**Kerf Taper Defect Minimization Based on Abrasive Waterjet Machining of Low Thickness Thermoplastic Carbon Fiber Composites C**/**TPU**

**Alejandro Sambruno 1,\*, Fermin Bañon 1, Jorge Salguero 1, Bartolome Simonet <sup>2</sup> and Moises Batista <sup>1</sup>**


Received: 27 October 2019; Accepted: 10 December 2019; Published: 13 December 2019

**Abstract:** Carbon fiber-reinforced thermoplastics (CFRTPs) are materials of great interest in industry. Like thermosets composite materials, they have an excellent weight/mechanical properties ratio and a high degree of automation in their manufacture and recyclability. However, these materials present difficulties in their machining due to their nature. Their anisotropy, together with their low glass transition temperature, can produce important defects in their machining. A process able to machine these materials correctly by producing very small thermal defects is abrasive waterjet machining. However, the dispersion of the waterjet produces a reduction in kinetic energy, which decreases its cutting capacity. This results in an inherent defect called a kerf taper. Also, machining these materials with reduced thicknesses can increase this defect due to the formation of a damage zone at the beginning of cut due to the abrasive particles. This paper studies the influence of cutting parameters on the kerf taper generated during waterjet machining of a thin-walled thermoplastic composite material (carbon/polyurethane, C/TPU). This influence was studied by means of an ANOVA statistical analysis, and a mathematical model was obtained by means of a response surface methodology (RSM). Kerf taper defect was evaluated using a new image processing methodology, where the initial and final damage zone was separated from the kerf taper defect. Finally, a combination of a hydraulic pressure of 3400 bar with a feed rate of 100 mm/min and an abrasive mass flow of 170 g/min produces the minimum kerf taper angle.

**Keywords:** AWJM (Abrasive waterjet machining); CFRTP (Carbon fiber-reinforced thermoplastics); kerf taper; RSM (response surface methodology); ANOVA (Analysis of variance); C/TPU (carbon/polyurethane)

#### **1. Introduction**

The use of composite materials in industry has generated a large number of publications and research. Within their wide classification, carbon fiber–reinforced (CFRP) or glass fiber–reinforced (GFRP) polymer matrix composites are the most interesting [1–3]. These materials have an excellent weight-to-mechanical-properties ratio and have been of great importance in recent years, especially in the aerospace and automotive sectors, although others, such as sport, wind energy, and construction, also make use of these composites [4].

However, the type of polymeric matrix used in these materials is thermoset. This generates a series of drawbacks in production and application of these materials, especially in terms of recyclability and processing times [5]. For this reason, there is an alternative to this kind of matrix. In recent years, carbon fibers have been combined with a thermoplastic polymer (CFRTP) to replace thermosets [6,7]. Due to their chemical composition, these polymers have a major advantage over thermosets, as they can be reshaped after curing. In addition, within the wide range of thermoplastic polymers, there are high-performance polymers. These are able to reach large service temperature ranges and achieve excellent impact resistance [8,9]. Also, compared to thermosets, CFRTPs have a high degree of automation in their manufacturing and recyclability. This makes these materials strategic for various industries, such as automotive, aeronautics, civil, or sports [10].

Thermoplastic polyurethane (TPU) stands out. It is an elastic elastomer that can be manufactured by various methods and subsequently machined. According to Biron et al. [11], these polymers have a high performance and a current consumption level. Due to this, they can provide a considerable number of combinations of physical properties that make them extremely flexible materials and adaptable to a multitude of uses [12].

However, due to their complex nature, they are highly difficult to machine in order to obtain their final geometry. The main disadvantage is due to their reduced glass transition temperature. In most conventional technologies, such as milling or drilling, the temperatures generated exceed the glass transition temperature of CFRTP, giving rise to defectology.

Masek et al. [13] carried out a study on milling CFRTPs with different cutting geometries. The thermoplastic matrix used was polyphenylene sulfide (PPS). When undergoing dry machining, i.e., in absence of cooling liquids, the temperatures reached softened the thermoplastic matrix. This boosted the excess removal of the thermoplastic matrix, leaving the reinforcement free in the form of a burr or fraying. This issue is also generated in the machining of composite materials with a thermoset matrix [14]. This, together with the abrasive and adhesive wear generated on the tool, makes conventional processes ineffective when machining CFRTPs.

However, there are non-conventional technologies that make it easier to machine materials that are difficult to machine with conventional technology. Abrasive waterjet machining (AWJM) is now of great interest for the machining of thermoset and thermoplastic composites due to its excellent flexibility and high material removal performance [15,16]. Its main advantage compared to other processes is the reduction of thermal defects during machining. In this sense, the temperatures reached are very low, and CFRTPs and CFRPs can be machined without matrix removal [17–19].

However, AWJM presents defectology due to the inherent nature of the process. The jet, when hitting the material, generates a reduction in kinetic energy. This produces a decrease in its cutting capacity, giving rise to a conical geometry known as a taper [20,21]. This is usually associated with two geometric factors (Figure 1)—Upper width (Wt) and lower width (Wb), giving rise to the angles α ( ◦) and β ( ◦). The sum of these angles gives the taper angle or the kerf taper (KT, Φ).

**Figure 1.** Detail of the cut section where it is appreciated: The initial damage region (IDR), the smooth cutting region (SMC), and the rough cutting region (RCR).

Nevertheless, the methodology for evaluation of conicity used in most articles can generate failures in their measurements. The formation of the zone known as the initial damage region (IDR) is due to the erosive action of abrasive particles, which produce a combination between this defect and the taper angle. In this way, the evaluation of upper width (Wt) can be increased due to this erosive action, giving rise to a dispersion in the evaluated taper, as observed in results shown in references [22–24].

Other researchers [20,24–26], however, have taken into account three regions with different defectology that may appear in the cut section (Figure 1). These are the upper region, called the initial damage region (IDR), where a greater erosive effect is produced due to the impact of the waterjet and abrasive particles on the surface of material; the central region, called the smooth cutting region (SCR), which presents a more homogeneous cut due to the stabilization of the waterjet on the cutting slot; and the lower region, called the rough cutting region (RCR), where the waterjet disperses again, losing a great deal of kinetic energy.

The taper defect is of great importance because it occurs in any material and can result in final geometries that do not have the required dimensions; it especially can result in reduced thicknesses.

Machining a composite material using AWJM creates a series of defects regardless of the matrix the composite is made of. The jet is conditioned by the change of materials that compose the composite. The matrix with which the composite is created will influence, to a greater or lesser extent, the generation of defects after machining. Authors such as Masek et al. [15] and Rao et al. [14] have similar conclusions after machining composites with different matrices. For that reason, due to the fact that CFRTP composition is close to CFRP, similarities can be established in their results.

Dhanawade et al. [27] carried out a study on abrasive waterjet cutting in a thermoset polymeric matrix composite material. The CFRP used was 26 mm thick. In this study, a response surface methodology was carried out in which an ANOVA statistical analysis was performed to determine the influence of the cutting parameters. Dhanawade established that the most influential parameter in the taper angle was hydraulic pressure. An increase in the kinetic energy of the waterjet is produced by increasing this parameter. This increases your cutting capacity and reduces the conicity of the cut. In this way, the kerf taper is directly influenced by the amount of impact of abrasive particles and kinetic energy given by the waterjet.

In addition, an increase in the feed rate of the machine decreases the overlap of abrasive particle impacts, reducing its cutting capacity and thus increasing the taper angle. Kinetic energy is also reduced with an increase in the distance between jet and the material—called the stand-off distance (SOD)—Because it generates a greater dispersion of the jet at exit.

The abrasive mass flow also has a high influence on the conicity generated during cutting. A small increase in this parameter decreases the conicity obtained due to the greater cutting capacity of the jet. However, an excessive increase in the amount of abrasive particles produces a collision between them, rounding their edges and reducing their cutting capacity, which generates a greater angle of conicity.

Similar results were obtained by El-Hofy [17]. In this study, the minimum conicity that can be obtained was indicated by applying high hydraulic pressure combined with a small stand-off distance. The conicity obtained is reduced by increasing the feed rate, contrary to the findings of Dhanawade et al. [27]. This is because, at high pressures, an increase in feed rate generates a smaller upper width (Wt), producing a more constant cut.

The distance between the focusing tube and the surface is a very important parameter for obtaining the proper conicity. This is mainly due to a loss of kinetic energy in the form of dispersion of the jet when leaving the focusing tube. Most studies indicate that a recommended distance is usually 2–3 mm [20,28,29].

Popan et al. [30] studied the influence of the variation of stand-off distances for a thickness of 6 mm. In this study, a reduction in this parameter of up to 0.5 mm reduced the upper cutting width (Wt), thus decreasing the taper. In addition, a reduction in stand-off distance produces a decrease in the radius of zone affected by erosion (IDR) due to the initial impacts of abrasive particles.

Also, the thickness of the material has a fundamental role in the conicity generated by machining. A reduction in material thickness enhances the influence of parameters considered less decisive in large thicknesses. Wong et al. [31] studied waterjet cutting in a thermoset composite material with a 3 mm thickness. In this study, hydraulic pressure and abrasive mass flow (AMF) take second place. In this way, the main parameter that affects the conicity of the cut is the combination of stand-off distance and feed rate. The combination of a high distance with a high feed produces maximum conicity.

In view of the above, more information is required on the influence of cutting parameters on conicity and on the reduction of this defect. In addition, as there is no literature focusing on waterjet machining with abrasive CFRTPs, it is necessary to determine the influence on matrix change [13]. Also, methodology established in most articles, gives rise to considerable errors in the assessment of this defect, by not separating it from the area affected by abrasive particles.

For these reasons, this article proposes the evaluation of taper angle using a new methodology based on image processing. In addition, influence of cutting parameters will be determined by means of an ANOVA statistical analysis, in order to discuss the results obtained in machining of thermoset composite materials.

Finally, by means of a response surface methodology (RSM), a mathematical model will be obtained that predicts the conicity generated in abrasive waterjet cutting of low-thickness thermoplastic matrix composite materials.

#### **2. Materials and Methods**

In this article, carbon fiber (Twill 200 g/m2) was used as reinforcement, and thermoplastic resin (TPU, polyurethane) was used to manufacture the CFRTP composite. This composite was manufactured by a thermoforming process. Table 1 shows its main characteristics, as well as the fiber and matrix, respectively.


**Table 1.** Fiber, matrix, and carbon fiber–reinforced thermoplastic (CFRTP) characteristics.

A three-axis water-jet machine (TCI Cutting, BP-C 3020, Valencia, Spain) was used for the experimentation. The AWJM machine was equipped with an ultra-high capacity pump (KMT, Streamline PRO-2 60, Bd Nauheim, Germany). The water orifice of the machine had a diameter of 0.30 mm. The diameter and length of the focusing tube were 0.8 mm and 94.7 mm, respectively. All trials were carried out by a 120 mesh Indian garnet abrasive material.

In order to carry out the experimental design, a response surface methodology (RSM) was set up. This kind of methodology has already been employed by some authors in several experimental studies of the same order [27,31]. A face-centered composite design (FCD) with a total of 20 trials (8 factorial points–23, 6 axial points–2 <sup>×</sup> 3, and 6 center points) was established and carried out using Minitab® 18 software (18.1, Minitab, LLC, State College, PA, USA).

A complementary experimental design was carried out. Because of this design, experimentally obtained data can be matched with data predicted by Minitab analytical software (18.1, Minitab, LLC, State College, PA, USA). This comparison makes it possible to obtain the error generated between these values and confirms the accuracy of the response surface model.

Three main parameters, which include hydraulic pressure, feed rate, and abrasive mass flow, were employed to determine their influence of the kerf taper generated. These parameters were designated based on the limitations of the CNC machine used, as well as the levels most employed in reviewed literature [17,22,24,31,32]. Also, they were converted into three different levels (–1, 0, 1) that represent minimum, central, and maximum values, respectively (Table 2). In order to establish a stand-off distance in accordance with the results of other authors [20,28,29], 2.5 mm was the stand-off distance used in all the tests.


**Table 2.** Cutting parameters set.

Figure 2 shows the distribution of 20 test. They are machined in a 170 × 25 mm specimen with an 8 mm gap to optimize material consumption. Before machining, a horizontal cut was made at coordinate 0.0 in order to ensure the perpendicularity of each cut with the final machined part. A cutting length of 15 mm was fixed for each trial. Furthermore, each single cut starts 10 mm before the material side to achieve a constant flow of water and abrasive. Machining was carried out on three specimens (KT1, KT2, KT3) of the same CFRTP in order to obtain reproducibility of the results achieved.

**Figure 2.** Experimental design scheme of CFRTP machining carried out.

On the basis of this methodology, an ANOVA analysis was developed in order to obtain the statistical influence of input parameters on output variables. Pressure, feed rate, and abrasive mass flow were changed in accordance with the fact that the experiment was conducted according to Box-Behnken design (three-level). In addition, RSM allows us to generate different contour diagrams or response surfaces from a second order polynomial Equation (1). There are several articles that have implemented this type of equation in order to develop the results obtained in the experiments carried out [31,33,34].

$$\mathbf{Y} = \mathbf{C}\_0 + \sum\_{i=1}^k \mathbf{C}\_i \mathbf{x}\_i + \sum\_{i=1}^k \mathbf{C}\_{ii} \mathbf{x}\_i^2 + \sum\_{i$$

*Y* corresponds to the expected response, in this case the kerf taper generated (KT), *xi* are the parameters used in the study (P, FR, AMF), *C*0, *Ci*, *Cii*, *Cij* are the regression coefficients, and ε is the random error of the model.

A stereoscopical microscope (Nikon, SMZ 800, Tokyo, Japan) was employed in order to obtain macrographies of each slot (Figure 3a). Image processing software made it possible to define the contour of the smooth cutting region (SCR) generated (Figure 3b). After machining, a first analysis was carried out to establish the range that delimits the three separate zones in section of cut. Later, the region obtained was split into 100 points. A trend line that adjust to those points was created. The intersection of this trend line with the value 0 mm (minimum thickness) and 2.08 mm (maximum thickness) was forced (Figure 3c).

**Figure 3.** Macrographies obtaining procedure: (**a**) positioning in stereoscopical microscope; (**b**) image of a slot with the smooth cutting region (SCR) pointed out; (**c**) graph of the SCR points with intersection at 0.0 mm and 2.08 mm.

These intersection points are used to obtain the top kerf width (Wt, mm) and the bottom kerf width (Wb, mm). Finally, the kerf taper defect (KT) is defined as shown in Equation (2), where *t* is thickness of CFRTP in millimeters.

$$KT\left(^{\circ}\right) = 2 \ast \text{atan}\left(\frac{\frac{W\_l - W\_b}{2}}{t}\right) \tag{2}$$

#### **3. Results**

The kerf taper values obtained in the three specimens (KT1, KT2, KT3), as well as the average kerf taper and its standard deviation (average KT), are shown in Table 3.

All the results of the mean values given in Table 3 are positive. This means that, according to Equation (2), the upper width of the cut is always greater than the lower width. It follows that the geometric shape obtained in all machined slots has a "V" shape. This geometric effect is produced by the material thickness together with the transverse feed rate and energy amount (pressure and focusing tube diameter). These variables affect the shape distortion of the slot [35]. It should be pointed out that the kerf taper defect generated in waterjet machining is independent of the thickness of material. This defect will be greater or smaller according to this thickness, but it will always happen, even in materials of small thicknesses, such as the CFRTP used in this article.

Average kerf taper values between 2.15◦ and 7.79◦ were obtained. It is necessary to remember that there is currently no article that analyzes the taper defect in abrasive waterjet machining of thermoplastic composite materials. Some of reviewed literature [22,24,27] shows values close to the range obtained in this experiment, although some specific kerf taper values are different. It must be taken into account that the composites used in the other articles are made of a thermoset matrix. Most of them contain a higher glass transition temperature than the thermoplastic resin used in this experiment. In addition, fixed variables such as the focusing tube diameter and abrasive grain size change during the mixing process and could generate different results.

On the other hand, not all of the existing literature takes into account the three areas generated in cutting slot—The initial damage region (IDR), the smooth cutting region (SCR), and the rough cutting region (RCR). The emphasis in this article is on the independent treatment of such areas. Several authors [17,22,24,27] calculate the kerf taper defect without taking this indication into account. This could cause the kerf taper values to be altered by the rounding radius generated on the top surface of machined material. This radius occurs when the waterjet hits the surface to be machined. Abrasive particles, in a first instant of contact, meet a wall that they must pass through. Not all of them are able to do it, so they disperse along the upper surface of the material, producing a rounding at the input of cut.


**Table 3.** Kerf taper values obtained in all tests.

Furthermore, taking into account the RCR zone means that there may be an error when obtaining the values. In this area, the waterjet comes out of machined material, resulting in a new opening. In composite materials, carbon fibers and the matrix can become detached by creating loose yarns or cavities. Therefore, 10% of the cutting slot as was chosen as the RCR zone.

Two macrographies of the cutting section of two machined slots with different parameter combinations are shown in Figure 4. A rounded radius produced in the upper face of the cutting slot is shown in both figures. This defect is usually caused by the collision of the waterjet and abrasive particles with the top face of material. The radius obtained for Figure 4a is 0.063 mm, while the radius generated in Figure 4b is 0.037 mm.

**Figure 4.** Cutting path macrograph for machining under conditions: (**a)**. P 1200 bar, FR 100 mm/min, AMF 340 g/min; (**b)**. P 2500 bar, FR 300 mm/min, AMF 340 g/min.

This confirms the randomness that can be obtained in two slots machined on the same material. In addition, the point that separates IDR zone from SCR is found at different heights. Figure 4a shows the point at a height equivalent to 80.50% of total thickness (2.08 mm), and Figure 4b shows it at 87.25% of that thickness.

To sum up, taking into account the thickness of material used in this article, cutting section was split according to 0–10% of the thickness for the rough cutting region, 10–75% for the smooth cutting region and, 75–100% for the initial damage region. This article considers the kerf taper defect in the SCR (Figure 5).

**Figure 5.** Detail of a real cut section where it can be seen the areas: Rough cutting region (RCR) 0–10%, smooth cutting region (SCR) 10–75%, initial damage region (IDR) 75–100%.

#### *3.1. Statistical Analysis*

An ANOVA analysis of the obtained kerf taper values is shown in the Table 4. As discussed in the methodology section, a second order quadratic model was employed. This model allows us to relate the input parameters used in experiment (pressure, feed, rate and abrasive mass flow) with the results obtained after machining. The ratio between both variables makes it possible to create greater or lesser accuracy between them. The p-value of this model is less than 0.05, which indicates that it is statistically significant. In addition, a high F-value will make variable more relevant in the analysis.


**Table 4.** ANOVA analysis of the kerf taper values obtained.

As can be seen in Table 4, pressure and feed rate are the most significant parameters in taper defect. This is deduced because p-value is 0, i.e., the significance is maximum. It is observed that the AMF parameter has a p-value of 0.15, which implies that this variable has less influence on the generation of the taper angle. In addition, it can be seen that the F-value for pressure variable triples to that obtained for feed rate. This allows us to deduce that, although both variables are significant, hydraulic pressure has greater weight in the generation of the kerf taper.

These statistical results are consistent with the articles related to the topic studied. Therefore, it can be concluded that, for generation of a taper defect, the order of parameters according to their influence is hydraulic pressure, feed rate, and abrasive mass flow.

Equation (3) shows mathematical model obtained for analyzed response surface methodology. This equation presents an R2 of 93.85%, which implies a value very close to 100%. In later sections, a verification of Equation (3) will be performed from input variables shown in Table 3.

$$KT = 1.00 + (0.7P + 124.8FR + 153AMF + 0.08FR^2 - 0.17AMF^2 - 0.04P \ast FR - 0.13FR \ast AMF) \ast 10^{-4} \tag{3}$$

#### *3.2. E*ff*ect of Hydraulic Pressure on Kerf Taper*

The effect of hydraulic pressure on variation of the kerf taper is shown in Figure 6. To discuss these data, feed rate and abrasive mass flow variables have been kept fixed and at their intermediate level (FR = 300 mm/min; AMF = 225 g/min). Three machined specimens have been classified with different colors. Thus, red color corresponds to test piece 1, yellow to test piece 2. and green to test piece 3. In addition, each figure shows the mean value of taper defect obtained for each test. This value was represented with a discontinuous line followed by mean value and resulting deviation. Pressure is one of the most influential variables in machining, therefore Figure 6 contains images that facilitate visual compression.

**Figure 6.** Variation of the kerf taper in three specimens as a function of pressure (FR = 300 mm/min; AMF = 225 g/min).

At first sight, the taper decreases as pressure increases. By taking a look at the mean values obtained and pressures involved, it can be seen how the resulting data adjust to a large extent to a linear regression. Higher pressure means an increase in kinetic energy generated by the waterjet. This increase in kinetic energy leads to a higher material removal. Consequently, the walls of the slot are subjected to a greater force in removing the material that causes a more vertical final state.

By looking at the graph with values of each specimen independently, it can be seen how specimen 2 in all cases has a taper value smaller than 1 and 3. This may have been affected by the nature of the composite. The material is composed by long carbon fibers and thermoplastic matrix sheets. The arrangement of these elements along the composite is crucial to carry out the machining. In this way, a fiber yarn displaced at the time of manufacturing or an irregular consolidation of matrix along the surface could alter its homogeneity (Figure 7). Nevertheless, the decreasing tendency of the taper defect as hydraulic pressure increases is reflected in three specimens studied. In this case, a value of

3400 bar generates the lowest taper, being 2.15◦. It should be noted that the thickness of composite employed is considered thin, which could make it easier for kinetic energy created by pressure to generate a homogeneous wall in slot.

**Figure 7.** Macrographs of a composite cross-section with (**a**). thermoplastic matrix; (**b**). thermoset matrix.

A study carried out by Dhanawade et al. [27] shows a similar trend to that generated in this research. The material used in its study is a composite formed by carbon fibers and thermostable epoxy resin. They agree that an increase in pressure generates a decrease in taper defect. In addition, Dhanawade et al. use a hydraulic pressure that reaches 4000 bar, obtaining a taper angle that oscillates from 2.2◦ to 3.8◦. It can be deduced that these results agree with those obtained in this article. Therefore, if the pressure parameter is analyzed in isolation, it seems that the kind of resin used in composite material does not greatly influence the kerf taper generated.

Ruiz-Garcia et al. [20] carried out a study on the analysis of the kerf taper defect in the abrasive waterjet machining of CFRP/UNS A97075 stack. In that paper, the kerf taper results obtained were found in a range of 1◦. Ruiz-Garcia et al. used lower feed rates than those used in this article. This resulted in a greater homogeneity of taper defects as well as a smaller variation of them. In addition, the matrix used by Ruiz-Garcia et al. was epoxy resin, which has a higher vitreous transition temperature than the thermoplastic resin used in this experiment (TPU—polyurethane, 145 ◦C). The use of a thermoset resin could allow the composite to achieve greater mechanical properties than the CFRTP employed in this experiment.

#### *3.3. E*ff*ect of Feed Rate on Kerf Taper*

Figure 8 shows the effect of feed rate on the kerf taper defect. The distribution of elements in graph is similar to the one shown in Figure 6. As for previous section, this figure contains 3 images that make it easier to understand. It can be seen how, unlike for pressure, average values of kerf taper rise as feed rate increases.

A slower cut is made when a slot is made with a minimum speed of 100 mm/min, causing a more homogeneous fracture along the surface of material. In this case, waterjet is able to pass through material and remove each layer of carbon fiber and matrix in an orderly way. This effect, together with abrasive particles, reduces the influence of cohesion nature of a composite material on the generation of kerf taper. Therefore, it follows that applying a low feed rate, kerf taper achieved will be smaller, or in other words, upper and lower width of slot are values closer to each other.

On the other hand, when a high feed rate is applied, a loss of kinetic energy is generated in cutting channel. These could produce a decrease in material removal and a decrease in abrasive particles affecting the surface of material. On this occasion, the waterjet is more susceptible to the nature of the material. Different layers of carbon fiber and matrix take advantage of the reduced energy of the jet to make it difficult to pass through the composite. This can lead to the slot walls not being perpendicular, resulting in the upper width of slot being greater than the lower.

Thus, the lowest taper value will be produced for a feed rate of 100 mm/min, being 2.55◦, and the highest value will be produced with a feed rate 500 mm/min, resulting in 5.64◦. The lower thickness of the material employed, combined with a low feed rate, are parameters that help to create a homogeneous cut by AWJM.

**Figure 8.** Variation of kerf taper in three specimens as a function of feed rate (P = 2500 bar; AMF = 225 g/min).

Everything discussed above is consistent with Wong et al. [31]. In this paper, the authors analyze the taper defects in a carbon fiber thermostable matrix (epoxy). The FR used oscillated in 1000–2500 mm/min, which is a little bit higher than that carried out in this article. However, the authors conclude that a greater feed rate implies a lower amount of abrasive particles affecting the material. The decrease in the amount of these particles caused a dirtier and more random cut.

As the cutting speed increases, the upper and lower widths of the slot decrease. However, the width of the bottom surface has a greater decreasing tendency than the top surface. This is consistent with articles that study the taper defect in other kinds of materials [36,37].

#### *3.4. E*ff*ect of Abrasive Flow Rate on Kerf Taper*

The influence of the abrasive mass flow (AMF) on generation of taper defect is shown in Figure 9. In Section 3.1, it was concluded that this parameter is the least influential of the three used in this article. However, this fact does not imply that the amount of abrasive employed does not affect the results. In fact, by looking at the trend of the mean values plotted in Figure 9, it can be seen how it ascends as the amount of abrasive increases. The upward trend caused by AMF is less than that caused by pressure and feed rate. Therefore, this parameter is the least influential of those used.

It should be noted that an excessive increase in AMF can lead to a loss of kinetic energy. In this case, abrasive particles are more likely to collide with each other, causing a more disturbed cut, which translates into greater erosion at the input of slot, a greater difference between the upper and lower widths of the slot, and greater fraying at the outlet surface of the material [38].

In this case, a smallest kerf taper will be produced with a small amount of abrasive, 170 g/min, resulting in an angle of 3.00◦. For the highest amount of abrasive, an angle of 4.56◦ is obtained.

Ruiz-Garcia et al. [20] achieved an upward trend similar to that obtained in this experiment. The use of a higher abrasive flow means a greater difference between the upper width of the slot and the lower width. Due to that, it can be noted that the abrasive flow rate used in AWJM is not linked to the kind of resin employed in the manufacture of composite.

**Figure 9.** Variation of kerf taper in three specimens as a function of abrasive mass flow rate (P = 2500 bar; FR = 300 mm/min).

#### *3.5. Response Surface*

A response surface allows two input parameters to interact with an output variable, keeping all other parameters constant. The ANOVA analysis carried out in Section 3.1 gave hydraulic pressure and feed rate the greatest significance on the machining process. Therefore, FR and P have been represented together with the kerf taper in Figure 10, keeping AMF = 225 g/min fixed.

**Figure 10.** Contour plot of kerf taper defect as a function of most influential variables: Pressure and feed rate.

As can be seen in this figure, both parameters seem very significant. A value close to 3400 bar combined with various feed rate combinations offer the lowest kerf taper values (Figure 11). As a function of P-value, both P and FR were significant, while according to F-value, pressure tripled the influence of feed rate. This shows that a single pressure results in a range of kerf taper values (<3◦) for the whole range of feed rates used in this experiment.

**Figure 11.** Combination that minimizes kerf taper defect (P = 3400 bar; FR = 100 mm/min; AMF = 340 g/min).

On the other hand, a combination of 1200 bar of pressure and 500 mm/min of feed rate seems to be the most unfavorable in the study of kerf taper, and it seems to be the element that greatly increases the upward trend. As speed increases, cutting capacity decreases due to the loss of kinetic energy in the waterjet. To this effect, it would be necessary to add the reduction of the number of abrasive particles that affect the material.

In addition, the polyurethane matrix applied in this article has a melting temperature of 145 ◦C. Abrasive waterjet cutting is a technology that generates a lower temperature than other conventional machining technologies, such as milling or drilling [14]. This process makes it easier to machine temperature-sensitive materials. High temperatures could lead to thermoplastic matrix softening, generating defects in the final quality of the slot. The kerf taper values achieved are similar to those studied by Wong et al. [31]. This could mean that the effect of temperature on the thermoplastic matrix is not enough to alter the kerf taper.

According to our mathematical model, a combination of P = 3400 bar, FR = 172.73 mm/min, and AMF = 170 g/min should result in the lowest kerf taper value of 1.79◦. The degree of desirability of the result achieved is also obtained. Individual and compound desirability evaluates how well a combination of parameters satisfies the objectives defined for output variables.

Individual desirability (d) evaluates how adjustments optimize a single response. The compound (D), on the other hand, looks at how adjustments optimize a set of responses in general. This variable has a range of 0 to 1, 1 being the ideal case, and 0 meaning that some of answers obtained are outside acceptable limits. In this case, a maximum desirability was generated, with a value of 1, which implies that the combination of cutting parameters selected offers a desirable result.

#### *3.6. Mathematical Model Validation*

Table 5 shows the taper values obtained from the complementary experimental design together with the same values predicted by Equation (3).


**Table 5.** Complementary DOE for validation of the mathematical model.

In order to evaluate the mathematical model carried out in this experiment, a comparison between combinations of parameters not used in original DOE and predicted values was carried out (Figure 12).

**Figure 12.** Kerf taper values (experimental and predicted).

It should be noted that, in most cases, experimental values are below those predicted at a similar distance. When the errors tabulated in Table 5 are observed, it can be seen that, for pressures of 1200 and 2500 bar, errors oscillate in a range of 0–20%, while highest pressure of 3400 bar generates high errors with values of up to 49.84%.

The average error obtained is 20.49%. Experimental values follow the trend of the predicted values but maintain an almost constant difference between them. This difference may be due to the anisotropy and nature of material, as seen in Figure 7. This model could be used to predict the trend that will follow the kerf taper as a function of parameters used, although the error obtained must be taken into account.

#### **4. Conclusions**

An experimental study on the influence of cutting parameters on the generation of a geometric defect, called a kerf taper, focused on the machining of carbon fiber composite materials with thermoplastic matrix, was developed. A face-centered composite experimental design (FCD) based on a response surface methodology (RSM) was development. This type of experimental design has given rise to a second order polynomial equation that relates input parameters to output variable (kerf taper).

The literature review allowed for the selection of pressure, feed rate, and abrasive mass flow as the most influential input parameters in the machining performed while keeping other parameters, such as stand-off distance or size of abrasive particles, fixed.

A second experimental design was used to verify the second order polynomial equation generated by the taper obtained, which contrasts combinations of parameters not used in the original DOE with values predicted by model. An error of 20.49% was obtained, which can be considered small if the anisotropy and nature of a composite material are taken into account.

Three zones along thickness of material have been identified—The rough cutting region at 0–10%, the smooth cutting region at 10–75%, and the initial damage region at 75–100%. In addition, only the Smooth Cutting Region was taken into account for the development of this experiment.

The kerf taper defect was studied in three specimens of the same thermoplastic composite material in order to obtain an average value and its respective deviation. Marginal graphs show how hydraulic pressure causes a decrease in taper generated, and feed rate and abrasive mas flow produce an increase in the same.

ANOVA analysis has indicated that hydraulic pressure and feed rate are the most influential parameters in abrasive waterjet machining. The slot walls become more vertical at high pressures and low feed rates. This is due to a higher concentration of energy impacting the composite to be machined, which translates into higher material removal. Also, the mathematical model obtained for analyzed response surface methodology has presented an R2 of 93.85%.

The effect of temperature does not seem to influence the quality of the results obtained by AWJM. After a concise literature review, it seems that the results obtained in taper defect agree with those obtained by other scientific authors.

Finally, a combination of cutting parameters that minimizes kerf taper defect was found, resulting in a pressure of 3400 bar, a feed rate of 100 mm/min, and an abrasive mass flow of 340 g/min, producing an upper-lower width ratio close to 1, i.e., 0.75◦. This small kerf taper defect means that for specific applications of AWJM could be considered as a high precision process.

**Author Contributions:** A.S. and F.B. developed machining tests. M.B. and J.S. developed data treatment. F.B., A.S., M.B., B.S., and J.S. analyzed the influence of the parameters involved. F.B. and A.S. collaborated in preparing figures and tables and F.B., A.S., M.B., B.S., and J.S. wrote the paper.

**Funding:** This work was developed with the support of a pre-doctoral industrial fellowship financed by NANOTURES SL, the Mechanical Engineering and Industrial Design Department and Vice-Rectorate of Transference and Technological Innovation of the University of Cadiz.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Defect Analysis and Detection of Cutting Regions in CFRP Machining Using AWJM**

#### **Pedro F. Mayuet Ares 1,\*, Franck Girot Mata 2, Moisés Batista Ponce <sup>1</sup> and Jorge Salguero Gómez <sup>1</sup>**


Received: 31 October 2019; Accepted: 2 December 2019; Published: 5 December 2019

**Abstract:** The use of composite materials with a polymeric matrix, concretely carbon fiber reinforced polymer, is undergoing further development owing to the maturity reached by the forming processes and their excellent relationship in terms of specific properties. This means that they can be implemented more easily in different industrial sectors at a lower cost. However, when the components manufactured demand high dimensional and geometric requirements, they must be subjected to machining processes that cause damage to the material. As a result, alternative methods to conventional machining are increasingly being proposed. In this article, the abrasive waterjet machining process is proposed because of its advantages in terms of high production rates, absence of thermal damage and respect for the environment. In this way, it was possible to select parameters (stand-off distance, traverse feed rate, and abrasive mass flow rate) that minimize the characteristic defects of the process such as taper angle or the identification of different surface quality regions in order to eliminate striations caused by jet deviation. For this purpose, taper angle and roughness evaluations were carried out in three different zones: initial or jet inlet, intermediate, and final or jet outlet. In this way, it was possible to characterize different cutting regions with scanning electronic microscopy (SEM) and to distinguish the statistical significance of the parameters and their effects on the cut through an analysis of variance (ANOVA). This analysis has made it possible to distinguish the optimal parameters for the process.

**Keywords:** AWJM; waterjet; CFRP; kerf taper; surface quality

#### **1. Introduction**

Carbon fiber reinforced composite materials with a polymeric matrix (CFRP) are currently widely used in the industry mainly because they possess excellent specific and customizable properties, which allows CFRP characteristics that are impossible to achieve with other materials. In addition, owing to the maturity reached by the different forming technologies, their cost is increasingly approaching that of other structural materials, such as titanium or Inconel alloys. For this reason, these materials are frequently used in different industrial sectors, especially those that require incorporating weight reductions in their manufactured components [1,2].

Although CFRP applications are usually linked to the fields of transport, construction, and energy, in recent years, their use has begun to spread to other sectors such as the naval industry and in applications in consumer goods related to sport and entertainment [3].

However, in spite of all this, the CFRPs continue to generate problems after their conformation. In general, after lamination and curing, CFRPs require a machining process until reaching their final shape owing to the dimensional and geometric requirements demanded by different industries,

especially the aerospace sector [4–6]. For this reason, it is common to perform contour milling and drilling operations on these materials with conventional machining technologies, which entails a series of issues [4,7,8].

The stiffness and abrasion of the carbon fiber together with the heat sensitivity of the matrix make the machining an industrial challenge. In general, during the machining of polymer matrix composite materials, a continuous chip is not formed, but rather a micro-chip or high hardness dust. This dust generates an abrasive environment that causes wear of the cutting tool with loss of material and initial geometry [9]. In addition, it must be removed from the cutting area to avoid damage to the cutting equipment and associated personnel. However, this is not the only problem, because the temperature generated during the process, which is increased by abrasion, causes a softening of the matrix, and even its degradation [10,11]. This can cause damage to the material and the appearance of thermal adhesion on the tool, which favors wear. This whole process is inherent to the nature of composite materials and can affect the surface integrity of the part causing damage such as delaminations, fiber fraying, degradation, or micro-cracks [12,13].

In addition, the possibility of personalization or customization of properties makes the possibilities of configuration of the material almost infinite. For the machining process, this means that the same process with the same characteristics can lead to different results.

As a consequence of the above, increasingly more alternatives to traditional machining are being proposed, where abrasive waterjet machining (AWJM) may be an alternative thanks to a relevant number of specific advantages [14–19]:


Although waterjet cutting is an increasingly used technology, there are difficulties in finding optimal machining parameters for CFRP that reduce the appearance of defects and improve the dimensional and geometrical quality of the machined component.

These defects produce a special negative impact on the surface integrity of the parts obtained owing to dimensional distortions of taper, a progressive increase in roughness, and striation owing mainly to the delay of the jet when it lacks kinetic energy. As a result, it is possible to find up to three possible cutting regions [20–22]:


The defects mentioned are directly related to parameters such as traverse feed rate (TFR), stand-off distance (SOD), water pressure (WP), and abrasive mass flow rate (AMFR), as well as to material conditions and part thickness [23,24]. Table 1 shows the main technological parameters and their influence on the defects mentioned.

**Table 1.** Influence of main abrasive waterjet machining (AWJM) parameters on cutting quality. TFR, traverse feed rate; SOD, stand-off distance; WP, water pressure; AMFR, abrasive mass flow rate; RCR, rough cutting region; SCR, smooth CR.


There are publications that use similar materials and parameters that study defects and the dimensional and geometrical quality of the tests performed. However, in the study of microgeometry or surface quality, where there are several criteria in relation to possible areas of roughness, it has been detected that there are no publications that identify the influence of parameters in different regions.

In this article, the main objective is to study the influence of the main technological parameters in AWJM in order to obtain cutting conditions that minimize the appearance of defects by analyzing each cutting region. Likewise, the detection of different cutting regions characteristic of the process will be analyzed.

For this purpose, straight cuts using AWJM technology were performed to determine the influence of the main cutting parameters on CFRP composite material in contour machining operations. Specifically, roughness was measured in three differentiated zones in order to detect the different regions (IDR, SCR, and SCR) that can be produced during cutting, trying to distinguish the border of each of them through statistical analysis and scanning electronic microscopy (SEM).

#### **2. Materials and Methods**

#### *2.1. Experimental Development*

For the experimental development, a CFRP composite plate formed with 20 layers of prepreg 0.2 ± 0.1 mm thickness (Carbures, Cádiz, Spain) was used to form a 4 mm final plate. The main characteristics of the material are shown in Table 2.



The machining process consisted of the generation of 24 straight cuts, combining the parameter levels shown in Table 3. The length of each test was 180 mm in order to guarantee stable cutting conditions. For this purpose, Mecanumeric MECAJET (Mecanumeric, Marssac-sur-Tarn, France) waterjet machine was employed for cutting the composite, as shown in Figure 1. Table 4 shows the cutting parameters that were kept constant, where the pressure used in the tests is the maximum allowed by the equipment.


**Table 3.** Cutting parameters selected for the tests.

**Figure 1.** Mecanumeric MECAJET performing carbon fiber reinforced composite material with a polymeric matrix (CFRP) cutting.


**Table 4.** Constant parameters during the tests.

#### *2.2. Test Evaluation*

The variables evaluated were the angle of taper T and the roughness through the parameter Ra (arithmetic average of the roughness profile) distributed in three zones: Zone 1, Zone 2, and Zone 3, as shown in Figure 2. The distribution of roughness measurements was carried out as follows:


**Figure 2.** Defects diagram and evaluation zones of the cutting process with (**a**) parameters for measuring taper; (**b**) roughness measurement zones.

For the evaluation of straight cuts, optical evaluation of the machined material was performed by means of the scanning electronic microscope (SEM) technique. For that, a Hitachi SU 1510 (Hitachi, Tokio, Japan) microscope was used for SEM inspection. With respect to roughness measurements, a station Mahr Pertometer Concept PGK 120 (Mahr, Göttingen, Germany) was used.

For T calculation, the expression of Equation (1) was used, where T is the conical angle of the slot, Wt is the width of the slot at the jet inlet, Wb is the slot width at the jet outlet, and t is the thickness of the sample. For the measurement of Wt and Wb, the software ImageJ was used. A previous calibration was carried out to obtain a pixel/mm ratio that allows to establish a correct measurement directly on the image [32,33]. In addition, it is important to note that the area affected by erosion caused by the loss of jet coherence at the jet inlet was differentiated, as shown in Figure 3.

$$T = \tan^{-1} \left( \frac{\mathcal{W}t - \mathcal{W}b}{2t} \right) \tag{1}$$

**Figure 3.** Difference between (**a**) cutting at material inlet cut at the entrance of the material showing the width at the top along with the erosion-affected zone; (**b**) cutting at material outlet showing the width at the bottom.

#### *2.3. Statistical Analysis*

The analysis of results was carried out by comparing combinations of parameters through interaction graphs. In this phase, an attempt was made to identify growth or decrease trends between parameters in relation to the variables studied.

In a second phase, the objective was to quantify the influence of the parameters on the cutting process, by means of an analysis of variance (ANOVA) with a 95% confidence interval. Thus, the F-value and the *p*-value were analyzed to measure the evidence against the null hypothesis and the significance (S) of each parameter.

Finally, contour graphs were represented, emphasizing the discussion of parameters whose significance was demonstrated by ANOVA. The analysis was carried using Minitab statistical software.

#### **3. Results and Discussion**

#### *3.1. Global Analysis of Results*

The results obtained after the measurement process are shown in Table 5. The interaction graphs obtained for each of the four variables are described below in order to visualize trends between the levels of parameters used.


**Table 5.** Results obtained during the evaluation for each combination of parameters.

Figure 4 shows the interaction graph for the variable T, where the different marginal relationships between parameters are observed. In a first observation, it is shown how the highest results of T are obtained when the levels of the parameters SOD and TFR are 4.5 mm and 2100 mm/min, respectively. This is in good agreement with the works of [29,33]. Thus, with a high value of SOD, the jet loses coherence and increases T. An increase of the TGF means that the jet remains for less time impacting the same area of the piece with the consequent loss of its penetration capacity. The combination of these two factors with high levels favors the formation of the defect, and vice versa. AMFR does not have a defined influence for both levels. Indeed, for 300 g/min and 600 g/min, the taper does not seem to increase considerably, although it is true that, for the highest level, there seems to be a slight increase in taper [34]. This could be because of an excess of particles directed by the jet that impact each other before reaching the cutting surface, so their size varies owing to fractures between particles, as well as their kinetic energy before impact.

**Figure 4.** Interaction graph for T. TFR, traverse feed rate; SOD, stand-off distance; AMFR, abrasive mass flow rate.

Figures 5–7 shown the interaction graphs for the roughness values obtained in Zone 1, Zone 2, and Zone 3, respectively.

**Figure 5.** Interaction graph for Zone 1.

**Figure 6.** Interaction graph for Zone 2.

**Figure 7.** Interaction graph for Zone 3.

Zone 1. This zone contains the highest roughness measurements, where some Ra values reach 15 μm. This shows the existence of an initial damage region at the input of the compound produced by the random impact of particles and consequent deformation of the material at the beginning of the cut. Thus, Figure 5 shows how SOD and TFR are the parameters that influence the process, increasing the roughness as higher values are selected [22]. An example of this can be the comparison of test 1 (TFR = 300 mm/min, SOD = 1.5 mm, and AMFR = 300 g/min) and test 19 (TFR = 2100 mm/min, SOD = 1.5 mm, and AMFR = 300 g/min), where the roughness experiences an increase from 5.87 μm to 8.71 μm. Finally, the AMFR parameter does not seem to show a clear influence during the machining process, because the values in this area do not vary considerably [35]. Figure 8 shows an image taken by SEM distinguishing the transition zone from IDR to SCR. A first observation shows that the IDR zone is completely damaged by the impact of particles, while the SCR zone maintains certain integrity in terms of the structure of the material. Specifically, the particles that erode the surface of the material produce the area affected by erosion by damaging the matrix. Subsequently, the fibers without a matrix are broken in the area where the jet penetrates, generating the mechanized groove. In this process, some particles are embedded in the material in the upper zone as a result of the impact on the material or collisions of particles with each other before impacting [36,37].

**Figure 8.** Border between the initial damage region (IDR) and smooth cutting region (SCR) formation. Particles embedded in the surface of the material and another group fragmented as a result of the cutting process are observed. Test 12. TFR = 900 mm/min; SOD = 4.5 mm; AMFR = 600 g/min.

Zone 2. The values obtained in this area show a decrease in roughness with respect to previous values. This is because of two different factors: this zone does not show deformation caused by the random impact of particles as in the previous case and the jet still contains sufficient kinetic energy because the measurement is made in an area close to the entrance of the jet. This is in good agreement with the search for a SCR zone that shows a cut without the appearance of defects or striations [21]. Figure 8 shows how the SOD parameter reaches the maximum roughness values, around 10 μm, for the most unfavorable cutting conditions for the highest levels of SOD and TFR. It should be noted that, once again, AMFR does not seem to show a clear trend in roughness variation when values of 300 g/min or 600 g/min are selected, although it is true that, for the latter value, the roughness seems to decrease when TFR presents levels of 300 mm/min and 900 mm/min.

Zone 3. This zone presents similar values to those obtained in the previous zone, although the behavior of the parameters of roughness varies. The SOD parameter does not seem to have a clear influence on the process in this case, as the results are kept within the stability when TFR and AMFR are fixed, as shown in Figure 6. In addition, it is observed that, although TFR continues to maintain a growth in roughness for the highest feed rate values, the AMFR parameter shows an even greater change in its behavior. Thus, an increase in the abrasive level of 600 g/min shows a clear decrease in roughness compared with 300 g/min. This indicates that the jet requires more abrasiveness to maintain low roughness values in this zone. This phenomenon is shown especially at high feed rates, where roughness decreases by up to 25%. Therefore, although the definitive values show values similar to those in Zone 2, a change in the influence of parameters is observed, which will be studied in depth with the ANOVA.

Figure 9 shows an SEM image of a test carried out with the highest level of speed and the lowest level of abrasiveness. Precisely, these levels would favor the appearance of RCR, but as can be seen, the zone appears free of striations. In addition, at the outlet of the jet, there is a delamination formed by the combination of cutting parameters. Specifically, the pressure combined with the expansion of the jet in the material produces stresses that can prevent the layers of the composite from remaining together, causing their separation and the formation of cracks. As the cutting process continues, the abrasive particles lodge in the cracks and consequently expand, forming delaminations [38–40].

**Figure 9.** Absence of striation or waviness that visibly differentiates the difference between the smooth cutting region (SCR) and rough CR (RCR). Test 22. TFR = 2100 mm/min; SOD = 3.0 mm; AMFR = 300 g/min.

#### *3.2. ANOVA*

This section analyses the degree of influence of each parameter by zone. For this purpose, Table 6 shows the F-value and *p*-value for T, Zone 1, Zone 2, and Zone 3.


**Table 6.** Analysis of variance (ANOVA) of the evaluated variables.

In Figure 10a, the main effects graph for variable T is shown. The data reflect that the parameters that have significance in the process are SOD and TFT, with F values of 21.45 and 20.18, respectively. Specifically, the SOD parameter seems to have a more definite influence on the formation of the defect when the selected level increases from 3.0 mm to 4.5 mm, as reflected in the slope of the graph, while the same increase in slope for TFR was detected in the initial levels from 300 mm/min to 900 mm/min [26]. AMRF does not seem to have a definite influence on the formation of T.

**Figure 10.** Parameter interaction graph for the response variable for (**a**) T; (**b**) Zone 1; (**c**) Zone 2; and (**d**) Zone 3.

As for the formation of possible roughness zones that can be detected, Figure 10b–d show the main effect graphs for Zone 1, Zone 2, and Zone 3. The degree of influence of each parameter on the three variables is described below [31,41–43]:



Therefore, everything seems to indicate that, as described, the analysis by zones reveals that, although it is possible to establish that there are two identified zones of roughness, IDR and SCR, the measurements carried out in Zone 3 reveal a change in the importance of parameters, revealing that TFR, and above all, AMFR, acquire greater significance to the detriment of SOD. Therefore, it could be considered that, with a larger plate thickness, it would have been possible to detect the presence of striations [30].

#### *3.3. Analysis of Contour Graphs for Significant Parameters*

This section shows the contour graphics as a function of the significant variables. The aim of this analysis is to evaluate the most favourable cutting conditions within the range of parameters studied.

#### 3.3.1. Taper Analysis

Figure 11 shows the contour graph for T as a function of TFR and SOD. In this case, the AMFR parameter is irrelevant. The data obtained reflect how the cutting parameters where the taper decreases are in the range of feed rates and reduced distances. In this way, the jet can remain longer eroding the material reducing the loss of coherence of the abrasive jet. These parameters coincide with the levels of TFR = 300 mm/min and SOD = 1.5 mm, although it is reflected in the graph that distances up to 3 mm can maintain the efficiency of the cut, minimizing the growth T. In this case, the conicity can be maintained in values lower than 1◦.

**Figure 11.** Contour graph of T as a function of parameters with significance: TFR and SOD.

#### 3.3.2. Roughness Analysis

As in the previous case, Figure 12 shows the contour graphs for Zone 1, Zone 2, and Zone 3. In the first two cases, the parameters with significance in the process are TFR and SOD, while at the output of the jet, the AMRF parameter is the most relevant with TFR.

**Figure 12.** Roughness contour graphs as a function of significant parameters: (**a**) Zone 1: TFR and SOD; (**b**) Zone 2: TFR and SOD; and (**c**) Zone 3: TFR and AMFR.

It is shown that, globally, the results where roughness decreases occur when TFR and SOD are reduced, while the AMFR parameter increases. This is in good agreement with the works of [18,33], although it should be noted that, with this process, it has not been possible to obtain roughness levels lower than 4 μm. In addition, it is necessary to mention that Zone 1, corresponding to IDR, contains the highest roughness results, as has been revealed. For Zone 2 and Zone 3, the most favorable results are less than 5 μm. Although, it is to be expected that in Zone 3, identified as the possible RCR, the results are higher, and the comment has been made that the thickness of the specimens has a considerable influence. However, the ANOVA reveals that there is a change of trend in the significance of the

variables that has allowed to reveal that SOD has no influence in Zone 3, highlighting the importance of AMFR in the cutting process.

#### **4. Conclusions**

A study was carried out on the influence of the main technological parameters on abrasive water jet involved in the formation of defects and roughness zones on CFRP material. From the study carried out in this article, the following conclusions are drawn:


Once the analysis of the data was completed, contour graphs with the significant parameters for each variable were represented in order to record the parameters that minimize taper and roughness defects. From these results, the following conclusions are also drawn:


On the above basis, the experiment carried out shows that, in order to obtain the minimum T values and high surface quality during the cutting process of CFRP composite specimens, SOD values between 1.5 and 2.0 mm, reduced TFR values around 300 mm/min, and high AMFR values must be selected.

Finally, in order to avoid the appearance of cracks and delaminations, it is recommended to establish a compromise between the pressure used and the thickness of the composite plate. Thus, it is established as a line of future works to obtain cuts with the absence of delaminations under the considerations made throughout this article.

**Author Contributions:** Conceptualization, P.F.M.A.; Methodology, P.F.M.A. and F.G.M.; Software, P.F.M.A. and M.B.P.; Validation, J.S.G.; Formal Analysis, P.F.M.A. and F.G.M.; Investigation, P.F.M.A.; Resources, F.G.M. and J.S.G.; Data Curation, P.F.M.A. and F.G.M.; Writing—Original Draft Preparation, P.F.M.A.; Writing—Review & Editing, P.F.M.A. and M.B.P.; Supervision, M.B.P. and F.G.M.; Project Administration, J.S.G.

**Funding:** This work has received financial support from programme for the Promotion and Impulse of Research and Transfer of the University of Cadiz. Project: PR PR2017-086, Machining of composite materials of strategic use in the aeronautical industry using AWJM.

**Acknowledgments:** To Serge Tcherniaeff and Madalina Calamaz, for their kind help and support during the tests at ENSAM in Bordeaux. To Mariano Marcos Bárcena, for promoting the research carried out in this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **On the Machinability of an Al-63%SiC Metal Matrix Composite**

#### **David Repeto \*, Severo Raul Fernández-Vidal, Pedro F. Mayuet, Jorge Salguero and Moisés Batista \***

Department of Mechanical Engineering & Industrial Design, Faculty of Engineering, University of Cadiz, Av. Universidad de Cádiz 10, E-11519 Puerto Real-Cádiz, Spain; raul.fernandez@uca.es (S.R.F.-V.); pedro.mayuet@uca.es (P.F.M.); jorge.salguero@uca.es (J.S.)

**\*** Correspondence: david.repeto@uca.es (D.R.); moises.batista@uca.es (M.B.); Tel.: +34-956-483-406 (M.B.)

Received: 31 October 2019; Accepted: 3 March 2020; Published: 6 March 2020

**Abstract:** This paper presents a preliminary study of aluminium matrix composite materials during machining, with a special focus on their behavior under conventional processes. This work will expand the knowledge of these materials, which is considered to be strategic for some industrial sectors, such as the aeronautics, electronics, and automotive sectors. Finding a machining model will allow us to define the necessary parameters when applying the materials to industry. As a previous step of the material and its machining, an experimental state-of-the-art review has been carried out, revealing a lack of studies about the composition and material properties, processes, tools, and recommended parameters. The results obtained and reflected in this paper are as follows; SiC is present in metallic matrix composite (MMC) materials in a very wide variety of sizes. A metallographic study of the material confirms the high percentage of reinforcement and very high microhardness values registered. During the machining process, tools present a very high level of wear in a very short amount of time, where chips are generated and arcs are segmented, revealing the high microhardness of the material, which is given by its high concentration of SiC. The chip shape is the same among other materials with a similar microhardness, such as Ti or its alloys. The forces registered in the machining process are quite different from conventional alloys and are more similar to the values of harder alloys, which is also the case for chip generation. The results coincide, in part, with previous studies and also give new insight into the behavior of this material, which does not conform to the assumptions for standard metallic materials, where the hypothesis of Shaffer is not directly applicable. On the other hand, here, cutting forces do not behave in accordance with the traditional model. This paper will contribute to improve the knowledge of the Al-63%SiC MMC itself and the machining behavior.

**Keywords:** metal matrix composite; Al-SiC; microstructure; machining

#### **1. Introduction**

Metallic matrix composite (MMC) materials are the result of the combination of a metallic alloy matrix with reinforcement [1], giving rise to a unique combination of mechanical properties, which surpasses those of the individual components [2,3]. This improvement is given by the incorporation of a ductile metal matrix of reinforcements particles with a high strength and modulus of elasticity [4,5]. When compared to monolithic alloys, MMCs offer superior strength and stiffness values, lower weight and thermic expansion coefficients, and, in some cases, the ability to operate at high temperatures [6]. Because of its exceptional properties, and despite the complexities of its behavior throughout the machining process, there exists great industrial interest in MMC's: several potential areas of application can be covered by these materials.

Each MMC is unique and its composition corresponds to a general criterion, which represents an added difficulty to its replicability of laboratory experiments, as well as subsequent industrial production.

The uneven distribution of the reinforcement accounts for the dispersion found by its behavior during the machining process, although some manufacturers that commercialize these products try to combine the matrix and straighteners in a particular manner in the lab in an attempt to control the process from the beginning.

A standard commercial material would guarantee similar results in successive experiments, although the use of a specific aluminium matrix is not currently well defined, and the choice appears to be conditioned by the matrix properties, as its behavior is improved by the addition of reinforcements. The microstructural analysis of the material revealed a distribution of reinforcements typical of an MMC, highlighting the high concentration (63%) and the differences in size, as well as the random distribution. Improving the quality and homogeneity of reinforcement particles would facilitate the MMC manufacturing process in terms of the required specifications. This is the part of the process where an exhaustive control is generally lacking in the literature.

Although the military industry has a specific interest in MMC applications (mainly for ballistics), the automotive sector has opened a broader field for these materials, motivated by the search of lighter vehicles. In the electronics sector, MMCs have direct applications in the manufacturing of microprocessors, due to their excellent heat transfer properties. Nowadays, MMCs are considered as strategic materials, forming part of the essential elements in many advanced technologies [7].

MMCs are designed according to their final purpose, based on the properties of the metal matrix (Al, Mg, Ti, Cu, etc.) and the particle reinforcement characteristics, varying by application and manufacturer [8]. Materials which are more resistant and possess a lower weight are required nowadays to replace lightweight alloys, and MMCs are in the best position to satisfy these requests. Adding ceramic reinforcements to an aluminium matrix helps to dramatically increase some properties, such as microhardness, thermal conductivity, and strength.

Al-based MMCs are usually manufactured with continuous (long fibers) or discontinuous reinforcements (short fibers, whiskers, wires, or irregular and spherical particles) [9,10].

Particulate-based metal matrix composites (PMMCs) are of particular interest, as they exhibit higher ductility and lower anisotropy than fiber-reinforced MMCs [11]. Because of this, reinforcements are distributed in a 4:1 ratio—in favor of the particles against short fibers [12]—and the selection of SiC as a reinforcement with an aluminium matrix is over 60% in this regard, because of its mechanical properties, characteristics, physical, and chemical properties, and low cost of production when compared with other reinforcements which could be used, such as Al2O3, with around 30% [13]. The rest of the various materials are not relevant in terms of their composition percentage, where 10%, which is quite dispersed, can be found for B4C, TiC, or hybrids of SiC and Al2O3 [14–16].

In terms of reinforcement quantity, [6,11,17–23], most of applications include at least 20% reinforcement, which can be considered as the highest ratio. Regarding reinforcement sizes, these are often between 3 and 65 μm; however, three-quarters of the studied sizes are ~20 μm [24].

The number of papers found regarding the machinability of Al-based MMCs with particulate reinforcement similar to the material studied here (over 60% Al) is small, and these papers are rare [25,26]. Consequently, it was decided to investigate this kind of material, which is the main objective of this paper.

#### **2. Machining of Metal Matrix Composites**

Quigley studied factors affecting the turning [27] of MMC 5083 AlSiC with 25% Al and found that the conventional and coated tool flank wear was very high; the surface finish was better than that which was expected theoretically, due to the tool morphology and material effect (BUE); and that tool wear leads to a loss in dimensional accuracy.

El-Gallab studied tool performance and workpiece surface integrity [11] when turning Duralcan F3S.20S AlSiC (A356/20% SiC) with Al2O3/TiC, TiN, and PCD tools, where all of the BUE and flank wear (VB) of all forms were measured. The cutting parameters (the speed of cut, feed, and depth of cut) play a key role in determining the amount of tool flank wear, as well as the size of the built-up edge. El-Gallab also noticed [19] that no research has yet been carried out to determine the effect of the cutting parameters on the workpiece surface integrity and sub-surface damage during the machining of an AlSiC particulate-based metal matrix composite, where cutting parameters have a significant effect on the form of the chips produced. In general, at low feed rates and small cut depths, the chips tended to be continuous, and this observation contradicts Monaghan's results [28]; even though the parameters and materials were the same, there was a 5% SiC difference between them. A reduction in the surface roughness can be noticed with the increase in feed rate, and this effect is attributed to the reduction in the flank wear of the tool. This could be attributed to the stable built-up edge, which protects the tool from wear by abrasion. Manna investigated the machinability of an AlSiC MMC (A413/15% SiC) [29] and found that the lower built-up edge (BUE) is formed during the machining of AlSiC MMC at a high speed and low cut depth, while also observing a better surface finish at a high speed with a low feed rate and low cut depth.

Davim studied the optimization of cutting parameters based on orthogonal arrays [21], where turning A356/20SiCp-T6 with Poly Crystalline Diamond (PCD) tools showed that the cut speed is the main factor that affects tool wear and power consumption, whereas the feed rate is the main factor for surface roughness (Ra). Also, in 2007, Davim made a correlation between the chip compression ratio and shear plane angle or chip deformation during the turning of MMCs, showing that the shear angle decreases with the chip compression ratio. On the contrary, chip deformation has been shown to increase with the chip compression ratio [30]. The Merchant model gives, in general, an overestimation of the shear plane angle value in the cutting of Al-based MMCs.

Dabade investigated the effect of a change in size and volume fraction of reinforcement (Al/20–30 SiCp; 220–600) on the mechanism of chip formation by changing the processing conditions and tool geometries [31]. Here, the results were that at a lower cutting speed (40 m/min), thin needle-type flakes, as well as segmented chips are formed, whereas at higher cutting speeds (120 m/min), generally, semicontinuous, continuous, scrambled ribbon, and tubular helix chips are formed. The length of chip and the number of chip curls increases with the increase of feed rate at any given cutting speed and cut depth. The size and volume fraction of reinforcement significantly influences the chip formation mechanism.

One of the conclusions that can be drawn about the different manufacturing systems of MMCs is that they must evolve over time in terms of the method of incorporation of reinforcements into the matrix, so that the desired properties are established and maintained. Another concern, although to a lesser extent, is that the temperature reached during the manufacturing process should be kept as low as possible. The papers we have studied reflect the effort to manufacture a material that faithfully follows the design specifications of the experiment and does not raise concern about the scope of its cost. The objective in this study, differently to the objectives of other studies reported in the literature, is to move the manufacturing method into industry.

Although MMC production is relatively well adjusted to its final product shape, machining is unavoidable [32,33]. Nowadays, improvements of this process are the main focus of many research efforts [34]. Nevertheless, it is the combination of matrix and reinforcements that creates the enhanced properties of an MMC that hinder its machining, even for matrix-based aluminium alloys, which are considered to have a high machinability. Despite this, the machining of aluminium alloys is not exempt from difficulties, traditionally owing to the great capability of the material to adhere to tool edges and, above all, the shear angle [35].

The reinforcement itself represents an added difficulty, as the tool encounters a heterogeneous material throughout its path. If the reinforcement is harder than aluminium, as is the case, the machining becomes even more complex. Regarding MMCs with ceramic reinforcements (Al2O3 and SiC), the situation is further complicated by the abrasiveness of these materials, resulting in extremely damaging machining for traditional tools, shortening their service life drastically.

As the difficulty in machining MMCs increases because of the abrasion phenomenon described above, a greater force is required to pull the chips and the amount of energy required increases, which can greatly influence the total efficiency of the process [36]. The greatest obstacle encountered by MMCs in replacing monolithic alloys is the difficulties associated with their machining, as the tools required suffer from intense wear owing to the presence of the reinforcements, making it a highly inefficient process [6,37].

The shape, type, presentation, and concentration of the reinforcement greatly influence the wearing process. Similarly, a great dispersion between the responses in MMCs can be detected, as the characteristics of the particular composites integrating them can result in the manifestation of completely opposite properties.

In this paper, a study of the machinability of an Al-based MMC with a high concentration (63%) of SiC reinforcement has been performed. Machinability tests have been carried out by orthogonal machining (shaping) from some values of speed and deep of cut. The geometry of the chips obtained, as well as the characterization of cutting tool wear, have been studied by optical and scanning microscopy techniques; also, cutting forces are measured. This paper will allow to establish the basis of a parametrical analysis in regards MMC's with high content SiC reinforcement or some other materials characterized by a similar behavior.

#### **3. Experimental Procedure**

The experimental procedure has been divided into two phases: The first one develops a microstructural characterization of the MMC to be machined, and this is necessary to know the distribution of the reinforcements. The second phase is focused towards the machining of this MMC. During and after the machining, the chip behavior has also been studied via high-speed video film and metallographical methods, including Stereoscopic Optical Microscopy (SOM) and Scanning Electron Microscopy (SEM) techniques.

#### *3.1. Material Characterization*

For this study, a commercial MMC sheet (ref. AlSiC-9) composed of an aluminium UNS A03562 (A356.2) matrix with 63% SiC reinforcement was used. The composition of the A365.2 Al alloy, obtained from the webpage Matweb, is shown in Table 1.


**Table 1.** Composition of the metallic matrix composite (MMC) matrix alloy [38].

Even though this material has a commercial distribution, this does not mean that it is unnecessary to study it because it is not an alloy under international regulations. The sample was 180.17 mm wide and 136.89 mm long, with a thickness of 5.55 mm. The main usage of this plate was to support an electronic array for an insulated gate bipolar transistor (IGBT), provided by CPS Technologies Corp, Norton, MA, USA. The material properties are shown in Table 2.


**Table 2.** Composition and some properties of the MMC used [39].

To characterize the microstructure, some samples were cut into an appropriate size and polished, prior to etching with Keller's reactant. After, optical evaluation of the etched surface was carried out, as can be seen in Figure 1, using a Nikon SMZ 800 stereoscopic microscope and a Nikon Epiphot 200 metallographic microscope (Nikon Instruments, Amsterdam, Netherlands), both of which were equipped with digital high-resolution cameras.

**Figure 1.** Metallography of the AlSiC MMC with 63% Al.

Additionally, microhardness was measured with the HMV-2 (Shimadzu, Kioto, Japan) microhardness tester to evaluate the behavior in different phases of the matrix, as well as the properties of the reinforcement particles. Forces of 980.70 mN and 1.96 N were applied, using 100 and 200 grams, respectively, during 15 seconds, which corresponded to a Vickers Hardness (HV) value between 0.1 and 0.2, respectively, according to UNE-EN ISO 6507 [40].

#### *3.2. Machining Process*

To study the machinability but avoid complex cutting geometries, it is typical to use machine tools with a rectilinear cutting movement, as this is the simplest machining model and it can be extrapolated to an oblique cutting model. Therefore, an orthogonal cutting configuration in a shaping machine (GSP 2108 R.20. GSP, Paris, France) was used, as shown in Figure 2.

**Figure 2.** GSP 2108 R.20 shaping machine tool.

All tests were performed in dry conditions, and a new cutting tool was used in each trial. The cutting parameters used were based on the combination of 4 cutting speeds and 2 cut depths selected from previous studies [41,42]. This is shown in Table 3.

**Table 3.** Machining parameters MMC AlSiC.


Every test was carried out for at least 1 or 3 tool paths. The machining time ranged from 0.15 to 0.45 s, whereas the measured machining lengths were between 45 and 120 mm. The cutting forces were acquired by a Kistler 9257B dynamometer (Kistler Instruments, Winterthur, Switzerland), while the cutting process was filmed at high speed with a Photron APX RS (Photron, San Diego, CA, USA) camera.

A WC/6%Co "blank" cutting-tool from Sandvik (ref. H13A, without coating) was selected, with a rake angle of 0◦ and a clearance angle of 12◦, as shown in Figure 3.

**Figure 3.** Blank cutting tool. (**a**) H13A from Sandvik. (**b**) Cutting geometry.

Chip morphology was analyzed according to ISO 3685:1993 (annex G). This is also a useful indicator of tool life. Angle wear can be observed by observing the tool wear via its initial profile, as shown in Figure 4.

**Figure 4.** Orthogonal cutting configuration and evaluation zone for flank wear.

Further evaluation of the material, chips, and tools was performed with a Quanta 200 scanning electron microscope (FEI, Hillsboro, OR, USA) equipped with a Phoenix Energy dispersive X-ray spectroscopy (EDX) system (EDAX, Mahwah, NJ, USA).

#### **4. Results**

#### *4.1. Introduction*

The manufacturing process of the MMC sheet was based on the method of infiltration by pressing the aluminium alloy over a preform of SiC. Infiltration was made in a cast created to give the final shape to the sheets, and its design corresponds to the net shaping criteria and techniques. Because of the manufacturing process, a skin of aluminium is formed over the sheet surface, which can reach a thickness of 0.08 mm and would need to be removed to find the "pure" MMC.

The images captured and shown above, Figure 5; allow the observation of the irregular dispersion of the reinforcement over the MMC surface, and also, its different sizes. Reinforcement shows two singular characteristics, namely, irregular shapes and a range of different sizes. The uneven distribution of the reinforcement sizes has been reported previously [6,43].

**Figure 5.** Stereoscopic Optical Microscopy (SOM) image at 40× magnification of the aluminium MMC with SiC reinforcements.

Using the picture processing software Image J, the areas occupied by each reinforcement were measured in four different places within the sheet. For this, a minimum-area size filter has been used for the initial pictures, so that smaller sizes are not considered, thereby eliminating the noise effect. The number of detectable size reinforcements in each of the four samples analyzed varies, almost reaching 12.50% for the those of the same material and between very similar study areas, with the lack of homogeneity being around 10%. Depending on the relative position of the reinforcement, the properties of the material can differ significantly.

The percentage of area occupied by detectable sizes of the reinforcement varies between 43.16% and 55.13%. Nonetheless, these values do not overlap with the maximum or minimum reinforcement quantities. The size and quantity of reinforcements is scattered, so that the properties of the material might have some heterogeneity.

Table 4 shows the microhardness values taken in different areas and samples of material. Relevant parameters are also included in the table. Registered values of microhardness, from highest to lowest, are shown. The highest value belongs to Sample 1 and was obtained in the reinforcement. The second value, from Sample 2, was taken in the matrix. Sample 3 had the second highest value, registered in the matrix-reinforcement interface. The last value, from Sample 4, was also taken from the matrix.


**Table 4.** Microhardness (HV) of the aluminium MMC.

#### *4.2. Machining Process*

The high-speed film detected the formation of burrs from the very beginning of the machining process, which obstruct the visualization of the cutting zone. Furthermore, a great number of shoots were observed, and, although the surfacing of segmented and jagged chips in all cases is significant, this is an odd behavior for the matrix material at this particular cutting depth. Both of these properties provide some information about the brittleness of the chip (Figure 6).

The literature review on chip formation established that the machining process of aluminium MMCs with SiC reinforcements generates "sawtooth" chips because of the shape of cross section used to produce them [44]. However, a significant amount of the machined material was reduced to powder. This experiment corroborates [45] that reinforcements, which have a higher hardness, cause a reduction in MMC ductility, facilitating the appearance of these kinds of jagged chips. The tool rake angle of 0◦, and even negative values, noticeably influences the formation of the chips.

Regarding the shoots, these present the phenomenon described [46]. The material cannot withstand the cutting tension and it breaks and is shot away once the chip has reached its maximum size. Some of the materials studied during the literature review do not belong to the metal matrix composites with ceramic reinforcement group. These are mostly very hard steels and some alloys employed in aeronautics, such as the titanium alloy Ti6Al4V or a nickel alloy known as Inconel 718. From the results obtained, we can observe a similar behavior in the MMC in terms of the chip formation mechanism and the type of chip resulting from the machining.

**Figure 6.** (**a**) Scheme of the tool position and images of the machining as obtained with high-speed film: (**b**) Vc = 20 m/min, one tool path, and d = 0.2 mm; (**c**) Vc = 30 m/min, three tool paths, and d = 0.2 mm; (**d**) Vc = 50 m/min, three tool paths, and d = 0.2 mm.

#### *4.3. Chips Characterization*

One of the characteristic aspects identified during the review of published papers was the cyclic variation of the shear angle along the machining process. This cyclic change of the shear angle in tandem with the chip formation angle can be verified [47]. In line with this, some fluctuations in the components of the cutting forces were observed while machining a nickel alloy, namely, Inconel 718 [48], although the resultant force did not change, owing to the cyclic variation of the chip segmentation (changes in the chip thickness from the shear angle). This phenomenon is still yet to be proven to occur in the case of aluminium MMC reinforced with SiC. The shootings observed during the film recording cannot allow us to confirm the adherence of the material to the cutting edge, although this is proven in later analysis.

After machining under the different experimental conditions scheduled, the morphology of the chips obtained were determined to be of the segmented type with a curved profile. Attending to International Standard Organization standard ISO 3685:1993, the chip formed during the cutting process has characteristics which are related to the work material, tool material, tool geometry, condition of the cutting edges, cutting edge position, and cutting data and conditions. According to annex G, these chips are of the 6.2 type (arched and shredded), which indicates that chip movement is produced towards the workpiece and in the direction of feed motion. However, during the cyclic chip-forming process, the shear angle is not simply a constant value, but changes cyclically as the cyclic chip formation takes place [48]. While machining ductile materials, chip formation is accompanied with very severe plastic deformation at the shear zone, where if a work material does not have enough ductility, this will result in deformation, which is limited by the crack initiation at the surface where no hydrostatic pressure exists [44]. As the reinforcement percentage is much higher in the case of the matrix, greater hardness is registered and the material is less ductile, resulting in the generation of a discontinuous chip because of high reinforcement concentration in the matrix [49].

Cutting forces in the machining of hard materials are, in spite of their hardness, not necessarily high because of the following two effects, namely, relatively small plastic deformation of the chip due to the crack formation mentioned above, and the relatively small area of tool-chip contact, which reduces the friction force [44].

The addition of SIC particle reinforcement into the aluminium matrix has caused a reduction in ductility and makes the material ideal for producing semicontinuous chips, which can be easily discarded after machining. This addition could be beneficial in terms of machinability; however, it creates some fluctuation in the force measurements [49]. Clarifying the mechanism and factors responsible for sawtooth chip formation and exploring the relationship between the formation of sawtooth chips and cutting force fluctuation is of great importance to the development of an effective cutting process monitoring strategy [48]. The face of the chip in contact with the tool is a smooth and shiny surface with crevices. This can be attributed to the lateral distortion forces induced by friction, which is a differentiating characteristic from traditional aluminium alloys [50].

The reverse or back side of the chip shows an irregular profile which is matt and discontinuous, allowing the shearing effects to show through and forming the characteristic sawtooth shape. Additionally, a burr area formed because of the fragility of the chip is observed in the high-speed film. It is possible to observe SiC particles near the chip surface, and these particles could damage the tool [51].

These effects occurred under all of the studied conditions (Figure 7). The same shine and smoothness on the exterior size of the chips was observed [48]. This phenomenon is attributed to the high tensions which were created when in contact with the tool, and the shearing tensions occurring on the tool–chip interface. In the fracture zone of the chip, a lack of homogeneity on the fracture surface can be observed, and it can be concluded that said fracture cannot be considered ductile, but its appearance resembles that of a brittle fracture. This coincides with the increasing tenancy, related to the incorporation of reinforcements to an aluminium alloy, seen with the traditional characteristics of an MMC.

#### *4.4. Tools Characterization*

In Figure 8, the rake faces of the tool are shown. The wear of the tool is significant in all cases, as can be seen by loss of tool material in the cutting edge and the material adhered in the rake face. Note that secondary adhesion is the most common mechanism related to the machining of aluminium alloys, and, in general, and it appears in this case with the MMC matrix. However, the SiC reinforcements should cause abrasion wear to the tool, and this favors material loss of the tool and provokes flank wear. Adhesion is presented almost consistently throughout the tool edge, creating an adhered layer or BUL (built-up layer). However, a clear relationship with the cutting parameters has not been revealed, although the BUL appears to increase as the machining time does, causing more damage to the tools after three tool paths.

**Figure 7.** SEM images of MMC chip at Vc = 20 m/min, d = 0.2 mm, after three tool paths. (**a**) Front side. (**b**) Burrs at the front side. (**c**) Back side. (**d**) Reinforcement SiC particle in the back side.

The tool wear mechanism seems to be a mix between the dominant ones for each phase of the material. The secondary adhesion, distinctive for aluminium alloys (the matrix material), is boosted by high temperatures, as it is a thermomechanical mechanism. Besides, there is a loss of material produced by the abrasion that SiC reinforcements cause, which eliminates material from the tool edge and flank. This mechanism will also cause a rise in the temperature due to friction, which will favor secondary adhesion. The described mechanisms acting synergistically will result in the tool being rendered unusable after only very short machining times.

This behavior is found to be similar to those of different materials such as stacks, although it presents an added difficulty as the machining is not done in batches.

It is also remarkable that this mechanism seems to be dependent on cutting speed, as well as the machining time, and the effect increases at low velocities. This can be attributed to the change in behavior produced by friction, as an increase in friction is paired with greater abrasion, causing plasticity within the matrix, which results in an increase in adhesion, and thus the synergetic effect.

To quantify the adhesive wear, we quantified the length of contact between the tool and chip, referred to as h. After this analysis, it was noted that there is a fairly constant length, settling at 0.375 mm. This value allows quantification of the area damaged by secondary adhesion in the tool. Note that, according to the calculation made earlier, this value differs by up to 80% of the calculated value, meaning that the Shaffer model could not be applied for these materials, and that additional information is still needed to ensure the value of the shear angle. The tools were also analyzed with SEM/EDS techniques (Figure 9).

Analyzing the material adhered shows that it is material from the MMC; however, it features a different concentration of Al/SiC, depending the tool zone. In this form, zones rich in Al and others rich in SiC exist. This suggests that the reinforcement can be carried out at a high speed. This effect is in accordance with the particles shown by high-speed film and with the particles incorporated into the surface of the chip, where the effect can increase damage to the tool.

This fact could be considered secondary, because although it is of great importance from the point of view of the process, skipping particles of SiC with a high degree of abrasion and the projection itself can damage the tool, and this can also represent significant damage to equipment, meaning extreme care must be paid when machining these materials.

However, the general appearance of the tool is similar to that which is obtained during the machining of other aluminium alloys, and even the wear area, which manifests adhesion behavior that appears in the machining of other aluminium alloys in other processes [15,36]. Then, it is possible that the mechanism of predominant wear is secondary adhesion, as in most other commonly used aluminium alloys. However, some SiC particles have been deposited on the rake face. These particles can behave like the intermetallic particles in aluminium alloys, but with an increased abrasion power and concentration, and this increases abrasion and flank wear. This abrasion effect is different to all other aluminium alloys and provokes the rapid damage that has been shown previously.

The SiC particles were deposited close to the cutting edge (Figure 10), and although the rake face (blue area, tungsten rich area) was predominantly covered by aluminium (yellow area, aluminium-rich area), it appears that many areas are covered with material from the reinforcement (red area, carbon-rich area).

**Figure 9.** SEM/EDS analysis of the rake face of the cutting tool (Vc = 50 m/min, d = 0.2 mm, and one tool path). *Y*-axis in cps units. Two details of tool wear: figures on the **left** (red frame) are showing aluminium adhesion and figures on the **right** (blue and yellow frames) are showing SiC adhesion.

**Figure 10.** Scanning electron microscope analysis of the tool, where Vc = 40 m/min and d = 0.2 mm, and one tool path was used: (**a**) Original image. (**b**) Spectroscopy image with concentration by color: Al (yellow), W (blue), and Si (red).

Additionally, data taken from the characteristic zones (Figure 11) in the cutting edge show a high concentration of aluminium, which decreases when moving away from the edge (Figure 11, yellow areas). On the other hand, here, the reinforcements are distributed randomly, resulting in a non-homogeneous distribution of compounds. There are areas of very thin, electrotransparent material covered by the matrix alloy, whereas other areas only appear to be embedded with the reinforcement, as shown in the analysis earlier. It can be said that these reinforcements are firmly fixed on the tool without requiring the intervention of the aluminium (Figure 11, white zones).

**Figure 11.** Spectroscopy image of compositional analysis of the cutting edge and the rake face (Vc = 20 m/min, d = 0.2 mm, one tool path).

Meanwhile, in areas close to the cutting edge, areas of both the matrix and reinforcement coexist, as has been previously seen. This suggests that although the secondary adhesion in the case of aluminium alloys is a thermomechanical process, in this material, the reinforcement induces a significant mechanical effect and, therefore, introduces the well-defined abrasion behavior.

To observe the flank wear, images of the profiles of the tools were analyzed (Figure 12). It is still possible to identify the material adhered and a high level of abrasion on the tools, denoted by the blurring observed in the high-speed film.

It is possible to appreciate a regrown edge in all tools, where bigger sizes arise from those produced at a higher cutting speed. This occurs similarly in other aluminium alloys during analogous processes [27,51]. Furthermore, it is possible to observe the effect of material loss in the tool, as well as flank wear. This damage is increased with the increase of cutting speed and time spent machining, and it also appears after short machining times.

This might indicate that the interval of stable evolution in machining is practically nonexistent, and the loss of material from the tool is produced in such a short time that it would lead to the catastrophic breakage of the tool after only very short machining times.

After analyzing the tool with SEM (Figure 13), it is possible to see a similar behavior with abrasive particles which are stuck or embedded on different areas of the tool, and the presence of lines of abrasion marks, symptomatic of flank wear, which, in this case, differs from the previous one in intensity, since it seems to be more pronounced. This behavior is maintained almost independently of machining time, although the loss of material of the tool is very marked in the first moments of machining and progresses rapidly. Therefore, abrasion is a very important phenomenon, in addition to (or possibly even more than) the secondary adhesion, which can lead to the futility of the tool after only a very short time.

**Figure 13.** SEM analysis of the tool profile (Vc = 50 m/min, d = 0.2 mm, and three tool paths).

To analyze the loss of material in the flank, the profiles of the tools have been studied. The flank wear was measured using image processing techniques. The angle that forms the profile of the original rake face with the rake face after machining has been studied, in order to subsequently measure the parameter of flank wear according to ISO 3685. The data are shown in Table 5 and are represented in Figure 14.



**Figure 14.** Flank wear evolution as a function of cutting speed and different machining times.

It can be seen that there does not seem to be a definite pattern here, and this can be related with the random distribution of the reinforcement when it is projected. However, the flank wear in all cases was greater than the flank wear accepted by ISO 3685 (300 μm), and this value is exceeded after only very short machining times.

According to this value, the tool must be replaced after only one tool path. However, after three tool paths, a striking effect takes place; however, wear increases clearly in a few cases, which would lead to an increase in the adhered material, whereas in other cases, it appears to decrease. This manifested adhesion fills the gaps that were occupied by the tool material and, therefore, this apparently causes the value to drop.

This effect is false; however, as the bonded material does not display the mechanical properties of the tool, it will tend to fall off easily, pulling particles from the tool with it.

Therefore, the general trend is an increase in the loss of material from the tool in line with the increase in cutting speed and machining time, reaching values that exceed double the value recommended for the replacement of the tool after only a very short period of machining.

This flank wear provokes a tapping effect on the tool that increases the friction and affects the cutting forces. The values of the cutting forces in the different tests are shown in Table 6.


**Table 6.** Average values of the cutting forces obtained in the machining tests.

#### *4.5. Cutting Forces*

The machining of MMC reinforced with SiC generate chips of a "sawtooth" type, and thus a friction phenomenon appears, which causes fluctuation cutting forces [49]. The segmentation frequency of the sawtooth chips and the fluctuation frequency of the cutting forces are highly similar. This

indicates that the formation of the sawtooth chips is the most important factor influencing the periodical fluctuation of the cutting force components in the turning of Inconel 718 [48].

In the traditional cutting process, the component of force in the direction of cutting, Fc, is the most important property of the component, and it has the biggest value. The second largest component, the vertical component of the force, Fy, is greatly different. Studying the data obtained, this can be corroborated; however, Fy is much higher than the expected values, being greater than the values of Fc even after three tool paths. Increasing the cutting speed and the machining time increases the cutting forces. This is the same behavior observed during the tool wear study.

The forces registered in two axes have been combined to form resultant M; a comparative table; Table 6; and a graphic design, Figure 15.

**Figure 15.** Cutting forces depending on the speed of cutting for several machining tool paths.

According to the composition of the resultant of the forces, the modulus has been obtained through the square root of the quadratic addition of the components, as shown in the formula below.

$$M = \sqrt{Fc^2 + Fy^2}$$

If analyzed more thoroughly (Figure 15), when considering only one tool path, it can be seen that with a Vc of 20, the values for both forces (Fc and M) are at their lowest. At this initial point, both values are increasing, where M is more significant than Fc, until reaching a peak Vc of 30, where both forces decreased until they were almost parallel up until a Vc of 40. Once this point was reached, from here to the end (Vc of 50) the values remained almost horizontal.

In the case of three tool paths, this is similar to the previous example. From Vcs of 20 to 30, the values increased; however, once reaching this peak, as in the case of one tool path, the values reduced until a Vc of 30. Between a Vc of 40 and 50, once again these values increased instead of remaining similar, as in the case of the previously registered values at a Vc of 40 for both cases, where Fc and M were both higher in the case of TP3 than TP1.

Even though the force Fc is similar in the one tool path case, the three tool path values are quite different for Fc or M, where M is always greater.

Note that although machining times are very low, this still provides evidence of the great influence of wear. This influence, as seen in the analysis of the tool, gives rise to the increase in cutting speed, which may cause increased wear and even an increase in flank wear. This would mean that the phenomenon of abrasion is increasingly more important, and, as noted, would lead to the catastrophic failure of the tool.

As seen in Figure 15, there is a dependency with the machining time that grows with the cutting speed. Slower speeds show an almost stabilized behavior, whereas the tendency is much more pronounced with increasing speeds.

On the other hand, in the case of the increased abrasion in the previously observed profile of the tool, which grows with the cutting speed, the phenomena causing this is lateral stress, and it therefore cannot be explained with standard theories about orthogonal cutting, thus an Fx force cannot exist.

When comparing the values of forces obtained with other light alloys, there are important differences to note. If compared with a Ti alloy [52], it can be seen that the forces are slightly lower when moving to depths of 0.2 mm in the range of 800 to 1500 N. However, when compared with forces that are obtained in an alloy of aluminium, it can be seen how the ranges are inferior and even with more aggressive settings and in more complex processes, they are only able to reach about 500 N [53]. This again confirms the hypothesis that increasing the concentration of reinforcement translates into increased tenacity, which causes an increase in the forces that by their inherent abrasive behavior leads to a more significant increase in damage, which is evident when considering the rapid loss of material in the cutting tools.

A brief summary of results can be found below.


#### **5. Conclusions**

Regarding the chip analysis, this confirmed the behavior previously described by other authors, showing a shredded arch type with a segmented or sawtooth morphology.

The tools have suffered severe wear, even in the best cutting conditions.

With regard to the cutting forces, it can be ensured that the effect of abrasion causes a predominant effect of friction on the rake face that manifests itself in a very marked increase in the force Fy.

On the other hand, the machining time is a determining factor and the increase in the wear causes a simultaneous increase in the forces, reaching values close to those found in alloys in less than one second, and surpassing those of most other aluminium alloys.

The best results have been obtained with the average values of the parameters: speed and deep of cut. The highest speed and lowest depth of cut is not always the best option.

**Author Contributions:** D.R., M.B., and J.S. conceived and designed the experiments; D.R., S.R.F.-V., and P.F.M. performed the experiments; D.R. and M.B. analyzed the data; D.R. and M.B. wrote the paper; S.R.F.-V., P.F.M. and J.S. revised and corrected the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has received financial support from the Spanish Government through the Ministry of Economy, Industry, and Competitiveness, the European Union (FEDER/FSE) and the Andalusian Government (PAIDI).

**Acknowledgments:** The authors acknowledge CPS Technologies for providing the material used for the experimentation. A very special acknowledgement to Mariano Marcos, who initiated the development of this research (in memoriam) and to Franck Girot, who guided us in some of the procedures of MMCs.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Configuration Optimisation of Laser Tracker Location on Verification Process**

#### **Sergio Aguado \*, Pablo Pérez, José Antonio Albajez, Jorge Santolaria and Jesús Velázquez**

Design and Manufacturing Engineering Department, Universidad de Zaragoza, María Luna 3, 50018 Zaragoza, Spain; pperezm@unizar.es (P.P.); jalbajez@unizar.es (J.A.A.); jsmazo@unizar.es (J.S.); jesusve@unizar.es (J.V.) **\*** Correspondence: saguadoj@unizar.es

Received: 11 November 2019; Accepted: 18 December 2019; Published: 10 January 2020

**Abstract:** Machine tools are verified and compensated periodically to improve accuracy. The main aim of machine tool verification is to reduce the influence of quasi-static errors, especially geometric errors. As these errors show systematic behavior, their influence can be compensated. However, verification itself is influenced by random uncertainty sources that are usually not considered but affect the results. Within these uncertainty sources, laser tracker measurement noise is a random error that should not be ignored and can be reduced through adequate location of the equipment. This paper presents an algorithm able to analyse the influence of laser tracker location based on nonlinear optimisation, taking into consideration its specifications and machine tool characteristics. The developed algorithm uses the Monte Carlo method to provide a zone around the machine tool where the measurement system should be located in order to improve verification results. To achieve this aim, different parameters were defined, such as the number of tests carried out, and the number and distribution of points, and their influence on the error due to the laser tracker location analysed.

**Keywords:** laser tracker; machine tool; uncertainty; Monte Carlo method; verification

#### **1. Introduction**

Machine tools (MTs) are increasingly implemented in the industrial sector, which is itself increasingly competitive and seeks to increase production at a lower cost. For this, detection and reduction of MT errors is necessary.

Currently, there are two different ways to obtain MT geometric errors: direct and indirect measurement methods. Direct measurement methods consist of measuring the influence of every individual error from each axis in a particular position of the workspace of the MT [1]. Alternatively, indirect measurement methods obtain the joint influence of MT geometric errors based on multi-axis movement and its kinematic model. These are more widely used, especially in long range MTs, where direct methods require large scales, expensive dimensional measurement systems, and more time to check them [1]; so, the limitations of direct measurement cause indirect measurement to prevail in this type of machine.

Volumetric verification, using a laser tracker (LT) as a measurement system, is based on indirect measurement of geometric errors, characterising their combined effect [2]. So, the accuracy of verification results depends, among others, on errors of the MTs but also on the errors of the measurement system used. These latter errors are often ignored, and it is assumed that the performance of the measurement system is sufficiently accurate.

All measurements have a degree of uncertainty made up of systematic and random error sources. The systematic errors of LTs, such as environmental conditions or component assembly, can be estimated and compensated by software. However, random errors, such as LT measurement noise, cannot be compensated but can be reduced by the appropriate location of the measurement system, so improving verification results [3].

To find the optimal LT location, the technical specifications of the encoders, the characteristics of the MTs [4], physical restrictions such as the range of the laser tracking receiver [5], and even temperature variations [6] are required.

This paper presents a developed algorithm able to determine the influence of LT measurement noise on the verification results. The algorithm takes into consideration LT characteristics and MT workspace. In addition, the developed software uses the Monte Carlo method to provide the area where the LT should be located with its probability distribution function (PDF).

#### **2. Materials and Methods**

#### *2.1. LT as Verification Measurement System*

A LT is a portable measurement system that provides, in a spherical coordinate system, the position of a measured point. It is often composed of a laser mechanism oriented by means of angular encoders, an interferometer block, a position-sensitive device (PSD), optics responsible for the beam division, a reflector, and a control unit. Point coordinates are determined by comparing the measurement beam with the reference beam from the laser interferometer together with the combination of the azimuth and polar angle encoders of its head, which provide two rotational degrees of freedom of the LT (Figure 1).

**Figure 1.** Errors due to encoders and sensor. Position-sensitive device (PSD).

#### 2.1.1. Error Sources in an LT

Like any other measurement system, LTs are affected by systematic and random errors. Currently there are three standards concerning performance evaluation of LTs: ASME B.89.4.19-2005 [7], VDI/VDE 2617-10 [8], and ISO 10360-10 [9]. These three standards provide different tests to verify the performance of an LT according to the specifications of the manufacturer, reducing the influence of LT errors on the measurement.

Gallagher [10] classified error sources as: angular encoder, tracking system, and component misalignments. Knapp [11] divided sources of errors into those due to environmental factors, data capture, approximations, and simplifications.

Errors due to the interferometer and optics are the result of environmental influences and LT calibration. Atmospheric effects, variations in the speed of light, and turbulence affect the physical characteristics of the laser beam [12]. The environmental conditions, pressure, temperature, and humidity produce variations in the refractive index of the air. These variations result in errors in the laser wavelength and finally, in the measured distance [10]. In a factory workshop without a temperature-controlled environment, the temperature can significantly fluctuate through the day. In [13] authors reported an example of an aircraft assembly facility with temperature variations of 8 ◦C over 4 h and variation on the vertical directions of 2.2 degrees. During the aircraft assembly process, if the beginning and the ending temperatures of the measurement survey vary by more than 2.2◦, then

the survey is considered void and has to be repeated. Nevertheless, environmental conditions present a systematic behaviour described analytically. Therefore, the LT control unit can compensate for this influence due to its meteorological position.

Moreover, installation of LT optics introduces a series of intrinsic errors such as the Abbe error, cosine error, and depth error. If the reflector does not move parallel to the measurement axis, a cosine error will occur. In the same way, if the reflector does not move along the measurement axis of the interferometer, an Abbe error occurs. Similarly, an error of calibration between the home and reflector provides a depth error that will be transferred to all measurement points.

Additionally, the main sources of error in a PSD are its resolution and the calibration procedure that was used to determine the relationship between the sensor output and the beam offset from the centre of the target used to calculate the measured point. This is minimised by the sub-system, consisting of two stepper motors, two optical angular encoders, and a motion control card. The two motors produce the azimuthal and polar rotation of the beam tracking system, allowing the laser beam to move towards the centre of the PSD target, minimising the offset. Depending on the resolution of the encoders used, a better adjustment of the offset will be made (Figure 1).

#### 2.1.2. LT Location in the Verification Process

The presence of LTs is increasing daily in machining and metrology companies, as tools to improve the accuracy of MTs through verification. Although LTs can be used to measure errors through geometric or pseudo-geometric verification [14], they are more frequently used in volumetric verification.

For this, the equipment should be located inside the MT kinematic chain in the same place as the workpiece [2,15]. MT kinematic chains are classified based on the movement of the workpiece and tool. The MT presented in this paper has an XFYZ configuration, where F determines the fixed part of the machine, X represents the axis that moves the part and the LT during the verification process, and Y and Z represent the axes that move with the tool [2].

The MT+LT kinematic chain mathematically links the tool centre point with the part of the machine, taking into consideration the sequence of movement and geometric errors of the MT (Equation (1)):

$$
\overline{X} + \overline{R\_x}\,\overline{T\_{ll}} + \overline{R\_x}\,\overline{R\_{ll}}\,\overline{X\_{ll}} = \overline{Y} + \overline{R\_y}\,\overline{Z} + \,\overline{R\_y}\,\overline{R\_z}\,\overline{T} \tag{1}
$$

where *X*,*Y*, and *Z* represent the translational vectors of the X, Y, and Z axes, respectively, with their geometrical errors and nominal displacements. *Rx*, *Ry*, and *Rz* are the rotational matrices of the X, Y, and Z-axes defined by their rotational errors. *Xlt* and *Tlt* represent the translation and rotational matrices between the LT and the origin of the MT coordinate system. Finally, *T* describes the offset of the tool [2].

Figure 2 shows the physical space available to locate the LT. Additionally, LT angular limitations such as maximum and minimum azimuth and polar encoders, and minimum radial distance or height couplings should be taken into account when locating the LT.

**Figure 2.** Machine tools (MTs) kinematic chain with XFYZ configuration, where F determines the fixed part of the machine, X represents the axis that moves the part and the LT during the verification process, and Y and Z represent the axes that move with the tool. Laser tracker (LT).

#### 2.1.3. Influence of LT Location on MT Volumetric Verification

While systematic errors can be compensated by the LT control unit, other errors, such as the angle of incidence on the retro-reflector, or errors in the PSD sensor, due to angular encoders and the interferometer, produce a non-systematic error commonly known as measurement noise.

The influence of measurement noise on measured points is modelled with Equations (2)–(4). These Equations link data from the encoders and radial distances with their uncertainty, providing the uncertainty of a measured point in Cartesian coordinates:

$$u\_x^2 = u\_r^2 \cdot \sin^2 \theta \cdot \cos^2 \varphi + u\_\theta^2 \cdot r^2 \cdot \cos^2 \theta \cdot \cos^2 \varphi + u\_\varphi^2 \cdot r^2 \cdot \sin^2 \theta \cdot \sin^2 \varphi \tag{2}$$

$$u\_y^2 = \ u\_r^2 \cdot \sin^2 \theta \cdot \sin^2 \varphi + u\_\theta^2 \cdot r^2 \cdot \cos^2 \theta \cdot \sin^2 \varphi + \ u\_\varphi^2 \cdot r^2 \cdot \sin^2 \theta \cdot \cos^2 \varphi \tag{3}$$

$$u\_z^2 = \
u\_r^2 \cdot \cos^2 \theta + \
u\_0^2 \cdot r^2 \cdot \sin^2 \theta \tag{4}$$

where *r* is the radial measured distance, ur, the radial uncertainty, θ, the azimuth angle, *u*θ, the azimuth angle uncertainty, ϕ, the polar angle, and *u*ϕ, the polar angle uncertainty.

As LTs work with an absolute coordinate system and MT to verify, nominal MT points are not in the same coordinate system when are measured. So, their real uncertainty depends on verification of the LT location in the MT workspace.

#### *2.2. LT Location Algorithm*

#### 2.2.1. Working Principles

The main aim of the developed algorithm was to provide the location of the area where the influence of the measurement system noise is smaller than the admissible error. The Guide to the Expression of the Uncertainty in Measurement (GUM) provides a framework for evaluating and expressing measurement uncertainty evaluating type A, type B, and combined uncertainties. Type A uncertainty is evaluated using statistical means, while type B is only evaluated based on experience or

other information. However, the estimation of uncertainties using GUM relies on assumptions, such as non-linearity of the mathematical model, that are not always fulfilled [16]. In these cases, supplement 1 to the GUM describes the problem of uncertainty evaluation in terms of probability density functions to obtain the best estimate thorough the Monte Carlo method.

In this case, the influence of measurement noise is obtained through optimisation based on the Levenberg–Marquardt method, taking into consideration the following information:


The working principle of the developed algorithm is presented in Figure 3. First, the user introduces configuration parameters: LT characteristics, angular and radial uncertainties, limits of available workspace, maximum admissible error, mesh of measurement points, number of tests to simulate, and convergence criteria.

**Figure 3.** Working principle of the location algorithm.

Then, the algorithm begins to perform a test loop for k = 1 to k = n, with n being the number of tests defined by the user. Next, the algorithm randomly takes a value from the angular and radial PDF for each point. These values will be fixed throughout the test k, changing from one test to the next. Simultaneously, the algorithm looks for a random position within the available space for the initial location parameters. These parameters are defined by a 1 × 6 vector (d, l, h, α, β, δ), which transforms coordinates from the MT coordinate system to the LT coordinate system. Parameters d, l, and h represent a translation between the MT coordinate system and the LT coordinate system on the x, y, and z-axes, respectively, and α, β, and δ are the Euler angles that relate the orientation of the LT coordinate system to that of the machine tool, rotating first around the x-axis, then the y-axis, and finally around the z-axis.

If the restrictions are met, then the uncertainty of each point is calculated using Equations (2)–(4). If not, the algorithm looks for others. Afterward, the objective function (5) is calculated:

$$
\mu\_{\text{max}} = \left(\mu\_{\text{max},x}^2 + \mu\_{\text{max},y}^2 + \mu\_{\text{max},z}^2\right)^{\frac{1}{2}}.\tag{5}
$$

This function is defined from a 1 × 3 vector made up from (*umax*,*x*, *umax*,*y*, *umax*,*z*), considering the most restrictive criteria as admissible errors (all maximum uncertainties are at the same point). In this way, the influence of measurement uncertainty in the verification points will always be equal to or less than the residual optimisation result.

During optimisation, the algorithm modifies in each iteration *j*, the location parameters d, l, h, α, β, and δ, changing the spherical coordinates r, θ, and ϕ of each point to minimise the uncertainty influence.

When the optimisation is finished, the algorithm returns the optimisation parameters with the residual error. If the residual error is less than the admissible error introduced by the user, the algorithm stops. If not, the software divides the MT workspace into two areas and repeats the process. Moreover, the algorithm provides the PDF that defines the uncertainty behaviour depending on the location of the LT.

#### 2.2.2. Case Study

All tests carried out had common simulation conditions: (a) the workspace to verify, defined by its limits of movement: 0 mm ≤ x ≤ 1500 mm, 0 mm ≤ y ≤ 600 mm, and 0 mm ≤ z ≤ 400 mm. (b) The available workspace around the MT where the LT could be located. This space was divided into two areas: narrow and wide. The narrow area had as available location parameters: 350 mm ≤ h ≤ 2000 mm, −500 mm ≤ d ≤ 2000 mm, and −2000 mm ≤ l ≤ −500 mm. The wide area had as available location parameters: 350 mm ≤ h ≤ 2000 mm, −2000 mm ≤ d ≤ −500 mm, and −500 mm ≤ l ≤ 2000 mm. As an additional restriction, the algorithm did not allow location of the LT inside the verification workspace (Figure 4). (c) The LT limits introduced in the algorithm were: azimuth angle θ −235◦ ≤ θ ≤ 235◦ and polar angle ϕ −60◦ ≤ ϕ ≤ 77◦. (d) The PDF that defined the angular and radial uncertainties were normal distributions with μ = 20 μrad and σ = 1.5 μrad for the angular encoder and 4 μm ± 0.8 μm/m for the radial. Finally, the optimisation criteria limits were the same for all tests. These limits were: maximum iterations set at 1000, the minimum parameter variation set as 1 <sup>×</sup> <sup>10</sup>−<sup>12</sup> and the minimum objective function variation set as 1 <sup>×</sup> <sup>10</sup><sup>−</sup>5.

**Figure 4.** Admissible LT locations areas and workspace zones.

This paper studied the influence of the spatial distribution of MT workspace points, the number of points used to determine the LT location and the number of Monte Carlo tests used. Point distributions can be a mesh or a cloud. The number of points studied were 48 or 175 (Figure 5), and the number of Monte Carlo tests carried out were 100, 1000, and 10,000.

**Figure 5.** Distribution and number of points studied.

#### **3. Results**

#### *3.1. Uncertainty Due to LT Location*

The first tests carried out to study the uncertainty of locating an LT in the narrow and wide areas used a mesh distribution of points, with 175 points and 10,000 Monte Carlo tests to obtain optimal values of d, l, h, α, β, and δ.

As the colourmap of Figure 6 shows, when the LT is located in the wide area the error range was from 27.1 to 72.0 μm. That is to say, the test with the least influence of LT noise with specific values of *ur*,*i*, *u*θ,*i*, and *u*ϕ,*<sup>i</sup>* with *i* = 1.175, provides a maximum uncertainty value of 27.1 μm, while the optimal parameters d, l, h, α, β, and δ in the test with the maximum uncertainty produce a value of 72.0 μm, taking into account that each test had different initial location parameters in the available workspace of Figure 4, with an initial error higher than final one presented in Figures 6 and 7 (residual error).

**Figure 6.** Error and LT location area in the wide zone using a laser–residual error.

When the LT is located in the wide area (Figure 6) there is a zone of conical shape where the tests present a high concentration of optimal locations with uncertainty values between 27.1 and 72.0 μm. So, the LT should be located in the wide area between −830 mm ≤ d ≤ −500 mm, 500 mm ≤ l ≤ 1000 mm, and 700 mm ≤ h ≤ 850 mm where the cone is registered.

When the LT is located in the narrow area, as shown in Figure 7a, noise uncertainty due to LT location increases from 56.2 μm to 170.5 μm. However, when the LT is located in the narrow zone there is an area to locate the LT of rectangular shape with l = −500 mm, 350 mm ≤ h ≤ 600 mm, and 0 mm ≤ d ≤ 600 mm, where the uncertainty is less than 115 μm. Figure 7b shows the histogram of residual errors, which allows study of the PDF that defines the behaviour of LT location influence. These errors are similar in the narrow and wide areas.

**Figure 7.** (**a**) Error and LT location area in the narrow zone using an LT. (**b**) Histogram of residual error.

When the residual error is higher than the introduced admissible error, the algorithm divides the verification area so that x = 750 mm (named as workspace 1 and workspace 2 in Figure 4). Then, the software analyses the influence of LT on these areas as independent workspaces, maintaining the location conditions. Table 1 compares the maximum and minimum errors when the MT workspace is divided.


**Table 1.** Influence of LT uncertainty depending on location and number of devices.

This shows that there is a relevant reduction inside the new workspace near to the LT in the narrow zone, where the minimum influence is reduced from 56.2 μm to 20.6 μm and the maximum is from 170.5 μm to 47.1 μm in Workspace 1, a reduction of approximately 70%. In the wide zone, Workspace 2, the reduction is not meaningful, around 3%. If two LTs are located on wide zones, the influence of LT uncertainty, minimum and maximum, is around 20% and 25% smaller, respectively.

#### *3.2. Influence of Design Conditions on Location Results*

Tests carried out using a unique LT in narrow or wide areas, as presented in the previous section, required a computational cost of around 6 h using a commercial PC. This was increased when the MT workspace was divided.

This value is too high for in situ machine verification. To reduce it, several configurations were tested, to study the influence of:


Due to the very large number of tests carried out, only the more relevant ones are presented here. Table 2 presents the computational cost of different design configurations depending on the number of points and tests. The distribution of points did not have a significant influence on computational cost.


**Table 2.** Computational time for different test configurations.

To study whether errors are significantly affected by different design configurations is necessary. Figure 8 shows the errors introduced by a unique LT in the wide zone, depending on the test configuration. The blue column represents the mean error of tests performed for each configuration. The red vertical lines show the range of the error produced for each configuration. The upper end is the maximum error chosen for a test and the lower end the minimum. For example, the design of a configuration consisting of a mesh of 175 points and 10,000 tests has an average error of 40.2 μm, a maximum error of 72.0 μm, and a minimum error of 27.1 μm, with a total range of 44.9 μm. The ninth column of the graph in Figure 8 is equivalent to Figure 6 and the results of the lower left configuration in Table 1.

**Figure 8.** Error of LT location in the wide zone using one LT, depending on the type and number of tests, and the distribution and number of points.

In Figure 8 it can be seen that the mean error due to LT location is similar in all configurations, with a range of 33.7–42.87 μm. However, the maximum error range is 48.19–72.01 μm. Also, there seems to be a lower limit around the zone of 20 μm.

The configuration parameters that have more influence on measurement error due to LT location were studied based on statistical design of experiment (DOE) [17]. Three input parameters were studied: parameter *A* = points distribution: mesh or cloud; parameter *B* = number of points: 48 or 175; and parameter *C* = number of tests: 100 or 10,000.

Figure 9 shows the results of the DOE applied to the maximum and mean error, representing the effect and the basic contribution of each parameter. The most relevant is the number of points in both cases. The greater the number of points, the greater the error. The number of tests has a large influence on maximum error but not on the average, causing different effects. The type of point distribution is the least relevant parameter in error due to LT location. The combination has the opposite effect on maximum error, compared to individual (Figure 9a). Similar behaviour is observed in the averages (Figure 9b).

**Figure 9.** Effect and basic contribution of point distribution, number of points and number of tests on maximum error (**a**) and average error (**b**).

To study whether the influence of these parameters can be modelled as lineal regressions, the Scheffler regression function was used [18] to give the maximum and average errors (Equations (6) and (7)):

$$\text{Amazerror } (\mu m) = 62.77 + 1.94A + 5.225B + 4.740C - 0.745AB - 0.900AC - 1.330BC - 0.600ABC \tag{6}$$

*average error* (μ*m*) = 38.187 − 0.234*A* + 2.789*B* − 1.036*C* − 0.004*AB* − 0.764*AC* − 0.516*BC* + 0.181*ABC*. (7)

To validate the adequacy of Equations (6) and (7), tests of different configurations, with 1000 tests, 48 and 175 points, and mesh and cloud distributions were used. In Table 3 we can see that these parameters do not have a linear behaviour, as might be anticipated from Figure 8.


**Table 3.** Adequacy of Scheffler regression functions for the average and maximum error values.

Table 4 shows the influence, in the wide zone, of distribution, number of points, and number of tests if the MT workspace is divided. Conclusions drawn from the results obtained are the same as those of the wide zone using one LT. The same is seen with the DOE tests.

**Table 4.** Influence of design parameters on wide zone LT location area and after division of the MT workspace.


Similar results were obtained when dividing the workspace volume into two areas: regardless of the design, there is a reduction in the maximum and average values of the error introduced. The error in Zone 1, compared to using only one LT, reduced from 34% to 21% in average values and from 50% to 21% in maximum error. In Zone 2, the average error was reduced from 42% to 22% and the maximum error from 50% to 21% (Table 4, Figure 10). As shown in Figure 10, when the MT workspace is divided, the range of error is reduced from 50.2 μm to 35.6 μm, and a minimum error support zone is also found at around 20 μm.

**Figure 10.** Error of the LT location in the wide zone. One zone vs. two zones with different configurations.

#### **4. Discussion**

Tests carried out show that there is no unique optimal position to locate the LT. As its uncertainty is defined by a PDF, each verification point will be affected by different values in each test. Therefore, there is one area where the PDF of LT influence is optimum. This depends on the measurement systems characteristic, therefore, the first step is to provide an adequate equipment characterization.

When only one LT is used to verify the whole MT workspace, the verification results can be improved by locating the LT in the wide area, inside the estimated zone with a cone shape. The Monte Carlo analysis provides an uncertainty range from 27.1 to 72 μm, providing a maximum error around 60% smaller than that obtained when the LT is located in the narrow area.

If the residual error obtained is too high, the division of the workspace into two zones provides an improvement in uncertainty due to LT location. This is especially relevant in the narrow zone, where the maximum error in workspace 1 is reduced by around 70%. If two LTs are used and located in the wide zone, their influence compared to the use of just one LT is improved by around 25%. Thus, the use of two workspaces and two LTs reduces their location influence. These results show that, in these cases, the greater the distance of measurement, the greater the mistake is committed. Therefore, the LT might be placed near the workspace to verify. One should recall that there is a minimum distance allowable for each equipment.

Tests carried out to study the influence of design configuration show that the number of points is the most relevant parameter, followed by the number of tests, and the points distribution. Moreover, we demonstrate that their relationship cannot be modelled as linear regression functions. Therefore, users should assess the computation costs against the accuracy of the method to determine the configuration parameters.

**Author Contributions:** Conceptualisation: S.A., J.A.A. and J.S.; Methodology: S.A., P.P. and J.A.A.; Formal Analysis: S.A., J.S., P.P. and J.V.; Resources: J.A.A., P.P., J.V. and S.A.; Writing—original draft preparation: S.A., P.P. and J.A.A.; Writing—reviewing editing: J.A.A., J.S., P.P. and S.A.; Software: S.A. and J.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Ministerio de Economía, Industria y Competitividad de España with project number Reto 2017-DPI2017-90106-R., and by the Aragon Government (Department of Industry and Innovation) through the Research Activity Grant for research groups recognised by the Aragon Government (T56\_17R Manufacturing Engineering and Advanced Metrology Group).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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