# Comparative Study of Chip Formation in Orthogonal and Oblique Slow-Rate Machining of EN 16MnCr5 Steel

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

_{s}and γ

_{o}). Hereby, a new method of obtaining chip roots has been designed. The new method can be used to prevent changes in the microstructure of material by demonstrating a non-deformed and thermally uninfluenced chip root.

## 3. Materials and Methods

#### 3.1. Cutting Tools, Machined Material, and Measuring Equipment

_{c}, cutting depth a

_{p}, tool angles λ

_{s}, and γ

_{o}, were used in the experiments. The range of values was chosen based on industrial requirements. It is necessary to point out that lowest value of cutting speed was based on the speed limitations of the machine, where the highest value corresponds to 60% of the machine power. The range of cutting depth values a

_{p}was given by the planing machine, while the limitations were connected with a maximal cross-section of a chip. The values of rake angle γ

_{o}were positive, in order to achieve the lowest possible specific cutting resistance values. The maximum angle value γ

_{o}was selected in view of achieving sufficient bending strength of the cutting wedge. The angle of tool cutting edge inclination λ

_{s}was chosen from zero up to a value that is four times higher than is commonly used in practice, in order to make the extent of the dependence under investigation large enough.

_{s}= 0°, 10°, and 20°. The used cutting tools and their geometries are presented in Table 1.

_{o}and the angle of tool orthogonal clearance α

_{o}have been varied in the 2nd and 3rd phase of experiments to obtain a better view of chip formation and more reliable results. Changes in the angles’ values are organized in Table 2.

_{o}, preliminary input tests were performed. The tests were carried out using 3D measuring equipment RAPID CNC THOME (Zimmer Maschinenbau GmbH, Kufstein, Austria) that is shown in Figure 3, where details of the measuring process are also presented.

_{o}was measured for each of the cutting tools used. The protocols from measurements confirmed the values listed in Table 1 and Table 2, while the deviation of all measured values did not exceed 5% and the average angles of tool orthogonal rake for planing necking tools and straight roughing tools were γ

_{o}= 8.138 = 8°2´0´´ or γ

_{o}= 3.159 = 3°2´1´´, respectively.

^{−2}and a good carrying resistance, e.g., piston bolts, camshafts, levers, and other automobile and mechanical engineering add-ons. The chemical composition of this steel, as given by European EN standards, has been verified by spectral analysis at the FMT TU Kosice with the seat in Presov, and is presented in Table 3.

#### 3.2. Design of the Composite Plan of the Experiment

- Y—column vector of measured quantities,
- X—matrix of independent variables,
- b—coefficient of a regression function.

^{T}Y = X

^{T}X b,

^{T}X

^{−1}X

^{T}Y.

^{k}, where k is a number of variables and N is a number of measures (e.g., considering 5 variables within an experiment, where 243 measurements should be performed in total because N = 3

^{5}= 243). [45]

_{j}is a variable (in the case of presented research it is one of the cutting parameters that will be varied), j, u are indexes that define a parameter, and b

_{j}is a j-th correlation coefficient.

- A core of plan that can be
- two-level 2
^{k}plan for k < 5, or as - shortened replica 2
^{k-p}for k ≥ 5, where p is a level of significance (Grubbs’ test);

- The star points α with coordinates: (±α, 0, ..., 0); (0, ±α, 0, ..., 0); ...; (0, 0, ..., 0, ±α);
- The measurements done at the basic level; or in the middle of the plan at x
_{1}= x_{2}= ... = x_{k}= 0 (the number of measurements in the middle of the plan is n_{0}).

^{k}+ 2k + n

_{0}, if k < 5, or

N = 2

^{k-p}+ 2k +n

_{0}, if k ≥ 5.

_{0}= 1 [48] is chosen, with no boundary. The matrix of the orthogonal composition plan for k, α, and n

_{0}is given in Table 4. In its general form, it is not orthogonal because the relations on the left sides of Equations (6) and (7) differ from zero:

- m—a number of evaluated measurements within the Grubbs´ test;
- T
_{ik}—measured value of k-th issue in the i-th group, k = 1, 2, 3; i = 1, 2, ..., 24, 25; - $\overline{{T}_{i}}$—average value of measured issues of the i-th group; calculation according to the equation;
- S
_{Ti}—standard deviation of measured issue of the i-th group; - H
_{p}(m)—critical value of Grubbs´ testing criteria for m values (m = 3), where p is a level of significance and usually it is H_{p}(m) = 0.05.

_{1}, f

_{2}), where the degrees of freedom f

_{1}= Nq (q is a number of significant coefficients) and f

_{2}= N(m − 1).

#### 3.3. Process of Obtaining Samples

## 4. Results and Discussion

#### 4.1. Types of Chips

_{c}and cutting depth a

_{p}at tool angles for γ

_{o}= 16°, λ

_{s}= 0°, κ

_{r}= 0°.

_{o}at the minimum values caused formation of a crumbly chip and the angle of inclination of the main cutting edge λ

_{s}has influenced the chip shape in the way that is graphically presented in Figure 7.

_{s}inclination and acquired the character of a spiral chip. In orthogonal cutting, at which κ

_{r}= 0° and λ

_{s}= 0°, a spiral flat chip was formed, which in some cases passed into a spiral conical chip. For κ

_{r}= 0° and λ

_{s}= 20°, a conical–helical long chip was constituted. In oblique cutting, where κ

_{r}= 60° and λ

_{s}= 0°, a conical–helical short chip was generated. At κ

_{r}= 60° and λ

_{s}= 20°, the chip shape changed to a coiled chip, while at a rake angle γ

_{o}= 11°, it was a tubular coiled chip and at γ

_{o}= 3° it was a strip coiled chip.

_{c}at the planing can be calculated with Equations (20) and (21), respectively, where h

_{c}is the chip width, a

_{p}is cutting depth, γ is the tool rake angle, and Φ is the shear angle [1,12,50,51]:

#### 4.2. Temperature Measuring

_{0,05}(f

_{1}, f

_{2}), given by [22], is G

_{0.05}(f

_{1},f

_{2}) = 0.2705, where the degrees of freedom were f

_{1}= N = 25 and f

_{2}= m − 1 = 3 − 1 = 2.

^{2}= 0.91 and 0.94, respectively:

- a)
- For orthogonal cutting:$$\begin{array}{l}y=3.2502{x}_{0}-3.7533{x}_{1}+3.1462{x}_{2}+4.2035{x}_{3}-0.1865{x}_{4}-0.1553{x}_{1}{x}_{2}\\ \hspace{1em}\hspace{1em}\hspace{1em}+0.3467{x}_{1}{x}_{3}+0.0385{x}_{1}{x}_{4}+0.4106{x}_{2}{x}_{3}-0.0202{x}_{2}{x}_{4}\\ \hspace{1em}\hspace{1em}\hspace{1em}+0.0304{x}_{3}{x}_{4}+1.6486{x}_{1}^{2}+3.1542{x}_{2}^{2}-2.8264{x}_{3}^{2}-0.042{x}_{4}^{2}\end{array}$$
- b)
- For oblique cutting:$$\begin{array}{l}y=2.9212{x}_{0}-10.4247{x}_{1}-7.2462{x}_{2}+4.4859{x}_{3}+0.1295{x}_{4}-0.4264{x}_{1}{x}_{2}\\ \hspace{1em}\hspace{1em}\hspace{1em}-0.2621{x}_{1}{x}_{3}+0.0625{x}_{1}{x}_{4}+0.5108{x}_{2}{x}_{3}+0.0251{x}_{3}{x}_{4}\\ \hspace{1em}\hspace{1em}\hspace{1em}+5.4295{x}_{1}^{2}-6.6225{x}_{2}^{2}-2.6781{x}_{3}^{2}+0.0676{x}_{4}^{2}\end{array}$$

- The dependency of temperature T on cutting speed v
_{c}and on the cutting depth a_{p}; - The dependency of temperature T on cutting speed v
_{c}and angle of tool orthogonal rake γ_{o}; - The dependency of temperature T on cutting speed v
_{c}and on the angle of tool cutting edge inclination λ_{s}.

_{o}at the machining of manganese chromium steel has a similar character in both cutting methods (Figure 9), while the highest values of temperature have been measured at mean values of γ

_{o}. The influence of cutting speed also has the same character at both orthogonal and oblique cutting, and the maximum temperature has been reached at the minimal value of cutting speed.

_{s}on the temperature is almost identical in both orthogonal and oblique cutting (Figure 10). The influence tool cutting edge inclination is almost imperceptible in both cases compared to the impact of speed.

#### 4.3. Measurement of Microhardness HV According to Vickers

^{2}of the dependencies for both types of machining (orthogonal and oblique) were 0.92 and 0.93, respectively. Regression functions are specified by the following equations:

- a)
- For orthogonal cutting:$$\begin{array}{l}y=-5.0009{x}_{0}+17.2807{x}_{1}+5.2179{x}_{2}0.575{x}_{3}+0.1881{x}_{4}-1.5626{x}_{1}{x}_{2}\\ \hspace{1em}\hspace{1em}\hspace{1em}-0.1588{x}_{1}{x}_{3}+0,0397{x}_{1}{x}_{4}-0.2036{x}_{2}{x}_{3}-0.0623{x}_{2}{x}_{4}\\ \hspace{1em}\hspace{1em}\hspace{1em}-0.0376{x}_{3}{x}_{4}-9.2084{x}_{1}^{2}+3.3134{x}_{2}^{2}-0.4774{x}_{3}^{2}+0.0915{x}_{4}^{2}\end{array}$$
- b)
- For oblique machining:$$\begin{array}{l}y=-1.2673{x}_{0}+7.7671{x}_{1}+9.0532{x}_{2}+5.5376{x}_{3}+0.2281{x}_{4}+0.7224{x}_{1}{x}_{2}\\ \hspace{1em}\hspace{1em}\hspace{1em}-0.2077{x}_{1}{x}_{3}+0.0846{x}_{1}{x}_{4}-0.6964{x}_{2}{x}_{3}-3.6942{x}_{1}^{2}+8.2721{x}_{2}^{2}\\ \hspace{1em}\hspace{1em}\hspace{1em}-3.8696{x}_{3}^{2}+0.1162{x}_{4}^{2}\end{array}$$

## 5. Conclusions

- The effect of the change in cutting speed in a given experiment on the chip shape appeared to be insignificant.
- The angle of the orthogonal tool rake caused a crumbly chip formation at minimum values, rather than at the maximum values.
- The cutting depth affected the radius of curvature of the chip. When increasing the thickness of the cut layer, the radius of chip curvature increased.

_{s}and the tool cutting edge angle κ

_{r}. At a zero angle of inclination of the main cutting edge, a shorter chip was produced than at an angle of inclination of the main cutting edge of 20°. At the same time, at a 20° angle of inclination of the cutting edge, the chip obtained a so-called chamfer along the edges, which is adequate to the angle of inclination of the main cutting edge, thus compressing the chip in the inclination direction of λ

_{s}leading to the shape obtaining characteristics of a spiral chip.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

γ_{o} | angle of tool orthogonal rake (°) |

λ_{s} | angle of tool cutting edge inclination (°) |

α_{o} | angle of tool orthogonal clearance (°) |

κ_{r} | tool cutting edge angle (°) |

κ_{r}´ | tool minor (end) cutting edge angle (°) |

ε_{r} | tool included angle (°) |

Φ | shear angle (°) |

a_{p} | depth of cut (mm) |

v_{c} | cutting speed (mmin^{−1}) |

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**Figure 3.**Preliminary tests of input angles of tool orthogonal rake γ

_{o}, (

**a**) Overall view on the testing equipment RAPID CNC THOME, (

**b**) Detail view on the measuring of a tool orthogonal rage angle.

**Figure 5.**The principle of the designed method for instantaneous contact interruption between a tool and workpiece showing (

**a**) orthogonal cutting, (

**b**) oblique cutting, (

**c**) real workpiece.

**Figure 6.**The shapes of chips and their dependence on cutting speed v

_{c}and cutting depth a

_{p}at tool angles for γ

_{o}= 16°, λ

_{s}= 0°, κ

_{r}= 0°.

**Figure 7.**The shapes of chips of EN 16MnCr5 steel and their dependence on tool cutting edge angle κ

_{r}, angle of tool cutting edge inclination λ

_{s}, and angle of tool orthogonal rake γ

_{o}at a

_{p}= 0.2 mm, v

_{c}= 15 mmin

^{−1.}

**Figure 8.**The dependence of temperature T on cutting speed v

_{c}and cutting depth a

_{p}, (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 9.**The dependence of temperature T on cutting speed v

_{c}and angle of tool orthogonal rake γ

_{o}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 10.**The dependence of temperature T on cutting speed v

_{c}and angle of tool cutting edge inclination λ

_{s}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 12.**Dependency of microhardness HV on the cutting speed v

_{c}and on the cutting depth a

_{p}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 13.**Dependency of microhardness HV on the cutting speed v

_{c}and on the orthogonal rake angle γ

_{o}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 14.**Dependency of microhardness HV on the cutting speed v

_{c}and on the angle of tool cutting edge inclination λ

_{s}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 15.**Dependency of microhardness HV on the cutting depth a

_{p}and on the orthogonal rake angle γ

_{o}. (

**a**) Orthogonal cutting; (

**b**) oblique cutting.

**Figure 16.**Dependency of microhardness HV on the cutting depth a

_{p}and on the angle of tool cutting edge inclination λ

_{s}

_{.}(

**a**) Orthogonal cutting; (

**b**) oblique cutting.

Tool Angle | Planing Necking Tool | Straight Roughing Tool | ||
---|---|---|---|---|

κ_{r}—tool cutting edge angle | 0° | 60° | ||

κ_{r}´—tool minor (end) cutting edge angle | - | 20° | ||

ε_{r}—tool included angle | - | 100° | ||

γ_{o}—angle of tool orthogonal rake | 8° | 3° | ||

α_{o}—angle of tool orthogonal clearance | 15° | 15° | ||

λ_{s}—angle of tool cutting edge inclination | 0° | 0° | ||

10° | 10° | |||

20° | 20° |

Changes in Angles | |||
---|---|---|---|

2nd phase | γ_{o} | 12° | 7° |

α_{o} | 11° | 11° | |

3rd phase | γ_{o} | 16° | 11° |

α_{o} | 7° | 7° |

Steel | C (%) | Mn (%) | Si (%) | Cr (%) | P (%) | S (%) |
---|---|---|---|---|---|---|

EN 16MnCr5 | 0.14–0.19 | 1.10–1.40 | 0.17–0.37 | 0.80–1.10 | max 0.035 | max 0.035 |

N | x_{o} | x_{1} | x_{2} | … | x_{k} | Description |
---|---|---|---|---|---|---|

2^{k} (k < 5) or 2^{k-p} (k > 5) | +1 | −1 | −1 | … | −1 | a core of the plan |

+1 | +1 | −1 | … | −1 | ||

+1 | −1 | +1 | … | −1 | ||

+1 | +1 | +1 | … | −1 | ||

+1 | −1 | −1 | … | +1 | ||

+1 | +1 | −1 | … | +1 | ||

+1 | −1 | +1 | … | +1 | ||

+1 | +1 | +1 | … | +1 | ||

2k | +1 | −α | 0 | … | 0 | the star points of the plan |

+1 | +α | 0 | … | 0 | ||

+1 | 0 | −α | … | 0 | ||

+1 | 0 | +α | … | 0 | ||

+1 | 0 | 0 | … | −α | ||

+1 | 0 | 0 | … | +α | ||

n_{0} | +1 | 0 | 0 | … | 0 | the measurements in the middle of the plan |

+1 | 0 | 0 | … | 0 | ||

+1 | 0 | 0 | … | 0 |

Variables | Symbols | −1 | −α | 0 | +α | +1 | |
---|---|---|---|---|---|---|---|

Cutting speed (mmin^{−1}) | v_{c} | x_{1} | 6 | 8.25 | 10.5 | 12.75 | 15 |

Cutting depth (mm) | a_{p} | x_{2} | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 |

Angle of tool orthogonal rake – orthogonal cutting (°) | γ_{o} | x_{3} | 8 | 10 | 12 | 14 | 16 |

Angle of tool orthogonal rake – oblique cutting (°) | γ_{o} | (x_{3}) | 3 | 5 | 7 | 9 | 11 |

Angle of tool cutting edge inclination (°) | λ_{s} | x_{4} | 0 | 5 | 10 | 15 | 20 |

Code | Specific Values of Variables |
---|---|

−1 | x_{min} |

−α | [(x_{max} + x_{min})/2] − [(x_{max} − x_{min})/2α^{2}] |

0 | (x_{max} + x_{min})/2 |

+α | [(x_{max} + x_{min})/2] + [(x_{max} − x_{min})/2α^{2}] |

+1 | x_{max} |

Type of Cutting | Shear Angle Φ (°) | Shrinkage Factor K |
---|---|---|

Orthogonal cutting | 31.7 | 1.75 |

42.2 | 1.3 | |

Oblique cutting | 30.2 | 1.77 |

42.4 | 1.21 |

**Table 8.**Experimentally obtained values of temperature in cutting zone for orthogonal and oblique machining of EN 16MnCr5 steel.

No. | v_{c} (m∙min^{−1}) | a_{p} (mm) | γ_{o} (°) | λ_{s} (°) | T (°C) | |
---|---|---|---|---|---|---|

Orthogonal Cutting | Oblique Cutting | |||||

1. | −1 | −1 | −1 | −1 | 86.8 | 63.8 |

2. | +1 | −1 | −1 | −1 | 58.7 | 63.0333 |

3. | −1 | +1 | −1 | −1 | 72.5333 | 55.2333 |

4. | +1 | +1 | −1 | −1 | 66.4667 | 48.8 |

5. | −1 | −1 | +1 | −1 | 78.5333 | 40.5333 |

6. | +1 | −1 | +1 | −1 | 50.3333 | 41.1333 |

7. | −1 | +1 | +1 | −1 | 69.9 | 46.5 |

8. | +1 | +1 | +1 | −1 | 51.5 | 48 |

9. | −1 | −1 | −1 | +1 | 72.2333 | 50 |

10. | +1 | −1 | −1 | +1 | 68.3333 | 96.6 |

11. | −1 | +1 | −1 | +1 | 73 | 62.8667 |

12. | +1 | +1 | −1 | +1 | 38.9667 | 72.8333 |

13. | −1 | −1 | +1 | +1 | 61.3667 | 62.8333 |

14. | +1 | −1 | +1 | +1 | 70.8 | 60.8333 |

15. | −1 | +1 | +1 | +1 | 62.6 | 61.7 |

16. | +1 | +1 | +1 | +1 | 72.3667 | 67.9333 |

17. | −α | 0 | 0 | 0 | 103 | 45.1 |

18. | +α | 0 | 0 | 0 | 90.6667 | 95.5333 |

19. | 0 | −α | 0 | 0 | 85.3333 | 74.5667 |

20. | 0 | +α | 0 | 0 | 93.3 | 62.9333 |

21. | 0 | 0 | −α | 0 | 94 | 99.2333 |

22. | 0 | 0 | +α | 0 | 74.8 | 61.3 |

23. | 0 | 0 | 0 | −α | 91.1333 | 57.3333 |

24. | 0 | 0 | 0 | +α | 72.3 | 84.7667 |

25. | 0 | 0 | 0 | 0 | 79.3 | 62.8333 |

**Table 9.**Experimentally obtained values of microhardness HV measured in the area of the shear angle at chips.

No. | v_{c} (mmin^{−1}) | a_{p} (mm) | γ_{o} (°) | λ_{s} (°) | HV (kgmm^{−2}) | |
---|---|---|---|---|---|---|

Orthogonal Cutting | Oblique Cutting | |||||

1. | −1 | −1 | −1 | −1 | 218.567 | 337.267 |

2. | +1 | −1 | −1 | −1 | 268.833 | 232.667 |

3. | −1 | +1 | −1 | −1 | 308.4 | 400.1 |

4. | +1 | +1 | −1 | −1 | 253.933 | 281.767 |

5. | −1 | −1 | +1 | −1 | 240.9 | 293.9 |

6. | +1 | −1 | +1 | −1 | 238.533 | 221.2 |

7. | −1 | +1 | +1 | −1 | 330.533 | 270.733 |

8. | +1 | +1 | +1 | −1 | 204.6 | 216.267 |

9. | −1 | −1 | −1 | +1 | 216.767 | 211.067 |

10. | +1 | −1 | −1 | +1 | 319.367 | 229.7 |

11. | −1 | +1 | −1 | +1 | 293.733 | 233.167 |

12. | +1 | +1 | −1 | +1 | 196.667 | 363.533 |

13. | −1 | −1 | +1 | +1 | 184.9 | 245.767 |

14. | +1 | −1 | +1 | +1 | 213.933 | 190.367 |

15. | −1 | +1 | +1 | +1 | 160.7 | 192.667 |

16. | +1 | +1 | +1 | +1 | 165,367 | 216.833 |

17. | −α | 0 | 0 | 0 | 239.9 | 273.233 |

18. | +α | 0 | 0 | 0 | 230.2 | 237.9 |

19. | 0 | −α | 0 | 0 | 270.867 | 254.9 |

20. | 0 | +α | 0 | 0 | 321.533 | 318.433 |

21. | 0 | 0 | −α | 0 | 301.333 | 329.567 |

22. | 0 | 0 | +α | 0 | 271.967 | 194.767 |

23. | 0 | 0 | 0 | −α | 265.667 | 167.1 |

24. | 0 | 0 | 0 | +α | 448.367 | 279.7 |

25. | 0 | 0 | 0 | 0 | 301.2 | 305.533 |

© 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**

Monkova, K.; Monka, P.P.; Sekerakova, A.; Hruzik, L.; Burecek, A.; Urban, M.
Comparative Study of Chip Formation in Orthogonal and Oblique Slow-Rate Machining of EN 16MnCr5 Steel. *Metals* **2019**, *9*, 698.
https://doi.org/10.3390/met9060698

**AMA Style**

Monkova K, Monka PP, Sekerakova A, Hruzik L, Burecek A, Urban M.
Comparative Study of Chip Formation in Orthogonal and Oblique Slow-Rate Machining of EN 16MnCr5 Steel. *Metals*. 2019; 9(6):698.
https://doi.org/10.3390/met9060698

**Chicago/Turabian Style**

Monkova, Katarina, Peter Pavol Monka, Adriana Sekerakova, Lumir Hruzik, Adam Burecek, and Marek Urban.
2019. "Comparative Study of Chip Formation in Orthogonal and Oblique Slow-Rate Machining of EN 16MnCr5 Steel" *Metals* 9, no. 6: 698.
https://doi.org/10.3390/met9060698