e number of two-dimensional surface prole pa- rameters that have been developed over the years for just the stylus-based instruments – discounting the three-dimensional contact and non-contact varieties, has created a situation where many users simply do not understand, nor indeed comprehend the intrinsic dierences between them! A term was coined some years ago to show exasperation by many metrolo- gists’ with this ever-increasing development of such parameters. Many researchers and companies were totally disenchanted with their confunsion and plight, so they simply called the predicament: ‘parameter- rash’. However, here we need not concern ourselves with this ‘vast expanse of surface descriptors’ , as only a few of the well-established parameters and discuss just the most widely-utilised ones. It is worth making Figure 161. ‘Lay’ indicated on drawings, plus the relative cost of manufacture for dierent production processes. Machinability and Surface Integrity Figure 162. Anticipated process ‘roughness’ and their respective grades. [Source: ISO 1302, 2001]. Chapter Figure 163. Surface texture data-capture, with techniques for the derivation of the arithmetic roughness parameter: Ra. Machinability and Surface Integrity the point, that all of these two-dimensional surface pa- rameters can be classied into three distinct groupings and just some of these parameters are: 1. Amplitude parameters (Ra, Rq, Wa, Wq, Pa, Pq) 51 – with Ra 52 being universally recognised for the ‘international’ parameter’ for roughness. It is: ‘e arithmetic mean of the absolute departures of the roughness prole from the mean line’ (i.e. see Fig. 163b and c). It can be expressed as follows: Ra lr l r zx dx (units of m) NB e Ra parameter is oen utilised in appli- cations to monitor a production process, where a gradual change in the surface nish can be antici- pated, making it seem to be ‘ideal’ for any form of machinability trials, but some caution is required here, as will be seen shortly in further discussion concerning this ‘surface descriptor’. By way of com- parison, another previously used amplitude param- eter is given in Appendix 10 and is the ‘R Z (JIS)’ (i.e. 10-point height) parameter. Other useful parameters of the assessed prole, to be shortly discussed in more detail, include: ‘Skewness’ (Rsk, Wsk, Psk), which is oen utilised in association with ‘Kurtosis’ (Rku, Wku, Pku), producing the so- called: ‘Manufacturing Process Envelopes’ – as a means of ‘mapping’ and correlating machined surface topog- raphies. 2. Spacing parameters (Rsm, Wsm, Psm) – can be de- ned as: ‘e mean spacing between prole peaks at the mean line, measured within the sampling length’ (i.e. depicted along a machined cusp – at diering 51 e designation of the letters follows the logic that the pa- rameter symbol’s rst capital letter denotes the type of prole under evaluation. For example, the: Ra* – calculated from the roughness prole; Wa – derives its origin from the waviness prole; with the latter in this logical sequence, namely the Pa – being derived from the primary prole. Here, in this discus- sion and for simplicity, only the rst term in the series – e.g. ‘Ra’ notation – will be used. *Ra is today shown in the International Standard (i.e. ISO 4287: 1997) as being denoted in italics, while in the past, it was usually shown as follows: ‘R a ’ , but even now, many companies still use this particular notation. 52 Historically, the classication of the relative roughness of sur- faces was initially developed in England and was then termed: ‘Centre Line Average’ (CLA), while in the USA its equivalent term was the ‘Arithmetic Average’ (AA). feedrates in Fig. 169a and b). It can be expressed in the following manner: Rsm n i=n i= si XS+XS +XS + XSn n Where: n = number of peak spacings. NB e Rsm parameter needs both height and spac- ing discrimination and, if not specied the default height bias utilised is 10% of: Rz, Wz, or Pz, – where these are the ‘Maximum height of prole’. As can be seen from the ‘idealised’ machined surface topog- raphy given in Fig. 169a and b, the spacing param- eters are particularly useful in determining the feed marks. Moreover, the Rsm parameter relates very closely to that of the actual programmed feed rev –1 of either the cutter, or workpiece – depending on which production process was selected. See also, Appendix 10 for a graphical representation of the previously utilised ‘High Spot Count’ (HSC) parameter. 3. Hybrid parameters (Rmr, Wmr, Pmr, R∆q, W∆q, P∆q, Rpk, Rk, Rvk) – each of these ‘hybrids’ will now be briey mentioned. Rmr, or its alternative notation Mr is the ‘Material ratio curve’ , which can be dened as: ‘e length of the bearing surface (ex- pressed as a percentage of the evaluation length ‘L’) at a depth ‘p’ below the highest peak (i.e. see Fig. 165). – Rmr: It is oen known as the ‘Abbott-Firestone curve’ , the mathematics of this Rmr-curve can be ex- pressed in the following manner: Rmr b+b+b=B +bn n n i=n i= bi NB is ‘Material ratio curve’ represents the pro- le as a function of level. More specically, by plot- ting the bearing ratio at a range of depths in the prole trace, the manner by which the bearing ratio changes with depth, provides a method of charac- terising diering shapes present on the prole (i.e. see Fig. 165 and Appendix 10). – R∆q: e R∆q parameter, can be dened as: ‘e root mean square (rms) slope of the prole within the sampling length’ (i.e. see how its angle changes at diering machining feedrate conditions shown in Fig. 169b and c), it can be mathematically ex- pressed as follows: Chapter R q lr l r θx ¯ θ dx Where: ¯ θ lr l r θxdx θ = slope of the prole at any given point. • Rpk, Rk, Rvk: ese parameters (i.e. see Appendix 10 for graphi - cal representations of the parameters), were origi- nally designed for the control of potential wear in automotive cylinder bores in volume production by the manufacturing industry. Today, Rpk, Rk and Rvk are employed across a much more diverse-eld by a range of industries. Such hybrid parameters are an attempt to explain – in numerical terms, the respective form taken from the prole’s trace of the ‘material ratio curve’ (Rmr), hence: – Rpk parameter – is the ‘reduced peak height’ , il- lustrating that the top portion of a bearing sur- face will be quickly worn-away when for exam- ple, an engine initially begins to run, – Rk parameter – is known as the ‘kernal rough- ness depth’ , therefore the long-term running – ‘steady-state wear’ of this surface will inuence for example, the performance and life of the au- tomotive cylinder(s), – Rvk parameter – is the ‘trough depth’ this in- dicates that the surface topography has an oil- retaining capability, specically via the ‘trough depths’ which have been purposely ‘cross- honed’ 53 into the bore’s surface. Arithmetic roughness parameter (Ra) Although the Ra ‘amplitude parameter’ has been widely quoted ‘Internationally’ , there are a few provi - 53 ‘Cross-honing’ , uses either: (ne) Abrasives/CBN/Diamond – ‘stones’ , that are tted into a ‘honing head’ which then rotates and oscillates within a hole, or an engine’s bore. e critical parameters are the rotational speed (Vr) oscillation speed (Vo), the length and position of the honing stroke, the hon- ing stick pressure (Vc). e inclination angle of the cross-hon- ing action, is a product of the up-/down-ward head motion (Vo) and the rotational speed for the head (Vo). is complex action of rotating and linear motion, generates the desired cross-honed ‘Lay-pattern’ within the bore – for improved oil retention. sos, or conditions that must be met, if it is to be utilised satisfactorily, these are: • e Ra value over one sampling length represents the average roughness. e eect of a spurious non- typical peak, or valley within the prole’s trace be- ing ‘averaged-out’ so will have only a small inu- ence on the Ra value obtained; • e evaluation length contains several sampling lengths (Fig.163a), this ensures that the Ra value is representative of the machined surface under test; • An Ra value alone is meaningless, unless quoted with its associated metre cut-o (λc) length. Repeat- ability of the Ra value will only occur at an identi- cal length of metre cut-o; • If a dominant surface texture pattern occurs (Lay), then the Ra readings are taken at 90° to this direction; • at Ra does not provide information as to the shape of either the prole, or its surface irregulari- ties. Dierent production processes generate diverse surface nishes, for this reason its is usual to quote both the anticipated Ra numerical value along with the actual manufacturing process; • Ra oers no distinction between peaks and valleys on the surface trace. e most confusing argument concerning the use of an Ra value alone, is that its numerical value is not only meaningless, but it can have catastrophic conse- quences if interpreted incorrectly. ese opinions can be substantiated by close observation of Fig. 164a, where an identical numerical Ra value produces widely divergent surface topographies. In addition, if a designer’s engineering application called for a ‘bearing surface’ (Fig. 164ai), rather than a ‘locking surface’ (Fig. 164aiii), then the numerical value of 4.2 µm in isola- tion, becomes pointless, as it tells the designer nothing about the ‘functional’ surface topography. is prob- lem is exacerbated when the wrong surface topography is selected for a specic engineering application. For ex- ample, a ‘locking surface’ applied to a bearing industrial application in a harsh environment, can be expected to catastrophically fail aer very little in-service time. Skewness (Rsk, Wsk, Psk) and Kurtosis (Rku, Wku, Pku) Parameters ese surface descriptors of ‘skewness’ and ‘kurtosis’ are oen derided as simply ‘statistical’ amplitude pa- rameters, that can introduce spurious results and as a consequence, having little use in engineering applica- tions. However, when used in the correct context, they can provide a valuable insight into the overall shape of Machinability and Surface Integrity Figure 164. Arithmetic roughness parameter (Ra) can give a misleading representation of the surface topography, so skewness (Rsk) and kurtosis (Rku) may provide help in the interpretation of the surface. [Courtesy of Taylor Hobson] . Chapter the surface topography, if used in conjunction with the Ra value (Fig. 164). is is particularly true for many machining applications and where a comparison of ‘Manufacturing process envelopes’ is required – more on this subject shortly. Both skewness and kurtosis can be mathematically dened, as follows: • Skewness parameter (Rsk): e measure of the symmetry of the prole about the mean line’. Skewness has the ability to distinguish between asymmetrical (i.e. having ‘biased tails’) of identical Ra numerical values (i.e depicted in Fig. 164bii). Skewness can be expressed as follows: Rsk R qlr l r z xdx . • Kurtosis parameter (Rku): Measure of the ‘sharpness’ of the surface prole’ . Kur- tosis can be expressed in the following manner (i.e shown in Fig. 164bi): Rku R qlr l r z xdx . Discussing both ‘skewness’ and ‘kurtosis’ in turn, im- plies that they are separate parameters, but this is not the case, when one observes Figs. 164bi and bii. How- ever, to begin with and for ease, each of these param- eters will be individually mentioned. e Rsk param- eter cannot distinguish if a prole’s trace has peaks 54 that are relatively evenly distributed above, or below the mean line (i.e. Fig. 164aiii), or being inuenced by any isolated peak, or valley (i.e. this topography is shown to good eect in Fig. 164ai) – within the sam- pling length. e Rsk parameter of an amplitude distribution curve as illustrated in Fig. 164bii, indicates a certain amount of bias that could be either in an upward, or downward direction (i.e shown either as: le- and right-ward, in this example). e amplitude distribu- tion curve’s contour can be very informative as to the overall structure of the surface topography. If this curve is symmetrical in nature then it indicates regularity of the prole trace (Fig. 164ci), conversely, an asym- metrical surface’s trace will be indicative of a ‘skewed’ amplitude distribution curve (Fig. 164cii). Utilising 54 ‘Peaks’ , are oen known by a variety names, such as ‘spikes’ , or to use a more scientic term this would be: ‘asperities’. the skewness parameter distinguishes between prole traces having if not similar, or identical Ra values. Machined surfaces can exhibit a broad range of surface topography-related conditions. For example, a boring operation with a relatively long length-to-di- amter ratio may result in bar deection (i.e. elastic de- formation) and occasion the cutting insert to deect, producing large peak-to-valley undulations along the bore (waviness). Super-imposed onto these longer wavelengths are small-amplitude cyclical peaks – peri- odic oscillations, indicating vibrations resulting from the boring process. us, the consequential surface prole for the bored hole, would portray the interac- tions from the boring bar deformations and any har- monic oscillations. e likely outcome of such a bor- ing operation and the bar’s relative motion, would be reected in the prole trace, exhibiting a low average prole height, but with a large range of height values. Moreover, a highly negative skewness is indicative of a good bearing surface, particularly if some valleys are present to allow for subsequent oil-retaining abilities (Fig. 164cii). e shape of the amplitude distribution curve in terms of its relative ‘atness’ , or ‘spikeness’ can also relay useful information concerning the ‘dispersion’ , or ‘randomness’ of the surface prole, which can be quantied by means of the surface descriptor known as kurtosis (Rku). However, unlike skewness (Rsk), kurtosis can detect if the prole peaks are distributed in an even manner across the sampling length’s trace (Fig. 164ci), or vice-versa. is latter case of producing both a ‘spiky’ and ‘skewed’ distribution having either a positive, or negative skew to its resultant distribu- tion with its associated surface topography – is shown in Fig. 164cii. As a consequence of this ability to dif- ferentiate the variations of the actual surface topog- raphy, Rku is a benecial parameter in the prediction of in-service component performance, with particular respect to any potential lubrication-retention issues, or for any succeeding industrial wear behaviour cir- cumstances. Material Ratio Curve (Rmr) e material ratio curve (Rmr) represents the prole as a function of level. Specically, by plotting the bearing ratio at a range of depths for the prole, the manner by which the bearing ratio changes with depth, provides a method of characterising dierent shapes present on the prole (i.e. see Fig. 165). e bearing area fraction Machinability and Surface Integrity Figure 165. Hybrid surface texture parameters – spacing and depth. [Courtesy of Taylor Hobson]. Chapter can be dened as: ‘e sum of the lengths of individual plateaux at a particular height, normalised by the total assessment length’ – with this parameter designated by Rmr (Fig. 165ai and aii). In the majority of circumstances mating surfaces demand specic ‘tribological conditions’ 55 : these are the direct result of particular machining operational sequences. Normally, the initial production opera- tion will establish the general shape of the machined surface – by ‘roughing-out’ – providing a somewhat coarse nish, with subsequent operations to improve and enhance the nish, resulting in the desired de- sign properties. is machining strategy provides the operational sequence that will invariably remove sur- face peaks from the original machining process, but oen leaves any deep valleys intact. is standardised industrial machining practice of ‘roughing and n- ishing’ , produces a type of surface texture known as a ‘stratied surface’. When these ‘stratied surfaces’ occur, the height distributions tend to be negatively skewed making it somewhat dicult for an ‘averaging parameter’ like Ra to represent the surface eectively to the designer’s specication, or in matters concern- ing quality control. In the diagrammatic representation for the deriva- tion of the Abbott-Firestone curve 56 , or ‘Material ratio curve’ (Rmr) shown in Fig. 165b, this enables the user to select diering slices, or depths through the prole, with these ‘slices’ having a specic ratio for the pro- portions of air-to-material. e top of the highest peak within the prole trace having been evaluated, estab- lishes the reference, or zero percentage line for the Rmr curve. Calculation of this curve is inuenced by the largest peak’s height in relation to the others, although in reality, the eect of a single peak on a surface’s in- 55 ‘Tribology’ , was a technology that originated about 40 years ago, its name was derived from the Greek ‘τριβοσ’ translated: ‘Tribos’ – meaning ‘rubbing’ so that the literal translation would be the ‘science of rubbing’. Today, tribology can be more accurately dened as: ‘e science and technology of interacting surfaces in relative motion and of related subjects and practices’ (Williams, 1996, et al.). 56 ‘Abbott-Firestone curve’ , was named aer two researchers in the USA working in the early days of surface topography – circa 1933. ey dened the ‘Bearing area fraction’ at a given height above the mean line as: ‘e proportional length of all plateaux which would result if the surface were abraded away, down to a level plane at that height’ (omas, et al., 1999). service function has little signicance. In order to mi- nimise the eect of a single peak on the Rmr curve, an articially-induced reference line is chosen to shi this line below the highest peak – as illustrated in Fig. 165b – this value now being expressed as a material ratio percentage (i.e. in this example the Rmr being at 45%). Specifying for example, an Rmr at the 5% refer- ence line (Fig. 165d), testies that the top 5% of the prole is not included as part of the calculation for the ‘material ratio’. e selection of the zero line beneath the highest measureable peak will be dependent on the topography of the associated peaks in the prole trace, but industrial practice suggests the reference level is usually set between 2% to 5%. .. Machined Surface Topography Tool nose insert geometry (Fig. 166a) plays a impor- tant role in the resultant machined surface topography of a turned component’s surface. Longitudinal turn- ing operations will leave the residual eects of this partial tool nose geometry on the workpiece surface as ‘machined cusps’ forming the dominant prole on the turned surface topography (Figs. 166b and 169). is geometry is a complex relationship of curved and linear inter-connected portions whose insert prole is ‘fashioned’ onto the turned surface – being apprecia- bly inuenced by the pre-selected feedrate (Fig. 166a). erefore, according to the ‘Shaw-model’ (1984, et al.) – being a somewhat ‘simplied geometry’ with- out chip-breakers present, with an enlarged view of the turning insert’s nose region (Fig. 166a and b), its resultant surface topography can be dened by three distinct insert-related factors, these are: 1. Nose radius – r = OT (i.e. illustrated in Fig. 166b), 2. End-cutting edge angle – denoted by C e (i.e. shown in Fig. 166a), 3. Side-cutting angle – denoted by C s (Fig. 166a). In eect, there are three discrete ‘turning-cases: I, II and III,’ that may occur when utilising the tool nose cutting insert geometry shown (Fig. 166a), when com- puting the theoretical peak-to-valley (R th ) surface tex- ture. When a very light D OC and its associated feedrate is imparted onto the workpiece’s surface, then ‘Case I’ conditions will be met – illustrated by the high-den- sity cross-hatched portion of the insert‘s geometry de- picted in Fig. 166a. e mathematics of the theoretical cusp height (R th ) in Fig. 166b, is given by the following expression: Machinability and Surface Integrity Figure 166. How the ‘residual inuence’ of the turning insert’s partial geometry combined with feedrate, aect the subsequent machined component surface topography . Chapter . on the prole (i.e. see Fig. 1 65) . e bearing area fraction Machinability and Surface Integrity Figure 1 65. Hybrid surface texture parameters – spacing and depth. [Courtesy of Taylor Hobson]. . roughness parameter: Ra. Machinability and Surface Integrity the point, that all of these two-dimensional surface pa- rameters can be classied into three distinct groupings and just some of these. production processes. Machinability and Surface Integrity Figure 162. Anticipated process ‘roughness’ and their respective grades. [Source: ISO 1302, 2001]. Chapter Figure 163. Surface texture