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(Fig. 153a–c). e inuence of this irregular harmonic rotational belt-driven rotation can be gained from the schematic representation shown in Fig. 153d, where a repeating-series of ‘tumbling three-lobed harmonic’ geometric shapes are reproduced on the workpiece. e irregular, but periodic nature of the rotational action of the belt-driven headstock is reproduced on the workpiece by a series of kinematic combinations of headstock rotation and linear motion supplied by the longitudinal feed of the cutting tool along the part (Fig. 153d). If a direct-drive headstock conguration is utilised (Fig. 153e), then there is virtually no har- monic inuence associated from the machine, so more consistent turned components result. Returning to Fig. 152, the overall machine-tool- workpiece system, can be isolated to consider the simple eect of a cantilevered cutting tool that is in- adequately supported, or the unlikely occurrence of too small a cross-sectional area – making it somewhat ‘under-strength’. e main cutting force in turning op - erations is the tangential force (i.e. see Fig. 19), it re- sults from several factors, such as: • Resistance to rotation – caused by the workpiece material’s inherent shear strength, • Undeformed chip thickness – resulting from the ra- dial D OC selected, • Orientation of cutter rake angle geometry – this being a combination of either a positive, neutral, or negative rakes, plus to a lesser degree, the eect of shape and size of the tool nose radius, • Feedrate – in combination with D OC , will heavily inuence the size of the eective chip thickness and play a dominant role in the resulting surface tex- ture. In the upper diagram in Fig. 152, the tangential force is simplistically shown contacting the cutting insert at the point. e application of the cutting force here, causes a large bending moment to occur at the pivot point – as shown. e resultant dynamic action of this eect, is depicted in the lower diagram of Fig. 152, where the tool has been elastically deected in a down- ward manner by this bending moment. Moreover, as the resistance to deection increases with the tool’s downward direction, this intensies the pressure from the inherent tool-body mechanical strength, enabling a certain degree of recovery, therefore there is a partial upward motion of the tool. is cyclical upward, then downward tool point motion is repeated at a periodic medium-frequency, causing a sinusoidal motional ef- fect with this being harmonically reproduced on the turned surface. High-frequency harmonics can also be Table 10. The harmonic behaviour related to either the component manufacturing process, or its measurement Harmonic: Cause: 1 st (1 upr) Function of measurement – only caused by the setting-up error on the instrument being used to measure the departures from roundness. The amplitude of this harmonic is equal to the eccentricity of the part, relative to the spindle axis of the roundness instrument. 2 nd (2 upr) Function of measurement, or manufacture – this aspect of harmonics is generally termed ovality and can be caused either by a setting-up error of the roundness instrument, or the part being machined out-of-square to its axis of rotation. 3 rd –7 th Function of manufacture – these harmonics are normally introduced by the work-holding technique during manufacture. By way of illustration, if a three-jaw chuck were used to hold a relatively delicate part and excessive clamping force was employed, then upon machining and subsequent workpiece removal a three-lobed part would be the result. 15 th -upwards Function of material and manufacture – this aspect of harmonic behaviour is usually introduced to the part by either machine tool instability (i.e. self-excited vibration – chatter), or by the reaction of the materials used in the component’s manufacture – cutting insert/toolholder, lubricant – if any used. Upr: undulations per revolution NB Higher harmonics may be the result of instrument noise, or vibration. [Courtesy of Taylor Hobson] . Machinability and Surface Integrity Figure 153. By utilising turning centre headstocks with direct-drive spindles – for ‘harmonic supres- sion’, a signicant improvement in machined roundness will result. [Courtesy of Yamazaki Mazak] . Chapter superimposed onto the medium-frequency harmon- ics, this aspect can be shown to good eect by a ‘power spectrum analysis’ 22 of the harmonic behaviour during machining. For a simple turning operation, the resultant cutting forces occur from the consequential combination of: a workpiece material’s shear strength, its undeformed chip thickness, the cutting insert geometry and ac- companying nose radius, which has a signicant aect on the harmonic ‘departures from roundness’ of the turned part. So that the eect of these variables in the cutting generation process can be seen, while simplify- ing the discussion, only external-diameter operations will be mentioned concerning these process-based roundness relationships – in the following section. .. Turned Roundness – Harmonics and Geometrics A typical operation on a either an engine-/centre-lathe, or a turning centre, is schematically illustrated in Fig. 154. is involves a longitudinal turning process – the workpiece being shown as partially completed – us- ing a ‘light-turning and nishing cutting insert’ , as it progresses along the turned part. Here, the turning application has a long and slender workpiece this be- ing held in a work-holding device: chuck, or collet – at the headstock end, with further support 23 supplied by 22 ‘Power spectrum analysis’ , is a useful aid in process monitor- ing of the cutting capabilities – giving a good interpretation of the anticipated surface topography (i.e its ‘micro-terrain’). A major advantage of utilising the ‘power spectrum’ as a diag- nostic aid, is that it can separate-out any process-related tool problems. NB More details concerning the application of ‘power spec- trum analysis’ can be obtained from the References by either Whitehouse (1997), or Smith (2002). 23 ‘Programmable and xed steadies’ are oen used to give addi- tional support to the long and slender parts, to minimise ‘bar- relling eects’ – created by increased tool push-o the further away the tool’s longitudinal distance becomes from the inu- ence of the tailstock/headstock. Hence, the part has smaller turned diameters toward its ‘supports’ steadily increasing in diameter toward its centre, then reducing again – creating a ‘barrel-like prole’ along the entire turned bar’s length. either a ‘dead-’ , or ‘rotating-centre’ 24 – at the tailstock end. As the orthogonally-oriented cutting insert (i.e. having a zero-plan approach angle) turns along the workpiece, a ‘moving step’ is seen to be present as the ‘emerging diameter’ occurs – to its set dimensional size (Fig. 154). If a very high quality toleranced part is to be turned, then it is desirable to review the operation more critically, as some unexpected and unwanted features may be present in the nal machined com- ponent. As the turning insert has an orthogonal ori- entation to the axis of rotation of the part (Fig. 154), it might be thought that no radial force component occurs, but this is not the case, as the tool nose radius can create a radial force aecting the turned surface. e radial force has little eect on the part’s harmon- ics when close to the tailstock as shown by the cross- sectional harmonic eect indicated in section ‘C-C’ (Fig. 154). Once the cutting insert has progressed some distance along the workpiece, the contributing and supporting inuence by the tailstock is lessened and the eect of this radial force component increases, as exhibited by section ‘B-B’ , this being amplied still further in section ‘A-A’. Here (i.e. section ‘A-A’), the harmonic departures from roundness are signicant, a fact that has been recognised by precision turners for many years. Experienced machinists when turn- ing parts having long length-to-diameter ratios, will t either a ‘xed-steady’ , or more preferably a ‘moving- steady’ close to the tool cutting zone – on the opposite side of the workpiece – to counteract ‘push-o’ by the radial force, while minimising component eccentric- ity/run-out. If twin-turrets (i.e. upper and lower) are tted to turning centres, then ‘balanced turning’ 25 can be utilised as an alternative machining strategy. ere is a direct link between cutting forces and the geometric shape of the insert, this eect being illus- 24 ‘Rotating centres’ , can introduce their own eccentric error into the turning process, as they are less rigid than their ‘dead-cen- tre’ counterparts, but the latter, has a rotational speed restric- tion – otherwise ‘dead-centre burn-out’ is likely and is there- fore not practicable for high-production volume demands. 25 ‘Balanced turning’ , situates one cutting edge slightly ahead of the other in their respective opposing turrets. In this manner, the radial force components for each cutting insert have the eect of ‘virtually’ cancelling each other out, allowing long and slender workpieces to be successfully turned. A produc- tion bonus being the removal of greater workpiece material stock per pass. Machinability and Surface Integrity trated in Fig. 155. In these diagrams a simplistic repre- sentation for a range of cutting insert proles is shown and for clarity, the tangential force has been excluded, with just the axial and radial force components indi- cated for each type of cutting insert shape. Assuming that the overall cutting data is identical in each case (i.e. the same: rotational speed, feedrate, D OC , insert rake angle, plus workpiece material), then the only variable in the longitudinal turning process here will be the cutting insert shape its orientation. e com- ponent cutting forces – axial and radial, will vary for each tool prole in their respective magnitudes, due Figure 154. Machined roundness is inuenced by a number of factors: unbalanced cutting forces, non-integral headstock and lack of support on slender/long workpieces . Chapter to the variation in plan approach angles. In the case of the orthogonal insert (0°) plan approach angle, the ax- ial force dominates with virtually no radial force com- ponent present, this axial force being directly linked with the feedrate. e displayed prole chart for this harmonic roundness trace (i.e. section on ‘A-A’), for the 0° plan approach angle, shows virtually negligible harmonic eects. If a triangular-shaped cutting insert geometry was selected, in this case having an 15° plan approach, here there is a slight reduction in the axial force component and a corresponding increase in its radial counterpart. is slight increase in the radial Figure 155. Turned roundness can be signicantly aected by the insert shape, its approach angle – which aects cutting forces – resulting in harmonic out-of-roundness . Machinability and Surface Integrity force, in combination with a marginally longer cut- ting edge being in contact with the workpiece’s ‘tran- sient surface’ 26 , leads to a slight increase in the har- monics on the displayed prole chart (‘B-B’). As the obliquity of the insert’s plan approach angle increases, as depicted by the square-shaped cutting insert, being inclined at an angle of 45°, then the axial and radial force components equalise. Here, the considerable radial force component has a signicant eect on the displayed prole trace, as illustrated by the section at ‘C-C’ , where the harmonics have increased, but with a notable vibrational tendency superimposed onto this primary harmonic. is increase in vibration during turning, is the result of two noteworthy factors: rstly, the length of the transient surface has increased – with this square insert’s greater plan approach angle; sec- ondly, as a result of this rst condition of increased obliquity, the radial force aects workpiece rigid- ity, which is compromised, leading to an exacerbated turned part surface roundness and accompanying chatter-marks. Finally, when turning with a round insert geometry, this will lead to a vast increase in the radial force com- ponent, which in turn may cause signicant harmonic out-of-roundness, if a very rigid set-up is not utilised. In this case, the round insert’s displayed prole trace, shows evidence of a signicant increase in vibration – chatter – present, which has a dramatic eect on the prole of primary harmonic (section on ‘D-D’) – more will be said on the subject of ‘chatter-marks’ on the component’s surface shortly. e rationale for this notable harmonic amplication when using round in- serts is the product of several interrelated factors. e transient surface in contact with the round/curved prole has been markedly increased, together with the plan approach at the tangency position – with respect to the workpiece – being at a maximum; thus, the combination these two factors leads to a momentous deterioration in workpiece rigidity and as a result here, the vibration will especially increase. 26 ‘Transient surface’ , can be dened as: ‘e part of the surface formed on the workpiece by the cutting edge and removed dur- ing the following cutting stroke, [by the next] revolution of the tool, or workpiece’ (Boothroyd, 1975). NB In the case thread-turning operations, the transient ank’s surface only remains until the next pass of the screw-cutting insert obliterates it, or until the nal thread depth is reached. If a large volume of workpiece stock has to be re- moved in a series of roughing cuts, a strong insert is necessary, therefore the problem associated with the harmonic behaviour of cutting insert geometry be- comes of less importance. is latter fact allows either a square, or round cutting insert to be utilised due to their intrinsic strength and if vibration is a problem, then a ‘nishing cut’ with an insert having an 0° plan approach geometry would remove any probable sur- face chatter-marks. e case of turning with a round insert geometry is worthy of a closer investigation, as several factors in- uence the harmonic roundness of a workpiece turned with its curved prole. For example, let us consider several conditions for employing a standardised round insert and its subsequent aect on the harmonics of the turned part. If one assumes that an identical: ro- tational speed, feedrate and workpiece material was used, but having diering D OC ’s – to isolate variabil- ity in the turning process. In the rst example using a small D OC , the radial force component is large in com- parison to the axial force, but the harmonic workpiece roundness is not compromised here – as these forces are minute. Conversely, an extreme example of using a round insert might be when employing a larger D OC . Here, the radial force component has been reduced in comparison to the axial component, although the magnitude of these forces will be considerably greater than in the former case. e pressure exerted on the very long contact region at the transient curved sur- face, creates potential harmonics in the turned part as the resultant force has now signicantly increased. So, the inuence of an increased D OC , in combination with the round insert prole can create a very long contact region at the transient surface, thereby causing un- wanted harmonic eects on the turned surface. In Appendix 9, a visual impression is given of the principal techniques for roundness measurement and its assessment, together with some of the ltering ef- fects are highlighted. 7.3 Chatter in Machining Operations In the machining of metals, chatter (Fig. 156) is a form of self-excited vibration introduced by the closed-loop force-displacement response to cutting. e plastic de- formation during machining operations is always pro- Chapter ceeded by elastic deformation – the situation is akin to that of it acting somewhat like a ‘big spring’ 27 . More- over, the mechanism by which a cutting process dissi- pates energy is termed chatter and vibration, also this being a function of the workpiece’s rotational speed. Any chatter/vibration can clearly be heard as an un- wanted machining noise by an experienced machinist, who would then modify the speed accordingly. ere are a wide variety of causes for chatter, including the process-induced eects from the cutting forces, which may be the result of changes in: the cutting velocity; chip cross-sectional area; tool/chip interface friction; BUE, variations in the workpiece composition; or the most common factor being process modulation result- ing in regeneration of vibration. If greater energy is input into the dynamic ‘machining-loop’ than can be readily dissipated by the following: mechanical work; damping, or friction, then an ‘equilibrium status’ is re- quired and this output is via the somewhat superu- ous eect of the generation of chatter/vibration. Vibration is a debilitating process aecting both the machined surfaces and reducing tool life in any ma- chining operation, consequently it must be appropri- ately identied – classied, then one has the potential to nd the actual cause of this unwanted eect and resolve it accordingly. In essence, in machining opera- tions there are three types of vibration that may tran- spire, these are: • Free vibration – this being the response to sudden change, or to any initial condition, where the vibra- tional amplitude decreases with time, occurring at the system’s natural frequency, NB An interrupted machining operation, or work- piece feature can create this vibrational eect and it frequently appears as shadows, or lines following a surface discontinuity. • Forced vibration – can be regarded as a response to a periodic – repetitive timing – input that occurs at an identical frequency. At this point, the vibrational 27 ‘Spring-cuts’ , are always present in any ductile component machining operation, resulting from the relaxation of the forces and the elastic recovery of the tool and workpiece aer the cutting insert’s passage along the part. In fact, if the tool is repositioned once more at the beginning of the original cut, then simply fed along the component, it will take a minute cut – assuming that the tool’s edge is still suciently sharp, this is termed the ‘spring-cut’. amplitude stays constant for a set of input condi- tions, being non-linearly related to speed. NB e most common examples of this eect are caused by: cutter imbalance, cutting teeth impact- ing on workpiece, tooling misalignments, plus the occurrence of any form of rotational system reso- nance. • Self-excitation vibration, or chatter – occurs through the system’s periodic response to a con- stant input, which may intensify in amplitude – be- coming unstable, oen occurring – regardless of the input, but close to the natural frequency of the system. NB Chatter is due to waviness regeneration in the machined surface, it commonly occurs during metal cutting operations (i.e. see Fig. 156a). What is chatter and how might can be characterised? Degarmo, et al. (2003), has produced a list of the fol- lowing factors that can indicate the onset of chatter, these being characterised by: • Sudden onset of vibration – whose amplitude will rapidly increase until a maximum threshold – sat- uration – is reached (i.e sounding like either: a screech, whine, or buzz), • Chatter frequency is near to that of the machin- ing system’s natural frequency (i.e critical fre- quency) – changing only slightly with any process parameter variations. e largest force-displace- ment response occurs at ‘resonance’ 28 enabling the maximum dissipation of energy, • Chatter produces unacceptable surface texture (Fig. 156a) – normally highlighted by either an an- gular, or helical pattern (i.e. the visual appearance 28 ‘Resonance’ , is of practical importance in many engineering applications, because relatively few oscillatory forces can re- sult in large vibrational amplitudes that can cause damage, or interfere with the functioning of the system. NB e classic example of this phenomenon was found when ranks of soldiers marched across a bridge in unison (i.e. ‘in- step’) which, if it coincided with one of the bridge’s resonant frequencies, could create damage to the structure – despite the fact that the bridge could safely support their overall weight. Hence, the order to ‘break-rank’ (i.e randomising both their pacing and steps) when proceeding over a structure such as a bridge was mandatory. Machinability and Surface Integrity Figure 156. Vibration and chatter in machining operations, with their machine tool damping characteristics. Chapter is either ‘pearled’ , or ‘sh-scaled’) superimposed over the normal cutting insert’s feed marks, • Visible surface undulations – these eects are re- produced in the direction of feed, being the prod- uct of either serrated, or wavy chip formations, of variable thicknesses. .. Chatter and Chip Formation – Significant Factors Influencing its Generation e stability of the cutting process and the onset of re- generative chatter is inuenced by a range of factors, such as the: cutting stiness (K s ) 29 of the workpiece material – related to its machinability; parameters of the machining process (e.g. speed, feed, D OC , chip width – total); insert cutting geometry (e.g. rake and clearance angles, edge preparation, insert shape and size); cutting process dynamic characteristics (e.g. machine-tooling-workpiece/xturing). Hence, during machining operations on the workpiece, the chip is formed by shearing over the chip area, producing the cutting, or tangential force (F T ). e magnitude of this tangential force is heavily inuenced by the product of the workpiece material’s stiness (K s ) and the chip area, as follows: F T = K s × t × w Where: F T = tangential force (N), K s = workpiece material’s stiness (N mm –2 ), t = chip thickness (mm), w = chip width (mm). e direction of the tangential force (F T ) is predomi- nantly aected by the cutting insert’s rake and clear- ance angles, together with the edge preparation on the insert. In many single-/multi-point machining opera- tions used to generate for example a milled surface, there is a requirement to overlap the adjacent cutting paths (Fig. 84c). For most single-point machining op- 29 ‘Cutting stiness’ (K s ), is closely associated with that of ‘ow stress’*, but is more simple to calculate and can be thought of as a workpiece material property, being dependent on its hardness. *‘Flow stress’ , can be dened as: ‘e stress required to sustain plastic deformation at a particular strain’ ( Kalpakjian, 1997). erations, this former over-lapping of tool paths does not take place in the same manner, but will only occur aer one complete revolution of either the workpiece, or tool. In operations by either milling (Fig. 85), or drilling (Fig. 50), an overlap takes place in a fraction of a revolution, this being dependent upon how many cutting edges are present on the tool. In the Degarmo, et al. (2003) machining model shown in (Fig. 157a), the cutting or tangential force (F c ) 30 generation may cause a relative displacement ‘X’ between the cutting insert and the workpiece, aecting the uncut chip thickness (t), this results in changing the cutting force. is coupled relationship between displacement in the ‘Y’ direction – modulation direc- tion – and the resultant cutting force, creates a closed- loop response system. Here, the modulation direction is normally at 90° to the machined surface, so denes the chip thickness. As a consequence of these inter- related factors, there is a phase-shi (ε) between the subsequent overlapping machined surfaces, resulting in a variable chip thickness and modulation of the displacement, causing chatter vibration to take place. Accordingly, this phase-shi between overlapping cut- ting paths is accountable for the production of chatter (Fig. 157b). Moreover, there is a favoured speed cor- responding to a phase-locked condition (e.g. when ‘ε=0’), resulting in a constant chip thickness (t). By obtaining a constant chip thickness, this results in a ‘steady-state’ cutting force generation with it and, the eradication of the feed-back mechanism for regenera- tive chatter. In essence, this is the goal for all machin- ing operators, as they attempt to achieve this eect by vary the cutting speeds for a given set of conditions for a particular machining operation. .. Chatter – Important Factors Affecting its Generation In the previous sections, a brief discussion was made concerning just some of the causes of regenerative chatter mechanisms. It is worth looking in greater de- tail at the reasons why this superuous chatter occurs, explaining how and why it is generated in the hope of 30 In the Degarmo, et al. (2003) model diagrammatically shown in Fig. 157a, they use the term and nomenclature of: ‘cutting force’ and ‘F c ’ , whereas previously in the text, this has been referred to as the ‘tangential force’ , denoted by ‘F T ’. Machinability and Surface Integrity Figure 157. A chatter model, with potential chatter conditions and the application of the ‘stability lobe diagram’. [Source: Degarmo, Black & Kosher, 2003] . Chapter . ‘break-rank’ (i.e randomising both their pacing and steps) when proceeding over a structure such as a bridge was mandatory. Machinability and Surface Integrity Figure 156. Vibration and chatter. result of instrument noise, or vibration. [Courtesy of Taylor Hobson] . Machinability and Surface Integrity Figure 1 53. By utilising turning centre headstocks with direct-drive spindles –. allowing long and slender workpieces to be successfully turned. A produc- tion bonus being the removal of greater workpiece material stock per pass. 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