Turning and Chip-breaking Technology Part 2 pps

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Turning and Chip-breaking Technology Part 2 pps

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entering angle of 45° and lead angle of 45° is utilised, giving rise to equal axial and radial component forces. In ‘case II’ , the entering angle has changed to 75° and lead angle is now 15°, these altered angles change the component forces, with an increase in the axial force while reducing the radial force. In ‘case III’ , an or - thogonal cutting action occurs, with only a 90° enter- ing angle (i.e. the lead angle reduces to zero), showing a large increase in the axial force component at the expense of the radial force component which is now zero 10 . In ‘case IV’ , an oblique cutting action has re- turned (i.e. as in ‘cases I and II’), but here the entering angle has changed to -15°, with the lead angle 75°, this produces a large axial component force, but the radial component force direction has now reversed. is last tool plan approach angle geometry (i.e. ‘case IV’), is similar to the geometry of a light turning and facing tool, allowing cylindrical and facing operations to be usefully undertaken – but the tool’s point is somewhat weaker that the others, with the tool points becoming of increased strength from right to le. erefore, in ‘case I’ , for a given feedrate and constant D OC , the cut length/area is greater than the other ‘cases’ shown and with this geometry, it enables the tool to be employed for heavy roughing cuts. Returning to ‘case III’ , if this tool is utilised for nish turning brittle-based work- piece materials, then upon approaching the exit from a cut, if the diameter is not supported by a larger shoul- der diameter, then the axial component force /pressure, will be likely to cause edge break-out (i.e. sometimes termed ‘edge frittering’), below the machined surface diameter at this corner (i.e. potentially scrapping the machined part). In mitigation for this orthogonal cut- ting tool geometry, if longer slender workpieces re- quire cylindrical turning along their length, then with the radial force component equating to zero, it does not create signicant ‘push-o ’ and allows the part to be successfully machined 11 . A single-point turning geometry is subject to very complex interactions and, as one geometric feature is modied such as changing the entering angle, or in- 10 In all of these cases, it is assumed – for simplicity – that there is no nose radius/chamfer on the tool and it is innitely sharp. 11 In order to minimise the eects of the radial force component when cylindrically turning long slender workpieces with ‘Case I and II’ tool geometries, the use of a programmable steady, or a ‘balanced turning operation’ (i.e. utilising twin separately programmable turrets on a turning centre, with tools situ- ated virtually opposite each other running parallel during the turning operation – see Fig. 41), will reduce this ‘push-o ’. creasing the tool’s nose radius, this will inuence other factors, which in turn could have a great impact on the: type of machined surface nish produced, expected tool life and the overall power consumption during the operation. In fact, the main factors that inuence the application of tooling for a specic turning operation are: I. Workpiece material – machinability, condition (i.e. internal/external), mechanical and physical properties, etc., II. Workpiece design – shape, dimensions and ma- chining allowance, III. Limitations – accuracy and precision require- ments, surface texture/integrity, etc., IV. Machine tool – type, power, its condition and specications, V. Stability – loop stiness/rigidity (i.e. from the cutting edge to its foundations), VI. Set-up – tool accessibility, workpiece clamping and toolholding, tool changing, VII. Tool programme – the correct/specied tool and its tool osets, etc., VIII. Performance – cutting data, anticipated tool-life and economics, IX. Quality – tool delivery system and service. In order to gain an insight into the complex and im- portant decisions that have to be made when select- ing tooling for the optimum production of either part batch sizes, or for continuous production runs, then the following section has been incorporated. .. Cutting Toolholder/Insert Selection When deciding upon the correct selection of a tool- holder/cutting insert for a given application, a range of diverse factors must be considered, as indicated in Fig. 21. As can be seen by the diagram (Fig. 21) and associated text and captions, there are many other variables that need to be considered prior to selection of the optimum toolholder/insert. Generally, the xed conditions cannot be modied, but by ‘juggling’ with the variable conditions it is possible to accomplish the best compromise toolholder/insert geometry, to opti- mise these cutting conditions for the manufacture of a specic workpiece and its intended production re- quirements. Whenever toolholders and cutting inserts are required for a specic manufacturing process, it is important to view the tooling selection procedure as a logical progression, in order to optimise the best Turning and Chip-breaking Technology  Figure 21. The factors that must be considered prior to commencing a turning operation, when utilising indexable inserts .  Chapter  possible tools/inserts for the job in hand. Perhaps the following selection strategy for a ‘start point’ in choice and application of turning tools, can be undertaken according by the following step-by-step approach: Start Point → Edge clamping system, ↓ Toolholder size and type, ↓ Insert shape, ↓ Insert size, ↓ Nose radius, ↓ Insert type, ↓ Tool material, ↓ Cutting data → Final Tool- holder and Insert Selection Edge Clamping System Initially, the tool holder clamping system should be selected to provide optimum performance in dier- ent applications over a wide range of workpiece geom- etries. e type of machining operation and to a lesser extent, the workpiece size determines tool holder se- lection. For example, roughing-out operations on big components will make considerably dierent demands, to that of nishing passes on small components. NB Pin, clamp and lever are just three of the insert clamping systems available – consultation with the tool suppliers at this point might be benecial. Toolholder Size and Type Once the clamping system has been selected, the size and type of toolholder must be determined, with its selection being inuenced by: feed directions (i.e. see Fig. 22 for turning insert shapes and feed directions), size of cuts, workpiece and toolholder situated in the machine for accessibility requirements. e work- piece’s shape plays a decisive role if surface contouring is necessary, this is particularly relevant for machining part access, as a toolholder is dened by its: eective entering and point angles 12 , together with the insert’s shape (see Fig. 22). Toolholders should be the largest possible size for the turning centre’s tool turret, this requirement is vi- tal, as it reduces the ‘tool overhang ratio’ – providing rigidity and integrity to stabilise the insert’s cutting edge. NB Appendix 1a shows the ISO ‘Code Key’ – for Ex- ternal Toolholders. Appendix 1b shows the ISO ‘Code Key’ – for Solid Boring Bars. Appendix 1c shows the ISO ‘Code Key’ – for Car- tridges. Insert Shape e insert shape should be selected relative to the en- tering angle needed for the tool’s accessibility, or ver- satility. Here, the largest suitable point angle should be chosen for strength and economy (see Fig. 23). In Fig. 23, is illustrated a practical example of how chang- ing only one variable – insert geometry (shape) – can inuence an insert’s turning application. e shape of an insert will determine its inherent weakness, or strength, which is of particular relevance if rough- turning operations are necessary. Furthermore, insert shape will inuence whether it is prone to vibration, or not and its predictable tool life. Hence, if one is con- cerned about vibrations of either the tool, workpiece, or both, then a weaker insert such as a light turning and facing geometry with less cutting edge length ex- posed in-cut, might be more suitable. Variable condi- tions such as the selection of insert’s geometric shape can aect other machining parameters and, this is valid for other insert factors, so a compromise will al- ways occur in any machining application. 12 Eective entering angles (κ 1 ) must be carefully selected when the operation involves proling, or copying. e maximum proling angle (β) is recommended for each tool type – if ‘workpiece fouling’ is to be avoided. NB κ 1 =  κ  +  β   (for plunging into a surface), whereas κ 1 =  κ   – β   (for ramping-out of a surface), κ 1 =  κ   (β = 0°) for cylindrical turn- ing, Where: eective entering angle (κ 1 ), entering angle (κ), maximum in-copy angle (β). Always select the smallest enter- ing angle that the part geometry will allow. Turning and Chip-breaking Technology  Figure 22. Tool paths in nish turning operations. [Courtesy of Sandvik Coromant].  Chapter  NB Appendix 1d shows the ISO ‘Code Key’ – for In- dexable Inserts. Insert Size An indexable insert size is directly related to the tool- holder selected for the operation, with the entering angle and insert shape having previously been estab- lished. Only the matching-shaped insert can be tted into the seat of a particular toolholder, as its shape and size are predetermined by the seating dimensions. In roughing-out operations, the largest cutting depth for a given toolholder, will inuence the insert size. For any insert, the eective cutting length has to be determined (see Fig. 20b), as the entering angle will inuence the size of the insert selected. If the eective cutting edge length is less than the depth of cut (D OC ), a larger insert should be chosen, or the D OC should be reduced. Sometimes in more demanding turning operations, a thicker insert – of the same geometric shape – gives extra reliability. Figure 23. Selecting indexable inserts for turning operations. [Courtesy of Stellram]. Turning and Chip-breaking Technology  Nose Radius Of particular relevance in any turning operation is the insert’s tool nose radius (r ε – see Fig. 17), as it is the key factor with regard to: • inherent strength in roughing operations, • the resulting surface texture from nishing opera- tions. Further, the size of the nose radius aects vibrational tendencies (see Fig. 23) and in certain instances, the feedrates. e nose radius is the transition between the major and minor cutting edges, which determines the strength, or weakness of the point angle (see Figs. 16a and 17), therefore it is an imperative factor to get right. In general, roughing-out should be undertaken with the largest possible nose radius, as it is the strongest tool point (see Fig. 23). Further, a larger tool nose ra- dius permits higher feedrates, although it is important to monitor any possible vibrational tendencies. Later in the relevant section, more will be said on the inu- ence that the insert’s tool nose radius plays in the nal machined surface texture, but it is worth mentioning here that the feedrate for roughing operations should be set to approximately half the size of the nose radius utilised. e size of the nose radius has an aect on the power consumed in turning in conjunction with the material’s yield strength and chip-forming ability, par- ticularly in rough-turning operations. e maximum material removal rate (MMR) can be obtained by a combination of high feedrate, together with a moder- ate cutting speed, with other limiting factors, such as depth of cut (D OC ), tool’s nose radius, under consider- ation. Oen, the machine tool’s power (P) availability c an sometimes be a limiting factor when mmR is the requirement and, in such circumstances the cutting speed is usually lowered somewhat. For a given nose radius and cutting insert geometry, the power can be derived, to ensure that the machine tool will be able t o cope with this pre-selected mmR, in the following manner: Machine tool’s power requirement (P): P = tangential force (F T ) x cutting speed (V C ) P = F T × V C P = k C × A × V C ∴ P = k C × f × a P × V C (kW) Where: f = feed/rev (mm/rev) a P = depth of cut (mm) Cutting speed (V C ) V C = πDN/1000 (m/min) Where: D = workpiece diameter (mm) N = workpiece rotational speed (rpm) Specic cutting force (k C ): k C = F T /A (N/mm 2 ) Where: A = cutting area (mm 2 ) For example, for nishing operations, with the nose radius in combination with the feedrate (i.e. pre-se- lected), this will aect the surface texture and part ac- curacy, in the following manner: Machined surface texture (Rt): (Rt, this parameter being: maximum prole height) Rt = f 2 /8 × r ε x 1000 (µm) Where: f 2 = feedrate per revolution (mm/rev) r ε = nose radius (mm) NB  e surface texture parameter ‘Rt’ , can be con- verted into other surface texture parameters – as nec- essary. By utilising either: larger turning insert tool nose ra- dius, ‘wiper insert’ (yet to be discussed), a more posi- tive plan approach angle, or in certain circumstances, a higher cutting speed, the surface texture can be im- proved. In general, the coordination of the tool’s nose radius and the pre-selected feedrate in nishing op- erations, indicates that the feed should be kept below a certain level to achieve an acceptable machined sur- face texture value. Insert Type e cutting insert type is for the most part determined by the previously selected geometry – see Appendix 1d for the selection of indexable inserts. In reality, vari- ous cutting conditions and workpiece materials make dierent demands on the insert’s cutting edge. For ex- ample, when machining hardened steel parts, this will be completely dierent from that to the machining of aluminium components. 48 Chapter 2 Once the insert shape has been established in con- nection with its plan approach angle together with the nose radius dimension, this just leaves the type of ge- ometry to be found. In this instance, the type of insert geometry refers to the ‘working area’ (i.e. nominally found by its depth of cut and feedrate – more will be said concerning this topic later, when ‘chip-breaking envelopes’ will be discussed). Additional factors can inuence the type of cutting geometry choice, such as: machine tool’s condition, its power, the stability of the workpiece-tool-machine set-up, other factors that could aect geometry selection include: whether con- tinuous, or intermittent cutting occurs, any tendency toward vibration while machining. Turning operations can be separated into a number of ‘working areas’ , be - ing based upon the removal of workpiece material and the generation of accurate machined component di- mensions, in combination with specic surface texture requirements – as shown in Table 3. When establishing an insert type, the feedrate and depth of cut should be identied with one of the ‘working ranges’ (i.e. from Table 3), as the various in- sert types to be chosen relate to this chart. It should be borne in mind that the most suitable ‘working area’ selected, will vary, in combination with such factors as the insert’s: size, shape and nose radius. Tool Material e penultimate evaluation to be made concerning tooling decision-making is the choice of insert mate- rial, or combination of materials that constitute the cutter’s tool edge. Today, manufacturers of tooling have a strategy for continuous improvement with varia- tions in both tool matrices and coatings being consid- erable. Not only are cutting tool material research and development an on-going intensive activity, but their application for wider ranges of machining applica- tions are being considerably enhanced. A brief review of just some of the current tool materials and coatings have been previously mentioned in Section 1.2, with the main range of cutting tool materials being: ce- mented carbides, coated cemented carbides, ceramics, cermets, cubic boron nitride, polycrystalline diamond and monolithic (i.e. natural) diamond. NB A good ‘start-point’ for most machining opera- tions, is to consider coated carbides initially, then if these grades prove unsatisfactory, for whatever reason, select one of the other materials – perhaps aer con- sultation with a cutting tool manufacturer, or aer a machinability testing procedure. Cutting Data Once all of the physical, metallurgical and geometrical factors for the cutting tool have been established for the machining operation, then it is necessary to set, or calculate the cutting data – oen these criteria can be found from tooling manufacturers recommendations and cutting data tables. Certain variable factors such as feedrate should have already been made, allowing the cutting speed to be calculated, from the well-known expression (below): V C = πDN/1000 (m min –1 ) Where: V C = cutting speed (m min –1 ) D = Workpiece diameter (mm) 13 N = rotational speed (rpm) 13 In the case of drilling, reaming and tapping operations, it is the diameter of the cutting tool that is used in the calculation. For any other internal machining operations – such as in bor- ing, it is the initial hole diameter that is employed in the cut- ting speed calculation. Table 3. Typical working areas for external turning opera- tions Type of machining operation: Feedrate (f ): Depth of cut (D OC ): Extreme nishing 0.05 to 0.15 0.25 to 2.0 Finishing 0.1 to 0.3 0.5 to 2.0 Light roughing 0.2 to 0.5 2.0 to 4.0 Roughing 0.4 to 1.0 4.0 to 10.0 Heavy roughing >1.0 6.0 to 20 Extremely heavy roughing >0.7 8 to 20 (mm) (mm) [Courtesy of Sandvik (UK) Ltd] . Turning and Chip-breaking Technology  Once again, manufacturers data tables are oen useful ‘starting-points’ for estimating the initial cutting pa- rameter information. Considerable care must be taken if the material has either a high work-hardening ten- dency, or intrinsic bulk (i.e. workpiece material) hard- ness, as this can inuence the numerical data selected. Moreover, the plan approach angle also has an eect on the numerical value for the parameter, for example, oblique machining allows a higher value than for or- thogonal machining. 2.2 History of Machine Tool Development and Some Pioneers in Metal Cutting .. Concise Historical Perspective of the Development of Machine Tools Toward the end of the 1700’s, any high-quality machin- ing at the time meant tolerances of 0.1mm being con- sidered as ‘ultra-precision’ , with this level of tolerance having steadily improved from the beginning of the Industrial Revolution. Pioneers in machine tool devel- opment such as John Wilkinson (1774), developed the rst boring machine, this being capable of generating a bored hole of 1270 mm in diameter, with a error of about 1 mm. A contemporary of Wilkinson, namely Henry Maudslay (1771–1831), invented many preci- sion machine tools, but he was particularly noted for the design and development of the rst engine lathe. Slightly later, Sir Joseph Whitworth (1803–1887), de- veloped the rst modern-day Vee-form screwthread and nut (i.e. 55° included angle – ‘Whitworth thread’), thereby enabling precision feed-motion to be achieved via suitable gear trains on such machine tools. ese early fundamental advances in machine design, al- lowed others and in particular, Joseph R. Brown (1852) to design the ‘dividing engine’. is newly-de- veloped equipment, allowed precision engraving of the hand dials on machine tool axes, enhancing them with much better machinist’s judgment in both rotary and linear control, in combination with consistent repeatability by the skilled operative. Shortly aer these developments, Eli Whitney produced the origi- nal milling machine, which was rened still further by the Cincinnati Screw and Tap Company in 1884. is ‘Cincinnati machine’ was a direct forerunner of today’s manual controlled knee-type milling machine tools. Of particular note was the ergonomic grouping of the controls centrally for a more ecient hand con- trol by the skilled operator. At this time the machine tool still utilised the Vee-form screw thread, with the Acme-form (ie having the ability to take-up backlash) still someway o development. Steady development and renement of a range of machine tools continued into the the rst half of the 20 th century until the next major ‘milestone’ oc- curred. is signicant development was the ‘modern’ numerically-controlled (NC) machine. Around the late 1940’s, the ‘recirculating ballscrew’ 14 was designed so that it could take-up backlash in both directions of rotation for machine tool axes. ese early ‘ballscrews’ were tted to a converted Cincinnati Milling Machine Company’s ‘Hydro-Tel’ die-sinking machine tool, at MIT (Massachusetts Institute of Technology). is military research-funded project having been commissioned by the United States Air force – who required complex free-form aeronautical parts to be automatically machined for the latest aircra. is research was undertaken by MIT, in association with ‘Cincinnati’ and the Parsons Tool Company. e binary-coded punched-paper tape, controlled the simultaneous machine tool axes using alpha-numeri- cal characters (ie the forerunner of today’s programs using ‘G- and M-coded’ CNC controllers), through a 14 Who, when and where ‘recirculating ballscrew’ design and development took place is open to some debate. As propo- nents in the UK say it was Alfred Herbert and Sons, whereas in the United States, the Parsons Tool Company are oen quoted as the originators. However, what is not in question, is that with its unique ‘Gothic’ arch’ (i.e. Ogival geometry), having point contacts between the screw and the adjacent re- circulating balls, allows the assembly to be pre-loaded in-situ, thereby eliminating any appreciable backlash allowing accu- rate control of these axes. NB e previous Acme taper thread (i.e. 29° included angle) tted to ‘conventional’ machine tools had an eciency of no better that 40% – with backlash present, whereas today’s hardened ‘ballscrews’ have eciencies of ~90%, coupled to an impressive rigidity (~900 N µm –1 ) and minimal ‘stick-slip’ , therefore minimising the so-called ‘ballscrew wind-up’ due to the action of torque-eects in combination with the cutting forces.  Chapter  valve-driven hydraulically-servo controlled ‘computer’ called ‘Whirlwind’. In the late 1970’s, with the advent of microproces- sor technology, these later NC machine tools were converted to Computer Numerical Control (CNC), oering a signicant stride forward in operator-us- ability, via on-board editing – without the costly and timely re-punching of NC paper tapes each time a minor modication occurred to the NC program. Today, CNC machine tools have fast multiple-proces- sor controls, with on-line computer graphics, enabling new programs to be written and ‘prove-out’ while the machine tool cuts other components, or the programs can be automatically down-loaded by a Direct Nu- merical Control (DNC) data-link from the CAD/CAM workstation, or via remote satellite-linkage from other sites either locally, or internationally. e design and development of some of today’s and the future machine tools, utilise ultra-fast CNC microprocessors, coupled to orthogonal multi-axes linear-induction motor- driven slideways, that can be precisely monitored via laser-controlled positional encoders, with ultra-fast co-axial spindles. Moreover, non-orthogonal-axes controlled machine tools are under development, us- ing simultaneous mulitple-axes slideway control, with hybrids having tool spindles that incorporate multiple angular orientation together with their linear slideways for truly sculptured free-form surface machining capa- bilities. Even today, operations carried out by several machine tools are now being incorporated into one hybid machine tool, with such as: turning, milling and grinding at one set-up. In the near future, the machine tools will have slideway acceleration/decelerations of faster >5g’s, with these machines having the ability to: rough-turn, mill, heat-treat, grind critical features, all remotely-controlled via satellite from the CAD/CAM designer, signicantly speeding-up the product devel- opment process time-to-market. .. Pioneering Work in Metal Cutting – a Brief Resumé Basic research into metal cutting did not commence until approximately 70 years aer the rst machine tool was introduced. In 1851, early research by Cocquilhat was into the work required to machine a given volume of material by drilling. By 1870, the terms ‘chip’ and ‘swarf ’ were introduced by the Russian engineer Time, where he attempted to explain how chips were formed. In 1873, Hartig tabulated research into metal cutting in a book, which was the rst authoritative work on the subject. A more practical metal cutting description was given by Tresca (1878), ustilising visio-plasticity models 15 . In 1881, a presentation at the Royal Society of London by Lord Rayleigh of Mallock’s metal cut- ting research ndings was given. Mallock’s scientic study of carefully etched specimens of the workpiece and attached chip for both ferrous and non-ferrous metals, where he observed them using a microscope (magnication: x5). Mallock correctly surmised from his investigation of his ‘models’ that the cutting pro- cess was basically one involving shearing and, that friction occurred in forming the chip, emphasizing the importance of this friction along the cutting tool’s face – between the chip and the tool. e sharpness of the cutting edge was also mentioned and the rea- sons for instability of the cutting process, leading to unwanted vibrations, or ‘chatter’. Moreover, Mallock employed basic lubricants in this work, noting that the application of lubrication reduced chip/tool inter- face friction. ese general observations by Mallock mentined above, oer a surprisingly close approxi- mation to today’s theories on the ‘mechanics of metal cutting’ , although his equations for the work done in internal shearing and chip and tool friction were in- correct, surprisingly, he was unaware of the ‘plasticity models’ by Tresca and his theory of ‘plastic heating’. To compound the metal cutting problems still further, in 1900, an unfortunate ‘step backward’ in the under- standing of the metal cutting process was taken by Reuleaux. He suggested that a crack occurred ahead of the tool’s point and likened the cutting action to that of splitting wood, regrettably having popular support for some years. In 1907, a seminal paper by the now-famous Amer- ican researcher Taylor, who published his 26 years of 15 Tresca’s visio-plasticity models, involved scoring a grid of accurate closely-spaced lines onto the edge of a specimen of metal to be machined, then partially cutting it at a preset depth of cut and leaving the chip attached. He then investi- gated the plastic deformation that had taken place as these grids were distorted and buckled by the action of machining. Both lighter and deeper cut depths were investigated in this manner, across a range of metal specimens. Tresca noted that ner depths of cut introduced greater plastic deformation than larger cut depths, stating that stier and more powerful ma- chine tools were needed to benet from these recommended greater depths of cut (i.e. undeformed chip thickness). Turning and Chip-breaking Technology  practical experience into investigation and research ndings in metal cutting. Taylor, was fascinated by the application of time-and-motion studies that could be applied within the machine shop and in particular, ‘piece-work systems’ 16 . In order to enable the progres- sion through optimisation of these time-and-motion studies, new cutting tool materials were employed, in particular high-speed steels (HSS). Taylor investi- gated the eect that tool materials and in particular, cutting conditions had, on tool life during roughing operations, in order to assist in the application of these time-and-motion studies. His principal objective was to establish empirical laws that would enable optimum 16 Piece-work systems are where a set time allowance is given for a particular job, or a batch and, a bonus is agreed if the worker performs this task within the allotted time. cutting conditions to be attained. By establishing op- timum cutting data for metal cutting operations and employing ‘piece-work systems’ at the company, Taylor was able to increase the Bethlehem Steel Company’s output by 500%. Of particular note, was the fact that the empirical law governing the cutting tool and its anticipated tool life 17 is still used today, in the study of machining economics – more will be said on this topic later in Chapter 7 (Machinability and Surface Integrity). Notable in the years prior to World War Two, were the contributions made into the generation of data on cutting forces and tool life, initially by Boston (1926) 17 Taylor’s machinability work produced a fundamental dis- covery, namely, that the interface temperature existing at the tool’s cutting edge controlled the tool-wear rate. Figure 24. The formation of a continuous chip, based upon the ‘deck of cards’ principle. [After: Piispanen, 1937].  Chapter  . smallest enter- ing angle that the part geometry will allow. Turning and Chip-breaking Technology  Figure 22 . Tool paths in nish turning operations. [Courtesy of Sandvik Coromant].  Chapter  NB. 4.0 to 10.0 Heavy roughing >1.0 6.0 to 20 Extremely heavy roughing >0.7 8 to 20 (mm) (mm) [Courtesy of Sandvik (UK) Ltd] . Turning and Chip-breaking Technology  Once again, manufacturers. inserts for turning operations. [Courtesy of Stellram]. Turning and Chip-breaking Technology  Nose Radius Of particular relevance in any turning operation is the insert’s tool nose radius (r ε

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