Metal Machining - Theory and Applications Episode 2 Part 4 pptx

angular velocity V h /(R c –t 2 ) at point h, from the ICM analysis, is always greater than that of V g /R c at point g: without a force at B, the chip path would penetrate the tool. The contact forces at C are assumed to obey Coulomb’s laws of friction. While the chip slips on the work surface t t = m d s t holds. If the relative velocity between the chip and workpiece becomes zero, then the chip is regarded as adhering to the surface. The adhered chip does not slide again until t t > m s s t . The static and dynamic friction coefficients m s and m d are assumed to be 0.3 and 0.2, respectively. As for a fracture criterion in the chip beyond its formation region, it is assumed that a crack nucleates and develops from the chip’s rough free surface when the maximum prin- cipal stress or the maximum shear stress exceeds a critical value s 1c or t c . A crack that satisfies s 1c propagates in the direction of minimum principal stress, whereas one that satisfies t c grows in the direction of maximum shear stress. In this work, s 1c = 880 MPa and t c = 440 MPa have been found to give good representations of practice. To follow the crack growth, it is necessary to subdivide the elements around the crack tip; and this requires reorganization of the node connectivity too. Remeshing around the point B is also required – and a small time step of ≤ 10 –6 s (for the cutting speed of 100 m/min) is also needed. Simulation results Figure 8.23 shows the chip shape simulated with changing w G and h B = 0. As w G increases from 1.6 mm to 2.0 mm, the radius of the broken chips becomes larger; and at w G = 2.6 mm chip breakage does not occur. Cutting edge design 253 Fig. 8.22 Initial finite element model used for chip breakability analysis Childs Part 2 28:3:2000 3:18 pm Page 253 Increasing h B aids chip breakage. Figure 8.24 shows the development of chip shape with time for w G = 2.6 mm but h B = 0.4 mm. Plastic deformation with e — ˘ > 10 s –1 takes place at the hatched regions in the figure and the chip breaks after 25 ms (the time t is measured from the instant at which the chip first collides with the workpiece surface). The figure also records the contact forces. F BH and F BV are the horizontal and vertical force components acting at point B, and F CH and F CV are those at point C. The small size of the forces at C and the almost constant forces at B throughout the chip breaking cycle support the approximation that contact of the chip with the work does not much alter the flow in the primary shear region. 254 Applications of finite element analysis Fig. 8.23 Predicted chip shape with changing w G ( h B =0) Childs Part 2 28:3:2000 3:18 pm Page 254 The effect of undeformed chip thickness t 1 is considered in Figure 8.25, which compares the predicted chip shape with experiment at w G = 2.14 mm and h B = 0. When t 1 is increased from 0.10 mm to 0.36 mm, the chip shape is changed from continuous to segmented. In partic- ular, an ear- (or e-) type chip is generated at t 1 = 0.25 mm. The simulated chip morphology, including curl and thickness, is in good agreement with experiment (similar observations have been reported by Jawahir, 1990). When the rake angle is decreased, the segmentation is accel- erated and chips with a smaller radius are produced (Shinozuka et al., 1996b). 8.4.2 Three-dimensional cutting edge design Tools with cut-away rake faces, to restrict the chip contact to be shorter than it would natu- rally be, have advantages beyond that of chip control considered in the previous section. Smaller cutting forces, lower cutting temperature, longer tool life, better surface finish and the prevention of tool breakage can be achieved in practice, provided the restriction is properly chosen (Chao and Trigger, 1959; Jawahir, 1988). Slip-line field plasticity theory has been applied to two-dimensional machining with a cut-away tool, to analyse the changes to chip flow caused by a restricted contact (Figure 6.6 – Usui et al., 1964). Here, a closer-to-practice three-dimensional ICM finite element analysis is introduced of the Cutting edge design 255 Fig. 8.24 Variation of chip shape and forces at w G =2.6 mm and h B =0.4 mm Childs Part 2 28:3:2000 3:18 pm Page 255 effect – on steady-state chip formation, tool temperature and wear – of varying a cut-away in the region of the nose radius of a single point P20-grade turning tool, used to turn an 18%Mn–18%Cr alloy steel, at a cutting speed of 60 m/min, a feed of 0.2 mm, and a depth of cut of 2 mm, without coolant. The mechanical and thermal properties and friction and wear behaviour, assumptions (from measurements) are listed in Table 8.4. Simulation model The three-dimensional analysis has been developed from the two-dimensional ICM scheme described in Section 7.3. Figure 8.26 shows the analytical model for machining with a single point tool at zero cutting edge inclination angle. The x- and y-axes are, respectively, parallel and perpendicular to the cutting direction, and the z-axis is set along the major cutting edge. The tool is assumed to be stationary and rigid, while the work- piece has boundaries moving towards the tool at the specified cutting speed. Apart from 256 Applications of finite element analysis Fig. 8.25 Comparison of predicted chip shape with experiment ( w G =2.14 mm and h B =0) Childs Part 2 28:3:2000 3:19 pm Page 256 the obvious differences stemming from converting two-dimensional finite element stiff- ness equations to three-dimensional ones, the main complication is allowing the chip to flow in the z-direction. The formulation of sliding friction behaviour at the tool–chip inter- face is modified to allow for this: for a node i contacting the rake face, the following condi- tions are imposed on the finite element stiffness equation: Cutting edge design 257 Table 8.4 Mechanical and thermal properties used in simulation Flow stress characteristics: s — = A (e — ˘ /1000) M (e — /0.3) N GPa where A = 2.01 exp(–0.00177T), M = 0.00468 exp(0.00355T), N = 0.346 exp(–0.000806T) + 0.111 exp{–0.0000315(T–375) 2 } Friction characteristic: τ/k = 1 – exp(– µσ n /k) dh ⎛ C 2 ⎞ Wear characteristic: — = C 1 σ n exp ⎜– —— ⎟ ds ⎝ T ⎠ Young’s modulus E = 206 GPa, Poisson’s ratio ν = 0.3, Friction constant µ = 1.6, Wear constants C 1 = 14.67 MPa –1 , C 2 = 21 930 K Thermal conductivity K Density, ρ Specific heat, C [W m –1 K –1 ] [kg m –3 ] [J kg –1 K –1 ] Workpiece 12.6 7950 502 (18%Mn–18% Cr steel) Insert (carbide P20) 66.9 11200 402 Shank (0.55% C steel) 36.0 7750 461 Fig. 8.26 Three-dimensional machining model and boundary conditions Childs Part 2 28:3:2000 3:19 pm Page 257 dt u˘ i dt w˘ i F ˘ ˘ ix ′ = ( —— ) ————— F ˘ iy′ , F ˘ iz = ( —— ) ————— F ˘ iy′ , v˘ i = 0 ds n (u˘ i 2 + w˘ i 2 ) ½ ds n (u˘ ˘i 2 + w˘ i 2 ) ½ (8.4) where x′ and y′ are the local coordinate system as shown in the figure, F ˘ iy′ is the rate of normal force on node i, and (u˘′ i , v˘′ i , w˘′ i ) are the velocities of node i in the (x′, y′, z′) direc- tions. (dt/ds n ) is the effective friction coefficient given by the differentiation of the fric- tion characteristic, equation (2.24c). A further complication in description arises when a chip flows into a cut-away groove in a primary (plane) rake face of a tool. Although this has been dealt with in the example of Section 8.4.1, in the simulation in this section it is assumed that a chip makes contact only with the primary rake face. Figure 8.27 shows the finite element structure of the model. It is an assembly of linear tetrahedral elements (7570 elements and 1887 nodes in all). The mesh shown is an ICM initial-guess for turning with a plane rake faced tool, with cutting occurring over the major and minor cutting edges and over the tool nose radius. The tool geometry is (a p = 0˚, a f = 0˚, g p = 6˚, g f = 6˚, k′ r = 15˚, y = 15˚, R n = 1 mm) where the terms are defined in Figure 6.16. The mesh is automatically generated from a specified shear plane angle and chip flow direction, the tool geometry, feed and depth of cut. Cutting with this conventional, plane, tool is analysed as well as cutting with two cut-away tools derived from it. Views of the two cut-away tools, types I and II, are shown in Figure 8.28. Both of these tools have a secondary rake of angle 15˚ superimposed on the primary rake. The type I tool has a restricted primary land width r that is constant along the major cutting edge but reduces around the tool’s nose radius, to zero at the minor cutting edge, in the same way that the uncut chip thickness varies. The type II tool has a restricted land width that is constant 258 Applications of finite element analysis Fig. 8.27 Initial finite element mesh for a tool geometry (0º, 0º, 6º, 6º, 15º, 15º, 1.0mm) and f =0.2 mm, d =2 mm Childs Part 2 28:3:2000 3:19 pm Page 258 around both the major and minor cutting edges. The influences of these design differences, and also of varying the width r relative to the feed f are studied. The value of r over the major cutting edge, divided by f, is referred to as the restriction constant K. Simulation and experimental results The simulation predicts that type I tools should create lower deformation in the workpiece and lower tool temperature and wear than the plane faced or type II tools; and that K = 1.2 is a good value for the restriction constant. Experimental measurements, with tools of different rake face geometries created by electro-discharge machining, of tool forces, rake face temperatures – using a single-wire thermocouple (Figure 5.19(b), Usui et al., 1978) – and tool wear, support this. Figure 8.29 shows the final predicted chip shape and the distribution of equivalent plastic Cutting edge design 259 Fig. 8.28 Rake face geometries of types I and II cut-away tools Fig. 8.29 Equivalent plastic strain rate distribution and chip configuration when machining 18%Mn–18%Cr steel at a cutting speed of 60 m/min, f = 0.2 mm and d = 2 mm with (a) conventional, (b) type I and (c) type II P20 carbide tools Childs Part 2 28:3:2000 3:19 pm Page 259 strain rate for the plane-faced tool and type I and II tools with K = 1.2. The type I tool produces narrower plastic regions in the chip and workpiece, and less plastic deformation over the finished surface, than the type II and plane tools. As well as the plane and type II tools causing more deformation in the work surface beneath the major cutting edge, the type II tool generates a thicker chip at the minor cutting edge, and the chip flow angle is larger than for the other tools. Figure 8.30 shows temperature distributions over the rake faces. The dark region repre- sents the contact area with the chip, and the symbol * indicates the location of the highest temperature. The maximum temperature of the type I tool is 50 to 100˚C lower than the others. The type II tool produces a higher temperature than the type I tool at the minor cutting edge and nose radius, where the chip contact area is wider. However, the distance of the highest temperature from the major cutting edge is almost the same for both. Figure 8.31 shows the predicted contour lines of constant wear rate. The distribution and the isotherms in Figure 8.30 are closely correlated because temperature dominates the wear (Table 8.4 and equation (4.1c)). The wear of the type II tool is severe at the corner and near the major cutting edge, while the type I tool yields less wear along all its edges. Comparisons with experiment are shown in Figures 8.32 to 8.34. Figure 8.32 shows experimental measurements of cutting force variation with restriction constant K for the type I tools. Experimentally, there is a minimum in all the force components at around K = 1.2. The predicted forces show a similar tendency: predictions for the conventional and type II tools are also included in the figure. Figure 8.33 shows the measured and predicted rake face temperatures of the conven- tional and type I (K = 1.2) tools in the direction of chip flow at the midpoint of the depth of cut. A temperature difference of about 100˚C can be seen in both the predictions and experiments, although prediction and experiment are not in absolute agreement with each other. 260 Applications of finite element analysis Fig. 8.30 Tool rake face isotherms in the conditions of Figure 8.29: (a) conventional, (b) type I; and (c) type II tools Fig. 8.31 Contours of constant crater wear rate, conditions of Figure 8.29: (a) conventional; (b) type I; and (c) type II tools Childs Part 2 28:3:2000 3:19 pm Page 260 Figure 8.34 compares the differences in wear profiles at a cut distance of 600 m, obtained both by profilometry and microphotography. The type I tool shows least tool wear, more than 10% less than with the conventional tool: the similarity in wear distribu- tion with that predicted in Figure 8.31 is clear. In summary, a finite element machining simulation has been employed to analyse the turning of a difficult-to-machine 18%Mn–18%Cr high manganese steel with a sintered carbide three-dimensional cut-away tool. A cut-away design in which the primary restricted contact length varies along the cutting edge in proportion to the uncut chip thick- ness has been found to give a better performance than one with a restricted contact which is constant along the major and minor cutting edges and around the tool nose radius; and it is also better than a plane rake faced tool. A restriction constant of around 1.2 has been found to give the least cutting forces, leading to reductions in cutting temperature and tool wear. Cutting edge design 261 Fig. 8.32 Cutting force dependencies on restriction constant Fig. 8.33 Comparison of predicted and measured rake temperatures at the midpoint of the depth of cut, for plane and type I tools Childs Part 2 28:3:2000 3:19 pm Page 261 8.5 Summary A new concept of computational or virtual machining simulation is starting to emerge, based on the theoretical background surveyed in Chapter 7, to support the increasing demands of high productivity, quality and accuracy of modern automated machining prac- tice. There is no doubt that advances in computing capability and graphical visualization technologies will bring further developments in the field of machining simulation. At present, finite element simulation is mainly of use to mechanical and materials engi- neers, as a tool to support process understanding, materials’ machinability development and tool design. However, the computing time required by this method is too long for it to be of use in machine shops for online control and optimization, although it can help offline evaluation and rationalization of practical experience. Online control requires other sorts of machining models. These and their relationships with finite element models are the subject of the next and final chapter of this book, which considers how to use modelling and monitoring in the production engineering context of process planning and improvement. References Chao, B. T. and Trigger, K. J. (1959) Controlled contact cutting tools. Trans ASME J. Eng. Ind. 81, 139–151. Hazra, J., Caffarrelli, D. and Ramalingam, S. (1974) Free machining steels – the behavior of type I MnS inclusions in machining. Trans ASME J. Eng. Ind. 97, 1230–1238. Jawahir, I. S. (1988) The tool restricted contact effect as a major influencing factor in chip breaking: an experimental analysis. Annals CIRP 37(1), 121–126. Jawahir, I. S. (1990) On the controllability of chip breaking cycles and modes of chip breaking in metal machining. Annals CIRP 39(1), 47–51. Jawahir, I. S. and van Luttervelt, C. A. (1993) Recent developments in chip control research and applications. Annals CIRP 42(2), 659–693. 262 Applications of finite element analysis Fig. 8.34 Measured crater depth and optical micrographs of worn tools at a cut distance of 600 m: (a) conventional, (b) and (c) type I and II tools, K = 1.2 Childs Part 2 28:3:2000 3:19 pm Page 262 [...]... = 500f 0 .46 d 0.810 + 23 77(VS1.93 – 0.007ln V) × (VB 0 .26 – 0.007ln V) (VN –0.33 – 0.007ln V) Ff = 629 f 0.30 d 0. 720 + 1199(VS 3.58 – 0. 023 V 0 .27 ) × (VB –0.66 – 0 .23 V 0 .27 ) (VN 0.03 – 0 .23 V 0 .27 ) Fc = 1862f 0. 94 d 1.11 + 26 77(VS 0 . 24 – 0.05ln V) × (VB 0 .23 – 0.05ln V) (VN 0.16 – 0.05ln V) } (9.2b) where Fd, Ff, and Fc are values in N; V, f and d are in m/min, mm/rev and mm, respectively; and the... CIRP 23 (2) , 20 7 21 2 Pekelharing, A J (1978) The exit failure in interrupted cutting Annals CIRP 27 (1), 5–8 Recht, R F (19 64) Catastrophic thermoplastic shear J Appl Mechanics 31 (2) , 189–193 Sandstrom, D R and Hodowany, J N (1998) Modeling the physics of metal cutting in high speed machining Int J Machining Sci and Tech 2, 343 –353 Shaw, M C., Usui, E and Smith, P A (1961) Free machining steel (part. .. Shaw, M C (1999) Mechanics of saw-tooth chip formation in metal cutting Trans ASME J Manuf Sci and Engng 121 , 163–1 72 Williams, J E., Smart, E F and Milner, D (1970) The metallurgy of machining, Part 2 Metallurgia 81, 51–59 Yamaguchi, K and Kato, T (1980) Friction reduction actions of inclusions in metal cutting Trans ASME J Eng Ind 103, 22 1 22 8 Yamane, Y., Usuki, H., Yan, B and Narutaki, N (1990) The formation... Shirakashi, T (19 82) An evaluation method of fracture strength of brittle materials with disk compression test J Mat Sci Soc Japan 19 (4) , 23 8 24 3 Usui, E., Obikawa, T and Matsumura, T (1990) Chip formation and exit failure of cutting edge (2nd report) J Japan Soc Prec Eng 56(5), 911–916 Childs Part 2 28:3 :20 00 3:19 pm Page 26 4 26 4 Applications of finite element analysis Vyas, A and Shaw, M C (1999)... 9.3.3 deals with rule-based tool selection systems, a branch of knowledge-based engineering Childs Part 3 31:3 :20 00 10:37 am Page 26 6 26 6 Process selection, improvement and control Fig 9.1 Model-based systems for design and control of machining processes: (a) CAD assisted milling process simulator and planner (Spence and Altintas, 19 94) and (b) machining- scenario assisted intelligent machining system...Childs Part 2 28:3 :20 00 3:19 pm Page 26 3 References 26 3 Johnson, W and Kudo, H (19 62) The Mechanics of Metal Extrusion Manchester: Manchester University Press Lemaire, J C and Backofen, W A (19 72) Adiabatic instability in the orthogonal cutting of steel Metallurgical Trans 3 (2) , 47 7 48 1 Maekawa, K., Kitagawa, T and Childs, T H C (1991) Effects of flow stress and friction characteristics... Eng Ind 100, 23 6 24 3 Usui, E., Ihara, T and Shirakashi, T (1979) Probabilistic stress-criterion of brittle fracture of carbide tool materials Bull Japan Soc Prec Eng 13 (4) , 189–1 94 Usui, E., Maekawa, K and Shirakashi, T (1981) Simulation analysis of built-up edge formation in machining of low carbon steel Bull Japan Soc Prec Eng 15 (4) , 23 7 24 2 Usui, E., Ihara, T., Kanazawa, K., Obikawa, T and Shirakashi,... Kline et al (19 82) , Kline and De Vor (1983) and Moriwaki et al (1995): { }{ F* t F*/F* r t { }{ { }{ F* t F*/F* r t or = F* t F*/F* r t = = k t0 + k t 1 dR + k t 2dA + k t 3 f + k t4dR dA + k t5dR f 2 + k t6 dA f + k t 7 d 2 + k t8 dA + k t9 f 2 R k r 0 + k r1d R + k r2d + k f + k r4d d + k d f A R A 2 r5 R 2 r3 2 + k r6 dA f + k r7 d R + k r8 d A + k r 9 f k t1( fav )–kt2 ′ k r1( f av)–kr2 ′ } k t0 +... Page 26 8 26 8 Process selection, improvement and control A regression model example of such a non-linear equation (to be used in Section 9 .4) , for machining a chromium molybdenum low alloy steel BS 709M40 (British Standard, 1991) with a triple-coated carbide tool insert of grade P30 and shape code SPUN 120 3 12 (International Standard, 1991), held in a tool holder of code CSTPR T (International Standard,... simulation of high speed machining Int J for Num Methods in Engng 38, 3675–36 94 Nakayama, K (19 62) A study on the chip breakers Bull Japan Soc Mech Eng 5(17), 1 42 150 Naylor, D J., Llewellyn, D T and Keane, D M (1976) Control of machinability in medium-carbon steels Metals Technol 3(5/6), 25 4 27 1 Obikawa, T and Usui, E (1996) Computational machining of titanium alloy – finite element modeling and a few results . (carbide P20) 66.9 1 120 0 4 02 Shank (0.55% C steel) 36.0 7750 46 1 Fig. 8 .26 Three-dimensional machining model and boundary conditions Childs Part 2 28:3 :20 00 3:19 pm Page 25 7 dt u˘ i dt w˘ i F ˘ ˘ ix. f = 0 .2 mm and d = 2 mm with (a) conventional, (b) type I and (c) type II P20 carbide tools Childs Part 2 28:3 :20 00 3:19 pm Page 25 9 strain rate for the plane-faced tool and type I and II tools. oxide layer in machining resulphurised free-cutting steels and cast irons. Wear 139, 195 20 8. 26 4 Applications of finite element analysis Childs Part 2 28:3 :20 00 3:19 pm Page 26 4 9 Process selection,