A Chip Formation Study of the Micro-Cutting of Commercially Pure Titanium

Abstract

In recent years, micro-cutting has been employed to obtain components that are more detailed and/or have great surface quality, regardless of dimensions, like dental implants. In the manufacturing of medical/dental components, titanium and its alloys are biomaterials of great notability. Like in conventional machining, sustainability is a delicate issue because it does not only depend on environmental aspects. One simple solution would be to perform dry machining. However, in the machining of difficult-to-cut materials, like titanium and its alloys, the use of cutting fluids is generally recommended to avoid the high temperature causing damage to the tool and/or machined surface. Concerned with the quality surface that is required for dental components, this work investigates the use of cutting fluid in the micro-cutting of commercially pure titanium. Orthogonal micro-cutting experiments were carried out under dry and wet conditions, using cutting fluid at room and cooled temperatures. To evaluate the lubri-cooling performance, cutting efforts, the friction coefficient, specific cutting energy, and chip formation analysis were compared. The outcomes indicated that, under the test conditions, the use of dry cutting and high feed levels had a positive effect on micro-cutting performance.

1. Introduction

In the past, micro-cutting was a technique strongly correlated with the manufacturing of micro and meso devices, i.e., with the fabrication of parts with small dimensions. Nowadays, micro-cutting is employed to manufacture components of the most diverse sizes, aiming to improve the surface quality. Micro-cutting is a technique characterized by the employment of cutting conditions on a micro-scale, which allows for the attainment of a wide range of geometries in a short time [1].

To highlight the use of micro-manufacturing techniques, Byrne, Dornfeld and Denkena [2] debated their use in an ABS system, which allowed for reducing the weight of devices by 90% between 1995 and 2016. Micro-cutting still has several gaps to fill, particularly when applied to difficult-to-cut materials. The manufacturing of difficult-to-cut materials is strongly associated with high costs and poor productivity [3]. In the machining of difficult-to-cut materials, low cutting speeds can be used to avoid high temperatures since, due to the poor heat dissipation, the melting point can be reached, hampering the lubri-cooling of the cutting region [4].

Titanium and its alloys can be considered difficult-to-cut materials due to their low thermal conductivity and their chemical reactivity at high temperatures [5]. Titanium and its alloys are widely used in the aerospace, biomedical, and automotive industries due to their high strength-to-weight ratio and high corrosion resistance. In the field of biomedical engineering, titanium and its alloys are used for the manufacturing of implants and surgical instruments [6].

According to Shah et al. [7], Ti-6Al-4V titanium alloy is used in the manufacturing of orthopaedics components, and commercially pure titanium (Ti-CP), or grade 2, is generally used for dental components. Chauhan et al. [8] cited the great combination of properties that emphasize the use of Ti-CP for dental implants. The authors highlighted that the surface quality of the implants influences mechanical properties and corrosion behavior. In the manufacturing of dental components, like pillars, screws, and implants, micromachining processes were included to provide a great cost benefit [9].

In the machining of difficult-to-cut materials, the use of cutting fluids is considered essential. During the micromilling of Ti-CP, Kieren-Ehses et al. [10] observed that the cutting forces decreased when cutting fluids were employed, reducing the built-up edge formation. In the micro-milling of Ti-6Al-4V titanium alloy, Ziberov et al. [11] observed an improvement in the quality of the machined surface when lubri-cooling was employed. However, the tool life was higher in dry conditions.

Generally, cutting fluids improve the machining performance, reducing heat and the friction coefficient. However, they can seriously damage human health and the environment [12]. Furthermore, during the cutting, if the cooling presents low efficiency, the cutting temperature will increase, reducing strength and increasing the plasticity of the material, causing material adhesion in the tool and in the machined surface [13]. According to Yan et al. [14], the lubri-cooling of the shear deformation zone can reduce the hardness or ductility of materials due to the adsorption.

Most of the investigations on cutting fluids in machining aim to study lubricant concentration, vegetal oil-based types, and eco-friendly lubri-cooling systems, such as minimum quantity lubrication (MQL), cryogenic lubri-cooling, and others. Generally, the temperature of the cutting fluid is a neglected variable in conventional cutting, although cutting efficiency can be strongly affected. For example, in the grinding of SAE 52100 hardened steel, 60 ± 2 HRC, the extension of hardness can be reduced in 92% using fluid between 5 and 15 °C in the place of fluid at room temperature (28 ± 1 °C) [15].

When talking about innovation in machining, sustainability must be considered, covering economic, environmental, and social issues [16]. To quantify the sustainability in innovations more effort must be employed. Sustainability is a crucial target that rules the manufacturing sector, developing systems that encompass monitoring/metrology processes and artificial intelligence [17]. Orthogonal cutting can be considered a feasible alternative for studying sustainability aspects in the machining process—for example, a new coating or a cooling technique. In orthogonal cutting, the analysis of chip removal can reveal important information. The chip removal process can be evaluated considering several aspects, like microstructure, cutting conditions, lubri-cooling, and others [18].

According to Savkovic et al. [19], chip formation studies can be used to analyze the influential factors during the separation of materials. The authors highlighted the importance of the shear plane angle, which indicates the plastic deformation direction, among the machinability theories, which can be considered a machinability criterion. In this way, due to their mechanical and thermal properties, the cutting performance of titanium and its alloys can be studied through chip formation analysis. The machining of titanium and its alloys is characterized by its low thermal conductivity, because the heat during the cutting is concentrated at the cutting edge, increasing the temperature and plastic deformation [20].

Thus, this work presents a cutting-fluids study in the micro-cutting of commercially pure titanium (Ti-CP)—a biomaterial used in dental pins and implants. It involves comparing the chip formation, cutting efforts, and cutting specific energy under dry and wet conditions. Due to the low thermal properties of Ti-CP, the emulsion was employed at different temperatures: room temperature (about 24 °C) and cooled (about 9 °C). The interest of this work was evaluating the influence of cutting fluid temperatures on a micro-cutting phenomenon—the ploughing effect. Furthermore, we observed the possibility of improving the micro-cutting mechanism in Ti-CP, which would avoid any surface damage that can be caused during the cutting.

2. Material and Method

To undertake orthogonal micro-cutting in commercially pure titanium (Ti-CP), grade 2, we used a Romi CNC lathe, model GL 240M (Santa Barbara d’Oeste, Brazil), with a maximum power of 22.5 kW and a maximum rotation of 6000 rpm. The cutting fluid was pumped using a Grundfos pump, model CRK2-70/7 A-W-A-AUUV (São Bernado do Campo, Brazil), with a flow rate of 3 m³/h and a rated head of 67.7 m at 3500 rpm. A pipe of Ti-CP with an outer diameter of 12.7 mm and wall thickness of 0.89 mm was used as the workpiece. Uncoated carbide inserts, ISO TPGN 160304 H13A, and a holder, ISO CTGPL 2020 K16, both from Sandvik Coromant (Sandviken, Sweden), were used in this work. After assembly, the rake angle was equal to 6°, while the clearance angle was 5°.

The micro-cutting parameters were based on Lauro et al. [21] (

Table 1. Cutting parameters in micro-cutting of Ti-CP.

Parameter	Unit	Level
		−1	0	1
Cutting speed (vc)	m/min	60	-	120
Feed rate (f)	μm/rev	10	-	50
Fluid condition	Dimensionless	Dry	Room temperature	Cooled

). A 2²3 factorial was used, considering cutting speed (v_c) and feed rate (f) with two levels and cutting fluid with three levels. The tests were developed randomly, and all conditions were repeated twice. The feed rate was defined with a lower level and a level higher than the cutting-edge radius, at about 20 μm. The cutting length was fixed at 25 mm for all tests. The micro-cutting was carried out in dry and wet conditions. In the wet case, emulsions at 5% were employed at room and cooled temperatures, respectively, at about 24 °C and 9 °C. Paiva, Ruzzi, and Silva [15] observed that, during grinding, the use of cutting fluid at temperatures between 5 and 15 °C avoided thermal damage. Figure 1 shows the experimental setup.

Figure 2 presents a schematic illustration of the orthogonal micro-turning tests. In Figure 2a, a top view of the orthogonal turning scheme is visualized. A balance length of 50 mm was used to fix the workpiece. The wall of the pipe of Ti-CP defines the width of cut (b = 0.89 mm). The feed movement is performed in the direction of the axis of the workpiece, with the complete removal of the workpiece wall, reducing it in length and collecting the chip for evaluation. Feed and cutting forces are monitored during the orthogonal cutting. Figure 2b defines the orthogonal cutting terminology, where h is the undeformed chip thickness, which, in the orthogonal cutting, is equal to the feed, f, and h’ is the chip thickness, which is measured after cutting.

A piezoelectric dynamometer was used to monitor the cutting forces with a sampling rate of 4 kHz. The wavelet transform was employed to denoise the signal, discarding a portion at the beginning and at the end of the cutting, according to Figure 3. After the signal treatment, the values of the cutting force (F_c) and the Feed force (F_f) were used to calculate the machining force (F_m), according to Equation (1), the friction coefficient (μ), according to Equation (2), and the cutting specific energy (u_c), according to the Equation (3). In the equations, F_m is the machining force (N), F_c is the cutting force (N), F_f the is feed force (N), μ is the friction coefficient (dimensionless), γ is the tool rake angle (rad), u_c is the cutting specific energy (J/mm³), v_c is the cutting speed (m/s), V_rem is the removal volume at time increment (mm³), and Δt is the time increment (s).

$$F_m=\sqrt{F_c^2+F_f^2},$$

(1)

$$\mu ={\displaystyle \frac{F_f+F_c\times \tan \gamma }{F_c-F_f\times \tan \gamma }}$$

(2)

$$u_c={\displaystyle \frac{v_c\times F_m\times \Delta \mathrm{t} }{V_{rem}}},$$

(3)

A Mitutoyo microscope, model TM 510, equipped with the Motic digital imaging system was used to measure the chip thickness (h’). The chip thickness was used to calculate the chip compression ratio (ζ), according to Equation (4), and the chip deformation (ε), according to Equation (5), where ζ is the chip compression ratio (dimensionless), h’ is the chip thickness (mm), and h is the uncut chip thickness (mm). A scanning electron microscope (SEM), TM 3000 from Hitachi, was used to analyze the chip formation. The SEM images were segmented, as observed in Figure 4, to enhance the spilling surface. In the following step, through Equation (6), the ratio between the total slipping surface area (S_slip) and the total chip surface (S_total) was calculated in mm².

$$\zeta ={\displaystyle \frac{h^{\prime }}{h}},$$

(4)

$$\epsilon ={\displaystyle \frac{{\zeta }^2-2\zeta \times \sin \gamma +1}{\zeta \times \cos \gamma }},$$

(5)

$$S_{\%}={\displaystyle \frac{S_{slip}}{S_{total}}}\times 100,$$

(6)

To define the shear plane angle, three models were used based on Silva et al. [22]: the Experimental model (φ_exp), the Merchant model (φ_Merc), and the Lee–Shaffer model (φ_L-S), which are shown in Equation (7), Equation (8), and Equation (9), respectively, where φ_exp is the Experimental shear-plane angle model, γ is the tool rake angle (rad), ζ is the chip compression ratio (dimensionless), φ_Merc is the Merchant shear-plane angle model, and φ_L-S is the Lee–Shaffer shear-plane angle model. The experimental model, φ_exp, considers the shear stress to be equal to the shear strength of the workpiece, while the Merchant model, φ_Merc, considers the derivative of the shear stress, and the Lee–Shaffer model, φ_L-S, takes the maximum shear direction as the shear plane [22].

$${\phi }_{exp}=\arctan {\displaystyle \frac{\cos \gamma }{\zeta -sen \gamma }},$$

(7)

$${\phi }_{\mathrm{Merc}}={\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{1}{2}}\cdot \left(\mathit{arctan}\mu -\gamma \right),$$

(8)

$${\phi }_{\text{L-S}}={\displaystyle \frac{\pi }{4}}-\mathit{arctan}\mu +\gamma ,$$

(9)

3. Result and Discussion

Table 2. Experimental design and responses.

Control Factors			Responses
vc	f	fluid-	Fc	Ff	Fm	μ	uc	ζ	ε	S%	φexp	φmerc	φL-S
(m/min)	(μm/rev)		(N)	(N)	(N)	-	(J/mm3)	-	-	-	(°)	(°)	(°)
60	10	Dry	28.67	15.20	32.45	0.67	3.30	1.81	2.17	14.96	30.20	31.03	17.06
120	10	Dry	24.69	13.70	28.24	0.70	2.87	1.98	2.29	18.58	27.89	30.49	15.97
60	50	Dry	73.17	33.01	80.27	0.58	1.63	1.29	1.87	17.64	39.98	32.86	20.72
120	50	Dry	73.17	33.01	80.27	0.58	1.63	1.29	1.87	8.39	39.95	32.86	20.72
60	10	Room	30.57	18.92	35.95	0.77	3.66	1.63	2.05	30.30	33.04	29.12	13.25
120	10	Room	32.41	16.07	36.18	0.63	3.68	1.97	2.28	23.28	28.11	31.81	18.63
60	50	Room	91.55	44.49	101.79	0.62	2.07	1.43	1.93	27.75	36.88	32.04	19.08
120	50	Room	85.29	37.84	93.31	0.58	1.90	1.17	1.83	15.31	43.05	33.04	21.08
60	10	Cooled	32.87	19.94	38.45	0.76	3.91	1.99	2.30	30.29	27.81	29.38	13.76
120	10	Cooled	31.64	18.14	36.48	0.72	3.71	1.56	2.00	26.13	34.41	30.09	15.18
60	50	Cooled	93.38	49.10	105.50	0.67	2.15	1.17	1.83	26.16	43.06	31.13	17.26
120	50	Cooled	81.55	41.22	91.38	0.64	1.86	1.38	1.91	26.33	37.86	31.59	18.18
60	10	Dry	25.38	14.97	29.47	0.74	3.00	1.73	2.11	24.54	31.51	29.73	14.46
120	10	Dry	23.78	14.33	27.76	0.76	2.83	1.77	2.14	31.79	30.79	29.46	13.93
60	50	Dry	77.95	37.70	86.59	0.62	1.76	1.24	1.85	8.47	41.21	32.10	19.19
120	50	Dry	74.90	34.13	82.31	0.59	1.68	1.24	1.85	8.91	41.28	32.75	20.50
60	10	Room	31.59	18.42	36.57	0.73	3.72	1.88	2.22	31.48	29.21	29.88	14.76
120	10	Room	30.81	16.68	35.04	0.69	3.57	1.68	2.08	29.20	32.21	30.78	16.56
60	50	Room	87.86	43.30	97.95	0.63	1.99	1.26	1.85	14.73	40.83	31.88	18.77
120	50	Room	82.12	38.02	90.49	0.60	1.84	1.19	1.83	12.03	42.46	32.58	20.16
60	10	Cooled	34.11	18.13	38.63	0.67	3.93	1.64	2.05	33.85	32.87	31.00	17.01
120	10	Cooled	32.44	18.02	37.11	0.70	3.78	1.82	2.17	27.90	30.05	30.47	15.94
60	50	Cooled	94.80	48.20	106.35	0.65	2.17	1.16	1.82	16.74	43.28	31.53	18.05
120	50	Cooled	84.68	40.35	93.80	0.61	1.91	1.09	1.81	27.35	45.18	32.26	19.52

presents the experimental design with the measured outcomes. The cutting force, F_c, presented an average value equal to 56.64 N with a minimum equal to 23.78 N and a maximum equal to 94.80 N. For the feed force, F_f, the mean was 28.45 N, with 13.70 N and 49.10 as minimum and maximum values, respectively. The machining force presented 63.43 N as the mean result, with 27.76 N and 106.35 N as minimum and maximum values. The friction, μ, varied from 0.5755 to 0.7743 with a mean value equal to 0.6638. The specific energy in the micro-cutting, u_c, varied from 1.634 J/mm³ to 3.932 J/mm³, with a mean value equal to 2.690 J/mm³. The chip compression ratio, ζ, presented a mean of 1.516 varying from 1.093 to 1.990. The chip deformation, ε, presented a minimum of 1.809 and a maximum of 2.296, with a mean equal to 2.004. The mean of slipping surface ratio, S_%, was 22.172%, with a minimum and maximum equal to 8.392 and 33.852, respectively. The experimental shear angle, φ_exp, varied from 27.81° to 45.48°, with a mean equal to 35.96°. The Merchant shear angle, φ_Merc, presented a mean value equal to 31.24°, varying from 29.12° to 33.04°. Finally, the Lee–Shaffer shear angle, φ_L-S, varied from 13.25° to 21.08°, with a mean value equal to 17.49°.

Figure 5 shows the correlation plot matrix of the outputs. At the main diagonal, experimental kernel density plots are provided, to evaluate the distribution of each variable. Most of the outputs present an asymmetrical bimodal distribution, with a higher probability in the lowest results and small probability in the highest results. In the left lower part, scatter plots of all pairwise combinations of the outcomes are plotted. Associated with that, the pairwise Pearson correlation coefficients are depicted in the right upper part. The greater the number of ‘*’, the higher the significance of the correlation.

Figure 6 shows a correlation plot heat matrix with dendrograms grouping the most correlated outputs. As can be observed, there are two groups of responses with positive pairwise correlations: one composed by F_f, F_m, F_c, φ_exp, φ_Merc, and φ_L-S, and the other composed of ε, ζ, u_c, µ, and S_%. The correlation among outputs of distinct groups is negative.

The dendrogram of Figure 6 formed groups of variables in a hierarchical way. In the first group of correlated outputs, the Merchant and Lee–Shaffer shear angles are perfectly correlated and linked in the initial connection of the dendrogram. Another pair of responses is linked in a first level, F_m and F_c, i.e., machining and cutting force, since the first is calculated considering the last, which is the most important force component in magnitude. Then, Ff (the feed force) is linked with the two, as expected. The experimental shear angle is linked firstly to the cutting force components, and finally, this group of four variables is linked with the group of shear angle responses. The correlation between the experimental shear angle and the machining force will deepen later. For the second mentioned group, ζ and ε are grouped in the first level. These outputs measured, respectively, the chip compression ratio and the chip deformation, being physically related. The second is calculated in function of the first, according to Equation (5), justifying their strong correlation. The specific cutting energy, u_c, is then linked to these outputs in a second level of the dendrogram. The specific cutting energy is also related to the energy expended in chip deformation and removal. The friction coefficient, µ, is grouped in the next level of the plot, since the friction coefficient is also related to tangential and cutting forces considering rake angle correction. Therefore, we expected a positive correlation between friction coefficient u_c because some of the energy to remove material will be lost through the friction coefficient. Finally, S_% is the last response in the group, which measures the ratio between slipping and the chip surface, which is expected to be positively correlated with the friction coefficient.

It is important to evaluate the correlations more carefully. The model to estimate the specific cutting energy, u_c, depicted in Equation (3), presents a proportional relation between u_c and F_m. However, Figure 5 points out a negative correlation between the outputs. Figure 7a presents the scatter plot of these responses, with points separated into two groups according to the feed values. As can be observed, the pattern of positive correlations inside the groups obeys the model. In the micro-cutting, we expected the machining force to be lower with lower feed values. However, it can be observed that the highest results of the specific cutting energy, u_c, were obtained with the smallest feed of f = 10 μm/rev. This can indicate the occurrence of ploughing. In the case of the highest feed value, f = 50 μm/rev, the specific cutting energy decreases significantly as a consequence of the correct chip removal through cutting instead of ploughing.

Obviously, the u_c calculation through Equation (3) includes the proportional effect of the machining force, F_m, but there is an inversely proportional effect of V_rem, which, in turn, is directly proportional to the feed, f. However, in a conventional cutting regime, the growth in F_m with the feed increase would be enough to keep constant specific cutting energy, u_c, which is related to the Ti-CP strength under cutting. As this does not occur in the studied case, an increase in the specific energy with the small feed level supports the ploughing presence, with f = 10 μm/rev. To better support the occurrence of this phenomenon, the ratio between spilling and chip surfaces, S_%, which can also be termed the slipping surface ratio, was also evaluated as a more direct and experimental measure of ploughing. Figure 7b shows the scatter plot of F_m and S_%, with data separated according to feed level. The higher the S_%, the higher the possibility of ploughing. The highest S_% occurred with the smallest feed value.

Figure 8 shows the correlations between F_m and the shear angle. In the three estimates of the shear angle, the correlation between F_m and φ inside groups is not as clear as the general correlation presented in Figure 5 and Figure 6. It is clear that, for both F_m and φ, the feed level is a good discriminant. It is known from the literature that the shear angle is useful for identifying the ploughing, with the smallest values indicating the possibility of the occurrence of this effect [21]. As observed, in this study, the smallest values of the shear angle occurred with the smallest feed level.

To better evaluate the effect of the cutting conditions and the lubri-cooling in the orthogonal cutting of Ti-CP, it is important to evaluate the effects of these parameters in the outputs. ANOVA will be presented for all models, but only the most important of the evaluated responses will be plotted, due to the observed correlation between them.

Table 3. ANOVA for the forces during micro-cutting of Ti-CP.

Factor	Fc		Ff		Fm
	F-Value	p-Value	F-Value	p-Value	F-Value	p-Value
Cutting speed (vc)	25.004	0.309 × 10−3	51.828	1.09 × 10−5	39.177	4.20 × 10−5
Feed rate (f)	5219.458	<2 × 10−16	2517.936	2.57 × 10−15	5751.485	<2 × 10−16
Fluid cond. (fluid)	77.113	1.41 × 10−7	82.316	9.83 × 10−8	99.639	3.36 × 10−08
vc*f	11.092	5.99 × 10−3	16.657	1.522 × 10−3	15.454	0.002
vc* fluid	2.926	0.092	4.237	40.529 × 10−3	3.632	0.058
F* fluid	8.423	0.005	15.344	0.493 × 10−3	12.152	0.001
vc*f* fluid	4.719	0.031	3.765	0.054	5.634	0.019
	R2	R2adj	R2	R2adj	R2	R2adj
	99.78%	99.58%	99.57%	99.18%	99.80%	99.62%

presents the ANOVA for the forces during the micro-cutting of Ti-CP. The main effects of v_c, f, and fluid condition were statistically significant (p-value < 0.05 = α). Regarding the interactions, the term v_c*f was significant in F_c, while all twice interactions were significant in F_f and, in the case of F_m, v_c*f and the third-order interaction, v_c*f* fluid, were significant.

Figure 9 shows the third-order interaction plot of f, v_c, and fluid on F_m. Consider that a statistical positive effect implies an increase in the response with the increase in the quantitative factor or independent variable, while a negative effect means that the response decreases with the increase in the level of the quantitative factor. The feed presents a positive effect, i.e., in the machining force, while v_c presents a negative effect on F_m. The dry condition presented the smallest cutting force levels on F_m. The change of the cutting speed from 60 to 120 m/min decreased F_m by 7.3% on average, while the increase in the feed rate from 10 to 50 μm/rev increased F_m by 169.2%. Compared with the dry condition, the use of cutting fluid increased the machining force by 19.9% and 22.4%, on average, for the room and cooled temperatures, respectively.

In this work, the use of cutting fluid increased the forces during the cutting. High cutting forces can be indicative of a low temperature at the tool–chip interface [23]. In the turning of Ti-6Al-4V alloy with cryogenic lubri-cooling, Hong, Ding and Jeong [24] observed that the cutting forces increased with the decrease in the temperature in this interface due to workpiece material embrittlement.

To better understand the specific differences between means, the multiple comparison test of Scott–Knott was performed. The test was performed on the interaction f* fluid and v_c* fluid. Figure 10 shows the Scott–Knott test result for the interaction f* fluid. The comparison is performed inside each feed level. For the case of f = 10 μm/rev, the test grouped the fluid conditions in the flood with room and cooled temperatures, while the dry condition presented a statistically significant difference and the lowest F_m. For f = 50 μm/rev, it can be observed that all fluid conditions are statistically different, with dry resulting in the lowest F_m, followed by room and cooled fluid.

Figure 11 presents the Scott–Knott test result for the interaction v_c* fluid. As observed for v_c = 60 m/min, all fluid conditions are statistically different. For v_c = 120 m/min, the fluid at room temperature and cooled fluid presented similar performance, both losing to the dry condition.

Table 4. ANOVA for friction coefficient and cutting specific energy for micro-cutting.

Factor	μ		uc
	F-Value	p-Value	F-Value	p-Value
Cutting speed (vc)	4.637	0.052	28.483	0.177 × 10−3
Feed rate (f)	60.209	5.13 × 10−6	2557.387	2.35 × 10−15
Fluid condition (fluid)	1.416	0.280	126.195	8.74 × 10−9
vc* f	0.010	0.924	0.126	0.729
vc* fluid	2.687	0.109	0.995	0.398
f* fluid	1.417	0.280	21.616	0.105 × 10−3
vc*f* fluid	1.236	0.325	3.389	0.068
	R2	R2adj	R2	R2adj
	86.72%	74.55%	99.59%	99.21%

presents the ANOVA for the friction coefficient, μ, and for the cutting specific energy for micro-cutting, u_c. The model for the friction coefficient presented 74.55% of the data variability, with statistical significance only for the effect of the feed rate. The increase in the feed rate entailed a 13.8% decrease in the friction coefficient. In the case of the specific cutting energy, the effects of v_c, f, fluid, and the interaction f* fluid were statistically significant. The increase in the cutting speed and feed rate from the low to the high levels caused a reduction in the specific energy, on average, of 6.1% and 46.2%, respectively. When compared to the dry condition, the use of cutting fluid increased the cutting specific energy by 19.9% (at room temperature) and 25.2% (with cooled cutting fluid). The model presented 99.21% of data variability explanation. Since μ and u_c are positively correlated and the model for u_c presented better goodness-of-fit measures, effects plots will be discussed for this response. Figure 12 shows the interaction plot for the specific cutting energy.

The Scott–Knott test was performed considering the significant interaction for u_c, f* fluid. Figure 13 shows the results. For the smallest feed level, all fluid conditions present statistical significance in differences. For the highest feed rate, the fluid in the flood under room and cooled temperature conditions was classified in the same group, while the dry condition presented a statistical difference on average, with the smallest specific energy. As previously discussed, low specific energies can be related to the ploughing effect.

The ANOVA for the friction coefficient and for the cutting specific energy for the orthogonal micro-cutting of Ti-CP are shown in Table 4, with a significance level of 0.05. For the friction coefficient, only the feed rate was statistically significant. When we analyzed the specific cutting energy, the individual factors and the interaction between the feed rate and fluid condition were statistically significant. The Scott–Knott test (Figure 13) indicated that there was a statistical difference between all fluid conditions for the feed rate of 10 µm/rev. However, for the feed rate of 50 µm/rev, the use of cutting fluid at different temperatures did not show a statistical difference.

Table 5. ANOVA for chip compression, chip deformation and slipping surface ratio for micro-cutting.

Factor	ζ		ε		S
	F-Value	p-Value	F-Value	p-Value	F-Value	p-Value
Cutting speed (vc)	0.013	0.910	0.001	0.974	0.701	0.419
Feed rate (f)	84.972	8.57 × 10−7	65.553	3.32 × 10−6	18.802	0.968 × 10−6
Fluid cond. (fluid)	0.458	0.643	0.236	0.793	7.547	0.008
vc*f	0.149	0.706	0.088	0.772	0.032	0.861
vc* fluid	0.272	0.766	0.272	0.767	0.992	0.399
f* fluid	0.022	0.979	0.060	0.943	0.851	0.451
vc*f* fluid	1.161	0.346	0.941	0.417	1.896	0.193
	R2	R2adj	R2	R2adj	R2	R2adj
	86.72%	74.55%	85.12%	71.48%	77.82%	57.49%

presents the ANOVA for the chip compression ratio, ζ, chip deformation, ε, and the ratio between the spilling surface and chip surface or slipping surface ratio, S. As can be observed, for the three models, only the feed was statistically significant. Regarding the data variability explanation, the chip compression ratio presented the best result, followed by chip deformation and slipping surface ratio, with 74.55%, 71.48%, and 57.49%, respectively. Figure 14 shows the effects plot of the studied factors on the chip compression ratio. The average percent reduction caused by the change of feed levels, from low to high, in ζ, ε, and S is 30.6%, 14.0%, and 34.9%, respectively. The effects of v_c and fluid are not statistically significant, with the feed, f, being the factor responsible for explaining most of the data variability. The negative effect of f in ζ and ε is related to the decrease in the chip thickness h’ with the highest feed level. Since there is no difference between the fluid conditions regarding these outputs of removed material deformation, the dry condition is a sustainable option that presents the same efficiency as flood conditions at room and cooled temperatures in the chip removal process.

The Scott–Knott test for ζ is not necessary, since a post hoc test is important only when a factor with three or more levels is statistically significant, and the ANOVA is enough to ensure the difference in the two-level cases. However, for S_%, the fluid was statistically significant. Therefore, the Scott–Knott test was performed for this factor and the result is presented in Figure 15. As can be observed, the emulsions in the flood in both room and cooled conditions were classified in the same group, while the dry condition was distinguished with the smallest average S_%. Therefore, since S_% presents low results in dry conditions, ploughing was likely to occur in the fluid conditions with an emulsion in the flood, no matter the fluid temperature.

Figure 16 shows some SEM images of chip surfaces with the respective slipping surface ratio, S_%. The dry condition provided a better result for S_%. A higher ratio indicates that ploughing is more likely to occur. The higher the ratio of the slipping surface to the total surface measured, the higher the friction coefficient, and therefore, the ploughing. The slipping surfaces are represented by the black areas in the segmented images. It is observed that the dry condition presented the best result when compared with the wet fluid condition, no matter the fluid temperature.

Table 6. ANOVA for shear-plane angle models.

Factor	${\mathit{\phi }}_{\mathit{e}\mathit{x}\mathit{p}}$		${\mathit{\phi }}_{\mathit{M}\mathit{e}\mathit{r}\mathit{c}}/{\mathit{\phi }}_{\mathit{L}-\mathit{S}}$
	F-Values	p-Values	F-Values	p-Values
Cutting speed (vc)	0.070	0.796	4.927	0.047
Feed rate (f)	101.148	3.37 × 10−7	63.553	3.9 × 10−6
Fluid cond. (fluid)	0.698	0.517	1.642	0.234
vc* f	0.205	0.659	0.041	0.843
vc* fluid	0.374	0.696	2.746	0.104
f* fluid	0.062	0.940	1.610	0.240
vc*f* fluid	1.349	0.296	1.162	0.346
	R2	R2adj	R2	R2adj
	89.86%	80.57%	87.35%	75.75%

presents the ANOVA for the shear angle considering the experimental model and Merchant/Lee–Shaffer models. These last two cases resulted in the same F and p-values, since the models are perfectly correlated, as corroborated by Figure 17. Only the feed presented statistical significance in the shear angle for both models. While the experimental model presented 80.57% of data variability explanation, the models of Merchant and Lee–Shaffer for the shear angle accounted for 75.75% of data variability.

Lauro et al. [21] observed that chip compression, chip deformation, and the Lee–Shaffer shear-plane angle model can indicate the ploughing effect, with high specific cutting energy and low shear-angle results indicating ploughing. Taking the shear-plane angle model, the reduction of ploughing effect is discarded when considering the change in the fluid condition. The relevant change in shear angle is observed with the feed, with the ploughing likely to occur with f = 10 μm/rev. In this case, the Scott–Knott test is not necessary, since only a factor with two levels was statistically significant.

4. Conclusions

In this paper, an experimental investigation was performed to study the micro-cutting of commercially pure titanium. From this investigation, the main conclusions drawn are the following:

✓

Dry micro-cutting was feasible, considering forces as well as the friction coefficient and specific cutting energy.

✓

Feed rate was the most important condition regarding the ploughing effect and, consequently, the efficiency in micro-cutting. We observed the highest results for the specific cutting energy and slipping surface ratio with the smallest feed level, with the highest studied feed level being enough to avoid the ploughing.

✓

Image segmentation can be considered a great tool for studying chip morphology.

The main scientific contribution of this paper is the study of important micro-cutting outputs regarding the efficiency of the micro-cutting of Ti-CP. It was observed that, despite the highest feed generating the highest force levels, the specific cutting energy was higher in the smallest feed level, due to relationship between the feed level and the cutting-edge radius. The chip compression ratio and other outputs also highlight the difficulty of removing materials with feed levels smaller than the radius of the cutting edge. These results are supported for all cutting fluid strategies tested.

For future studies, it is recommended to assess the crack formation or residual in micro-cutting, aiming to reduce corrosion, since commercially pure titanium is used in the manufacturing of dental implants.