# Wear of Abrasive Tools during CMC Machining

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

#### 2.1. CMC Materials

- -
- CMCs are 1/3 the weight of the nickel superalloys currently used.
- -
- CMCs can operate at temperatures up to 260 °C higher than Ni superalloys.
- -
- Higher service temperatures mean less thrust cooling air is diverted, allowing engines to run at higher thrust and/or more efficiently.
- -
- Engines also run at higher temperatures, burning fuel completely, reducing fuel consumption and emissions.
- -
- Similarly, CMCs in industrial power generation turbines could reduce environmental pollution and the cost of electricity.

#### 2.2. CMC Abrasive Machining

^{®}), were carried out in the 1990s by Danglot, J. [3] and Girot, F. [4], in collaboration with diamond tool manufacturers. Sepcarb-Inox

^{®}(45 vol% of woven carbon fiber, 50 vol% CVI silicon carbide matrix, and 5 vol% of porosity) contour milling or trimming is the least known machining method. Planning or face-milling operations are quite limited (Figure 3).

#### 2.3. Abrasive Tools

#### 2.4. Wear of Abrasive Tools

- ➢
- Visual inspection: Start with a visual inspection of the abrasive tool. Look for signs of wear on the tool’s surface, such as (i) loss of sharpness on abrasive grains or edges; (ii) formation of chips, cracks, or fractures on the abrasive material; or (iii) change in color or surface texture due to wear. Early signs of wear may not be immediately obvious, so regular inspections are important.
- ➢
- Measurement of tool dimensions: Measure the key dimensions of the abrasive tool before and after machining CMCs. These dimensions can include diameter, thickness, mass, and any relevant geometrical features. A reduction in these dimensions can indicate wear.
- ➢
- Tool wear rate calculation: Calculate the tool wear rate using the following formula:$$ToolWearRate\left(Vw\right)=\frac{\left(InitialToolDimension-FinalToolDimension\right)}{Totalmaterialremoved}$$

- ➢
- Surface finish analysis: Evaluate the surface finish of the machined CMC parts. As the tool wears, it may produce surface defects such as chattering, scratches, or poor finish quality. A noticeable deterioration in surface finish can be an indicator of tool wear.
- ➢
- Cutting forces monitoring: Monitor the cutting forces during machining. A sudden increase in cutting forces or abnormal fluctuations can suggest tool wear. You can use force sensors or dynamometers to accurately measure cutting forces.
- ➢
- Acoustic emission analysis: Acoustic emission monitoring can detect subtle changes in tool wear by analyzing the sound emitted during machining. Abrupt changes or unusual patterns in acoustic emission signals can indicate tool wear [10].

## 3. Fractals for Wear Modeling and Control

#### 3.1. The Importance of Wear of Diamond Tools for Machining CMCs

#### 3.2. The Use of Fractals for Machining Analysis

_{0}= 0 to x

_{1}= 0.3 mm. The data between the coordinates x

_{1}= 0.3 to x

_{2}= 1.3 mm correspond to the area where the abrasive tool has not machined CMC. The area from x

_{3}= 2 to x

_{4}= 5.1 mm is where machining has occurred. Between x

_{2}= 1.3 and x

_{3}= 2 mm there is uncertainty regarding the location of the tool with respect to the CMC plate during machining, and that is why it was not analyzed.

#### 3.3. Proposed Method to Determine the Fractal Dimension

- -
- The roughness must be isotropic: the surface must not present directionality in its fractal pattern. The isotropy of the surface is important since it allows the dimension reduction method to be used to calculate the surface fractal (D_surf) as the fractal dimension value along a certain direction of a profile (D_prof) + 1 [20,24]. An example of isotropic and anisotropic roughness is shown in Figure 6.
- -
- The section (map) from which the fractal dimension will be calculated must be square or rectangular in shape, and must be aligned along a convenient coordinate system, as shown in Figure 2.

- -
- Divide the surface into sections along the direction containing the greatest quantity of data, and obtain roughness profiles perpendicular to the direction containing the least quantity of data. In the case of Figure 5, the largest quantity of data is along the X coordinate (columns) and the direction with the least quantity of data is along the Y direction (rows).
- -
- The selection of the roughness profile will depend on the area of the surface to be analyzed. For example, Figure 7 shows a roughness profile from x
_{3}= 2 to x_{4}= 5.1 mm, in the area where the tool has machined CMC.

- -
- The number of roughness profiles will be equal to the smallest number of data along that direction; in the case of Figure 5, from n
_{row}= 1 (y = 0 mm) to n_{row}= 96 (y = 0.95 mm). - -
- Calculate the fractal dimension for the section of each roughness profile as shown in Figure 5. To calculate the fractal dimension, the power spectral density (PSD) method is recommended [27]. Each coordinate on the X axis represents time in a wave, and the amplitude of the same wave is represented by the roughness height on the Z coordinate.
- -
- Power spectral density requires the selection of a way to estimate the energy of the wave (in this case the roughness profile). One can use the classic methods: “method of autocorrelation method, periodogram method, Bartlett method, and Welch method”. According to Shen et al. [28], the Bartlett and Welch methods are the most precise, and that is why the latter (Welch) has been selected.
- -

- -

- -
- The estimated values ${D}_{{surfn}_{row}}$ of each roughness profile are adjusted to a logistic type distribution [30]. The logistic distribution was chosen due to its relative simplicity and because it adapts very well to the way in which the ${D}_{{surfn}_{row}}$ data obtained from each roughness profile are distributed (Figure 9).
- -
- The value of ${D}_{surf}$ for the entire fractal surface is given by Equation (3).

## 4. CMC Abrasive Machining Experiments

#### 4.1. Material Used in the Abrasive Machining Tests

^{®}Standard) and Cf/SiC (SIGRASIC

^{®}) CMCs. This last material can be adapted to the required application with a behavior controlled by the matrix (matrix dominated with milled fibers (MFs)), mixed (short fibers (SFs)), or controlled by the reinforcement (fiber-dominated with long fibers (LFs)). SIGRASIC

^{®}LF was selected because it is the type of material used in aircraft engine applications [31].

^{3}plates.

#### 4.2. Tools and Machining Equipment

#### 4.3. Damage Measurement Methodology

^{2}/cm). To do this, the color picture was changed to a black and white one and digitized (Figure 13).

## 5. Wear Results

#### 5.1. Tool Wear Evolution

#### 5.2. Multiple Linear Regression of Fractal Dimension

## 6. Relationships between Wear, Forces, Damage, and Roughness

#### 6.1. Evolution of Cutting Forces

^{®}).

#### 6.2. Multiple Linear Regression of Cutting Forces

#### 6.3. Evolution of the Damage to the Material

#### 6.4. Multiple Linear Regression of Chipped Area

#### 6.5. Multiple Linear Regression of Maximum Chipping

#### 6.6. Evolution of the Roughness of the CMC Sample

#### 6.7. Multiple Linear Regression of Roughness Sa

#### 6.8. Multiple Linear Regression of Roughness Sz

#### 6.9. Multiple Linear Regression of Roughness Sq

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

CMC | Ceramic matrix composite |

CVI | Chemical vapor infiltration |

D_surf | Surface fractal dimension |

D_prof | Fractal dimension value along a certain direction of a profile |

ΔD | Fractal dimension variation with respect to the previous test |

β | Slope calculated on a log–log scale of the fit line for the power spectral density data |

n_{row} | Row number of the roughness profile |

H | Hurst coefficient |

Vc | Cutting speed of the tool (m/s) |

N | Rotation speed of the tool (rpm) |

Vf | Feed velocity (mm/min) |

ae | Radial pass (mm) |

Fc | Cutting load (N) |

Fn | Normal load (N) |

Sa | Arithmetical mean height |

Sz | Maximum height |

Sq | Root mean square height |

## Appendix A. Surface Analysis of the Abrasive Tool with a Leica DCM 3D System

Ref | Top View of Part of the Abrasive Tool Analyzed | 3D View of the Same |

[1]Vc = 2 m/sVf = 100 mm/minae = 1 mm | ||

[2]Vc = 7 m/sVf = 100 mm/minae = 1 mm | ||

[3]Vc = 12 m/sVf = 100 mm/minae = 1 mm | ||

[4]Vc = 17 m/sVf = 100 mm/minae = 1 mm | ||

[5]Vc = 17 m/sVf = 500 mm/minae = 1 mm | ||

[6]Vc = 12 m/sVf = 500 mm/minae = 1 mm | ||

[7]Vc = 7 m/sVf = 500 mm/minae = 1 mm | ||

[8]Vc = 2 m/sVf = 500 mm/minae = 1 mm | ||

[9]Vc = 17 m/sVf = 1000 mm/minae = 1 mm | ||

[10]Vc = 12 m/sVf = 1000 mm/minae = 1 mm | ||

[11]Vc = 17 m/sVf = 100 mm/minae = 2.5 mm | ||

[12]Vc = 17 m/sVf = 1000 mm/minae = 1 mm |

## Appendix B. Surface Picture of the Abrasive Tool with a Leica DCM 3D System

Ref | Pictures Used for the Analysis with Leica DCM 3D |

[1]Vc = 2 m/sVf = 100 mm/minae = 1 mm | |

[2]Vc = 7 m/sVf = 100 mm/minae = 1 mm | |

[3]Vc = 12 m/sVf = 100 mm/minae = 1 mm | |

[4]Vc = 17 m/sVf = 100 mm/minae = 1 mm | |

[5]Vc = 17 m/sVf = 500 mm/minae = 1 mm | |

[6]Vc = 12 m/sVf = 500 mm/minae = 1 mm | |

[7]Vc = 7 m/sVf = 500 mm/minae = 1 mm | |

[8]Vc = 2 m/sVf = 500 mm/minae = 1 mm | |

[9]Vc = 17 m/sVf = 1000 mm/minae = 1 mm | |

[10]Vc = 12 m/sVf = 1000 mm/minae = 1 mm | |

[11]Vc = 17 m/sVf = 100 mm/minae = 2.5 mm | |

[12]Vc = 17 m/sVf = 1000 mm/minae = 1 mm |

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**Figure 1.**CMCs offer higher temperature capability compared to metals such as titanium and nickel (

**top graph**) and alloys such as Inconel (e.g., IN738, IN939, and IN792 DS in

**bottom graph**).

**Figure 3.**Different milling possibilities (planning or facing and trimming) and examples of climb and conventional trimming or milling.

**Figure 4.**Different types of diamond tool and detail of the diamond grain setting for electrolytic bond wheels.

**Figure 5.**Topographic map of a diamond grinder. The map size is 1536 points in the X direction (columns) and 288 in the Y direction (rows).

**Figure 6.**Topography of electrodeposited surface. On the anisotropic surface, the fractal behavior is in a defined direction. (

**left**) Anisotropic surface, (

**right**) isotropic surface.

**Figure 7.**Roughness profile of a part of the section (Sn), of the tool surface as shown in Figure 5. In this case, the profile has been selected from the area in which the tool has suffered wear from machining CMCs.

**Figure 8.**Calculation of the slope β = −2.7497 for the estimation of the power spectral density of the roughness profile in Figure 4.

**Figure 12.**Kistler dynamometer and assembly used for testing. Zone where fractal analysis is performed.

**Figure 13.**Image of the machined surface of the CMC (

**top**), the delimitation of the damage (

**center**), and its binary equivalent (

**bottom**) for measurement with ImageJ.

**Figure 14.**Evolution of the fractal dimension of the tool surface with the cutting force on the tool.

**Figure 15.**Evolution of the fractal dimension variation with respect to the previous test with the test number.

**Figure 17.**Evolution of diamond grain damage with the different test. (

**a**) New tool; (

**b**) after test 3; (

**c**) after test 4; (

**d**) after test 12.

**Figure 19.**Evolution of the cutting force with the cutting speed and comparison with data from Danglot’s work (grey squares) [3].

**Figure 22.**Evolution of the chipped area as a function of the feed velocity for different cutting speeds.

**Figure 23.**Evolution of the chipped area as a function of the fractal dimension variation with respect to the previous test.

**Figure 24.**Evolution of the maximum chipping as a function of cutting speed for different feed rates and comparison with data from Danglot’s work (grey squares) [3].

**Figure 25.**Evolution of the maximum chipping as a function of the feed velocity for different cutting speeds and comparison with data from Danglot’s work (grey squares) [3].

**Figure 26.**Evolution of the maximum chipping as a function of the fractal dimension variation with respect to the previous test.

**Figure 27.**Aspect of the machined surface highlighting internal porosities for the following parameters: Vc = 2 m/s; Vf = 500 mm/min and ae = 1 mm.

Abrasive Tool Reference | Type | Vc | Feed | Pass |
---|---|---|---|---|

DZY-N 25.0 10/12 D126 | Diamond 106–125 μm | 15–25 m/s wet | 0.01–0.05 mm/rev | ≤6 mm |

Ref. | Vc (m/s) | N (rpm) | Feed Vf (mm/min) | Pass ae (mm) |
---|---|---|---|---|

[1] | 2 | 1529 | 100 | 1 |

[2] | 7 | 5350 | 100 | 1 |

[3] | 12 | 9172 | 100 | 1 |

[4] | 17 | 12.994 | 100 | 1 |

[5] | 17 | 12.994 | 500 | 1 |

[6] | 12 | 9172 | 500 | 1 |

[7] | 7 | 5350 | 500 | 1 |

[8] | 2 | 1529 | 500 | 1 |

[9] | 17 | 12.994 | 1000 | 1 |

[10] | 12 | 9172 | 1000 | 1 |

[11] | 17 | 12.994 | 100 | 2.5 |

[12] | 7 | 5350 | 1000 | 1 |

**Table 3.**Values of the fractal dimension of the tool surface as a function of the test number and the cutting force applied to the tool.

Test Number | D_surf | R^{2} | Fc (N) | ΔD_surf |
---|---|---|---|---|

0 | 2.1896 | 0.9889 | 0 | 0 |

1 | 2.1902 | 0.9524 | 20.65 | 0.0006 |

2 | 2.1132 | 0.9532 | 12.35 | −0.077 |

3 | 2.0982 | 0.9488 | 13.77 | −0.015 |

4 | 2.1731 | 0.8761 | 11.06 | 0.0749 |

5 | 2.0594 | 0.9649 | 27.92 | −0.1137 |

6 | 2.1228 | 0.9534 | 28.56 | 0.0634 |

7 | 2.1403 | 0.9043 | 40.53 | 0.0175 |

8 | 2.0427 | 0.9743 | 52.15 | −0.0976 |

9 | 2.1068 | 0.9634 | 25.23 | 0.0641 |

10 | 2.1916 | 0.8921 | 27.17 | 0.0848 |

11 | 2.0815 | 0.9627 | 20.54 | −0.1101 |

12 | 2.1336 | 0.9278 | 55.86 | 0.0521 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

Fc | 0.1055 | 0.0298 | 3.5441 | 99.47 | 0.53 | |

ae | 2.1531 | 0.4638 | 4.6423 | 99.91 | 0.09 | |

Fc. ae | −0.1065 | 0.037 | −2.8775 | 98.35 | 1.65 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 53.9936 | 3 | 17.9979 | 37.3736 | 100 | 0 |

Residues | 4.8157 | 10 | 0.4816 | |||

Total | 58.8093 | 13 | 4.5238 | R = 0.9582 |

**Table 5.**Evolution of the machining loads, CMC damage, and roughness during the different tests performed. Sa (arithmetical mean height), Sz (maximum height), and Sq (root mean square height) are the surface texture parameters of the machined sample.

Test Number | Chipped Area mm^{2}/cm | Maximum Chipping μm | Fc N | Fn N | Sq μm | Sz μm | Sa μm |
---|---|---|---|---|---|---|---|

1 | 0.1729 | 105 | 20.65 | 2.72 | 23.8 | 309 | 18.5 |

2 | 0.0809 | 63 | 12.35 | 3.76 | 40.2 | 223 | 33.3 |

3 | 0.0589 | 57 | 13.77 | 4.51 | 26.3 | 162 | 20.9 |

4 | 0.0189 | 48 | 11.06 | 4.66 | 21.4 | 170 | 16.6 |

5 | 0.0591 | 55 | 27.92 | 1.81 | 30.7 | 208 | 24.5 |

6 | 0.1296 | 61 | 28.56 | 1.5 | 21.4 | 187 | 16.7 |

7 | 0.2329 | 113 | 40.53 | 2.11 | 27.5 | 189 | 22.1 |

8 | 0.2838 | 193 | 52.15 | 2.34 | 18 | 153 | 14.1 |

9 | 0.1665 | 106 | 25.23 | 1.47 | 28.4 | 217 | 22.7 |

10 | 0.2109 | 158 | 27.17 | 1.48 | 30.9 | 241 | 24.9 |

11 | 0.0383 | 117 | 20.54 | 1.67 | 44 | 352 | 36.3 |

12 | 0.4097 | 302 | 55.86 | 2.46 | 35.7 | 225 | 28.6 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

ae | 10.2834 | 2.3217 | 4.4292 | 99.87 | 0.13 | |

Vf | 0.0748 | 0.01 | 7.4545 | 100 | 0 | |

Vf × Vc | −0.0037 | 0.0008 | −4.844 | 99.93 | 0.07 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 11,299.5072 | 3 | 3766.5024 | 73.6568 | 100 | 0 |

Residues | 511.3586 | 10 | 51.1359 | |||

Total | 11,810.8658 | 13 | 908.5281 | R = 0.9781 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

Vc | −0.0092 | 0.0021 | −4.3775 | 99.76 | 0.24 | |

D_surf | 0.0644 | 0.0127 | 5.0636 | 99.90 | 0.10 | |

Vf × Vc | 0.0000 | 0.0000 | −3.1989 | 98.74 | 1.26 | |

Vf × ae | 0.0004 | 0.0001 | 7.1231 | 99.99 | 0.01 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 0.4305 | 4 | 0.1076 | 136.2415 | 100 | 0 |

Residues | 0.0063 | 8 | 0.0008 | |||

Total | 0.4369 | 12 | 0.0364 | R = 0.9926 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

D_surface | 19.0108 | 6.6851 | 2.8438 | 98.07 | 1.93 | |

Vf × Vc | −0.0184 | 0.0031 | −5.9483 | 99.98 | 0.02 | |

Vf × ae | 0.3552 | 0.0450 | 7.8854 | 100.00 | 0.00 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 210,992.6347 | 3 | 70,330.8782 | 85.4064 | 100.00 | 0.00 |

Residues | 7411.3653 | 9 | 823.4850 | |||

Total | 218,404.0000 | 12 | 18,200.3333 | R = 0.9829 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

ae | 9.6457 | 3.8650 | 2.4956 | 96.83 | 3.17 | |

D_surf | 5.8533 | 2.1842 | 2.6799 | 97.69 | 2.31 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 6682.2530 | 2 | 3341.1265 | 104.8799 | 100.00 | 0.00 |

Residues | 318.5670 | 10 | 31.8567 | |||

Total | 7000.8200 | 12 | 583.4017 | R = 0.9770 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

ae | 94.9904 | 29.0894 | 3.2655 | 99.15 | 0.85 | |

D_surf | 53.3817 | 16.4389 | 3.2473 | 99.12 | 0.88 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 599,370.4741 | 2 | 299,685.2370 | 166.0718 | 100.00 | 0.00 |

Residues | 18,045.5259 | 10 | 1804.5526 | |||

Total | 617,416.0000 | 12 | 51,451.3333 | R = 0.9853 |

Variable | Coefficient | Standard Deviation | t Student | Confidence % | Risk % | |
---|---|---|---|---|---|---|

ae | 11.1078 | 4.4838 | 2.4773 | 96.73 | 3.27 | |

D_surf | 7.7930 | 2.5339 | 3.0755 | 98.83 | 1.17 | |

Source | Square sum | DoF | Mean squares | Fisher | Confidence % | Risk % |

Regression | 10,355.9493 | 2 | 5177.9746 | 120.7717 | 100.00 | 0.00 |

Residues | 428.7407 | 10 | 42.8741 | |||

Total | 10,784.6900 | 12 | 898.7242 | R = 0.9799 |

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## Share and Cite

**MDPI and ACS Style**

Girot Mata, F.A.; Renderos Cartagena, M.A.; Alonso Pinillos, U.; Aramburu, B.I.
Wear of Abrasive Tools during CMC Machining. *Machines* **2023**, *11*, 1021.
https://doi.org/10.3390/machines11111021

**AMA Style**

Girot Mata FA, Renderos Cartagena MA, Alonso Pinillos U, Aramburu BI.
Wear of Abrasive Tools during CMC Machining. *Machines*. 2023; 11(11):1021.
https://doi.org/10.3390/machines11111021

**Chicago/Turabian Style**

Girot Mata, Franck Andrés, Mario Alfredo Renderos Cartagena, Unai Alonso Pinillos, and Borja Izquierdo Aramburu.
2023. "Wear of Abrasive Tools during CMC Machining" *Machines* 11, no. 11: 1021.
https://doi.org/10.3390/machines11111021