# Cutting Force When Machining Hardened Steel and the Surface Roughness Achieved

^{*}

## Abstract

**:**

^{−1}, the feed rates of 0.05 and 0.1 mm·rev

^{−1}and the cutting widths of 0.2 and 0.35 mm, were evaluated The evaluation assessed the surface quality by both touch and non-touch methods. A structural equation with the appropriate constants and exponents was then constructed from the data obtained using the dynamometer. The experiment confirmed the potential of achieving a value of the average arithmetic profile deviation Ra in the range of 0.3–0.4 when turning hardened steels with cubic boron nitride.

## 1. Introduction

^{−1}, with a feed rate of 0.3 mm·rev

^{−1}and a depth of cut of 0.1 mm. In addition, uncoated CBN was also used as a substrate for the (Ti, Al) N coating. Hanel et al. [12] tested an ultra-hard cutting material, specifically nanocrystalline cubic boron nitride (BNNC). This material was fabricated using a high-pressure–high-temperature (HP–HT) process. The starting material was a pyrolytically deposited hexagonal boron nitride (PBN), which was transformed at temperatures of 1400–2200 °C and pressures of 10–20 GPa during direct synthesis without any binder. The average crystallite size of this material was 50–100 nm and it was, therefore, significantly smaller than that of the conventional polycrystalline cubic boron nitride (PCBN) cutting materials. Compared to conventional PCBN cutting materials, this material had an increased hot-hardness and a better temperature resistance. Testing was carried out by turning grooves in hardened steel.

## 2. Materials and Methods

- Machining hardened components by finishing technology with a CBN tool;
- Carrying out an experiment to measure the cutting forces;
- Evaluation of the force analysis;
- Development of a structural equation;
- Evaluation of the surface quality of the functional surface by the touch method;
- Evaluation of the surface quality of the functional surface by non-contact method.

- Universal lathe SV 18 RD;
- Dynamometer Kistler 9257B;
- Taylor Hobson Surtronic S 100 roughness gauge;
- Alicona Infinite Focus G5 non-contact instrument.

#### 2.1. Implementation of the Cutting Force Measurement Experiment

- Outer diameter (mm) 32;
- Length (mm) 60.

#### 2.2. Technological Conditions of Machining When Measuring with a Kistler Dynamometer

^{−1}. The power of the main motor at maximum rpm is 10 kW. The main advantage of this conventional lathe is the added potential for placing the measuring probes of the Kistler dynamometer on the back of the slide.

- Tool holder PCLNL 2525 M 12 in left-hand version;
- Replaceable insert CNGA 120408 S 01020B shown in Figure 2, made of TB310, polycrystalline cubic boron nitride, suitable for use without cutting fluid.

- Cutting speed v
_{c}, which depends on the number of revolutions and diameter of the workpiece; - The feed rate f, which is defined by the movement of the tool per revolution;
- The cutting edge width a
_{p}, which is determined by the tool’s approach to the cutting edge.

- Orthogonal face angle γ
_{o}= 0°; - Orthogonal back angle α
_{o}= 0°; - Orthogonal edge angle β
_{0}= 90°.

- Orthogonal face angle γ
_{o}= −6°; - Orthogonal back angle α
_{o}= 6°; - Blade inclination angle λ
_{s}= −6°; - Main blade setting angle κ
_{r}= 95°; - Angle of adjustment of the secondary blade κ
_{r}’ = 5°.

_{p}given here are informative; the parameters used in the study provided data to determine the structural equation. One tool was used for the whole series of samples.

_{p}is then reversed. In the last part of Figure 3c, the label of the Kistler 9257B dynamometer is shown with the individual directions of the axes of the cutting resistance against the cutting forces when the dynamometer is placed in the front part of the caliper. This then corresponds to the directions of the x-axis for the sliding force F

_{f}, the z-axis for the cutting force F

_{c}and the y-axis for the passive force F

_{p}.

_{c}, f and a

_{p}. A full factorial design of the experimental plan was chosen. The specific values of the cutting conditions are in Table 3. These are always four combinations of feed rate, f, and blade cutting width, a

_{p}, at three different cutting speeds, v

_{c}. This range of cutting conditions was chosen to cover the possible cutting conditions for finishing machining. At the same time, this range of cutting conditions allows empirical data to be obtained for the construction of the structural equation.

#### 2.3. Measurement of Cutting Forces with a Kistler Dynamometer

_{c}, the passive force, F

_{p}, and the feed force, F

_{f}. The measuring apparatus consisted of a dynamometer, a Kistler 5070A hub amplifier and a data acquisition and analysis system by means of which the data were transferred to a computer. As each sub-sample was machined, a measurement was run and after turning was completed, the values were recorded and stored in DynoWare. The measurement was set to 60 s to cover all the machine times when machining each sample. The sampling rate was set to 2000 Hz. The unwanted extreme measurement dates were filtered out.

#### 2.4. Surface Quality Measurement by the Touch Method

#### 2.5. Surface Quality Measurement by Non-Contact Method

- Using a 50× lens;
- Filter was Lc [µm] 800;
- Profile measurement path length [mm] was 4.

## 3. Results

#### 3.1. Evaluation of Cutting force Measurements with the Kistler Dynamometer

_{p}and f are the main factors. Considering that the p-Value = 0.003, it can be concluded that these factors are significant with a reliability of 99.7%. Cutting speed, v

_{c}, is almost negligible in terms of the effect of the F

_{c}and their interactions with a

_{p}. The interaction with f is moderate in terms of the significance level.

_{Fc}of about ±0.05. Graphically, the interactions and dependencies are depicted in Figure 9. The low influence of v

_{c}and the high influence of f and a

_{p}

_{,}due to the orthogonal distribution, are clearly visible.

_{p}and f on the cutting force F

_{c}. By referring to the contour representation, it is possible to observe the relationships and optimize the process, also the uniform distribution of the dependence for both f and a

_{p}can be seen.

#### 3.2. Derivation of the Structural Equation

_{c}for turning material in the hardened state is based on the data in Table 4 and on the following Equation (1):

_{Fc}, the exponents x

_{Fc}, y

_{Fc}and z

_{Fc}and the variables—in this case the blade width, a

_{p}, the feed, f, and possibly the cutting speed, v

_{c}. The values of the constant C

_{Fc}and the exponents x

_{Fc}, y

_{Fc}and z

_{Fc}, depend on the specific machining conditions and are valid within a certain range. Furthermore, the type of material and its condition have an influence, which can be expressed by the machinability class. When calculating the cutting force according to this equation, we have to consider an inaccuracy which will be proportional to the difference between our machining conditions and those used to calculate the constant C

_{Fc}and the exponents x

_{Fc}, y

_{Fc}and z

_{Fc}. The cutting speed term in the general formula is therefore not included and its possible influence is reflected in the value of the constant C

_{Fc}. From Table 4 the individual values of Fc are averaged for the combinations of feed f and cutting edge width a

_{p}used and listed in Table 6 for use in the following calculation:

_{Fc}, y

_{Fc}and subsequently the constant C

_{Fc}.

#### 3.2.1. Derivation of the Exponent x_{Fc}

_{Fc}, a constant displacement value f is assumed and the equation takes the following form (3):

_{Fc}can be defined as the directive of the line tg α:

_{Fc}from the data in Table 6:

#### 3.2.2. Derivation of the Exponent y_{Fc}

_{Fc}, a constant value of the cutting edge width a

_{p}is assumed and the equation takes the following form (7):

_{Fc}can be defined as the directive of the line tg α:

_{Fc}from the data in Table 6:

_{p}is 0.35 mm:

#### 3.2.3. Determination of the Constant C_{Fc}

_{Fc}and y

_{Fc}, the constant C

_{Fc}can be determined using Equation (2) by substituting one of the combinations of the blade width a

_{p}, the feed rate f and the corresponding averaged value of the measured cutting force F

_{c}from Table 6:

#### 3.2.4. Final Form of the Structural Equation

_{c}after adding the rounded numerical values of the constant C

_{Fc}, and the exponents x

_{Fc}, y

_{Fc}

_{,}is given in Equation (12):

_{Fc}, y

_{Fc}, the structural equation can be written in the simplified form (13):

- Material 10 Cr6 in hardened condition (HRC) 64–62;
- Cutting edge width a
_{p}(mm) 0.1–0.45; - Feed f (mm·rev
^{−1}) 0.05–0.15; - Cutting speed v
_{c}(m·min^{−1}) 110–200.

#### 3.3. Evaluation of the Surface Quality of the Functional Area

#### 3.3.1. Evaluation of the Surface Quality of the Functional Area by the Touch Method

#### 3.3.2. Evaluation of the Surface Quality of the Functional Area by the Non-Contact Method

- Ra—Average arithmetic deviation of the profile;
- Rz—Maximum profile height;
- Rmr—Mutual material ratio for (Mr = 50%, an offset Rδc = 0.1 μm);

- Rk—Core roughness depth, height of the core material;
- Rpk—Reduced peak height, mean height of the peaks above the core material;
- Rvk—Reduced valley height, mean depth of the valleys below the core material;
- Rmr1—Peak material component, the proportion of peaks above the core material;
- Rmr2—Peak material component, the fraction of the surface which will carry the load.

## 4. Discussion

_{c}= 130 m·min

^{−1}, there are no significant differences due to changes in the cutting width a

_{p}and feed per revolution f. In general, the resulting surface finish depends mainly on the feed rate f; the lower the feed rate f, the lower the surface finish. The average values of the arithmetic deviation of the profile under consideration, Ra, are between 0.3 and 0.4 μm. For a cutting speed of v

_{c}= 130 m·min

^{−1}, the best combination of cutting conditions appears to be a

_{p}= 0.35 mm and f = 0.05 mm·rev

^{−1}, with an average Ra value of 0.34 μm. The best (i.e., the smallest) values of the Ra parameter were obtained for a cutting speed of v

_{c}= 155 m·min

^{−1}in combination with a

_{p}= 0.35 mm and f = 0.05 mm·rev

^{−1}, where the average Ra value is 0.23 μm, i.e., sample 6. However, for the same cutting speed v

_{c}and increasing the feed per revolution to f = 0.1 mm·rev

^{−1}with the same a

_{p}value, the average Ra value was 0.48 μm, an increase of approximately 209% (for sample 8). These fluctuations may also be due to inaccuracies during the measurement or a crack may appear on the surface of the sample that was measured. These factors can be eliminated by repeating the measurements more often. At a cutting speed of v

_{c}= 180 m·min

^{−1}it can be observed that more stable surface quality values are recorded in connection with the increase of the feed per revolution f from 0.05 mm to 0.1 mm. The average value of the parameter Ra is at 0.3 μm. Again, the small number of measurements is evident here, specifically for sample 10 (f = 0.05 mm·rev

^{−1}and a

_{p}= 0.35 mm), where the resulting Ra values fluctuate more, as seen in the highest value of the standard deviation. As for the resulting average Ra values, for samples 5, 6, 9, 11 and 12, a value lower than Ra = 0.30 μm was obtained. These samples have cutting speeds of v

_{c}= 155 m·min

^{−1}and v

_{c}= 180 m·min

^{−1}. In general, based on the results obtained from the contact measurements, it can be stated that out of 12 machined samples with different combinations of cutting conditions, 11 samples were below Ra = 0.4 μm on average during the measurements. It is difficult to reach this value with conventional finishing tools made of materials other than CNB. It follows that the CNB insert material is able to replace finishing operations such as grinding in certain cases. After performing comparative measurements of selected samples on the Alicona instrument, it can be stated that for samples 5 and 6 almost the same values were obtained as for the touch method. For sample 8, where the touch method measured an average value of Ra = 0.48, the non-contact method measured Ra = 0.328, which also places this sample among the compliant pieces. For sample 12, where the average value of Ra = 0.3 was measured by the touch method, the average value of Ra = 0.198 was measured by the non-contact method. From the above, it can be concluded that the actual surface quality after turning with the CBN tool is better than that shown by the touch measurement.

_{c}153 m·min

^{−1}, feed f 0.05 mm·rev

^{−1}and tool tip radius 0.8 mm. They address the reduction of energy consumption in metal machining. The premise is to determine the energy consumption by direct or indirect measurement. The manufacturing process under consideration is the finishing turning of mainly hardened steels. In this paper, it is proposed to use the measured cutting forces to calculate the power consumption in metal finishing turning, where the depth of cut is usually less than the cutting tool tip radius. Patel, V.D. and Gandhi, A.H. [27] addressed the use of AISI D2 steel as a material for bearing raceways, forming dies, punches, forming rolls, etc. Experiments on the finishing turning of hardened AISI D2 steel using cubic boron nitride (CBN) tools were carried out with different combinations of cutting speed (80, 116 and 152 m·min

^{−1}), feed rate (0.04, 0.12 and 0.2 mm·rev

^{−1}) and tool tip radius (0.4, 0.8 and 1.2 mm) using a full-factorial design for the experiments. Based on the experimental results, an empirical model of cutting forces as a function of cutting parameters (i.e., cutting speed, feed rate, and tool tip radius) has been developed. This model is based on the DOE experiment and is not due to an empiric theory. The results are comparable, but not quite universal, for the full range of a

_{p}and f as in the equations in this paper.

## 5. Conclusions

- The construction of an empirical structural equation allows the prediction of the cutting force in hard turning finishing under similar machining conditions;
- The use of inserts from another manufacturer achieved similar surface quality results;
- The machined surface could be accepted for the four selected samples if Ra = 0.3 was taken as the cut-off value. If this cut-off value was extended to Ra = 0.4, all samples would pass;
- Comparative measurements of surface roughness values by the non-contact method showed similar or better results than the contact method.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Diagram of the location of the Kistler 9257B dynamometer during the experiment (

**a**), table indicating the directions of cutting resistance (

**c**) and diagram of the distribution of cutting forces during turning (

**b**) [22].

**Figure 5.**Force load history of sample 5 (v

_{c}= 155 m·min

^{−1}, f = 0.05 mm·rev

^{−1}, a

_{p}= 0.2 mm).

**Figure 6.**Force load history of sample 6 (v

_{c}= 155 m·min

^{−1}, f = 0.05 mm·rev

^{−1}, a

_{p}= 0.35 mm).

**Figure 7.**Force load history of sample 8 (v

_{c}= 155 m·min

^{−1}, f = 0.1 mm·rev

^{−1}, a

_{p}= 0.35 mm).

**Figure 8.**Force load history of sample 12 (v

_{c}= 180 m·min

^{−1}, f = 0.1 mm·rev

^{−1}, a

_{p}= 0.35 mm).

**Figure 17.**Profile measurement display of the surface: (

**a**) part 5, (

**b**) part 6, (

**c**) part 8, (

**d**) part 12.

**Figure 18.**Spatial contrast profile display of the surface: (

**a**) part 5, (

**b**) part 6, (

**c**) part 8, (

**d**) part 12.

Steel | C | Si | Mn | Cr | Mo | P | S |
---|---|---|---|---|---|---|---|

100Cr6 | 0.93–1.05 | 0.15–0.35 | 0.25–0.45 | 1.35–1.60 | max.0.1 | 0.025 | 0.015 |

r_{ε} | a_{p} | f | v_{c} | d | d_{1} | l | s |
---|---|---|---|---|---|---|---|

(mm) | (mm) | (mm·rev^{−1}) | (m·min^{−1}) | (mm) | (mm) | (mm) | (mm) |

0.8 | 0.1–2.7 | 0.02–0.20 | 100–200 | 12.7 | 5.16 | 12.9 | 4.76 |

Sample No. | v_{c} (m·min ^{−1}) | F (mm·rev ^{−1}) | a_{p}(mm) |
---|---|---|---|

1 | 130 | 0.05 | 0.2 |

2 | 0.05 | 0.35 | |

3 | 0.1 | 0.2 | |

4 | 0.1 | 0.35 | |

5 | 155 | 0.05 | 0.2 |

6 | 0.05 | 0.35 | |

7 | 0.1 | 0.2 | |

8 | 0.1 | 0.35 | |

9 | 180 | 0.05 | 0.2 |

10 | 0.05 | 0.35 | |

11 | 0.1 | 0.2 | |

12 | 0.1 | 0.35 |

Sample No. | v_{c} (m·min ^{−1}) | f (mm·rev ^{−1}) | a_{p} (mm) | Force F_{c} (N) | Force F_{f} (N) | Force F_{p} (N) | Resulting Force F (N) |
---|---|---|---|---|---|---|---|

1 | 130 | 0.05 | 0.2 | 121.4 | 49.0 | 71.0 | 148.9 |

2 | 0.05 | 0.35 | 165.6 | 99.7 | 114.1 | 224.5 | |

3 | 0.1 | 0.2 | 167.9 | 64.8 | 112.8 | 212.4 | |

4 | 0.1 | 0.35 | 224.9 | 117.4 | 175.5 | 308.5 | |

5 | 155 | 0.05 | 0.2 | 133.6 | 54.8 | 72.3 | 161.5 |

6 | 0.05 | 0.35 | 153.9 | 106.6 | 115.3 | 219.9 | |

7 | 0.1 | 0.2 | 171.7 | 59.5 | 97.3 | 206.2 | |

8 | 0.1 | 0.35 | 206.1 | 128.3 | 175.5 | 299.6 | |

9 | 180 | 0.05 | 0.2 | 119.0 | 47.1 | 68.7 | 145.3 |

10 | 0.05 | 0.35 | 147.5 | 87.7 | 103.3 | 199.0 | |

11 | 0.1 | 0.2 | 152.1 | 62.2 | 123.2 | 205.5 | |

12 | 0.1 | 0.35 | 199.1 | 118.6 | 197.4 | 304.5 |

Source | DF | Adj. SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

Model | 9 | 20,301.8 | 2255.75 | 81.69 | 0.012 |

Linear | 4 | 18,992.1 | 4748.02 | 171.95 | 0.006 |

v_{c} | 2 | 131.2 | 65.60 | 2.38 | 0.296 |

f | 1 | 9464.1 | 9464.08 | 342.74 | 0.003 |

a_{p} | 1 | 9396.8 | 9396.80 | 340.30 | 0.003 |

2-Way | 5 | 1309.7 | 261.93 | 9.49 | 0.098 |

Interactions | |||||

v_{c}*f | 2 | 533.7 | 266.86 | 9.66 | 0.094 |

v_{c}*a_{p} | 2 | 33.3 | 16.66 | 0.60 | 0.624 |

f*a_{p} | 1 | 742.6 | 742.61 | 26.89 | 0.035 |

Error | 2 | 55.2 | 27.61 | ||

Total | 11 |

**Table 6.**Averaged values of cutting force F

_{c}for combinations of feed f and cutting edge width a

_{p}.

Combination f and a _{p} | f (mm·rev ^{−1}) | a_{p}(mm) | F_{c}(N) |
---|---|---|---|

1 | 0.05 | 0.2 | 124.7 |

2 | 0.05 | 0.35 | 155.6 |

3 | 0.1 | 0.2 | 163.9 |

4 | 0.1 | 0.35 | 210.3 |

**Table 7.**Values of selected surface quality parameters obtained under the specified cutting conditions.

Sample No. | v_{c}(m·min ^{−1}) | f (mm·rev ^{−1}) | a_{p}(mm) | Ra (µm) | Rz (µm) | Rmr (%) |
---|---|---|---|---|---|---|

1 | 130 | 0.05 | 0.2 | 0.38 | 2.27 | 48.9 |

2 | 0.05 | 0.35 | 0.34 | 2.17 | 48.7 | |

3 | 0.1 | 0.2 | 0.36 | 2.17 | 46.7 | |

4 | 0.1 | 0.35 | 0.37 | 2.23 | 47.7 | |

5 | 155 | 0.05 | 0.2 | 0.27 | 1.63 | 52.6 |

6 | 0.05 | 0.35 | 0.23 | 1.43 | 49.4 | |

7 | 0.1 | 0.2 | 0.35 | 2.17 | 48.8 | |

8 | 0.1 | 0.35 | 0.48 | 2.87 | 47.9 | |

9 | 180 | 0.05 | 0.2 | 0.28 | 1.73 | 51.1 |

10 | 0.05 | 0.35 | 0.36 | 2.07 | 50 | |

11 | 0.1 | 0.2 | 0.3 | 1.9 | 50.7 | |

12 | 0.1 | 0.35 | 0.3 | 1.93 | 50.4 |

Sample No. | Ra Measured (µm) | Ra Average (µm) | Standard Deviation | ||
---|---|---|---|---|---|

1 | 0.41 | 0.40 | 0.32 | 0.38 | 0.049 |

2 | 0.33 | 0.39 | 0.30 | 0.34 | 0.046 |

3 | 0.34 | 0.33 | 0.41 | 0.36 | 0.044 |

4 | 0.38 | 0.37 | 0.37 | 0.37 | 0.006 |

5 | 0.27 | 0.27 | 0.28 | 0.27 | 0.006 |

6 | 0.21 | 0.27 | 0.20 | 0.23 | 0.038 |

7 | 0.38 | 0.29 | 0.37 | 0.35 | 0.049 |

8 | 0.47 | 0.49 | 0.49 | 0.48 | 0.012 |

9 | 0.26 | 0.28 | 0.30 | 0.28 | 0.020 |

10 | 0.41 | 0.38 | 0.28 | 0.36 | 0.068 |

11 | 0.31 | 0.29 | 0.29 | 0.30 | 0.012 |

12 | 0.28 | 0.31 | 0.31 | 0.30 | 0.017 |

Sample No. | Ra (µm) | Rz (µm) | Rk (µm) | Rpk (µm) | Rvk (µm) | Rmr1 (%) | Rmr2 (%) |
---|---|---|---|---|---|---|---|

5 | 0.273 | 1.459 | 0.883 | 0.217 | 0.255 | 11.77 | 91.83 |

6 | 0.232 | 1.471 | 0.547 | 0.296 | 0.35 | 7.59 | 74.62 |

8 | 0.328 | 1.644 | 1.068 | 0.191 | 0.175 | 10.65 | 94.85 |

12 | 0.196 | 1.302 | 0.665 | 0.269 | 0.186 | 9 | 94.36 |

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## Share and Cite

**MDPI and ACS Style**

Osička, K.; Zouhar, J.; Sliwková, P.; Chladil, J. Cutting Force When Machining Hardened Steel and the Surface Roughness Achieved. *Appl. Sci.* **2022**, *12*, 11526.
https://doi.org/10.3390/app122211526

**AMA Style**

Osička K, Zouhar J, Sliwková P, Chladil J. Cutting Force When Machining Hardened Steel and the Surface Roughness Achieved. *Applied Sciences*. 2022; 12(22):11526.
https://doi.org/10.3390/app122211526

**Chicago/Turabian Style**

Osička, Karel, Jan Zouhar, Petra Sliwková, and Josef Chladil. 2022. "Cutting Force When Machining Hardened Steel and the Surface Roughness Achieved" *Applied Sciences* 12, no. 22: 11526.
https://doi.org/10.3390/app122211526