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Vol. 8. Issue 5.
Pages 4198-4208 (September - October 2019)
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Vol. 8. Issue 5.
Pages 4198-4208 (September - October 2019)
Original Article
DOI: 10.1016/j.jmrt.2019.07.028
Open Access
Investigation of the burr formation during the drilling of free-form surfaces in al 7075 alloy
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Erkan Bahçe
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erkan.bahce@inonu.edu.tr

Corresponding author.
, Burak Özdemir
Inonu University, Faculty of Engineering, Department of Mechanical Engineering, 44280 Malatya, Turkey
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Figures (14)
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Tables (9)
Table 1. Radial distance between the drill centre and point p.
Table 2. The first contact point on the free-form surface of the cutting lip.
Table 3. Chemical composition of Al7075.
Table 4. Mechanical and physical properties of Al7075.
Table 5. Experimental parameters.
Table 6. Experimental results.
Table 7. Signal-to-noise (S/N) ratio values.
Table 8. ANOVA results.
Table 9. NLR analysis summary table.
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Abstract

The use of free-form shapes has become widespread to design complex products that have to fulfil engineering requirements as well as aesthetic criteria. Conventional drilling with twist drilling still remains one of the most economical and efficient machining processes for hole making as well as for riveting and fastening structural assemblies in the aerospace and automotive industries. In drilling, one of the major issues of the process pertains to burrs formation, which affects the quality of the final product and, thus, the capability to meet the part desired functionality. Though it is noted that drilling operations produce burrs on the machined parts, burrs removal on free form surface is more difficult, producing an increase of both the time and cost for deburring.

In this study, the effects of drilling parameters on the formation of burrs during the drilling of free-form surfaces were examined. A free-form surface manufactured from Al7075 was drilled using different exit surface angle, spindle speed and feed rate parameters. The drilled workpiece was then scanned using a 3D scanner to obtain data related to burr formation and burr height. By evaluating these data via the TAGUCHI, ANOVA and NLR statistical methods, optimum drilling parameters for minimum burr height were determined. In addition, a mathematical model for predicting burr height was developed, with first fracture points, hole morphology and the burr formation process investigated based on images taken during and after drilling. The lowest burr height was measured 15° exit surface angle, 2300rpm spindle speed and 0.1mm/rev feed rate. In addition, a mathematical model was developed using NLR analysis which estimate actual results by 90.26%.

Keywords:
Free-form surface
Drilling
Burr formation
Full Text
1Introduction

Due to the increased usage of free-form surfaces in the automotive, aerospace and biomedical industries, among others, a need has arisen to control the burring that occurs during the manufacture of these surfaces. The burrs that are formed during the drilling process have various effects, including the creation of a distortion margin at the edges, difficulty in mounting, and decreased dimensional accuracy. However, the cost of burr removal may vary depending on the precision of the hole, the complexity of the part, as well as burr shape and size. For example, whereas Gillespie [1] reported that the cost of deburring constituted 30% of the total production cost for parts such as aircraft engines that require high-precision manufacture, Hockauf et al. [2] and Kalpakjian and Schmid [3] expressed that the same process constituted only 14% of the production cost of automobile parts.

Many methods such as tool design and the statistical evaluation of machining parameters have been and are still being developed in the manufacturing industry in order to solve these problems. A general review of the literature regarding studies investigating deburring reveals an emphasis on new-concept tool design and the statistical optimisation of drilling parameters in the drilling of flat surfaces (DFS), where the hole axis and hole surface are perpendicular to one another.

In research focusing on new tool design, the effects of variation in parameters such as the drill tip angle, cutting lip and helix angle of the manufactured tools on burr size have been widely investigated [4–7].

Related studies have attempted to achieve reduced burr formation by changing tool geometric dimensions at different rates. Kim et al. and Kubota et al. conducted some experiments by using different types of drill bits such as standard, countersink and stepped, and they reported that the type and size of the drill bits had considerable effects on the burr size [4,5].

Statistical evaluation of the effect of variation in machining parameters (spindle speed, feed rate, tool diameter) on burr size has been carried out using analytical techniques. Kilickap [6] used Taguchi and response surface methodologies for minimising the burr size and the surface roughness in drilling Al-7075, and concluded that the best results for surface roughness and burr size were obtained at lower cutting speed and feed rates while at higher point angle. Varatharajulu et al. [7] used Box–Behnken design to study the effects of the drilling parameters such as spindle speed and feed rate and to predict the burr size as a function of input parameters on drilling Duplex 2205. The developed model, which was analysed by using ANOVA, establishes a good correlation between spindle speed and feed rate that influences the burr size. Kundu et al. [8] studied on the development of a burr height prediction model during machining aluminium alloy using Response Surface Methodology and found by performing ANOVA that drill diameter was the most important factor to affect formation of burr height. Sokołowski [9] studied on the data related with the force and reported that the axial drilling force had important effects on burr height. Pilny et al. [10] varied the cutting data, clamping conditions and drill geometry to optimise the burr size in their study and achieved satisfactory results in the drilling process of sheets of wrought aluminium alloy. Khan et al. [11] investigated the effects of cutting parameters on burr formation using Taguchi method, and the orthogonal array, signal-to-noise ratio, and ANOVA was employed to optimise the drilling parameters. Mondal et al. [12] developed an artificial neural networks (ANN) model to minimise burr formation by using cutting parameters, they observed that the model showed close matching with the experimental results.

A large number of studies in the literature have examined the formation of burrs in both DFS and in the drilling of non-flat surfaces. For example, Min et al. [13] analysed the influence of the exit surface angle on drilling burr formation, associating it with their so-called ‘interaction angle’. Ton et al. [14] investigated burr formation on inclined exit surfaces, designing a new deburring tool with which to remove such burrs. Heisel and Schaal [15] examined burrs occurring on intersecting holes, developing a calculation method with which to predict burr height during the drilling of these holes.

All the reported methods, It was focused on control of burr formation on plate surface. However, burr formation on the free-form surface, which is widely used in product, is notable that the studies carried out. In this framework, the present study aimed to determine and statistically evaluate the effects of feed rate, spindle speed and exit surface angle on burr formation, height and hole morphology observed during the drilling of free-form surfaces, which have become widely used in recent times.

2Drilling of free-form surfaces

The drill apparatus under study comprises a chisel edge and two helical cutting lips, with a taper angle that meets the flutes with a helix angle of a standard twist drill. For such apparatus the drilling mechanics must be analysed in two different sections, i.e. the chisel and cutting lip regions, because the chisel edge does not cut but rather spreads the material sideways via an indentation mechanism as explained by Altintas [16].

Considering the studies on drilling mechanics performed by Altintas [16] and the studies on burr formation performed by Aurich et al. [17], the first fracture point on the exit surface in DFS occurs at the end of the drill bit, represented by point I in Fig. 1. However, for free-form surfaces, the first fracture point varies between points I and III depending on the curvature of the surface.

Fig. 1.

Helical drill geometry.

(0.12MB).

In Fig. 1, w is the chisel web offset from the drill axis, φ is the chisel edge angle, ψ is the tip angle and I, II, III represent the points on the cutting edge.

Aurich et al. [17] modelled burr formation in DFS in five parts: steady state, initiation, development, initial fracture and final burr, using the finite element method. During the steady-state stage of drilling, the drill tip enters the work piece completely, with a bulge forming during the subsequent initiation stage due to plastic deformation taking place while the drill moves towards the exit of the hole. During the development stage, the bulge increases in size and expands in all directions, before reaching its maximum width and growing to an end point during the initial fracture stage; the first fracture then occurs due to the low flexibility of the drill bit (Fig. 2a). Finally, the bulge is torn and curls inward to form the burr. Burr formation stages occurring on free-form surfaces are similar to the first four stages described for DFS, but the fifth stage is different. During the fifth stage of the drilling of free-form surfaces, the first fracture point in burr formation occurs not only at the end point of the drill bit but also varies depending on the curvature of the exit surface. This situation is illustrated clearly in Fig. 2b.

Fig. 2.

Initial fracture stage of burr formation.

(0.13MB).

Knowing of the first point of fracture at the exit during the drilling of free-form surfaces plays an important role in defining the mechanism of burr formation. To illustrate this situation analytically, the coordinates of each point on the cutting lip relative to a reference point must be expressed.

Accordingly, Fig. 3 illustrates a Cartesian coordinate system in which the drill axis is parallel to axis z, the lip offset from the drill axis due to the chisel edge is parallel to axis x, and the axis normal to the lip is parallel to axis y, with the centre at the drill tip O.

Fig. 3.

Determination of the coordinates of the drill cutting lip.

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As can be seen in Fig. 3, the first fracture point p is defined as a point between point O and point h on the cutting lip, considering the bottom of the flute where the lips and chisel edge meet (the plane of z=0). The radial distance between the drill centre and the lip and helical flute intersection at elevation z=h is r(h)=R, where the drill diameter is R. By generalising this situation as in Table 1, we can define the coordinates of each point on the cutting lip Altintas [16].

Table 1.

Radial distance between the drill centre and point p.

z=z=z=
r(0)=wsin(π−φ)  r(a)=R  r(z)=y(0)2+[x(0)+Dp]2 =w2+[w cot(π−φ)+z tan ψ]2 
Coordinates
x(0)=r(0)cos(π−φ)  x(h)=R cos θ(a)  x(z)=r(z)cos θ(z) 
y(0)=w  y(h)=w  y(z)=r(z)sin θ(z) 

The free-form surfaces obtained using NURBS, Bezier and B-spline surfaces are typically expressed in terms of a parameter such as t. In the drilling of free-form surfaces, the curve form in the exit area of the drill shows variability. Considering that this curved form can be convex or concave, the first contact point on the surface of the drill can be expressed, with the main equations of the curves forming the free-form surface being the xt and yt equations, which depend on the t parameter. Accordingly, if defined as β=(π−ψ/2) as in Fig. 1, the inclination angle of the tangent at the intersection point of the drill's AA axis (Fig. 3) with the free-form surface can be calculated as follows:

The first fracture point on the surface can then be generalised as in Table 2.

Table 2.

The first contact point on the free-form surface of the cutting lip.

If the curve at the intersection area of the drill's AA axis with the surface is convex, the first contact point at the cutting lip is:If the curve at the intersection area of the drill's AA axis with the surface is concave, the first contact point at the cutting lip is:
tan α≤tan β  tan α>tan β  tan α≤tan β  tan α>tan β 
Point I  Point III  Point I  Point p 

The scenarios described in Table 2 represent the first contact points of the cutting lips depicted in Fig. 2b.

3Material and method3.1Experimental material and parameters

For the production of the free-form surfaces used in the drilling tests, Al7075 material, which is widely used in the medical, aerospace and automotive industries, was selected and machined in a CNC milling machine. The chemical and mechanical/physical properties of this material are shown in Tables 3 and 4, respectively.

Table 3.

Chemical composition of Al7075.

Chemical composition (wt.%)
Si  0.4 
Fe  0.5 
Cu  1.2–2.0 
Mn  0.3 
Mg  2.1–2.9 
Cr  0.18–0.28 
Zn  5.1–6.1 
Ti  0.2 
Others  0.15 
Al  Balance 
Table 4.

Mechanical and physical properties of Al7075.

Mechanical parameters values
Density (g/cm32.81 
Hardness (HB)  60.0 
Ultimate tensile strength (MPa)  228 
Tensile yield strength (MPa)  103 
Elongation at break (%)  16.0 

For the design of the free-form surface, the B-spline curve theory was used, with the curve equation created in the MATLAB 2012a software program and the parametric surface thus obtained. The surface data were then converted into a CAD model (Fig. 4). Control points and knots with which to define the freedom of the surface form were randomly selected. Drilling tests were then carried out using a CNC machine; channels were opened on the drill entry surface to ensure that the drill feed distances, from the point where the drill axis intersected the surface curve, were equal (Fig. 4). The drilling experiments were carried out using different exit surface angles of 15°, 30° and 45° in order to determine the effect of variation in the inclination between the drill axis and the hole exit surface.

Fig. 4.

CAD image of the free-form surface.

(0.06MB).

The drilling experiments were conducted in dry conditions using an HSS drilling tool in accordance with the DIN 338/RN standard, with Ø=7.5mm, a 30±3° helix angle and a 118° tip angle. The experiments were carried out according to a Taguchi design and each experiment was repeated 3 times. Holes were drilled at 20mm intervals into the specimens, with the values of the other experiment parameters given in Table 5.

Table 5.

Experimental parameters.

Level  Exit surface angle, A  Spindle speed, B (rpm)  Feed rate, C (mm/rev) 
15°  1300  0.1 
30°  1800  0.2 
45°  2300  0.3 
3.2Method3.2.1Burr height measurement

For the measurement of the burrs formed on the exit surface after drilling, 3D scanning was carried out using a DAVID SLS-3 3D scanner. After scanning, sections were taken at 45° intervals as shown in Fig. 5a for each hole, with burr heights determined based on the literature by measuring the distance between the peak and exit surface, as depicted in Fig. 5b. For each hole, the average burr height was calculated as the arithmetic average of the measured 8 burr height values.

Fig. 5.

Burr height measurement method.

(0.22MB).

In addition, images were obtained with an ELP-USB500W02M-AF60 camera placed at the bottom of the drilling axis for the detection of the first fracture points at the exits of the holes (Fig. 6). Then, using these images, the first break points for each hole were analysed.

Fig. 6.

Stages of burr formation (under a spindle speed of 1800rpm and feed rate of 0.1mm/rev).

(0.17MB).
3.2.2Taguchi method

Depending on the number of parameters investigated, a great number of experiments may be required to achieve a result, leading to an increase in time spent and manufacturing costs, and reducing productivity. Owing to its orthogonal experimental design, the Taguchi method significantly reduces the number of experiments that must be carried out and minimises the effects of uncontrolled factors (noise) Bates and Watts [18]. As a result, the Taguchi method was also applied in the present study.

The method was carried out by determining 3 parameters and 3 levels of each parameter, then selecting the L27 Taguchi orthogonal array. For each of the experiments’ different factor combinations, the S/N ratios of the data were calculated using the Minitab 17 software program according to the smallest best equation as expressed by the following equation:

where y represents the obtained burr height values and n represents the number of experiments.

3.2.3Nonlinear regression (NLR) analysis

Although the Taguchi method enables the determination of parameter values that produce optimum experimental results, mathematical models of these test results must be established in order to numerically calculate to what extent each parameter affects burr height. One of the most effective methods used in the design of such models is NLR analysis, which was explained by Bates and Watts as a combination of regression and ANOVA for the comparison and modelling of variable data [18]. A typical NLR model can be expressed via the following equation:

where Yn represents the dependent variable, Xn represents the independent variable, f represents the expectation function, θ represents the model parameter and Zn represents the error value.

4Results and discussion

Based on the experiments conducted regarding the drilling of free-form surfaces, it was found that the feed rate, spindle speed and exit surface angle have a significant effect on burr formation, burr height and burr shape. The stages of burr formation on the free-form surfaces were also examined, with a statistical evaluation of burr heights carried out using the Taguchi method, ANOVA and NLR analysis.

4.1Stages of burr formation during the drilling of free-form surfaces

The angle between the hole axis and hole surface during the drilling of the analysed free-form surfaces (i.e. the exit surface angle) was found to affect the first fracture point (Fig. 2b), as can be clearly seen in the camera images taken at the base of the sample during the experiments (Fig. 6).

For each of the three different exit surface angles tested, during the first stage of burr formation the drill forms a bulge due to plastic deformation as it moves towards the exit of the hole (Figs. 6 and 7). In the second stage however, the first fracture point varies depending on the exit surface angle; whereas for a 15° exit surface angle the first fracture point is formed near the drill bit, i.e. at point I in Fig. 1, for a 30° exit surface angle the burr is formed between points I and III on the cutting edge of the drill, while for a 45° exit surface angle the burr is formed at point III on the cutting edge. During the third stage, the bulge formed by plastic deformation grows, expands and tears. In the fourth stage, the burr formed around the hole reaches its final state.

Fig. 7.

Schematic representation of the first fracture points at the exit surface for each stage of burr formation and exit surface angle.

(0.36MB).

Ko and Lee [19] divided burrs into 3 groups according to burr cap formation:

Type A (no cap by fracture), Type B (burr with cap) and Type C (burst burr without cap). In the present study, a Type B burr cap was observed under a 15° exit surface angle, while a Type C burr cap was observed under both 30° and 45° exit surface angles (Fig. 8).

Fig. 8.

Burr cap images after the drilling experiments conducted with different exit surface angles: (a) 15°, (b) 30° and (c) 45°.

(0.11MB).

In the literature Aurich et al. [17] and Bahce et al. [20,21] burrs have been classified as uniform, transient or crown in shape. According to the experimental results obtained here, the shape of all the burrs is similar to that of transient burrs (Fig. 9). Therefore, whereas previous studies have found that drilling parameters have an effect on exit burr shape if the angle of the exit surface is 0°, in the present study the exit surface angles and drilling parameters had no effect on burr shape as no variation in the latter was recorded. Here, deformation after the first fracture point on the free-form surface occurred in quadrants II, III and IV according to the presented coordinate system (Fig. 9).

Fig. 9.

Burr formation around the hole: (a) 15°, (b) 30° and (c) 45° exit surface angle.

(0.13MB).

It was also found that the drilling parameters had no significant effect on the angular area of burr formation around the hole, with burrs formed in the region 110–357° counterclockwise around the hole in all experiments (Fig. 10).

Fig. 10.

Section of non-burr formation across the hole periphery (Δθ) under a spindle speed of 1800rpm and feed rate of 0.1mm/rev: (a) 15°, (b) 30° and (c) 45° exit surface angle).

(0.12MB).

Although it is difficult to determine precisely Δθ the hole periphery due to the fact that the burr has an unstable structure, it was observed here that Δθ increased with an increase in the exit surface angle. In addition, no stable relationship was found between a change in either the feed rate or spindle speed and the possible non-burr section across the hole periphery.

4.2Taguchi analysis and experimental results

According to the results obtained from the drilling tests, the effects of varying the exit surface angle (A), spindle speed (B) and feed rate (C) on the average height of the exit burrs are shown in Table 6.

Table 6.

Experimental results.

Exp. no.  ParametersAverage burr height (mm) 
  A  B  C   
0.4121 
0.3386 
0.9320 
0.0991 
0.2940 
0.9025 
0.1753 
0.2484 
1.5818 
10  0.2891 
11  0.3839 
12  1.5186 
13  0.3433 
14  0.4096 
15  0.8966 
16  0.1965 
17  0.2870 
18  1.0964 
19  0.2056 
20  0.5758 
21  0.4668 
22  0.4526 
23  0.6745 
24  1.0112 
25  0.4269 
26  0.4093 
27  1.2654 

Fig. 11 displays main effect graphs for the S/N ratios determined based on the obtained test results, with the delta values in Table 7 indicating the difference between the highest and lowest values of the factors affecting burr height. Thus, according to the obtained S/N ratio values, the feed rate has the most influence on burr height, followed by the exit surface angle and spindle speed, respectively.

Fig. 11.

Main effect diagrams for S/N ratios of burr height.

(0.06MB).
Table 7.

Signal-to-noise (S/N) ratio values.

Level  A  B  C 
8.0620  6.4818  11.6801 
6.4034  6.6445  8.3356 
5.3855  6.7247  −0.1649 
Delta  2.6765  0.2429  11.8450 
Rank 

When the obtained S/N ratios are examined according to the “smaller is better” (i.e. less noise and thus a higher ratio value) condition, in this case level 1 for factor A, level 3 for factor B and level 1 for factor C, the optimum test conditions comprise an exit surface angle of 15°, a spindle speed of 2300rpm and a feed rate of 0.1mm/rev. In addition, Fig. 12 illustrates that burr height increases with an increase in the values of all three test parameters.

Fig. 12.

Variation in average burr height with increasing test parameter values. (a) Exit surface angle, (b) spindle speed and (c) feed rate.

(0.21MB).

The observed increase in burr height with feed rate can be explained by increased deformation in the cutting area as a result of rising quantities of cut material. Such a situation causes the deformed material, not subjected to cutting, to overflow out of the hole exit area, thereby increasing the burr height. This finding is similar to that reported by both Lauderbaugh [22] and Kim and Dornfeld [23]. Furthermore, analysis of the graphs shown in Fig. 12 reveals that burr height also increases with an increase in spindle speed. In this case, as reported in the study of Varatharajulu et al. [7], as the drill moves towards the hole exit, the temperature rise caused by the higher spindle speed increases the ductility of the material in the cutting area, resulting in greater levels of plastic deformation around the hole. In addition, the angle of the exit surface is not 0°, which further affects the height of the burr. In the drilling tests conducted with an exit surface angle of between 15° and 45°, burr height increased at greater angles. Since the exit surface is free formed, the stresses at the cutting edges vary depending on the form of the surface after the first fracture point, which causes instability in cutting forces. This in turn leads to the orientation of the deformation traces in the cutting area, as is clearly visible in the cross-sectional views of the tested holes depicted in Fig. 13. In this figure it can be seen that whereas the orientations along the hole axis take the form of helical traces, those at the hole exit are angular in orientation after the first point of fracture.

Fig. 13.

Cross-sectional views obtained under a spindle speed of 1800rpm and feed rate of 0.1mm/rev (exit surface angle: (a) 15°, (b) 30° and (c) 45°).

(0.22MB).

Finally, an increase in the exit surface angle also increased the orientation area, likely caused by changes in the radial forces after the first fracture point.

4.3Analysis of variance (ANOVA)

Similarities between the average parameter values and the effects of these parameters on burr height were determined proportionally by analysing parameter variance, with the obtained ANOVA results presented in Table 8. The calculated Fvalue and Fcritical values from the F table, taking into account the values of df1/df2, were then compared according to these criteria.

Table 8.

ANOVA results.

Source  DF  Adj. SS  Adj. MS  F-Value  P-Value  %Contribution 
A  0.01666  0.00833  0.14  0.87  0.4 
B  0.02535  0.01268  0.21  0.81  0.6 
C  3.24601  1.623  27.28  72.5 
Error  20  1.19005  0.0595      26.6 
Total  26  4.47808        100 

In the F table, df1/df2=2/20, corresponding to Fcritical=3.4928, with the F values of the experiment set being FA=0.14, FB=0.21 and FC=27.28. Thus,

According to these results, since the F values of factors A (exit surface angle) and B (spindle speed) are smaller than the corresponding Fcritical values, it is understood that there is no significant difference between the factors and the population variances. In contrast, the F value of factor C (feed rate) is larger than the Fcritical value, indicating a significant difference. Similar results were obtained regarding p values:

When the contribution rates are examined, it can be seen that factor C (feed rate) has the greatest effect on mean burr height, accounting for 72.5% of total variance. In contrast, factors A (exit surface angle) and B (spindle speed) contribute only 0.4% and 0.6%, respectively.

4.4NLR results

After determining the respective impact rates of the factors affecting burr height, a mathematical model was developed using NLR analysis to estimate the dependence of burr height on the 3 independent factors.

4.4.1Mathematical model

The predicted values obtained via NLR analysis and summary of the residual values calculated in the Minitab 17 package are presented in Table 9. According to this table, the estimated values obtained using the NLR model reflect 90.26% of the experimental results.

Table 9.

NLR analysis summary table.

Analysis of variance
Source  DF  Adj. SS  Adj. MS  F-Value  P-Value 
Regression  16  4.04184  0.252615  5.79  0.004 
A  0.00213  0.002126  0.05  0.83 
B  0.00119  0.001188  0.03  0.872 
C  0.00355  0.003551  0.08  0.781 
A×A  0.07568  0.075676  1.73  0.217 
B×B  0.01069  0.010689  0.25  0.631 
C×C  0.00214  0.002139  0.05  0.829 
A×B  0.01637  0.016374  0.38  0.554 
A×C  0.10023  0.100231  2.3  0.161 
B×C  0.07734  0.077341  1.77  0.213 
A×A×B  0.15992  0.159924  3.67  0.085 
A×A×C  0.02654  0.02654  0.61  0.453 
A×B×B  0.11376  0.113761  2.61  0.137 
A×B×C  0.01196  0.011958  0.27  0.612 
A×C×C  0.09317  0.093168  2.14  0.175 
B×B×C  0.04876  0.048757  1.12  0.315 
B×C×C  0.07337  0.073374  1.68  0.224 
Error  10  0.43623  0.043623     
Total  26  4.47808       
Model summary
S  R-sq.  R-sq (adj.)  R-sq (pred.) 
0.208862  90.26%  75%  4.36% 

In the mathematical model, the relationship between mean burr height and the drilling parameters (A – exit surface angle, B – spindle speed, C – feed rate) was established by three-point crossing with non-standardised categorical coefficients. The mathematical equation expressing the NLR method is given below:

By using the obtained NLR mathematical model, it is thus possible to estimate burr height in the drilling of free-form surfaces with a confidence interval of 95% and with 90.26% accuracy.

4.4.2Validations

Residual values for the validation of the NLR mathematical model were calculated in order to determine the difference between actual and estimated values. The largest standard abnormal residuals were determined for experiments 12 (0.365) and 21 (−0.211) (Fig. 14). No changes were thus made to the mathematical model to show the effect of all test results, although experiments 12 and 21 were excluded from further study, with a new NLR analysis producing a value of R2=98.03. The residual values displayed in Fig. 14 reveal a deflection between the estimated model and the test results of generally between (−0.1) and (+0.1), indicating a close match and a uniform distribution with the exception of the 2 outlying values.

Fig. 14.

Validation of the NLR model.

(0.24MB).

The above results show that the experimental results and NLR estimates overlap for the vast majority of the model data, and that the model can respond decisively to new experimental datasets.

5Conclusions

Experimental analysis of the drilling of free-form surfaces using different drilling parameters has been presented. By examining the burr formation process, first fracture points were determined at the edges of the different exit surfaces. Regardless of the drilling parameters, it has been shown that burrs only occur within a certain region (at between 110° and 357°) around the hole. The traces that the tool formed on the inner surface of the hole during the drilling process were examined considering the position of the first fracture points. These traces were found to be oriented within the region after the first breakpoints due to force imbalance.

The obtained burr heights and drilling parameters were then evaluated using the Taguchi method, enabling the parameter values producing minimum burr height to be determined (15° exit surface angle, 2300rpm spindle speed and 0.1mm/rev feed rate). In general, it was observed that burr height increases with an increase in all three of the tested drilling parameters. ANOVA was also performed between the drilling parameters to determine their impact ratings with respect to burr height. According to the ANOVA results, parameter C (feed rate) most affects burr height, accounting for 72.5% of variability. Finally, a mathematical model was developed using NLR analysis to determine the relationship between drilling parameters and burr height. This model enabled the prediction of burr heights for different drilling parameter values, with the estimated and actual (experimental) results overlapping by 90.26%.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgment

This study was supported by the by Scientific Research Project Coordination Unit of Inonu University (BAP-Project ID 96-2015/20).

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