The laws of electromagnetic energy radiation from a black body are well known. The power radiated per unit area per unit wavelength W l depends on the absolute temperature T and wavelength l according to Planck’s law: 2phc 2 1 W l = ——— ————— (5.5) l 5 ch (e lkT – 1 ) where h (Planck’s constant) = 6.626 × 10 –34 Js,c (speed of light) = 2.998 × 10 8 m s –1 and k (Boltmann’s constant) = 1.380 × 10 –23 JK –1 . Equation (5.5) can be differentiated to find at what wavelength l max the peak power is radiated (or absorbed), or integrated to find the total power W. Wien’s displacement law and the Stefan–Boltzmann law result: l max T = 2897.8 mmK (5.6) W[W m –2 ] = 5.67 × 10 -8 T 4 Figure 5.20 shows the characteristic radiation in accordance with these laws. Temperatures measured in industry are usually 2000 K or less. Most energy is radiated in the infrared range (0.75 mm to 50 mm). Therefore, infrared measurement techniques are needed. Much care, however, must be taken, as real materials like cutting tools and work materials are not black bodies. The radiation from these materials is some fraction a of the black body value. a varies with surface roughness, state of oxidation and other factors. Calibration under the same conditions as cutting is necessary. One of the earliest measurements of radiation from a cutting process was by Schwerd (1933). Since then, methods have followed the development of new infrared sensors. Point measurements, using collimated beams illuminating a PbS cell sensor, have been used to measure temperatures on the primary shear plane (Reichenbach, 1958), on the tool flank Temperatures in machining 153 Fig. 5.20 Radiation from a black body Childs Part 2 28:3:2000 3:11 pm Page 153 (Chao et al., 1961) and on the chip surface (Friedman and Lenz, 1970). With the develop- ment of infrared sensitive photographic film, temperature fields on the side face of a chip and tool have been recorded (Boothroyd, 1961) and television-type infrared sensitive video equipment has been used by Harris et al. (1980). Infrared sensors have continued to develop, based on both heat sensing and semicon- ductor quantum absorption principles. The sensitivity of the second of these is greater than the first, and its time constant is quite small too – in the range of ms to ms. Figure 5.21 shows a recent example of the use of the second type. Two sensors, an InSb type sensitive in the 1 mm to 5 mm wavelength range and a HgCdTe type, sensitive from 6 mm to 13 mm, were used: more sensitive temperature measurements may be made by comparing the signals from two different detectors. Most investigations of temperature in metal cutting have been carried out to under- stand the process better. In principle, temperature measurement might be used for condi- tion monitoring, for example to warn if tool flank wear is leading to too hot cutting conditions. However, particularly for radiant energy measurements and in production conditions, calibration issues and the difficulty of ensuring the radiant energy path from the cutting zone to the detector is not interrupted, make temperature measurement for such a purpose not reliable enough. Monitoring the acoustic emissions from cutting is 154 Experimental methods Fig. 5.21 Experimental set-up for measuring the temperature of a chip’s back surface at the cutting point, using a diamond tool and infrared light, after Ueda et al . (1998) Childs Part 2 28:3:2000 3:11 pm Page 154 another way, albeit an indirect method, to study the state of the process, and this is consid- ered next. 5.4 Acoustic emission The dynamic deformation of materials – for example the growth of cracks, the deforma- tion of inclusions, rapid plastic shear, even grain boundary and dislocation movements – is accompanied by the emission of elastic stress waves. This is acoustic emission (AE). Emissions occur over a wide frequency range but typically from 100 kHz to 1 MHz. Although the waves are of very small amplitude, they can be detected by sensors made from strongly piezoelectric materials, such as BaTiO 3 or PZT (Pb(Zr x Ti 1–x )O 3 ; x = 0.5 to 0.6). Figure 5.22 shows the structure of a sensor. An acoustic wave transmitted into the sensor causes a direct stress E(DL/L) where E is the sensor’s Young’s modulus, L is it length and DL is its change in length. The stress creates an electric field T = g 33 E(DL/L) (5.7a) where g 33 is the sensor material’s piezoelectric stress coefficient. The voltage across the sensor, TL, is then V = g 33 EDL (5.7b) Typical values of g 33 and E for PZT are 24.4 × 10 –3 V m/N and 58.5 GPa. It is possible, with amplification, to detect voltages as small as 0.01 mV. These values substituted into equation (5.7b) lead to the possibility of detecting length changes DL as small as 7 × 10 –15 m: for a sensor with L = 10 mm, that is equivalent to a minimum strain of 7 × 10 –13 . AE Acoustic emission 155 Fig. 5.22 Structure of an AE sensor Childs Part 2 28:3:2000 3:11 pm Page 155 strain sensing is much more sensitive than using wire strain gauges, for which the mini- mum detectable strain is around 10 –6 . The electrical signal from an AE sensor is processed in two stages. It is first passed through a low noise pre-amplifier and a band-pass filter (≈100 kHz to 1 MHz). The result- ing signal typically has a complicated form, based on events, such as in Figure 5.23. In the second stage of processing, the main features of the signal are extracted, such as the number of events, the frequency of pulses with a voltage exceeding some threshold value VL, the maximum voltage VT, or the signal energy. The use of acoustic emission for condition monitoring has a number of advantages. A small number of sensors, strategically placed, can survey the whole of a mechanical system. The source of an emission can be located from the different times the emission takes to reach different sensors. Its high sensitivity has already been mentioned. It is also easy to record; and acoustic emission measuring instruments are lightweight and small. However, it also has some disadvantages. The sensors must be attached directly to the system being monitored: this leads to long term reliability problems. In noisy conditions it can become impossible to isolate events. Acoustic emission is easily influenced by the state of the material being monitored, its heat treatment, pre-strain and temperature. In addition, because it is not obvious what is the relationship between the characteristics of acoustic emission events and the state of the system being monitored, there is even more need to calibrate or train the measuring system than there is with thermal radiation measurements. In machining, the main sources of AE signals are the primary shear zone, the chip–tool and tool–work contact areas, the breaking and collision of chips, and the chipping and fracture of the tool. AE signals of large power are generally observed in the range 100 kHz to 300 kHz. Investigations of their basic properties and uses in detecting tool wear and chipping have been the subject of numerous investigations, for example Iwata and Moriwaki (1977), Kakino (1984) and Diei and Dornfeld (1987). The potential of using AE is seen in Figure 5.24. It shows a relation between flank wear VB and the amplitude level 156 Experimental methods Fig. 5.23 An example of an AE signal and signal processing Childs Part 2 28:3:2000 3:11 pm Page 156 of an AE signal in turning a 0.45% plain carbon steel (Miwa, 1981). The larger the flank wear, the larger the AE signal, while the rate of change of signal with wear changes with the cutting conditions, such as cutting speed. References Boothroyd, G. (1961) Photographic technique for the determination of metal cutting temperatures. British J. Appl. Phys. 12, 238–242. Chao, B. T., Li, H. L. and Trigger, K. J. (1961) An experimental investigation of temperature distri- bution at tool flank surface. Trans. ASME J. Eng. Ind. 83, 496–503. Diei, E. N. and Dornfeld, D. A. (1987) Acoustic emission from the face milling process – the effects of process variables. Trans ASME J. Eng. Ind. 109, 92–99. Friedman, M. Y. and Lenz, E. (1970) Determination of temperature field on upper chip face. Annals CIRP 19(1), 395–398. References 157 Fig. 5.24 Relation between flank wear VB and amplitude of AE signal, after Miwa et al. (1981) Childs Part 2 28:3:2000 3:11 pm Page 157 Harris, A., Hastings, W. F. and Mathew, P. (1980) The experimental measurement of cutting temper- ature. In: Proc. Int. Conf. on Manufacturing Engineering, Melbourne, 25–27 August, pp. 30–35. Iwata, I. and Moriwaki, T. (1977) An application of acoustic emission to in-process sensing of tool wear. Annals CIRP 26(1), 21–26. Kakino, K. (1984) Monitoring of metal cutting and grinding processes by acoustic emission. J. Acoustic Emission 3, 108–116. Miwa, Y., Inasaki, I. and Yonetsu, S. (1981) In-process detection of tool failure by acoustic emission signal. Trans JSME 47, 1680–1689. Reichenbach, G. S. (1958) Experimental measurement of metal cutting temperature distribution. Trans ASME 80, 525–540. Schwerd, F. (1933) Uber die bestimmung des temperaturfeldes beim spanablauf. Zeitschrift VDI 77, 211–216. Shaw, M. C. (1984) Metal Cutting Principles. Oxford: Clarendon Press. Trent, E. M. (1991) Metal Cutting, 3rd edn. Oxford: Butterworth Heinemann. Ueda, T., Sato, M. and Nakayama, K. (1998) The temperature of a single crystal diamond tool in turning. Annals CIRP 47(1), 41–44. Williams, J. E, Smart, E. F. and Milner, D. (1970) The metallurgy of machining, Part 1. Metallurgia 81, 3–10. 158 Experimental methods Childs Part 2 28:3:2000 3:11 pm Page 158 6 Advances in mechanics 6.1 Introduction Chapter 2 presented initial mechanical, thermal and tribological considerations of the machining process. It reported on experimental studies that demonstrate that there is no unique relation between shear plane angle, friction angle and rake angle; on evidence that part of this may be the influence of workhardening in the primary shear zone; on high temperature generation at high cutting speeds; and on the high stress conditions on the rake face that make a friction angle an inadequate descriptor of friction conditions there. Chapters 3 to 5 concentrated on describing the properties of work and tool materials, the nature of tool wear and failure and on experimental methods of following the machining process. This sets the background against which advances in mechanics may be described, leading to the ability to predict machining behaviours from the mechanical and physical properties of the work and tool. This chapter is arranged in three sections in addition to this introduction: an account of slip-line field modelling, which gives much insight into continuous chip formation but which is ultimately frustrating as it offers no way to remove the non-uniqueness referred to above; an account of the introduction of work flow stress variation effects into model- ling that removes the non-uniqueness, even though only in an approximate manner in the first instance; and an extension of modelling from orthogonal chip formation to more general three-dimensional (non-orthogonal) conditions. It is a bridging chapter, between the classical material of Chapter 2 and modern numerical (finite element) modelling in Chapter 7. 6.2 Slip-line field modelling Chapter 2 presented two early theories of the dependence of the shear plane angle on the friction and rake angles. According to Merchant (1945) (equation (2.9)) chip formation occurs at a minimum energy for a given friction condition. According to Lee and Shaffer (1951) (equation (2.10)) the shear plane angle is related to the friction angle by plastic flow rules in the secondary shear zone. Lee and Shaffer’s contribution was the first of the slip- line field models of chip formation. Childs Part 2 28:3:2000 3:11 pm Page 159 6.2.1 Slip-line field theory Slip-line field theory applies to plane strain (two-dimensional) plastic flows. A material’s mechanical properties are simplified to rigid, perfectly plastic. That is to say, its elastic moduli are assumed to be infinite (rigid) and its plastic flow occurs when the applied maxi- mum shear stress reaches some critical value, k, which does not vary with conditions of the flow such as strain, strain-rate or temperature. For such an idealized material, in a plane strain plastic state, slip-line field theory develops rules for how stress and velocity can vary from place to place. These are considered in detail in Appendix 1. A brief and partial summary is given here, sufficient to enable the application of the theory to machining to be understood. First of all: what are a slip-line and a slip-line field; and how are they useful? The analy- sis of stress in a plane strain loaded material concludes that at any point there are two orthog- onal directions in which the shear stresses are maximum. Further, the direct stresses are equal (and equal to the hydrostatic pressure) in those directions. However, those directions can vary from point to point. If the material is loaded plastically, the state of stress is completely described by the constant value k of maximum shear stress, and how its direction and the hydrostatic pressure vary from point to point. A line, generally curved, which is tangential all along its length to directions of maximum shear stress is known as a slip-line. A slip-line field is the complete set of orthogonal curvilinear slip-lines existing in a plastic region. Slip- line field theory provides rules for constructing the slip-line field in particular cases (such as machining) and for calculating how hydrostatic pressure varies within the field. One of the rules is that if one part of a material is plastically loaded and another is not, the boundary between the parts is a slip-line. Thus, in machining, the boundaries between the primary shear zone and the work and chip and between the secondary shear zone and the chip are slip-lines. Figure 6.1 sketches slip-lines OA, A′D and DB that might be such boundaries. It also shows two slip-lines inside the plastic region, intersecting at the point 2 and labelled a and b, and an element of the slip-line field mesh labelled EFGH (with the shear stress k and hydrostatic pressure p acting on it); and it draws attention to two regions labelled 1 and 3, at the free surface and on the rake face of the tool. The theory is devel- oped in the context of this figure. As a matter of fact, Figure 6.1 breaks some of the rules. Some correct detail has been sacrificed to simplify the drawing – as will be explained. Correct machining slip-line fields are introduced in Section 6.2.2. The variation of hydrostatic pressure with position along a slip-line is determined by force equilibrium requirements. If the directions of the slip-lines at a point are defined by the anticlockwise rotation f of one of the lines from some fixed direction (as shown for example at the centre of the region EFGH); and if the two families of lines that make up the field are labelled a and b (also as shown) so that, if a and b are regarded as a right- handed coordinate system, the largest principal stress lies in the first quadrant (this is explained more in Appendix 1), then p + 2kf = constant, along an a-line } (6.1) p – 2kf = constant, along a b-line Force equilibrium also determines the slip-line directions at free surfaces and friction surfaces (1 and 3 in the figure) – and at a free surface it also controls the size of the hydro- static pressure. By definition, a free surface has no force acting on it. From this, slip-lines 160 Advances in mechanics Childs Part 2 28:3:2000 3:11 pm Page 160 intersect a free surface at 45˚ and the hydrostatic pressure is either +k or –k (depending respectively on whether the free surface normal lies in the first or second quadrant of the coordinate system). At a friction surface, where the friction stress is defined as mk (as introduced in Chapter 2), the slip lines must intersect the surface at an angle z (defined at 3 in the figure) given by cos 2z = m (6.2) As an example of the rules so far, equation (6.1) can be used to calculate the hydrosta- tic pressure p 3 at 3 if the hydrostatic pressure p 1 is known (p 1 = +k in this case) and if the directions of the slip-lines f 1 , f 2 and f 3 at points 1, 2 and 3 are known (point 2 is the inter- section of the a and b lines connecting points 1 and 3). Then, the normal contact stress, s n , at 3 can be calculated from the force equilibrium of region 3: p 3 = k – 2k[(f 1 – f 2 ) – (f 2 – f 3 )] } (6.3) s n = p 3 + k sin 2z Rules are needed for how f varies along a slip-line. It can be shown that the rotations of adjacent slip-lines depend on one another. For an element such as EFGH f F – f G = f E – f H or } (6.4) f H – f G = f E – f F From this, the shapes of EF and GF are determined by HG and HE. By extension, in this example, the complete shape of the primary shear zone can be determined if the shape of the boundary AO and the surface region AA′ is known. Slip-line field modelling 161 Fig. 6.1 A wrong guess of a chip plastic flow zone shape, to illustrate some rules of slip-line field theory Childs Part 2 28:3:2000 3:11 pm Page 161 One way in which Figure 6.1 is in error is that it violates the second of equations (6.4). The curvatures of the a-lines change sign as the b-line from region 1 to region 2 is traversed. Another way relates to the velocities in the field that are not yet considered. A discontinuous change in tangential velocity is allowed on crossing a slip-line, but if that happens the discontinuity must be the same all along the slip-line. In Figure 6.1, a discon- tinuity must occur across OA at O, because the slip-line there separates chip flow up the tool rake face from work flow under the clearance face. However, no discontinuity of slope is shown at A on the free surface, as would occur if there were a velocity discontinuity there. 6.2.2 Machining slip-line fields and their characteristics A major conclusion of slip-line field modelling is that specification of the rake angle a and friction factor m does not uniquely determine the shape of a chip. More than one field can be constructed, each with a different chip thickness and contact length with the tool. The possibilities are fully described in Appendix 1. Figure 6.2 sketches three of them, for a = 5˚ and m = 0.9, typical for machining a carbon steel with a cemented carbide tool. The estimated variations along the rake face of s n /k and of the rake face sliding velocity as a fraction of the chip velocity, U rake /U chip , are added to the figures, and so is the final 162 Advances in mechanics Fig. 6.2 Possibilities of chip formation, α = 5º, m = 0.9 Childs Part 2 28:3:2000 3:11 pm Page 162 [...]... should not be ignored in machining analyses Slip-line field modelling may also be applied to machining with restricted contact tools (Usui et al., 19 64), with chip breaker geometry tools (Dewhurst, 19 79) , with negative rake tools (Petryk, 19 87), as well as with flank-worn tools (Shi and Ramalingham, 19 91 ) , to give an insight into how machining may be changed by non-planar rake face and cutting edge modified... Summary In summary, the slip-line field method gives a powerful insight into the variety of possible chip flows A lack of uniqueness between machining parameters and the friction stress Fig 6.6 Slip-line field models of cutting with (a) zero rake restricted contact and (b) chip breaker geometry tools, after Usui et al ( 19 64) and Dewhurst ( 19 79) Childs Part 2 28:3:2000 3 :12 pm Page 16 7 Introducing variable... 6.3.2) Childs Part 2 28:3:2000 3 :12 pm Page 17 1 Introducing variable flow stress behaviour 17 1 Fig 6 .10 Shear strain rate variations along a central stream-line, and peak shear strain rate changes with cutting speed and feed, as described in the text In this case, the best-fit constant of proportionality C is 5 .9 In many practical machining operations, peak shear strain rates are of the order of 10 4/s It... derivation of equations (6 .1) (Appendix 1, Section 1. 2.2), and removing the constraint of no strain hardening, it is easy to show that ∂p ∂f ∂k —— + 2k —— – —— = 0 ∂s1 ∂s1 ∂s2 along an a – line ∂p ∂f ∂k —— – 2k —— – —— = 0 ∂s2 ∂s2 ∂s1 along a b – line } (6.5) where s1 and s2 are distances along an a and a b slipline respectively In Figure 6.8(a), as in Figure 6 .1, AC is a b line and CA′ an a line After... slip-line fields for slow speed machining of mild steels, after (a) Palmer and Oxley ( 19 59) , and (b) Roth and Oxley ( 19 72) by the free surface boundary condition there Palmer and Oxley resolved the contradiction by suggesting that plastic flow was not steady at the free surface The smoothed free surface in Figure 6.8(a) is, in reality, corrugated and therefore the slip-lines should not be constrained... relation between m and l Figure 6.5 shows, as the hatched Childs Part 2 28:3:2000 3 :12 pm Page 16 5 Slip-line field modelling 16 5 Fig 6.4 Slip-line field predicted ranges of tan(φ+λ–α), dependent on φ, for α = 0º Fig 6.5 Effects of elastic contact on relations between l and m Experimental data for carbon steels, (after Childs, 19 80) region, the slip-line field predicted relationship between l and m for a =... this way (Palmer and Oxley, 19 59) In addition to flow calculations in deriving this field, Palmer and Oxley also applied the force equilibrium constraint, that the slip-lines should intersect the free surface AA′ at 45˚ The field is for a mild steel machined at the low cutting speed of 12 mm/min and a feed of 0 .17 mm At the low strain rates and temperatures generated in this case, departures from perfect... of the theory of constant shear flow stress Figure 6.3(b) supports the view that if cutting could be carried out with 30˚ rake angle tools, the spread of allowable specific forces would be very small and it would not matter much that slip-line field theory cannot explain where in the range a particular result will Childs Part 2 28:3:2000 3 :11 pm Page 16 4 16 4 Advances in mechanics Fig 6.3 Slip-line field... force R across OA″ is given by ps 1 s ∂k tan(f + l – a) = ——— – — ——— —— kOA″ 2 kOA″ ∂s1 (6.9a) The size of R (with d, the depth of cut) is found from R cos(f + l – a) = sd.kOA″ (6.9b) Oxley showed how to relate the second term on the right-hand side of equation (6.9a) to the work-hardening behaviour of the material, expressed as s= s0en — — (6 .10 ) and to the shear strain-rate on OA″, from equation (6.6),... expected of a non-hardening material They depend on the direction changes along the lines The exit region OBDA′ is visually similar in this example to the non-hardening slip-line field proposed by Dewhurst (Figure 6.2(c)) The whole field is this, with the primary shear plane replaced by a work hardening zone of finite width In a parallel series of experiments, Stevenson and Oxley ( 19 69 70, 19 70– 71) extended . Smart, E. F. and Milner, D. ( 19 70) The metallurgy of machining, Part 1. Metallurgia 81, 3 10 . 15 8 Experimental methods Childs Part 2 28:3:2000 3 :11 pm Page 15 8 6 Advances in mechanics 6 .1 Introduction Chapter. Ind. 10 9, 92 99 . Friedman, M. Y. and Lenz, E. ( 19 70) Determination of temperature field on upper chip face. Annals CIRP 19 (1) , 395 – 398 . References 15 7 Fig. 5.24 Relation between flank wear VB and. Emission 3, 10 8 11 6. Miwa, Y., Inasaki, I. and Yonetsu, S. ( 19 81) In-process detection of tool failure by acoustic emission signal. Trans JSME 47, 16 80 16 89. Reichenbach, G. S. ( 19 58) Experimental