Metal Machining - Theory and Applications Episode 1 Part 9 pptx

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 i

The laws of electromagnetic energy radiation from a black body are well known The

power radiated per unit area per unit wavelength W ldepends on the absolute temperature

T and wavelength l according to Planck’s law:

(elkT– 1 )

where h (Planck’s constant) = 6.626 × 10–34J s, c (speed of light) = 2.998 × 108m s–1and

k (Boltmann’s constant) = 1.380 × 10–23J K–1

Equation (5.5) can be differentiated to find at what wavelength lmaxthe peak power is

radiated (or absorbed), or integrated to find the total power W Wien’s displacement law

and the Stefan–Boltzmann law result:

lmaxT = 2897.8 mm K

(5.6)

W[W m–2] = 5.67 × 10-8T4

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

(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)

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 dislocadeforma-tion 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 BaTiO3or PZT (Pb(ZrxTi1–x)O3; 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

where g33is the sensor material’s piezoelectric stress coefficient The voltage across the sensor, TL, is then

Typical values of g33and E for PZT are 24.4 × 10–3V 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

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

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)

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

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

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-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

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

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

As an example of the rules so far, equation (6.1) can be used to calculate the

hydrosta-tic pressure p3at 3 if the hydrostatic pressure p1is known (p1= +k in this case) and if the directions of the slip-lines f1, f2and f3at 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, sn,

at 3 can be calculated from the force equilibrium of region 3:

p3 = k – 2k[(f1 – f2) – (f2 – f3)]

sn = p3 + 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

fF– fG= fE– fH

fH– fG = fE– fF

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

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 sn/k and of the rake face sliding velocity

as a fraction of the chip velocity, Urake/Uchip, 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