# Estimation of Drag Finishing Abrasive Effect for Cutting Edge Preparation in Broaching Tool

^{1}

^{2}

^{3}

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## Abstract

**:**

_{e}prediction were performed using machine learning by an artificial neural network ANN. The results achieved indicate that the influencing factors on r

_{e}, MRR, and roughness, in order of importance, are drag depth, drag time, mixing percentage, and grain size, respectively. The reproducibility accuracy of r

_{e}is reliable compared to traditional processes, such as brushing and blasting. The prediction accuracy of the r

_{e}of preparation with ANN is observed in the low training and prediction errors 1.22% and 0.77%, respectively, evidencing the effectiveness of the algorithm. Finally, it is demonstrated that the DF has reliable feasibility in the application of edge preparation on broaching tools under controlled conditions.

## 1. Introduction

_{e}prediction was performed by means of an ANN for the purpose of suppressing real tests under experienced system considerations and capabilities. Consequently, the algorithm will help to select rounding conditions for future needs and applications.

## 2. Materials and Methods

_{e}, respectively.

#### 2.1. Materials and Equipment

_{2}O

_{3}) abrasive grains were used in two different sizes, 24 and 46, according to the sieve aperture given by ASTM D E 11-70 (Figure 1a).

#### 2.2. Preparation by Drag Finishing

_{e}) is measured using an Alicona InfiniteFocusG5 profile measuring device. At this point, in addition to extracting the achieved edge radius, the removed area (Ar) is also determined geometrically by Equations (1) and (2) [4], for the purpose of observing the behavior with respect to time. Where, r

_{1n}is the nominal initial radius, r

_{2n}is the radius reached, and K

_{β}is the material removal coefficient function of the wedge angle β (Figure 2).

#### 2.3. Repeatability and Reproducibility Analysis, R&R

_{e}randomly from the parts. The 24 parts are composed of r

_{e}measurements at DF times of 0, 20, 30, and 40 min at 3 immersion depth and 2 different locations. Three replicates of the 24 measurements are performed. Therefore, each technician performs 72 measurements for a total of 210 measurements.

#### 2.4. Cutting Edge Radius Prediction

_{ij}(n) is the new connection weight between node “i” and node “j” of the previous layer and ΔW

_{ij}(n) is the synaptic weight correction.

^{2}. These metrics are presented in Equations (4), (5), and (6), respectively.

_{exp}represents the experimental values, and ${\widehat{y}}_{pred}$ expresses the predicted values, SSE and SST are the sum of squares of the residuals and the total sum of squares, respectively.

## 3. Results and Discussion

_{e}, the results of the surface quality, the results of the R&R analysis, and the accuracy of the prediction through the artificial neural network.

#### 3.1. Preliminary Tests, Influence and Behavior of Factors

_{e}(response). It can be observed that in no case is the behavior of the response variable linear, as it is increasing both for DT, GZ, and ID. In general, all the factors have a significant influence on r

_{e}. Therefore, the control of each of them is important when obtaining a specific r

_{e}in the tool.

_{e}, i.e., a large GZ gives a large r

_{e}, while a smaller GZ gives a small r

_{e}. The combination of abrasive grain sizes resulted in obtaining an approximate average r

_{e}. The general trend of r

_{e}as a function of ID is increasing. The trend of the curve indicates that with a deeper depth the radius can grow exponentially. However, the maximum depth of the tank limits the depth of the process and the amount of abrasive material. To minimize r

_{e}variations, the particle mixer should be used whenever possible. This element uniforms the mixture and avoids the segregation of particles of different sizes or the appearance of the nutshell effect [23,24]. Finally, the effect of the SiC percentage on the cutting edge radius of the tool showed a particular behavior. At a SiC percentage in the mixture RM of 66%, a larger r

_{e}is obtained than that obtained with an RM of 50% and 75%, respectively, being the RM of 75% with which relatively smaller radius edges were obtained.

_{e}can be observed in Figure 8. In the first instance, the average values of the r

_{e}increase over time are shown, starting from an original tool radii between 7 and 9 μm, and reaching a final radius of 26 μm. On the other hand, the progress of r

_{e}obtained at different ID depths from 5 to 120 mm is shown, represented by points A to D, reaching a maximum radius of 43 µm. It follows from the above that the combined effect of DT and ID on r

_{e}has a direct incremental relationship, but it is not linear.

_{e}is shown in Figure 9. For each GZ, the increase in r

_{e}increases in different proportions as we increase ID. As an example, for combination A, the radius size is doubled from the initial radius to the final radius, and for combination B, the radius reached is about three times the initial radius. In industrial application, this result can be translated into different cutting edge preparation control possibilities. With combination B, the largest cutting edge radii could be obtained at any depth compared to the other two combinations. On the other hand, if a fine control of the cutting edge radius increment is desired, combinations A and AB will allow this control. This is possible primarily because of the size of the abrasive grain. That is, the larger the grain size, the greater the cutting edge and cutting capacity [14]. In addition, it is understood from physics that, as the immersion depth increases, the greater the pressure of the grain surface interaction of the cutting edge, which will contribute to greater material removal.

_{β}, but when analyzing the same cutting edge, it becomes a constant value, as it is directly dependent on the wedge width β.

#### 3.2. Surface Roughness Analysis at the Cut Edge

_{e}cutting edge radius by the drag finishing process versus the immersion depth is presented in Figure 12. Where, the subscripts i and f correspond to the initial and final roughness, respectively. For all the cases shown, the reduction in the surface roughness is remarkable. At the same time, there is greater uniformity in Ra and greater variability in Rz. By definition, Rz is more sensitive to the detection of imperfections in the machined surface; therefore, it is widely used for the control and monitoring of surface irregularities [25,26,27]. However, the Rz values obtained by drag finishing are lower or equal to those originally obtained in the manufacture of cutting tools by grinding operation [25,26]. Considering the effect produced by the percentage of SiC in the abrasive mixture (Figure 12a), it can be observed that lower SiC content allows for achieving a higher Rz compared to the higher inclusion of SiC in the mixture. This means that the presence of 50% alumina in the mixture has a higher abrasive capacity. Similarly, the effect of abrasive grain size on surface roughness is shown in Figure 12b. It is observed that there is no significant variation in the different abrasive grit sizes used, but there is a slight reduction when using a 750 grit rather than a 390 grit. A particular opposite effect occurs between the two grit sizes used as the immersion depth increases, which should be studied further to know if the behavior is maintained or is a particular case of the tested conditions. However, that proved to be the great advantage of applying drag finishing for edge rounding with a higher surface quality. This is clearly seen in the reduction in surface roughness by three times Ra and greater than two times Rz for all cases.

#### 3.3. Repeatability and Reproducibility R&R Analysis

_{e}of the process.

_{e}, as well as the percentage of contribution to the variance. First, it shows us that the measurement system variation is equal to 18.49% of the process variation. This indicates that the system is in the marginal zone (Figure 13a), where acceptance is possible as long as its limitations, the importance of the application, and the cost are known [19,20].

#### 3.4. Cutting Edge Radius Prediction by ANN

_{e}by ANN, machine learning by the supervised learning method, with the backpropagation gradient descent training algorithm. A maximum number of interactions (epochs) of 1000 was chosen. Cross validation was used to improve the generalization capability. A data set of 324 r

_{e}measurements was obtained as input. Eighty percent of the data were used for training and 20 for validation. It took 141 epochs to find the best training. This means that the errors are no longer reduced, but stabilized (Figure 14). A coefficient of determination of 0.961 with a standard deviation of 0.00631 was obtained. Therefore, the prediction was continued.

_{e}predicted by the neural network was compared with the corresponding experimental values and is shown in Figure 15. In addition, the average percentage of prediction errors was found to be 9.33% compared to the actual experimental values of the shear edge radius.

## 4. Conclusions

_{2}O

_{2}at different grain sizes and percentages of mixture are used to prepare uncoated tungsten carbide broaching tools by a drag finishing process. Important parameters, such as time and drag depth were controlled to determine the evolution of cutting edge rounding, material removal rate, repeatability and reproducibility, surface topography, and develop a prediction model by ANN. The important conclusions are:

- -
- The parameters incident to obtaining a cutting edge radius were, in order of importance: plunge depth, dragging time, abrasive mix percentage, and abrasive size.
- -
- The incidence of tool location is very important in obtaining a specific radius cutting edge value. In this process, location is understood as the positioning angle and depth of dragging. As for the positioning angle, the horizontal positioning of the broach during dragging causes a superior rounding on the first cutting edge (33 μm) which can be up to two times larger than the radius of the other cutting edges (18 μm). On the other hand, depending on the depth of dragging, the radius of the cutting edge increases in a progressive non-linear way. On average, the growth ranges from 12 μm at 5 mm depth to 31 μm at 120 mm depth. As far as roughness is concerned, it could be identified that the incidence is greater for the abrasive inclusion rate than the grain size. The substantial reduction in surface defects by Ra and Rz are a third of its original measure. On average from initial Ra: 0.3 microns to final Ra: 0.09 microns, and from initial Rz: 1.7 microns to final Rz: 0.5 microns.
- -
- In terms of accuracy of the reproduction of the tool cutting edge radius, it is very acceptable compared to traditional processes, such as brushing and blasting. Obtaining from the R&R study of the reproducibility source a standard deviation of 1.22 that corresponds to 11.86% of the process variation.
- -
- The prediction accuracy of the preparation radius with ANN was 93.7%, which demonstrates the effectiveness of the algorithm.
- -
- The limitation of the drag finishing process is essentially related to the tool dimensions. In this case, long broaches would make it difficult to locate, hold, and therefore reproduce the geometry of the cutting edge on all the teeth.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Drag finishing process: (

**a**) microscope images of abrasive particles and characteristic, (

**b**) drag finishing machine, and (

**c**) broaching tool.

**Figure 4.**(

**a**) The mounting of the broaching tool with different orientations, (

**b**) the movement of abrasive particles against the first dragged tooth in horizontal orientation, and (

**c**) relative movements of the tool in the drag finishing process.

**Figure 5.**Results of the four cutting edge rounding of the broaching tool, drag finishing in a horizontal position.

**Figure 8.**Combined effect of the drag time DT and the drag depth ID on the cutting edge radius r

_{e}.

**Figure 11.**Improvement of surface defects at the cutting edge, (

**a**) original factory surface, (

**b**) post-treatment improved surface.

**Figure 12.**Behavior of the surface roughness against, (

**a**) percentage of silicon carbide RM, (

**b**) abrasive grain size GZ.

**Figure 13.**Measurement system capacity, (

**a**) determination zones, general rule, (

**b**) variability of measurement by technician.

**Figure 14.**ANN application prediction errors, (

**a**) mean absolute error (MAE), (

**b**) mean squared error (MSE).

Factors | I | II | III |
---|---|---|---|

Abrasive type | SiC | Al_{2}O_{3} | - |

Grain size [µm] | 390 (A) | 390 + 750 (AB) | 750 (B) |

SiC mixing ratio [%] | 50 | 66 | 75 |

Drag time [min] | 10/10 | 15/15 | 20/20 |

Drag depth [mm] | 40 | 60 | 80 |

Fuente | Standard Deviation (SD) | Study Variation (6 × SD) | % Study Variation (% SV) | Variance Component (CV) | % Contribution (CV) |
---|---|---|---|---|---|

Gage R&R total | 1.9132 | 11.4793 | 18.49 | 3.660 | 3.42 |

Repeatability | 1.4676 | 8.8058 | 14.18 | 2.154 | 2.01 |

Reproducibility | 1.2274 | 7.3643 | 11.86 | 1.506 | 1.41 |

Technician | 0.2474 | 1.4842 | 2.39 | 0.061 | 0.06 |

Technician*Ref_measure | 1.2022 | 7.2132 | 11.62 | 1.445 | 1.35 |

Part to part | 10.1703 | 61.0216 | 98.28 | 103.434 | 96.58 |

Total variation | 10.3487 | 62.0920 | 100.00 | 107.095 | 100.00 |

Data Set | MAE | MSE | R^{2} |
---|---|---|---|

Training | 0.0162 | 0.0585 | |

Validation | 0.01869 | 0.0643 | 0.937 |

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## Share and Cite

**MDPI and ACS Style**

Pérez-Salinas, C.F.; del Olmo, A.; López de Lacalle, L.N.
Estimation of Drag Finishing Abrasive Effect for Cutting Edge Preparation in Broaching Tool. *Materials* **2022**, *15*, 5135.
https://doi.org/10.3390/ma15155135

**AMA Style**

Pérez-Salinas CF, del Olmo A, López de Lacalle LN.
Estimation of Drag Finishing Abrasive Effect for Cutting Edge Preparation in Broaching Tool. *Materials*. 2022; 15(15):5135.
https://doi.org/10.3390/ma15155135

**Chicago/Turabian Style**

Pérez-Salinas, Cristian F., Ander del Olmo, and L. Norberto López de Lacalle.
2022. "Estimation of Drag Finishing Abrasive Effect for Cutting Edge Preparation in Broaching Tool" *Materials* 15, no. 15: 5135.
https://doi.org/10.3390/ma15155135