An Iterative Size Effect Model of Surface Generation in Finish Machining

Journal of

Manufacturing and Materials Processing

Article

An Iterative Size Effect Model of Surface Generation in Finish Machining Ian Brown 1,2 1 2

*

and Julius Schoop 1,2, *

Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA; iansbrowninc@gmail.com Institute for Sustainable Manufacturing, University of Kentucky, Lexington, KY 40506, USA Correspondence: julius.schoop@uky.edu; Tel.: +1-859-323-8308

Received: 9 June 2020; Accepted: 30 June 2020; Published: 2 July 2020

Abstract: In this work, a geometric model for surface generation of finish machining was developed in MATLAB, and subsequently verified by experimental surface roughness data gathered from turning tests in Ti-6Al4V. The present model predicts the behavior of surface roughness at multiple length scales, depending on feed, nose radius, tool edge radius, machine tool error, and material-dependent parameters—in particular, the minimum effective rake angle. Experimental tests were conducted on a commercial lathe with slightly modified conventional tooling to provide relevant results.

Additionally, the model-predicted roughness was compared against pedigreed surface roughness data from previous efforts that included materials 51CrV4 and AL 1075. Previously obscure machine tool error effects have been identified and can be modeled within the proposed framework. Preliminary findings of the model’s relevance to subsurface properties have also been presented. The proposed model has been shown to accurately predict roughness values for both long and short surface roughness evaluation lengths, which implies its utility not only as a surface roughness prediction tool, but as a basis for understanding three-dimensional surface generation in ductile-machining materials, and the properties derived therefrom.

Keywords: roughness; material side flow; minimum uncut chip thickness; finishing; multi-path

1. Introduction The roles of minimum uncut chip thickness and side flow on increasing surface roughness in finish turning have been acknowledged for some time. However, these two phenomena are not often considered to be related. Moll [1] was perhaps the first to record the discrepancy between actual and kinematically predicted surface roughness values at low feeds. Sokolowski [2] introduced the premise of a minimum uncut chip thickness (hmin ), defined formally as the chip thickness required to remove material from the workpiece. The hmin effect is now widely recognized as resulting from the finite sharpness of the cutting edge (cutting edge radius, re ), and Albrecht [3] was among the first to demonstrate the relevance of the cutting edge radius to process forces, as well as surface generation. Analytically determining the exact behavior of hmin has proven difficult, but it is generally understood to increase with edge radius [4]. Brammertz [5] applied the idea of hmin to turning, theorizing that, due to this phenomenon, there must be some part of the uncut chip thickness left on the surface of the workpiece, at the location where the chip thickness approaches zero on the secondary edge; Brammertz famously termed this area of uncut workpiece material the ”Spanzipfel”.

In many subsequent studies, this material is assumed to behave elastically (spring back), which implies significant surface roughness increase at low-feed rate, high-nose radius conditions (i.e., low kinematic roughness) [6,7]. The kinematic roughness equation was modified by Brammertz [5], as shown in the

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following equation, to account for the roughness increase caused by the Spanzipfel material left on the J. Manuf. Mater.

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(1) đ??ľđ?‘&#x;đ?‘Žđ?‘šđ?‘šđ?‘’đ?‘&#x;đ?‘Ąđ?‘§ đ?‘…đ?‘Ą /đ?‘…đ?‘§ =8rc + 2 ∙ (1 + f 2 ) 8đ?‘&#x;đ?‘?

2 đ?‘“ where f isf is feed, rc risc is tool nose where feed, tool nosecorner cornerradius, radius,and andhmin hminrepresents representsthe theminimum minimum uncut uncut chip chip thickness. thickness.

Note that the leftmost term in Equation (1) is the kinematic roughness equation, which predicts Note that the leftmost term in Equation (1) is the kinematic roughness equation, which predicts the theroughness roughness of a surface created by assuming perfect material removal, as shown in Figure 1a. of a surface created by assuming perfect material removal, as shown in Figure 1a. While While Equation (1) does predict the commonly observed discrepancy in actual and kinematically Equation (1) does predict the commonly observed discrepancy in actual and kinematically predicted predicted roughness at low-feed that actual roughness values surface surface roughness at low-feed rates, rates, studiesstudies show show that actual roughness values tendtend to to be be substantially substantiallysmaller smaller than those predicted by this equation at low kinematic roughness [8,9]. than those predicted by this equation at low kinematic roughness [8,9]. Indeed, Indeed, this discrepancy be traced to Brammertz’s underlying assumption that any material this discrepancy can becan traced back toback Brammertz’s underlying assumption that any material within within the Spanzipfel region spring back elastically, indicated Figure1b.

1b.InInreality, reality, it it is is clear the Spanzipfel region willwill spring back elastically, as as indicated inin Figure clear that that some plastic deformation will occur to the uncut material, which is subject to significant deformation some plastic deformation will occur to the uncut material, which is subject to significant deformation during movement underneath the cutting tool and/or flow.side Shawflow. and Cookson [10] Cookson hypothesized during movement underneath the cutting tool side and/or Shaw and [10] later that the hminlater material will plastically when it is pulled under the tool, andthe should hypothesized that the hminbematerial willdeformed be plastically deformed when it is pulled under tool, notand account fornot the account roughness at small feeds. However, an early (1961), almost forgotten should fordiscrepancy the roughness discrepancy at small feeds.

However, an early (1961), landmark work by landmark Lambert [11] ingeniously thatdemonstrates the material that the is left behindthat due almost forgotten work

by Lambertdemonstrates [11] ingeniously material is to left Sokolowski’s hmin effect is not confined toisBrammertz’s region.

Rather, Lambert found behind due to Sokolowski’s hmin effect not confinedSpanzipfel to Brammertz’s Spanzipfel region. Rather, theLambert materialfound underthe hmin is left behind edge. Therefore, the commonly material under hover min is the left entire behindengaged over thecutting entire engaged cutting edge.

Therefore, used generation assumptions used to arrive atused the to Brammertz-type models are notmodels valid for thesurface commonly used surface generation assumptions arrive at the Brammertz-type are workpiece responding in aresponding plastic manner (i.e., most metals and plastics). not validmaterials for workpiece materials in a plastic manner (i.e., most metals and plastics).

(a)

(b)

Figure 1. (a) Simulated surface from turning,created createdassuming assumingperfect perfectchip chipremoval; removal;(b) (b)Simulated Simulated Figure 1. (a) Simulated surface from turning, surface created by assuming material the Spanzipfel left on the surface and behaves surface created by assuming material in the in Spanzipfel region isregion left onisthe surface and behaves elastically. elastically.

As an alternative cause for increased roughness at small feeds, material side flow (MSF) has been investigated some extent.

Sata investigated MSF’s onmaterial roughness forflow different As anto alternative cause for[12] increased roughness at influence small feeds, side (MSF)materials has been investigated [12]machining investigated MSF’s materials. influence on roughness different and found it to to be some more extent. relevantSata in the of ductile A few studies for have noted materials and found it to be more in the machining of ductile materials.

A few studies have that observed MSF is responsible forrelevant surface roughness deterioration in finish turning [13–16].

Finish noted that observed MSF is responsible for surface roughness deterioration in finish turning [13–16]. turning conditions (high cutting speeds, low feeds and depth of cut) lead to high temperatures at the Finish turninginterface, conditions (high cutting low feeds andplasticization, depth of cut) lead to high tool/workpiece causing severespeeds, workpiece material which thentemperatures encourages at Typical the tool/workpiece interface, causing severe workpiece which then MSF. surface geometry indicative of MSF is shown belowmaterial in Figureplasticization, 2. encourages MSF. Typical surface geometry indicative of MSF is shown below in Figure 2.

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Figure 2. Simulated surface created bybyassuming Figure 2. Simulated surface created assumingsome someconstant constantamount amountofofmaterial materialisispushed pushedto tothe the side during each workpiece revolution. side during each workpiece revolution.

Kishawy and Elbestawi [17] investigated the MSF phenomenon and noted that roughness was Kishawy and Elbestawi [17] investigated the MSF phenomenon and noted that roughness was significantly influenced byby cutting significantly influenced cuttingtool tooledge edgepreparation, preparation,which whichininturn turndirectly directlyinfluences influences the the value value of of hmin .

However, Kishawy et al. did not include a cutting edge radius parameter when developing hmin. However, Kishawy et al. did not include a cutting edge radius parameter when developing thethe FEA model presented inin [16].

FEA model presented [16].Liu Liuand andMelkote.

Melkote.[18] [18]developed developedaamodel modelfor forsurface surface roughness roughness prediction that accounts for side flow in diamond turned surfaces, but considered prediction that accounts for side flow in diamond turned surfaces, but considerededge edgeradius radius to to be be negligible (a reasonable assumption for single crystal diamond tools at practical feeds).

El-Wardany negligible (a reasonable assumption for single crystal diamond tools at practical feeds). El-Wardany and Elbestawi [14] thoroughly investigated and Elbestawi [14] thoroughly investigatedthe theoccurrence occurrenceofofMSF MSFand andnoted notedthat thatititwas wasinfluenced influenced byby tool nose radius, feed, tool wear, and hmin , mentioning , tool nose radius, feed, tool wear, and hmin , mentioningthat thatedge edgeradius radiushas hasaadirect directeffect effecton onhhmin min, and therefore MSF. Many similar studies look to tool edge surface roughness and tool wear to account and therefore MSF. Many similar studies look to tool edge surface roughness and tool wear to account forfor side flow.

While these parameters are certainly relevant, little work sought to define evident side flow.

While these parameters are certainly relevant, little has work has sought tothe define the relationship between roughness due to side flow, in light presented in this paper min . The evident relationship between roughness due to side flow,ofinhlight of hwork min. The work presented in this seeks to establish this relationship explicitly. paper seeks to establish this relationship explicitly.

Recent contributions in the study of machined roughness have focused on this relationship.

Recent contributions in the study of machined roughness havesome focused some on this Ozel et al. [19] Ozel showed of the edge is relevant parameter parameter in the hard relationship. et al.the [19]condition showed the condition of athe edge isroughness a relevant roughness in turning of H13 steel. and Karpat [20]Karpat subsequently demonstrated the effectiveness of an ANN the hard turning of Ozel H13 steel.

Ozel and [20] subsequently demonstrated the effectiveness of model for predicting a single dataset.

This dataset. model considered edge geometry on an ANN model forroughness predictingwithin roughness within a single This modeltool considered tool edge a limited basis. andbasis.

Melkote [21] studied edge geometries in hard turning of steel and geometry on Thiele a limited Thiele and Melkote [21] studied edge geometries in AISI hard 52100 turning of AISI concluded that larger tool edge increased roughness by ploughing phenomena.

Zhao et al. [22] 52100 steel and concluded thatradii larger tool edge radii increased roughness by ploughing phenomena.

Zhao et al.

[22] presented a limitedon investigation ontool the effect tool edge radius onroughness surface roughness presented a limited investigation the effect of edgeof radius on surface in AISI in AISI 52100 steel.et Childs et al. have [8,23] experimentally have experimentally investigated effect cuttingedge edgeradii radii 52100 steel.

Childs al. [8,23] investigated the the effect of of cutting surfaceroughness roughnessininfinish finish turning turning in multiple that machine tooltool error can onon surface multiplematerials, materials,and andfound found that machine error on conventional conventional machines. machines. Geometric Geometric canbebea amore moredominating dominatingfactor factor of of finish finish turning roughness on modeling surface roughness that accountsfor fortool tooledge edgegeometry geometrywas wasperformed performedin in[24], [24],but butlacks lacks modeling of of surface roughness that accounts significant validation and makes quite different assumptions than the model presented in this work. significant validation and makes quite different assumptions than the model presented in Schultheiss [25] presented analytical roughnessmodel modelthat thattakes takesinto intoaccount accounthmin hmin,, but but their their Schultheiss et et al.al.

[25] presented anan analytical roughness definition and determinationofofhmin hminrelies relieson on questionable questionable assumptions. definition and determination assumptions.Kountanya Kountanya[26] [26]developed developeda three dimensional model that accounted for tool edge radius and roughness effects, and showed a three dimensional model that accounted for tool edge radius and roughness effects, and showed similar trends as previous two dimensional efforts.

Knuefermann [9] developed a geometric model similar trends as previous two dimensional efforts. Knuefermann [9] developed a geometric model to to predict surface roughness based tool geometry, edgeand defects and asynchronous error, yet predict surface roughness based on tool on geometry, edge defects asynchronous error, yet ultimately ultimately does side not consider sidedue flow dueradius. to toolFurthermore, edge radius. many Furthermore, many recent does not consider flow effects to effects tool edge recent optimization optimization studies of finish turning do not consider the effect of tool edge radius [27–29].

Hence, studies of finish turning do not consider the effect of tool edge radius [27–29]. Hence, the relationship relationship of roughness to of side light of edge radius) has to been of the roughness increase due to sideincrease flow (indue light toolflow edge(inradius) hastool been demonstrated be demonstrated to be relevant, yet is not commonly considered in recent works, and requires clarifying. relevant, yet is not commonly considered in recent works, and requires clarifying.

Roughness models thatdodoconsider considerthe theeffect effectofofh hminare areoften oftenconcerned concernedwith withmicrocutting microcutting or or Roughness models that min diamond turning, whereedge edgechamfers/radii chamfers/radiiare aresososmall small(on (onthe thescale scaleofofnanometers, nanometers, rather rather than than diamond turning, where micrometers) they may nearly be neglected at reasonable feeds, as stated in [15]. Zong et al. [30] micrometers) they may nearly be neglected at reasonable feeds, as stated in [15]. Zong et al. [30] developed a model to predict roughness in diamond turning and gave consideration to MSF. Chen developed a model to predict roughness in diamond turning and gave consideration to MSF. Chen and and Zhao [31] established a roughness prediction model that demonstrated an increase in roughness

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Zhao [31] established a roughness prediction model that demonstrated an increase in roughness due to side flow. He et al. [32] has developed a model for diamond turning that incorporates plastic side flow based on a minimum chip thickness value. However, the incorporation of side flow is rather simple and relies upon multiple fitting of constants for calibration. In diamond turning, edge roughness is often a more relevant parameter than the minute value of hmin found on diamond tools, yet is not highly relevant in the comparatively duller tooling of precision and conventional machining.

Additionally, these previous works have been primarily concerned with mathematically investigating surface roughness phenomena, and generally do not approach the understanding of the geometry of surface generation mechanics.

Little published work exists on the influence of tool edge radius on roughness due to process damping in turning. Alternatively, many studies have studied the evident link between observed vibration and surface roughness [9,33,34]. However, predicting this small-scale vibrational error in industrial applications is not trivial. Chatter prediction has been studied in depth as noted by Altintas and Weck [35]. However, chatter is deemed outside the scope of this work, as it is generally not acceptable in finish machining. Recently, observations were made by Biermann and Baschin [36] in micromilling surfaces regarding improved roughness due to process damping related to tool edge radius. Yusoff et al. [37] remarked that the role of edge geometry was significant in the damping of ‘macroscopic’ milling. Budak and Tunc. [38] present an excellent approach to modeling process damping in turning. However, the effort is still primarily concerned with chatter. Generally, previous efforts have not considered tool edge geometry’s effects on small positional errors of the tool that lead to surface roughness increase in very fine finishing.

This article outlines an iterative geometric model which is based on novel assumptions, intended to more accurately capture surface generation in finish machining (using finish turning as a representative process to demonstrate the methodology). This effort will be concentrated on examining the surface roughness prediction capabilities of a new iterative modeling approach, which is an indication of valid surface generation assumptions. It is worth mentioning that the same assumptions that give rise to surface finish also have significant implications for subsurface characteristics as well. While such surface integrity characteristics are outside the scope of the current manuscript, subsequent work will illustrate the intimate connection between the present (geometric) work, and surface integrity (thermomechanical material property) evolution.

2. Materials and Methods The following model was developed on a Dell Precision 3630 Desktop, with an Intel i9-9900 CPU. The model was developed in MATLAB, version 2019b. No toolboxes or third-party functions were used in any part of development.

The experimental work to calibrate the proposed model was conducted by means of face turning trials on a HAAS TL2 CNC lathe, as shown in Figure 3. Modified Kennametal TPGN (triangle) geometries of the uncoated, fine-grained carbide grade K-68 were used. The workpiece material was a cylindrical bar of Ti-6Al4V (60 mm diameter, annealed condition, 35 HRC).

A range of feeds and nose radii, outlined in Table 1 below, was selected to provide various combinations of uncut chip geometry and kinematic roughness. Beyond this table, differing conditions of nose radius and feed will be merged and often referred to as one factor: predicted kinematic roughness Rt /Rz and Ra , the equations for which are shown below. All other variable parameters were held constant during these trials. Constant parameters of some consequence include cutting speed (vc ), held at 288 m/min, depth of cut (ap ), held at 0.25 mm, and coolant/lubrication, which was not present.

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(a)

(b)

Figure3.3.(a) (a)HAAS HAASTL2 TL2 CNC CNC lathe lathe used used to perform cutting Figure cutting tests; tests; (b) (b) Kennametal KennametalTPGN TPGNK-68 K-68tool toolofof 0.8 mm mm tool being touched off the Ti-6Al4V workpiece. rcrc== 0.8 workpiece.

đ?‘“2 đ?‘…đ?‘Ą /đ?‘…đ?‘§ = f 2 đ?‘?

Rt /Rz = 8đ?‘&#x; 2 đ?‘“ 8r c đ?‘…đ?‘Ž = 32đ?‘&#x; f2đ?‘?

Ra = 32rc

(2) (2) (3)

(3)

Table 1. Experimental parameters.

Feed f 0.1 mm 0.1 mm 0.1 mm 0.2 mm 0.2 mm

Nose Radius rc Theoretical/Kinematic Roughness Rt Edge Radius re Table 1. Experimental parameters.

3.2 mm 0.39 Âľ m 12.5 Âľ m Feed f 0.8Nose Theoretical/Kinematic Edge Radius20reÂľ m mm Radius rc 1.56 Âľ mRoughness Rt 3.13Âľm Âľm 0.1 mm 0.4 mm 3.2 mm 0.39 12.5 Âľm 30 Âľ m 0.1 mm 0.8 mm 0.8 mm 1.56 20 Âľm 6.25Âľm Âľm 0.1 mm 0.4 mm 0.4 mm 3.13 30 Âľm 12.5Âľm Âľm 0.2 mm 0.2 mm

0.8 mm 0.4 mm

6.25 Âľm 12.5 Âľm

The preparation of experimental cutting tool edges was accomplished by a novel honing method developed by the authors that createscutting tool edge geometry by accuracy of less The preparation of experimental tool radii edgeswith wasfinal accomplished a novelvariance honing method than 20%. by This upon the of aradii HAAS milling machine equipped with a developed themethod authorsrelies that creates tooluse edge withVF-2 finalCNC geometry accuracy variance of less than diamond paste-impregnated buffing wheel.

An example of the tool edge radii generated by this 20%. This method relies upon the use of a HAAS VF-2 CNC milling machine equipped with a diamond methodology is shown in Figure The tools honed this method veryby low roughness.is paste-impregnated buffing wheel.4.An example of theby tool edge radiiexhibit generated thisedge methodology to each test condition, the workpiece face was prepared for the next condition by shownPrior in Figure 4. The tools honed by this method exhibit very low edge roughness. chamfering the sharp edge and cleaned up with an unworn sharp tool in order to standardize initial Prior to each test condition, the workpiece face was prepared for the next condition by chamfering conditions. After each condition, the machined surface was parted from the main bar for subsequent the sharp edge and cleaned up with an unworn sharp tool in order to standardize initial conditions. analysis. In total, 15 surface specimens were generated. Each condition and associated tool edge was After each condition, the machined surface was parted from the main bar for subsequent analysis. utilized for the production of a single sample. Each edge was subsequently checked for tool wear to In total, 15 surface specimens were generated. Each condition and associated tool edge was utilized for ensure the surface was not affected by wear artifacts, as shown in Figure 4d. The subsequent surface the production of a single sample. Each edge was subsequently checked for tool wear to ensure the roughness measurements were conducted on a Zygo NewView 7300 scanning white light surface was not affected by wear artifacts, as shown in Figure 4d. The subsequent surface roughness interferometer with a spatial resolution of approximately 2 nm (manufactured by AMETEK Inc., measurements were conducted on a Zygo NewView 7300 scanning white light interferometer with Berwyn, PA, USA). Three scans were completed on each sample at different locations to ensure a spatial resolution of approximately 2 nm (manufactured by AMETEK Inc., Berwyn, PA, USA). significant values.

Three scans were completed on each sample at different locations to ensure significant values.

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(a)

(b)

(c)

(d)

Figure4.

4. (a) Rake edge of of a Kennametal TPGN K-68 tooltool of rcof = 3.2 re = Figure Rake face faceview viewofofthe themodified modified edge a Kennametal TPGN K-68 rc =mm, 3.2 mm, µ m; (b); tool cloudmap produced via scanning white light interferometer; (c) subsequent analysis r30 = 30 µm; (b); tool cloudmap produced via scanning white light interferometer; (c) subsequent e of tool cloudmap via MATLAB; (d) used exhibiting tool/workpiece contact discoloration and analysis of tool cloudmap via MATLAB; (d)tool used tool exhibiting tool/workpiece contact discoloration limited adhesion, but no tool (edge or nose) wear. and limited adhesion, but no tool (edge or nose) wear.

3.3. Results Results and and Discussion Discussion 3.1.

3.1. Model Model Assumptions Assumptions In more appropriate assumptions must be be made.

One key Inorder ordertotodevelop developa amore moreaccurate accuratemodel, model, more appropriate assumptions must made.

One assumption relates to the behavior of material along the cutting edge under h , i.e., the Spanzipfel key assumption relates to the behavior of material along the cutting edgemin under hmin, i.e., the region.

Indeed, much of themuch current is based on is Brammertz’s Spanzipfel assumption, Spanzipfel region.

Indeed, of understanding the current understanding based on Brammertz’s Spanzipfel where material of chip thickness below hmin flows underneath tool, whilethe material of chip thickness assumption, where material of chip thickness below hmin flowsthe underneath tool, while material of above h is evacuated entirely from the workpiece.

This represents an on/off transition between min chip thickness above hmin is evacuated entirely from the workpiece. This represents an on/off ploughing and cutting, and inand turncutting, impliesand thein creation of a perfect copy of tool profile onthe the transition between ploughing turn implies the creation of the a perfect copy of workpiece alongfor theall tool edgealong where material is above assumptions give tool profilefor onall thepoints workpiece points the tool edge where hmaterial is above hmin. These min . These rise to the pointed Spanzipfel regionSpanzipfel of materialregion (as can seen in is not generally assumptions give rise to the pointed of be material (asFigure can be1b), seenwhich in Figure 1b), which observed on real observed machinedon surfaces.

In ordersurfaces. to realizeInmore modeling of surface roughness, is not generally real machined orderaccurate to realize more accurate modeling of itsurface is imperative to (at qualitatively) match the model mechanics to the reality of the reality cutting roughness, it isleast imperative to (at least qualitatively) match the model mechanics to the process.

This includes the fact that some material doesmaterial indeeddoes flowindeed under the with back of the cutting process. This includes the fact that some flowtool, under thespring tool, with subsequently alongoccurring the flank/clearance of the tool, asface wellof as the occurrence of side flow spring back occurring subsequently along theface flank/clearance tool, as well as the occurrence of side flow of some magnitude—both having been qualitatively of some magnitude—both phenomena having beenphenomena qualitatively established

by Lambertestablished [11].

by Lambert [11].Dow [39] have calculated the spring back of machined material to be a linear function Arcona and and Dowfor [39] have material, calculatedwhich the spring of machined to be a linearof of theArcona tool edge radius a given followsback logically from the material hmin and conservation functionconsiderations. of the tool edge radius for a given material, follows hmin and volume Work to quantify this spring back which has been done. logically However,from morethe experimental conservation of volume considerations.

Work to quantify this spring back has been done.

However, understanding of the effect of material properties and tool parameters on the size of this spring back experimental understanding of of[4,40,41]. material properties and it tool parameters on the size ismore required for full understanding ofthe its effect nature At this point, seems clear that material of this back is required for full understanding of itsedge, nature [4,40,41].

At this it seems less thanspring the hmin flows and is deformed under the cutting to be recovered afterpoint, the tool passes clear that material less than the hmin flows and is deformed under the cutting edge, to be recovered after the tool passes over it. This recovery is often assumed to be largely due to the elastic properties

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of the bulkrecovery material.isHowever, much to of be thelargely material near theelastic surfaceproperties is plastically deformed due to over it. This often assumed due to the of the bulk material. ploughing andofshear deformation, Oxley and Challen’s [42] work on However, much the material near as theillustrated surface is by plastically deformed due to foundational ploughing and shear the nature of polishing and wear mechanisms.

Nevertheless, the work presented here shall assume deformation, as illustrated by Oxley and Challen’s [42] foundational work on the nature of polishing that fullmechanisms. spring back will occur for any of the tool edge where material in this region is will well and wear Nevertheless, the section work presented here shall assume that full spring back supported either side to prevent side material flow, i.e.,inplane strain may be supported assumed. from either side occur for anyfrom section of the tool edge where this region is well Material at the two extreme ends of the uncut chip region, i.e., near the free surfaces of the cut to prevent side flow, i.e., plane strain may be assumed. onMaterial the primary and the secondary cutting edges, is not under plane strain constraint, and at the two extreme ends of the uncut chip region, i.e., near the free surfaces of the cutwill on therefore be susceptible to being “squeezed” out sideways from in between the flank and workpiece, the primary and the secondary cutting edges, is not under plane strain constraint, and will therefore be as mentioned in Pekelharing Gieszen’sfrom workin[13].

As a the result, the Spanzipfel region, which is susceptible to being “squeezed” and out sideways between flank and workpiece, as mentioned located at the extreme (secondary) edge of the uncut chip region, does not form.

Rather, in Pekelharing and Gieszen’s work [13]. As a result, the Spanzipfel region, which is located atsome the material in this region is displaced sideways by the advancing tool edge, due to the high stresses and extreme (secondary) edge of the uncut chip region, does not form. Rather, some material in this region lack of plane stress. In the presented model, we assume that the amount of material which is displaced is displaced sideways by the advancing tool edge, due to the high stresses and lack of plane stress. as side flow is directly related to the geometric area of the Spanzipfel.

In the presented model, we assume that the amount of material which is displaced as side flow is These assumptions lead to a side flow region which is dependent upon feed, nose radius, and directly related to the geometric area of the Spanzipfel. edge radius, as well as a raised part surface that is established by the elastic spring back of hmin.

These assumptions lead to a side flow region which is dependent upon feed, nose radius, Notably, side flow occurs due to hmin in a similar manner as the Brammertz effect is assumed to occur. and edge radius, as well as a raised part surface that is established by the elastic spring back of hmin .

However, the occurrence and transition between flow underneath the tool (not technically the Notably, side flow occurs due to hmin in a similar manner as the Brammertz effect is assumed to Brammertz effect, but ploughing/severe plastic deformation akin to the mechanics of polishing and occur. However, the occurrence and transition between flow underneath the tool (not technically the burnishing) and side flow is affected by the ‘boundary conditions’ of the deformation (i.e., presence Brammertz effect, but ploughing/severe plastic deformation akin to the mechanics of polishing and or absence of rigid material constraints due to adjacent material in the uncut chip), as stated burnishing) and side flow is affected by the ‘boundary conditions’ of the deformation (i.e., presence or previously. absence of rigid material constraints due to adjacent material in the uncut chip), as stated previously.

3.2. Model Development 3.2. Model Development The proposed iterative geometric model initializes by assuming some starting workpiece surface The proposed iterative geometric model initializes by assuming some starting workpiece surface geometry after a single workpiece revolution, as shown below in Figure 5a. Any tool geometry and geometry after a single workpiece revolution, as shown below in Figure 5a. Any tool geometry and feed may be defined for this model. However, to clearly represent the process in the following figures, feed may be defined for this model. However, to clearly represent the process in the following figures, the following parameters have been selected: rc = 0.4 mm, hmin = 6.5 µ m, and f = 0.1 mm. the following parameters have been selected: rc = 0.4 mm, hmin = 6.5 µm, and f = 0.1 mm.

(a)

(b)

Figure Initial model workpiecegeometry; geometry;(b) (b)tool toolgeometry geometryimposed imposedon onthe thepreviously previouslydefined defined Figure 5. 5. (a)(a) Initial model workpiece workpiece geometry. workpiece geometry.

The curved region in middle the middle of Figure 5aideal is the tool projection copied onto the The curved region in the of Figure 5a is the toolideal projection copied onto the workpiece workpiece offset to by hmin for the assumption thatless thethan material less surface, offsetsurface, to the interior bythe hmininterior to account forto theaccount assumption that the material hmin will than hon min the willother recover side of thebetool.

It should notedsection that theincurved section in this recover sideon ofthe theother tool. It should noted that thebe curved this and subsequent and subsequent figures represented a circleyet in appears the model, be elliptical herescaling due to figures is represented as is a circle in the as model, to yet be appears ellipticaltohere due to the the scaling differential of the x and y axes.

The lower linear region is somewhat arbitrary, but is differential of the x and y axes. The lower linear region is somewhat arbitrary, but it is includeditas as an initial condition necessary simplify theof computation of future anincluded initial condition necessary to simplify thetocomputation future iterations.

Theiterations. height of The this height linear of this linear region is again, arbitrary, but set equal to the value of kinematically predicted roughness region is again, arbitrary, but set equal to the value of kinematically predicted roughness Rt /Rz in Rt/Rz in order to approximate the geometry of any previously generated surface. The upper linear

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Process. 2020, x FOR PEER of REVIEW 8 of 18is order to Mater. approximate the4, geometry any previously generated surface. The upper linear region the existing material surface, to be machined. This will move vertically relative to the other geometry region is the material depending onexisting the depth of cut.surface, to be machined. This will move vertically relative to the other geometry depending on the depth has of cut.

Once initial surface geometry been created, the tool geometry is imposed on the workpiece Once initial surface geometry been created, the in tool geometry is imposed on theisworkpiece geometry for the upcoming tool pathhas segment, as shown Figure 5b. The tool geometry composed geometry for the upcoming tool path segment, as shown in Figure 5b. The tool geometry is composed of two profiles, shown here as solid black and dashed black. The exterior solid profile represents the of two profiles, shown here as solid black and dashed black. The exterior solid profile represents the true tool profile, while the interior dashed profile represents the tool profile shape, offset by hmin . true tool profile, while the interior dashed profile represents the tool profile shape, offset by hmin. A A profile has been added to this image to show where the uncut chip thickness drops below hmin , profile has been added to this image to show where the uncut chip thickness drops below hmin, creating the Spanzipfel geometry discussed previously. The plane stress region which occurs at the creating the Spanzipfel geometry discussed previously. The plane stress region which occurs at the opposing end of the uncut chip (on the primary edge) is not typically considered relevant to the final opposing end of the uncut chip (on the primary edge) is not typically considered relevant to the final surface geometry, and therefore is not considered in this model. surface geometry, and therefore is not considered in this model.

In order to model the surface profile created by this new tool path segment, this Spanzipfel In order to model the surface profile created by this new tool path segment, this Spanzipfel region is then transposed into the open space between the workpiece and tool, as shown in Figure 6. region is then transposed into the open space between the workpiece and tool, as shown in Figure 6.

A transition surface profile is computed that begins at the peak of this transposed MSF area and A transition surface profile is computed that begins at the peak of this transposed MSF area and gradually approaches the dashed hmin profile. This profile is formulated so that volume is conserved in gradually approaches the dashed hmin profile. This profile is formulated so that volume is conserved this region, accounting for the displaced side flow volume. Once this profile reaches hmin , the newly in this region, accounting for the displaced side flow volume. Once this profile reaches hmin, the newly generated profile (dashed black) over the remainder of the tool edge, generatedsurface surfacewill willbe befound foundat atthe the hhmin min profile (dashed black) over the remainder of the tool edge, not the full tool profile (solid black). not the full tool profile (solid black).

(a)

(b)

Figure6.6.(a) (a)Tool Toolgeometry geometry imposed imposed on on new new surface Figure surface profile, profile, altered altered by bythe thecurrent currenttool toolpath pathsegment; segment; (b)magnified magnified examples geometry thatthat clarify the side and surface (b) examples ofofthe themodel model geometry clarify the flow side transition flow transition and profile surface construction. profile construction.

Theseprofiles profilesare arethen then consolidated consolidated to form the new surface These surface profile, profile, and and the the tool toolgeometry geometryisis translated by the feed to begin this process for the next path, shown in Figure 7a.

This iterative translated by the feed to begin this process for in Figure 7a. This iterativeprocess process repeateduntil untilthe thealtered altered surface surface profile profile reaches reaches an isisrepeated an adequate adequate length lengthand andequilibrium equilibriumisisestablished, established, shownbelow belowin inFigure Figure7b.

7b. This This figure figure also also shows shows the asasshown the inclusion inclusion of of the the assumption assumptionthat thatmaterial material spring back will alter the surface profiles generated by the model, as can be seen in the spring back will alter the surface profiles generated by the model, as can be seen in theworkpiece workpiece model’sfinal finalsurface surfacebeing beingsubstantially substantially higher higher than than the the tool tool nose nose minima minima at model’s at all all points. points.

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(b) (b)

Figure 7.

Tool geometry the new path position imposed on the surface profile generated by the Figure 7. (a) (a) Tool geometry in the new path position imposed on thesurface surfaceprofile profilegenerated generatedby bythe the Figure 7. (a) Tool geometry inin the new path position imposed on the previous path; surface profile created iterative model, shown equilibrium. previous path; (b) surface profile created by the iterative model, shown at equilibrium. previous path; (b)(b) surface profile created byby thethe iterative model, shown atat equilibrium.

ItIt was found, through comparison experimental data, that the surface profiles overpredicted It was found, through comparison toto experimental was found, through comparison to experimentaldata, data,that thatthe thesurface surfaceprofiles profilesoverpredicted overpredicted roughness.

This follows logically from observation of machined studies as noted in previous roughness.

This follows logically from observation roughness.

This follows logically from observationofofmachined machinedstudies studiesasasnoted notedin inprevious previous efforts; efforts; roughness peaks generally round, not sharp, portrayed Figure 7b.

To address this, profiles roughness peaks areare generally round, not sharp, asas portrayed roughness peaks are generally round, not sharp, as portrayedinin inFigure Figure7b.

7b.To Toaddress addressthis, this,profiles profiles were subsequently filtered with aa Gaussian filter—the window size which was adjusted according were subsequently filtered with Gaussian filter—the window sizeofof ofwhich whichwas wasadjusted adjustedaccording according were subsequently filtered with a Gaussian filter—the window size to the square root of the feed at each condition.

The result of this Gaussian filtering on the current to the square root feed each condition.The Theresult resultofofthis thisGaussian Gaussianfiltering filteringon onthe thecurrent current to the square root of of thethe feed at at each condition. profile is 88 below. profile is shown shown in Figure Figure below. profile is shown in in Figure 8 below.

Figure 8. profile created iterative model, shown equilibrium after Gaussian Figure 8. Surface profile created byby thethe iterative model, shown Figure 8.Surface Surface profile created by the iterative model, shownatat atequilibrium equilibriumafter afterGaussian Gaussianfiltering. filtering.

The model thenthen calculates roughness valuesvalues Rt /Rz and Rzaz for different conditions The model calculates roughness RRtt/R and RRaaprofiles for profiles under different The model then calculates roughness values /R andthe for the theunder profiles under different of conditions nose radius, edge radius and feed.

The modeled roughness values are then plotted against predicted conditions of of nose nose radius, radius, edge edge radius radius and and feed. feed. The The modeled modeled roughness roughness values values are are then then plotted plotted kinematic to show the relationship between edge radius and kinematically predicted against predicted roughness to relationship between tool and against roughness predicted kinematic kinematic roughness to show show the thetool relationship between tool edge edge radius radius and surface roughness on the model predicted values of R and R /R . kinematically predicted surface roughness on the model predicted values of R a and R t /R z . kinematically predicted surface roughness on the model predicted values of Ra and Rt/Rz. a t z 3.3.3.3.

Model Validation Model Validation 3.3.

Model Validation While two of of the parameters utilized inin this model are easily determined, hmin While two parameters utilized this model are easily determined, hhmin is dependent upon While two of the the parameters utilized in this model are easily determined, minis isdependent dependentupon upon thermomechanical variables and difficult to predict for a given condition.

Empirical measurement thermomechanical of thermomechanical variables variables and and difficult difficult to to predict predict for for aa given given condition. condition. Empirical Empirical measurement measurementof of hmin is is most directly achieved by measuring hhmin most directly achieved by measuring the workpiece spring back on the flank face under plane min is most directly achieved by measuringthe theworkpiece workpiecespring springback backon onthe theflank flankface faceunder underplane plane strain conditions, i.e., orthogonal turning oror shaping cuts. strain conditions, i.e., orthogonal turning shaping cuts.

Ongoing efforts of in situ characterization strain conditions, i.e., orthogonal turning or shaping cuts.Ongoing Ongoingefforts effortsof ofin insitu situcharacterization characterization areare carried out by the authors to further improve the accuracy of the h characterization carried out by the authors to further improve the accuracy of the h min characterization for different are carried out by the authors to further improve the accuracy of themin hmin characterizationfor fordifferent different workpiece materials.

From such observations, workpiece materials.

From such observations, there seems exist minimum effective rake angle workpiece materials.

From such observations,there thereseems seemstoto toexist existaaaminimum minimumeffective effectiverake rakeangle angle (y )) that remains constant edge radius varied for given machining condition.

This phenomena (yeff remains constant asas edge radius isis varied for (y)effeffthat that remains constant as edge radius is varied fora aagiven givenmachining machiningcondition. condition.This Thisphenomena phenomena been previously investigated recent literature [43], and has often been termed as ratio of hashas been previously investigated inin recent has been previously investigated in recentliterature literature[43], [43],and andhas hasoften oftenbeen beentermed termedas asaaaratio ratioof of hhmin min/r /ree,, rather rather than thanyyeffeff [44,45].

[44,45]. From Fromthe the authors’ authors’ investigations, investigations, as as well well as as inverse inverse determination determinationof of hhmin min

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hmin /re , rather than yeff [44,45]. From the authors’ investigations, as well as inverse determination from pedigreed surface roughness data, e.g., the Knuefermann and Childs data, yeff values and of h from pedigreed surface roughness e.g., the Knuefermann Childs values min corresponding hmin/re values, shown in Table data, 2, were determined.

It should and be noted thatdata, theseyeff values andnot corresponding hmin /rconstants, Table 2, were determined.

It should be noted that these e values, shown are purely material as theyinlargely vary with cutting interface temperature, which values are not purely material constants, as they largely vary with cutting interface temperature, which depends on a few variables—of which, material properties and cutting speed are typically deemed depends on a few material propertiesAland cutting speed typically deemed most relevant.

The variables—of cutting speedswhich, used with the materials 1075, 51CrV4, andare Ti-6Al4V are 200, most relevant.

The cutting speeds used with the materials Al 1075, 51CrV4, and Ti-6Al4V are 200, 200, 200, and 288 m/min, respectively. and 288 m/min, respectively.

Table 2. Material properties, and empirically determined material-specific yeff and hmin/re values for the Table 2. workpieces Material properties, relevant studied. and empirically determined material-specific yeff and hmin /re values for the relevant workpieces studied.

hmin/re Young’s Thermal Material Ultimate Tensile Strength Material yeffyeffhmin /re (+/−0.05) Conductivity (+/−0.05) Ultimate Tensile Strength Young’s Modulus ModulusThermal Conductivity ◦ AL1075 1075 −71 AL −71° 51CrV4 −68◦ 51CrV4 −68° Ti-6Al4V −67◦ Ti-6Al4V −67°

0.06 0.06 0.07 0.07 0.08

0.08

90 MPa90 MPa 1950 MPa 1950 MPa 1100 MPa

1100 MPa

69 GPa 69 GPa 190 GPa 190 GPa 115 GPa

115 GPa

236236 W/mK W/mK 46.6 W/mK 46.6 W/mK 7.2 W/mK

7.2 W/mK

The measured measuredroughness roughnessvalues valuesfrom fromcutting cuttingtrials trialsdescribed described Section 2 are shown below The ininSection 2 are shown below in in Figure 9.

9. The Themodel modelwas wasfound foundtotobe beiningood goodagreement agreementwith withthe theexperimental experimental results given Figure results forfor thethe given range of tool edge radii, with initial deviation from kinematic roughness occurring between 0.8 and range of tool edge radii, with initial deviation from kinematic roughness occurring between 0.8 and 2 µm Rz. Surface finish in all samples was free of major defects when observed optically at up 2 µ m Rz. Surface finish in all samples was free of major defects when observed optically at up to 50× to 50× magnification.

As often has often reported by other efforts, larger edge radii produced a higher magnification.

As has beenbeen reported by other efforts, larger tooltool edge radii produced a higher surface roughness roughness at at low low feeds feedsthan thansmall smalltool tooledge edgeradii, radii,while whilegenerating generatingessentially essentially same surface thethe same roughness when whenthe themeasured measuredvalues valuesapproached approachedthe thepredicted predictedkinematic kinematic values. may noted roughness values.

It It may bebe noted that the themodel modelslightly slightlyunderpredicts underpredictsroughness roughnessvalues valuesacross across the board, especially feed increases. that the board, especially as as feed increases.

This is is most most likely likely due dueto toprocess processinstability instabilityfound foundatathigher higherchip chipthicknesses. thicknesses.

This

Figure9.9.Roughness Roughness(R (Rz)zmodel ) model(lines) (lines) compared data gathered through experimental investigation Figure compared toto data gathered through experimental investigation in Ti-6Al4V. Ti-6Al4V. in

As mentioned mentionedabove, above,aakey keyfinding findingofofthe theproposed proposedmodel modelisisitsitsdeviation deviation from predicted As from thethe predicted kinematic roughness at a point very near to where actual (measured) roughness values deviate, kinematic roughness at a point very near to where actual (measured) roughness values deviate, as as shown in Figure 9.

However, when compared to the data in Figure 10, the as-developed model shown in Figure 9. However, when compared to the data in Figure 10, the as-developed model (dashed line) line) begins begins to to predict predictvalues valuesbelow belowwhat whatisismeasured, measured,atatleast leastwhen whenproper proper ISO surface (dashed ISO surface roughness measurement standards are maintained (i.e., using long evaluation lengths).

The causes roughness measurement using long evaluation lengths). causes of thisthis discrepancy are twofold: edgeedge roughness and machine tool error. large deviation of discrepancy are twofold: roughness and machine tool The error.

Theroughness large roughness found byfound the data from longer lengths in Figure 10 can to machine tool deviation by the data from evaluation longer evaluation lengths in Figure 10 be canattributed be attributed to machine errorerror thatthat plays a significant role roughness.While Whilethe the as-developed, tool plays a significant roleatatlow lowpredicted predicted kinematic kinematic roughness. as-developed, unadjusted surface generation model developed here is still valid for short roughness evaluation

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unadjusted surface generation model developed here is still valid for short roughness evaluation lengths (that eliminate the effect of machine tool error/waviness) at these feed rates, the additional lengths (that eliminate the effect of machine tool error/waviness) at these feed rates, the additional (machine/dynamic) error introduces waviness among other artifacts to the standard measurement of (machine/dynamic) error introduces waviness among other artifacts to the standard measurement of RR t /R z and Ra . This discrepancy is relevant, but not resolved without considering machine dynamics. t/Rz and Ra. This discrepancy is relevant, but not resolved without considering machine dynamics.

Figure10.

10.Roughness Roughness(R (Rt )t) model model (lines) (lines) compared to data adapted Figure adapted from from Knuefermann Knuefermann[9] [9];; roughness roughness measurements waviness on on the the measurementswere weretaken takenin inboth bothlong long and and short short lengths lengths to to show show the influence of waviness roughness roughnessobtained obtainedwith withISO-standard ISO-standard(long) (long)roughness roughnessevaluation evaluation lengths. lengths. Material: 51CrV4.

The of shorter roughness evaluation lengths is moreisrelevant when evaluating surface generation Theuse use of shorter roughness evaluation lengths more relevant when evaluating surface phenomena than strictly as roughness), the model assumes perfectly spaced,perfectly planar toolpaths, generation (rather phenomena (ratherroughness), than strictly as the model assumes spaced, unlike that occur under a dynamically oscillating machine tool/workpiece interface.

In comparing planarthose toolpaths, unlike those that occur under a dynamically oscillating machine tool/workpiece the unadjusted model output to the data found by the short evaluation length measurement in interface. In comparing the unadjusted model output to the data found by the short evaluation data length Figure 10, it is apparent that some still some exists discrepancy at extremelystill small feedatrates (lowersmall than measurement data in Figure 10, it discrepancy is apparent that exists extremely those adopted ‘macroscopic’ finish machining of metals).

The authors hypothesize this feed typically rates (lower than in those typically adopted in ‘macroscopic’ finish machining of metals). The hypothesize thisroughness is due to the lack of edge roughness in the by surface profiles isauthors due to the lack of edge incorporated in the surfaceincorporated profiles generated the proposed generated theedge proposed model.

This toola edge roughness causeevaluation a relative increase in as short model.

Thisby tool roughness will cause relative increasewill in short roughness the evaluation roughness aspast the some actuallevel. roughness reduces level. However, short actual roughness reduces However, as thepast shortsome evaluation length dataasinthe Figure 10 evaluation length data in Figure 10 shows, the point at which the roughness begins to deviate is at an shows, the point at which the roughness begins to deviate is at an extremely low feed, leading to the extremelythat lowthe feed, leading model to the conclusion that presented model is likely valid for most conclusion presented is likely valid forthe most new tools of commercial quality.

Tool new edge tools of commercial quality. edge roughness does not seemlevels to befound a significant factor at the roughness does not seem to be Tool a significant factor at the parameter in this work. parameter levels found in this Moreover, Knuefermann [9]work. showed that turning is often capable of creating surfaces that have lower Moreover, Knuefermann [9]The showed thatposit turning is often capable creating surfaces that have roughness than the tool edge itself. authors this effect is due to theoftool becoming approximately lower roughness thanUpon the tool itself.ofThe posit this effect is due to the tool becoming smooth when cutting. theedge entrance theauthors tool to the cut, small tool defects (typical of new or approximately smooth when cutting.

Upon the entrance of the tool to the cut, small tool defects slightly worn tools) will act as small cutting edges themselves. The material cut by these small edges will (typical of new or slightly worn tools) will act as small cutting edges themselves.

The material be displaced into the defect, promptly filling this region, leading to a much smoother tool edge. cut by these small edges will unadjusted be displacedmodel into the defect, promptly filling this region, leading to aslightly much It follows that this is accurate for surfaces generated by tools in even smoother tool edge. worn condition, when evaluated by short evaluation length roughness methods. It should be noted It follows unadjusted model surfaces generated by tools initeven that while tool that edgethis roughness will playisaaccurate role in for surface roughness generation, willslightly not be worn condition, when evaluated by short evaluation length roughness methods.

It should be noted a significant factor until the roughness caused by the tool edge itself is of the same magnitude as that while tool edge roughness will play a role in surface roughness generation, it will not a the roughness generated by kinematic and side flow effects. Due to machine tool error andbe side significant factor until the roughness caused by the tool edge itself is of the same magnitude as the flow effects, it is unlikely that this roughness (under benign tool edge roughness conditions) would roughness generated by kinematic and side flow effects. Due to machine tool error and side flow contribute significantly to standard roughness measurements of long evaluation length in non-precision effects, it is unlikely that this roughness (under benign tool edge roughness conditions) would applications due to the other effects’ dwarfing the height of the small surface variations caused by the contribute significantly to standard roughness measurements of long evaluation length in nontool edge roughness. precision applications due to the other effects’ dwarfing the height of the small surface variations caused by the tool edge roughness.

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3.4. Machine Tool Error Incorporation 3.4. Machine Tool Error Incorporation In comparison to the data gathered by the finish machining of aluminum in [8], the present In comparison to predicts the data gathered by the finish machining of aluminum in [8], the present model’s model’s raw output significantly lower surface roughness at low kinematic roughness.

As raw output predicts significantly lower surface roughness at low kinematic roughness.

As hypothesized hypothesized by Childs et al., this relative rise in roughness for this dataset is again most likely due by ettool/vibrational al., this relativeerror. rise in roughness for mirrors this dataset is again most likely due to machine to Childs machine Indeed, this data the roughness trends due to machine tool tool/vibrational error.

Indeed, this data mirrors the roughness trends due to machine tool error (MTE) error (MTE) found over longer evaluation lengths in similar work performed by Knuefermann [9]. found over longer evaluation in similar work performed

by Knuefermann [9]. used Childs al. [8,23] Childs et al.

[8,23] utilized lengths rather long evaluation lengths, similar to the length inetthe long utilized ratherin long evaluation lengths, to the length usedcaused in the long assessments in Figure 10. assessments Figure 10. Over suchsimilar an interval, waviness

by MTE will contribute a Over such an interval, waviness caused by MTE will contribute a substantially to the overall surface substantially to the overall surface roughness measurement. Had these roughness measurements roughness measurement.

Hadevaluation these roughness been analyzed with aitshorter evaluation been analyzed with a shorter lengthmeasurements to eliminate waviness components, is likely the data length waviness components, is likely the data would beroughness, more significantly related wouldtobeeliminate more significantly related to the itsurface generation-induced rather than MTE.to the surface generation-induced roughness, rather than MTE. Visualization of the influence of MTE Visualization of the influence of MTE over low kinematic roughness conditions is seen below in over low11. kinematic roughness conditions is seen below in Figure 11.

Figure

Figure typical of of way way axis-induced axis-inducederror. error.

Figure11.

11. Surface Surface profile altered by MTE (MTE), typical

Inspection long evaluation evaluation length lengthroughness roughnessvalues valuesreveals reveals Inspectionof ofthe the difference difference between between short short and and long that givenevaluation evaluationlength) length) causes a constant offset of roughness deviation thatMTE MTE (over (over aagiven causes a constant offset valuevalue of roughness deviation for a for a given tool/machine combination, as in shown [9]. Toforcorrect for this discrepancy, MTE was given tool/machine combination, as shown [9]. Toincorrect this discrepancy, MTE was quantified quantified taking the difference between the model and measured roughness values lowkinematic kinematic by takingbythe difference between the model and measured roughness values at at low roughness added to to the the model’s model’sroughness roughnessatatevery every roughness(where (wherethe themagnitude magnitude of of MTE MTE is highest), and added point. methodology enables thethe model to approximate roughness deviation for a for given point.This Thiscalibration calibration methodology enables model to approximate roughness deviation a machine, tool, and workpiece in light of spindle error, way travel error, servo instability, given machine, tool, and workpiece in asynchronous light of asynchronous spindle error, way travel error, servo hydraulic vibration, etc. vibration, Previous methodologies performed have this calibration bythis utilizing a vibration instability, hydraulic etc. Previous have methodologies performed calibration by sensor placed somewhere nearplaced the tool/workpiece presented method eliminates the need utilizing a vibration sensor somewhere interface. near the This tool/workpiece interface.

This presented method eliminates the for retroactive such measurement by utilizing retroactive surface roughness for such measurement by need utilizing surface roughness measurement instead.

However, this measurement instead.

However, this necessary thecases efficiency of by theMTE, roughness necessary calibration reduces the efficiency of thecalibration roughnessreduces model in affected yet no model in technique cases affected byfor MTE, yet no accessible forby predicting increased accessible exists predicting roughnesstechnique increasedexists caused MTE for aroughness given machine, tool, caused

by MTE for a given machine, tool,combinations and workpiece All such calibrations. parameter and workpiece combination.

All such parameter wouldcombination. necessitate independent combinations would necessitate calibrations.

Upon inspection of differentindependent MTE constants for various tool edge radii, a logarithmic trend of Upon inspection different MTE for various edge radii, a logarithmic trend of MTE-induced roughnessofwith respect to reconstants was revealed, wherebytool increasing re leads to less MTE-induced MTE-induced roughness with respect to r e was revealed, whereby increasing r e leads to less MTE-is roughness in the affected machining regimes. The authors hypothesize that the reason for this trend induced roughness in damping the affected machining regimes.

The authors hypothesize that the reason for that of positional error caused by increased ploughing forces and vibrational error damping this trend is that of positional error damping caused by increased ploughing forces and vibrational caused by viscoelastic shear-damping behavior, as depicted below in Figure 12. A roughness-reducing errorsimilar damping caused by viscoelastic effect to this has also been notedshear-damping in milling [36]. behavior, as depicted below in Figure 12. A roughness-reducing effect similar to this has also been noted in milling [36].

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(a)

(b) Figure12.12.(a)(a) Tool/workpiece interface model depicting the tendency of a edge smallradius edge toradius to Figure Tool/workpiece interface model depicting the tendency of a small promote promote less MTE damping; (b) tool/workpiece interface model depicting the tendency of a large less MTE damping; (b) tool/workpiece interface model depicting the tendency of a large edge radius to edge in radius result in more proportional MTE damping, to hthe increase in hmin. result moretoMTE damping, to proportional the increase in min .

Themechanism mechanismofofploughing ploughingforces forcesin inthe the damping damping of MTE-induced roughness The roughness is is thought thoughtto tobe be duetoto the reaction machine to the revolving workpiece, induced via cyclical cutting due the reaction of of thethe machine tooltool to the revolving workpiece, andand induced via cyclical cutting force force variation.

Commonly, is found the spindle or ways. cutting with these imperfect variation.

Commonly, MTE isMTE found in the in spindle or ways.

WhenWhen cutting with these imperfect tools, tools, the engagement of the tool and workpiece in the cut will vary by some amount.

When utilizing the engagement of the tool and workpiece in the cut will vary by some amount. When utilizing a small a small edgethis radius, this engagement not change the ploughing forces appreciably tool edgetool radius, engagement variancevariance does notdoes change the ploughing forces appreciably due to due to the small areaploughing where ploughing forces be developed.

The negligible increase in ploughing the small area where forces can be can developed.

The negligible increase in ploughing force force causes very little deflection in the machine tool when this small engagement variance is causes very little deflection in the machine tool when this small engagement variance is encountered. encountered.

Therefore, the position of the tool is accurate to the ways and spindle of the machine, Therefore, the position of the tool is accurate to the ways and spindle of the machine, and whatever and exists whatever errorelements exists in is these elements is “copied” to the workpiece. error in these “copied” to the workpiece.

Alternatively, when a tool of larger edge radius is utilized on the the same same machine, Alternatively, when a tool of larger edge radius is utilized on machine, an an increase increasein in engagement between the tool and workpiece (caused by MTE) will cause more ploughing force, due engagement between the tool and workpiece (caused by MTE) will cause more ploughing force, due to to the increased amount of material being required to flow under the tool edge.

The increased the increased amount of material being required to flow under the tool edge. The increased ploughing ploughing will in turn presentresistance substantial to dynamic forceassociated variationswith associated with force will in force turn present substantial toresistance dynamic force variations the machine the machine tool and workpiece (F dyn). As the engagement variance is caused by imperfections within tool and workpiece (Fdyn ). As the engagement variance is caused by imperfections within the machine the machine tool, deflection response to these engagement variances shall lead to a surface that is a tool, deflection response to these engagement variances shall lead to a surface that is a slightly smoother slightly smoother “copy” of the instrument’s axes. Additionally, viscoelastic shear-damping behavior “copy” of the instrument’s axes. Additionally, viscoelastic shear-damping behavior caused by the caused by the increased amount of material being plasticly deformed under the tool will substantially increased amount of material being plasticly deformed under the tool will substantially dampen sudden dampen sudden positional changes or vibration, such as machine tool harmonic frequencies or positional changes or vibration, such as machine tool harmonic frequencies or asynchronous spindle asynchronous spindle error. Increased shear damping can eliminate chatter by inhibiting the error. Increased shear damping can eliminate chatter by inhibiting the progression of vibrational progression of vibrational excitation. After this damping trend was incorporated into the model, it was found that it was in good agreement with results from [23], as shown below in Figure 13.

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excitation. After this damping trend was incorporated into the model, it was found that it was in good J. Manuf. Mater. Process. 2020, 4, x FOR PEER REVIEW 14 of 18 agreement with results from [23], as shown below in Figure 13.

Figure13.

13.Roughness Roughness (Rzz) model al.al.

[23] .

Figure model (lines) (lines)compared comparedto toroughness roughnessdata dataadapted adaptedfrom fromChilds Childsetet [23].

TheMTE-affected MTE-affected roughness roughness is shown to be predicted The predicted by by the the adjusted adjustedmodel modelwith withsome someaccuracy. accuracy.

Material:Al Al 1075.

1075.

Material:

These phenomena described describedpreviously. previously.The Theoften-noted often-noted Theseresults resultsverify verify the the suggested suggested damping phenomena trendof ofaalarge largeedge edge radius radius to increase surface roughness relative to trend to aasmall smalltool tooledge edgeradius radiusisisshown shown beinaccurate inaccurate for for machining machining processes heavily totobe heavily affected affected by

by MTE. MTE. The Thedamping dampingofofMTE MTEby byedge edge radiiisisshown shownin in Figure Figure 13 13 by by the relative difference between radii between the the (dashed) (dashed)unadjusted unadjustedmodel modelvalues values andthe the(solid) (solid)adjusted adjusted model model values. values. Smaller and Smaller edge edge radii radii show show aa significant significantincrease increaseininroughness roughness whenadjusted adjustedfor forMTE-induced MTE-induced roughness, roughness, while larger radii exhibit when exhibitaalesser lesserincrease increasewhen whenadjusted adjusted forMTE-induced MTE-inducedroughness. roughness. These findings demonstrate for demonstrate that thatin insome somecases, cases,surface surfaceroughness roughnessmay may actually be improved by a larger edge radius.

While this model appears to capture the data well actually be improved by a larger edge radius. While this model appears to capture the data well onon the the lower of the kinematic roughness scale displayed there is some discrepancy considerableat lower end ofend the kinematic roughness scale displayed here, there here, is some considerable discrepancy at higher kinematic roughness. is also likely MTE as well instability as some higher kinematic roughness.

This is also likelyThis caused

by MTE as caused well as by some additional additional instability due to larger uncut chip thickness generally encountered at these conditions. due to larger uncut chip thickness generally encountered at these conditions. Notwithstanding these Notwithstanding these small discrepancies, the model put shown forth intothis text has been shown toof small discrepancies, the model put forth in this text has been approximate the deviation approximate the deviation of surface roughness at low kinematic roughness in 51CrV4 steel, AL 1075, surface roughness at low kinematic roughness in 51CrV4 steel, AL 1075, and Ti-6Al4V. and A Ti-6Al4V. major advantage of this model lies in that it may be calibrated to any machine in a trivial A major advantage of this by model lies in that it may be calibrated anyofmachine in a trivial manner.

This may be achieved performing a single finish cut with atotool known edge radius manner.

This may be achieved by performing a single finish cut with a tool of known edge radius (preferably approximately 10–20 µm, so that the MTE-induced roughness is of a higher amplitude) (preferably approximately 10–20 µ m, so that the MTE-induced a higher amplitude) and subsequently measuring the long evaluation length surfaceroughness roughnessisofofthe generated surface. and subsequently measuring the long evaluation length surface roughness of the generated surface.

Comparing this measured surface roughness to the value predicted by the unadjusted model will Comparing this measured surface roughness to the value predicted by all theother unadjusted will reveal the MTE-induced roughness for this tool edge radius, whereby surfacemodel roughness reveal the MTE-induced roughness for this tool edge radius, whereby all other surface roughness values may be predicted for varying finishing parameters, outside of excessive chatter or roughness values may be predicted for varying finishing parameters, outside of excessive chatter or roughness increasing effects such as inclusions or grain pullout. increasing effects such as inclusions or grain pullout.

Additionally, further investigation of this geometric model enabled the discovery of geometrically defined multi-path (adjacent feed-direction passes) effects. In Figure 14 below, it may be observed that for a given edge radius, different kinematic roughness values lead to quite different

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2020,investigation 4, x FOR PEER REVIEW 15 of 18 Additionally, further of this geometric model enabled the discovery of geometrically defined multi-path (adjacent feed-direction passes) effects. In Figure 14 below, it may be observed that 14akinematic shows a surface thatvalues has very overlap between theconditions. ploughing for surface a given conditions. edge radius,Figure different roughness leadlittle to quite different surface areas, indicated by the dashed profiles in the subsurface; most of the surface is comprised of Figure 14a shows a surface that has very little overlap between the ploughing areas, indicatedmaterial by the that has only in been once, indicating a surface has been efficiently, i.e.,been with dashed profiles theploughed subsurface; most of the surface is that comprised ofmachined material that has only relatively limited ploughing.

In Figure 14b, the model geometry exhibits a subsurface that has been ploughed once, indicating a surface that has been machined efficiently, i.e., with relatively limited heavily ploughed.

The entire surface is shown to have been ploughed multiple asploughed. evidenced ploughing.

In Figure 14b, the model geometry exhibits a subsurface that has been times heavily by the coincident dashed line profiles.

While the surface appears to be smoother due to the larger The entire surface is shown to have been ploughed multiple times as evidenced by the coincident noseline radius, this surface has been ploughed much greater which is radius, knownthis to generate dashed profiles.

While the surface appears toto beasmoother due toextent, the larger nose surface additional heat, and may lead to altered subsurface characteristics. Further analysis should has been ploughed to a much greater extent, which is known to generate additional heat, and may investigate subsurface integrity correlations and mechanisms related to these size effects, e.g., lead to altered subsurface characteristics. Further analysis should investigate subsurface integrity residual stresses and strain hardening. correlations and mechanisms related to these size effects, e.g., residual stresses and strain hardening.

(a)

(b)

Figure Model-generated surface geometry showing the toolprofile profileprojection projectionpath pathand andlight light Figure 14. 14. (a) (a) Model-generated surface geometry showing the tool overlapping previoustool toolpaths, paths, modeled mm,mm, hmin =hmin 5 µ m, f = 0.1 overlapping of of previous modeled with withrcr=c 0.4 = 0.4 = and 5 µm, andmm; f =(b) 0.1modelmm; surface geometry showingshowing heavy overlapping of previous paths (multi-path condition), (b) generated model-generated surface geometry heavy overlapping of previous paths (multi-path modeled with r c = 1.6 mm, h min = 5 µ m, and f = 0.1 mm. condition), modeled with rc = 1.6 mm, hmin = 5 µm, and f = 0.1 mm.

4. Conclusions and Outlook 4. Conclusions and Outlook This work presents anan iterative geometric model forfor the prediction This work presents iterative geometric model the predictionofofsurface surfaceroughness roughnessininfinish finish machining, built upon unique assumptions about the size effect in machining.

The present model machining, built upon unique assumptions about the size effect in machining. The present model establishes a novel method for modeling relatively complex, MTE-influenced surface surface roughness values establishes a novel method for modeling relatively complex, MTE-influenced roughness thatvalues are dependent on tool edge Complex integrity effects, sucheffects, as strain hardening, that are dependent onradius. tool edge radius.surface Complex surface integrity such as strain hardening, thermal softening, recrystallization residual stressare evolution are intimately to the thermal softening, recrystallization and residualand stress evolution intimately tied to thetied surface surface mechanics generation which mechanics whichmodel the present appears to accurately capture.effort In a generation the present appears model to accurately capture.

In a preliminary preliminary effort to consider these effects, thepresent multi-path geometry present within the model has to consider these effects, the multi-path geometry within the model has been identified. been Theidentified. proposed model considers the engagement and geometry of the tool and workpiece in light of proposed model considers the rise engagement andand geometry of spring the toolback. and workpiece in light complexThe ploughing mechanisms that give to side flow material In this sense, it is of complex ploughing mechanisms that give rise based’, to side flow material the spring back. In this sense, fitting to consider this model qualitatively ‘physics as it and incorporates dominating physical it is fitting to consider model qualitatively ‘physicssurface. based’, Future as it incorporates the dominating phenomena which lead to this the generation of the machined work to consider complex physical phenomena which lead toresponse the generation of the machined surface.

Future to consider thermomechanical workpiece material will, however, be necessary to yield a morework comprehensive complex thermomechanical material responsecomparisons will, however, be necessary to yield more model.

Within the cutting speedworkpiece range under investigation, with experimental dataashow comprehensive model.

Within the cutting speed range under investigation, comparisons with that this model predicts the deviation of surface roughness from the kinematically predicted roughness experimental datafinish showmachining that this conditions. model predicts the deviation of surface roughness from the very well under most kinematically predicted roughness very under most models, finish machining conditions.

The authors envision semi-analytical well (physics-based) such as the one presented in this The authors envision semi-analytical (physics-based) models, such as the one presented in this present work, to offer a solid foundation for implementing data-based approaches (e.g., machine present work, to offer a solid foundation for implementing data-based approaches (e.g., machine learning) more efficiently. In practice, initial process planning in industry could be carried out using learning)semi-analytical more efficiently.models.

In practice, initial process planning in industry carried out using fast-acting, As production data, e.g., actual surfacecould and be subsurface quality fast-acting, semi-analytical models. As production data, e.g., actual surface and subsurface quality metrics, are collected over time, the semi-analytical model can be further refined, yielding a ‘smart,’ increasingly accurate model for future process modeling and optimization.

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metrics, are collected over time, the semi-analytical model can be further refined, yielding a ‘smart,’ increasingly accurate model for future process modeling and optimization.

As finish machining typically determines the final workpiece quality in terms of dimensional tolerances, surface roughness and surface integrity, the authors propose that tool edge radius/wear limits need to be set in such a manner as to maintain acceptable quality. This is the common practice in industry, although typically with respect to dimensional tolerances and surface roughness, and not with difficult-to-measure surface integrity parameters, such as residual stresses, subsurface microstructure and strain hardening. While analysis of such parameters lies outside the scope of the present study, the geometric ‘boundary conditions’ of the tool/workpiece engagement are predicted quite well with the proposed geometric model. Therefore, subsequent work will focus on expanding the current model to provide inputs to the authors’ concurrently developed surface integrity models, which require knowledge of multi-path effects and full-surface ploughing insight identified in this foundational work.

Author Contributions: Conceptualization, I.B. and J.S.; Investigation, I.B.; Software, I.B.; Supervision, J.S.; Validation, I.B.; Writ—original draft, I.B. and J.S.; Writing—review & editing, I.B. and J.S. All authors have read and agreed to the published version of the manuscript.

Funding: This research received no external funding.

Conflicts of Interest: The authors declare no conflicts of interest.

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