Figure 169. How the feedrate inuences the machined cusp/surface roughness value ‘Sm’ and its aect on the wavi- ness parameter ‘Δq’, plus surface topography of actual longi- . tudinal CNC turned P/M ferrous compacts – cut with diering nose radii. [Courtesy of Joel (UK) Ltd.] Machinability and Surface Integrity  the considerably larger eective tool nose radius, act- ing like a ‘wiper-blade’ blending-out and obliterating the surface’s cusps. is technique of utilising a large tool nose geometry has traditionally been used by pre- cision turners to improve the overall surface nish. .. Manufacturing Process Envelopes e principal features of manufacturing process en- velopes and indeed, for many amplitude distribution curves is that they can be approximated by the so- called ‘beta-function’ – ‘β’ (Fig. 170a). Here, the func- tion has two parameters that are independent of one another enabling them to be used as a means of sur- face characterisation. e notation ‘a’ is the allocated weighting for the prole ordinates measured from the lowest valley and above, with notation ‘b’ being given to weighting the prole from the highest peak down. Hence, peaks and valleys have accordingly dierent weights. One of the problems that has arisen from util- ising this technique for a topographical prole, which has somewhat discredited them for certain applica- tions, is how and in what manner can one determine ‘a’ and ‘b’. e ‘beta-function’ is normally dened within a set range of: 0→1, being expressed in the following man- ner: β(a, b) =  �  z a− (a − z) b− dz . If by changing the range of the ‘beta-function’ equa- tion above, from: 0→1 to Rp + Rv, or indeed with that of Rt, then substituting σ (i.e. the standard deviation of the distribution) with Rq, the beta-function param- eters ‘a’ and ‘b’ become: a = Rv (Rv Rp – Rq 2 /Rt Rq 2 ) b = Rp (Rv Rp – Rq 2 /Rt Rq 2 ). e fact that any dominant peak, or valley within the assessment length is only raised to a unit power, in- fers additional stability over the ‘skewness/kurtosis ap- proach’. e problem with this ‘beta-function’ method is in accurately determining ‘sound’ results from the Rv and Rp, which conrms the diculty that obtain- ing information from peak/valley measurement and then deriving valid information is fraught with com- plications. In Figs. 170: ‘ai’ it is symmetrical; with ‘aii’ being asymmetrical; for their respective ‘beta-func- tions’ , these relationships are based upon a class of sta - tistically-derived ‘Pearson distributions’ 59 . In the sym- metrical case (Fig. 170ai) the skewness equates to zero; conversely, for an asymmetrical series of results (Fig. 170aii), skewness can be either positively, or negatively skewed (i.e see Fig. 164bii). Nevertheless, even allow- ing for these limitations, an example of the groups of manufacturing process envelopes for a range produc- tion processes is illustrated in Fig. 170b. Here, the pro- duction processes can be simplistically classied and grouped into either a ‘bearing’ , or ‘locking’ surface topography. e ‘bearing-/locking-groupings’ indicate that certain production processes can achieve specic functional surfaces for particular industrial applica- tions. ese ‘groupings’ (Fig. 170b), also indicate that the general classications are less distinct than might otherwise be supposed, as certain processes can be provide either a ‘locking’ , or a ‘bearing’ surface condi - tion – termed ‘intermediate groupings’. Typical of such an ‘intermediate group’ are the P/M drilled compacts. One reason for this is that any P/M ‘secondary ma- chining’ oen utilises twist drills, which may produce 59 ‘Pearson product moment correlation coecient’* – to give it its full title, is a statistical association utilised when a ‘rela- tionship’ exists between several quantities and it is a measure of the extent of this aliation, thus producing its ‘correlation coecient’ which can then be utilised. *For example, having a sample of pairs of observations ‘x’ and ‘y’ , the value ‘r’ of this ‘Pearson coecient’ , is given by the ‘generalised formula’ , below: r = Σ(x – x ) (y – y) /√ Σ(x – x) 2 Σ(y – y) 2 (Bajpai, et al., 1979): e calculated ‘Pearson coecient’ should lie either close to –1, or +1. If the calculated value is close to –1 then the ‘straight-line trend’ is in a downward direction, conversely, if the calculated value is close to +1 then the ‘straight-line trend’ direction is upward. If the value is close to zero (0), then no correlation exists, so the pairing of the data is disparate and cannot be utilised. With calculated data that is reasonably close to either –1, or +1, a ‘regression line’ (i.e. using linear regression) can be calculated based upon the general straight- line formula: Y = a + bX   Where a ‘regression line of Y on X’ for the two constants ‘a’ and ‘b’ respectively are: b = nΣxy – (Σx)(Σy)/n(Σx 2 ) – (Σx) 2   a = Σy – bΣx/n Where a ‘regression line of X on Y’ for the two constants ‘a’ and ‘b’ respectively are: b = nΣxy – (Σx)(Σy)/n(Σy 2 ) – (Σy) 2   a = Σx – bΣy/n NB e ‘regression line’ being the equivalent of the ‘least squares line’ , allows data on each axes to be compared – with some degree of condence.(Wild, et al.,1995)  Chapter  Figure 170. The ‘beta-function’ and typical ‘manufacturing process envelopes’. Machinability and Surface Integrity  a ‘saw-toothed prole’ to the hole’s surface, along with pores in the compact that are open to the ‘free-surface’ of the hole. e hole topography may have this ‘saw- toothed eect’ present, it being a combination of the drill’s partial lip and margin occurring at the feed rev –1 periodicity, formed by the drill spiralling-down and around the hole’s periphery. Hence, the drill’s passage creates a positive skewness via drilled ‘saw-toothed cusps’ , while the pores can introduce negative skew - ness – creating a potential ‘intermediate group’ to the manufacturing process envelope groupings. .. Ternary Manufacturing Envelopes (TME’s) In machining operations the dominant factor that in- uences surface topography has been shown to be the tool’s feedrate. In Fig. 171, the feedrate, in conjunc- tion with the principal factors such as surface texture (Ra) and roundness (i.e least squares circle – LSC), are utilised to dene the limits for these ‘Ternary manu- facturing envelopes’ (TME’s). By using such diverse factors as: surface texture, roundness and processing parameters (feedrate), for the major axes on the ter- nary graph, enables the surface to be characterised in a unique manner. Such TME’s dier quite consider- ably from the more usual and restricted ‘manufactur- ing process envelopes’ alluded to in the previous section – the skewness and kurtosis axes of the manufacturing envelopes, might otherwise mask crucial information. e ‘TME approach’ gives a psuedo three-dimensional representation on its ternary axes, which can be ex- ploited to illustrate how the inuence of changing a parameter – such as feedrate – modies the relation- ship of the associated surface texture and roundness values for the nal machined result. As an example of the eectiveness of this TME ap- proach to the complex problem of machining data analysis, Fig. 171 has been drawn from an actual machinability trial. If one observes this TME graph closely for a pre-selected range of turning and boring processes, indicated in Fig. 171, with specic reference here, to turning operations – by way of illustrating the TME’s expediency. e TME shows how – for the turning operations – at low feedrate (0.10 mm rev –1 ) the surface texture is closely conned to a relatively small spread of values – nominally around 0.5-1.5 µm Ra, whereas its associated roundness lies between approximately 5 and 50 µm LSC. As the feedrate in- creased in an arithmetic progression to 0.25 mm rev –1 , the range of the surface texture bandwidth propor- tionally expanded to 1.5 at approximately 5-6.5 µm Ra, with a corresponding roundness ranging from 8 to 48 µm LSC, giving a proportional bandwidth of 1.6. As the feedrate was raised even higher, to 0.40 mm rev –1 , it was not surprising to note that this also produced increases in both the surface texture and its propor- tional bandwidth, with similar values with respect to its roundness. ese ‘machinability and metrology trends’ allow examination of both the bandwidth vari- ability and the aect of dierent feedrates on other disparate factors – such as its machined roundness. Similar trends occurred for the boring operation, but here only two feedrates were employed, by applica- tion of this analysis technique via the ‘TME-approach’ to a concise machinability trial, complex analysis of the TME is possible. e pseudo three-dimensional graph, oers perhaps an unusual insight into the mul- tifaceted inter-relationships that exist aer workpiece machining. e TME shows that simply examining one metrological parameter in isolation to those that could aect it, may mask vitally important relation- ships and trends that would otherwise remain unseen. By careful selection of the parameters for the respec- tive axes, perhaps based upon the feedrate (i.e. here, normally situated along the X-axis), allows an appre- ciation of the whole surface at any instant along the three graph’s axes. 7.6 Machining Temperatures Ever since Taylor in 1907, recognised that elevated tool and workpiece temperatures in metal cutting played a crucial role in inuencing tool edge wear rates, the subject has been one of intensive study. Moreover, that the tool/chip interface temperature has a control- ling inuence on the rate of crater wear and the fact that tool life can be drastically curtailed by these in- duced machining temperatures, as such, the topic has received considerable research attention. Here, space will only allow a brief resumé of this complex temper- ature-induced machining problem. During metal cutting in particular, there are sev- eral temperature eects that need to be considered. In Fig. 51, an orthogonal single-point cutting operation is schematically illustrated, indicating the distribution of heat sources within the three deformation zones. In  Chapter  Figure 171. ‘Ternary manufacturing envelopes’ for the production processes of turning and boring, axes: feedrate, roundness and surface texture . Machinability and Surface Integrity  particular, the heat generated in the main ‘body’ within the cutting region via both the primary and secondary zones is a result here, of the workpiece’s plastic defor- mation. Still more intensive heat is generated at the tool/chip interface – along the rake face, with the ma- jority of heat being swept away with the chips, while the remainder of heat is either conducted through the tool, or conducted/convected into the workpiece. As- suming that no coolant application is present in the machining operation, then any heat loss to the ambi- ent air becomes insignicant. An equation has been developed that governs the temperature distribution – via its isothermal gradients – in machining (Fig. 172), this being an ‘energy-based equation’ as follows: ρC∂T∂t  V  T  k  T  ˙ q   (Source: Tay, et al., 1993). erefore, in steady-state machining operations, the transient term will disappear and at the region of the tool (i.e. insert) only the conduction term remains. ∴ Rate of heat generation (˙q) = σ ˙ε Where: ‘σ’ was obtained from an emprical function of: ‘ε’ , ‘˙ε’; plus ‘T’. NB  is rate of heat generation only exists within the primary and secondary deformation zones. By way of example of how the temperature genera- tion/distribution occurs in orthogonal cutting, in the more-easily understood ‘Boothroyd machining model’ (i.e. being in a slightly modied form – by the author), this workpiece material is in a state of ‘continuous motion’ during cutting (Fig. 172). If specic points are selected to show how temperatures occur as they pass along/through these deformation zones then, the points: ‘X, Y and Z’ can be considered for special observation. So, as the workpiece material enters the cutting region at point ‘X’ , it begins to move toward the cutting insert. It approaches and passes through the primary deformation zone where it is heated-up until it leaves this zone, it is then swept-away by the formed chip. Equally point ‘Y’ , passes through both the primary and secondary deformation zones (i.e see Fig. 51 for these deformation zones) and contin- ues to heat-up until it leaves the secondary deforma- tion zone. In both of the above cases, these points (i.e. namely: X and Y) are cooled as heat is conducted into the chip’s body (as it exit’s the cut), where it eventually achieves a uniform temperature right the way through. Prior to this occurring, the maximum temperature occurs along the cutting insert’s rake face, some dis- tance from the actual cutting edge (i.e see Fig. 172). Conversely point ‘Z’ , which remains attached to the workpiece, is heated by conduction from the primary deformation zone and some heat is also conducted from the secondary deformation zone into the body of the cutting insert, while the tertiary deformation zone will also impart some heat into the machined surface of the workpiece. Many thermal and thermographical techniques have been developed over the years to obtain accurate isothermal temperatures within the: cutting zones: tool/insert interface plus rake face vicinity; together with the machined surface region of the workpiece. Moreover, ‘indirect methods’ have been utilised to obtain similar thermal historical data from within these dynamic and harsh environments, but only one of these techniques will be mentioned in the next sec- tion. .. Finite Element Method (FEM) e popular approach today, to obtaining ‘simulated’ thermal data is by employing the ‘Finite element method’ (FEM), to calculate temperature distributions in the vicinity of the cutting regions (Fig. 173). Typical of this approach and worth mentioning in some de- tail, was that conducted and described by Tay (1993), where he experimentally-obtained information re- garding: velocity, strain and strain-rate distributions, by utilising a printed-grid and quick-stop technique. e rate of heat generation within the primary defor- mation zone was determined from the equation: (˙q) = σ ˙ε. From the deformed grid pattern (Fig. 173a), the ac- tual dimensions of the triangular deformation zone, as well as the velocity distribution along the tool/chip interface can be established and analysed. By this FEM technique, it is possible to determine the shear-strain rate within the secondary deformation zone at the tool/chip interface: (˙γ int ) has been found to be approximately constant and equal to: V c/ δt 2 . e shear strain-rate within the  Chapter  Figure 172. Typical temperature distributions (isotherms) during machining, illustrated across the: chip, insert and work- piece; at relatively low cutting speed . Machinability and Surface Integrity  secondary deformation zone tends to be linear in na- ture from: (˙γ int ) – at the interface, → zero – at the boundary of the triangular secondary zone. e frictional stress along the tool/chip interface can be assumed to be constant along the rst half of the contact region, then linearly decreasing to zero at its end. e frictional heat source distribution at this interface, can be obtained from stress and velocity dis- tributions at this location. In Fig. 173a, the basic ‘FEM mesh’ is shown, with typical temperature distributions obtained from this being illustrated in Fig. 173b. e accuracy of this particular example for the ‘Tay-model’ for the total sum of all heat sources was within 2.6% of actual mea- sured power consumption (F c U). Moreover, the values of ‘β’ calculated from the temperature distributions closely-agreed to those obtained some years earlier by Boothroyd (1963). e FEM approach to machin- ing data capture and analysis covers these and other related parameters and clearly indicates the power of simulation – more will be mentioned on this subject later in the chapter. 7.7 Tool Wear and Life Introduction e working environment for most machining pro- cesses is extremely harsh, with pressures exerted onto a minute area of tool tip being of the order of >1600 MPa, with localised temperatures reaching over 750°C creating a sterile surface at the tool/chip inter- face, making this an ideal state for a pressure-welding condition. In attempting to minimise this anity be- tween the work-hardened chip – oen this plastic de- formation making the chip >5 times harder than that of the parent workpiece material, means that there are several ways of relieving this tool/chip anity. e ob- vious one is to use a cutting tool material that is in- ert to the workpiece such as a either a: ceramic, or mixed-ceramic cutting insert composition, or some- thing similar, but this may not prove to be satisfactory, particularly if interrupted cutting conditions are antic- ipated. In this situation above, perhaps by utilising a multi-coated cemented carbide insert this may reduce this ‘adherence-tendency’. Lastly, the correct grade of ‘ood-coolant’ may: lower the interface temperature, reduce friction here, while somewhat improving the machined surface texture. When only partial success is achieved by employing the above tooling strategies, the last resort may be to adjust the cutting data to en- hance and provide a ‘less-abusive machining regime’ , while simultaneously improving the ‘steady-state’ wear conditions. So far, no mention has been made here concern- ing frictional eects in the cutting process. Friction is very complex subject which relates not only to: chip ow-stress and ‘stiction’ 60 problems at the chip/tool in- terface, but concerns the tribological conditions along this interface. Cutting tool rake and ank faces are never perfectly smooth, as even when faces and edges have been either been ground, or super-nished the abrasive nature of the super-nishing process pro- duces an abraded surface that approaches the grit size of the abrasive medium. erefore, to the naked eye the insert’s surface looks smooth, but at the ‘micron- level’ of surface magnication (i.e. 1 × 10 –6 m), the cut- ting insert’s surface has localised ‘high-spots’ , or as - perities present. ese asperities signicantly reduce the contact area produced between the forming chip and its contact at the interface on the tool’s rake face. Not only can these asperities considerably decrease the ‘real area of contact’ and as a result increase the coe- cient of friction here, but the asperities may be either ‘plastic’ , or ‘elastic’ in nature 61 . In Table 11 (i.e. exper- imental data extracted from: Childs, et al., 2000, con- cerning surface texture assessment of cutting insert faces), comparison is made between a small sample of 60 ‘Stiction’ , is sometimes confused with its ‘close alternative’ this being: ‘stick-slip’. ese terms are worth stating, to ex- plain their respective dierences and have been dened in the following manner: ‘Stiction’ is: ‘e phenomenon at an inter- face where the frictional stress is equal to the shear yield stress of the soer material.’ ‘Stick-slip’ is: ‘A jerky motion between sliding members due to the formation and destruction of junctions.’ (Kalpakjian, 1984) 61 ‘Plastic asperities – on a plastic chip’ , these are ‘high-spots’ that will sink into the chip and how they achieve this action, does not depend on local conditions at interface contact, but on the bulk plastic ow eld. Specically, the lower the hydro- static stress in the bulk ow eld, the less eort is required for these asperities to sink.‘ Asperities – on an elastic foundation’ , this situation is ex- tremely complex phenomena and put simply, in conditions of low contact stresses, the chip beneath these asperities is elas- tic. (Childs, et al., 2000)  Chapter  cutting insert surface conditions, clearly illustrating that even when ‘super-nishing’ 62 an insert’s face it still has asperities present. .. Tool Wear Introduction On a single-point turning tool’s cutting insert, the main regions of wear are normally conned to the: rake face; ank; trailing clearance face; together with 62 ‘Super-nishing’ , is based on the phenomenon that a lubricant of a given viscosity* will establish and maintain a separating lm between two mating surfaces, if their roughness does not exceed a specic value and, if certain critical pressure – keep- ing them apart – is not exceeded. us, as minute peaks occur on the cutting insert’s surface, they are then cut away by the abrasive (e.g. minute diamond abrasive in a lubricant – oil – suspension) this being applied with a controlled pressure – until a required level of smoothness has been achieved. NB e maximum stock removed from the insert will be ap- proximately 50 µm.(Degarmo et al., 2003) *Viscosity relates specically to oils, which will vary with temperature. Dierent oils vary by dissimilar amounts for the same temperature, this is why the ‘viscosity index’ (VI) has been developed. the actual nose radius (Fig. 174). Likewise, the type of wear pattern provides important information as to the eectiveness of the overall machining operation. Considerable time and eort has been spent by both researchers and tooling companies, ensuring that tool wear mechanisms and their respective classications for specic machining operations are understood. So, by knowing the anticipated wear behaviour for a cut- ting insert for a specic machining operation, this al- lows the user to optimise productivity by ensuring that the ‘ideal’ tool grade and its associated geometry, will produce the desired machining conditions with the correct type of cut for the chosen workpiece materi- al’s composition. A range of factors can inuence tool wear when component machining, these are: material removal rate; ecient chip control; machining eco- nomics, precision and accuracy demanded; plus the machined surface texture requirements. If one magnies then inspects the wear pattern on a worn cutting edge, then it is reasonably straightfor- ward to establish both the cause and remedy for the indicated type of wear (i.e see Appendix 11), this will allow subsequent tooling to be more adequately con- trolled during following machining operations. In order to ensure that the correct tool has been selected, it is really only down to basic ‘good engineering prac- tices’ , namely: • that the initial selection of criteria for the cutting data is sound; Table 11. Cutting insert surface texture and contact stress severity data. ← 10k local /E* [°] → Tool finish: Surface texture data: Al/HSS: Cu/HSS: Brass/WC Steel/WC Ra [µm] ∆q [°] CVD-coated 0.2-0.5 3-7 1.2 1.9 2.8 1.8 Ground 0.1-0.25 2-4 1.2 1.9 2.8 1.8 Super-nished 0.03 0.4 1.2 1.9 2.8 1.8 * When s/k is <0.5, an asperity is totally elastic – if the plasticity index is <5 and totally plastic if its >50. As s/k increases to 1, these critical plasticity index values reduce. In large s/k conditions of metal machining, an asperity would normally be ‘fully-plastic’ , if: ∆q ≥ 10k local /E*. NB ‘s’ = Shear strength and ‘k’ = local shear stress. [Source Childs, et al., 2000] . Machinability and Surface Integrity  . ‘T’. NB  is rate of heat generation only exists within the primary and secondary deformation zones. By way of example of how the temperature genera- tion/distribution occurs in orthogonal cutting,. z) b− dz . If by changing the range of the ‘beta-function’ equa- tion above, from: 0→1 to Rp + Rv, or indeed with that of Rt, then substituting σ (i.e. the standard deviation of the distribution) with. power of simulation – more will be mentioned on this subject later in the chapter. 7. 7 Tool Wear and Life Introduction e working environment for most machining pro- cesses is extremely harsh, with