Statistical modeling of basic machinability parameters in drilling of metals.

Anghel, Cornelia ; Petropoulos, Georgios ; Vaxevanidis, Nikolaos 等

1. INTRODUCTION

Cutting processes are widely used in industry to manufacture both metallic and non metallic products, providing high form and dimensional accuracy, and surface quality with high degree of flexibility. Machinability of an engineering material is a crucial technological property that denotes its adaptability to machining processes in view of factors such as cutting forces, tool wear, and surface roughness. Effective and reliable machinability databases for cutting of metals are of paramount importance to assist manufacturers to apply proper machining conditions and relevant decision making. When carrying out machinability investigations data mining is necessary instead of a one-at-a-time factor approach. Such data mining techniques are Taguchi, response surface methodology and others accompanied by statistical design of experiments (Montgomery, 1997). Drilling is one of the most common cutting operations being necessary for machine building and assembling in a variety of applications (Bakkal et al., 2005). But it should be borne in mind that drilling especially when opening new holes is essentially a rough machining method and cannot meet satisfactorily the aforementioned requirements (Basavarajappa, 2007). The experimental investigation on basic machinability parameters in conventional drilling, which will be described in the following, attempts to give insight into the crucial parameters that rule the drilling performance and to model this complicated behavior (Petropoulos et al., 2007). Parameters that do not contribute to safe conclusions are rejected during the statistical design of the models (Petropoulos & Vaxevanidis, 2005).

2. EXPERIMENTAL

2.1. Measuring force system set-up - Surface roughness measurements

The cutting force and torque measurements were undertaken by a 4-axis 9272 KISTLER dynamometer.

The DynoWare software was used for processing of the measurements. The evaluation of surface roughness was realized by a Sutronic 3+ Rank Taylor Hobson profile-meter using the Talyprof software.

The average values of three measurements of the parameter [R.sub.a] are considered in each case.

2.2. Drills

The drills used in the experiments are twist drills of cylindrical shank made of high speed steel with 5% in cobalt according to DIN 338 HSS-Co (high speed steel cobalt alloyed).

2.3 Work-piece materials--Specimens

Specimens made of St37 steel and Aluminum alloy 5005, according to DIN 17100 and DIN AlMg, respectively. St37 steel is a carbon steel of wide use, relatively soft and possessing good machinability.

Al 5005 is an aluminum alloy of medium hardness, also widely used in structural applications.

Principal mechanical and physical properties of both materials used for processing are listed in Table 2. The great difference in hardness between the two alloys is evident, a fact that will be considered in the statistical analysis of the experiments.

3. RESULTS AND DISCUSSION

3.1. Dry drilling.

In the tests 27 holes were drilled, corresponded to the combinations of 3 feed rates and 9 rotational frequencies. The results are illustrated in the corresponding diagrams in Fig. 1.

[FIGURE 1 OMITTED]

In view of the foregoing diagrams it is clear that two stages are noticed on the relevant curves. At low values of cutting speed both M and F tend to reduce, whilst they further increase with increase in rotational frequency. The effect of the latter is more pronounced on the axial force; the torque increases less significantly.

This behavior could be attributed to trapping of the chip and the difficulty to be removed from the opening hole due to the increased cutting speed. Concerning the influence of feed on B and F it is obvious that is more significant compared to that of cutting speed. Besides some exceptions surface roughness Ra increases when feed increases. The significant fluctuations observed are related to random phenomena like chip generation and removal under non repetitive conditions.

3.2. Wet drilling

The drilling tests were performed with the same cutting factors using three different cutting oils (neat oils) with viscosity varied from 4,80 cS to 11.30 cS at 80[degrees]C .

Considering the experimental findings it was observed that when using the oil of intermediate viscosity the values of torque and force were higher compared to drilling performance with the rest oils; the use of the oil of the lowest viscosity gives slightly lower values of M and F than the oil of the highest viscosity.

As expected, the values of both magnitudes are pronounced in the case of dry drilling but the trends followed in association with the cutting conditions are similar.

4. STOCHASTIC MODELLING

4.1 Statistical experimental design

In Fig. 2 some response surface graphs illustrate the formed models. Summing up, in Table 3 comparative results from ANOVA are shown regarding the statistical validity and the most significant factors of the developed models.

[FIGURE 2 OMITTED]

Axial force

F = 1371.5 + 491.7[X.sub.1] + 453.0[X.sub.2] + 641.2[X.sub.3] + 106.6[X.sub.4] - 38.7 [X.sub.12] + 145.1 [X.sub.4.sup.2] + 133.5[X.sub.1][X.sub.2] + 187.7[X.sub.1][X.sub.3] + 238.9[X.sub.2][X.sub.3] + 11.9 [X.sub.1][X.sub.4] + 108.2[X.sub.2][X.sub.4] + 115.5[X.sub.3][X.sub.4] [R.sup.2] = 0.959 ([X.sub.1]:work-piece material, [X.sub.2]: drill diameter, [X.subl.3]: feed, [X.sub.4] : rotational frequency)

Torque

M = 804.9 + 252.5[X.sub.1] + 294.0[X.sub.2] + 337.6[X.sub.3] - 8.0[X.sub.4] + 81.5[X.sub.1] [X.sub.2] + 82.54[X.sub.1] [X.sub.3] - 63.7[X.sub.1] [X.sub.4] + 133.1[X.sub.2] [X.sub.3] - 63.9[X.sub.3.sup.2] [R.sup.2] = 0.979

Roughness

Ra = 5.9 + 0.5[X.sub.1] - 0.3[X.sub.2] - 0.2[X.sub.3] - 0.2[X.sub.4] + 0.3[X.sub.1] [X.sub.2] - 0.2[X.sub.2] [X.sub.4] - 0.2[X.sub.3] [X.sub.4] - 0.8[X.sub.4.sup.2] [R.sup.2] = 0.412

Hole oversize

[[epsilon].sub.D] = 0.3 + 0.03[X.sub.1] + 0.02[X.sub.2] + 0.0[X.sub.3] + 0.02[X.sub.4] + 0.035[X.sub.1] [X.sub.2] + 0.03[X.sub.1] [X.sub.4] + 0.02[X.sub.2] [X.sub.4] + 0.06X[X.sub.3.sup.2] + 0.04[X.sub.4.sup.2] [R.sup.2] = 0.403

5. CONCLUSIONS

From the initial tests conducted dry and replicated using cutting oils, the most physically significant factors leading to safe conclusions were detected that could be introduced to the stochastic models. In the lubricated tests the values of torque, cutting force and surface roughness were higher compared to dry drilling, as expected.

No clear connection of the viscosity of each oil type with the results was found.

The range of cutting speed was limited to medium values, as high cutting speed values increase the cutting forces and are unfavorable for chip removal.

6. REFERENCES

Bakkal M., A.J. Shih, S.B. Mc Spadden, R.O. Scattergood, Thrust force, torque, and tool wear in drilling the bulk Metallic glass, International Journal of Machine Tools and Manufacture (ISSN: 0890-6955), 45(7-8), pp. 863-872, 2005.

Basavarajappa S., Chandramohan , M. Prabu, K. Mukund, M. Ashwin, Drilling of hybrid metal matrix composites-Work piece surface integrity, International Journal of Machine Tools and Manufacture (ISSN: 0890-6955), 47(1), pp 92-96, 2007.

Montgomery D.C, Design and analysis of experiments, John Wiley & Sons, 4th ed (ISBN: 978-0-471-48735-7), 1997.

Petropoulos G, I, Ntziantzias, P. Reis, J. P. Davim, Predicting machinability parameters on drilling Glass Fibber Reinforced Plastics using Response Surface Methodology, International Journal of Materials and Product Technology (in press) (ISSN 0268-1900), Greece, 2007.

Petropoulos, G.P., Vaxevanidis N. A topographic description of the bearing properties of electro-discharge machined surfaces, Proc. 2nd Int. Conf. on Manufacturing Engineering ICMEN (ISBN 960-243-615-8), Kassandra-Chalkidiki, 7 Oct, 2005, pp. 159-166, Greece.

Table 1. Dimensional characteristics
of the drills used in the experiments

 Total Twist
Diameter length length
 (mm) (mm) (mm)

 8 117 75
 10 133 87
 12.5 151 101

Table 2. Mechanical and physical properties
of the work-piece materials.

 St 37 Al 5005

Density (Mg/
[m.sup.3]) 7.91 2.70

Hardness (HB) [less than or [less than or
 equal to] 135 equal to] 51
Maximum tensile
strength (MPa) 415 145

Yield point (MPa) 205 35

Special heat 447 900
(J/kgr x K)

Thermal 360 205
conductivity
(W/m-K)

Melt point
([degrees]C) 1510 652

Table 3. Validity assumptions and statistically most significant
factors of the stochastic models

 [[epsilon]
 [R.sub.a] .sub.D]
 F (N) M (N cm) ([micro]m) (mm)

[R.sup.2] 0.959 0.979 0.412 0.403

Conformity
to full full partial partial
hypotheses

Statistically
more significant Feed Dia Mat Feed
factor

Statistically
most Dia*Fee Dia*Fee Mal*Dia Mat*Dia
significant d d
interaction