Metal Machining - Theory and Applications Episode 2 Part 4 pptx

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 co

angular velocity Vh/(Rc–t2) at point h, from the ICM analysis, is always greater than that

of Vg/Rcat 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 tt = mdst 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 tt > msst The static and dynamic friction coefficients msand mdare 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 s1cor tc A crack that

satisfies s1cpropagates in the direction of minimum principal stress, whereas one that

satisfies tc grows in the direction of maximum shear stress In this work, s1c= 880 MPa

and tc= 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 ≤ 10–6s (for the cutting speed of 100 m/min) is also needed

Simulation results

Figure 8.23 shows the chip shape simulated with changing wGand hB = 0 As wGincreases

from 1.6 mm to 2.0 mm, the radius of the broken chips becomes larger; and at wG = 2.6

mm chip breakage does not occur

Fig 8.22 Initial finite element model used for chip breakability analysis

Increasing hBaids chip breakage Figure 8.24 shows the development of chip shape with

time for wG= 2.6 mm but hB= 0.4 mm Plastic deformation with e—˘ > 10 s–1takes 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 FBHand FBVare the horizontal and vertical force components acting at point

B, and FCHand FCV 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

Fig 8.23 Predicted chip shape with changing wG(hB=0)

The effect of undeformed chip thickness t1is considered in Figure 8.25, which compares

the predicted chip shape with experiment at wG = 2.14 mm and hB = 0 When t1is 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 t1 = 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

Fig 8.24 Variation of chip shape and forces at wG=2.6 mm and hB=0.4 mm

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

Fig 8.25 Comparison of predicted chip shape with experiment (wG=2.14 mm and hB=0)

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 inter-face, the following condi-tions are imposed on the finite element stiffness equation:

Table 8.4 Mechanical and thermal properties used in simulation

Flow stress characteristics: s— = A (e—˘/1000) M

(e—/0.3) NGPa

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(–µσn/k)

Wear characteristic: — = C1σnexp ⎜– —— ⎟

Young’s modulus E = 206 GPa, Poisson’s ratio ν = 0.3, Friction constant µ = 1.6,

Wear constants C1 = 14.67 MPa –1, C2 = 21 930 K

Thermal conductivity K Density,ρ Specific heat, C

[W m –1 K –1 ] [kg m –3 ] [J kg –1 K –1 ]

(18%Mn–18% Cr steel)

Fig 8.26 Three-dimensional machining model and boundary conditions

dt u˘i dt w˘i F˘ ˘ ix′= (——)————— F˘ iy′, F˘ iz= (——)————— F˘ iy′, v˘ i= 0

dsn (u˘i2+ w˘i2)½ ds

n (u˘ ˘i2+ w˘i2)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/dsn) is the effective friction coefficient given by the differentiation of the fric-tion characteristic, equafric-tion (2.24c) A further complicafric-tion in descripfric-tion 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 (ap= 0˚, af=

0˚, gp= 6˚, gf = 6˚, k′r= 15˚, y = 15˚, Rn= 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

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

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

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

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

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

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

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

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

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