# Influence of the Nose Radius on the Machining Forces Induced during AISI-4140 Hard Turning: A CAD-Based and 3D FEM Approach

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. CAD-Based Application for Designing Turning Inserts

#### 2.2. CAD-Based Layout of the Turning Process

_{t}is the tangential force, F

_{r}is the radial force, and F

_{a}represents the feed force. Moreover, Figure 2b includes two schematics that focus on the angles related to the cutting process and the feed direction. These angles are inherited from the tool-holder and the turning insert geometry. Thus, the lead angle was 75° and both the rake and inclination angle were negative with a value of −6°.

#### 2.3. Pre-Processing of the 3D FE Turning Model

#### 2.3.1. Configuration of the Insert-Workpiece Interface

#### 2.3.2. Modeling of the Insert-Workpiece Materials

_{0}, and T

_{m}stand for the reference temperature, the ambient temperature, and the melting temperature of the workpiece material, respectively. To adapt the model for the present case, the constants that are available in Table 2 for the AISI-4140 flow stress were used. All the important properties as well as the model constants of the steel material are available in the software’s library.

_{max}is the maximum tensile principal stress; $\overline{\sigma}$ denotes the effective stress; ε

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

_{pl}stands for the plastic strain. This criterion is widely accepted and was implemented in early FE studies such as in the formability of solid cylindrical and ring test specimens by Kobayashi and Lee [33] as well as in the determination of workability in bar extrusion and drawing by Oh et al. [34]. Later, Oyane et al. [35] attempted to predict the fracture strain in actual metal working processes using the basic criterion.

_{f}is the frictional shear stress; μ denotes the shear friction coefficient; and σ

_{n}represents the tool-chip interface stress. Previous studies [38,39] suggest a value of friction coefficient between 0.5 and 0.6 when studying the machining of AISI-4140 steel at cutting speeds and feed rates similar to the ones used in the present work. Considering the conditions utilized in this research, the shear friction coefficient for the numerical model was set to 0.577 [40].

## 3. Results and Discussion

#### 3.1. Assessment of the Cutting Force Components Using FEM

_{r}), the tangential force (F

_{t}), and the feed force (F

_{a}) that were generated during AISI-4140 hard turning with the CNGA120404 (re = 0.40 mm) insert. Similarly, Figure 5d–f corresponded to the CNGA120408 (re = 0.80 mm) insert and consequently Figure 5g–i relate to the CNGA120412 (re = 1.20 mm) insert. The following cutting conditions apply for all the previously mentioned sets: V

_{c}= 150 m/min, f = 0.14 mm/rev, and ap = 0.30 mm. All force versus time diagrams are divided into two phases: the entry phase where force increases quickly as soon as the tool touches the uncut surface of the material and the following steady state phase where force maintains a steady mean value. Finally, when the tool finishes its pass on the workpiece and material removal ends, the force value rapidly decreases until it reaches zero.

_{main}is high. Furthermore, based on the findings of Aouici et al. [24] the experimental analysis of the machining components for the next indicative conditions: V

_{c}= 115 m/min, f = 0.11 mm/rev, and ap = 0.30 mm showed an increased correlation with the equivalent simulated results that were derived from the present study. That is, F

_{r}= 202.3 N, F

_{t}= 146.0 N, and F

_{a}= 86.6 N for the experiments and F

_{r}= 214.4 N, F

_{t}= 137.5 N, and F

_{a}= 77.4 N for the simulations, leading to an estimated relative error of 6.0%, −5.8%, and −10.6%, respectively.

- The radial force is the component that contributes to the resultant machining force the most. In test number nine, for example, this contribution was approximately 56.6%, 65.3%, and 69.2% for each value of nose radius of 0.40 mm, 0.80 mm, and 1.20 mm, respectively. The same trend was observed in the rest of the tests.
- Any increase in feed rate affects all forces except the feed force. Even though the amount of change is not significant, it cannot be considered negligible either. Specifically, an increase in the feed rate from 0.08 mm/rev to 0.11 mm/rev increased the resultant machining force by about 7.6%, 16.0%, and 7.7% for each nose radius (0.40 mm, 0.80 mm, and 1.20 mm, respectively). Similarly, when the feed rate changed from 0.11 mm/rev to 0.14 mm/rev, the feed rate rose by approximately 10.9%, 13.7%, and 10.4% for the same nose radii, respectively.
- In contrast, the nose radius of the inserts had a notable impact on the generated cutting forces. The main machining force increased by 28% on average when the nose radius of the tool changed from 0.40 mm to 0.80 mm. Furthermore, the tool with the 1.20 mm nose radius produced even higher forces. The change from the 0.80 mm nose radius to the 1.20 mm increased F
_{main}by 35% on average. - Finally, any change in cutting speed had a limited effect on the turning forces. A slight decrease in cutting forces was noted as lower cutting speeds were applied. In particular, by lowering cutting speed from 150 m/min to 115 m/min, the decrease was estimated as approximately 4.5% and for the equivalent shift from 115 m/min to 80 m/min, the reduction was found to be close to 3.4%.

#### 3.2. Modelling of the Resultant Cutting Force Using RSM

_{0}denotes the fixed term, X

_{i}are the input variables (cutting speed, feed rate and nose radius), and b

_{i}, b

_{ij}, b

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

_{main}is the resultant machining force in N; V is the cutting speed in m/min; f is the feed rate in mm/rev; and re represents the insert’s nose radius in mm.

#### 3.3. Validation of the RSM Based Model

^{2}term and the f × re term contributed the most, indicating the strong influence of the corner radius to the generated forces. In addition, the total sum of squares was used to express the total variation of the response, which can be visualized with the aid of the data points dispersion graph (see Figure 7a). Last but not least, the p-value of the regression model suggests that the probability of acquiring extreme results is thin.

- The nose radius had a strong impact on the resultant turning force. In fact, an increase from 0.40 mm to 1.20 mm almost doubled the resultant force regardless of the conditions.
- Any increase in feed rate acts as increasing the main cutting force, but at a much lower grade compared to the effect of the nose radius.
- Finally, any change in the cutting speed did not seem to have a significant influence on the main cutting force.

_{c}= 100 m/min, f = 0.10 mm/rev, and re = 0.40 mm), II (V

_{c}= 120 m/min, f = 0.10 mm/rev, and re = 0.80 mm), III (V

_{c}= 140 m/min, f = 0.10 mm/rev, and re = 1.20 mm), IV (V

_{c}= 100 m/min, f = 0.12 mm/rev, and re = 0.40 mm), V (V

_{c}= 120 m/min, f = 0.12 mm/rev, and re = 0.80 mm), and VI (V

_{c}= 140 m/min, f = 0.12 mm/rev, and re = 1.20 mm). The lowest level of agreement (relative error of 10.8%) between the predicted value of F

_{main}and the simulated one was found in test number 5, a fact that indicates that the model provides safe predictions.

## 4. Conclusions

- F
_{r}is the governing force during hard turning of AISI-4140, which in most cases represents two-thirds of the produced resultant machining force. - When feed rate changed from 0.08 mm/rev to 0.11 mm/rev F
_{main}gained an average increase of about 10.4%. Similarly, a shift from 0.11 mm/rev to 0.14 mm/rev increased F_{main}by approximately 11.7%, regardless of the nose radius value. - The nose radius of the cutting edge affects the generated cutting forces substantially. It was highlighted that a higher value of nose radius leads to higher values of cutting forces, and depending on the applied cutting conditions, the increase percentage exceeded 30% in most cases.
- Finally, changing the cutting speed did not seem to influence the main cutting force notably.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) The physical model of the PCBNR2525M12 tool-holder and (

**b**) the CAD-based tool-workpiece setup.

**Figure 3.**(

**a**) The physical model of the CNGA120408T01020 ceramic and (

**b**) the analogous CAD model with detailed geometry.

**Figure 5.**(

**a**–

**c**) Sample machining forces versus time diagrams for 0.40 mm nose radius, (

**d**–

**f**) 0.80 mm, and (

**g**–

**i**) 1.20 mm.

**Figure 6.**(

**a**) Comparison of the radial force, (

**b**) the tangential force, (

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

**d**) the resultant machining force based on the different nose radii.

**Figure 7.**Residual analysis graphs: (

**a**) probability plot, (

**b**) residuals versus fitted values, (

**c**) error histogram, and (

**d**) residuals versus order.

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

I | 80 | 0.08 | 0.40 |

II | 115 | 0.11 | 0.80 |

III | 150 | 0.14 | 1.20 |

**Table 2.**The Johnson–Cook model constants for AISI-4140 steel [13].

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

106 | 1167 | 0.0352 | 0.1424 | 0.763 | 20 | 1547 |

Mechanical Properties | AISI-4140 | Ceramic |

Young’s Modulus (GPa) | 212 @ 20 °C | 415 |

192 @ 300 °C | ||

164 @ 600 °C | ||

Density (kg/m^{3}) | 7850 | 3500 |

Poisson’s ratio | 0.30 | 0.22 |

Hardness (HRC) | 60 | − |

Thermal Properties | AISI-4140 | Ceramic |

Heat capacity (J/kgK) | 362 @ 20 °C | 334 |

446 @ 300 °C | ||

610 @ 600 °C | ||

Thermal expansion (μm/mK) | 11.9 @ 20 °C | 8.4 |

13.6 @ 300 °C | ||

14.9 @ 600 °C | ||

Thermal conductivity (W/mK) | 41.7 @ 20 °C | 7.5 |

41.4 @ 300 °C | ||

34.1 @ 600 °C |

Cutting Parameters | F_{main} (N) | ||||||
---|---|---|---|---|---|---|---|

Std Order | V_{c} (m/min) | f (mm/rev) | ap (mm) | re (mm) | Experiments | FE Model | Relative Error (%) |

1 | 80 | 0.08 | 0.30 | 0.80 | 189.8 | 207.7 | 9.4 |

2 | 80 | 0.11 | 0.30 | 0.80 | 244.6 | 250.2 | 2.3 |

3 | 80 | 0.14 | 0.30 | 0.80 | 282.3 | 264.5 | −6.3 |

4 | 115 | 0.08 | 0.30 | 0.80 | 225.7 | 232.1 | 2.8 |

5 | 115 | 0.11 | 0.30 | 0.80 | 264.1 | 266.2 | 0.8 |

6 | 115 | 0.14 | 0.30 | 0.80 | 300.9 | 281.5 | −6.4 |

7 | 150 | 0.08 | 0.30 | 0.80 | 238.0 | 249.6 | 4.9 |

8 | 150 | 0.11 | 0.30 | 0.80 | 267.7 | 281.2 | 5.1 |

9 | 150 | 0.14 | 0.30 | 0.80 | 316.9 | 320.7 | 1.2 |

Cutting Parameters | F_{main} (N) | ||||
---|---|---|---|---|---|

Std Order | V_{c}(m/min) | F (mm/rev) | re (mm) | FE Model | RegressionModel |

1 | 80 | 0.08 | 0.40 | 182.3 | 176.3 |

2 | 80 | 0.11 | 0.40 | 194.1 | 190.6 |

3 | 80 | 0.14 | 0.40 | 213.6 | 212.9 |

4 | 115 | 0.08 | 0.40 | 186.5 | 182.8 |

5 | 115 | 0.11 | 0.40 | 201.0 | 200.3 |

6 | 115 | 0.14 | 0.40 | 221.3 | 225.8 |

7 | 150 | 0.08 | 0.40 | 190.2 | 190.5 |

8 | 150 | 0.11 | 0.40 | 206.5 | 211.1 |

9 | 150 | 0.14 | 0.40 | 233.7 | 239.8 |

10 | 80 | 0.08 | 0.80 | 207.7 | 236.0 |

11 | 80 | 0.11 | 0.80 | 250.2 | 256.2 |

12 | 80 | 0.14 | 0.80 | 284.5 | 284.5 |

13 | 115 | 0.08 | 0.80 | 232.1 | 241.2 |

14 | 115 | 0.11 | 0.80 | 266.2 | 264.6 |

15 | 115 | 0.14 | 0.80 | 301.5 | 296.1 |

16 | 150 | 0.08 | 0.80 | 249.6 | 247.5 |

17 | 150 | 0.11 | 0.80 | 281.2 | 274.1 |

18 | 150 | 0.14 | 0.80 | 320.7 | 308.8 |

19 | 80 | 0.08 | 1.20 | 319.1 | 313.7 |

20 | 80 | 0.11 | 1.20 | 346.9 | 339.9 |

21 | 80 | 0.14 | 1.20 | 371.3 | 374.3 |

22 | 115 | 0.08 | 1.20 | 323.3 | 317.6 |

23 | 115 | 0.11 | 1.20 | 344.4 | 347.0 |

24 | 115 | 0.14 | 1.20 | 382.6 | 384.5 |

25 | 150 | 0.08 | 1.20 | 322.4 | 322.7 |

26 | 150 | 0.11 | 1.20 | 347.4 | 355.2 |

27 | 150 | 0.14 | 1.20 | 392.3 | 395.9 |

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

Regression | 9 | 113,045 | 12,560.6 | 238.87 | 0.000 |

Residual Error | 17 | 894 | 52.6 | ||

Total | 26 | 113,939 | |||

R-sq (adj) = 98.80% | |||||

Term | PECoefficient | SECoefficient | t-Value | p-Value | |

Constant | 158.1 | 59.8 | 2.64 | 0.017 | |

V | −0.109 | 0.611 | −0.18 | 0.861 | |

f | −822 | 774 | −1.06 | 0.303 | |

re | 48.8 | 39.5 | 1.24 | 0.233 | |

V^{2} | 0.00046 | 0.00242 | 0.19 | 0.853 | |

f^{2} | 4504 | 3289 | 1.37 | 0.189 | |

re^{2} | 56.6 | 18.5 | 3.06 | 0.007 | |

V × f | 3.03 | 1.99 | 1.52 | 0.147 | |

V × re | −0.093 | 0.150 | −0.62 | 0.540 | |

f × re | 498 | 174 | 2.86 | 0.011 |

Test No. | Simulated F_{main} (N) | Predicted F_{main} (N) | Relative Error (%) |
---|---|---|---|

I | 197.4 | 189.7 | −3.9 |

II | 242.1 | 257.0 | 6.2 |

III | 316.4 | 341.3 | 7.9 |

IV | 217.6 | 203.1 | −6.6 |

V | 248.8 | 275.6 | 10.8 |

VI | 385.7 | 365.1 | −5.3 |

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## Share and Cite

**MDPI and ACS Style**

Tzotzis, A.; García-Hernández, C.; Huertas-Talón, J.-L.; 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.
https://doi.org/10.3390/mi11090798

**AMA Style**

Tzotzis A, García-Hernández C, Huertas-Talón J-L, 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(9):798.
https://doi.org/10.3390/mi11090798

**Chicago/Turabian Style**

Tzotzis, Anastasios, César García-Hernández, José-Luis Huertas-Talón, and Panagiotis Kyratsis.
2020. "Influence of the Nose Radius on the Machining Forces Induced during AISI-4140 Hard Turning: A CAD-Based and 3D FEM Approach" *Micromachines* 11, no. 9: 798.
https://doi.org/10.3390/mi11090798