either entirely eliminating it, or at the very least, min- imising its aect on the overall machining process. Chatter during machining can result from a range of multifarious and oen linked-factors, they include: • Depth of cut (D OC ) – can be considered as the prin- cipal cause and, for the prospective control of chat- ter. e D OC delineates the chip width, acting as the feed-back gain 31 within the closed-loop cutting process, NB e machining processes ‘stability limit’ – be- ing the threshold between stable cutting and chat- ter – can be determined from trial-and-error by simply incrementally increasing the D OC until the commencement of chatter, then‘backing-o ’ at this level. e prediction of chatter’s onset can be found analytically, this value being based upon thorough knowledge of material stiness and cutting system dynamics. • Rotational speed – is probably the simplest param- eter to modify, thereby altering chatter and its as- sociated amplitude, NB e peripheral speed of either the rotating tool, or workpiece, aects the phase-shi between overlapping surfaces and its associated vibration regeneration. • Feed – for milling operations the feed per tooth de- nes the average uncut chip thickness (t), inuenc- ing the magnitude of the cutting process. Chatter is not unduly aected by the feedrate selected, but feed does have an eect on the predictable severity of vibration during machining, NB As no cutting force exists if the vibration oc- curs in the ‘Y’ direction – resulting in loss of con- tact between the tool and workpiece – the maxi- mum amplitude of chatter vibration will be limited by its feed. 31 ‘Gain’ , can be practically dened in the following way: ‘e ratio of the magnitude of the output of a system with respect to that of the input – the conditions of operation and measure- ments must be specied’ (Smith, 1993, et al.). • Cutting stiness (K s ) – is a material property con- nected to: shear ow stress; hardness, as well as work-hardening characteristics of the workpiece, this factor oen being referred to in a metaphorical sense of its material’s machinability characteristics, NB Materials that might oer poorer comparative machinability, for example titanium, require con- siderably higher cutting forces leading to a greater displacement in the ‘Y’ direction and as such, oer a less stable cutting action. • Width of chip (total) – is equivalent to the product of the D OC multiplied by the number of cutting edges engaged in the cut. Furthermore, the total cut width will inuence the stability of the cutting process, NB At a preset D OC corresponding to that of the ‘stability limit’ , increasing the number of engaged cutting edges, will result in chatter, or vice-versa. • Cutting tool geometry – inuences both the direc- tion and the magnitude of the cutting force, in particular the quantity of the force component in the modulation direction ‘Y’. So, an increased force occurring in the ‘Y’ direction, causes amplied dis- placement and vibration at 90° to the surface, creat- ing ideal conditions for chatter. Other cutting insert geometrical factors that can inuence the cutting stability include the following: – Back rake angle (α) – as it is inclined to a more positive angle, the length of the commencement of the shearing zone decreases, this in turn, re- duces the magnitude of the cutting force (F c ). As the back rake inclination becomes larger, then this directs the cutting force in a more tangential manner, thereby reducing the force component in the ‘Y’ direction – creating improved stability at higher speeds, NB An insucient feedrate in comparison to the insert edge radius produces a less ecient cutting action, with more tool deection and reduced ma- chining stability. – Clearance angle – reduction (γ) – has the eect of increasing the frictional contact at the inter- face between the tool and workpiece, possibly having a process damping eect. is potential stabilising eect could be the result of energy Machinability and Surface Integrity dissipation – heat transformation, which could result in decreased tool life, with the superu- ous eect of thermal distortion of the machined part, or an increase in the workpiece’s heat-af- fected zone (HAZ), NB On a newly-tted cutting insert, if initial wear occurs, this can sometimes have a stabilising eect for the onset of chatter. – Nose radius – size, insert shape – diamond tri- angular, square, round, plan approach angle – positive, neutral, negative – all inuence the area of the chip shape and its corresponding ‘Y’ direction. e orientation of the modulation direction ‘Y’ toward a dynamically more-rigid direction angle, allows a decrease in vibrational response, giving greater overall process stability – having notably less chattering tendencies. As machining process stability is a direct result of characteristics of dynamic force displacement between both the workpiece and the cutting insert, all of the various factors of a machining system: machine tool; spindle; tooling; workpiece; workholding – in varying degrees, can inuence chatter. To increase process sta- bility of the machining system, it is necessary to maxi- mise the dynamics, this being the overall product of its static stiness and damping capacity. Further, machin- ing stability can be increased by utilising tooling with the greatest possible diameter with the minimum of tool overhang. By way of a caution concerning chatter frequency, this normally occurs near the most exible vibrational mode of the machining system. .. Stability Lobe Diagrams In Fig. 157c, a ‘Stability lobe diagram’ (SLD) is de- picted, which relates to the: total cut width that can be machined, to the tooling’s rotational speed, for a speci- ed number of cutting inserts. For example referring to the: Degarmo, et al. (2003) diagram, suppose the total width of cut was maintained below a minimum level 32 , then the process stability would exhibit ‘speed 32 If the total cut width was maintained below a minimum level, in practical terms this would be of limited value for many ma- chining systems. independence’ , or an ‘unconditional stability’. Hence, at relatively slow speeds an increased stability can be achieved within the process damping region – as shown. e ‘conditional stability’ lobe regions of the diagram, permit an increased total cut width (i.e the D OC x number of cutting edges, these being engaged in the cut) at dynamically preferred speeds, at which the phase-shi ‘ε’ between overlapping, or consecutive cutting paths approaches zero. In Fig. 157c, stability lobe number ‘N’ refers to the complete vibration cycles existing between overlapping surfaces. Moreover, the higher speeds correspond to lower lobe numbers, pro- viding the utmost potential increase in the total cut width and material removal rate – this being due to the greater lobe height and width. If the total cut width exceeds the stability threshold – even assuming that the cutting process is operating at the desired speed, chatter will occur. So, the larger the total cut width above the ‘stability limit’ , the more unstable and ag - gressive the chatter vibration becomes. Referring to the diagrammatic representation of the SLD on the graph in Fig. 157c, if a chatter con- dition arises, such as that found at point ‘a’ , the ro- tational speed is attuned to the initial recommended speed (i.e. when ‘N=1’), resulting in stable machining at point ‘b’ on this diagram. e D OC can be incremen- tally increased until the onset of chatter again – as the threshold stability is crossed at point ‘c’. By utilising a hand-held ‘speed analyser’ 33 whilst the chatter contin- ues – under the previously-selected operating condi- tions, this will result in the ‘analyser’ giving a modied speed recommendation that corresponds to point ‘d’. Now, if required, the D OC can be progressively incre- 33 ‘Speed analysers’ , are normally hand-held devices that pro- duce dynamically-favoured speed recommendations and are commercially available. Such ‘speed analyser’* equipment when utilised for a cutting process, can show the relative mo- tion between the tooling and the workpiece and recommends the appropriate speed to avoid chatter-eects. *‘Speed analysers’ can be successfully used for many industrial applications, such as those involving: High-speed; in-chip, hardened-die machining; multi-point cutting operations – milling, etc.; Turning and boring operations. ese ‘speed anal- ysers’ can also be employed for workpiece compositions rang- ing from ductile metals (i.e. aluminium and steel grades) and brittle materials (i.e. cast irons and brasses, etc.), together with some non-metallics (plastics, etc.) and composite materials (carbon bre, etc.). Chapter mentally increased to point ‘e’ 34 – this being a ‘safe- limit’ for the optimum machining operation. 7.4 Milled Roundness – Interpolated Diameters Circular features such as bosses, circular rebates, etc., can be CNC milled by utilising a specic word-ad- dress ‘circular interpolation’ 35 command. is CNC function creates precise and accurate circular control in two slideways simultaneously, while the milling cutter mills around the workpiece, as depicted in Fig. 158. Here, the milling cutter’s rigidity plays an impor- tant role in the quality of the nal machined feature, this being based upon the ‘rigidity square rule’ 36 . e deected milling cutter illustrated in Fig. 158-right, having lack-of-rigidity will produce some unwanted eects on the nal milled part. Cutter deection not only introduces the potential for chatter vibration, but if used to mill up to square shoulder, its deection distorts the component geometry and introduces har- monic variation to the circular interpolated feature. So that minimal change takes place in a milled prole, it is advisable to keep to cutter lengths having short 34 Generally-speaking, it is not advisable to attempt to maintain both the D OC and the total cut width at the stability thresh- old , because any variation in the: workpiece aecting its cut- ting stiness ‘K s ’; speed errors; or perhaps small changes in the overall dynamic characteristics of the machining system, could result in crossing the stability limit, creating severe chatter. For example, in a milling application, the amplitude of chatter vibration can be limited by a provisional feed per tooth reduction , until an established and desired speed has been achieved oering a stable D OC . 35 ‘Circular interpolation’ , is a block of entered information di- recting the CNC system to cut, either an arc, or a circle, (e.g. G02 – in a clockwise, or G03 anti-clockwise direction). 36 ‘Rigidity square rule’ – for milling cutters states: ‘Cutter rigid- ity decreases by the ‘square’* of the distance from the holder’ (Smith, 1993, et al.). *For example, if a cutter ‘stood-out’ from its respective tool- holder by 50 mm to mill a circular feature (Fig.158 – le), then, if all other machining conditions remained the same and, then cutter was replaced by one of 100 mm long (Fig. 158 – right), it would now be 4 times less rigid, causing serious tool deec- tion. stand-o distances, conducive with correct and cur- rent operational practices. ere are several distinct problems involved in the milling high-quality circular interpolated features and, a slight digression into basic machine tool induced-er- rors is necessary to clarify the circumstances for the problems exhibited in Fig. 159. Most of today’s ma- chine tools have what is termed ‘orthogonally-orien- tated axes’ 37 and in the case of the popular three-axis vertical machining centre congurations, if the axes have not been recently calibrated, then considerable ‘error’ 38 can be introduced into the nal milled part features. It has been well-proven that a machine tool equipped with three orthogonal sideways: ‘X-axis’; ‘Y-axis’ – in the horizontal plane, together with the ‘Z-axis’ – in the vertical plane, can introduce up to 21 kinematic ‘errors’ into the cutting process. e kine- matics for any machine tool are quite complex, when it has the ability to provide motion to all its axes simulta- neously, although these errors are oen small, they are 37 ‘Orthogonally-orientated axes’ , (is briey mentioned in Foot- note 2) refers to the fact that each axis is positioned at 90° with respect to each other, oen situated on top of another axis. For example, on a typical 3-axis vertical machining centre, the ‘Y-axis’ sits on top of the ‘X-axis’ , but at right-angles to it, conversely, the ‘Z-axis’ is situated at 90° to these axes – hence the term ‘orthogonal’. NB Non-orthogonal machine tools exist, oen having com- plex ‘kinematics’* between ve and six axes. erefore with these machine tools, in order to machine (i.e. mill) a straight- line. all the axes must be in synchronised control to achieve this linear action. *Kinematics, comes from the Greek word ‘Kinesis’ , which means ‘Motion’. It can be dened as: ‘e study of motion with- out regard for the cause‘ (Lombardi, 2001). In machine tool terminology, it refers to the translational eects of both lin- ear and angular motions. It is principally concerned with the eects of the ‘degrees of freedom’ for a ‘free-body’ in three-di- mensional space (also see: Footnote 47, in Chapter 3). 38 ‘Error’ is now not considered as an appropriate metrological term for any form of calibration, the recommended term to- day, is: ‘uncertainty’*. *‘Uncertainty’ , has been simply dened as: ‘e doubt that exists about the result of any measurement’ (Bell/NPL, 1999). is is why today, uncertainty in measurement is a combina- tion of many factors, some physical, while others are induced. Hence, another term, along with all of these uncertainty fac- tors has been coined, which is its ‘Uncertainty budget’ – this being a simple mathematical calculation, based upon a sum- mary of these uncertainty calculations. Machinability and Surface Integrity Figure 158. The eect of increased milling cutter length on the resultant circular interpolated prole on the workpiece. Chapter Figure 159. The generated errors produced when circular interpolating at high feedrates when high-speed machining. Machinability and Surface Integrity but signicant ‘errors’ , which can be said to be simplis- tically produced as a result of: • Linear motions (six) – created by the displacement of the forward-and-backward motion of the X-, Y- and Z-axes slideway movements, introducing par- ticular non-linearities into the slideway position- ing, • Rotational motions (three) – yaw, pitch and roll for each axis. All of these partial rotational motions can be practically-described in the following manner: • Yaw is the side-to-side ‘crabbing-motion’ along the slideway, NB ‘Yaw’ is normally the result of too much clear- ance (i.e. ‘slop’) in the adjacent slideway members. • Pitch introduces a backward-and-forward rock- ing (pitching) action normal to the slideway, as the moving element traverses along the axis, NB ‘Pitching’ is probably due to the ‘prole/wavi- ness’ (i.e. long-frequency eects) in its respective slideway. • Roll is the clockwise-and-anticlockwise rotational motion along the slideway. NB ’Roll’ could be introduced by two ‘adjacent ways’ situated on each slideway, but not being coin- cident with respect to each other (i.e. laying in the same respective plane), causing a limited pivoting action – along the ‘line-of-sight’ of the axis as it tra- verses along its length. • Squareness (three) – these ‘errors’ occur due to the fact that each axis may not be at 90° (i.e. square) to one another. ese types of 21 ‘kinematic machine-induced er- rors’ can be appreciably reduced by the application of calibration through laser-based techniques. To a lesser extent, these ‘errors’ can be minimised via ballbar ar- tifact-based methods, oering a quick ‘health-check’ by either static, or dynamic assessment techniques. e results of either the laser, or ballbar, can be fed back into the machine’s CNC controller for dynamic corrections as cutting takes place, oering a consid- erable improvement in the machine’s subsequent ac- curacy and precision. e above machine tool calibra- tion techniques are somewhat beyond the scope of the present discussion, the same could be said for ‘ther- mally-induced errors’ , however, they can also inuence the machined part surface and the machine tool’s pro- ling abilities. Moreover, ‘error-mapping techniques’ and sophisticated in-process control by an associated ‘dynamic error compensation system’ , have been shown to extensively reduce the eects of the ‘variety of er- rors’ that can be present on the machine tool, but once again, these topics are mentioned only for further re- search applications – as necessary. e circular interpolated milled prole shown in Fig. 159, shows signicant departures from roundness of the milled workpiece, which is a function of most of the previously discussed kinematically- and thermally- induced machine tool ‘errors’ , together with the possi - bility of some ‘load-induced errors’. is diagrammatic representation (i.e. Fig. 159), indicates that several ‘errors’ on the milled circular interpolated prole are present. At relatively slow simultaneous feeding-mo- tions of the two axes (‘X-’ and ‘Y-axis’), it will generate a reasonable facsimile of the required circular feature. However, then by somewhat increasing this milled in- terpolation speed, the apparent roundness will appre- ciably degrade, the reasons for this degradation, might be the result of: • Servo-spikes – these unwanted eects occur at the ‘axis transition points’ 39 at their respective 90° angu- lar intervals, oen termed ‘quadrant-points’ , • Back-lash – possibly resulting from any form of axis reversals, originating from the recirculating ballscrews 40 , creating a slight ‘o-set’ , or ‘mismatch’ at the axis transition points, • Servo-errors – when both axes are simultaneously moving, their respective linear speed should be 39 ‘Axis transition points’ , are where the ‘servo-spikes’ occur. ey result from a reversal of one of the axes at this angular position and, its associated motor power-surge creating this ‘spike’. Normally, the ‘spike’ is associated aerward by a cor- responding, but very small localised slack here, as axis take-up begins once more at these ‘quadrant-points’ on the circular- interpolated feature (i.e. see the inset and magnied diagram in Fig. 159). 40 ‘Recirculating ballscrews’ , are not supposed to have any ap- preciable back-lash present, as they are normally pre-stressed by applying loads by the application of either: tension-, or compression-shimming. However, as the pitch of any the screw has minute errors present, these are usually ‘mapped-out’ by the original machine tool builder – using the recognised In- ternational Standard laser-calibration techniques. Although, once the machine tool has been operating for sometime and either local ballscrew-wear occurs, or perhaps the machine has had the occasional ‘tool-crash’ , this can introduce and af- fect both its pitching- and back-lash-errors. Chapter perfectly matched, allowing either a partial arc, or circular feature to be reproduced. If non-syn- chronised motion occurs, oen termed ‘servo-mis- match’ 41 between these two axes, then an elliptical prole – usually inclined at an 45° angle occurs, • Squareness – when orthogonal (squareness) is not maintained between the two interpolating axes, then the net result will look similar to that of a milled angular elliptical prole shape, which is un- aected by the selected circular interpolation rota- tional direction. Considerably more machine tool-induced factors can aect a milled circular interpolated prole. ese ‘er- rors’ can be found, isolated and then reduced by di- agnostically interrogation by using dynamic artefacts, such as the ballbar. Ballbars and their associated in- strumentation can not only nd the sources of error, they can prioritise their respective magnitudes – to show where the main ‘error-sources’ occur, then in- stigate any feed corrections into the CNC controller to nullify these ‘machine-induced errors’. As a result of eliminating such ‘error-sources’ , this enables the milled circular contouring and overall performance to be appreciably enhanced. 7.5 Machined Surface Texture Introduction to Surface Texture Parameters When a designer develops the features for a component with the requirement to be subsequently machined utilising a computer-aided design (CAD) system, or by using a draughting head and its associated draw- ing board, the designer’s neat lines delineate the de- sired surface condition, which can be further specied by the requirement for specic geometric tolerances. In reality, this designed workpiece surface condition cannot actually exist, as it results from process-in- duced surface texture modications. Regardless of the method of manufacture, an engineering surface must have some form of ‘topography, or texture’ associated 41 ‘Servo-mismatch’ , can oen be mistaken for a ‘squareness er- ror’ , but if the contouring interpolation direction is changed, from G02 (clockwise) to G03 (anti-clockwise) rotation, then an elliptical prole will ‘mirror-image’ (‘ip‘) to that of the op- posite prole – which does not occur in ‘squareness errors’. with it, resulting from a combination of several inter- related factors, such as the: • Inuence of the workpiece material’s microstruc- ture, • Surface generation method which includes the cut- ting insert’s action, associated actual cutting data and the eect of cutting uid – if any, • Instability may be present during the production machining process, causing induced chatter, result- ing from poor loop-stiness between the machine- tooling-workpiece system and chosen cutting data, • Inherent residual stresses within the workpiece can occur, promoted by internal ‘stress patterns’ 42 – causing latent deformations in the machined com- ponent. From the restrictions resulting from a component’s manufacture, a designer must select a functional sur- face condition that will suit the operational constraints for either a ‘rough’ , or ‘smooth’ workpiece surface. is then raises the question, posed well-over 25 years ago – which is still a problem today, namely: ‘How smooth is smooth?’ is question is not as supercial as it might at rst seem, because unless we can quantify a surface accurately, we can only hope that it will function cor- rectly in-service. In fact, a machined surface texture condition is a complex state, resulting from a combi- nation of three distinct superimposed topographical conditions (i.e. as diagrammatically illustrated Fig. 160a), these being: 42 ‘Stress patterns’ , are to be expected in a machined compo- nent, where: corners, undercuts, large changes in cross-sec- tions from one adjacent workpiece feature to another, etc., produce localised zones of high stress, having the potential outcome for subsequent component distortion. ‘Modelling’ a component’s geometry using techniques such as: nite ele- ment analysis (FEA), or employing photo-elastic stress analy- sis* models or similar simulation techniques, will highlight these potential regions of stress build-up, allowing a designer to nullify, or at worst, minimise these potential undesirable stress regions in the component’s design. *Photo-elastic stress analysis displays a stress-eld, normally a duplicate of the part geometry made from a thin two-dimen- sional (planar) nematic liquid crystal, or more robustly from a three-dimensional Perspex model, which is then observed through polarised light source. is polarised condition, will highlight any high-intensity stress-eld concentrations in the part , which allows the ‘polarised model’ to be manipulated by applying either an un-axial tension, or perhaps a bi-axial bending external stress to this model, showing dynamically its potential stress behaviour during its intended in-service con- dition. Machinability and Surface Integrity Figure 160. Surface texture comprises of: ‘long-’, ‘medium-’ and ‘short-components’, together with the ‘direction of the dominant pattern’ – superimposed upon each other. [Courtesy of Taylor Hobson] . Chapter 1. Roughness – comprising of surface irregularities occurring due to the mechanism of the machining production process and its associated cutting insert geometry, 2. Waviness – that surface texture element upon which roughness is superimposed, created by fac- tors such as the: machine tool, or workpiece deec- tions, vibrations and chatter, material strain and other extraneous eects, 3. Prole – represents the overall shape of the ma- chined surface – ignoring any roughness and wavi- ness variations present, being the result of perhaps the long-frequency machine tool slideway errors. e above surface topography distinctions tend to be qualitative – not expressible as a number – yet have considerable practical importance, being an estab- lished procedure that is functionally sound. e com- bination of roughness and waviness surface texture components, plus the surface’s associated ‘Lay’ 43 are shown in Fig. 160a. e ‘Prole’ is not depicted, as it is a long-frequency component and at best, only its partial aect would be present here, on this diagram. e ‘Lay’ of a surface tends to be either: anisotropic, or isotropic 44 in nature on a machined surface topog- raphy. When attempting to characterise the potential functional performance of a surface, if an anisotropic ‘lay-condition’ occurs, then its presence becomes of vital importance. If the surface texture instrument’s stylus direction of the trace’s motion over the assessed topography is not taken into account, then totally mis- representative readings result for an anisotropic sur- face condition occur – as depicted in Fig. 160b. is is not the case for an isotropic surface topography, as relatively uniform set of results will be present, regard- less of the stylus trace direction across the surface (i.e. 43 ‘Lay’ , can simply be dened as: e direction of the dominant pattern’ (Dagnall, 1998). 44 ‘Anisotropic, or isotropic surfaces, either condition can be in- dividually represented on all machined surfaces. Anisotropy, refers to a surface topography having directional properties, that is a dened ‘Lay’ , being represented by machined feed- marks (e.g. turned, shaped, planed surfaces, etc.). Conversely, an isotropic surface is devoid of a predominant ‘Lay’ direc- tion, invariably having identical surface topography charac- teristics in all directions (e.g. shot-peening/-blasting and, to a lesser extent a multi-directional surface-milling, or a radially- ground surface, etc.). see Fig. 161a – for an indication of the various clas- sications for ‘Lay’). Returning once more to Fig. 160b, as the stylus trace obliquity changes from trace ‘A’ , inclining to - ward trace ‘E’ , the surface topography when at ‘E’ has now become at, giving a totally false impression of the true nature of the actual surface condition. If this machined workpiece was to be used in a critical and highly-stressed in-service environment, then the user would have a false sense of the component’s potential fatigue 45 characteristics, potentially resulting in ei- ther premature failure, or at worst, catastrophic fail- ure conditions. In Fig. 162, the numerical data (ISO 1302:2001), has been developed to establish and de- ne relative roughness grades for typical production processes. However, some caution should be taken when utilising these values for control of the surface condition, because they can misrepresent the actual state of the surface topography, being based solely on a derived numerical value for height. What is more, the ‘N-number’ has been used to ascertain the arithmetic roughness ‘Ra’ value – with more being mentioned on this and other parameters shortly. e actual ‘N-value’ being just one number to cover a spread of potential ‘Ra’ values for that production process. Neverthe- less, this single numerical value has its merit, in that it ‘globally-denes’ a roughness value (i.e.‘Ra’) and its accompanying ‘N-roughness grade’ , which can be used by a designer to specify in particular a desired surface condition, this being correlated to a specic production process. e spread of the roughness for a specic production process has been established from experimental data over the years – covering the maxi- mum expected ‘variance’ 46 – which can be modied 45 ‘Fatigue’ , can be dened as: ‘e process of repeated load, or strain application to a specimen, or component’ (Schaer, et al., 1999). Hence, any engineering component subjected to repeated loading over a prescribed time-base, will normally undergo either partial, or complete fatigue. 46 ‘Variance’ , is a statistical term this being based upon the standard deviation, which is normally denoted by the Greek symbol ‘σ’. us, variance can be dened as: ‘e mean of the squares of the standard deviation’ (Bajpai, et al., 1979). us, σ = √Variance, or more specically for production op- erations: � s n n j= x j ¯ x *s = the standard deviation of a sample from a production batch run. Machinability and Surface Integrity depending upon whether a ne, medium, or coarse surface texture is obligatory. Due to the variability in any production process being one of a ‘stochastic out- put’ 47 , such surface texture values do not reect the likely in-service performance of the part. Neither the surface topography, nor its associated integrity has been quantied by assigning to a surface representa- tive numerical parameters. In many instances, ‘surface engineering’ 48 is utilised to enhance specic compo- nent in-service condition. It was mentioned above that in many in-service engineering applications the accompanying surface texture is closely allied to its functional performance, predominantly when one, or more surfaces are in mo- tion with respect to an adjacent surface. is close proximity between two mating surfaces, suggests that the smoother the surface the better, but this is not nec- essarily true if the surfaces in question are required to maintain an ecient lubrication lm between them. e apparent roughness of one of these surfaces with respect to the other, enables it to retain a ‘holding- lm’ in its associated topographical ‘valleys’ 49 . While another critical factor that might limit the designer’s choice of the smoothness of an engineering surface’s selection, is related to its production cost (i.e. see Fig. 161b). erefore, if the designer requires a very smooth machined surface, it should be recognised that its manufacturing time is considerably longer – so its respective cost will be greater to that of a rough sur- face, this being exacerbated by a very close dimen- sional tolerance requirement. 47 ‘Stochastic processes’ , are dened as: ‘A process which has a measurable output and operating under a stable set of condi- tions which causes the output to vary about a central value in a predictable manner’ (Stout, 1985). 48 ‘Surface engineering’ , is applying suitable discrete technolo- gies to create surface lms (e.g. 10 to 100 nm thick), or by ma- nipulating the surface atomic layers (e.g. 2 to 10 atomic layers, approximately 0.5 to 3 nm), to enhance the ‘engineered’ sur- face condition (i.e. Source: Vickerman, 2000). 49 ‘Surfaces’ , are recognised to have topographical features that mimic the natural world. So a regular/irregular engineering surface can exhibit both peaks and valleys, not unlike moun- tainous terrain. .. Parameters for Machined Surface Evaluation In order that a machined workpiece’s surface texture can be determined using stylus-based (two-dimen- sional) instrumentation, three characteristic lengths are associated with this surface’s prole (i.e. see Fig. 163a), these are: 1. Sampling length 50 – is determined from: the length in the direction of the X-axis used for identifying the irregularities that characterise the prole under evaluation. erefore, virtually all surface de- scriptors (i.e. parameters) necessitate evaluation over the sampling length. Reliability of the data is enhanced by taking an average of the sampling lengths as depicted by the evaluation length shown in Fig. 162a. Most of today’s stylus-based surface texture instruments undertake this calculation au- tomatically, 2. Sampling length – can be established as: the to- tal length in the X-axis used for the assessment of the prole under evaluation. From Fig. 163a, this length may include several sampling lengths – typi- cally ve – being the normal practice in evaluating roughness and waviness proles. e evaluation length measurement is the sum of the individual sampling lengths (i.e. it is common practice to em- ploy a 0.8 mm sampling length for most surface texture assessments), 3. Traverse length – can be dened as: the total length of the surface traversed by the stylus in mak- ing a measurement. e traverse length will nor- mally be longer than the evaluation length (i.e. see Fig. 163a), this is due to the necessity of allowing ‘run-up’ and ‘over-travel’ at each end of the evalua- tion length. ese additional distances ensure that any mechanical and electrical transients, together lter edge eects are excluded from the measure- ment. 50 ‘Sampling length’ , is oen termed ‘Meter cut-o ’ , or simply the ‘cut-o ’ length and its units are millimetres. e most common cut-os are: 0.25, 0.8, 2.5, 8.0, 25.0 mm. e 0.8 mm sampling length will cover most machining production pro- cesses. In any surface texture evaluation, it is essential that the cut-o is made known to the Inspector/Metrologist reviewing this surface topographical data. Chapter . behaviour during its intended in-service con- dition. Machinability and Surface Integrity Figure 160. Surface texture comprises of: ‘long-’, ‘medium-’ and ‘short-components’, together with the ‘direction. energy Machinability and Surface Integrity dissipation – heat transformation, which could result in decreased tool life, with the superu- ous eect of thermal distortion of the machined part, . roughness and waviness surface texture components, plus the surface s associated ‘Lay’ 43 are shown in Fig. 160a. e ‘Prole’ is not depicted, as it is a long-frequency component and at best,