# Simulation Study on Single-Lip Deep Hole Drilling Using Design of Experiments

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. SLD Experiments

_{c}= 80 m/min and the feed per tooth f = 0.042 mm/rev. Each drilling test was repeated three times [10].

#### 2.2. SLD Simulation: FEM

#### 2.2.1. Constitutive Law

- Workpiece material

_{m}is the melting temperature; and T

_{a}is the ambient temperature. The input values are given in Table 2.

_{1}–d

_{5}are failure parameters, λ is the stress triaxiality, ${\dot{\epsilon}}_{0}$ is the reference strain rate, and T* is the dimensionless temperature. The failure parameters d

_{1}–d

_{5}were determined by means of a sensitivity analysis in order to produce more realistic chip forms. In Table 3, the values for the JC damage initiation model are listed.

^{3}. ABAQUS also permits the deletion of elements using state variables [19]. Therefore, one solution-dependent state variable and one variable controlling the element deletion mechanism are activated to represent material failure.

- Tool material

#### 2.2.2. Step Definition

#### 2.2.3. Interaction Properties

^{2}K). When creating the interaction, the surface of the tool is defined as the master surface and the set of nodes of the workpiece as the slave surface. The penalty contact method is selected as a mechanical constraint. This method produces less stringent enforcement of contact constraints compared with kinematic contact. However, it permits the definition of more general types of contact, for example, multiple contacts per node [19]. Finally, the finite sliding setting is chosen, which allows any arbitrary motion of the surfaces.

#### 2.2.4. Boundary Conditions

#### 2.2.5. Discretization

#### 2.3. SLD Simulation: Design of Experiments

_{A/B/Ci}are the determined coefficients and A, B, and C are the factors according to the level i.

_{GP}refers to the distance between the circle formed by the shank and the circle formed by the drill head, as shown in Figure 6a. A rectangular platform below the guide pad was created to control the height. A height of 0.85 mm was chosen instead of the middle height 0.75 mm because of the minimum platform size required for a mesh without poor elements.

_{z}is much lower than that selected. Simulating low feed rates means longer simulation times, which are not realistic within the time frame of this research. Therefore, high speeds are selected, and then the results are compared with the experiment by means of extrapolations. Due to the necessity of few complete tool rotations leading to full contact of the guide pads with the workpiece to be able to investigate the effect of the guide pad heights on the residual stress, the cutting speed v

_{c}exceeds the applied values in the experiment, too. The designed experiment generates an experiment with 12 runs.

## 3. Results

#### 3.1. SLD Simulations

#### 3.1.1. Chip Formation

#### 3.1.2. Temperature Evolution

#### 3.1.3. Feed Force Evolution

#### 3.1.4. Residual Stress

#### 3.2. SLD Simulation: Design of Experiments

#### 3.2.1. Temperature

_{GP}= 0.5 mm, f

_{z}= 40 mm/s, and v

_{c}= 427.5 m/min, and the highest temperature of 1560 °C results with h

_{GP}= 1 mm, f

_{z}= 80 mm/s, and v

_{c}= 532.7 m/min. Excluding the results of h

_{GP}= 0.85 mm, f

_{z}= 80 mm/s, and h

_{GP}= 1 mm, f

_{z}= 80 mm/s, the difference between the maximum temperature values is not significant. This is because of a slow temperature increase in the high cutting speed range. Although at first glance, there are no significant differences in the generated maximum temperature, it is evidently indicated that the three factors (guide pad height, feed rate, and cutting speed) interact with each other. These interactions are investigated by means of analysis of variance (ANOVA) for the main effects and interactions. As a result, all the coefficients from the regression model in Equation (4) and the effect of each factor and interaction were obtained (Table 7).

^{2}value, which is a measure for the goodness of a regression, is 98.63%, slightly lower than expected. To visually identify the significant effects, a Pareto chart for standardized effects was created from the calculated values (see Figure 11a).

#### 3.2.2. Feed Force

^{2}value of 99.97% indicates a high goodness of the results obtained from the regression model. This is supported by the adjusted coefficient of determination, R

^{2}(adj), which is 99.84%. The visualization of the results of this analysis is presented in the Pareto chart in Figure 13a. According to the Pareto chart, the cutting condition with the most significant effect on the feed force is the feed rate, followed by cutting speed and the interaction between them. The main effects plots in Figure 13b demonstrate how the cutting conditions influence the feed force.

#### 3.2.3. Residual Stress

^{2}value of 98.81% indicates a slightly lower goodness of the results obtained from the regression model, which is in the range of the results from the maximum temperature. For visualizing the standardized effects, a Pareto chart for standardized effects was created from the calculated values (see Figure 15a). A significant effect of the feed rate as well as the guide pad heights was observed. This was already indicated by the dashed line in Figure 14a of the model responses. The main effect plot in Figure 15b shows the tendency of the factors. An increasing feed rate leads to increasing compressive stresses. This could be explained by the increasing temperature in the process, which reduces the strength of the material. Thus, the drill head causes higher plastic deformation and finally higher compressive stress. The effect of increasing compressive stress with increasing guide pad height is clear from 0.5 to 0.85 mm but counterintuitive from 0.85 to 1.0 mm, where the compressive stress decreases. The reason for this observation could be the damage model, which eliminates distorted elements from the mesh. Due to the extension of the guide pad to 1.0 mm, more elements with high compressive stresses could be removed. The remaining elements lead to a lower averaged compressive stress value. The influence of the damage model on the residual stress state in the subsurface has to be evaluated in further studies.

## 4. Conclusions

- Although some assumptions and simplifications regarding the drill head and the drilling conditions were made, the chip formation and the temperature evolution were reproduced successfully. Moreover, the feeding force evolution as well as the residual stress were modeled with qualitative agreement.
- A full factorial DoE study was carried out applying three factors with two (feed rate, cutting speed) and three (guide pad height) levels, respectively.
- The extensive DoE study delivered clear effects of the selected factors, such as the feed rate, cutting speed, and guide pad height, on the maximum temperature in the drill head, the feed force, as well as the residual stress in the subsurface.
- The regression model delivers an R
^{2}value of 99.97% for the feed force response, which indicates a high goodness of the results. For the responses of the maximum temperature and residual stress, R^{2}values of 98.63% and 98.81% were obtained, respectively. These values could be improved by more data or another regression model. - ANOVA of the maximum temperature shows a significant effect from the feed rate. An increasing feed rate leads to increasing temperatures.
- Significant effects of the feed rate, cutting speed, and the interaction between both on the feed force were obtained by ANOVA. An increasing feed rate and a decreasing cutting speed lead to larger chips, which have to be cut by the driller. Thus, higher forces occur in the process.
- The residual stress is significantly affected by the guide pad height and the feed rate. Increasing factors lead to increasing compressive stresses.
- Regression models for the feed force, maximum temperature, and residual stress were developed, and their corresponding coefficients were successfully determined.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

SLD | Single-lip drill |

BTA | Boring and Trepanning Association |

EET | Element elimination technique |

DoE | Design of experiment |

CAD | Computer-aided design |

PTC | Positive temperature coefficient |

FEM | Finite element method |

JC | Johnson–Cook |

ANOVA | Analysis of variance |

f | Feed per tooth, mm/rev |

v_{c} | Cutting speed, m/min |

ρ | Density, kg/m^{3} |

ν | Poisson’s ratio |

E | Young’s modulus, GPa |

ε | Strain, mm/mm |

σ | Flow stress, MPa |

$\dot{\epsilon}$ | Strain rate, 1/s |

λ | Stress triaxiality |

h_{GP} | Guide pad height, mm |

δ | Conductivity, W/m K |

α | Thermal expansion coefficient, µm/m K |

k | Gap conductance, W/m^{2} K |

q | Heat flux per unit area, W/m^{2} |

T | Temperature, K |

T_{a} | Ambient temperature, K |

T_{m} | Melting temperature, K |

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**Figure 1.**Schematic representation of the experimental setup for SLD (

**a**) and CAD of the single-lip deep drill with a changeable insert and guiding pads from the company Gühring AG for the FEM simulation (

**b**).

**Figure 2.**Feed force evolution (

**a**) and drilling torque evolution (

**b**) measured in an experiment for a cutting depth of 20 mm, a feed of 0.042 mm/rev, and a cutting speed of 68 m/min [10].

**Figure 3.**Thermography image of the backside of the workpiece at the moment of breakthrough (

**a**) and maximum temperature at the cutting edge measured in the experiment (

**b**) [10].

**Figure 4.**Location of the reference point (

**a**) and symmetry/antisymmety/encastre boundary condition (

**b**).

**Figure 6.**Definition of guide pad height (

**a**) and chip formation after 0.055 s with a feed of 0.64 mm/rev (80 mm/s) and a cutting speed of 427.5 m/min (

**b**).

**Figure 7.**Lateral and front views of the formed chip with a feed of 0.64 mm/rev and a cutting speed of 427.5 m/min in the simulation (

**a**) and chips obtained from the experiment (

**b**).

**Figure 8.**Temperature in the drill head under the following cutting conditions: a feed of 0.64 mm/rev and a cutting speed of 472.5 m/min (

**a**). Development of the maximum temperature at the cutting edge and the drill head with a feed of 0.64 mm/rev and a cutting speed of 472.5 m/min in the simulation (

**b**).

**Figure 9.**Simulated feed force evolution applying a feed of 0.64 mm/rev and a cutting speed of 472.5 m/min (

**a**) and tangential residual stresses after one rotation with a feed of 0.64 mm/rev and a cutting speed of 472.5 m/min (

**b**).

**Figure 10.**Average temperature at the cutting edge in the steady-state region (

**a**) and maximum temperature in the drill head (

**b**).

**Figure 11.**Pareto chart of the standardized effects for drill head maximum temperature (

**a**) and main effects plot for drill head maximum temperature (

**b**).

**Figure 13.**Pareto chart of the standardized effects for the feed force (

**a**) and main effects plot for the feed force (

**b**).

**Figure 14.**Influence of the cutting conditions on the average residual stress (

**a**) and representation of the evaluated subsurface volume (

**b**).

**Figure 15.**Pareto chart of the standardized effects for the residual stress (

**a**) and main effects plot for the residual stress (

**b**).

**Table 1.**Elastic properties of DIN 42CrMo4 [16].

Young’s Modulus (GPa) | Poisson’s Ratio (-) | Temperature (K) |
---|---|---|

217 | 0.3 | 173 |

213 | 0.3 | 273 |

212 | 0.3 | 293 |

207 | 0.3 | 373 |

199 | 0.3 | 473 |

192 | 0.3 | 573 |

184 | 0.3 | 673 |

175 | 0.3 | 773 |

164 | 0.3 | 873 |

69 | 0.3 | 1773 |

A (MPa) | B (MPa) | C (-) | n (-) | m (-) | T_{m}(K) | T_{a}(K) |
---|---|---|---|---|---|---|

595 | 580 | 0.023 | 0.133 | 1.03 | 1793 | 300 |

d_{1} | d_{2} | d_{3} | d_{4} | d_{5} | ${\mathit{T}}_{\mathit{m}}$ (K) | ${\mathit{T}}_{\mathit{a}}$ (K) | ${\dot{\mathit{\epsilon}}}_{0}$ (1/s) |
---|---|---|---|---|---|---|---|

0.1 | 0.04 | −0.02 | 1 | 0.12 | 1793 | 300 | 1 |

**Table 4.**Thermal expansion, conductivity, and specific heat of DIN 42CrMo4, depending on the temperature [22].

Temperature (K) | Thermal Expansion (µm/m K) | Conductivity (W/m K) | Specific Heat (J/kg K) |
---|---|---|---|

173 | 10.8 | - | 291.24 |

273 | 11.7 | - | 354.04 |

293 | 11.9 | 41.7 | 361.89 |

373 | 12.5 | 43.4 | 389.36 |

473 | 13.0 | 43.2 | 418.41 |

573 | 13.6 | 41.4 | 445.88 |

673 | 14.1 | 39.1 | 479.64 |

773 | 14.5 | 36.7 | 531.45 |

873 | 14.9 | 34.1 | 610.73 |

1773 | 14.9 | 34.1 | 610.73 |

1923 | - | 34.1 | 610.73 |

**Table 5.**Input data for the tool material made of tungsten carbide with 15% cobalt [23].

Property | Unit | Value |
---|---|---|

Density, ρ | kg/m^{3} | 15,700 |

Young’s modulus, E | GPa | 524 |

Poisson’s ratio, ν | - | 0.23 |

Thermal expansion, α | µm/m K | 6.3 |

Conductivity, δ | W/m K | 82.2404 |

Specific heat, C_{p} | J/kg K | 579.45 |

Run Order | Guide Pad Height (mm) | Feed Rate (mm/s) | Cutting Speed (m/min) |
---|---|---|---|

1 | 0.5 | 40 | 427.5 |

2 | 0.5 | 40 | 532.7 |

3 | 0.5 | 80 | 427.5 |

4 | 0.5 | 80 | 532.7 |

5 | 0.85 | 40 | 427.5 |

6 | 0.85 | 40 | 532.7 |

7 | 0.85 | 80 | 427.5 |

8 | 0.85 | 80 | 532.7 |

9 | 1.00 | 40 | 427.5 |

10 | 1.00 | 40 | 532.7 |

11 | 1.00 | 80 | 427.5 |

12 | 1.00 | 80 | 532.7 |

Term | Coefficient | SE Coefficient | T-Value | p-Value |
---|---|---|---|---|

Constant | 1247.7 | 15.8 | 79.05 | 0.0 |

Guide pad height (A) | ||||

0.5 | −121.7 | 22.3 | −5.45 | 0.032 |

0.85 | 49.8 | 22.3 | 2.23 | 0.155 |

Feed rate (B) | ||||

40 | −140.0 | 15.8 | −8.87 | 0.012 |

Cutting speed (C) | ||||

427.5 | −31.2 | 15.8 | −1.97 | 0.187 |

Guide pad height, feed rate (AB) | ||||

0.50, 40 | 121.0 | 22.3 | 5.42 | 0.032 |

0.85, 40 | −59.0 | 22.3 | −2.64 | 0.118 |

Guide pad height, Cutting speed (AC) | ||||

0.50, 427.5 | −17.3 | 22.3 | −0.78 | 0.519 |

0.85, 427.5 | 12.7 | 22.3 | 0.57 | 0.628 |

Feed rate, cutting speed (BC) | ||||

40, 427.5 | −19.5 | 15.8 | −1.24 | 0.342 |

^{2}= 98.63%; R

^{2}(adj) = 92.48%.

Term | Coefficient | SE Coefficient | T-Value | p-Value |
---|---|---|---|---|

Constant | 45.446 | 0.277 | 164.19 | 0.0 |

Guide pad height (A) | ||||

0.5 | −0.813 | 0.391 | −2.08 | 0.172 |

0.85 | 0.404 | 0.391 | 1.03 | 0.410 |

Feed rate (B) | ||||

40 | −21.672 | 0.277 | −78.30 | 0.0 |

Cutting speed (C) | ||||

427.5 | 6.683 | 0.277 | 24.14 | 0.002 |

Guide pad height, feed rate (AB) | ||||

0.50, 40 | 0.970 | 0.391 | 2.48 | 0.131 |

0.85, 40 | 0.207 | 0.391 | 0.53 | 0.649 |

Guide pad height, cutting speed (AC) | ||||

0.50, 427.5 | −0.385 | 0.391 | −0.98 | 0.429 |

0.85, 427.5 | 0.427 | 0.391 | 1.09 | 0.389 |

Feed rate, cutting speed (BC) | ||||

40, 427.5 | −1.862 | 0.277 | −6.73 | 0.021 |

^{2}= 99.97%; R

^{2}(adj) = 99.84%.

Term | Coefficient | SE Coefficient | T-Value | p-Value |
---|---|---|---|---|

Constant | 441.15 | 2.94 | −150.24 | 0.0 |

Guide pad height (A) | ||||

0.50 | 28.46 | 4.15 | 6.85 | 0.021 |

0.85 | −16.45 | 4.15 | −3.96 | 0.058 |

Feed rate (B) | ||||

40 | 29.40 | 2.94 | 10.01 | 0.010 |

Cutting speed (C) | ||||

427.5 | −7.51 | 2.94 | −2.56 | 0.125 |

Guide pad height, feed rate (AB) | ||||

0.50, 40 | −3.21 | 4.15 | −0.77 | 0.520 |

0.85, 40 | −9.20 | 4.15 | −2.22 | 0.157 |

Guide pad height, cutting speed (AC) | ||||

0.50, 427.5 | −2.25 | 4.15 | −0.54 | 0.642 |

0.85, 427.5 | 4.59 | 4.15 | 1.10 | 0.384 |

Feed rate, cutting speed (BC) | ||||

40, 427.5 | 2.10 | 2.94 | 0.72 | 0.549 |

^{2}= 98.81%; R

^{2}(adj) = 93.43%.

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## Share and Cite

**MDPI and ACS Style**

Fandiño, D.; Guski, V.; Wegert, R.; Möhring, H.-C.; Schmauder, S.
Simulation Study on Single-Lip Deep Hole Drilling Using Design of Experiments. *J. Manuf. Mater. Process.* **2021**, *5*, 44.
https://doi.org/10.3390/jmmp5020044

**AMA Style**

Fandiño D, Guski V, Wegert R, Möhring H-C, Schmauder S.
Simulation Study on Single-Lip Deep Hole Drilling Using Design of Experiments. *Journal of Manufacturing and Materials Processing*. 2021; 5(2):44.
https://doi.org/10.3390/jmmp5020044

**Chicago/Turabian Style**

Fandiño, Daniel, Vinzenz Guski, Robert Wegert, Hans-Christian Möhring, and Siegfried Schmauder.
2021. "Simulation Study on Single-Lip Deep Hole Drilling Using Design of Experiments" *Journal of Manufacturing and Materials Processing* 5, no. 2: 44.
https://doi.org/10.3390/jmmp5020044