioned ap-proaches on studying the surface generation in the diamond turning of composite materials hasreceived relatively little attention. In the present study, the following approaches were used toinvestigate the mechanisms underlying the surface generation in the diamond turning of thecomposite materials. These include:

(i) parametric analysis of surface roughness;(ii) cutting mechanic approach;(iii) 7nite element method;(iv) power spectrum analysis of surface roughness pro7les.

Parametric analysis is used to establish the interrelationships among the cutting parametersand the surface roughness. The results are explained with the aids of the theoretical analysisbased on the cutting mechanic and FEM approaches. Power spectrum analysis is used to revealand verify the mechanisms underlying the surface generation in diamond turning of the MMCs.

2.1. Parametric analysis of surface roughness

The surface quality in diamond turning is a5ected by a number of factors which includetool geometry, machining parameters, workpiece properties (both mechanical and thermal),


Fig. 1. Process of surface generation.

mechanical vibration induced during machining, etc. Theoretically, the arithmetic roughnessRa [21] of a machined surface can be represented by

Ra ∼ s2

32R=

f2

32RN 2 ; (1)

where s is the tool feed per workpiece revolution, f is the feed rate in mm min−1; N is thespindle speed in rpm and R is the tool nose radius. Eq. (1) does not involve depth of cut dwhich intuitively a5ect surface roughness of a diamond turned surface.

In the parametric analysis, the interrelationships between the surface roughness and the processparameters can be explored by the construction of parametric surfaces for di5erent combinationsof the process parameters. With the use of the non-linear multiple regression analysis method,it is possible to derive empirical surface roughness equations for the prediction of the surfaceroughness of the workpiece.

2.2. Cutting mechanics approach

The process of formation of machined surface is shown in Fig. 1. For a perfectly sharpcutting tool (i.e. zero radius of cutting edge), the layer to be cut (i.e. tc, the chip thickness)will be separated sharply or fracture along line OA and shear o5 in direction OS to becomethe chip. However, a cutting tool always processes a radius rn at the cutting edge. From anatural diamond tool, the cutting edge radius is in the order of about 0.01–0:5 �m [22]. In thiscase, the workpiece material will be separated along the line LM instead of OA. The part ofthe undeformed chip with thickness of Htc will be plastically compressed and extruded underthe round cutting edge to become the machined surface. After machining, the machined surfacewill be recovered elastically. The amount of elastic recovery depends on the Young’s moduleof the materials being cut.

Since the hard SiC particles in the Al6061=15SiCp MMC are embedded in the soft aluminummatrix, the mechanisms in the cutting of SiC particles depend largely on the deformation inthe Al matrix during cutting. As shown in the micrograph of Fig. 2, the cutting edge radius


Fig. 2. Microstructure of the Al6061=15SiCp composite.

Fig. 3. Graphical illustration of the (a) cut through and (b) pull out mechanisms in cutting SiC particles in thecomposite.

is in the same order as the average diameter of the SiC particles in the Al6061=15SiCp MMC.There is a signi7cant thick layer of undeformed chip (i.e. with the same order as the averagediameter of the SiC particles) at which complicated plastic and elastic deformations take place.These lead to two possible mechanisms for which the SiC particles are cut in diamond turning.As shown in Fig. 3, the SiC particles can be either cut through (Fig. 3a) or pulled out (Fig.3b) during diamond turning. For the cut through mechanism, the surface 7nish is better sincethe SiC particles are cut directly by the diamond tool and there is no pits and cracks left on thecutting surface after cutting. If the SiC particles are pulled out during diamond turning, cracksand pits will be formed on the cutting surface and this will cause poor surface 7nish.


The occurrence of these mechanisms depends largely on the strain rate and hence the amountof plastic deformation occurs around the SiC particles during cutting. As spindle speed increases,the strain rate increases and the aluminum matrix becomes more diOcult to deform. Under thiscondition, the SiC particles are more likely to be cut through than that to be pulled out. Sincethe amount of pits and cracks is reduced, a better surface 7nish can be achieved. Under lowspindle speed condition, the true strain rate decreases and the aluminum matrix becomes moreeasy to deform. The SiC particles are more likely to pulled out of the surface after machining.This results in an increased amount of pits and cracks and hence a poor surface 7nish.

2.3. FEM for the prediction of shear strain patterns

It is not an easy task to model mathematically and numerically the process of machining. Thiscould be due to the fact that, peculiarity of the machining process, highly localized stresses,strains and temperatures develop in the vicinity of machining. Although FEM is regarded as apowerful and commonly used numerical tools to model actual manufacturing processes, therewas little research work reported on FEM modeling of machining metal matrix composites.Most of work is on machining of isotropic materials such as copper and aluminum.

In the present study, the FEM was adopted in order to predict the shear strain patterns in theworkpiece. To understand the mechanisms of the material removal in the MMC material, thefour possible encounters of the tool with that of SiC elements have been studied as shown inFig. 4. These include:

(i) tool facing SiC element;(ii) tool facing Al-matrix;(iii) tool ploughing through SiC element (cut-through mechanism);(iv) tool ploughing through an Al-matrix.

For dynamic equilibrium of a body in motion, the following equation at a time station tnirrespective of material behavior can be constructed based on the principle of virtual work∫

�[��n]T�n d� −

∫�[�un]T[bn − �n Run − cnu n] d� −

∫�t

[�un]Ttn d�=0; (2)

where, �un is the vector of virtual displacements, ��n is the associated virtual strains, bn is thevector of applied body forces, tn is the vector of surface tractions, �n is the vector of stresses,�n is the mass density, cn is the damping parameter and · refers to di5erentiation with respectto time. The domain of interest � has two boundaries: �t on which boundary conditions tn arespeci7ed and �u on which displacements un are speci7ed.In this model, a total Lagrangian method is adopted and the model originally adopted by

one of the authors [23] for machining of FRPs will be modi7ed further to suit the presentanalysis. This two-dimensional model is treated as a plain strain case. A skyline procedurefor most eOcient matrix storage system has been employed in association with LDLT pro7lesolver for solving system of governing simultaneous equations. To approximate more closely,a second-degree approximation is used by discretizing the entire domain into 8-noded isopara-metric elements.


Fig. 4. Four possible cases of the tool encounters of the tool in cutting the SiC elements: (a) Case A: Tool facingSiC element; (b) Case B: Tool facing Al matrix; (c) Case C: Tool ploughing through Sic element; (d) Case D:Tool ploughing through Al matrix.

It is assumed that the entire domain of interest consists of two di5erent materials, they areSiC elements packed in a uniform aluminum matrix. Both these materials are treated as isotropicin nature and the entire system is perfectly homogenous with uniform packing density of thesematerials. Furthermore, the present study is restricted to the 7rst failure or just before the chipseparation from the work piece and also the presence of bonding material is neglected. Theload is applied incrementally through the tool. Because of the applied load the stresses andstrains are developed in the system. It is very important in the analysis of machining to knowwhen the failure or chip is being separated. For this, there are many criteria in the literaturefor materials in alloy form, but less for composites, which consists of more than one material.For this, it seems that the criterion proposed by Liangchi Zhang [24] is more appropriate whichcan be expressed as( |�n|

�n

)2+

( |�s|�s

)2¿ 1; (3)

where �n is the normal stress at the nearest Gaussian point of the tool tip, �s is the shear stress.Whereas, �n is the threshold of such normal stress and �s is the threshold of shear stress. It isemphasized that for normal failure stress criterion, �s must be set to a very large value such as10; 000 MPa. This will enable the material undergo failure only because of normal stress. So, inthe present analysis, an identi7er was installed to identify the material for each element. When,the tool faces an element, at the nearest Gaussian point to the tool, the failure criterion will be


selected accordingly. For SiC element it would be appropriate to select the normal stress failurecriterion.

2.4. Power spectrum analysis of surface roughness pro2les

2.4.1. Theoretical background of power spectrum analysisThe surface roughness pro7le of a machined surface provides a faithful signature of the

cutting process and variation of material properties. Moreover, an imprint of all the static aswell as dynamic forces, stress, strains and materials swelling during cutting is left in the surfaceroughness pro7le. In the present study, power spectrum analysis [25] is used as a means toextract the surface properties of a workpiece. This is undertaken by transforming the data of asurface roughness pro7le into frequency domain. The surface roughness pro7le of a diamondturned surface is expressed as a function denoted by z(nls) with n=0; 1; 2; : : : ; Ns − 1 where Nsis the number of equally spaced positions in the roughness pro7le and ls is the sample spacing.The power spectrum of the surface roughness pro7le can be de7ned as

Z(�k)=N−1∑n=0

z(nls) exp(−2!jnls�k); (4)

where k is an integer number, and �k is a frequency component of the surface roughness pro7lewhich represents the number of waves with a wavelength of #k within a unit length, i.e.

�k =1#k

=kL; (5)

where Ns is the total number of samples with spacing ls taken within the measured length L ofthe roughness pro7le, i.e.

Ns =Lls: (6)

The sample rate �sample is usually chosen to be at least twice of the highest non-zero frequencycomponent �max contained in surface roughness data in order to avoid the alias e5ect, i.e.

ls61

2�max; (7)

where ls is the sample spacing.The power spectral density (PSD) is directly determined from the discrete Fourier transform

DFT. In order to minimize the distortion of the true spectrum due to Gibb’s phenomenon, thespectral window corresponding to the Hanning lag window is used to get the PSD [26]. TheHanning window is used because it has spectral intensity concentrated at its main lobe in thefrequency domain and hence provides more smoothing through convolution operation in thefrequency domain.

2.4.2. Characterization of materials swelling in diamond turningDuring diamond turning, the workpiece material swells at the end of the active cutting edge

[27]. As shown in Fig. 5, this is due to the plastic side Kow [28] in which the metal left behindon the cutting edge is subjected to suOciently high pressure to cause the metal to Kow to the


Fig. 5. Surfaces generated with (a) the presence and (b) the absence of materials swelling.

side of the active cutting edge. Moreover, the cutting force along the main cutting edge of thetool (Ft in Fig. 5), which is required to provide two-dimensional cutting along the edge, pushesaside the work material near the tool nose causing it to Kow to the free surface [29]. In theregion below the chip, complicated elastic and plastic deformation occurs [21] which is causedby the indentation and=or burnishing by the cutting edge. As shown in Fig. 1, the workpiecematerial left behind the front clearance of the tool springs back or recovers after burnishing.

The combined e5ect of plastic side Kow, burnishing and elastic recovery will cause greaterand deeper tool marks to be formed on the machined surface and this is referred in the presentstudy as the materials swelling. The e5ect of materials swelling increases the power spectraldensity of the feed components in the surface roughness spectrum. The amount of swellingdepends on the properties of the material being cut. The softer and more ductile the material,the greater will be the swelling e5ect [27].

3. Experimental procedures

In the present study, a series of face cutting experiments was performed on the basal planeof the cylindrical Al6061=15SiCp composite workpiece under various cutting conditions. Theprocess parameters under investigation include spindle speed N , feed rate f, tool feed rate sand depth of cut d. The work material under investigation was Al6061=15SiCp composite asshown in Fig. 2. The composite material was provided by Advanced Composite Corporationmanufactured using the power metallurgy method followed by extrusion. The volume fraction is15% for SiC particles which are uniformly distributed in the matrix of aluminum alloy (6061).For the study of the e5ect of SiC particles reinforcement, an aluminum alloy (6061) specimenwas also machined in Part A. All face cutting tests were performed on the basal plane of thecylindrical workpiece using a two-axis CNC ultra-precision lathe (Optoform 30 from Taylor


Table 1Cutting conditions for the experiments in Part A

Cutting Spindle speed N Feed rate Tool feed rate Depth of cutconditions (RPM) f (mm min−1) s (mm rev−1) d (�m)

A1 5000 20.0 0.00400 1.0A2 5000 20.0 0.00400 3.0A3 5000 20.0 0.00400 5.0A4 5000 30.0 0.00600 1.0A5 5000 30.0 0.00600 3.0A6 5000 30.0 0.00600 5.0A7 5000 40.0 0.00800 1.0A8 5000 40.0 0.00800 3.0A9 5000 40.0 0.00800 5.0A10 8000 20.0 0.00250 1.0A11 8000 20.0 0.00250 3.0A12 8000 20.0 0.00250 5.0A13 8000 30.0 0.00375 1.0A14 8000 30.0 0.00375 3.0A15 8000 30.0 0.00375 5.0A16 8000 40.0 0.00500 1.0A17 8000 40.0 0.00500 3.0A18 8000 40.0 0.00500 5.0

Table 2Cutting conditions for Part B

Spindle speed (rpm) 8000Feed rate (mm min−1) 40Depth of cut (�m) 3Tool nose radius (mm) 0.762Rake angle −25

◦

Hobson Pneumo Co.). Single crystal diamond tools with rake angle of −25◦, front clearanceangle of 10◦ and tool nose radius of 0:762 mm were used throughout the experiments. Thesurface roughness of the diamond turned surface was measured by a Form Talysurf system. Apower spectrum analysis program was exclusively developed for determining the spectra of thesurface roughness pro7les of the workpiece.

Basically the experiments were divided into four parts, i.e. Parts A, B, C and D.Tables 1–3 summarized the cutting conditions for all parts of the experiments. In Part A,a parametric analysis, as described in Section 2.1, was undertaken to bring out the subtleinter-dependence among the process parameters and surface roughness and an empirical equa-tion was derived for the prediction of arithmetic roughness under various cutting conditions.Part B related to the analysis of the strain in cutting the SiC particulate reinforcement. Theanalysis was undertaken by a FEM program purposely built for the study. In Part C, groups ofcutting tests were conducted to investigate the inKuence of process parameters on the cuttingmechanics and hence surface roughness pro7les. Groups C1 and C2 involve those cutting tests


Table 3Cutting conditions for Part C

Cutting conditions Group no.

C1 C2 C3

Process parameters Spindle speed Feed rate Depth of cut

Set no. C1a C1b C2a C2b C2c C2d C3a C3bFeed rate 20 30 20 40 30 40 40 40(mm min−1)Spindle speed 5000 8000 8000 8000 5000 5000 5000 8000(rpm)Tool feed rate 0.0040 0.0038 0.0025 0.0050 0.0060 0.0080 0.0080 0.0050(mm rev−1)Depth of cut (�m) 5 5 3 3 3 3 3∗, 1, 3 3∗, 1, 3

∗Ideal roughness pro7le generated by computer program [30].

Table 4Cutting conditions for Part D

Cutting conditions Group no.

D1 D2 D3

Material related phenomena SiCp reinforcement Materials swelling Surface Integrity

Set no. D1 D2a D2b D3a D3bFeed rate (mm min−1) 30 20 30 20 30Spindle speed (rpm) 8000 5000 8000 5000 8000Tool feed rate (mm rev−1) 0.0038 0.0040 0.0038 0.0040 0.0038Depth of cut (�m) 1 3, 3∗ 3 1 1

∗Ideal roughness pro7le generated by computer program [30].

for studying the e5ect of spindle speed and feed rate on the surface generation. The e5ect ofdepth of cut was studied in Group C3. Part D focused on the material-related phenomena onthe surface generation. Face cutting tests were undertaken for studying the e5ect of SiC particlereinforcement and the swelling of tool marks on the formation of surface roughness (Table 4).The swelling of tool marks was characterized by power spectrum analysis of the surface rough-ness pro7les as discussed in Section 2.3. The dominant mechanisms of surface generation un-derlying the cutting processes were veri7ed using scanning electron microscopy (SEM).

4. Results and discussions

4.1. Part A. Parametric analysis

Parametric surfaces which depict the dependence of arithmetic roughness on feed rate anddepth of cut at di5erent spindle speeds were constructed based on the results of the surface


Fig. 6. Dependence of arithmetic roughness on depth of cut and feed rate at spindle speed of (a) 5000 and (b)8000 rpm.

roughness measurement. As shown in Fig. 6, smaller arithmetic roughness and thus better surface7nish are found at a higher spindle speed under various combinations of depth of cutting andfeed rate. At a cutting speed of 5000 rpm as shown in Fig. 6a, there is an optimum range of feedrates at which the arithmetic roughness is preferably small. Better surface 7nish can be achievedat small depths of cut. However, the parametric surface (Fig. 6b) is completely di5erent in shapefor a higher spindle speed of 8000 rpm. In this case, better surface 7nish is achieved at a largerdepth of cut and a higher feed rate. These 7ndings illustrate the prominence e5ect of spindlespeed on the surface 7nishing in diamond turning of the Al6061=SiCp composites.

In order to provide the upper and lower bound estimates of the arithmetic roughness, anon-linear multiple regression analysis method has been deployed to analyze the arithmeticroughness in the form of empirical equation. The empirical surface roughness equation takesinto consideration of spindle speed, feed rate and depth of cut. This approach enables practicingand design engineers for further mathematical and numerical analyses. The empirical equationobtained is as follows:

Ra=732970N−2:0685f0:2010d0:1170; (8)

where the arithmetic roughness Ra is in nm, the spindle speed N is in revolutions per second,feed rate is f in mm s−1 and depth of cut is in �m.

Fig. 7 shows a plot of the predicted arithmetic roughness values against the experimentalresults. The comparisons are made under the same cutting conditions as tabulated in Table 1.Although some scatter is observed, a good trend is predicted for the arithmetic roughness.

4.2. Part B. FEM analysis

Fig. 8 shows the constant shear strain patterns simulated by the FEM program for the fourcases as discussed in Section 2.3. There is a signi7cant change in the pattern according to the


Fig. 7. Actual values against predicted values for arithmetic roughness.

Fig. 8. Shear strain patterns for the four possible tool encounters in the composite: (a) Case A: Tool facing SiCelement; (b) Case B: Tool facing Al matrix; (c) Case C: Tool ploughing through Sic element; (d) Case D: Toolploughing through Al matrix.


Fig. 9. E5ect of spindle speed on the roughness pro7les generated under conditions in (a) Set C1a and (b) SetC1b, respectively.

presence of the SiC element in the Al-matrix. When the tool facing the SiC element, as inCase A, a maximum shear strain of 0.001 is observed at the top surface and the shear straindecreases progressively to 0.0001 around the tool tip. For case B, the shear strain is found tobe smaller than that of Case A. Whereas a shear strain of 0.0004 is observed at the surface,a small shear strain of 0.0001 is found below the tool tip and work piece interface. When thetool is ploughing through the Al-matrix, as in Case D, the shear strain is found to be 0.0003 atthe top surface and decreases progressively to 0.00005 near to the tool tip. Surprisingly, there isa reverse trend observed when the tool ploughs through the SiC element (a typical cut-throughmechanism as discussed in Section 2) as shown in Case C. Lower strains are observed as lowas 0.0001 at the surface and increased progressively to 0.0005 near to the tool tip.

4.3. Part C. Process factors on the cutting mechanics and surface generation

4.3.1. Spindle speedFig. 9 shows the e5ect of spindle speed on the surface generation. It appears that greater

surface roughness is obtained under a lower spindle speed. As shown in Fig. 9a, larger toolmarks are observed at a lower spindle speed (5000 rpm) even a nearly identical tool feed rate isused. In addition, there are some pits and cracks which are not clearly observed under a higherspindle speed (8000 rpm) as shown in Fig. 9b.The experimental 7ndings agree well with the theoretical analysis in Section 2.2. As spindle

speed increases, the strain rate increases and the amount of plastic deformation in the Al matrixis reduced. The SiC particles are more likely to be cut through than that to be pulled out.Therefore, the amount of pits and cracks is reduced and hence a better surface 7nish can beachieved.

4.3.2. Tool feed rateAs shown in Fig. 10, larger tool marks are observed at a higher tool feed rate. Moreover, the

amount of pits and cracks are found to increase with increasing tool feed rate. With a decreasein the tool feed rate, the amount of plastic deformation of the cutting surface decreases as well.This reduces the amount of cracks and pits and hence better surface 7nish.


Fig. 10. E5ect of tool feed rate on the roughness pro7les generated under conditions in (a) Set C2a, (b) Set C2b,(c) Set C2c and (d) Set C2d, respectively.

4.3.3. Depth of cutThe e5ect of the depth of cut is shown in Figs. 11 and 12 for the cutting speeds of 5000

and 8000 rpm, respectively. These 7gures are obtained for the feed rate of 40:0 mm min−1. Theideal surface roughness pro7le [30] is used to depict the tool marks formed on a perfect surface.Comparing the roughness pro7les in Figs. 11 and 12, greater tool marks are found at a lowerspindle speed for all depths of cut under investigation. At a lower spindle speed of 5000 rpm(Fig. 11), the amount of pits and cracks on the cutting surfaces is found to increase withincreasing depth of cut whereas that is not clearly observed under a higher spindle speed of8000 rpm (Fig. 12).As discussed in Section 2.2, there are two possible mechanisms for which the SiC particles

are cut in ultra-precision machining of the composites. The SiC particles may either be pulledout or cut through. Under low spindle speed condition, there is a greater opportunity for whichthe SiC particles are pulled out as the depth of cut increases. This results in the increasedamount of pits and cracks being formed on the cutting surface and hence poor surface 7nish.Since the cutting surface is less plastically deformed and less stress concentration is formedaround the SiC particles under a higher spindle speed, more and more SiC particles are cutthrough instead of being pulled out during cutting. As a result, the e5ect of depth of cut on thesurface generation is less signi7cant at a high spindle speed.

4.4. Part D: Materials related phenomena and spectrum analysis

4.4.1. Presence of SiCp reinforcementFig. 13a and b show the surface roughness pro7les of bare aluminum alloy (6061) and

Al6061=15SiCp composite, respectively. It is interesting to note that the presence of SiC particles


Fig. 11. E5ect of depth of cut on the surface roughness pro7les generated under conditions in Set C3a: (a) idealpro7le with depth of cut of 3 �m; (b) measured pro7le with depth of cut of 1 �m; and (c) measured pro7le withdepth of cut of 3 �m.

Fig. 12. E5ect of depth of cut on the surface roughness pro7les generated under conditions in Set C3b: (a) idealpro7le with depth of cut of 3 �m; (b) measured pro7le with depth of cut of 1 �m; and (c) measured pro7le withdepth of cut of 3 �m.


Fig. 13. E5ect of SiCp reinforcement on the surface roughness as cutting under condition D1 on (a) aluminum alloy(6061) and (b) Al6061=15SiCp MMC, respectively.

Fig. 14. (a) Ideal surface roughness pro7le and (b) its spectral plot generated under conditions in Set D2a.

causes greater tool marks and surface waviness formed on the machined surfaces. These couldbe attributed to the cutting of the hard SiC particles. When the cutting tool engages with thehard SiC particles, it suddenly releases from that state as it passes into soft Al matrix. Thereis a sudden shift in stress levels on the cutting tool and the tool experiences a sudden “stressrelaxation” due to the high sti5ness of the cutting system. The alternating change of stresslevels results in a Kuctuation of the cutting forces and hence the vibration that is induced inthe cutting system. The induced vibration increases the surface waviness and surface roughnessof the machined surface.

4.4.2. Swelling of tool marksFig. 14a and b show the ideal and measured roughness pro7les generated under condition

D2a. Excluding the e5ect of surface waviness due to the relative vibration between the tool andthe workpiece, it is found that the tool marks formed on the ideal roughness pro7le are smallerthan that of the measured one. Comparing with the corresponding spectral plots as shown inFigs. 14b and 15b, the peaks of the feed components (�mf;0 and �mf;1) in the measured powerspectrum are found to be higher than that of the ideal one. These a5ord the evidences of thepresence of swelling e5ect in diamond turning of the MMC materials. Figs. 16a and b show theroughness pro7le and its spectral plot generated under conditions in Set D2b. Comparing Figs.15a and 16a, it is shown that the swelling of tool marks in the roughness pro7les is substantially


Fig. 15. (a) Measured surface roughness pro7le and (b) its spectral plot generated under conditions in Set D2a.

Fig. 16. (a) Measured surface roughness pro7le and (b) its spectral plot generated under conditions in Set D2b.

reduced as the spindle speed increases from 5000 to 8000 rpm under an almost identical toolfeed rate. The argument is further supported by the decreased power spectral density of thefeed components in Fig. 16b as compared with that of Fig. 15b.

As the cutting tool passes the work surface, tool marks are generated on the machinedsurface. The size of the tool marks is related to the tool geometry, cutting parameters andthe plastic deformation of the materials. It is discussed in Section 2.2 that Kow stress andplastic deformation behavior of a material are strain rate dependent. At high spindle speed, theassociated high deformation rate is believed to lead to a reduced amount of deformation as thematerial becomes more diOcult to deform. Hence, the swelling of tool marks is reduced and abetter surface 7nish can be achieved.

4.4.3. Surface integrityFig. 17 shows the SEM micrographs of the surface layer of the Al6061=SiCp composites

generated under di5erent cutting speeds but with about identical tool feed rate. Cracks andpits are observed on the machined surfaces. Comparing Figs. 17a and b, it is found that theamount of cracks and pits are signi7cantly reduced and a better surface integrity is obtainedwith increasing spindle speed. One possible cause is the reduced amount of plastic deformationdue to strain rate e5ect which results in a smaller amount of cracks and pits. These 7ndingsagree well with the theoretical analysis in Section 2.2 and the observations in Section 4.3.


Fig. 17. SEM micrographs of the machined surfaces of Al6061=15SiCp composites generated under conditions in(a) Set D3a and (b) Set D3b, respectively.

From a natural diamond tool, the cutting edge radius is in the order of about 0.01–0:5 �m[31] which was found to be in the same order as the average diameter of the SiC particles inthe Al6061=15SiCp MMC [32]. The e5ects of the size and the density of the hard particles, suchas the SiC particles, also play a signi7cant role for the composite material. Yan and Zhang [33]carried out single-point scratching of Al6061=SiC composite by di5erent ceramic particles andthey reported that the e5ect of reinforcement on the speci7c energy was correlated to the ratio ofvolume fraction to particle radius. However, the applicability the results on single point diamondturning will need further clari7cation. Generation of dislocations and cracks in SiC particles,


interface debonding between matrix and reinforcements would also be the possible causes forthe subsurface damages of the materials [34]. Further work will be conducted to these areas soas to get a better understanding of the surface generation mechanisms in diamond turning ofAl=SiC metal matrix composite.

5. Conclusions

A detailed investigation of the factors a5ecting the surface generation in ultra-precision ma-chining of Al6061=SiCp metal matrix composites has been conducted. The investigation is basedon di5erent analytical approaches which include parametric analysis, the study of cutting me-chanics, FEM analysis and power spectrum analysis.

It is found that the surface roughness of the cutting surface is a5ected by both the processfactors and material factors. The results of parametric analysis indicate that the surface rough-ness and surface integrity can be signi7cantly improved by using high spindle speed and 7netool feed rate. Depth of cut appears not to be a factor a5ecting the surface roughness exceptunder low spindle speed condition. There is also an optimum tool rate at which the arith-metic roughness is the minimum. With the use of the non-linear multiple regression analysismethod, an empirical surface roughness is derived for the prediction of arithmetic roughness.It is found that the equation makes reasonably good estimation of arithmetic roughness undervarious cutting conditions.

The swelling of tool marks and the formation of pits and cracks on the cutting surface arefound to be the major causes for the degraded surface quality. They are found to be due tothe strain rate e5ect and hence the plastic deformation in the matrix material during diamondturning. It is also found that there are two possible mechanisms for which the SiC particlesare cut in diamond turning. The SiC particles can be either cut through or pulled out duringdiamond turning. For the cut through mechanism, the surface 7nish is better since the SiCparticles are cut directly by the diamond tool and there is no pits and cracks left on the cuttingsurface after cutting. If the SiC particles are pulled out during diamond turning, cracks and pitsare formed on the cutting surface and this will cause poor surface 7nish.

With the use of FEM analysis, it is possible to conjecture the strain patterns. Moreover, thee5ect of materials swelling can also be characterized from the power spectrum of the surfaceroughness pro7le. These 7ndings provide an important means for the optimization the surfacequality in ultra-precision machining of the metal matrix composites.

Acknowledgements

The authors would like to express their sincere thanks to the Research Committee of TheHong Kong Polytechnic University for 7nancial support of the research work.

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