# Effect of the Relative Position of the Face Milling Tool towards the Workpiece on Machined Surface Roughness and Milling Dynamics

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Method

^{′}= 0 mm means that e = 12.6/2 = 6.3 mm and when a

^{′}= 12.6 mm then e = −12.6/2 = −6.3 mm.

_{x}, F

_{y}, F

_{z}(minimum, maximum, average, and RMS (Root-mean-square)) and accelerations of vibrations a

_{x}and a

_{y}(RMS) for different values of relative position of face mill and workpiece, a′.

## 3. Results and Discussion

#### 3.1. Evaluation of Dynamics and Surface Roughness

_{c}= 1.77 ÷ 2.11. This indicates that in the milling process, 1 to 3 teeth, depending on tool rotational angle and selected radial immersion, are engaged simultaneously. The non-integer values of z

_{c}denote that in the milling process, the number of teeth engaged in the cutting is variable, which in its turn causes variations in maximal chip cross-sections per the consecutive teeth, and thus the changes in cutting force peak values per teeth (see Figure 3a–c). On the other hand, the variations in cutting force peak values can be also induced by the geometrical errors of the machine-toolholder-tool system (manifesting in axial run out), which contributes to the changes in real values of axial depths of cut per consecutive tooth.

_{y}, and feed normal force F

_{x}components’ absolute values are significantly higher than thrust force F

_{y}values. It should be noted that F

_{y}and F

_{x}components are directly correlated with milling kinematics and the chip decohesion process. On the other hand, the thrust force is only marginally dependent on chip formation mechanisms, and its value is strictly correlated with the rubbing and ploughing mechanisms occurring between the tool’s flank face and the machined surface. Thus, the potential growth of thrust force could be attributed to the relatively high friction coefficient between the workpiece and the tool flank face, as well as to the progressing tool wear.

_{i}(ψ

_{1}) found for different ${a}^{\prime}$ values. The a

_{i}(ψ

_{1}) corresponds to the uncut chip thickness during the initial contact of the tooth with the workpiece. The growth of ${a}^{\prime}$ values induces the increase of a

_{i}(ψ

_{1}). When the ${a}^{\prime}$ = 0 mm, the a

_{i}(ψ

_{1}) = 0 mm, and the growth of chip cross section (and thus cutting forces) is gradual. However, in the case of ${a}^{\prime}$ = 6.3 mm, the a

_{i}(ψ

_{1}) = 0.06 mm, and when ${a}^{\prime}$ = 12.3 mm, the a

_{i}(ψ

_{1}) = 0.08 mm. This reveals that initiation of chip formation during machining with higher ${a}^{\prime}$ values occurs at relatively high uncut chip thicknesses, and thus the impact of the cutting tooth on the workpiece can cause some forced vibrations, contributing to the growth of cutting force dynamic components. These relations can be also found for the root mean square (RMS) values of F

_{x}force in the function of ${a}^{\prime}$ (Figure 4a), i.e., the growth of ${a}^{\prime}$ factor leads to the increase in force. This means that the F

_{x}force component is strongly affected by milling dynamics. In order to further analyze these findings, the RMS values of accelerations of vibrations in the function of ${a}^{\prime}$ have been determined (see Figure 4b). It can be observed that in the case of vibrations in Y direction, the increasing trend together with the ${a}^{\prime}$ factor is found, which can be attributed to the relations between the initial uncut chip thicknesses a

_{i}(ψ

_{1}) and forced vibrations in milling.

_{x}force and A

_{y}accelerations of vibrations. Therefore, the correlation between the formation of surface roughness and process dynamics can be exposed. Nevertheless, during the face milling process, the formation of the surface profile can be also strongly affected by geometrical errors in the machine-toolholder-tool system, plastic and elastic deformations of the material being cut, homogeneity of the workpiece, as well as some random factors.

#### 3.2. Multicriteria Optimization of Face Milling.

_{tot}. Therefore, the problem of concurrent optimization of numerous output quantities has been reduced to the obtainment of 1 output measure, which leads to the maximization of the total response desirability. The optimization procedure has been carried out in Statistica 13 software.

- Root mean square values of cutting forces (F
_{x}, F_{y}, F_{z}); - Root mean square values of acceleration of vibration components (A
_{x}, A_{y}); - Surface roughness parameters (Ra, Rz).

_{x}), D(F

_{y}), D(F

_{z}), D(A

_{x}), D(A

_{y}), D(Ra), D(Rz)), the values of which were contained in the range <0, 1>. Therefore, the response desirability profiles for the outputs were obtained on the basis of the expressions shown in Equations (6)–(33):

_{_opt}) matching with the maximal value of the total desirability. The optimal solution searching algorithm is based on the simplex method.

_{_opt}= 3.15 mm. The face milling process with the selection of ${a}^{\prime}$

_{_opt}enables the obtainment of total desirability at the level of 0.57. This means that simultaneous achievement of the lowest response values is not possible with the application of ${a}^{\prime}$

_{_opt}. However, during face milling with ${a}^{\prime}$

_{_opt}= 3.15 mm, the cutting force components’ RMS values will not exceed 360 N for the F

_{x}, 265 N for the F

_{y}, and 185 N for the F

_{z}. The acceleration of vibration RMS values will not exceed 7.3 m/s

^{2}for the A

_{x}and 6 m/s

^{2}for the A

_{y}. Moreover, the surface roughness parameters will be at most 2 µm for the Ra and 12 µm for the Rz.

## 4. Conclusions

- (1)
- The changes in radial immersion of the face mill towards the workpiece, described by the ${a}^{\prime}$ factor, despite the selected constant values of axial depths of cut a
_{p}and milling widths B, affect the active number of teeth engaged in the workpiece. Consequently, it leads to the variations in maximal instant forces per consecutive teeth and can affect the milling vibration values and surface roughness. - (2)
- The value of ${a}^{\prime}$ factor directly characterizes the face milling process kinematics. The growth of ${a}^{\prime}$ value reduces the contribution of up milling kinematics in the whole face milling process towards the contribution of down milling. Conducted studies clearly show that in the case of ${a}^{\prime}$ = 0 (predominantly up milling), the lowest forces (in X and Z directions) and vibrations (in Y direction) are reached, which is attributed to the gradual immersion of the tool into the workpiece (and thus the gradual increase of uncut chip thickness in function of tool rotation angle).
- (3)
- Initiation of chip formation during face milling with higher ${a}^{\prime}$ values occurs at relatively high uncut chip thicknesses. Therefore, the dynamic contact between the tooth and workpiece can cause some forced vibrations, contributing to the growth of cutting force dynamic components. This relation has been confirmed by measurements of vibrations, which revealed the increasing trend of acceleration of vibration in Y direction together with the growth of ${a}^{\prime}$ factor.
- (4)
- The performed multicriteria optimization, based on determination of total desirability function, enabled the obtainment of optimal ${a}^{\prime}$ factor, and equaled to 3.15 mm. The face milling with the selection of optimal ${a}^{\prime}$ factor affects the reduction of cutting forces, vibrations, and surface roughness parameters. Therefore, these findings can be implemented in industrial applications. To put this another way, the selection of optimal tool radial immersion towards the workpiece ${a}^{\prime}$
_{_opt}during flat face milling with the milling width B lower than the cutter’s diameter D can contribute to improvements in process economics (resulting from the reduction of surface roughness and milling power).

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Ra | Arithmetic average value of surface roughness (µm) |

Rz | Mean surface roughness depth parameter (µm) |

D | Cutter diameter (mm) |

k_{r} | Major cutting edge angle (deg) |

z | Number of teeth |

d | Depth of cut (mm) |

v_{c} | Cutting speed (m/min) |

f_{z} | Feed per tooth (mm/tooth) |

a′ | Relative position of the face mill towards the workpiece (mm) |

e | Displacement of the cutter axis towards the workpiece (mm) |

a_{i} | Instant uncut chip thickness (mm) |

ψ_{1}, ψ_{in} | Inlet angle (deg) |

ψ_{2}, ψ_{out} | Out angle (deg) |

ψ | The contact angle (deg) |

θ | Tooth spacing angle (deg) |

ψ_{i} | Angular coordinate of the i-th tooth (deg) |

B | Milling width (mm) |

D_{r} | Direction of rotary motion |

D_{s} | Feed movement |

F_{x}, F_{y}, F_{z} | Components of the cutting forces (N) |

A_{x},A_{y} | Accelerations of vibrations (m/s^{2}) |

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**Figure 1.**Experimental part: (

**a**) Experimental setup, (

**b**) workpiece specification, (

**c**) milling cutter.

**Figure 2.**Types of installation of face Up and Down milling (${a}_{i}$, uncut chip thickness; ${\mathsf{\psi}}_{1}$ = ${\mathsf{\psi}}_{in}$, inlet angle; ${\mathsf{\psi}}_{2}$ = ${\mathsf{\psi}}_{out}$, out angle; $\mathsf{\psi}$, the contact angle; $\mathsf{\theta}$, tooth spacing angle; ${\mathsf{\psi}}_{i}$, angular coordinate of the i-th tooth; $B$, depth of milling; $e$, positions symmetry of cutter and workpiece; ${a}^{\prime}$, positions the end of the cutter diameter and the beginning of the workpiece; ${D}_{r}$, direction of rotary driven; ${D}_{s}$, feed movement; $1$, $2$, $3$, ${1}^{\prime}$, ${2}^{\prime}$, ${3}^{\prime}$, points determining the amount of chip scraps removed per one rotation of the cutter); (

**a**) Asymmetric circuit (Up milling), (

**b**) Asymmetric circuit (Down milling), (

**c**) Symmetric circuit (Up milling), (

**d**) Symmetric circuit (Down milling).

**Figure 4.**The root mean square values: (

**a**) The root mean square values of cutting force F

_{x}force as function of ${a}^{\prime}$; (

**b**) the root mean square values of acceleration of vibration A

_{x}as a function of ${a}^{\prime}$.

**Figure 5.**The surface roughness parameter: (

**a**) Ra as function of ${a}^{\prime}$; (

**b**) Rz as function of ${a}^{\prime}$.

Workpiece Material | Chemical Composition in wt% | Vickers Hardness, HV | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Carbon, C | Silicon, Si | Manganese, Mn | Nickel, Ni | Sulphur, S | Phosphorus, P | Chrome, Cr | Cuprum, Cu | Arsenic, As | Iron, Fe | ||

Max | 0.5 | 0.35 | 0.9 | 0.25 | up to 0.04 | up to 0.035 | up to 0.25 | up to 0.25 | up to 0.08 | ≈97 | 184 |

Min | 0.43 | 0.15 | 0.6 | 0 | - | - | - | - | - |

Material of the Cutting Part | Cutter Diameter, D, mm | Major Cutting Edge Angle, k_{r}, deg | Number of Teeth, z |
---|---|---|---|

PVD coated carbide (TiAlN + Al_{2}O_{3} on the rake face) + (ZrCN on the flank face) | 63 | 90 | 6 |

Depth of Cut, d, mm | Cutting Speed, v_{c}, m/min | Feed Per Tooth, f_{z}, mm/tooth | Relative Position of the Cutter, a′, mm |
---|---|---|---|

1 | 100.0 | 0.1 | 0, 0.3, 0.8, 3.3, 6.3, 9.3, 11.8, 12.3, 12.6 |

a/mm | Ψ_{1}, Inlet Angle, ^{0} | Ψ_{2}, Outlet Angle, ^{0} | Ψ, Contact Angle, ^{0} | z_{c}, Number of Active Teeth | Scheme in doc File | Description |
---|---|---|---|---|---|---|

0 | 0 | 126.9 | 126.9 | 2.12 | Figure 2a | Asymmetric (predominantly up milling) |

0.3 | 7.9 | 127.6 | 119.7 | 2 | Figure 2a | Asymmetric (predominantly up milling) |

0.8 | 12.9 | 128.7 | 115.8 | 1.93 | Figure 2a | Asymmetric (predominantly up milling) |

3.3 | 26.5 | 134.8 | 108.3 | 1.81 | Figure 2a | Asymmetric (predominantly up milling) |

6.3 | 36.9 | 143.2 | 106.3 | 1.77 | Figure 2c,d | Symmetric * |

9.3 | 45.2 | 153.6 | 108.4 | 1.81 | Figure 2b | Asymmetric (predominantly down milling) |

11.8 | 51.3 | 167.1 | 115.8 | 1.93 | Figure 2b | Asymmetric (predominantly down milling) |

12.3 | 52.5 | 172.1 | 119.6 | 1.99 | Figure 2b | Asymmetric (predominantly down milling) |

12.6 | 53.1 | 180 | 126.9 | 2.12 | Figure 2b | Asymmetric (predominantly down milling) |

Exp. No. | Inputs Parameters | Outputs Parameters | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Relative Position of Face Mill and Workpiece a′ | Roughness, Ra, µm | Roughness, Rz, µm | |||||||||

1 meas | 2 meas | 3 meas | 4 meas | Av | 1 meas | 2 meas | 3 meas | 4 meas | Av | ||

1 | 0 | 2.19 | 1.75 | 3.24 | 2.61 | 2.45 | 12.6 | 10.56 | 19.35 | 15.35 | 14.47 |

2 | 0.3 | 2.11 | 2.45 | 3.36 | 2.78 | 2.68 | 12.15 | 15.25 | 19.01 | 14.13 | 15.14 |

3 | 0.8 | 2 | 2.45 | 3.54 | 2.94 | 2.73 | 12.4 | 14.24 | 19.95 | 14.94 | 15.38 |

4 | 3.3 | 2.25 | 2.28 | 2.87 | 3.24 | 2.66 | 14.63 | 12.26 | 16.87 | 15.65 | 14.85 |

5 | 6.3 | 2.42 | 1.85 | 3.37 | 3.25 | 2.72 | 13.98 | 10.91 | 20.07 | 17.53 | 15.62 |

6 | 9.3 | 1.92 | 2.11 | 2.92 | 3.37 | 2.58 | 10.2 | 11.62 | 18.62 | 22.04 | 15.62 |

7 | 11.8 | 2.45 | 2.95 | 2.81 | 2.51 | 2.68 | 14.19 | 16.47 | 14.88 | 12.73 | 14.57 |

8 | 12.3 | 2.88 | 2.37 | 3.25 | 3.38 | 2.97 | 15.85 | 13.7 | 18.46 | 19.1 | 16.78 |

9 | 12.6 | 3.05 | 3.32 | 3.24 | 3.28 | 3.22 | 19.05 | 16.74 | 15.2 | 19.64 | 17.66 |

**Table 6.**The experimental components of the cutting force F

_{x}, F

_{y}, F

_{z}and the accelerations a

_{x}and a

_{y}.

Exp. No. | Inputs Parameters | Outputs Parameters | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Relative Position of Face Mill and Workpiece a′ | Force, F_{i}, N | Acceleration, A_{i}, m/s^{2} | |||||||||||||

F_{x} | F_{y} | Fz | A_{x} | A_{y} | |||||||||||

Min | Max | Aver | RMS | Min | Max | Aver | RMS | Min | Max | Aver | RMS | RMS | RMS | ||

1 | 0 | 129.4 | 544.4 | 307.5 | 321.5 | −437 | −97.7 | −255 | 263.5 | 44 | 271 | 169.7 | 176.6 | 7.67 | 4.48 |

2 | 0.3 | 65.9 | 576.2 | 312.1 | 331.2 | −424.8 | −153.8 | −303.4 | 308.5 | 83 | 300.3 | 183.7 | 188.5 | 7.89 | 5.55 |

3 | 0.8 | 58.6 | 534.7 | 318.3 | 334.9 | −439.5 | −119.6 | −292.3 | 299.8 | 92.8 | 268.6 | 182.9 | 188.6 | 7.93 | 6.03 |

4 | 3.3 | 144 | 561.5 | 345.6 | 357.5 | −427.3 | −95.2 | −249.8 | 261.2 | 48.8 | 271 | 181.4 | 186.8 | 8.73 | 6.87 |

5 | 6.3 | 170.9 | 585.9 | 382 | 391.3 | −432.1 | −31.7 | −208.1 | 223.9 | 53.7 | 271 | 176.3 | 182 | 6.74 | 6.12 |

6 | 9.3 | 188 | 590.8 | 404.9 | 412 | −439.5 | 34.2 | −156.5 | 180.6 | 58.6 | 266.1 | 179.5 | 184.3 | 6.44 | 5.94 |

7 | 11.8 | 175.8 | 625 | 408 | 416.3 | −405.3 | 68.4 | −126.7 | 156.7 | 51.3 | 273.4 | 173.4 | 179.7 | 7.69 | 6.35 |

8 | 12.3 | 266.1 | 605.5 | 431.5 | 435.1 | −363.8 | 90.3 | −99.6 | 141.7 | 114.8 | 297.9 | 187.8 | 191.2 | 7.42 | 6.46 |

9 | 12.6 | 271 | 654.3 | 435.3 | 439.2 | −341.8 | 102.5 | −92.3 | 137.8 | 105 | 295.4 | 187.8 | 191.5 | 9.4 | 6.35 |

© 2019 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**

Pimenov, D.Y.; Hassui, A.; Wojciechowski, S.; Mia, M.; Magri, A.; Suyama, D.I.; Bustillo, A.; Krolczyk, G.; Gupta, M.K. Effect of the Relative Position of the Face Milling Tool towards the Workpiece on Machined Surface Roughness and Milling Dynamics. *Appl. Sci.* **2019**, *9*, 842.
https://doi.org/10.3390/app9050842

**AMA Style**

Pimenov DY, Hassui A, Wojciechowski S, Mia M, Magri A, Suyama DI, Bustillo A, Krolczyk G, Gupta MK. Effect of the Relative Position of the Face Milling Tool towards the Workpiece on Machined Surface Roughness and Milling Dynamics. *Applied Sciences*. 2019; 9(5):842.
https://doi.org/10.3390/app9050842

**Chicago/Turabian Style**

Pimenov, Danil Yurievich, Amauri Hassui, Szymon Wojciechowski, Mozammel Mia, Aristides Magri, Daniel I. Suyama, Andres Bustillo, Grzegorz Krolczyk, and Munish Kumar Gupta. 2019. "Effect of the Relative Position of the Face Milling Tool towards the Workpiece on Machined Surface Roughness and Milling Dynamics" *Applied Sciences* 9, no. 5: 842.
https://doi.org/10.3390/app9050842