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Micro drilled holes are utilized in many of today's fabrication processes. Precision production processes in industries are trending toward the use of smaller holes with higher aspect ratios, and higher speed operation for micro deep hole drilling. However, undesirable characteristics related to micro drilling such as small signal-to-noise ratios, wandering drill motion, high aspect ratio, and excessive cutting forces can be observed when cutting depth increases. In this study, the authors attempt to minimize the thrust forces in the step-feed micro drilling process by application of the DOE (Design of Experiment) method. Taking into account the drilling thrust, three cutting parameters, feedrate, step-feed, and cutting speed, are optimized based on the DOE method. For experimental studies, an orthogonal array _{27}(3^{13})

Recently, with increasing demand for precise micro components production, the importance of micro hole drilling processes is increasing in fields such as medical instruments, aerospace engineering, and computer industries.[

To realize a more efficient micro-drilling process, a step-feed process is required instead of the one-pass drilling method. The step-feed process repeats drill feeding forward and backward with a certain number of steps, as shown in

In this paper, the thrust forces in 200μm micro deep hole drilling processes are minimized. The number of steps per one drilling, the feeding speed, and the spindle rpm are used as process parameters to determine the optimum drilling conditions. For this purpose, experimental works are carried out based on DOE (Design of Experiments), and the obtained experimental data are analyzed using ANOVA (Analysis of variance).[

DOE (Design of Experiments) provides a powerful means to achieve breakthrough improvements in product quality and process efficiency. From the viewpoint of manufacturing fields, this can reduce the number of required experiments when taking into account the numerous factors affecting experimental results. DOE can show how to carry out the fewest number of experiments while maintaining the most important information. The most important process of the DOE is determining the independent variable values at which a limited number of experiments will be conducted. For this purpose, Taguchi [

When optimizing process conditions to obtain higher quality products, it is necessary to carry out several steps. First, factors or conditions have to be selected, which predominantly affect the process results. These selected factors are divided into several levels, and all combinations are usually taken into account. In this case, the number of all possible combinations corresponds to the number of needed experiments. Here, orthogonal arrays make it possible to carry out fractional factorial experiments in order to avoid numerous experimental works as well as to provide shortcuts for optimizing factors. The orthogonal arrays are determined by the number of factors and levels considered in the process. They are usually described in the form _{A}(B^{C})

Degree of freedom (DOF) is a common term used in engineering and science. However, there is no visible interpretation of DOF applied to experimental data. Regarding statistical analysis of experimental data, DOF provides an indication of the amount of information contained in a data set. In DOE processes, DOF is applied to characterize four separate items as follows:

DOF of a factor = number of levels of the factor – 1

DOF of a column = number of levels of the column – 1

DOF of an array = total of all column DOFs for the array

DOF of an experiment = total number of results of all trials – 1

DOF is the minimal number of comparisons between levels of factors or interactions in order to improve process characteristics. The type of orthogonal array used in DOE can be selected by the DOF. When determining factors and levels, the orthogonal array has to be selected. In this case, the DOF is taken into account as a reference for selecting a certain type of orthogonal array. Determining the number of factors and levels, a suitable orthogonal array can be selected by the total DOF of the experiment, because the total DOF of factors and levels used in an orthogonal array is already determined [

ANOVA (Analysis of Variance) is a statistical technique that identifies factors significantly affecting the experimental results. ANOVA consists of (1) summing squares for distributions of all characteristic values (experimental data); (2) unbiased variance; (3) decomposing this total sum into the sums of squares for all factors used in the experiment; (4) calculating unbiased variances through the sums of squares for all factors over their DOF; (5) calculating the variance ratio F_{0} by dividing each unbiased variance by the error variance; and (6) searching which factors significantly affect experimental results by analyzing the error variance. This procedure can be accomplished by constructing an ANOVA table. An example of an ANOVA is described as follows. Taking into account a factor A whose number of levels is

If the total deviation of each datum _{ij}

Squaring this equation and summing

Here, the left side of _{T}_{A}_{E}_{T}_{A}_{E}

Here,
_{ij}_{i}_{i}

In the experimental studies, a micro drilling system employing a high speed air spindle is used. The drilling process is divided into a certain number of steps and the drill is fed into the workpiece and retracted repetitively. This allows avoiding micro drill fracture problems and providing enhanced chip and heat discharge.

In the experiments, SM45C specimens are used as workpieces. In order to fix the workpieces and dynamometer onto the micro drilling system, a fixture system is installed. The 200μm micro drill used for the experiment is shown in

When the step-feeding frequency is increased in order to reduce drilling force, the micro drill can easily be broken due to work-hardening. Furthermore, by reducing the drilling feedrate, the efficiency of the drilling process is deteriorated while increasing the drilling spindle speed leads to expansion of the size of the machined hole, because drill vibration becomes significant. In order to resolve these problems, the optimal drilling conditions are determined by using a DOE for the micro drilling process with SM45C workpieces and 200μm diameter drills. For this purpose, a _{27}(3^{13})

For the analysis of data acquired through DOE, Taguchi method is applied for gathering required data by using an orthogonal array and investigating the S/N ratio (Signal-to-Noise ratio) derived from these data. In the approaches, characteristics of loss functions are usually classified into “Smaller the Better Characteristics”, “Larger the Better Characteristics” and “Nominal the Best Characteristics”. In these experiments, “Smaller the Better Characteristics” are taken into account in order to determine drilling conditions for producing minimal drilling thrust. Taking into account the interactions of A*B and A*C, the factors are assigned and the experiments are carried out.

Through the results presented in

The process of ignoring a factor if it is deemed insignificant, called pooling, is done by combining the measure of influence of the factor with that of the error term. Finally, on the bases of the S/N ratio graphs and ANOVA, it can be declared that A1, B3, and C3 correspond to the factors producing minimal drilling thrusts and there are no interactions between A*B and A*C.

The process of ignoring a factor if it is deemed insignificant, called pooling, is done by combining the measure of influence of the factor with that of the error term. Finally, on the bases of the S/N ratio graphs and ANOVA, it can be declared that A1, B3, and C3 correspond to the factors producing minimal drilling thrusts and there are no interactions between A*B and A*C.

The objective of this study is to ascertain factors predominantly affecting drilling thrust in micro deep hole drilling processes. For this purpose, DOE (Design of Experiments) technique and ANOVA (Analysis of Variances) are used. Through this study, as presented in this paper, the conclusions can be summarized as follows:

In the 200micro drilling process, the experimental works designed by a _{27}(3^{13})

Through the S/N ratio graphs and ANOVA, it can be observed that A1, B3, and C3 correspond to the factors producing minimal drilling thrust; there are no interactions between A*B and A*C. Thus, the optimal conditions are A1, B3, and C3.

In this study, only the drilling thrust is taken into account as the most significant factor in order to optimize the step-feed micro drilling processes. It is possible, however, to consider other factors such as drill life, roughness, circularity of drilled holes, drilling time, burrs, etc. The selection of these factors depends on the main objectives of the required processes. The influence of interactions among the factors will be studied and discussed in our next study.

Diagram of step feeding micro drilling method.

Experimental setup for micro drilling.

Employed 200μm micro drill.

S/N Ratio response graph.

Interaction graph.

Machined result of micro step drilling.

One-way factional design.

Level of factor A | |||||
---|---|---|---|---|---|

_{1} |
_{2} |
_{3} |
_{l} | ||

x_{11} |
x_{21} |
x_{31} |
… | x_{11} | |

Repeat Of Experiments | x_{12} |
x_{22} |
x_{32} |
… | x_{12} |

x_{13} |
x_{23} |
x_{33} |
… | x_{13} | |

… | … | … | … | … | |

x_{1m} |
x_{2m} |
x_{3m} |
… | x_{14} | |

Sum of levels | T_{1} |
T_{2} |
T_{3} |
… | T_{1} |

Mean of levels | x̅_{1} |
x̅_{2} |
x̅_{3} |
… | x̅_{l} |

Specifications of experimental micro drilling system.

Diameter | Ø 0.1 ∼0.2 mm |

Revolution | Max. 50,000 rpm |

Torque | 500 gr-cm |

Air pressure (Bearing) | 5∼6 kg/cm^{2} |

Step feedrate | 0.01 ∼ 99.99 mm |

Standoff | 30 ∼ 200 mm |

Size of machine body | 300*350*680 mm |

Total stroke | 75 mm |

Weight | 35kg |

Measuring instrument of experiment for cutting force.

Workpiece | SM45C (35×35×2.3mm) |

Dynamometer | Kistler Co. (9257A) |

Amplifier | Kistler Co. (5011B) |

A/D converter | DAQ Card-Al_16XE-50 |

Microscope with built-in monitor | Microscope system (Sometech co.) |

Experiment design for an _{27}(3^{13})

Symbol factor | A feed | B step | A*B |
A*B | C rpm | A*C | A*C | e | e | e | e | e | e | Response (Thrust) | S/N (db) | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| |||||||||||||||||

Level | 1 | 30 | |||||||||||||||

2 | 60 | ||||||||||||||||

3 | 90 | ||||||||||||||||

| |||||||||||||||||

No | # |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 1 | 1 | 1 | 1 | 1st | 2nd | |

3 | 19 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 2.8 | 2.9 | -9.10 |

6 | 18 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 1 | 2 | 2 | 2 | 2.7 | 2.6 | -8.63 |

9 | 8 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 1 | 1 | 1 | 2.1 | 1.9 | -6.03 |

12 | 3 | 2 | 1 | 2 | 3 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3.7 | 3.3 | -10.90 |

15 | 5 | 2 | 2 | 3 | 1 | 3 | 1 | 2 | 1 | 2 | 3 | 2 | 3 | 1 | 3.4 | 3.3 | -10.50 |

18 | 12 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 2 | 3 | 1 | 1 | 2 | 3 | 3.0 | 2.9 | -9.40 |

21 | 23 | 3 | 1 | 2 | 2 | 3 | 2 | 1 | 3 | 2 | 1 | 3 | 2 | 1 | 5.1 | 5.2 | -14.24 |

24 | 24 | 3 | 2 | 3 | 3 | 3 | 2 | 1 | 1 | 3 | 2 | 2 | 1 | 3 | 4.6 | 4.8 | -13.44 |

27 | 9 | 3 | 3 | 1 | 1 | 3 | 2 | 1 | 2 | 1 | 3 | 1 | 3 | 2 | 4.1 | 3.9 | -11.93 |

| |||||||||||||||||

Note:

A*B means interactions between factor A and factor B

# means actual experimental order

Signal-To-Noise ratio response.

Symbol | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| |||||||||||||

A | B | A*B | A*B | C | A*C | A*C | e | e | e | e | e | e | |

Level 1 | -8.62 | -12.53 | -10.96 | -11.31 | -12.28 | -11.17 | -11.18 | -11.56 | -10.88 | -11.22 | -11.25 | -11.34 | -11.28 |

Level 2 | -11.34 | -11.24 | -12.05 | -11.81 | -11.27 | -11.55 | -11.31 | -11.22 | -11.15 | -11.30 | -11.50 | -11.18 | -11.28 |

Level 3 | -14.02 | -10.21 | -10.64 | -11.04 | -10.43 | -11.27 | -11.48 | -11.21 | -11.58 | -11.46 | -11.23 | -11.46 | -11.42 |

Max-Min | 5.40 | 2.32 | 1.41 | 0.77 | 1.85 | 0.38 | 0.30 | 0.35 | 0.70 | 0.24 | 0.27 | 0.28 | 0.14 |

A*B Interaction matrix

B1 | B2 | B3 | |
---|---|---|---|

A1 | -9.52 | -9.20 | -7.26 |

A2 | -12.32 | -11.12 | -10.57 |

A3 | -15.75 | -13.53 | -12.78 |

A*C Interaction matrix.

C1 | C2 | C3 | |
---|---|---|---|

A1 | -9.27 | -8.79 | -7.92 |

A2 | -12.67 | -11.08 | -10.26 |

A3 | -14.90 | -13.95 | -13.20 |

Analysis of variance.

Source | Sum of squares | DOF | Mean square | F_{0} |
---|---|---|---|---|

A | 127.39 | 2 | 63.67 | 12.96 |

B | 18.72 | 2 | 9.35 | 1.90 |

C | 11.71 | 2 | 5.86 | 1.19 |

A*B | -29.05 | 4 | -7.26 | -1.48 |

A*C | -10.41 | 4 | -2.60 | 0.53 |

e | 58.96 | 12 | 4.93 | |

Total | 177.26 | 26 |

Analysis of variance after pooling.

Source | Sum of squares | DOF | Mean square | F_{0} |
F (0.05) |
---|---|---|---|---|---|

A | 127.388 | 2 | 63.669 | 65.3 | 3.49 |

B | 18.7163 | 2 | 9.3518 | 9.58 | 3.49 |

C | 11.7107 | 2 | 5.855 | 6.00 | 3.49 |

e | 19.491 | 20 | 0.9745 | ||

Total | 177.256 | 26 |