Flank Contact Load Distribution at Cutting Tool Wear

Kozlov Victor NicolaevitchNational Research Tomsk Polytechnic University, Tomsk,

kozlov-viktor@bk.ru

Abstract: Wear of cutting tool in the most of cases occurs on the tool flank and causes increasing of cutting force which results aggravation quality of processed surface and accuracy, destruction of tool. Knowledge of distribution of contact load on the wear chamfer of tool flank is used for analysis of stressed state, calculation of strength and rational use of cutting tools. Experimental and theoretical study of contact load distribution on the wear chamfer of tool flank is described. Character of cutting tool wear is depended from ductility of machined material because character of normal contact load on the flank wear is depended from type of chip and it connects with bending of cut off surface. Solving of theory of elasticity task was used about action of force on the elastic semispace and equation was received for curve of elastic recovering. Distributions of contact load were received by experiments for ductile and brittle brass. Normal contact load were calculated for checking theoretical study which showed good results.

Keywords-component: tool wear, tool flank, distribution of contact load.

Abbreviation and symbols: mps – meter per second (cutting speed v); mmpr – millimeter per revolution (feed rate s); MPa – mega Pascal (specific contact load as stress σ or τ); hf – wear chamfer width of cutting tool flank, flank chamfer can be natural or artificial as for this article; xh – distance frome cutting edge on a surface of flank wear chamfer; σh – normal specific contact load on a flankchamfer; τh – tangential specific contact load on a flank chamfer; HSS – high speed steel (material of cutting tool); Py – radial component of cutting force (for sharp tool it is radial force on a face in the main); Pz – tangential component of cutting force; – rake angle of cutting tool; – relief angle of sharp cutting tool; h – relief angle of a flank wear chamfer; b – cut width; a – cut off layer thickness; a1 – chip thickness; Ka – chip thickness ratio (Ka = a1/a) as a grade of plastic deformation in chip making zone; Φ – shear angle; h – value, which determines depth of elastic deformation, for ordinary task it is equal to thickness of processed part or radius r of machined disk; q – intensity of loading in the section of chip formation (MPa).

I. INTRODUCTION

In the most cases wear of a cutting tool flank with width hf(Fig. 1, b) is more dangerous than wear on a face and increases the cutting force which results increasing of heat and leads to destruction of a cutting edge. Character of cutting tool wear depends on ductility of machined material: in the first time for ductile materials it is wear on a face of cutter with appearance of groove, and for brittle materials it in the main is wear on a flank of cutter with appearance of chamfer with width hf and with relief angle h , ordinary h≈0 °. Very often flank wear

take place faster with decreasing of feed rate s or cut off layer thickness a. We will try to explain this phenomenon.

II. THEORETICAL BASIS

While cutting area moves along a plate (Fig. 1, a), elastic compression of material is determined by the radial component cutting force Py (Fig. 1, b). Therefore, the magnitude of the elastic recovery should be proportional to this force. Since distribution of the normal load in the section 2l of chip making zone must be taken into account in this case, the loading can be performed with a plane punch of the base length 2l and width b.

Chip making zone is moving ahead of cutter and is accompanied by wave of elastic deformation that cause fall of processed surface on value Umax (Fig. 1, b). Recovering surface mn1j behind of cutting edge contact with surface of flank wear mn (with width hf) and is deformed addition to position mnj.

In the theory of elasticity this task is named as confusion of tasks when stresses are set on the section of [– , + ] (chip making zone) and transferences are set on the area of [ , +hf](Fig. 1, b) (on the surface of flank wear chamfer). Value hdetermines depth of elastic deformation.

Correct solving this task for real conditions of cutting is complex. That is why we will use the next assumptions:

1. We decide that plate is flat neglecting shoulder because of small value of cut off layer thickness a. Influence of this

а b

Figure 1. Scheme of force interaction between tool and conditional shear planewith shear angle Φ (a) and with bending of have machined surface by radial

component Py of cutting force (b)

978-1-4673-1773-3/12/$31.00 ©2013 IEEE

shoulder on stress-deformation condition of plate behind of cutting edge is not significant;

2. Length of section , where is loading (stresses q) is equal to projection of conditional shear plane on border of semispace: 2 =a ctg ;

3. On the section , only normal stresses act and its distribution are uniform;

4. Cutting tool acts with surface mnj as a solid body (Fig. 1, b).

Solving of Bussinesk task was used about action of force on the elastic semispace and equation was received for curve of elastic recovering:

)13,114,0(1)( 22

xq

xExU , (1)

where: 2b

Pq y is intensity of loading in the zone of chip

formation.

It is necessary take into account radius r of machined disk with diametrical feed rate s (for orthogonal cutting it is cut of layer thickness a). In this case force action will be determined by value U(x) (Fig. 1, b):

5,0222

22

)( )()13,114,027,1(1 xrrxx

qE

U x (2)

Equation (2) has maximum which coordinate х0 is determined by parameters Py, b, , r, transferring at right (far from cutting edge) with increasing of force interaction intensity on the section [– ,+ ].

Distribution of normal specific contact load on a flank chamfer (stresses σh) has analogical view:

5,02222

2

)1(64,0)13,114,027,1(64,0 xrrE

xxqh

(3)

III. EXPERIMENTAL CONFIRMATION OF EXTREME EPURES CHARACTER

Date of our experimental research are shown on Fig. 2. These date were received by free orthogonal cutting of ductile brass Л63 (63% Cu) disk with “sectional tool” at artificial flank chamfer with width hf = 2.4 mm and h = 0 °. Radial feed rate s for free orthogonal cutting of disk is equal to cut off layer thickness a.

Extreme character of epures is visible in cases of curve 1, 2, 3 at cutting of ductile brass. Maximum of normal flank contact load for less feed rate (s=0.06 mmpr) is near to cutting edge and its value is greater than others.

IV. CONFIRMATION OF EQUATION (3)

Distribution of normal flank contact load calculated by equation (3) at cutting of disk Л63 with diameter d = 200 mm is shown on Fig. 3. Initial date of Py, cut off layer thickness a,

chip thickness a1, chip thickness ratio Ka (for calculation of shear angle Φ) were taken from experiments. Good correlation of calculated and experimental date in position of extreme σh is visible for less feed rate s = 0.06 mmpr (Fig. 3, curve 1). Compare this result with curve 1 in the Fig. 2 for the same condition.

For greater cutting speed (v = 3.6 mps at s = 0.21 mmpr) there is also good correlation: maximum of normal flank contact load is near to cutting edge in comparison to less cutting speed (v = 1.7 mps at s = 0.21 mmpr) (Fig. 3, curve 3 and 2 correspondently) as it is in (Fig. 2, curve 3 and 2 correspondently).

Figure 3. Distribution of normal flank contact load calculated by equation (3) at cutting of ductile brass disk.

ordinate – normal specific contact load on a flank chamfer, σh (MPa); abscissa – distance from cutting edge on a surface of flank wear

chamfer, xh (mm). =0º, =10º, h=0º:

1 – s= 0.06 mmpr, v = 1.7 mps; 2 – s = 0.21 mmpr, v = 1.7 mps; 3 – s = 0.21 mmpr, v = 3.6 mps

Figure 2. Distribution of normal flank contact load on the width of flank wear chamfer; = 0º, = 10º, h = 0º.

ordinate – normal specific contact load on a flank chamfer, σh (MPa); abscissa – distance from cutting edge on a surface

of flank wear chamfer, xh (mm). Ductile brass Л63 – HSS: 1 – s = 0.06 mmpr, v = 1.7 mps;

2 – s = 0.21 mmpr, v = 1.7 mps; 3 – s = 0.21 mmpr, v = 3.6 mps; Brittle brass ЛМцА 57-3-1 – HSS: 4 – s = 0.41 mmpr, v = 1.7 mps

V. CONFIRMATION OF EXTREM CHARACTER OF GRAPHS BY OTHERS AUTHORS

The same result has been produced by others authors with "sectional tool" method at cutting aluminum alloy [2] (Fig. 4). It is seen in Fig. 4 that maximum contact loads appear at some distance from the cutting edge independently on the wear edge width but authors [2] could not explain this phenomenon.

Calculation of loading intensity in the chip formation zone for our research shows that with decreasing of feed rate (s = 0.06 mmpr) intensity of loading in the area of chip formation q is increased, which causes increasing of normal flank contact load, though cutting force is less in comparison with greater feed rate (see Fig. 2 and 3).

So, maximum of normal flank contact load and its disposition is determined not by cut of layer thickness a but intensity of loading in the area of chip formation q, which can be larger for less a, as it was shown by calculation.

This phenomenon increasing of flank forces at decreasing feed rate s (or cut off layer thickness a) was observed by others researches [2]. Similar influence of wave of elastic deformation is appeared at calibration, when with decreasing of interference value of normal contact load on cylindrical surface of caliber quite the reverse is increased.

VI. EXPERIMENTAL CONRADICTIONS But we have not extreme character with position of curve

maximum far from cutting edge in case of brittle brass ЛМцА 57-3-1 (57% Cu, 1% Al, 3% Mn) cutting (see Fig. 2, curve 4).

VII. EXPLANATION OF EXPERIMENTAL CONRADICTIONS Bending of cut off surface is appeared in result of action

of force Py in the chip making zone. At continuous chip for

ductile brass Л63 this force is stable. At discontinuous chip for brittle brass ЛМцА 57-3-1 this force is not stable: the last stage of chip forming – separating of element from workpiece – is accompanied by fast reducing of force Py (sometimes to zero) in the area of chip making zone on section [- , ] (Fig. 1, b) [1].

Elastic recovering of cut off surface (mn1j) creates additional pressure proportionally approximately to transference U(x) (Fig. 1, b). It changes character of normal contact load distribution on the flank wear – maximum is near to cutting edge as it is for brittle brass ЛМцА 57-3-1 (discontinuous chip) (Fig. 2, curve 4).

And the greater loading intensity in the area of chip formation the greater normal flank contact load though cutting force is less in comparison with greater feed rate.

This fact explains increasing of tool flank wear at appearance of discontinuous chip and with decreasing of feed rate at constant cutting temperature.

Flank normal force increases great with decreasing of friction coefficient. It is necessary take into account that conditional (average) friction coefficient on a face and a flank can be different because of the different ratio length of plastic and elastic contacts. From our point of view friction coefficient on the face is more impotent. It influences on an action angle and so for normal load on chip making zone and elastic recovering surface mn1j behind of cutting edge (Fig. 1, b).

Influence of chip making character on character of flank normal contact loads distribution was checked at cutting of titanium alloy which characterized discontinuous chip formation (Fig. 5).

Figure 5. Distribution of normal flank contact load on the width of flank wear chamfer at cutting of titanium alloy disk with diameter 200 mm; ordinate – normal specific contact load on a flank chamfer, σh (MPa); abscissa – distance from cutting edge on a surface of flank wear chamfer, xh (mm). = 0º, = 10º, h = 0º: 1, 2 – s = 0.41 mmpr, v = 1 mps; 3, 4 –

s = 0.11 mmpr, v = 1 mps; 2, 4 – experimental date; 1, 3 – calculated date

Figure 4. Distribution of flank contact load for some values of the flank wear when cutting an aluminum alloy [2]

ordinate – normal σh and tangential τh specific contact load on a flank chamfer (MPa); abscissa – distance from cutting edge on a surface of flank wear chamfer, xh (mm).

γ = 10°; αh = 0°; v = 0.01 mps; a = 0.2 mm; hf (h) = 1 and 0.5 mm.

Distribution of normal contact loads behind of part C' (left) (Fig. 6, curves 1 and 3) was calculated with equation (3) considering that intensity q is equal normal contact stress on section C' (q = σh) where is contact of recovering surface with artificial flank chamfer.

VIII. CONCLUSION

1. Character of normal contact load on the flank wear is depended from type of chip and it connects with recovering surface.

2. At continuous chip maximal normal contact load on the flank wear is far from cutting edge and this distance is depended from force interaction intensity in the zone of chip making.

References [1] Poletika M.F., Afonasov A.I. Contact conditions on the cutting flank at

discontinuous chip making. – Progressive technological processes in machine building. – Tomsk, 1997, pp. 14-17 (in Russia).

[2] Physical fundamentals of metals cutting processes.-Ostafjiev V.A., Stabin I.P., Rumbeshta V.A. and others. – Kiev, Visha shkola (The Higher School), 1976. – 136 pp (in Russia).