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

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 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

## References

- Klocke, F.; Raedt, H.-W.; Hoppe, S. 2D-FEM simulation of the orthogonal high speed cutting process. Mach. Sci. Technol.
**2001**, 5, 323–340. [Google Scholar] [CrossRef] - Elkaseer, A.; Abdelaziz, A.; Saber, M.; Nassef, A. FEM-based study of precision hard turning of stainless steel 316L. Materials
**2019**, 12, 2522. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ali, M.H.; Ansari, M.N.M.; Khidhir, B.A.; Mohamed, B.; Oshkour, A.A. Simulation machining of titanium alloy (Ti-6Al-4V) based on the finite element modeling. J. Brazilian Soc. Mech. Sci. Eng.
**2014**, 36, 315–324. [Google Scholar] [CrossRef] - Xiong, Y.; Wang, W.; Jiang, R.; Lin, K.; Shao, M. Mechanisms and FEM simulation of chip formation in orthogonal cutting in-situ TiB2/7050Al MMC. Materials
**2018**, 11, 606. [Google Scholar] [CrossRef][Green Version] - Saez-de-Buruaga, M.; Soler, D.; Aristimuño, P.X.; Esnaola, J.A.; Arrazola, P.J. Determining tool/chip temperatures from thermography measurements in metal cutting. Appl. Therm. Eng.
**2018**, 145, 305–314. [Google Scholar] [CrossRef] - Ye, G.G.; Chen, Y.; Xue, S.F.; Dai, L.H. Critical cutting speed for onset of serrated chip flow in high speed machining. Int. J. Mach. Tools Manuf.
**2014**, 86, 18–33. [Google Scholar] [CrossRef] - Shuang, F.; Chen, X.; Ma, W. Numerical analysis of chip formation mechanisms in orthogonal cutting of Ti6Al4V alloy based on a CEL model. Int. J. Mater. Form.
**2018**, 11, 185–198. [Google Scholar] [CrossRef] - Chen, G.; Ren, C.; Yang, X.; Jin, X.; Guo, T. Finite element simulation of high-speed machining of titanium alloy (Ti-6Al-4V) based on ductile failure model. Int. J. Adv. Manuf. Technol.
**2011**, 56, 1027–1038. [Google Scholar] [CrossRef] - Yanda, H.; Ghani, J.A.; Haron, C.H.C. Application of FEM in investigating machining performance. Adv. Mater. Res.
**2011**, 264–265, 1033–1038. [Google Scholar] [CrossRef] - Calamaz, M.; Coupard, D.; Girot, F. A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti-6Al-4V. Int. J. Mach. Tools Manuf.
**2008**, 48, 275–288. [Google Scholar] [CrossRef][Green Version] - Chiappini, E.; Tirelli, S.; Albertelli, P.; Strano, M.; Monno, M. On the mechanics of chip formation in Ti-6Al-4V turning with spindle speed variation. Int. J. Mach. Tools Manuf.
**2014**. [Google Scholar] [CrossRef][Green Version] - Arrazola, P.J.; Özel, T.; Umbrello, D.; Davies, M.; Jawahir, I.S. Recent advances in modelling of metal machining processes. CIRP Ann. Manuf. Technol.
**2013**, 62, 695–718. [Google Scholar] [CrossRef] - Tzotzis, A.; Markopoulos, A.; Karkalos, N.; Kyratsis, P. 3D finite element analysis of Al7075-T6 drilling with coated solid tooling. MATEC WEb Conf.
**2020**, 318, 1–6. [Google Scholar] [CrossRef] - Oezkaya, E.; Hannich, S.; Biermann, D. Development of a three-dimensional finite element method simulation model to predict modified flow drilling tool performance. Int. J. Mater. Form.
**2019**, 12, 477–490. [Google Scholar] [CrossRef] - Guo, Y.B.; Dornfeld, D.A. Finite element modeling of burr formation process in drilling 304 stainless steel. J. Manuf. Sci. Eng. Trans. ASME
**2000**, 122, 612–619. [Google Scholar] [CrossRef] - Rajesh Jesudoss Hynes, N.; Kumar, R. Simulation and Experimental Validation of Al7075-T651 Flow Drilling Process. J. Chinese Soc. Mech. Eng.
**2017**, 38, 413–420. [Google Scholar] - Gao, X.; Li, H.; Liu, Q.; Zou, P.; Liu, F. Simulation of stainless steel drilling mechanism based on Deform-3D. Adv. Mater. Res.
**2011**, 160–162, 1685–1690. [Google Scholar] [CrossRef] - Nagaraj, M.; Kumar, A.J.P.; Ezilarasan, C.; Betala, R. Finite element modeling in drilling of Nimonic C-263 alloy using deform-3D. Comput. Model. Eng. Sci.
**2019**, 118, 679–692. [Google Scholar] [CrossRef] - Thepsonthi, T.; Grul Özel, T. 3-D finite element process simulation of micro-end milling Ti-6Al-4V titanium alloy: Experimental validations on chip flow and tool wear. J. Mater. Process. Technol.
**2015**, 221, 128–145. [Google Scholar] [CrossRef] - Maurel-Pantel, A.; Fontaine, M.; Thibaud, S.; Gelin, J.C. 3D FEM simulations of shoulder milling operations on a 304L stainless steel. Simul. Model. Pract. Theory
**2012**, 22, 13–27. [Google Scholar] [CrossRef][Green Version] - Pittalà, G.M.; Monno, M. 3D finite element modeling of face milling of continuous chip material. Int. J. Adv. Manuf. Technol.
**2010**, 47, 543–555. [Google Scholar] [CrossRef] - Nan, X.; Xie, L.; Zhao, W. On the application of 3D finite element modeling for small-diameter hole drilling of AISI 1045 steel. Int. J. Adv. Manuf. Technol.
**2016**, 84, 1927–1939. [Google Scholar] [CrossRef] - Soo, S.L.; Dewes, R.C.; Aspinwall, D.K. 3D FE modelling of high-speed ball nose end milling. Int. J. Adv. Manuf. Technol.
**2010**, 50, 871–882. [Google Scholar] [CrossRef] - Wu, H.B.; Zhang, S.J. 3D FEM simulation of milling process for titanium alloy Ti6Al4V. Int. J. Adv. Manuf. Technol.
**2014**, 71, 1319–1326. [Google Scholar] [CrossRef] - Davoudinejad, A.; Tosello, G.; Parenti, P.; Annoni, M. 3D finite element simulation of micro end-milling by considering the effect of tool run-out. Micromachines
**2017**, 8, 187. [Google Scholar] [CrossRef][Green Version] - Tapoglou, N.; Antoniadis, A. 3-Dimensional kinematics simulation of face milling. Measurement
**2012**, 45, 1396–1405. [Google Scholar] [CrossRef] - Guo, Y.B.; Liu, C.R. 3D FEA modeling of hard turning. J. Manuf. Sci. Eng. Trans. ASME
**2002**, 124, 189–199. [Google Scholar] [CrossRef] - Valiorgue, F.; Rech, J.; Hamdi, H.; Gilles, P.; Bergheau, J.M. 3D modeling of residual stresses induced in finish turning of an AISI304L stainless steel. Int. J. Mach. Tools Manuf.
**2012**, 53, 77–90. [Google Scholar] [CrossRef] - Malakizadi, A.; Gruber, H.; Sadik, I.; Nyborg, L. An FEM-based approach for tool wear estimation in machining. Wear
**2016**, 368–369, 10–24. [Google Scholar] [CrossRef] - Buchkremer, S.; Klocke, F.; Veselovac, D. 3D FEM simulation of chip breakage in metal cutting. Int. J. Adv. Manuf. Technol.
**2016**, 82, 645–661. [Google Scholar] [CrossRef] - Magalhães, F.C.; Ventura, C.E.H.; Abrão, A.M.; Denkena, B. Experimental and numerical analysis of hard turning with multi-chamfered cutting edges. J. Manuf. Process.
**2020**, 49, 126–134. [Google Scholar] [CrossRef] - Tzotzis, A.; García-Hernández, C.; Talón, J.L.H.; Kyratsis, P. FEM based mathematical modelling of thrust force during drilling of Al7075-T6. Mech. Ind.
**2020**, 21, 1–14. [Google Scholar] [CrossRef] - Bensouilah, H.; Aouici, H.; Meddour, I.; Athmane, M. Performance of coated and uncoated mixed ceramic tools in hard turning process. Measurement
**2016**, 82, 1–18. [Google Scholar] [CrossRef] - Aouici, H.; Yallese, M.A.; Chaoui, K.; Mabrouki, T.; Rigal, J.F. Analysis of surface roughness and cutting force components in hard turning with CBN tool: Prediction model and cutting conditions optimization. Meas. J. Int. Meas. Confed.
**2012**, 45, 344–353. [Google Scholar] [CrossRef] - Benardos, P.G.; Vosniakos, G.C. Prediction of surface roughness in CNC face milling using neural networks and Taguchi’s design of experiments. Robot. Comput. Integr. Manuf.
**2002**, 18, 343–354. [Google Scholar] [CrossRef] - Masmiati, N.; Sarhan, A.A.D. Optimizing cutting parameters in inclined end milling for minimum surface residual— stressTaguchi approach. Measurement
**2015**, 60, 267–275. [Google Scholar] [CrossRef] - Quiza, R.; Figueira, L.; Davim, J.P. Comparing statistical models and artificial neural networks on predicting the tool wear in hard machining D2 AISI steel. Int. J. Adv. Manuf. Technol.
**2008**, 37, 641–648. [Google Scholar] [CrossRef] - Tzotzis, A.; Garcia-Hernandez, C.; Talón, J.L.H.; Kyratsis, P. CAD-based automated design of FEA-ready cutting tools. J. Manuf. Mater. Process.
**2020**, 4, 104. [Google Scholar] [CrossRef] - Tzotzis, A.; Garcia-Hernandez, C.; Talón, J.L.H.; Kyratsis, P. Influence of the nose radius on the machining forces induced during AISI-4140 hard turning: A CAD-based and 3D FEM approach. Micromachines
**2020**, 11, 798. [Google Scholar] [CrossRef] - Tzotzis, A.; Garcia-Hernandez, C.; Talón, J.L.H.; Kyratsis, P. 3D FE Modelling of machining forces during AISI 4140 hard turning. Strojniški Vestn. J. Mech. Eng.
**2020**, 66, 467–478. [Google Scholar] [CrossRef] - Scientific Forming Technologies Corporation. DEFORM, version 11.3 (PC); Documentation; Columbus, OH, USA, 2016. [Google Scholar]
- Hu, H.J.; Huang, W.J. Tool life models of nano ceramic tool for turning hard steel based on FEM simulation and experiments. Ceram. Int.
**2014**, 40, 8987–8996. [Google Scholar] [CrossRef] - Kobayashi, S.; Lee, C.H. Deformation mechanics and workability in upsetting solid circular cylinders. In Proceedings of the North American Metalworking Research Conference, Ontario, ON, Canada, 14–15 May 1973; Volume 1. [Google Scholar]
- Oh, S.I.; Chen, C.C.; Kobayashi, S. Ductile fracture in axisymmetric extrusion and drawing—Part 2: Workability in extrusion and drawing. J. Manuf. Sci. Eng.
**1979**, 101, 36–44. [Google Scholar] [CrossRef] - Oyane, M.; Sato, T.; Okimoto, K.; Shima, S. Criteria for ductile fracture and their applications. J. Mech. Work. Technol.
**1980**, 4, 65–81. [Google Scholar] [CrossRef] - Cockcroft, M.G.; Latham, D.J. Ductility and the workability of metals. J. Inst. Met.
**1968**, 96, 33–39. [Google Scholar] - Agmell, M. Applied FEM of Metal Removal and Forming, 1st ed.; Studentlitteratur: Lund, Sweden, 2018; ISBN 978-91-44-12507-7. [Google Scholar]
- Arrazola, P.J.; Matsumura, T.; Kortabarria, A.; Garay, A.; Soler, D. Finite element modelling of chip formation process applied to drilling of Ti64 alloy. In Proceedings of the 6th International Conference on Leading Edge Manufacturing in 21st Century, LEM, Saitama, Japan, 8–10 November 2011; pp. 1–6. [Google Scholar]
- Haglund, A.J.; Kishawy, H.A.; Rogers, R.J. An exploration of friction models for the chip-tool interface using an Arbitrary Lagrangian-Eulerian finite element model. Wear
**2008**, 265, 452–460. [Google Scholar] [CrossRef] - Meddour, I.; Yallese, M.A.; Bensouilah, H.; Khellaf, A.; Elbah, M. Prediction of surface roughness and cutting forces using RSM, ANN, and NSGA-II in finish turning of AISI 4140 hardened steel with mixed ceramic tool. Int. J. Adv. Manuf. Technol.
**2018**, 97, 1931–1949. [Google Scholar] [CrossRef] - Kyratsis, P.; Markopoulos, A.; Efkolidis, N.; Maliagkas, V.; Kakoulis, K. Prediction of thrust force and cutting torque in drilling based on the response surface methodology. Machines
**2018**, 6, 24. [Google Scholar] [CrossRef][Green Version] - Efkolidis, N.; Hernández, C.G.; Talón, J.L.H.; Kyratsis, P. Modelling and prediction of thrust force and torque in drilling operations of Al7075 using ANN and RSM methodologies. Strojniški Vestn. J. Mech. Eng.
**2018**, 64, 351–361. [Google Scholar] [CrossRef]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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