# Experiment and model of cutting force of heavy-duty milling water chamber head material

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## Abstract

The cyclic impact load of cutting force is one of the main factors that lead to the insert failure during the milling process. According to the asymmetrical heavy-duty milling process of water chamber head, the simulation milling experiments using actual machining parameters are conducted under laboratory conditions, and the change rule of milling force with cutting parameters is analyzed. Moreover, the simulation of interrupted cutting is carried out to study the cycle changes of cutting force and stress distribution of insert during the insert cutting-in and cutting-out workpiece. The dynamic cutting force model is established by considering the irregularity of the cutting area of circular insert and the variation of asymmetric milling thickness. Based on the analysis of comparison between the calculated value of the model and the experimental value, the cutting force model can describe the dynamic change of cutting force in milling process. It is of great significance to analyze and master the changing trend of dynamic cutting force for the study of insert failure and the formulation of reasonable processing parameters in milling process.

## Keywords

Heavy-duty milling Water chamber head Cutting force Cutting simulation Cutting state## List of symbols

*v*_{c}Cutting speed (m/min)

*f*_{z}Feed per tooth (mm/z)

*n*Spindle revolving speed (r/min)

*v*_{f}Feed speed (m/min)

*a*_{p}Axial cutting depth (mm)

*a*_{e}Radial cutting depth (mm)

*γ*_{f}Side rake angle (degree)

*γ*_{p}Back rake angle (degree)

*κ*_{r}Cutting edge angle (degree)

*δ*Cutting-in angle (degree)

*θ*Cutting-out angle (degree)

*γ*_{0}Rake angle (degree)

*α*_{0}Relief angle (degree)

*F*_{c}Main cutting force (N)

*F*_{f},Feed direction cutting force (N)

*F*_{p}Depth direction cutting force (N)

*τ*_{s}Shear stress (MPa)

*F*_{sh}Shear force (N)

*A*_{s}Main shear area (mm

^{2})*A*_{D}Cutting area (mm

^{2})- \(A_{D}^{{\prime }}\)
Cutting area based on asymmetric milling (mm

^{2})*β*Friction angle (degree)

*ϕ*Shear angle (degree)

*h*_{D}Cutting thickness (mm)

*θ*_{0,}*θ*_{1,}*θ*_{2}Used to calculate cutting area

*A*_{D}(degree)*θ’*Cutter position angle based on asymmetric milling (degree)

- \(\theta_{0}^{{\prime }} ,\theta_{1}^{{\prime }} ,\theta_{2}^{{\prime }}\)
Used to calculate cutting area \(A_{D}^{{\prime }}\) based on asymmetric milling (degree)

*R*Radius of circular insert (degree)

*R*_{c}Cutter diameter (mm)

- \(h_{D}^{{\prime }}\)
Cutting thickness based on asymmetric milling (mm)

- \(f_{z}^{{\prime }}\)
Feed per tooth based on asymmetric milling (mm/z)

## 1 Introduction

At present, the main principles of the modeling of cutting force are model based on the stress–strain relationship of workpiece material and cutting mechanics; the mechanical model of irregular cutting area established by means of unit cutting force integral; the model built by artificial neural networks [5]. Adem et al. [6] proposed a linear and nonlinear mathematical force model for end milling verified by experiment. Hao et al. [7] proposed a new method for predicting milling force of surface with variable curvature. Matsumura et al. [8] established the prediction model of cutting force based on chip flow model and energy dissipation model in the milling process of complex shape section. Dong et al. [9] predicted the cutting forces during milling thin-walled part using different diameter milling cutters. Ghorbani et al. [10] established the milling force model of circular insert adopting the method of unit cutting force coefficient. Lee et al. [11] considered the friction of the cutting edge, proposed the cutting edge force of the cutting edge, and improved the mechanical model of the cutting force. Wang et al. [12] studied the three-dimensional cutting force prediction model of spiral edge milling cutter based on Merchant oblique cutting theory. Dang et al. [13] established planar milling force model considering both the bottom and side edges, and they had the conclusion that the cutting force of the bottom edge is proportional to the edge length.

Liu et al. [14, 15, 16] based on the geometric analysis of ball end milling cutter and the principle of orthogonal cutting, considering the size effect of undeformed chip thickness and the effect of effective rake angle, proposed an improved theoretical dynamic cutting force model. In the further experimental verification and application of the above model, it is found that the cutting vibration has an important influence on the dynamic cutting force. Therefore, considering the influence of the tool vibration on the machined surface, the theoretical model is improved. In order to ensure the integrity of machining dynamics, the influence of cutting parameters and the vibration of tool and workpiece on the cutting force is considered comprehensively. The dynamic simulation model is established by using Simulink software and verified by experiments. Saffar et al. [17] researched the three-dimensional cutting force and deformation of milling cutter by using the finite element simulation and experiment method, and determined that the simulation method can be used to predict the cutting force and cutter deformation. Boyd et al. [18] improved the prediction of cutting force through orthogonal cutting simulation and measured heat-mechanical load.

Generally, the established milling force models didn’t indicate the change of cutting thickness in the cutting-in and cutting-out process, thus it was not possible to accurately describe the change of cutting force during interrupted cutting process. The dynamic milling force model was established based on the change of cutting thickness during asymmetric milling process of water chamber head material with method of cutting force experiments and intermittent cutting simulation. The results can provide basis for the research of insert failure.

## 2 Milling experiments of water chamber head material

### 2.1 Design of milling test scheme

*v*

_{c}and feed per tooth

*f*

_{z}are consistent with the actual cutting parameters. However, the feed speed of conventional milling machine in the laboratory cannot meet the requirements because of the high speed of heavy-duty milling. Thus, only two teeth are installed on the cutter for simulation experiment, which make the feed per tooth

*f*

_{z}consistent with the actual processing conditions, and avoid feed speed exceeding the parameters of conventional milling machine.

Milling experimental conditions

Cutting method | Heavy-duty milling | Simulation milling |
---|---|---|

Cutter diameter (mm)/number of teeth | 200/10 | 100/2 |

Cutting speed | 250/398 | 250/796 |

300/478 | 300/955 | |

350/557 | 350/1115 | |

Feed speed | 1/0.21 | 0.402/0.21 |

1.4/0.3 | 0.574/0.3 | |

1.8/0.38 | 0.726/0.38 | |

Axial cutting depth | 2 | 2 |

Radial cutting depth | 100 | 50 |

Cutter type | WIDIA M4000D200Z10ADJ | ZCCC FMR04-100-B32-RD16-06 |

Insert type | WIDIA RCMT1606M043M | WIDIA RDMT1605MOTX |

### 2.2 Analysis of experimental results

*v*

_{c}= 300 m/min and axial cutting depth

*a*

_{p}= 2 mm, the experimental values of the cutting force under different feeds are shown in Fig. 4.

*f*

_{z}= 0.3 mm/z and axial cutting depth

*a*

_{p}= 2 mm, the experimental values of the cutting force under different cutting speeds are shown in Fig. 5. The increase of feed per tooth leads to the increase of cutting area, so the cutting force is increasing. From the experimental value, it can get that the cutting force increased by about 29% when the feed per tooth is

*f*

_{z}= 0.38 mm/z relative to

*f*

_{z}= 0.21 mm/z. As the cutting speed increases, the cutting force decreases slightly. Through the analysis of experimental data, it can know that when the cutting speed

*v*

_{c}= 350 m/min, the cutting force is 10% less than that of

*v*

_{c}= 250 m/min.

## 3 Research on cutting state of insert during interrupted cutting

### 3.1 Determination of cutting-in and cutting-out type of insert

*δ*of cutter is close to 0°. By measuring the tool angle, side rake angle is

*γ*

_{f}= 4.88°, back rake angle is

*γ*

_{p}= 8.77°. Since the insert is round, the average cutting edge angle

*κ*

_{r}= arcsin (

*a*

_{p}/2

*R*)

^{1/2}= 20.7° was adopted. And side rake angle

*γ*

_{f}> cutting-in angle

*δ*= 3°. The discriminant of cutting-in type is Eq. (1):

According to the discriminant (1), it can be concluded that cutting-in type of insert is *S* type, as shown in Fig. 6b). The cutting-in point of insert is on the cutting edge. In the cutting-out process of interrupted cutting, the shear mechanism changes greatly and the shear direction is deflected. The cutting thickness of insert in the cutting-out location is gradually reduced because of asymmetric milling which causes cutting-out angle *θ* is less than 90°, as shown in Fig. 6c). Shear angle is deflected in the cutting-out process, and it can cause stress field change, cutting-out breakage and initiation and extension of cracks of insert. The shear angle deflection causes the load of rake face to be concentrated on cutting edge, which leads to instant increase of the stress of the cutting edge and the chance of the cutting edge breaking.

### 3.2 Simulation of stress-temperature distribution of insert

*v*

_{c}= 300 m/min,

*f*

_{z}= 0.3 mm/z,

*a*

_{p}= 2 mm. Cutting-out angle is

*θ*= 30°. Rake angle of insert is

*γ*

_{0}= 10°, and relief angle is

*α*

_{0}= 7°. Insert basis material is P-type cemented carbide, and coating is TiAlN material.

*S*type, and the stress is concentrated on the cutting edge, the cutting edge gradually contacts the workpiece. When the insert is cutting in the workpiece completely, the cutting force and the stress of cutting part of the insert reach the maximum. When the cutting state is stable, the cutting force decreased slightly and gradually stabilized. Cutting temperature of insert experiences gradual rise and maintains a smooth process. When the insert is cutting out the workpiece, cutting-out angle is very small. Although there is no negative shear phenomenon, the shear angle still has a deflection, and minimum shear angle is close to 0°. The insert-chip contact length becomes shorter, cutting force is focused on cutting edge, which is easy to cause cutting-out breakage of insert. The insert is subjected to cyclic loading during the interrupted cutting process, and the cutting force changed from 0 to about 1500 N.

## 4 Establishment of dynamic cutting force model

According to the dynamic response characteristics of the cutting process [19], the spindle of the machine tool drives the insert cuts into the workpiece material. Shear and extrusion are formed in the main shear zone where has shear strain. The cutting force of insert can be calculated through shear stress in the main shear zone. In order to calculate the load on the insert, based on the force relationship in the orthogonal cutting theory [20], the geometric shape and the force situation of the tool are assumed: (1) the cutting edge of the insert is assumed to be a straight edge, regardless of the friction force in the third deformation zone; (2) the normal stress *σ*_{s} and shear stress *τ*_{s} in the shear plane are assumed to be fixed; (3) It is assumed that the force applied on the chip and tool contact area is a pair of equilibrium forces with the resultant force applied on the shear plane.

*F*

_{c}, feed direction cutting force

*F*

_{f}, and depth direction cutting force

*F*

_{p}.

*τ*

_{s}in main shear area. Firstly, we can calculate shear force

*F*

_{sh}as follow:

*F*

_{sh}and

*τ*

_{s}are shear force and shear stress in the main shear zone;

*A*

_{s}is the area of the main shear area;

*A*

_{D}is the area of the cutting area.

*β*is the friction angle;

*γ*

_{0}is the rake angle;

*ϕ*is the shear angle.

*h*

_{D}of the insert is constantly changing. An integral method is used to calculate the cutting area:

*R*is the radius of circular insert.

*θ*

_{0},

*θ*

_{1}and

*θ*

_{2}in Fig. 11 can be expressed respectively by:

*θ*

_{0}≤

*θ*≤

*θ*

_{1}, ρ = OB. In the case of

*θ*

_{1}≤

*θ*≤

*θ*

_{2}, ρ = OA. ρ can be expressed by:

*A*

_{D}is divided into two parts by Angle

*θ*

_{1}, so Eq. (4) can be expressed as:

*h*is equal to

*R*subtract

*a*

_{p}.

*A*

_{D}in Eq. (9) is calculated based on feed per tooth

*f*

_{z}. Substituting the above formula into Eq. (3), the cutting force of the cutting area

*A*

_{D}can be calculated. Due to the asymmetric milling process of water chamber head, the cutting area of the insert is constantly changing with the rotation of the cutter, as shown in Fig. 12a). The cutting thickness is reduced to zero in the cutting-out workpiece, and the cutting trajectory of the cutter is similar to the cutting area figure of Fig. 11. When the position angle of cutter tooth is \(\theta_{0}^{\prime}\), the insert cuts in the workpiece by type

*S*, and the cutting in point is shown in Fig. 12b). The equation of \(f_{Z}^{\prime}\) in cutting process is:

*R*

_{c}is cutter diameter;

*a*

_{e}is radial cutting depth of cutter; \(\theta^{\prime}\) is position angle of cutter tooth. The Eq. (11) is substituted in Eq. (5), and the dynamic three angles are calculated respectively.

*f*

_{z}with \(f_{z}^{\prime}\) in Eqs. (5) and (9), the calculation formula of the instantaneous cutting area of the insert is obtained:

Cutting conditions and model parameters

Physical quantity | Value | Physical quantity | Value | ||
---|---|---|---|---|---|

| 0.21 | 0.3 | 0.38 |
| 8 |

| 49.7 | 50.3 | 50.7 |
| 498 |

| 44.6 | 38.9 | 29.4 |
| 2 |

| 27.7 | 30.5 | 35.3 |
| 48.6 |

## 5 Conclusions

- 1.
The cutting speed was 300 m/min, feed rate of each tooth was 0.3 mm, and axial cutting depth was 2 mm during heavy-duty milling of water chamber head. The maximum main cutting force reaches 1050 N in the milling process. The cutting force increased with the increase of feed rate of each tooth. The increase of cutting speed had little effect on the cutting force.

- 2.
When the insert was cutting into workpiece, main cutting edge was the first contact with the workpiece, and the stress was concentrated on the cutting edge. In the process of cutting out, the shear angle was deflected and decreased, and the stresses gradually converged to the cutting edge. The above conditions were provided for insert breakage.

- 3.
The calculation method of irregular cutting area of circular insert was presented during asymmetric milling with the goal of establishing mathematical model of dynamic cutting force of circular insert in asymmetric milling process. The dynamic cutting forces were calculated by using different position angles of cutter teeth. The model was verified by experiment value. The calculated value of the model can be used to represent the change of cutting force during milling process.

## Notes

### Funding

This research was financially supported by National Natural Science Foundation of China (No. 51675145).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no competing interests.

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