# The Effect of Coatings on Cutting Force in Turning of C45 Steel

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Cutting Force Model

#### 2.1. Force Decomposition in Turning

#### 2.2. Proposal of Methodology for Cutting Force Prediction

^{2}and for the cutting speed of the centre point (${\mathrm{v}}_{{\mathrm{c}}_{\mathrm{cp}}}$). The centre point is the point in the centre of a designed plan of experiments. The material constant ${\mathrm{m}}_{\mathrm{c}}$ determines the effect of the undeformed chip thickness on the specific cutting force. The material constant ${\mathrm{m}}_{{\mathrm{v}}_{\mathrm{c}}}$ determines the influence of the cutting speed on the specific cutting force. The undeformed chip thickness and the undeformed chip width are determined according to the schematics in Figure 2, which considers two cases. The first case is cutting a workpiece material using only the rounded part of the cutting edge, and the second case is cutting a workpiece material using both the rounded and straight parts of the cutting edge.

#### 2.3. Rounded Part of the Cutting Edge

#### 2.4. Straight Part of the Cutting Edge

#### 2.5. Resultant Equations for the Cutting Force Calculation

## 3. Design of Experiments

#### 3.1. Machine Tool

#### 3.2. Cutting Tool

_{r}) of the cutting tool holder was 90°, and the inclination angle (λ

_{s}) was 0°. The cutting edge radius (r) as well as the macrogeometry were measured with an Alicona InfiniteFocus G5. Each value for the cutting edge radius was evaluated as the average of 50 slices; see Figure 4b. As a matter of interest, all of the measured values of the cutting edge radius were smaller in our case than Bartoszuk found for similar coatings of custom-coated inserts [32]. A MarSurf LD 130 (Mahr, spol. s r.o., Proboštov, Czech Republic) was used to measure surface roughness values, which are shown in Table 1. The properties of both coated inserts are shown in Table 2.

#### 3.3. Workpiece

#### 3.4. Measuring Devices

#### 3.5. Design of Experiments for Uncoated and Coated Cutting Tools

_{n}), and factor B (no unit parameter) is characterised by the cutting speed (v

_{c}).

_{p}) was constant and equal to 2 mm. Although this is the maximum value recommended by the manufacturer, it was set so the insert could cut the workpiece material largely by the straight part of the cutting edge. The feed per revolutions (f

_{n}) has five levels and was set with respect to the cube points in the range 0.12–0.20 mm. The cutting speed (v

_{c}) also has five levels and was set relative to the cube points in the range 120–200 m/min.

## 4. Results and Discussions

#### 4.1. Accuracy of the Proposed Mathematical Model for Uncoated Cutting Tools

^{2}) of the obtained mathematical model was 98.9%. Accordingly, the equation of the specific cutting force with the impact of the chip thickness and cutting speed with the obtained material constants was quite precise for prediction of the specific cutting force in the range of cutting conditions used for the experiments.

#### 4.2. Comparing the Experimental Cutting Force Values of Uncoated and Coated Cutting Tools

#### 4.3. Determining the Coating Correction Factor

_{Coating}) that would be implemented into the proposed mathematical model; see Equation (4). This correction factor applies to each set of cutting conditions; it is calculated using the ratio between the cutting force determined from the proposed mathematical model, which was obtained for uncoated cutting tool inserts and the cutting force for a specific coating. The calculated correction factor values are shown in Table 10.

#### 4.4. Accuracy of the Proposed Mathematical Model for Coated Cutting Tools

## 5. Conclusions

- In the comparison of the experimental cutting force data for the uncoated and coated inserts, there was a statistically significant difference resulting from the paired t-test p-values (no coating–AlTiN: p-value = 0.011; no coating–TiAlCrN: p-value = 0.024), which were below the confidence level (α = 0.05); see Table 9. The percentage difference was found to be up to 4%;
- In the comparison of the experimental cutting force data for the two coated inserts, there was no statistically significant difference resulting from the paired t-test p-value (p-value = 0.392), which was above the confidence level (α = 0.05); see Table 9. This was despite the fact that the measured properties of the coatings were slightly different. The percentage difference was up to 1%;
- As there was no statistically significant difference between the two coated inserts, a linear regression was found for a coating correction factor that was valid for the two researched coatings, i.e., AlTiN and TiAlCrN. This regression included the impact of the feed per revolution as well as the cutting speed, which were statistically significant parameters according to the analysis of variance p-values (f
_{n}: p-value = 0.003; v_{c}: p-value = 0.017), which were below the confidence level (α = 0.05); see Table 12; - When the calculated cutting force data, which included the coating correction factor, were compared with the experimental data of the coated inserts, there was no statistically significant difference resulting from the paired t-test p-values (Model–AlTiN: p-value = 0.234; Model–TiAlCrN: p-value = 0.374), which were above the confidence level (α = 0.05); see Table 14. The percentage difference was found to be up to 0.6%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$\Delta {\mathrm{F}}_{\mathrm{c}}$ (%) | Percentage deviation between experimental and calculated cutting force values |

${\mathsf{\alpha}}_{\mathrm{o}}$ (°) | Clearance angle |

${\mathsf{\beta}}_{\mathrm{o}}$ (°) | Wedge angle |

${\mathsf{\gamma}}_{\mathrm{o}}$ (°) | Rake angle |

$\mathsf{\theta}$ (°) | Actual value of engagement angle of the rounded part of the cutting edge |

${\mathsf{\theta}}_{\mathrm{eng}}$ (°) | Engagement angle of the rounded part of the cutting edge |

${\mathsf{\kappa}}_{\mathrm{r}}$ (°) | Lead angle |

${\mathsf{\lambda}}_{\mathrm{s}}$ (°) | Inclination angle |

$\mathrm{A}$ (-) | No unit factor for DOE that corresponds to the feed per revolution |

${\mathrm{A}}_{\mathrm{D}}$ (mm^{2}) | Undeformed chip area |

${\mathrm{A}}_{{\mathrm{D}}_{1}}$ (mm^{2}) | Undeformed chip area of the rounded part of the cutting edge |

${\mathrm{A}}_{{\mathrm{D}}_{2}}$ (mm^{2}) | Undeformed chip area of the straight part of the cutting edge |

${\mathrm{a}}_{\mathrm{p}}$ (mm) | Depth of cut |

$\mathrm{B}$ (-) | No unit factor for DOE that corresponds to the cutting speed |

${\mathrm{b}}_{\mathrm{D}}$ (mm) | Undeformed chip width |

${\mathrm{b}}_{{\mathrm{D}}_{1}}$ (mm) | Undeformed chip width of the rounded part of the cutting edge |

${\mathrm{b}}_{{\mathrm{D}}_{2}}$ (mm) | Undeformed chip width of the straight part of the cutting edge |

$\mathrm{F}$ (N) | Resultant force |

${\mathrm{F}}_{\mathrm{c}}$ (N) | Cutting force |

${\mathrm{F}}_{{\mathrm{c}}_{1}}$ (N) | Cutting force of the rounded part of the cutting edge |

${\mathrm{F}}_{{\mathrm{c}}_{2}}$ (N) | Cutting force of the straight part of the cutting edge |

${\mathrm{F}}_{{\mathrm{c}}_{\mathrm{exp}}}$ (N) | Cutting force evaluated from experiment |

${\mathrm{F}}_{\mathrm{f}}$ (N) | Feed force |

${\mathrm{F}}_{\mathrm{p}}$ (N) | Passive force |

${\mathrm{f}}_{\mathrm{n}}$ (mm) | Feed per revolution |

${\mathrm{h}}_{\mathrm{D}}$ (mm) | Undeformed chip thickness |

${\mathrm{h}}_{{\mathrm{D}}_{1}}$ (mm) | Undeformed chip of the rounded part of the cutting edge |

${\mathrm{h}}_{{\mathrm{D}}_{2}}$ (mm) | Undeformed chip thickness of the straight part of the cutting edge |

${\mathrm{K}}_{\mathrm{Coating}}$ (-) | Correction factor of coating |

${\mathrm{k}}_{\mathrm{c}}$ (N/mm^{2}) | Specific cutting force |

${\mathrm{k}}_{{\mathrm{c}}_{1}}$ (N/mm^{2}) | Specific cutting force of the rounded part of the cutting edge |

${\mathrm{k}}_{{\mathrm{c}}_{2}}$ (N/mm^{2}) | Specific cutting force of the straight part of the cutting edge |

${\mathrm{k}}_{{\mathrm{c}}_{1.1}}$ (N/mm^{2}) | Specific cutting force for an undeformed chip area of 1 mm^{2} |

${\mathrm{m}}_{\mathrm{c}}$ (-) | Empirical constant that indicates the impact of the chip thickness on the specific cutting force |

${\mathrm{n}}_{\mathrm{c}}$ (-) | Empirical constant that indicates the impact of the cutting speed on the specific cutting force |

$\mathrm{r}$ (mm) | Cutting edge radius |

${\mathrm{r}}_{\mathrm{\epsilon}}$ (mm) | Nose radius |

$\mathrm{SD}$ (N) | Standard deviation of the cutting force |

${\mathrm{v}}_{\mathrm{f}}$ (mm/min) | Feed rate speed |

${\mathrm{v}}_{\mathrm{c}}$ (m/min) | Cutting speed |

${\mathrm{v}}_{{\mathrm{c}}_{\mathrm{cp}}}$ (m/min) | Cutting speed of the centre point |

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**Figure 2.**Cutting area when cutting: (

**a**) with the rounded part of the cutting edge; (

**b**) with the rounded as well as the straight part of the cutting edge.

**Figure 5.**Measuring devices used to measure the force effects in turning: (

**a**) PC; (

**b**) LabAmp 5167A Laboratory Charge Amplifier DAQ; (

**c**) 9257B dynamometer.

**Figure 7.**Dependence of the specific cutting force on undeformed chip thickness and cutting speed for uncoated inserts.

Parameter | Unit | Symbol | No Coating | Coating | |
---|---|---|---|---|---|

AlTiN | TiAlCrN | ||||

Cutting edge radius | μm | r | 8.94 ± 0.67 | 10.45 ± 1.28 | 11.42 ± 0.58 |

Surface roughness | μm | Ra | 0.13 | 0.16 | 0.24 |

Clearance angle | ° | α_{o} | 11 | 11 | 11 |

Wedge angle | ° | β_{o} | 79 | 79 | 79 |

Rake angle | ° | γ_{o} | 0 | 0 | 0 |

Property | Unit | Symbol | AlTiN | TiAlCrN |
---|---|---|---|---|

Coating thickness | μm | h | 2.2 | 4.3 |

Hardness | GPa | H | 23.8 ± 3.32 | 19.8 ± 1.9 |

Young’s modulus | GPa | E | 685 ± 25.1 | 469 ± 21.2 |

Chemical composition | % | Ti | 24.4 ± 0.14 | 13.3 ± 0.14 |

% | Al | 24 ± 0.03 | 14.8 ± 0.03 | |

% | Cr | - | 24.3 ± 0.06 | |

% | N | 51.6 ± 0.07 | 47.5 ± 0.27 |

Parameter | Unit | Symbol | Levels | ||||
---|---|---|---|---|---|---|---|

−α | −1 | 0 | +1 | +α | |||

Feed per revolution | mm | f_{n} | 0.103 | 0.12 | 0.16 | 0.20 | 0.217 |

Cutting speed | m/min | v_{c} | 103 | 120 | 160 | 200 | 217 |

Depth of cut | mm | a_{p} | 2 |

Type of Points | No Unit Parameters | Cutting Conditions | ||
---|---|---|---|---|

A | B | f_{n}(mm) | v_{c}(m/min) | |

Cube points | −1 | −1 | 0.12 | 120 |

+1 | −1 | 0.20 | 120 | |

−1 | +1 | 0.12 | 200 | |

+1 | +1 | 0.20 | 200 | |

Axial points | −α | 0 | 0.103 | 160 |

+α | 0 | 0.217 | 160 | |

0 | −α | 0.16 | 103 | |

0 | +α | 0.16 | 217 | |

Centre point | 0 | 0 | 0.16 | 160 |

Cutting Conditions | Results | ||
---|---|---|---|

f_{n}(mm) | v_{c}(m/min) | F_{c}(N) | SD (N) |

0.12 | 120 | 679.5 | 1.3 |

0.20 | 120 | 952.4 | 2.7 |

0.12 | 200 | 604.8 | 3.3 |

0.20 | 200 | 887.3 | 0.1 |

0.103 | 160 | 581.5 | 0.6 |

0.217 | 160 | 977.7 | 0.8 |

0.16 | 103 | 847.1 | 1.4 |

0.16 | 217 | 740.2 | 0.5 |

0.16 | 160 | 782.9 | 0.3 |

Cutting Conditions | Results | |||
---|---|---|---|---|

f_{n}(mm) | v_{c}(m/min) | F_{c exp}(N) | A_{D}(mm ^{2}) | k_{c}(N/mm ^{2}) |

0.12 | 120 | 679.5 | 0.240 | 2831 |

0.20 | 120 | 952.4 | 0.400 | 2381 |

0.12 | 200 | 604.8 | 0.240 | 2520 |

0.20 | 200 | 887.3 | 0.400 | 2218 |

0.103 | 160 | 581.5 | 0.206 | 2823 |

0.217 | 160 | 977.7 | 0.434 | 2253 |

0.16 | 103 | 547 | 0.320 | 2647 |

0.16 | 217 | 740.2 | 0.320 | 2313 |

0.16 | 160 | 782.9 | 0.320 | 2446 |

Mean | SD | SE Mean | 95% CI for μ_Difference | T-Value | p-Value |
---|---|---|---|---|---|

0.20 | 7.71 | 2.57 | (−5.72; 6.13) | 0.08 | 9.39 × 10^{−1} |

Cutting Conditions | No Coating | AlTiN | TiAlCrN | ||||
---|---|---|---|---|---|---|---|

f_{n}(mm) | v_{c}(m/min) | F_{c}(N) | SD (N) | F_{c}(N) | SD (N) | F_{c}(N) | SD (N) |

0.12 | 120 | 679.5 | 1.3 | 652.2 | 1.9 | 653.7 | 1.2 |

0.20 | 120 | 952.4 | 2.7 | 944.9 | 1.5 | 942.1 | 1.0 |

0.12 | 200 | 604.8 | 3.3 | 595.8 | 4.2 | 602.2 | 1.7 |

0.20 | 200 | 887.3 | 0.1 | 867.3 | 2.3 | 874.3 | 2.2 |

0.16 | 160 | 782.9 | 0.3 | 762.4 | 1.1 | 760.2 | 0.1 |

Data to Compare | Mean | SD | SE Mean | 95% CI for μ_Difference | T-Value | p-Value |
---|---|---|---|---|---|---|

No coating–AlTiN | 16.86 | 8.39 | 3.75 | (6.44; 27.28) | 4.49 | 1.10 × 10^{−2} |

No coating–TiAlCrN | 14.88 | 9.40 | 4.21 | (3.20; 26.56) | 3.54 | 2.40 × 10^{−2} |

AlTiN–TiAlCrN | −1.98 | 4.61 | 2.06 | (−7.71; 3.75) | −0.96 | 39.20 × 10^{−2} |

Cutting Conditions | F_{c} (N) | K_{Coating} (-) | ||||
---|---|---|---|---|---|---|

f_{n}(mm) | v_{c}(m/min) | Model | Experiment | AlTiN | TiAlCrN | |

AlTiN | TiAlCrN | |||||

0.12 | 120 | 662.3 | 652.2 | 653.7 | 0.985 | 0.987 |

0.20 | 120 | 945.1 | 944.9 | 942.1 | 1 | 0.997 |

0.12 | 200 | 602.9 | 595.8 | 602.2 | 0.988 | 0.999 |

0.20 | 200 | 860.3 | 867.3 | 874.3 | 1.008 | 1.016 |

0.16 | 160 | 767.4 | 762.4 | 760.2 | 0.993 | 0.991 |

Term | Coefficient | SE Coefficient | T-Value | p-Value |
---|---|---|---|---|

Constant | 9.44 × 10^{−1} | 9.91 × 10^{−3} | 95.30 | 0.00 |

f_{n} | 1.95 × 10^{−1} | 4.32 × 10^{−2} | 4.50 | 0.30 × 10^{−2} |

v_{c} | 1.34 × 10^{−4} | 4.30 × 10^{−5} | 3.10 | 1.70 × 10^{−2} |

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

Regression | 2 | 7.15 × 10^{−4} | 3.57 × 10^{−4} | 14.93 | 0.30 × 10^{−2} |

f_{n} | 1 | 4.85 × 10^{−4} | 4.85 × 10^{−4} | 20.24 | 0.30 × 10^{−2} |

v_{c} | 1 | 2.30 × 10^{−4} | 2.30 × 10^{−4} | 9.62 | 1.70 × 10^{−2} |

Error | 7 | 1.68 × 10^{−4} | 0.24 × 10^{−4} | ||

Lack of fit | 2 | 0.67 × 10^{−4} | 0.34 × 10^{−4} | 1.68 | 27.70 × 10^{−2} |

Pure error | 5 | 1.00 × 10^{−4} | 0.20 × 10^{−4} | ||

Total | 9 | 8.82 × 10^{−4} |

Cutting Conditions | F_{c} (N) | |||
---|---|---|---|---|

f_{n}(mm) | v_{c}(m/min) | Model | Experiment | |

AlTiN | TiAlCrN | |||

0.12 | 120 | 651.4 | 652.2 | 653.7 |

0.20 | 120 | 944.2 | 944.9 | 944.2 |

0.12 | 200 | 599.4 | 595.8 | 599.4 |

0.20 | 200 | 868.8 | 867.3 | 868.8 |

0.16 | 160 | 764.9 | 762.4 | 764.9 |

Data to Compare | Mean | SD | SE Mean | 95% CI for μ_Difference | T-Value | p-Value |
---|---|---|---|---|---|---|

Model–AlTiN | 1.22 | 1.95 | 0.97 | (−1.196; 3.636) | 1.40 | 2.34 × 10^{−1} |

Model–TiAlCrN | −0.46 | 1.03 | 0.46 | (−1.737; 0.817) | −1.00 | 3.74 × 10^{−1} |

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**MDPI and ACS Style**

Kovalčík, J.; Mašek, P.; Malý, J.; Kožmín, P.; Syrovátka, J.
The Effect of Coatings on Cutting Force in Turning of C45 Steel. *Materials* **2022**, *15*, 590.
https://doi.org/10.3390/ma15020590

**AMA Style**

Kovalčík J, Mašek P, Malý J, Kožmín P, Syrovátka J.
The Effect of Coatings on Cutting Force in Turning of C45 Steel. *Materials*. 2022; 15(2):590.
https://doi.org/10.3390/ma15020590

**Chicago/Turabian Style**

Kovalčík, Jaroslav, Petr Mašek, Jan Malý, Pavel Kožmín, and Jiří Syrovátka.
2022. "The Effect of Coatings on Cutting Force in Turning of C45 Steel" *Materials* 15, no. 2: 590.
https://doi.org/10.3390/ma15020590