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Procedia CIRP 14 (2014) 587 - 592

www.elsevier.com/locate/procedia

6th CIRP International Conference on High Performance Cutting, HPC2014

The influence of tool wear on the vibrations during ball end milling of

hardened steel

Szymon Wojciechowskia*, Pawel Twardowskia

aPoznan University of Technology,Piotrowo 3, Poznan 60-965, Poland * Corresponding author. Tel.: +48-061 6652608; fax: +48-061 6652200.E-mail address: sjwojciechowski@o2.pl..

Abstract

The work presented here, concentrates on the analysis of tool's vibrations generated during ball end milling process, including the influence of progressing tool wear. The process dynamics model including cutting parameters and tool wear width on the flank face (VBB) was developed. Experiments were carried out on hardened alloy steel X155CrVMo12-1 with sintered carbide (TiAlN coating) and cubic boron nitride (CBN) cutters. Instantaneous cutting forces and vibrations values were measured in three directions, in the range of progressing tool wear (VBB). The research revealed that vibrations generated in a stable milling process are strongly affected by the tool wear width on the flank face.

© 2014PublishedbyElsevier B.V.Thisisanopen access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selectionandpeer-review under responsibility of the International Scientific Committee of the 6th CIRP International Conference

on High Performance Cutting

Keywords: ball end milling, tool wear, dynamics

1. Introduction

The ball-end milling with inclined axis is usually applied in industry for the production of parts with complicated freeform surfaces. These parts are very often made of hardened steel, which requires the selection of appropriate machining technology, as well as tool material. Therefore ball end milling process of hardened steels is very often conducted in HSM (High Speed Machining) conditions.

The most popular cutting tool materials applied during HSM of hardened steel are: sintered tungsten carbides (WC) and cubic boron nitrides (CBN) [1]. According to [2], the application of CBN cutters is the most effective in the range of high cutting speeds, because of the presence of hot machining mechanism. The growth of cutting speed increases cutting temperature and thus the ductility of work material. Therefore, the authors of [3] indicate that CBN cutters can be effectively applied to the machining of hardened steels in the range of cutting speeds vc = 300 1200 m/min. Sintered carbides have significantly lower hardness and maximum cutting temperature than CBN materials. However their great popularity is related to the low price, as well as higher ductility and fracture toughness than cubic boron nitrides.

Nevertheless, independently of applied tool material, high speed machining of hardened steels induces the increase of cutting temperature, which as result can cause excessive tool wear [4].

Investigations [5] revealed that, the growth of tool wear width on the flank face during machining of hardened steel caused intense growth of cutting forces (especially the thrust force values). The excessive cutting force values are highly undesirable, because they significantly increase cutting power and can force unavoidable vibrations, which in turn affect machined surface texture [6], and tool wear. According to [3] the primary wear mechanism of tool materials during high speed milling of hardened steel is chipping induced by milling process dynamics, related to the generation of vibrations. However, progressing tool wear affects also the ploughing force value. The growth of this force increases the process damping and thus can inhibit the regeneration of chatter [7,8]. Therefore, reliable analysis of forces and vibrations is significant from the point of view of machining process technological effects, and thus needs further studies.

In this study, the analysis of shear and edge specific coefficients in function of progressing tool wear on the flank face during ball end milling of hardened steel is presented.

2212-8271 © 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the International Scientific Committee of the 6th CIRP International Conference

on High Performance Cutting

doi:10.1016/j.procir.2014.03.108

Obtained specific cutting force coefficients values are subsequently applied to the formulation of the cutter displacements (vibrations) model including tool wear effect.

2. Cutting forces and vibrations model

In order to determine cutter's instantaneous displacements related to cutter's deflections, induced by cutting forces Fx, Fy, Fz one should solve the following differential motion equation:

The elemental tangential dFtj, radial dFrj, and axial dFaj cutting forces acting on the j-th tooth, are expressed by:

m ■ *T (t) + Cx ■ ±r (t) + kx • xr (t) = Fx (t)

my • j>r(t) + Cy ■ yT (t) + ky • yT(t) = Fz(t)■ sina+Fy(t)■ cosa mz ■ ZT (t) + cz ■ zT (t) + kz ■ zT (t) = Fz (t) • cos a - Fy (t) • sin a

During ball end milling process of inclined surfaces, cutter's displacements (vibrations) in the tool coordinates are determined in the directions: perpendicular to the tool's rotational axis and collinear to the feed motion vector (yj(t)), perpendicular to the tool's rotational axis and feed motion vector (xj(t)) and parallel to tool's rotational axis (zj(t)).

In the equation (1) m,, c¡, kt denote modal parameters, (m -modal mass, c - damping coefficient, kt - stiffness coefficient) which can be determined using impact test, while Fx, Fy, Fz instantaneous cutting forces in the machine tool coordinates. In order to determine these cutting forces, mechanistic cutting force model, developed by Lee and Altintas [10] is applied. In this model, a set of curvilinear coordinate system normal to the ball envelope is used to specify the resultant force acting on the i-th infinitesimal segment of the cutting edge. Figure 1 depicts cutting forces acting on the cutter and tool coordinates for a ball end mill.

dFj = KJlj + KtcdAzj dFrj = KJlj + KrcdAj dFaj = Kaedlj + KacdAzj

where: Kte, Kre, Kae are the edge specific coefficients [N/mm], Ktc, Krc, Kac are the shear specific coefficients [N/mm2], dlj is the infinitesimal length of cutting edge [mm], Azj is the cross sectional area of cut [mm2].

The edge specific coefficients are depended on ploughing force, which is induced by the ploughing and rubbing phenomena occurring in the tool's flank face Aa (see Figure 2). During cutting, the work piece material which has the thickness lower than minimum uncut chip thickness (h<hmin) is not being cut but is ploughed and pressed under the tool's rake face [9] (Figure 2). This phenomena is induced mainly by the resiliency of the work piece material, as well as the occurrence of radius of tool arc cutting edge r„>0. This deformed material generates ploughing force acting on the tool's flank face. For the particular tool and work piece material ploughing force is depended mainly on the active length of cutting edge l, minimum uncut chip thickness hmin value and the appearance of chip regeneration mechanism. Nevertheless, the progressing abrasive tool wear VB on the flank face increases the contact length of tool and work piece (Figure 2), which in turn can significantly affect the ploughing force value.

Fig. 2. The distribution of ploughing force during orthogonal cutting with worn cutter (VB>0).

In order to calculate cutting forces acting on i-th infinitesimal segment of the cutting edge, it is necessary to determine cross sectional area of cut and active length of cutting edge, as well as calibrate specific coefficients.

On the basis of Figure 1 the instantaneous cutting forces in machine tool coordinates can be expressed:

Fig. 1. Geometry and tool coordinates for a ball milling cutter.

Fx = ZF ' sin V] ~ Frj • sin <Pr] ■ cos Vj - Faj • cos <Pr, ■ cos Vj ,

Fy Frj • sin <Prj sin V, - Faj ■ cos <Prj ■ sin V, - Ftj ■ cos V, ,

Fz =lLFrj ■ cos Vrj - Faj ■ sin Vrj ■

where: zc is the active number of teeth.

Positioning angles prj and of the j-th cutting edge found

in equation (3) are expressed by:

_ _ Vr1+Vr 2 ^ 2

9i = -30—V2 -(i-1) -I T|-2n(^-1)

where: pr1, pr2 are the initial and final positioning angle in the reference plane [rad],

Vn, V12 are the initial and final lag angle [rad], j is the ordinal number of tooth, N is the number of tool's rotation, n is the spindle rotational speed [rev/min], t is the time [s]. Instantaneous cross sectional area of cut can be calculated on the basis of equation:

Azj = R ■ fz • (l- cos(<Pr2 - «))• sin y.

where: R is the tool's radius [mm],

f is the feed per tooth [mm/tooth], a is the surface inclination angle [rad]. Infinitesimal length of cutting edge can be formulated from the expression proposed by [10], as:

a/ = + )2+-R!_d^

d^ J tan As

The r(y) expression in equation (7) can be formulated from:

- R -f-

I tanAs

In order to calculate the length of cutting edge and instantaneous cross sectional area of cut, it is necessary to define border conditions: yn, Vfi, Pn, Pr2. In this study, upward ramping process (Figure 3) was investigated.

Phase 1:

_ n■ n-t ^ 2( j-1)n

a =-> a. = ———4

30 1 z

2n(N -1)

-(1- cos cc) ■ tanAs + 2n(N-1)

0; Vi2= 0; Vn= 0; vr2= 0 Phase 2:

_% + 2(j -1)n + " 2 z

_ ap R -sin2 a

y/n= (1 - cos a)- tan As ys,2= (1 - cos cpr2 )• tan As

Vn =a (pr2 = a + arccos

C R - ap (Q ) R

In equation (13) ap(Q) denotes instantaneous depth of cut which depends on tool's rotation angle and is expressed by:

2n • j — 2n 11

ap (a) = sin2 a- |R sinj cos a- tanls - tanls +-+ 2n ■ N + a ^ - R sin2 a + a

Phase 3:

-2(j 1)n + 2n(N-1) + (1 -cosa)• taaÂs (15)

'Vir 0; ^2= 0; Wn= 0; ^2= 0

Fig. 3. Border conditions for the upward ramping process.

From the above deliberations and Figure 3 it is resulting that in case of upward ramping, tool cuts only when the phase 2 of tool immersion into the work piece occurs. It means that in milling with surface inclination, the active number of teeth can be less than one, and thus pulsating force can occur.

3. Experimental details

3.1. Work and tool materials

Investigations have been carried out on hardened cold-work tool steel X155CrVMo12-1 plate with hardness approx. 60 HRC and length Lf = 320 mm. Monolithic ball end mills made of sintered tungsten carbide (WC with TiAlN coating) and cubic boron nitride (CBN) were selected as milling cutters. Their geometry is presented in Table 1.

„ „ n 2( j 1)n ( a

a < a = —h —----arccosl 1--

R ■ sin a

Table 1. Cutting tools' geometry

d [mm] z 7° [°] A, [°] a° [°] rn [|^m]

WC 12 2 -15 30 6 5

CBN 12 2 0 0 6 5

In order to solve differential motion equation (1), modal parameters (m, c, k) were determined using impact test, and thus the following parameters were received: mxy = 0.019 Ns2/m, cx,y = 45 Ns/m, kx,y = 8481764 N/m, mz = 0.021

Ns2/m, cz

3.2. Research range and method

The measured quantities in the carried out research were: tool wear on the flank face VBB, cutting forces and vibrations fixed in machine tool coordinate system (Fx, Fy, Fz, Ax, A Az,). Cutting parameters applied in the research presented in the Table 2. Experiments were conducted on 5-axes CNC milling workstation (DECKEL MAHO Co., model DMU 60monoBL0CK), in upward ramping conditions, with surface inclination angle a = 45° (Figure 4). In all investigated cases tool's effective diameter was lower than the value of pick feed - Dej<br.

Table 2. Cutting parameters applied in the research

a [°] fz [mm] ap [mm] vc [m/min] n [rev/min]

45 0.02-0.1 interval 0.02 0.1 300 13505

Tool wear on the flank face VBB was measured - in the preliminary wear progress phase with the intervals of 5 passes, and in the stable wear progress phase with the intervals equaled to 50 passes (length of one pass - sample length Lj = 320 mm). The stereoscopic Carl Zeiss microscope was applied to measure tool wear VBB. The analysis of research results concerns the mean arithmetic value of tool wear VBB calculated for the two cutting edges of milling tool. The hooked up into a bed of a machine piezoelectric force dynamometer was used to measure total cutting force components. Its natural frequency is equal to 1672 Hz. In order to avoid disturbances induced by proximity of forcing frequency to gauge natural frequency, the band - elimination filter was applied. Acceleration of vibrations was measured using piezoelectric accelerometer, fixed to the work piece. Cutting force components and vibrations were measured (in machine tool coordinates - Figure 4), in following directions: direction X - Fx [N], Ax [m/s2], direction Y - Fy [N], Ay [m/s2], direction Z - Fz [N], Az [m/s2]. Measurements of cutting force components were carried out after each pass with variable feed per tooth value (from 0.02 to 0.1 mm/tooth). Subsequently, during the next 50 passes with constant feed per tooth value jz = 0.1mm/tooth, both cutting forces and tool wear weren't measured. After these 50 passes tool wear value, cutting forces and vibrations were measured for the variable feed per tooth values. This cycle was repeated until the tool wear had reached its dullness criterion (selected arbitrary as: 0.18 mm for CBN and 0.3 mm for WC).

Fig. 4. Cutting force components in machine tool coordinates.

3.3. The calibration of specific cutting force coefficients

In the investigations carried out it was assumed, that maximum instantaneous forces in X and Z direction (Fx, Fz) and minimum instantaneous forces in Y direction (Fy) per tool revolution are corresponding to maximum instantaneous values of cross sectional area of cut and active length of cut. In order to calibrate specific cutting force coefficients, maximum instantaneous forces per tool revolution in each direction (Fx, Fy, Fz) were acquired. These measured forces were substituted into equations for specific cutting force coefficients:

2(Ftcal - Fp )

K = 2(^1 -FJ K = 2(^1 -Fp). (i7)

2F 2F 2F

-ZIP K = P K = P

' l ' "" l ' re l

r"™ max max

where: Ftcal, Frcal, Facal are the cutting forces in tool coordinate system applied in calibration [N], Ftp, Frp, Fap are the ploughing forces in tool coordinate system applied in calibration [N], Azmax is the maximum value of cross sectional area of cut per tooth [mm2],

lmax is the maximum length of cut per tooth [mm]. Cutting forces in tool's coordinate system, applied in calibration can be calculated on the basis of equation:

Ftcal = 2 fc Sin Vcal - Fy C0SVcal I Facal = 2 (- Fx C0S Vcal C0S Vrcal ~ Fy sin Vcal C0S Vrcal ~ Fz sin Vrcal ) Frcal = 1 (- Fx C0S^cal sin^rcal " Fy si"^cal sin^rcal + Fz C0SVrcal )

Positioning angles qcah prcai applied for calibration, found in equation (19) can be calculated from the equation:

Val = Pmi

Vcal = Vrmx -

-ffmjn

Vr mix -V, 2

where: pmin is the minimal positioning angle per tooth [rad], ymax is the maximal positioning angle per tooth [rad], yrmin is the minimal positioning angle in the reference plane per tooth [rad],

Prmm is the maximal positioning angle in the reference plane per tooth [rad]. Estimated equations of specific cutting force coefficients are presented in the Table 3.

Table 3. Equations of specific cutting force coefficients

Form of equation

kte = 165VBB+53.2; kre = 385VBB +20.7; kae = -331VBB-16.7;

kac = 356645 VBB - 89792 VBB -2285; ktc = 91584 VBb2 - 51612 VBB +8488; krc = -841561 VBB2 + 303315 VBB-15470.

0.06 0.1 0.15 VS5 [mm]

indicating that progressing tool wear has also influence on the shear specific coefficients kic values acting on the rake face. However, this influence is described by a non-monotonous dependency (see equations in Table 3). It is probably caused by the progressing tool wear on the rake face, which influences effective rake angle values.

Figures 6 and 7 present estimated cutter's displacements in function of time for the various tool wear values VBB.

CBN kte = 200VBB+21.3; kre = 252VBB +30; kae = -166VBB -2.3; kac = 700 VBB3 - 6-106 VBB2 +558171 VBB - 14710; ktc = -700 VBb3 + 6-104 VBB2 -396780 VBb + 16497; krc = 0.6 VBB2 +196946 VBB - 240.

3.4. Results and discussion

The Figure 5 depicts edge specific coefficients Kie calculated on the basis of the measured cutting forces, in function of tool wear VBB.

Ï20 a.

5 10 1

0= 12 mm; s = 2; p,= 300m/min;/.i ap = 0.1 mm; a = = 0.02 mm/tooth," 4S"; WC IB, =0.1 mm

I 1 I 1 i [ j I 1 I_J —V, —fr

ï ï

j w W j w w u Wj 1

is g 20

I 10 £

D - 12 mm; ; = 2; ¡^ = 0.1 mm: tf = 45°: - iodm'min:= 0.02 mm/t«i(h; VBE AC 0.29 mm 1

—T, —ZT

Fig. 6. (a) modeled time course of cutter displacement for WC, VBB = 0.1 mm; (b) modeled time course of cutter displacement for WC, VBB = 0.29 mm.

B- l2mm:.-=2;<i,= C.l mm;a = 45°: CBN vr = 300utalJi;.£ = 0.02 mm tooth. VBB -0.03 mm

Fig. 5. (a) edge specific coefficients in function of tool wear for cubic boron nitride (CBN) cutter; (b) edge specific coefficients in function of tool wear for tungsten carbide (WC) cutter.

It can be found, that tool's flank wear VBB growth induced the linear increase of edge specific coefficients absolute values. This observation confirms the theory, that progressing abrasive tool wear VB on the flank face increases the contact length of tool and work piece (Figure 2), which consequently causes an increase in ploughing force value. From the Figure 5 can be also seen, that for worn CBN and WC cutters, the highest edge specific coefficient (and thereby ploughing force) value appeared in the radial direction (Kre, Fre), which is normal to the flank wear length VBB (Figure 2). It is worth

i> = 12 mm;: =2; a, = 0.1 mm;« = 45°; CBN 25 v, = 3ü0m/mia;/. = 0.02 mmVtoutb; Hi, = O.IK mm

liJUJLU J

~ jpirs- |JH**- pit"- ptf^ j

II 0.005 0.01 0.015

Fig. 7. (a) modeled time course of cutter displacement for CBN,

VBB = 0.03 mm; (b) modeled time course of cutter displacement for CBN,

VBB = 0.18 mm.

Figures 6 and 7 reveal, that the growth of the flank wear VBB caused an increase of cutter's displacement amplitude in three directions (XT, YT, ZT), for both investigated tool materials. It is resulting from the growth of specific cutting force coefficients together with flank wear, which consequently influences cutting forces, and thus cutter's displacements. This observation is also confirmed by the Figure 8, which presents estimated maximal cutter's displacements in function of tool wear.

" 20 -

Fig. 8. Modeled maximal cutter's displacement in function of tool wear for the tungsten carbide (WC) and cubic boron nitride (CBN) tools.

From the Figure 8 it can be seen, that maximal cutter's displacements (XT, YT, ZT) of CBN cutter for the flank wear VBB = 0.18 mm are lower than corresponding displacements for the WC cutter. This is attributed, to the lower cutting forces generated in milling with CBN cutters, in comparison to those generated with WC tools. This observation is partially confirmed by the vibrations (Ax Ay, Az) of work piece charts, measured during milling with CBN and WC cutters (Figure 9).

affected by the ploughing force value. The appearance of this force is related to the phenomena occurring in the tool's flank face, along the active length of cutting edge (e.g. tool wear).

4. Conclusions

In this work, the analysis of shear and edge specific coefficients in function of progressing tool wear on the flank face during ball end milling of hardened steel was presented. Obtained specific cutting force coefficients values were applied to the formulation of the cutter displacements (vibrations) model including tool wear effect.

The research revealed that tool's flank wear VBB growth induced the linear increase of edge specific coefficients absolute values, which is resulting from the growth of ploughing force value. The growth of these quantities can increase process damping and thus inhibit the regeneration of chatter. However, during the stable milling process it has direct influence on the vibrations growth, which is highly undesirable. The developed model revealed, that during ball end milling with cubic boron nitride (CBN) tools, cutter's displacements can be lower than those obtained for the tungsten carbide (WC) tool. Nevertheless, cutter's displacements obtained on the basis of this model need further experimental verification with the application of tool's displacement sensor (e.g. capacitive gap sensor), which can be applied to the accurate measurements of the cutter's working part instantaneous displacements. These measurements can be further applied to the analysis of phenomena occurring during the surface texture formation.

References

VBB [mm]

Fig.9. Measured RMS values of acceleration of vibrations in function of tool wear for the tungsten carbide (WC) and cubic boron nitride (CBN) tools.

During the milling with the flank wear VBB ~ 0.25 mm, the RMS values of vibrations in Ax and Az are higher for the WC tool in comparison to those for CBN cutter. However, for the lower VBB values, the contrary dependency is seen. It is also worth indicating, that, the Ax Ay, Az values were measured for the work piece in machine tool coordinates, while the XT, YT, ZT were calculated for the cutter in tool's coordinates. Nevertheless, both charts (Figures: 8 and 9) reveal that vibrations generated during ball end milling are increasing with the growth of flank wear.

In summary, results obtained on the basis of the developed model and experiments reveal that vibrations' amplitudes are

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