**3. The analysis of physical machinability indicators**

In this chapter the analysis of main physical machinability indicators, such as: cutting forces and vibrations will be presented. The set-up of cutting forces and vibrations measurements during face milling process is presented in Figure 6.

The hook up into bed of a machine piezoelectric force dynamometer was used to measure total cutting forces components [16]. Instantaneous force values were measured in feed force *Ff*, normal feed force *FfN* and thrust force *Fp* directions. Force dynamometer's 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. The acceleration of vibrations of tungsten carbide workpiece during milling was measured using piezoelectric accelerometer. These vibrations were measured in the same directions as cutting force components.

Machining Characteristics of Direct Laser Deposited Tungsten Carbide 109

In order to analyze forcing frequencies affecting cutting force components during milling of tungsten carbide, the FFT (Fast Fourier Transform) spectra were determined (Figure 8). From the Figure 8 it is resulting, that primary forcing frequency is tooth passing frequency *zfo.* Since number of teeth: *z*=2, the *zfo* frequency overlaps with the second harmonics of spindle speed frequency – 2*fo*. Therefore 2*fo* and *zfo* frequencies are dominant. It means that the dominative factor in *FfN* and *Fp* force time courses is milling process kinematics related to the cutting force generated by the each of teeth. Primary harmonic component *zfo* is accompanied by so-called "collateral bands" with the following values: *zfo* + *fo* and *zfo – fo.* They appearance is related to the occurrence of radial run out phenomenon. From the Figure 8 it can be also seen that frequency spectra of *FfN* and *Fp* force components consist of spindle speed frequency polyharmonics. Similar dependencies were observed for majority of investigated cutting force components

Figure 9 compares cutting forces in function of feed per tooth obtained during milling of tungsten carbide and hardened X153CrMoV12 steel (with 60 HRC hardness). It was observed that both in milling of tungsten carbide and hardened steel, cutting forces (*Ff* , *Ff N* , *Fp* ) are increasing monotonically with feed per tooth *fz* growth, what is typical dependency occurring in metal cutting processes. In tungsten carbide milling process, the highest force values appeared in thrust direction (*Fp* ), independently of feed per tooth *fz* value. As it was mentioned before, this phenomenon is probably caused by a friction of hard carbide particles on CBN tool flank face, which affects tool wear increase, and hence friction and thrust force *Fp* growth (it is worth indicating that after second experimental trial tool wear was *VBc* ≈ 0.07 mm). In case of milling of hardened steel, thrust force *Fp* has lower values than those obtained during milling of tungsten carbide. This is attributed to the significantly lower hardness of hardened steel (in comparison to tungsten carbide), which reduces tool wear intensity (tool wear after second trial: *VBc* ≈ 0), and thus values of thrust force *Fp* . The influence of work material's hardness on the cutting force values during machining is

Figure 10 depicts *RMS* values of vibrations in function of feed per tooth *fz* during milling of

frequency spectra.

described in details in [19].

tungsten carbide.

**Figure 8.** Frequency spectra of *FfN* and *Fp* force components

**Figure 6.** The set-up of force and vibration measurements during face milling of tungsten carbide [16]

Figure 7 depicts the tool wear (*VBc*) influence on *RMS* values of vibrations *Ap* and forces *Fp* .

**Figure 7.** *RMS* values of thrust force *Fp* and thrust vibrations *Fp* in function of tool wear *VBc*. Cutting conditions: *vc* = 68 m/min, *vf* = 180 mm/min, *ap* = 0.02 mm, *ae* = 6 mm

On the base of conducted investigations, clear relation between progressing tool wear and *RMS* values of forces and vibrations in thrust direction (*Fp* , *Ap* ) can be seen. Abovementioned relation is expressed by the correlation coefficient *R*2>0.8. Tool wear growth induced force *Fp* and vibration *Ap* increase, which stays in agreement with investigations [17] related to machining of hardened steel. It was stated that in machining process of tungsten carbide typical abrasion wear, (characterized by *VBc* indicator) concentrated mainly on flank face can be found. This phenomenon is probably caused by a friction of hard carbide particles on CBN tool flank face [18]. As a result, progressing abrasion of the tool binder induces the growth of friction force, which in turn is related to force and vibration (*Fp* , *Ap* ) increase. It is necessary to mention that, in remaining cutting force and vibration directions (*Ff* , *Af , Ff N* , *Af N* ) no correlation with tool wear *VBc* was found out (correlation coefficient *R*2 was lower than 0.1).

In order to analyze forcing frequencies affecting cutting force components during milling of tungsten carbide, the FFT (Fast Fourier Transform) spectra were determined (Figure 8). From the Figure 8 it is resulting, that primary forcing frequency is tooth passing frequency *zfo.* Since number of teeth: *z*=2, the *zfo* frequency overlaps with the second harmonics of spindle speed frequency – 2*fo*. Therefore 2*fo* and *zfo* frequencies are dominant. It means that the dominative factor in *FfN* and *Fp* force time courses is milling process kinematics related to the cutting force generated by the each of teeth. Primary harmonic component *zfo* is accompanied by so-called "collateral bands" with the following values: *zfo* + *fo* and *zfo – fo.* They appearance is related to the occurrence of radial run out phenomenon. From the Figure 8 it can be also seen that frequency spectra of *FfN* and *Fp* force components consist of spindle speed frequency polyharmonics. Similar dependencies were observed for majority of investigated cutting force components frequency spectra.

**Figure 8.** Frequency spectra of *FfN* and *Fp* force components

108 Tungsten Carbide – Processing and Applications

**Figure 6.** The set-up of force and vibration measurements during face milling of tungsten carbide [16]

*n*

*3D piezoelectric accelerometer*

**Measuring vibration amplifier** *NEXUS*  (*Brüel&Kjær*)

**Charge amplifier**  *(Kistler)*

*Fp Ff FfN*

*Ap Af AfN*

*Milling tool* 

*Workpiece*

*Piezoelectric force sensor* 

A/C

*Vf*

Figure 7 depicts the tool wear (*VBc*) influence on *RMS* values of vibrations *Ap* and forces *Fp* .

**Figure 7.** *RMS* values of thrust force *Fp* and thrust vibrations *Fp* in function of tool wear *VBc*. Cutting

On the base of conducted investigations, clear relation between progressing tool wear and *RMS* values of forces and vibrations in thrust direction (*Fp* , *Ap* ) can be seen. Abovementioned relation is expressed by the correlation coefficient *R*2>0.8. Tool wear growth induced force *Fp* and vibration *Ap* increase, which stays in agreement with investigations [17] related to machining of hardened steel. It was stated that in machining process of tungsten carbide typical abrasion wear, (characterized by *VBc* indicator) concentrated mainly on flank face can be found. This phenomenon is probably caused by a friction of hard carbide particles on CBN tool flank face [18]. As a result, progressing abrasion of the tool binder induces the growth of friction force, which in turn is related to force and vibration (*Fp* , *Ap* ) increase. It is necessary to mention that, in remaining cutting force and vibration directions (*Ff* , *Af , Ff N* , *Af N* ) no correlation with tool wear *VBc* was found out

conditions: *vc* = 68 m/min, *vf* = 180 mm/min, *ap* = 0.02 mm, *ae* = 6 mm

(correlation coefficient *R*2 was lower than 0.1).

Figure 9 compares cutting forces in function of feed per tooth obtained during milling of tungsten carbide and hardened X153CrMoV12 steel (with 60 HRC hardness). It was observed that both in milling of tungsten carbide and hardened steel, cutting forces (*Ff* , *Ff N* , *Fp* ) are increasing monotonically with feed per tooth *fz* growth, what is typical dependency occurring in metal cutting processes. In tungsten carbide milling process, the highest force values appeared in thrust direction (*Fp* ), independently of feed per tooth *fz* value. As it was mentioned before, this phenomenon is probably caused by a friction of hard carbide particles on CBN tool flank face, which affects tool wear increase, and hence friction and thrust force *Fp* growth (it is worth indicating that after second experimental trial tool wear was *VBc* ≈ 0.07 mm). In case of milling of hardened steel, thrust force *Fp* has lower values than those obtained during milling of tungsten carbide. This is attributed to the significantly lower hardness of hardened steel (in comparison to tungsten carbide), which reduces tool wear intensity (tool wear after second trial: *VBc* ≈ 0), and thus values of thrust force *Fp* . The influence of work material's hardness on the cutting force values during machining is described in details in [19].

Figure 10 depicts *RMS* values of vibrations in function of feed per tooth *fz* during milling of tungsten carbide.

Machining Characteristics of Direct Laser Deposited Tungsten Carbide 111

Regression equation *R*<sup>2</sup>

**Figure 11.** Specific cutting pressure *k <sup>i</sup>* in function of mean uncut chip thickness *h*

**10000**

**30000**

kc kcN kp

 **-** *k <sup>c</sup> - k cN - k <sup>p</sup>*

**50000**

*ki* **[MPa]**

**70000**

**90000**

Specific cutting pressure component Specific cutting pressure *ki*

**Table 1.** Regression equations of specific cutting pressure components

**4. The analysis of technological machinability indicators** 

Tangential *kc* = 388.9 *h* -0.872 0.873 Radial *kcN* = 385.4 *h* -0.845 0.901 Thrust *kp* = 644.1 *h* -0.798 0.915

Machined surface texture and tool wear are the essential factors determining cutting ability in practical applications. One of the most popular geometrical tool wear indicators is tool wear on the flank face designated by the *VB*. Its value can be measured using stereoscopic microscopes. The method of tool wear measurement is depicted in Figure 12. Machined surface texture can be examined using three and two dimensional (3D, 2D) measurements. 3D measurements can be achieved using stationary profilometer Hommelwerke T8000 (Figure 13). Two dimensional measurements can be made by T500 profilometer (Hommelwerke), equipped with T5E head and Turbo DATAWIN software. The sampling length *lr* = 0.8 mm, the evaluation length *ln* = 5·*lr* = 4.8 mm, the length of wave cut – off *λc*  (cut – off) = 0.8 mm and ISO 11562(M1) filter are usually applied in the measurements. As a result of 2D measurements the surface profile charts are received. On the basis of surface profile charts the *Ra* and *Rz* parameters can be calculated using appropriate software.

dynamics (e.g. machine tool stiffness).

From the Figure 11 it can be seen, that mean uncut chip thickness *h* growth is accompanied by the specific cutting pressure (*k <sup>c</sup>* , *k c N* , *k <sup>p</sup>* ) decrease. This phenomenon stays in agreement with the dependency observed in metal cutting processes. Between experimental specific cutting pressure values and calculated ones (based on regression analysis) some divergences can be seen. These divergences are expressed by the correlation coefficient *R*2>0.87 (table 1). Above-mentioned divergences have disadvantageous influence on mechanistic cutting force model accuracy. The reason of their occurrence could be attributed to milling process

**0 0,002 0,004 0,006 0,008 0,01 0,012** *h* **[mm]**

**Workpiece: Tungsten Carbide DLD; CBN mill;** *n***=1800 rev/min;**  *v <sup>c</sup>* **=68 m/min;** *a <sup>e</sup>* **=6 mm**

**Figure 9.** *RMS* values of force components in function of feed per tooth *fz* in milling of: a) tungsten carbide, b) hardened steel

**Figure 10.** *RMS* values of vibrations (*Af* , *Af N* , *Ap* ) in function of feed per tooth *fz* in milling of tungsten carbide

From the Figure 10 it can be seen, that feed per tooth *fz* growth induces monotonic increase of vibrations in all measured directions (*Af* , *Af N* , *Ap* ). It was observed that independently of feed per tooth *fz* value, vibrations in the thrust direction *Ap* have the smallest values, in comparison to the other measured directions. The reason of this phenomenon is probably connected with the highest tool stiffness in the thrust direction (parallel to rotational axle). The highest acceleration of vibration values (independently of feed per tooth *fz* value) occurred in the feed normal direction *Af N* . According to research: [20, 21], it could be caused by the direct contact of cutter radius and tool flank face with the machined surface, which is the major source of forcing vibrations, and also the smallest damping ratio in the feed normal direction compared to the other two axes.

In order to estimation of cutting forces in the broad range of cutting conditions, cutting force models can be applied. Majority of models assume that cutting force is proportional to sectional area of cut and the specific cutting pressures. Figure 11 depicts, empirically determined course of the specific cutting pressure in function of mean uncut chip thickness *ki*=f(*h*), in milling of tungsten carbide, while table 1 specific cutting pressure (*k <sup>c</sup>* , *k c N* , *k <sup>p</sup>* ) regression equations.

**Figure 11.** Specific cutting pressure *k <sup>i</sup>* in function of mean uncut chip thickness *h*

carbide, b) hardened steel

carbide

regression equations.

**Figure 9.** *RMS* values of force components in function of feed per tooth *fz* in milling of: a) tungsten

AfN Af Ap

*A fN A <sup>f</sup> A <sup>p</sup>*

**Figure 10.** *RMS* values of vibrations (*Af* , *Af N* , *Ap* ) in function of feed per tooth *fz* in milling of tungsten

*v <sup>c</sup>***=68 m/min**

**0 0,02 0,04 0,06 0,08 0,1 0,12** *f <sup>z</sup>* **[mm/tooth]**

**Workpiece: Tungsten Carbide DLD; CBN mill;**  *a <sup>p</sup>***=0.015 mm;** *a <sup>e</sup>***=6 mm** *n***=1800 rev/min;** 

From the Figure 10 it can be seen, that feed per tooth *fz* growth induces monotonic increase of vibrations in all measured directions (*Af* , *Af N* , *Ap* ). It was observed that independently of feed per tooth *fz* value, vibrations in the thrust direction *Ap* have the smallest values, in comparison to the other measured directions. The reason of this phenomenon is probably connected with the highest tool stiffness in the thrust direction (parallel to rotational axle). The highest acceleration of vibration values (independently of feed per tooth *fz* value) occurred in the feed normal direction *Af N* . According to research: [20, 21], it could be caused by the direct contact of cutter radius and tool flank face with the machined surface, which is the major source of forcing vibrations, and also the smallest damping ratio in the

In order to estimation of cutting forces in the broad range of cutting conditions, cutting force models can be applied. Majority of models assume that cutting force is proportional to sectional area of cut and the specific cutting pressures. Figure 11 depicts, empirically determined course of the specific cutting pressure in function of mean uncut chip thickness *ki*=f(*h*), in milling of tungsten carbide, while table 1 specific cutting pressure (*k <sup>c</sup>* , *k c N* , *k <sup>p</sup>* )

feed normal direction compared to the other two axes.

*Ai*

**\_***RMS* **[m/s2**

**]**

From the Figure 11 it can be seen, that mean uncut chip thickness *h* growth is accompanied by the specific cutting pressure (*k <sup>c</sup>* , *k c N* , *k <sup>p</sup>* ) decrease. This phenomenon stays in agreement with the dependency observed in metal cutting processes. Between experimental specific cutting pressure values and calculated ones (based on regression analysis) some divergences can be seen. These divergences are expressed by the correlation coefficient *R*2>0.87 (table 1). Above-mentioned divergences have disadvantageous influence on mechanistic cutting force model accuracy. The reason of their occurrence could be attributed to milling process dynamics (e.g. machine tool stiffness).


**Table 1.** Regression equations of specific cutting pressure components
