# Surface Topography Prediction Model in Milling of Thin-Walled Parts Considering Machining Deformation

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Force and Deformation Model

#### 2.1. Basic Mechanical Model

_{tc}, K

_{rc}and K

_{ac}and the edge force coefficients K

_{te}, K

_{re}and K

_{ae}are defined according to the material properties. The tangential, radial and axial forces of the jth disk with the ith edge are expressed as follows:

#### 2.2. Beam Deflection Model

#### 2.3. Instantaneous Cutting Thickness Model

## 3. Definition of Surface Topography

#### 3.1. Machining Surface Forming

#### 3.2. Surface Topography Model

#### 3.3. Define the Surface Generation Area

## 4. The Surface Topography Simulation

#### 4.1. Surface Topography Simulation Model

#### 4.2. Simulation Model

## 5. Experimental Validation

#### 5.1. Set-Up

#### 5.2. Experimental Validation

_{e}= 0.4, a

_{p}= 6 mm, f = 0.08 mm, S = 1000 rpm) of parameter simulation results, and it can be seen that the tool cutting-out trajectory has obvious deviation and the surface residual height changes.

## 6. Conclusions

- (1)
- Through the cutting force and the beam deformation model, the coupling calculation relationship between force and deformation was established, which can calculate the instantaneous deformation value of the workpiece (deformation value matrix). The instantaneous cutting thickness after deformation was obtained, and the contact relationship between the deformed tool and the workpiece was revealed, which changed the residual height of the machined workpiece surface. The experimental results showed that the error between the milling force prediction model and the measured value was 8.49–17.32%, and the error between the predicted deformation value and the measured deformation value was 7.45%.
- (2)
- The cutting force was calculated according to the tool geometric and cutting parameters. By obtaining the waveform of the force signal, the range of the surface contour generation area and the key angles in the surface generation process were defined as ${\theta}_{2}$, ${\theta}_{3}$ and ${\theta}_{4}$. A new surface formation zone after deformation can be determined by key angles and the deformation value. According to the tool trajectory, the starting point G in the surface formation process was given, which provided judgment conditions for the simulation calculation.
- (3)
- The deformation was introduced into the ideal trajectory, and the deformed tool trajectory was converted to the workpiece surface to form the final surface topography. Through the established three-dimensional surface topography simulation algorithm during the milling of thin-walled parts, the surface roughness, Ra, was obtained as the evaluation index, and the experimental results were compared. The maximum relative error of surface roughness, Ra, was 13.09%, and the average error was 7.45%. The simulation results of surface topography had good similarity with the measured results. This paper provides a reference for the prediction of surface topography and the study of milling mechanisms in side milling of thin-walled parts.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Beam model of the workpiece [37].

**Figure 4.**The waveform of the force signal for a single flute in a period. (

**a**) Type I, (

**b**) Type II and (

**c**) Type III [40].

**Figure 5.**The key angle of surface generation. (

**a**) The key angle selection of cutting force. (

**b**) Display of key angles. The contact relationship of the tool–workpiece affects the waveform of the force signal, which also affects the surface profile of the workpiece. This correlation is applicable to any side milling process.

**Figure 6.**The formation of the peripheral milling surface. (

**a**) The formation of the side milling surface. (

**b**) 2D trajectory of the tool tooth.

**Figure 7.**Surface topography formation area [38].

**Figure 11.**Experimental and simulation comparison of milling force. (

**a**) The 1st set of X-Force. (

**b**) The 1st set of X-Force. (

**c**) The 4th set of X-Force. (

**d**) The 4th set of X-Force. (

**e**) The 6th set of X-Force. (

**f**) The 6th set of X-Force.

**Figure 12.**Comparison of simulation results (a

_{e}= 0.4, a

_{p}= 6 mm, f = 0.08 mm, S = 1000 rpm). (

**a**) The simulation surface topography of the ideal tool path. (

**b**) The first set of parameter simulation results.

**Figure 13.**Measured (

**a**,

**c**,

**e**,

**g**) and simulated (

**b**,

**d**,

**f**,

**h**) surface topographies in Table 2. (

**a**) The 1st set of measurement topography. (

**b**) The 1st set of simulation topography. (

**c**) The 2nd set of measurement topography. (

**d**) The 2nd set of simulation topography. (

**e**) The 3rd set of measurement topography. (

**f**) The 3rd set of simulation topography. (

**g**) The 4th set of measurement topography. (

**h**) The 4th set of simulation topography.

**Figure 14.**The tool moves out of the workpiece position in Table 2. (

**a**) The 5th set of tools move out of the workpiece position. (

**b**) The 6th set of tools move out of the workpiece position.

No. | Radial Cutting Depth, a_{e}/mm | Axial Cutting Depth, a_{p}/mm | Feed Per Tooth, f/mm | Spindle Speed, S/rpm | Prediction Results (μm) | Measuring Results (μm) | Error (%) |
---|---|---|---|---|---|---|---|

1 | 0.4 | 6 | 0.08 | 1000 | 19.1 | 20.1 | 4.9 |

2 | 0.5 | 8 | 0.08 | 1000 | 19.8 | 21.3 | 7 |

3 | 0.6 | 6 | 0.08 | 1000 | 20.7 | 24.8 | 16.5 |

No. | Radial Cutting Depth, a_{e}/mm | Axial Cutting Depth, a_{p}/mm | Feed Per Tooth, f/mm | Spindle Speed, S/rpm | Prediction Results, Ra (μm) | Measuring Results, Ra (μm) | Error (%) |
---|---|---|---|---|---|---|---|

1 | 0.4 | 6 | 0.08 | 1000 | 0.3353 | 0.3792 | 13.09% |

2 | 0.4 | 8 | 0.08 | 1000 | 0.4381 | 0.4602 | 5.04% |

3 | 0.5 | 6 | 0.08 | 1000 | 0.3143 | 0.2902 | −7.67% |

4 | 0.5 | 8 | 0.08 | 1000 | 0.3358 | 0.3765 | 12.12% |

5 | 0.6 | 6 | 0.08 | 1000 | 0.4812 | 0.5257 | 9.25% |

6 | 0.6 | 8 | 0.08 | 1000 | 0.3627 | 0.4093 | 12.85% |

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**MDPI and ACS Style**

Chen, Z.; Yue, C.; Liu, X.; Liang, S.Y.; Wei, X.; Du, Y.
Surface Topography Prediction Model in Milling of Thin-Walled Parts Considering Machining Deformation. *Materials* **2021**, *14*, 7679.
https://doi.org/10.3390/ma14247679

**AMA Style**

Chen Z, Yue C, Liu X, Liang SY, Wei X, Du Y.
Surface Topography Prediction Model in Milling of Thin-Walled Parts Considering Machining Deformation. *Materials*. 2021; 14(24):7679.
https://doi.org/10.3390/ma14247679

**Chicago/Turabian Style**

Chen, Zhitao, Caixu Yue, Xianli Liu, Steven Y. Liang, Xudong Wei, and Yanjie Du.
2021. "Surface Topography Prediction Model in Milling of Thin-Walled Parts Considering Machining Deformation" *Materials* 14, no. 24: 7679.
https://doi.org/10.3390/ma14247679