# Digitized Stress Function-Based Feed Rate Scheduling for Prevention of Mesoscale Tool Breakage during Milling Hardened Steel

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## Abstract

**:**

## 1. Introduction

## 2. Evaluation of Maximum Thickness and Engaging Angle of the Uncut Chip for Tool Breakage Prediction

## 3. Prediction of the Maximum Tensile Stress in the Cutting Tool

## 4. Feed Rate Scheduling Based on Digitized Maximum Tensile Stress Function and Experimental Validation

#### 4.1. 1st Tool Path with Concave Curvature and Small Radial Cutting Depth

#### 4.2. 2nd Tool Path with Convex Curvature and Large Radial Cutting Depth

## 5. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

FEM | finite element method |

CEL | coupled Eulerian Lagrangian |

MRR | material removal rate |

$r$ | radius of end mill |

${f}_{t}$ | feed per tooth |

${t}_{c}$ | uncut chip thickness |

$\theta $ | angular position of end mill |

${a}_{p}$ | axial cutting depth |

${a}_{e}$ | radial cutting depth |

$N$ | spindle speed |

$TRS$ | transverse rupture strength |

$\alpha $ | uncut chip engaging angle |

${t}_{max}$ | maximum uncut chip thickness |

${\theta}_{entry}$ | tool entry angle respect to instantaneous feed direction |

${f}_{tip}$ | actual feed per tooth experienced by the tip of the end mill |

${S}_{max}$ | maximum tensile stress in the cutting tool |

$c$ | scaling factor for tool stress |

$F$ | feed rate |

${l}_{li}$ | length of transition for linear interpolation |

${l}_{arc}$ | length of transition for arc interpolation |

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**Figure 3.**Cutting process simulated by the 3D coupled Eulerian-Lagrangian (CEL) finite element method (FEM) model.

**Figure 7.**The 1st target contour (solid line) and corresponding tool path (chain line), dimensions in mm.

**Figure 13.**The 2nd target contour (solid line) and corresponding tool path (chain line), dimensions in mm.

Diameter | 3.0 mm | Radius of curvature of clearance face | 1.40 mm |

Helix angle | 30° | Rake angle of bottom cutting edge | 5° |

Rake angle | 16° | Clearance angle of bottom cutting edge | 8° |

Radius of curvature of rake face | 0.57 mm | Cutting edge radius | 10 μm |

Clearance angle | 10° |

No. | ${\mathit{f}}_{\mathit{t}}$ (mm) | ${\mathit{a}}_{\mathit{e}}$ (mm) | ${\mathit{t}}_{\mathit{m}\mathit{a}\mathit{x}}$ (mm) | $\mathit{\alpha}$ (°) | Tensile Stress (GPa) |
---|---|---|---|---|---|

1 | 0.090 | 0.500 | 0.066 | 48.2 | 3.14 |

2 | 0.100 | 0.500 | 0.073 | 48.2 | 3.31 |

3 | 0.110 | 0.500 | 0.080 | 48.2 | 3.62 |

4 | 0.120 | 0.500 | 0.087 | 48.2 | 3.87 |

5 | 0.125 | 0.500 | 0.091 | 48.2 | 4.05 |

6 | 0.130 | 0.500 | 0.094 | 48.2 | 4.20 |

7 | 0.090 | 0.625 | 0.072 | 54.3 | 3.52 |

8 | 0.100 | 0.625 | 0.080 | 54.3 | 3.79 |

9 | 0.110 | 0.625 | 0.088 | 54.3 | 3.97 |

10 | 0.120 | 0.625 | 0.096 | 54.3 | 4.34 |

11 | 0.080 | 0.750 | 0.069 | 60.0 | 3.57 |

12 | 0.090 | 0.750 | 0.077 | 60.0 | 3.63 |

13 | 0.100 | 0.750 | 0.086 | 60.0 | 4.03 |

14 | 0.110 | 0.750 | 0.094 | 60.0 | 4.51 |

15 | 0.080 | 0.875 | 0.072 | 65.4 | 3.78 |

16 | 0.085 | 0.875 | 0.077 | 65.4 | 4.10 |

17 | 0.090 | 0.875 | 0.081 | 65.4 | 4.15 |

18 | 0.095 | 0.875 | 0.086 | 65.4 | 4.37 |

19 | 0.100 | 0.875 | 0.090 | 65.4 | 4.44 |

20 | 0.070 | 1.000 | 0.066 | 70.5 | 3.87 |

21 | 0.075 | 1.000 | 0.070 | 70.5 | 3.97 |

22 | 0.080 | 1.000 | 0.075 | 70.5 | 3.99 |

23 | 0.085 | 1.000 | 0.080 | 70.5 | 4.26 |

24 | 0.090 | 1.000 | 0.085 | 70.5 | 4.51 |

25 | 0.070 | 1.125 | 0.068 | 75.5 | 3.93 |

26 | 0.075 | 1.125 | 0.072 | 75.5 | 4.21 |

27 | 0.080 | 1.125 | 0.077 | 75.5 | 4.41 |

28 | 0.085 | 1.125 | 0.082 | 75.5 | 4.61 |

29 | 0.090 | 1.125 | 0.087 | 75.5 | 4.71 |

30 | 0.070 | 1.250 | 0.069 | 80.4 | 4.33 |

31 | 0.075 | 1.250 | 0.074 | 80.4 | 4.26 |

32 | 0.080 | 1.250 | 0.079 | 80.4 | 4.74 |

33 | 0.085 | 1.250 | 0.084 | 80.4 | 4.67 |

34 | 0.090 | 1.250 | 0.089 | 80.4 | 5.12 |

35 | 0.070 | 1.375 | 0.070 | 85.2 | 4.46 |

36 | 0.075 | 1.375 | 0.075 | 85.2 | 4.45 |

37 | 0.080 | 1.375 | 0.080 | 85.2 | 4.83 |

38 | 0.085 | 1.375 | 0.085 | 85.2 | 4.94 |

39 | 0.090 | 1.375 | 0.090 | 85.2 | 5.27 |

40 | 0.070 | 1.500 | 0.070 | 90.0 | 4.36 |

41 | 0.075 | 1.500 | 0.075 | 90.0 | 4.57 |

42 | 0.080 | 1.500 | 0.080 | 90.0 | 4.84 |

43 | 0.085 | 1.500 | 0.085 | 90.0 | 5.06 |

44 | 0.090 | 1.500 | 0.090 | 90.0 | 5.19 |

A | B | C | D | E | F |
---|---|---|---|---|---|

373.7649 | −0.2070 | 9.0942 | −32.6897 | 1.5759 | 1.9833 |

01. | G90 G00 G54 X-1.5 Y-10. M03 S3000 |

02. | Z10. M07 |

03. | G01 Z-0.3 F900 |

04. | G01 Y2. F991 |

05. | G17 G02 X0.950 Y3.090 I5.5 F1081 |

06. | G02 X1.611 Y5.889 I4.550 J-3.090 F965 |

07. | G03 X5.272 Y14.728 I-8.839 J8.839 F965 |

08. | G01 Y15.828 F991 |

09. | G01 Y16.728 F760 |

10. | G03 X5.126 Y17.081 I-0.5 F760 |

11. | G02 X0. Y29.456 I12.374 J12.37 F1008 |

12. | G01 X-20. |

13. | M09 |

14. | G00 Z50. M05 |

15. | M30 |

01. | G90 G00 G54 X-1.5 Y-10. M03 S3000 |

02. | Z10. M07 |

03. | G01 Z-0.3 F365 |

04. | G01 Y0. |

05. | G17 G03 X-1.699 Y5.263 I-9. F365 |

06. | G03 X-2.636 Y6.364 I-7.301 J-5.263 F321 |

07. | G02 X-3.808 Y9.192 I2.828 J2.828 F321 |

08. | G01 Y9.722 F350 |

09. | G01 Y11.192 F337 |

10. | G02 X-1.025 Y17.910 I9.5 F337 |

11. | G03 X0. Y22.385 I-2.475 J2.475 F393 |

12. | G01 X-20. |

13. | M09 |

14. | G00 Z50. M05 |

15. | M30 |

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**MDPI and ACS Style**

Gao, Y.; Ko, J.H.; Lee, H.P.
Digitized Stress Function-Based Feed Rate Scheduling for Prevention of Mesoscale Tool Breakage during Milling Hardened Steel. *Metals* **2021**, *11*, 215.
https://doi.org/10.3390/met11020215

**AMA Style**

Gao Y, Ko JH, Lee HP.
Digitized Stress Function-Based Feed Rate Scheduling for Prevention of Mesoscale Tool Breakage during Milling Hardened Steel. *Metals*. 2021; 11(2):215.
https://doi.org/10.3390/met11020215

**Chicago/Turabian Style**

Gao, Yifan, Jeong Hoon Ko, and Heow Pueh Lee.
2021. "Digitized Stress Function-Based Feed Rate Scheduling for Prevention of Mesoscale Tool Breakage during Milling Hardened Steel" *Metals* 11, no. 2: 215.
https://doi.org/10.3390/met11020215