# CAD-Based 3D-FE Modelling of AISI-D3 Turning with Ceramic Tooling

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## Abstract

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## 1. Introduction

_{2}/7050Al composite, along with the strain rate and the developed temperatures with the aid of 2D-FEM. More similar researches prove that the use of FEM can become a valuable asset when investigating typical machining results such as the tool/chip contact temperatures [5], the chip formation mechanisms [6,7], and the generated cutting forces, as well as the tool wear mechanisms [8,9,10,11].

## 2. Materials and Methods

#### 2.1. Framework of the Turning Process

_{t}denotes the tangential force, F

_{r}is the radial force, and F

_{a}represents the feed force. In addition, Figure 1a includes two schematics that depict the position of the cutting insert and the feed direction. The position of the tool is defined with respect to the cutting angles which are inherited from the tool-holder and its geometry. Therefore, the lead angle is k

_{r}= 75° and both the rake (γ) and inclination angle (λ) are negative and equal to −6°. Finally, Figure 1b contains the full geometry of the tool.

^{3}= 64 experiments would occur. Due to the increased number of experiments, the Taguchi method was implemented in order to reduce the experiments number and thus save time and resources. This method is considered a robust parameter design, which can be used for the product or process design that enables the minimizing of variation and sensitivity to noise. Several researchers have successfully used the Taguchi method during their manufacturing-related studies [35,36,37]. In this study, the four-level design with three factors (V

_{c}, f, and a

_{p}) produces an L

_{16}orthogonal array, which leads to 16 experiments. Orthogonal arrays are design matrices that contain the factor settings used in the design of experiments to equally consider all levels of all factors. The signal-to-noise ratio (S/N) formula used in this design is nominal-the-best, which is represented by Equation (1). The S/N ratio is a measure of how a response varies relative to the nominal value under different noise conditions and is calculated for all combinations.

#### 2.2. D-FE Model Setup

#### 2.2.1. Definition of the Analysis Interface

_{conv}= 0.02 N/(s × mm × °C) for dry cutting and h

_{cond}= 45 N/(s × mm × °C).

#### 2.2.2. Modelling of Material Behavior

_{0}, and T

_{m}are the temperatures involved in the model, the reference temperature, the ambient temperature, and the melting temperature, respectively. Table 2 presents the flow stress constants for the AISI-D3 steel, which were adapted from the material’s flow stress diagrams found in the software’s library.

_{c}is the critical value of the fracture damage, σ

_{max}and $\overline{\sigma}$ denote the maximum tensile principal stress and the effective stress accordingly, ε

_{f}represents the limit fracture strain, and ε

_{pl}is the plastic strain.

_{f}is the frictional shear stress, μ is the shear friction coefficient, and finally, σ

_{n}denotes the tool-chip interface stress. Studies related to the machining of steel [48,49] suggest using a value of friction coefficient between 0.5 and 0.6 in general. Since these values are also proposed by DEFORM™, the friction coefficient was set to 0.6 for the presented simulation runs.

## 3. Results and Discussion

#### 3.1. FEM-Based Results of the Machining Forces

_{r}), Figure 3b for the tangential force (F

_{t}), and finally, Figure 3c for the feed force (F

_{a}) which were generated during turning of the AISI-D3 steel with the SNGA120408T01525 tool. The following cutting conditions apply for the obtained results: V

_{c}= 210 m/min, f = 0.12 mm/rev, and a

_{p}= 0.30 mm. The diagrams point out that the force increases rapidly as soon as the edge of the tool touches the uncut surface of the workpiece until the steady state phase is reached where the force maintains a steady mean value. To keep simulation times low, only a small part of the workpiece was cut. When the tool completes its pass on the workpiece and the material removal process ends, the force quickly decreases until it reaches zero. Even though the total time of the process is relatively low, the high number of time steps (approximately 2900 for this case) ensured the establishment of the steady state.

_{16}orthogonal Taguchi array. The design of experiments along with the results for each run are presented in Table 4.

#### 3.2. Statistically-Based Analysis of Machining Forces

_{16}design, which includes the three factors and the four levels, the results from the 16 simulation runs were used for the development of the statistical model. The generated model is a second order polynomial which is represented by Equation (5). Due to the fact that the relationship between the input variables and the output variable (response) is non-linear, the polynomial describing the model includes linear, quadratic, and cross-product terms. Therefore, Y is the response of the model (resultant machining force), a

_{0}represents the fixed term, X

_{i}are the input variables (cutting speed, feed, and depth of cut) and b

_{i}, b

_{ij}, b

_{ii}are the vectors that contain the regression coefficients (linear, quadratic, and cross-product, accordingly).

_{resultant}is the resultant machining force in N, whereas V, f, and a

_{p}are the cutting speed (m/min), the feed (mm/rev), and the depth of cut (mm), respectively.

#### 3.3. Model Validation Results

- Depth of cut is clearly the dominant parameter of the three and has the strongest effect on the resultant force. Actually, the produced forces are almost tripled as the depth of cut increases from the lowest value (0.10 mm) to the maximum (0.40 mm).
- Any increase in the feed acts to increase the resultant machining force. The level of increase is notable, especially as the tool cuts deeper.
- Lastly, the cutting speed seems to have a marginal influence on the F
_{resultant}. Despite this fact, a small increase is present at speeds between 100 and 150 m/min.

## 4. Conclusions

- The radial force is the component that affects the most the resultant machining force, contributing to the total value by up to 85%. It is noted that the contribution percentage is higher at lower values of the depth of cut.
- As the feed rise acts to increase the resultant machining force significantly, this trend is notable as the tool cuts deeper. On average, a shift from 0.08 to 0.20 mm/rev would increase F
_{resultant}by about 44.5, 48.6, 56, and 25% at the depth of cut equal to 0.40, 0.30, 0.20, and 0.10 mm, respectively. - Similarly, the depth of cut has a strong impact on the generated machining forces. Specifically, F
_{resultant}would rise on average by approximately 55, 33.3, and 25% in the case of the changing depth of cut from 0.10 to 0.20 mm, 0.20 to 0.30 mm, and finally, 0.30 to 0.40 mm, accordingly. - Finally, the influence of the cutting speed on the generated machining force is minimal. A slight increase in the F
_{resultant}is noticeable near the intermediate values of the cutting speed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) The Computer Aided Design (CAD) based tool-workpiece setup and (

**b**) the model of the SNGA120408T01525 insert.

**Figure 3.**Sample force vs. time diagrams for 0.30 mm depth of cut, 210 m/min cutting speed, and 0.12 mm/rev feed; (

**a**) radial force component, (

**b**) tangential force component, (

**c**) feed force component, and (

**d**) the evolution of the chip for the same conditions.

**Figure 5.**Residual analysis graphs: (

**a**) Probability plot, (

**b**) residuals vs. fitted values, (

**c**) residual histogram, and (

**d**) residuals vs. order.

**Figure 6.**Three-dimensional (3D) plots of the resultant turning force based on the polynomial solutions for each depth of cut.

Level | V_{c} (m/min) | f (mm/rev) | a_{p} (mm) |
---|---|---|---|

I | 75 | 0.08 | 0.10 |

II | 105 | 0.12 | 0.20 |

III | 150 | 0.16 | 0.30 |

IV | 210 | 0.20 | 0.40 |

**Table 2.**The Johnson-Cook model constants for the AISI-D3 steel [41].

A (MPa) | B (MPa) | C | n | m | T_{0} (°C) | T_{m} (°C) |
---|---|---|---|---|---|---|

1985.6 | 193 | 0.1524 | 0.2768 | 0.2852 | 20 | 1421 |

Mechanical Properties | AISI-D3 | Ceramic |

Young’s Modulus Ε (GPa) | 206.75 | 415 |

Density ρ (kg/m^{3}) | 7700 | 3500 |

Poisson’s ratio γ | 0.30 | 0.22 |

Hardness (HRC) | 63 | − |

Thermal Properties | AISI-D3 | Ceramic |

Heat capacity (J/kgK) | 381.26 @100 °C 429.90 @300 °C 555.42 @600 °C | 334 |

Thermal expansion (μm/mK) | 12.0 | 8.4 |

Thermal conductivity (W/mK) | 50.71 @100 °C 45.69 @300 °C 33.94 @600 °C | 7.5 |

Cutting Parameters | Simulated Cutting Forces | ||||||
---|---|---|---|---|---|---|---|

Standard Order | V_{c} (m/min) | f (mm/rev) | a_{p}(mm) | F_{r} (N) | F_{t} (N) | F_{a} (N) | F_{resultant} (N) |

1 | 75 | 0.08 | 0.10 | 193.2 | 85.1 | 35.4 | 214.1 |

2 | 75 | 0.12 | 0.20 | 269.5 | 118.8 | 74.6 | 303.8 |

3 | 75 | 0.16 | 0.30 | 426.4 | 206.4 | 106.2 | 485.5 |

4 | 75 | 0.20 | 0.40 | 489.2 | 302.6 | 164.7 | 598.3 |

5 | 105 | 0.08 | 0.20 | 262.1 | 95.8 | 70.8 | 287.9 |

6 | 105 | 0.12 | 0.10 | 209.4 | 78.6 | 36.4 | 226.6 |

7 | 105 | 0.16 | 0.40 | 465.7 | 275.4 | 159.7 | 564.1 |

8 | 105 | 0.20 | 0.30 | 421.1 | 208.6 | 112.3 | 483.2 |

9 | 150 | 0.08 | 0.30 | 332.6 | 126.8 | 118.9 | 375.3 |

10 | 150 | 0.12 | 0.40 | 405.9 | 212.1 | 158.8 | 484.7 |

11 | 150 | 0.16 | 0.10 | 204.1 | 98.7 | 38.4 | 229.9 |

12 | 150 | 0.20 | 0.20 | 324.5 | 152.6 | 63.4 | 364.2 |

13 | 210 | 0.08 | 0.40 | 327.8 | 159.5 | 145.6 | 392.5 |

14 | 210 | 0.12 | 0.30 | 312.1 | 160.3 | 98.6 | 364.5 |

15 | 210 | 0.16 | 0.20 | 287.6 | 132.4 | 61.3 | 322.5 |

16 | 210 | 0.20 | 0.10 | 217.2 | 94.9 | 36.4 | 239.8 |

F_{resultant} (N) | Relative Error (%) | ||||
---|---|---|---|---|---|

Standard Order | Simulated | Experimental | Predicted | Predicted vs. Simulated | Predicted vs. Experimental |

1 | 214.1 | 197.8 | 204.1 | −4.65 | 3.17 |

2 | 303.8 | 318.8 | 327.2 | 7.69 | 2.62 |

3 | 485.5 | 472.3 | 461.6 | −4.91 | −2.25 |

4 | 598.3 | 622.3 | 607.5 | 1.53 | −2.38 |

5 | 287.9 | 295.2 | 298.0 | 3.50 | 0.93 |

6 | 226.6 | 214.5 | 221.6 | −2.22 | 3.27 |

7 | 564.1 | 589.5 | 558.3 | −1.02 | −5.28 |

8 | 483.2 | 505.9 | 484.5 | 0.28 | −4.23 |

9 | 375.3 | 360.6 | 365.6 | −2.58 | 1.38 |

10 | 484.7 | 503.9 | 489.7 | 1.02 | −2.82 |

11 | 229.9 | 213.1 | 235.2 | 2.29 | 10.37 |

12 | 364.2 | 383.3 | 361.9 | −0.63 | −5.59 |

13 | 392.5 | 415.1 | 391.8 | −0.20 | −5.62 |

14 | 364.5 | 384.6 | 368.5 | 1.10 | −4.19 |

15 | 322.5 | 345.3 | 318.0 | −1.39 | −7.91 |

16 | 239.8 | 230.2 | 240.4 | 0.24 | 4.45 |

Source | Degree ofFreedom | Sum of Squares | Mean Square | f-Value | p-Value |

Regression | 9 | 222,884 | 24,764.9 | 90.24 | 0.000 |

Residual Error | 6 | 1647 | 274.4 | ||

Total | 15 | 224,531 | |||

R-sq (adj) = 98.17% | |||||

Term | PE Coefficient | SE Coefficient | t-Value | p-Value | |

Constant | 59.7 | 95.7 | 0.62 | 0.556 | |

V | 0.41 | 0.953 | 0.43 | 0.682 | |

f | 234 | 910 | 0.26 | 0.805 | |

a_{p} | 994 | 332 | 2.99 | 0.024 | |

V^{2} | −0.00178 | 0.00218 | −0.82 | 0.445 | |

f^{2} | −1031 | 2588 | −0.40 | 0.704 | |

a_{p}^{2} | −229 | 414 | −0.55 | 0.601 | |

V × f | 1.42 | 3.33 | 0.43 | 0.686 | |

V × a_{p} | −1.78 | 1.33 | −1.33 | 0.231 | |

f × a_{p} | 2408 | 1417 | 1.70 | 0.140 |

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**MDPI and ACS Style**

Kyratsis, P.; Tzotzis, A.; Markopoulos, A.; Tapoglou, N.
CAD-Based 3D-FE Modelling of AISI-D3 Turning with Ceramic Tooling. *Machines* **2021**, *9*, 4.
https://doi.org/10.3390/machines9010004

**AMA Style**

Kyratsis P, Tzotzis A, Markopoulos A, Tapoglou N.
CAD-Based 3D-FE Modelling of AISI-D3 Turning with Ceramic Tooling. *Machines*. 2021; 9(1):4.
https://doi.org/10.3390/machines9010004

**Chicago/Turabian Style**

Kyratsis, Panagiotis, Anastasios Tzotzis, Angelos Markopoulos, and Nikolaos Tapoglou.
2021. "CAD-Based 3D-FE Modelling of AISI-D3 Turning with Ceramic Tooling" *Machines* 9, no. 1: 4.
https://doi.org/10.3390/machines9010004